[{"data":1,"prerenderedAt":197575},["ShallowReactive",2],{"post-\u002Fblog\u002F2026\u002F0010-biography-of-claude-shannon":3,"i-mingcute:time-line":344,"i-ci:tag":344},{"post":4,"nextPost":354,"prevPost":133046},{"id":5,"title":6,"body":7,"description":13,"draft":341,"enableCodeHighlight":341,"enableCodeHightlight":341,"enableComment":342,"enableD2":341,"enableKatex":341,"extension":343,"image":330,"important":341,"location":344,"meta":345,"navigation":342,"ogImage":344,"path":346,"seo":347,"stem":348,"summary":349,"tags":350,"time":352,"__hash__":353},"blog\u002Fblog\u002F2026\u002F0010-biography-of-claude-shannon.md","克劳德·香农小传",{"type":8,"value":9,"toc":329},"minimark",[10,14,17,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,76,79,82,85,88,91,94,97,100,103,106,109,112,115,118,121,124,127,130,133,136,139,142,148,151,154,157,160,163,166,169,172,175,179,182,185,188,191,194,197,200,203,206,209,212,215,218,221,226,229,232,236,242,245,248,251,254,257,260,263,266,269,272,275,279,285,288,291,294,297,300,303,306,309,312,315,318,321,324],[11,12,13],"p",{},"美国 20 世纪 50 年代的某个深夜，贝尔实验室的走廊里很安静。一个瘦高的中年人骑着独轮车，从长长的走廊那头慢悠悠地滑过来，手里还抛着几个球。偶尔有加班的同事推开门，看一眼，笑一笑，又把头缩回去继续算他们的方程——大家早就习惯了。",[11,15,16],{},"克劳德·艾尔伍德·香农（Claude Elwood Shannon）最有分量的成就，是用一篇论文给「信息」下了数学定义，由此奠定了整个数字时代的理论根基。可是如果你问他的同事、家人和朋友他是个什么样的人，他们说的多半不是公式，而是独轮车、玩具、小机器和一个永远带着笑意的安静身影。",[18,19,20],"h2",{"id":20},"密歇根小镇的修理少年",[11,22,23],{},"1916 年 4 月 30 日，香农出生在美国密歇根州的佩托斯基，不久后全家搬到北边一个叫盖洛德的小镇，他在那里长大。父亲老克劳德做过商人，也当过遗嘱认证法官；母亲梅布尔是语言教师，后来做了盖洛德中学的校长。姐姐凯瑟琳比他大几岁，日后成了数学教授。家里的气氛是安稳、务实的：父亲有生意头脑，母亲爱读书，孩子们被允许把时间花在自己感兴趣的东西上。",[11,25,26],{},"香农从小就是个「动手的孩子」。他爱做航模，也做过无线电遥控的小船。最著名的一桩少年轶事，是他和一个住在大约半英里外的朋友之间架设的电报线：两个孩子没有现成的电线，就利用沿途的铁丝围栏，把它们接起来当作通信线路，晚上各自守在家里，用莫尔斯电码互相「发报」。对一个中西部小镇的男孩来说，这既是游戏，也是他第一次亲手搭起「通信系统」。",[11,28,29],{},"他还干过一份差事：给西联电报公司送电报。镇上的人看见他骑着车来来往往，也许想不到，这个孩子日后会为「通信」写下一套完整的数学理论。他修收音机的本事在镇上小有名气，据说当地一家百货商店的收音机坏了，也会请他去看看。",[11,31,32],{},"这里得补一点背景：香农的少年时代，正好赶上 1920 年代美国的无线电热。广播电台一座座冒出来，杂志上登着教人自己绕线圈、装矿石收音机的图纸，成千上万个男孩在自家阁楼上折腾「无线电」。香农赶上了这个浪潮的浪尖，而且他不是照着图纸装，是喜欢把东西拆开，弄清里面到底怎么回事。回头看，他一生的路数大概就是这个：感兴趣的不是「怎么用」，而是「它是怎么被装起来的」。",[11,34,35],{},"他的偶像是爱迪生。后来他发现自己和爱迪生居然是远亲，高兴了好一阵子。少年时代他还读到爱伦·坡的小说《金甲虫》，书里主人公靠破译密码找到宝藏，这个故事在他心里种下了对密码的迷恋，多年以后，战时的密码工作和他的信息论，都与这份兴趣有着隐秘的联系。另外，坡还写过一篇《被窃的信》，讲的是「猜对方下一手会怎么出」的心理游戏——二十多年后，香农在一份机器设计的备忘录里，又把这篇小说翻出来引用了一次。",[11,37,38],{},"这个阶段的香农，已经显出日后的底色：不爱张扬，不太合群，但遇到「有意思的东西」就会安静地一头扎进去，一玩就是几个小时。",[18,40,41],{"id":41},"一门选修课和一篇论文",[11,43,44],{},"1932 年，香农进入密歇根大学。他最后同时拿到了电气工程和数学两个学士学位，这个组合在当时并不常见，却像是为他日后的工作预先搭好的脚手架。",[11,46,47],{},"大学里有一件看起来很小的事，影响却极大：他在一门课上接触到了乔治·布尔的逻辑代数——一套只用「真」和「假」、「是」和「非」来做运算的符号系统。大多数同学把它当成一个哲学趣闻，香农却盯着它看了很久，因为他同时懂得电路：开关只有「开」和「关」两种状态，这不正好对应「真」和「假」吗？",[11,49,50],{},"毕业后，他去了麻省理工学院，做万尼瓦尔·布什的助手，管理一台著名的庞然大物——微分分析机。这是一台由轴、齿轮和大量继电器组成的机械模拟计算机，占满一间屋子。香农在它旁边一待就是很长时间，对着一堆纠缠的继电器电路琢磨：能不能找到一套规则，让人不靠反复试错就能设计出正确的开关电路？",[11,52,53],{},"1937 年，他交出了答案——硕士论文《继电器与开关电路的符号分析》。他证明了布尔代数可以用来描述和简化开关电路，也就是说，逻辑可以被「造」出来。",[11,55,56],{},"这篇论文在评价史上的位置，后来被反复提起。历史学家赫尔曼·戈德斯坦 1972 年写下了可能是最实在的一句：它「把数字电路设计从一门手艺变成了一门科学」。数学家所罗门·戈隆布则在 2001 年的悼文里说，这是「有史以来最伟大的硕士论文之一」。流传最广的一版出自哈佛大学的认知心理学家霍华德·加德纳，1985 年他写道，这或许「是这个世纪最重要、也最著名的硕士论文」。这句话后来被到处引用，有时还被人升格成「科学史家的定评」——其实加德纳是心理学家，不是科学史家，这一点值得记一笔。",[11,58,59],{},"还有一个评价来自他的老师本人。布什后来谈到这篇论文时说：「我当时就认为它是一篇经典之作——这个评价我很少给出。」",[11,61,62],{},"比论文本身更能说明问题的，是布什给人写推荐信时的措辞。1938 年，他在一封信里这样描述这个年轻人：「一个相当不合常规的年轻人……他非常害羞内向，极为谦逊，很容易被带偏。」在另一封推荐信里，布什又补了一句：「他腼腆、讨人喜欢，是需要被小心对待的那种人。」一位导师要一边极力推荐、一边提醒别人别把他吓跑，这件事本身就说明了香农是个什么样的人。",[11,64,65],{},"当时的他才二十出头，说起那篇论文却相当轻描淡写，更像是把两样好玩的东西拼到了一起。",[11,67,68],{},"其间他还在贝尔实验室度过了一个夏天，那是他与这家公司缘分的开始。布什后来建议他换个领域，于是他的博士论文竟是关于理论遗传学的，题目叫《理论遗传学的代数学》。为此他去了冷泉港，和遗传学家一起工作。他用数学处理孟德尔遗传，这篇论文并没有像硕士论文那样引起轰动，却再次显示了他的习惯：哪里有「结构」，就想用代数去看一看。",[11,70,71],{},[72,73],"img",{"alt":74,"src":75},"Claude Shannon in 1932","https:\u002F\u002Fimage-assets.dreams.plus\u002F202610162230267.png",[11,77,78],{},"1940 年，他拿到了博士学位。同一年，他与诺玛·莱沃结婚，但这段婚姻很短，两人很快就分开了。香农在感情上一向内敛，很少对外人谈起这些。",[18,80,81],{"id":81},"普林斯顿的拜访与贝尔实验室的夜晚",[11,83,84],{},"博士毕业后，香农去了普林斯顿高等研究院，在那里的几个月里，他见到了爱因斯坦、哥德尔和冯·诺依曼等人。普林斯顿的气氛很学院，学者们常在林荫道上散步、低声争论。香农既敬佩他们，又觉得自己并不真正属于这里：他更愿意在一间堆满零件的屋子里琢磨东西。",[11,86,87],{},"倒是有两位年长的数学家早早看出了他的分量。诺伯特·维纳在 1940 年前后这样评价这个年轻人：「一个才华与智力都极为出众的人……他已经做出了极具原创性的工作，毫无疑问是正在升起的一颗星。」而冯·诺依曼后来跟他的一次闲谈，给这门学科留下了一个沿用至今的词——这件事我们放到 1948 年再说。",[11,89,90],{},"1941 年，他加入了贝尔实验室，那个年代的贝尔实验室是一座奇特的「自由王国」，管理层相信让聪明人自己找事做，终会有收获。香农正好适合这样的环境。战争期间，他参与了防空火力控制系统的研究，也接触了保密通信和密码学方面的工作，其中包括著名的 SIGSALY 加密话音系统的相关研究。",[11,92,93],{},"他在贝尔实验室交到了几个真正投契的朋友，其中两个往后会反复出现。",[11,95,96],{},"一位是约翰·皮尔斯，日后被称作「通信卫星之父」的工程师。皮尔斯差不多是香农在实验室里最好的思想对手，两个人互相扔点子、合写论文、交换成堆的书。皮尔斯留下的说法里有一条后来被引用得最多：香农谈起自己的想法时，常常是从听别人抱怨某个系统开始的——「他漫不经心地听着，然后发明出一个新系统。」皮尔斯三番五次跟他说「这个想法你应该写出来」，香农的回答通常是：「‘应该’是什么意思？」",[11,98,99],{},"另一位是巴尼·奥利弗，后来去了惠普，也是「搜寻地外文明」计划最早的推动者之一。奥利弗与香农、皮尔斯三人合写过那篇《脉码调制的哲学》，还一起申请了专利。奥利弗晚年这样回忆自己在这个圈子里的位置：「我们成了朋友，所以很多理论可以说是我替他接生的。他把想法扔给我……我比谁都更早知道信息论。」",[11,101,102],{},"他的生活节奏在同事眼里有些古怪：不太爱开会，常常关上办公室的门独自思考，下班时间也不固定。他当时住在纽约格林威治村，每天要往返于曼哈顿与实验室之间。据说他爱在深夜工作，走廊里的独轮车也是从这个时期开始出名的。他一边骑，一边思考难题，对他而言，玩耍和思考本是同一件事的两面。",[11,104,105],{},"1943 年初，英国数学家艾伦·图灵访问贝尔实验室。两人在食堂里一起喝茶聊天，由于图灵的密码工作属于机密，他们没法谈具体项目，聊的主要是更宽泛的话题：机器能不能思考？能不能教机器学东西？",[11,107,108],{},"图灵后来在饭桌上向人复述过他印象深刻的一点：「香农不只想往大脑里喂数据，他还想喂文化层面的东西！他想给它放音乐。」（这句话是旁人的转述，见于安德鲁·霍奇斯的图灵传记，不是两人当时的通信。）图灵自己则傲慢得很可爱，他说他并不想造一个「强大的大脑」：「我想要的只是一个平庸的大脑，差不多像美国电话电报公司总裁那样的。」",[11,110,111],{},"有意思的是，两个人对这次交谈的记忆并不一样。近四十年后，香农接受口述史访问时回忆说，他们那次「完全没谈密码」，「谈得更多的是人脑和计算机器」这类问题；至于他自己关于信息的那套想法，图灵当时「并不认为方向是对的」，他「得到的差不多是负面的反馈」。一次被后人追认为「两个天才难得交会」的谈话，在当事人那里，其实还带着一点被质疑的味道。",[11,113,114],{},"这是两个隐居于各自世界里的天才难得的一次交会：一个刚从布莱切利园的机密里走出来，一个正准备写下通信的数学理论，而他们在饭桌上真正关心的，是造一个会想东西的机器。",[11,116,117],{},"在这些年里，香农一边为战争做事，一边在心里慢慢酝酿一个更大的问题：通信的本质到底是什么？在 1945 年的一份内部保密备忘录里，他已经用概率论的语言分析密码系统，战后这份工作以《保密系统的通信理论》为题公开发表。密码学与通信理论，在他脑中是同一枚硬币的两面。",[18,119,120],{"id":120},"一篇论文与一个安静的家",[11,122,123],{},"1948 年，《贝尔系统技术杂志》分两期连载了香农的论文《通信的数学理论》。这篇论文提出了一整套全新的概念：用「比特」衡量信息量；把信息源的不确定性定义为「熵」；证明了在噪声信道中，只要传输速率低于某个「信道容量」，就存在办法让错误率任意小。",[11,125,126],{},"「比特」这个词是同事约翰·图基提出来的，意思是「二进制数字」。图基是普林斯顿的统计学家，战争期间常驻贝尔实验室，据一份 1947 年 1 月的实验室备忘录，这个说法最迟在那时已经定下来了。香农在论文里最早把「bit」用作信息的单位，并且明确注明「此词由 J. W. 图基建议」。据说命名是在实验室的午餐桌上敲定的，有人提议叫「binit」，有人提议叫「bigit」，最后「bit」胜出。一个今天人人都在用的单位，诞生过程就是这么随便。",[11,128,129],{},"关于「熵」这个名字，有一个流传很广的故事：据说冯·诺依曼建议他用这个词，理由是反正没有人真正懂熵，辩论的时候他总能占上风。这个故事细节不一，可信度看起来也难以考证。",[11,131,132],{},"但值得补充的是，这个故事最早的出处其实是香农自己。1971 年，他在《科学美国人》上的一篇文章里回忆道：「我最头疼的是该叫它什么。我想过叫‘信息’，但这个词被用得太滥，于是决定叫‘不确定性’。后来我跟约翰·冯·诺依曼讨论，他有更好的主意。他对我说：‘你就叫它熵吧，有两个理由。第一，你的不确定性函数在统计力学里已经用这个名字了，它本来就有名字。第二，而且更重要：没有人真正知道熵到底是什么，所以辩论的时候你总是占上风。’」——所以这不是后人编的段子，而是他本人的追述；只是「1940 年前后的一次谈话、1971 年才写下来」这条时间线，本身也提醒我们：细节不必太当真。",[11,134,135],{},"论文发表之后的反响，皮尔斯有过一个很好的说法：这篇文章「像一颗炸弹，而且是一颗延时炸弹」。他后来在另一篇回顾里说，这件事「像一道凭空劈下来的闪电」，而且「我不知道还有哪套理论是这样一整套、几乎没什么前身和历史地冒出来的」。皮尔斯也留下了两句让同行记了一辈子的实话：1950 年以前发表的信息论文章，「大多数跟香农的工作没什么关系」；以及「我从没遇到过一个真正弄懂了信息论的物理学家」。",[11,137,138],{},"当时也不是没有冷脸。统计学家约瑟夫·杜布给 1949 年那本书写的书评就不客气，说它更像「有启发性」而非数学性的著作，「而且作者在数学上的意图并不总是体面的」。",[11,140,141],{},"真正把这篇论文推向公众的，是另一个人：洛克菲勒基金会的沃伦·韦弗。韦弗在战时管过科学动员，眼光极好。1949 年，他把自己的通俗介绍与香农的论文合在一起，出了《通信的数学理论》这本书。在给基金会主席的信里，韦弗把香农做的事比作「吉布斯为物理化学做过的事」。而在他自己那篇导言里，他写道：",[143,144,145],"blockquote",{},[11,146,147],{},"「communication（通信）这个词在这里将取一个非常宽泛的含义，包括一个头脑影响另一个头脑的全部过程。这当然不限于书面和口头的言语，还包括音乐、绘画、戏剧、芭蕾，事实上包括人的一切行为。」",[11,149,150],{},"韦弗还给出了那个著名的三层划分——技术的层次（符号传得多准）、语义的层次（符号多准确地传达了意思）、效果的层次（收到的意思多有效地改变了人的行动）。他最后甚至写下这样一句近乎诗的话：在这套理论里，「熵不只说算术的语言，它还说语言的语言」。",[11,152,153],{},"这就是「信息论热」的起点：一篇极其克制的数学论文，配上一篇极其热情的导言。往后几十年里，各种拿「信息」「熵」「冗余」去解释生物、心理、语言、经济、管理的文章层出不穷——而这桩公案，我们后面还会看到香农本人的反应。",[11,155,156],{},"对同行来讲，这篇论文的分量是不需要解释的。多年后，大卫·斯莱皮安在自己编的《信息论关键论文选》前言里写道：「本世纪大概没有哪一件工作，比香农 1948 年那篇文章更深刻地改变了人对通信的理解。」1998 年，在论文发表五十周年的综述里，塞尔希奥·贝尔杜第一次用了那个后来被反复引用的比喻：它是「信息时代的《大宪章》」。顺便说一句，《科学美国人》1990 年那篇专访里其实写的是「数字时代的《大宪章》」——两个版本后来常被混在一起，都算在《科学美国人》头上。",[11,158,159],{},"有意思的是，这样一篇改变世界的论文，作者本人几乎没有因此改变生活。他在发表之后依旧是那个爱摆弄东西、不爱应酬的人。",[11,161,162],{},"1949 年 3 月，他与贝尔实验室里的数值分析员贝蒂（玛丽·伊丽莎白·摩尔）结婚。据说牵线的人是皮尔斯——皮尔斯当时是贝蒂的上司。贝蒂是罗格斯大学的数学毕业生，聪明、幽默、有主见，既是他生活上的伙伴，也是工作上的搭档：他的一些论文手稿甚至是她的字迹抄写的，这让后来的研究者困惑了很久。她会吹钢琴，他会单簧管，两人下班后会找一些二声部的谱子合着弹。两人后来有了三个孩子。",[11,164,165],{},"还有一件圈里人都知道的小事。香农这篇论文出来的时候，诺伯特·维纳其实也在同一片水域里作业——他 1948 年出的《控制论》同样掀起了巨浪。两人的关系始终客气，维纳却在 1946 到 1947 年间私下抱怨过：「我的一个竞争者，贝尔电话公司的香农，要抢在我前面发表文章了。」香农这边对维纳一直很尊敬，说他是「我年轻时候的偶像」；至于两个人气质上的差别，麻省理工的托马斯·凯拉思后来总结得很直白：「维纳喜欢出风头，香农则完全不在乎这些。」",[11,167,168],{},"1949 年到 1950 年，他还发表了关于计算机下棋的论文，提出了让机器评估棋局、搜索走法的基本思路，这些想法后来成了计算机博弈的源头。",[11,170,171],{},"这件事值得多说两句。1950 年 3 月，他在《哲学杂志》上发表了《为计算机下棋编制程序》——这是这个题目上的第一篇技术论文；同年 2 月，《科学美国人》上还有一篇面向大众的《一台会下棋的机器》。文章中他把下棋程序分成两类，一类是硬算到底的「A 型」，一类是只搜有意思的分支的「B 型」，他自己更看好后者；他还估算出棋局的变化量大约是 10 的 120 次方，这个数字后来被叫作「香农数」。更早一点，1949 年他就在家里做出了一台用继电器控制的下棋机器，并且把它演示给国际象棋大师爱德华·拉斯克看过。有意思的是图灵当时也在做类似的事：他和戴维·钱珀瑙恩在 1948 年前后设计过一个下棋程序，因为没机器可用，只能自己拿纸笔一步一步地「手动运行」。图灵 1950 年那篇《计算机器与智能》里，还引用了香农的棋类文章。从香农的 A 型\u002FB 型分类往下，洛斯阿拉莫斯 1956 年的 MANIAC、伯恩斯坦 1958 年在 IBM 704 上的程序、麦卡锡他们在麻省理工写的程序，一直到 1967 年格林布拉特的棋程序，用的都是这套架子。",[11,173,174],{},"香农夫妇很爱玩杂耍、下棋，家里也总有一些稀奇古怪的小发明。对孩子们来说，这位爸爸并不严厉，更像一个爱和他们一起折腾的大朋友。",[18,176,178],{"id":177},"玩具机器与赌场","玩具、机器与赌场",[11,180,181],{},"如果说香农的理论成就是他的「正业」，那么他造的那些机器，就是他生活里最鲜活的部分。",[11,183,184],{},"1950 年，他做了一只名叫「忒修斯」的电动机械鼠，能够在迷宫里摸索前进，一旦走过一遍，它就能记住路线，第二次直接走到出口。名字来自那个用线团走出迷宫的希腊英雄。这只木老鼠本身只是个装着磁铁和几根铜丝触须的壳子，真正的「脑子」藏在地板下面：一整排从电话交换机上拆下来的继电器，驱动着一台带电磁铁的滑车，把老鼠拖着往四个方向走。触须碰到墙，对应的继电器就记下这一格有墙，老鼠拐九十度继续试，直到撞上一块铜做的「奶酪」，蜂鸣器响起来。二十五格的迷宫，大约两个比特记一格，全部记忆加起来也就几十个比特——而它第二次就能一路直着跑到出口。迷宫改了，它还能把学到的忘掉重学。这是最早的「学习机器」之一。香农自己后来开玩笑说：严格讲，「那只老鼠并没有在解迷宫，是迷宫在解那只老鼠。」",[11,186,187],{},"1951 年 3 月，他在梅西基金会的控制论会议上做了题为《一台迷宫求解机的展示》的报告（会议记录到 1952 年才出版，贝尔实验室同年还拍了一部短片，报纸杂志跟着报道了一轮，所以很多书上把年份写成 1952）。据说现场有位神经生理学家拉尔夫·杰拉德，看见老鼠在一个圈里绕来绕去，喊了一声「这是神经症！」，香农于是又给它加了一个「抗神经症回路」。",[11,189,190],{},"他造过一台「读心机器」，能根据人以前猜硬币正反的习惯来预测下一次选择。这件事有个具体的对手。贝尔实验室的同事戴夫·哈格尔巴格先做了一台专门猜硬币的机器，叫 SEER——「序列外推机器人」，机器里面记着八种局面（上一轮自己赢还是输、对手换没换招），每种局面配一个可以上下加减的计数器，靠这点统计去押下一次；据他那篇 1956 年的论文，这台机器跟人对打了九千多局，赢了大约五成三。香农 1953 年 3 月写了一份备忘录，标题就叫《一台读心的（？）机器》，开门见山地说，这是「对哈格尔巴格的机器的一个简化模型」。两人的机器后来被接在一起互相对打，因为没人按按钮，还得再串一台「裁判」机器来产生随机数。谁赢的说法不一：多数说法是香农那台简单些的机器小胜，也有说它「赢得相当轻松」的——但具体比分，恐怕已经没人说得清了。香农在备忘录里还写了一句有趣的话：这类游戏，冯·诺依曼和摩根施特恩用博弈论处理过，爱伦·坡在《被窃的信》里用心理学处理过，而他这台机器「更接近坡的玩法，而不是冯·诺依曼的」。",[11,192,193],{},"他还造过一台只有一个功能的「终极机器」：盒子上有一个开关，你把它拨到「开」，盒盖就会打开，伸出一只机械手，把开关拨回「关」，然后缩回去，盖上盖子。这个点子最初来自他的朋友马文·明斯基——1952 年夏天明斯基在贝尔实验室跟他共事，后来回忆说：「我提议做这个机器，香农喜欢它，就让公司做了一批，送给几位高管。」香农在自己的桌上留了一台。它是被作家阿瑟·克拉克写下来的，克拉克在贝尔实验室看见过它，1958 年这样描述：「它不过是一只小木匣，雪茄盒大小，一面装着开关。你一扳开关，里面就响起一阵愤怒而一本正经的嗡嗡声。盒盖慢慢抬起，一只手从下面伸出来，把开关拨回去，然后缩回盒里。盒盖啪地合上，像棺材合盖一样决绝……一台什么也不做、只把自己关掉的机器，让人有一种说不出的不祥感。」——半个多世纪后，这个点子在网上重新火了一遍，人们叫它「最没用的机器」，做的人多半并不知道它出自明斯基的玩笑和香农的手。",[11,195,196],{},"他还设计了一台只用罗马数字运算的计算机，起名 THROBAC，说的是「节俭的罗马数字回溯式计算机」，名字本身就像个玩笑。这台机器 1953 年 4 月留下了两份技术备忘录，实物今天是麻省理工博物馆的藏品。",[11,198,199],{},"他的「玩具房」是家里最神奇的地方。那里有各式各样的独轮车，其中包括一些特别古怪的设计：有一辆没有座垫，有一辆没有脚蹬，有一辆是双人的，还有一辆的轮毂是偏心的，踩起来人会一上一下地起伏——他说这是头一辆这么做的车，帮他调试的助手查理·曼宁一边担心他的安全，一边为它第一次骑成鼓掌。车库里的独轮车和「大小轮」堆得落了一层灰。有会杂耍的机器人，其中一个被装扮成喜剧演员 W.C. 菲尔兹的形象：那是用儿童建筑玩具搭出来的，用三个钢球，球在一个绷紧的鼓面上弹跳，靠两片摇摆的桨「接一下、抛一下」，出手的误差则用短短的沟槽去纠正——全机没有一个传感器。他还做过三个小丑的「永不掉球」杂耍装置，起因是贝蒂从蛋糕装饰店带回一个四英寸的小丑，「才一块九毛八」。他的得意是：「有史以来最厉害的杂耍家也没法把纪录保持几分钟，可我的小丑整夜都在抛，一次也不掉！」",[11,201,202],{},"据说他还造过会喷火的小号——一吹，喇叭口就喷出火苗；还有火箭动力的飞盘、烧汽油的弹跳杆、一双巨大的泡沫「水上行走鞋」、一根从厨房用缆线连到地下实验室的机械手指（一拉，手指就勾一勾，等于叫人）、一台能设定翻转次数的机械硬币、从门廊下滑到湖边的简易缆车。爱德华·索普第一次走进他家地下室时的感想，被传记作者记了下来：「一个搞小玩意的人的天堂……我这是遇到了终极小玩意爱好者。」",[11,204,205],{},"他对杂耍尤其着迷，甚至总结出了一个「杂耍定理」。它把五个量用一行等式联系起来：设每只手接球到把球抛出的时间为 D，球在空中滞留的时间为 F，一只手空着的比例为 V，那么 (F + D) × 手数 = (V + D) × 球数。这个式子直到今天还在杂耍圈里被引用。他也写过一篇《杂耍的科学》，投给了《科学美国人》，但那份稿子改了又改，最后没发表——他 1987 年接受采访时还说：「我是给《科学美国人》写了一篇，至今没发出来。」文章要等到他去世后，被收进 1993 年的《香农论文集》里才和读者见面。对别人来说，这些都是不务正业；对他来说，这是理解世界的另一种方式。",[11,207,208],{},"他的兴趣还延伸到了钱的世界。1961 年，他与数学家爱德华·索普合作，做了一台可穿戴的轮盘赌预测装置：一个香烟盒大小的模拟计算机，开关藏在鞋里用大脚趾操作，一只脚负责给轮盘计时，另一只负责给球计时，结果则用几个音调通过塞进一只耳朵的小喇叭报出来；连导线都用胶水粘上颜色，尽量跟皮肤和头发混在一起。它预测的不是具体哪一个格子，而是一段扇区。那年 8 月，他们带着它真的去了拉斯维加斯：香农在轮盘旁边计时，索普在赌台另一头下注，两位太太负责望风。机器是灵的，小堆的筹码慢慢变大堆；但麻烦在于那根比头发还细的耳机线老是断，一断就得停半天。有一次同桌一位女士「惊恐地看过来」，索普赶紧走开，才发现「那个小喇叭像一只外星虫子一样从我的耳道里探出头来」。香农自己事后总结得很平：「我们碰到一堆实际问题，实际上从来没赚到钱。」这件事他们守口如瓶到 1966 年才披露；今天它被追认为「第一台可穿戴计算机」，不过这个称呼是后人的追认，不是当时的说法。",[11,210,211],{},"同一件事还有个前传，主角是索普的黑杰克工作。索普那篇论文本来想叫《二十一点的制胜策略》，是香农劝他把标题改得平淡些，最后成了《二十一点的一种有利策略》，1961 年发表在《美国科学院院刊》上——投这篇稿子需要一位院士背书，香农正是那位数学部的院士，据索普回忆，香农在签字前把他「盘问」了一遍才放过他。后来那本《击败庄家》把算牌术传遍了全世界。至于去拉斯维加斯那次，是轮盘赌，不是黑杰克，很多人会把这两件事混在一起。",[11,213,214],{},"他对股票的态度同样如此。香农并不迷恋盯盘，他会买入自己看好的少数几家技术公司并长期持有，比如惠普、摩托罗拉，还有他的老朋友亨利·辛格尔顿掌舵的泰利达因——辛格尔顿从大学时代起就跟他相识，后来还把他请进了董事会。他 1987 年跟采访者算过这笔账：「泰利达因我们拿了二十五年，每年复合增长百分之二十七。」这个数字在当时的圈子里是件稀罕事。至于那个更著名的「年化百分之二十八、跑赢一千多家基金」的说法，出处是庞德斯通 2005 年的书，依据的是一份未曾发表的访谈笔记，听个大概即可，别当成审计过的账目。他自己对这套本事的总结倒是简单：「我们是基本面派，不是技术派。」他对那些画图形的人毫不客气，把「头肩顶」「深 V」之类称作「重要数据的一种非常粗糙的复制品」；至于经济学家说的有效市场，他直说「我根本不信」。他还留下一句在麻省理工流传很广的俏皮话：有人问他为什么不用自己那套选股方法，他说：「算了吧，手续费会把你吃光。」——另有一次他对人说：「我是靠股市挣钱的，不是靠证定理挣钱的。」家里的账目，其实主要是贝蒂在管。女儿佩吉后来说：「这从来都是他们两个人的项目……他们两个都是赌徒。」他们甚至用一台早期的苹果 II 型电脑，每晚算一遍持仓的增长速度。",[11,216,217],{},"同一时期，他还是 1956 年达特茅斯人工智能夏季研讨会的发起者之一，与麦卡锡、明斯基、罗切斯特一起，把「人工智能」这个话题带到了学界的桌面上。有个细节值得记下：他自己并不喜欢「人工智能」这个词，更愿意用老派的「自动机研究」——那年他和麦卡锡合编的那本论文集，名字就叫《自动机研究》。至于那场为期一个多月的讨论会，他本人到底待了多久，史料上并不清楚：会议没有留下正式的出席名单，有回忆说他到场聊过一两天就走了，也有同时代人的笔记把他记成在场者。能确定的是，他不是那个从头住到尾的人。",[11,219,220],{},"然而他又是个清醒的人。1956 年，他在《IRE 信息论汇刊》上写了一篇很短、不到六百词的社论，题目叫《跟风》。这篇文章今天读起来依然刺人：",[143,222,223],{},[11,224,225],{},"「信息论在最近几年变成了一股科学上的跟风热潮。它本来只是通信工程师的一件技术工具，却在通俗媒体和学术媒体上都得到了异乎寻常的关注……它大概已经被吹到了超出它实际成就的高度。」「大自然的秘密很少会一次让出好几条。」「人们会很容易发现，用上几个带劲的词，比如信息、熵、冗余，并不能解决我们所有的问题。」「这个行当无疑是被卖出去的，如果不是被卖过头的话……我们该做的是研究，而不是宣传。几篇第一流的论文，胜过一大批构思拙劣或者半途而废的文章。」",[11,227,228],{},"一个创立了一门学科的人，反而最先劝大家别神化这门学科——这种低调，几乎成了他性格的标签。",[11,230,231],{},"这篇社论不是没人回应，恰恰相反。维纳在三个月后同一份刊物上写了一篇《什么是信息论？》，客气地反驳说，不应该把信息论缩得那么窄；彼得·埃利亚斯则在 1958 年写了一篇讽刺社论，题目叫《两篇著名的论文》，虚构了一篇题为《信息论、光合作用与宗教》的文章来嘲笑滥用，末尾写：「我建议我们别再写这种东西了，把大量人力释放出来，去做那些真正需要研究的、激动人心的重要问题。」它常被后人称作学界最早的一次「索卡尔式恶作剧」的前身。罗伯特·法诺对此的感受很直接：「我不喜欢‘信息论’这个名字。克劳德也不喜欢。因为它听起来像是一门关于‘信息’的理论——可它不是，它是关于信息传输的，不是关于信息的。太多人没弄明白这一点。」贝蒂说得更家常：「那些人把他的话拉来拉去，他有点被惹烦了。他们不明白他想做的是什么。」",[18,233,235],{"id":234},"麻省理工的怪教授","麻省理工的「怪教授」",[11,237,238],{},[72,239],{"alt":240,"src":241},"Shannon SM ’40, PhD ’40, who taught at MIT from 1956 until his retirement in 1978, was known to many as the father of information theory and of modern digital communications.","https:\u002F\u002Fimage-assets.dreams.plus\u002F202610162232493.png",[11,243,244],{},"1956 年 1 月，香农向贝尔实验室请了长假，回到麻省理工做客座教授，头衔是「电气通信访问教授」；1957 年他正式留下，同时挂两个教授头衔——电气工程系的通信科学教授，以及数学系教授。1958 年 10 月，学校宣布他出任新设立的「唐纳科学讲席教授」，这笔讲席由费城的唐纳基金会捐资五十万美元设立，是当时麻省理工收到过的最大一笔讲席捐赠。他和家人搬到了马萨诸塞州的温彻斯特，住进一栋靠近上神秘湖的大房子。房子 1858 年为一位名叫艾伦·德怀特的女士所建，她是托马斯·杰斐逊的曾外孙女，房子的设计据说参考了蒙蒂塞洛。他们后来给它起了个名字：「熵之屋」。",[11,246,247],{},"在学生眼里，香农是个特别的老师。他不爱讲课，更不爱写文章，上课风格随意，有时偏离主题，把话题带到他自己最近在摆弄的玩意上。",[11,249,250],{},"莱昂纳德·克莱因罗克形容他的课「像一顿好饭：你去了，他给你的东西是干净的、直观的」。罗伯特·加拉格记得他讲课时的那种神情：「他不会说‘这一章的要点是什么什么’。他会说：‘昨天晚上我在琢磨这个，想出来一个挺有意思的看法。’说的时候嘴角还带着一点坏笑。」大卫·福尼则是被他的研究讨论班拉进这行的，福尼说，他的教学方法就是讲自己正在做的问题、半成品的结果、猜想；有些问题他有漂亮的结果，有些问题他除了把问题本身说清楚以外毫无进展——「而这对一个正在找论文题目的研究生来说，简直太好了。」赫尔曼·豪斯也记得一件小事：他去旁听香农的讨论班，香农「把我当作和他平等的人对待」，并且对他这个晚辈提了一个关键问题，后来长成了豪斯那本书的第四章。香农的课还有个技术性细节常被提起：他一边回答问题，一边用一只手把一截粉笔抛上抛下，从来没有失手过。有位学生的总结很干脆：「我们都像敬神一样敬香农。」",[11,252,253],{},"做导师这件事，他却躲得很彻底。他一生带出的博士生极少——按后来的统计，只有三个；同一时期，麦卡锡、明斯基那些人各自都带出了一整代人。加拉格的解释很实在：「他的博士生非常少……你要是待在麻省理工，身边站着香农这么个庞然大物，你得有相当大的自我，才敢开口请他带你。」有人劝他多带几个学生，他的回答是：「我当不了导师。我没办法给任何人建议。我不觉得自己有资格去建议别人。」",[11,255,256],{},"他的办公室很乱，邮件和文稿堆得老高，据说他很多信件长期无人回复。这件事有个物证：他给自己存信件的文件夹起了个名字，叫「我拖得太久还没回的信」。记者乔恩·格特纳有一句形容极为传神：「信号可以抵达克劳德·香农。然后就再也传不下去了。」有位 1969 年去麻省理工访问的苏联学者回忆，他在走廊里看见了「香农教授」的门牌，然后过了一年多才意识到，这扇门几乎没开过——香农已经很少来学校了。倒是有位同事借用他那间空掉的办公室时，在里面翻出一张一年前开出、还没兑现的支票。人们还常提到，他在教工俱乐部的午饭桌上算他的股票想法，餐巾纸写满就换一张。",[11,258,259],{},"他对学术的虚名、头衔、荣誉兴趣平平，常常对别人的称赞报以腼腆一笑。他的名头则越来越大：1966 年 12 月，美国国家科学奖章的消息公布，次年 2 月由约翰逊总统在白宫东厅颁发，同一年他还拿到了 IEEE 荣誉奖章。颁奖那天，七岁的女儿佩吉为了穿哪条裙子跟母亲争执了一路，最后是副总统汉弗莱的大笑把她吓到躲在母亲腿后面。贝蒂说：「他是个非常谦逊的人。他得过很多奖，但奖从没让他头脑发热，他也从不谈这些。」他那些荣誉博士的兜帽太多，于是自己做了一个可以旋转的架子挂起来，跟挂领带的架子差不多。",[11,261,262],{},"领奖和演讲则一直是他的软肋。1973 年，第一届「香农讲座」在以色列的阿什凯隆举行，埃尔温·伯利坎普后来回忆：「我从没见过那么严重的怯场。我根本想不到，一个人在朋友面前可以怕成这样。」他需要有人在后台替他做很久的心理建设，还得由一位朋友陪着才肯上台。他后来推掉类似的邀约时，理由是一句玩笑：「退休以后，贝蒂不擦窗户，我不做演讲。」",[11,264,265],{},"这些年里，他的另一桩爱好是音乐：他会吹单簧管，喜欢迪克西兰爵士乐，也常参加小型即兴演奏。楼下客厅里，他吹单簧管、贝蒂弹钢琴的二重奏，是这个家的日常。爵士乐里的即兴与结构，与他的科学趣味可谓同源。",[11,267,268],{},"他爱下棋，但并不在乎输赢；他自己做的下棋机器能赢一般水平的对手，他却更乐意站在旁边看机器怎么「思考」。他骑着独轮车穿过麻省理工的走廊，边走边杂耍，让路过的学生又惊又喜。",[11,270,271],{},"家里那三个孩子，是在一堆零件中间长大的。儿子罗伯特生于 1952 年，后来做计算机，1998 年先于父亲去世；安德鲁生于 1954 年，成了钢琴家和作曲家；女儿佩吉生于 1959 年，后来当了老师。家里那间被报纸叫作「玩具房」的两层附楼，孩子们只叫它「爸爸的房间」。佩吉回忆说，父亲在家工作的时间很多，去学校只是为了上课和见学生，「所以我从小到大觉得他老在身边，跟很多上班的人家不一样」。晚饭后谁洗碗，家里甚至有台会走的发条机器老鼠来决定：把它放在餐桌中间，看它往哪边掉下去，掉到谁那边就谁洗。有一次佩吉把一盒牙签撒在了门廊上，父亲没有生气，而是说：「你知道吗，用这个可以算出圆周率。」——他说的是投针问题。家里饭桌上的话题常常是股票，孩子们很早就被教着读《华尔街日报》。至于辅导作业，他会因为「新数学」的教材顺序不对而发一顿牢骚，然后一路讲到虚数上去，讲到孩子已经完全不指望他把题讲完。",[11,273,274],{},"1978 年，他从教授岗位上退休，此后更多地待在家中，把时间交给他的工坊、他的玩具和他的书。",[18,276,278],{"id":277},"熵之屋里的晚年","「熵之屋」里的晚年",[11,280,281],{},[72,282],{"alt":283,"src":284},"Claude Shannon's electromechanical mouse, which he called Theseus, was one of the earliest attempts to \"teach\" a machine to \"learn\" and one of the first experiments in artificial intelligence.","https:\u002F\u002Fimage-assets.dreams.plus\u002F202610162229686.png",[11,286,287],{},"退休后的香农依然享受生活：造机器，玩杂耍，和贝蒂一起旅行、散步，在家里招待来访的朋友。他不太谈自己的成就，也不爱做回顾。很多年后，来访者发现他的家里很少有显眼的荣誉陈列，反倒到处是工作台、零件和各式玩具。",[11,289,290],{},"他的动手能力没有退化，反而更放得开了。他做了一台解魔方的机器——这是真的，不是传说，那台机器今天也在麻省理工博物馆里；他还为魔方写过一首七十来行、带脚注的打油诗，标明要用《Ta-Ra-Ra Boom-De-Ay》的调子唱。1985 年，他获得了第一届京都奖，去京都领奖时做了一场题为《通信与计算的发展，以及我的爱好》的演讲，那是他晚年最长、也最完整的一次公开表述。他在演讲里说，历史上真正重要的不是帝王将相，而是「达尔文、牛顿、贝多芬这样的思想者和创造者」。",[11,292,293],{},"进入 80 年代，他的记忆开始衰退。1983 年，他去看医生，结论是「很可能处在阿尔茨海默病非常非常早期的阶段」（这是贝蒂的原话）。起初是忘电话号码、忘名字、忘面孔，出门去趟杂货店会忘了怎么回来，字迹也开始发抖。",[11,295,296],{},"1985 年，在英国布莱顿举办的国际信息论研讨会上，出现了一件令人难忘的事。他和贝蒂没有事先打招呼就出现在会场，在几个报告厅里进出，直到有人认出他来，消息才传开。晚宴上主办方把他请上台，他只简短地讲了几句，就被自己的掌声淹没了，最后说了一句：「这——太荒唐了。」然后就没什么可说的了，于是从口袋里掏出三个球，当场抛了起来。事后有人问主持人该怎么形容这件事，得到的回答是：「就像牛顿突然出现在一场物理学会议上。」参会者排起长队请他签名，很多年轻研究者是平生第一次见到这位读了一辈子其论文的人。当时的信息论学会会长也回忆说，那天在场的人里，大部分其实并不认得他，「但有一种嗡嗡声：香农来了，在哪儿，在哪儿？」——那是他最后几次公开露面之一。第二年，学会正式邀请他出席了在密歇根安娜堡举行的研讨会，那时病情已经相当明显：他做了一场十几分钟的晚宴讲话，里面还塞满了趣闻和玩笑，可贝蒂替他挡掉了大部分寒暄。",[11,298,299],{},"此后，病情逐渐加重。女儿佩吉说：「他会到处乱走。我们住在一条繁忙的街边……看着自己的亲人得这种病，是件很可怕的事。」有一阵子，家里参加了当地医院的阿尔茨海默病研究，贝蒂充当对照组。佩吉说：「有些日子他认得人，有些日子不认……有时候还是原来那个爸爸，有时候完全不知道自己在哪儿。」1992 年，佩吉还跟他有过一次关于研究生院的正常交谈；到 1993 年，罗伯特·法诺问他一件从前的事，香农只是回答：「我不记得了。」",[11,301,302],{},"1993 年他摔了一跤，髋骨骨折，康复得很慢。贝蒂本想让他在家里，还在「熵之屋」里布置了一间放得下病床的房间，最后在佩吉的劝说下，把他送进了梅德福的一家护理机构。贝蒂几乎每天去两次，佩吉说她「非常尽心」。贝蒂自己回忆：「中午我过去，护士们会排队坐在一张长凳上等我，因为我一进门，他脸上就会亮起来，咧嘴笑。」他在那里还会把助行架拆开来，琢磨更好的设计；听到音乐就用手指打拍子；护理人员会给他出些简单的算术题；他也会朝着楼梯和门外走。90 年代，他渐渐认不出身边的人。2001 年 2 月 24 日，克劳德·香农在这家护理机构去世，享年 84 岁。他的大脑捐给了阿尔茨海默病研究。",[11,304,305],{},"贝蒂比他多活了十六年，2017 年 5 月去世。他们结婚六十八年，从他还在贝尔实验室算信道容量，一直到「熵之屋」里的人渐渐走完。",[11,307,308],{},"他早年还给自己画过一场想象中葬礼的速写，那张图一点也不悲伤：一支爵士乐队在前面开道，六位独轮车手抬着棺材（图上写着「6 个骑独轮车的人 \u002F 1 位亲人」），后面跟着哭泣的寡妇、八人杂耍队和一台八条腿的杂耍机器，一辆「棋局彩车」上，棋手戴维·利维正在跟电脑对局，再往后是四只按斯金纳的方法训练过的猫、各种小机器、慢跑的人和一支四百一十七人的乐队。一个人能这样安排自己的葬礼，说明他对「正经」和「不正经」的分界，从一开始就没怎么放在心上。",[18,310,311],{"id":311},"一个把工作当成游戏的人",[11,313,314],{},"香农的一生没有戏剧性的冲突，没有激烈的论战，也没有惊人的野心，很多时候他就是在一间堆满零件的屋子里，对着一个有趣的问题发呆。他提出的理论，为今天的手机通信、互联网、数据压缩、纠错码和密码学等整个数字世界打下了地基；而他自己的日子，却过得像一个永远不肯长大的孩子。",[11,316,317],{},"同行对他的评价，几乎都带着一点无从下手的敬意。大卫·斯莱皮安说：「他真的是个天才。我认识的人里，只有他配得上这个词。」又说：「他数学并不算懂得深，但他能现造出他需要的数学。」罗伯特·加拉格的版本是：「他的眼光清澈得惊人。爱因斯坦也是这样。」至于他到底做了什么，加拉格还有一句更朴素的话：「是香农看出，二进制位是一切通信的基本元素。那是他真正的发现，整个通信革命都是从这里长出来的。」托马斯·科弗说：「香农把三个领域炸了出来。」詹姆斯·马西在密码学上补了一句：「毫不夸张地说，香农的文章标志着密码学从一门手艺变成了一门科学。」而马文·明斯基记住的却是另一面：「不管出现什么题目，他都带着兴致扑上去，用某种出人意料的办法去攻它。对他而言，问题看上去越难，找到新东西的机会就越大。」",[11,319,320],{},"他自己对这一切的解释，比任何评论都更实在。1987 年，他对采访者说：「我不认为我做事是为了得奖——虽然另一间屋子里放着两打奖章。我更主要是被好奇心驱动，从来不是为了钱。我只是想知道，东西到底是怎么被装起来的。」「答案找到之后，把它们写下来、发表出来，总是让我很痛苦……我做过很多事，从来没写出来过。太懒了吧。我楼上有一个文件夹，装的全是没写完的论文。」三年后，他又说了一句后来被引用得最多的话：「我一直在追逐自己感兴趣的东西，不太在意它有多少金钱价值，或者对世界有多少价值。我在完全没用的东西上花了很多时间。」",[11,322,323],{},"回望那些日常的小事：少年时在围栏上架起的电报线，独自在走廊里骑独轮车的深夜，家里摆满的各种怪机器，晚年杂耍时那一点羞涩的笑容，你会发现，这些并不是他「正业之外」的点缀，而恰恰是他创造力的来源。他相信好奇心，相信玩耍，也相信，好玩的东西往往藏着深刻的真理。",[143,325,326],{},[11,327,328],{},"卡德班克和斯隆在《自然》上的讣文里写过一句很准的话：香农大概能排进二十世纪科学主要人物名单的前列，「尽管他的名字对公众来说相对陌生」。这大概正是他本人会满意的位置。",{"title":330,"searchDepth":331,"depth":331,"links":332},"",2,[333,334,335,336,337,338,339,340],{"id":20,"depth":331,"text":20},{"id":41,"depth":331,"text":41},{"id":81,"depth":331,"text":81},{"id":120,"depth":331,"text":120},{"id":177,"depth":331,"text":178},{"id":234,"depth":331,"text":235},{"id":277,"depth":331,"text":278},{"id":311,"depth":331,"text":311},false,true,"md",null,{},"\u002Fblog\u002F2026\u002F0010-biography-of-claude-shannon",{"title":6,"description":13},"blog\u002F2026\u002F0010-biography-of-claude-shannon","从密歇根小镇那根架在铁丝围栏上的电报线，到贝尔实验室走廊里的独轮车，再到麻省理工那间堆满零件的办公室。他给「信息」下了数学定义，自己却一辈子只对有意思的东西负责。",[351],"thoughts","2026-10-16T22:03:15+08:00","FVIfEic5VrK7HmvsYttp69z46Fc79opnUYBtJpxN80w",{"id":355,"title":356,"body":357,"description":133035,"draft":341,"enableCodeHighlight":341,"enableCodeHightlight":341,"enableComment":342,"enableD2":341,"enableKatex":342,"extension":343,"image":330,"important":341,"location":344,"meta":133036,"navigation":342,"ogImage":344,"path":133037,"seo":133038,"stem":133039,"summary":133040,"tags":133041,"time":133044,"__hash__":133045},"blog\u002Fblog\u002F2026\u002F0011-about-the-f-divergence.md","f-散度族及其推论",{"type":8,"value":358,"toc":132974},[359,411,525,872,875,879,1099,1263,1339,2657,2662,3502,4169,4606,5063,5549,5553,5875,5918,5922,6058,6236,6293,6836,7008,7493,7706,7710,8761,9096,9194,9198,9439,9712,9748,10218,10373,10902,10905,10909,11011,11313,11318,12283,12951,13763,14606,14738,15667,16218,16516,16857,17391,17697,18313,19425,20245,20788,21134,21387,21625,21656,21752,21756,21788,21791,21794,21811,21814,21818,21821,21909,22145,22685,22850,23394,23397,23687,23972,24533,24536,24834,25529,25893,25897,26059,26536,26808,27204,27915,27918,28355,28358,28795,29064,30028,30281,30922,31160,31328,31515,31925,32431,33149,33875,33931,34176,34437,34854,34858,34860,35027,35096,35736,36131,36523,36532,36878,37493,37497,37499,37631,37699,38227,38234,38607,38980,39933,40782,40786,40788,40969,41285,41824,41986,42394,42457,42934,43552,44464,44655,45081,45085,45169,45510,45956,46332,46541,46813,46999,47537,48078,48504,48507,49362,49451,49720,49724,49727,50296,50763,50973,51101,51642,51855,51864,52366,52834,52838,55257,55261,55556,55560,55814,56481,56485,57442,58133,58635,58639,58991,59315,59420,60153,61026,61030,61849,61884,62135,62301,63347,64000,64006,64272,64770,64963,67153,68167,68477,68752,69264,70952,71842,73612,74375,74378,74789,74792,74795,74799,75103,75441,76207,76210,76571,76603,77092,77155,77950,78329,78377,78381,79261,79567,80709,82403,82407,84225,84231,84375,84777,85321,86448,87389,87395,87863,88548,88955,89028,89067,89465,89794,90046,90792,90857,92138,92783,97287,97294,97298,97301,99214,99473,99642,99646,99650,99653,100056,100262,101052,101178,101690,101694,102108,102366,102826,103532,103536,103597,103729,104116,104464,105694,105698,105884,106239,106242,106720,107110,107622,107905,108326,108586,108590,108593,108927,108931,108935,111895,114954,114957,114961,115014,115261,115474,115600,115961,116236,116613,116734,116739,116743,117780,117783,117787,117790,117849,117852,117856,118046,118050,118053,118582,118937,118941,118944,119516,119636,119640,119688,120091,120094,120098,120163,120167,120170,120524,120527,120531,120612,120966,121242,121400,121637,121903,122226,122598,123008,123883,124415,124685,124688,124692,124696,125047,125052,125791,126244,126582,126584,127185,127347,127353,127699,128215,128221,128795,129037,129041,129634,130025,130445,130793,131267,131271,131529,131844,131950,132484,132487,132491,132494,132971],[11,360,361,362,410],{},"f-散度族是概率分布之间差异的一大类度量，它用一个凸函数 ",[363,364,368,390],"span",{"className":365,"translate":367},[366],"katex","no",[363,369,372],{"className":370},[371],"katex-mathml",[373,374,376],"math",{"xmlns":375},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[377,378,379,386],"semantics",{},[380,381,382],"mrow",{},[383,384,385],"mi",{},"f",[387,388,385],"annotation",{"encoding":389},"application\u002Fx-tex",[363,391,395],{"className":392,"ariaHidden":394},[393],"katex-html","true",[363,396,399,404],{"className":397},[398],"base",[363,400],{"className":401,"style":403},[402],"strut","height:0.8889em;vertical-align:-0.1944em;",[363,405,385],{"className":406,"style":409},[407,408],"mord","mathnormal","margin-right:0.1076em;"," 来统一描述 KL 散度、JS 散度、全变差、卡方散度等许多常见散度。可以把它理解为「散度」的通用模板。",[11,412,413,414,442,443,524],{},"用一个凸函数 ",[363,415,417,430],{"className":416,"translate":367},[366],[363,418,420],{"className":419},[371],[373,421,422],{"xmlns":375},[377,423,424,428],{},[380,425,426],{},[383,427,385],{},[387,429,385],{"encoding":389},[363,431,433],{"className":432,"ariaHidden":394},[393],[363,434,436,439],{"className":435},[398],[363,437],{"className":438,"style":403},[402],[363,440,385],{"className":441,"style":409},[407,408],"（满足 ",[363,444,446,478],{"className":445,"translate":367},[366],[363,447,449],{"className":448},[371],[373,450,451],{"xmlns":375},[377,452,453,475],{},[380,454,455,457,462,466,469,472],{},[383,456,385],{},[458,459,461],"mo",{"stretchy":460},"false","(",[463,464,465],"mn",{},"1",[458,467,468],{"stretchy":460},")",[458,470,471],{},"=",[463,473,474],{},"0",[387,476,477],{"encoding":389},"f(1)=0",[363,479,481,514],{"className":480,"ariaHidden":394},[393],[363,482,484,488,491,495,498,502,507,511],{"className":483},[398],[363,485],{"className":486,"style":487},[402],"height:1em;vertical-align:-0.25em;",[363,489,385],{"className":490,"style":409},[407,408],[363,492,461],{"className":493},[494],"mopen",[363,496,465],{"className":497},[407],[363,499,468],{"className":500},[501],"mclose",[363,503],{"className":504,"style":506},[505],"mspace","margin-right:0.2778em;",[363,508,471],{"className":509},[510],"mrel",[363,512],{"className":513,"style":506},[505],[363,515,517,521],{"className":516},[398],[363,518],{"className":519,"style":520},[402],"height:0.6444em;",[363,522,474],{"className":523},[407],"）定义的散度模板：",[363,526,529],{"className":527,"translate":367},[528],"katex-display",[363,530,532,609],{"className":531,"translate":367},[366],[363,533,535],{"className":534},[371],[373,536,538],{"xmlns":375,"display":537},"block",[377,539,540,606],{},[380,541,542,550,552,555,559,562,564,566,574],{},[543,544,545,548],"msub",{},[383,546,547],{},"D",[383,549,385],{},[458,551,461],{"stretchy":460},[383,553,554],{},"P",[383,556,558],{"mathvariant":557},"normal","∥",[383,560,561],{},"Q",[458,563,468],{"stretchy":460},[458,565,471],{},[543,567,568,572],{},[383,569,571],{"mathvariant":570},"double-struck","E",[383,573,561],{},[380,575,576,579,581,603],{},[458,577,578],{"fence":394},"[",[383,580,385],{},[380,582,583,585,601],{},[458,584,461],{"fence":394},[586,587,588,595],"mfrac",{},[380,589,590,593],{},[383,591,592],{},"d",[383,594,554],{},[380,596,597,599],{},[383,598,592],{},[383,600,561],{},[458,602,468],{"fence":394},[458,604,605],{"fence":394},"]",[387,607,608],{"encoding":389},"D_f(P\\|Q)\n=\\mathbb E_Q\\left[\nf\\left(\\frac{dP}{dQ}\\right)\\right]",[363,610,612,701],{"className":611,"ariaHidden":394},[393],[363,613,615,619,676,679,683,686,689,692,695,698],{"className":614},[398],[363,616],{"className":617,"style":618},[402],"height:1.0361em;vertical-align:-0.2861em;",[363,620,622,626],{"className":621},[407],[363,623,547],{"className":624,"style":625},[407,408],"margin-right:0.0278em;",[363,627,630],{"className":628},[629],"msupsub",[363,631,635,667],{"className":632},[633,634],"vlist-t","vlist-t2",[363,636,639,662],{"className":637},[638],"vlist-r",[363,640,644],{"className":641,"style":643},[642],"vlist","height:0.3361em;",[363,645,647,652],{"style":646},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[363,648],{"className":649,"style":651},[650],"pstrut","height:2.7em;",[363,653,659],{"className":654},[655,656,657,658],"sizing","reset-size6","size3","mtight",[363,660,385],{"className":661,"style":409},[407,408,658],[363,663,666],{"className":664},[665],"vlist-s","​",[363,668,670],{"className":669},[638],[363,671,674],{"className":672,"style":673},[642],"height:0.2861em;",[363,675],{},[363,677,461],{"className":678},[494],[363,680,554],{"className":681,"style":682},[407,408],"margin-right:0.1389em;",[363,684,558],{"className":685},[407],[363,687,561],{"className":688},[407,408],[363,690,468],{"className":691},[501],[363,693],{"className":694,"style":506},[505],[363,696,471],{"className":697},[510],[363,699],{"className":700,"style":506},[505],[363,702,704,708,751,755],{"className":703},[398],[363,705],{"className":706,"style":707},[402],"height:2.4em;vertical-align:-0.95em;",[363,709,711,715],{"className":710},[407],[363,712,571],{"className":713},[407,714],"mathbb",[363,716,718],{"className":717},[629],[363,719,721,743],{"className":720},[633,634],[363,722,724,740],{"className":723},[638],[363,725,728],{"className":726,"style":727},[642],"height:0.3283em;",[363,729,731,734],{"style":730},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[363,732],{"className":733,"style":651},[650],[363,735,737],{"className":736},[655,656,657,658],[363,738,561],{"className":739},[407,408,658],[363,741,666],{"className":742},[665],[363,744,746],{"className":745},[638],[363,747,749],{"className":748,"style":673},[642],[363,750],{},[363,752],{"className":753,"style":754},[505],"margin-right:0.1667em;",[363,756,759,768,771,774,866],{"className":757},[758],"minner",[363,760,764],{"className":761,"style":763},[494,762],"delimcenter","top:0em;",[363,765,578],{"className":766},[767,657],"delimsizing",[363,769,385],{"className":770,"style":409},[407,408],[363,772],{"className":773,"style":754},[505],[363,775,777,783,860],{"className":776},[758],[363,778,780],{"className":779,"style":763},[494,762],[363,781,461],{"className":782},[767,657],[363,784,786,790,857],{"className":785},[407],[363,787],{"className":788},[494,789],"nulldelimiter",[363,791,793],{"className":792},[586],[363,794,796,848],{"className":795},[633,634],[363,797,799,845],{"className":798},[638],[363,800,803,819,830],{"className":801,"style":802},[642],"height:1.3714em;",[363,804,806,810],{"style":805},"top:-2.314em;",[363,807],{"className":808,"style":809},[650],"height:3em;",[363,811,813,816],{"className":812},[407],[363,814,592],{"className":815},[407,408],[363,817,561],{"className":818},[407,408],[363,820,822,825],{"style":821},"top:-3.23em;",[363,823],{"className":824,"style":809},[650],[363,826],{"className":827,"style":829},[828],"frac-line","border-bottom-width:0.04em;",[363,831,833,836],{"style":832},"top:-3.677em;",[363,834],{"className":835,"style":809},[650],[363,837,839,842],{"className":838},[407],[363,840,592],{"className":841},[407,408],[363,843,554],{"className":844,"style":682},[407,408],[363,846,666],{"className":847},[665],[363,849,851],{"className":850},[638],[363,852,855],{"className":853,"style":854},[642],"height:0.8804em;",[363,856],{},[363,858],{"className":859},[501,789],[363,861,863],{"className":862,"style":763},[501,762],[363,864,468],{"className":865},[767,657],[363,867,869],{"className":868,"style":763},[501,762],[363,870,605],{"className":871},[767,657],[11,873,874],{},"它统一了 KL、JS、全变差、卡方、Hellinger 等众多散度，具有非负性、联合凸性、变分对偶表示和数据处理不等式等核心性质，是信息论和生成模型理论中的基础工具。",[18,876,878],{"id":877},"_1-定义","1. 定义",[11,880,881,882,927,928,985,986,1015,1016,1044,1045,1098],{},"设 ",[363,883,885,904],{"className":884,"translate":367},[366],[363,886,888],{"className":887},[371],[373,889,890],{"xmlns":375},[377,891,892,901],{},[380,893,894,896,899],{},[383,895,554],{},[458,897,898],{"separator":394},",",[383,900,561],{},[387,902,903],{"encoding":389},"P,Q",[363,905,907],{"className":906,"ariaHidden":394},[393],[363,908,910,914,917,921,924],{"className":909},[398],[363,911],{"className":912,"style":913},[402],"height:0.8778em;vertical-align:-0.1944em;",[363,915,554],{"className":916,"style":682},[407,408],[363,918,898],{"className":919},[920],"mpunct",[363,922],{"className":923,"style":754},[505],[363,925,561],{"className":926},[407,408]," 是同一个可测空间 ",[363,929,931,956],{"className":930,"translate":367},[366],[363,932,934],{"className":933},[371],[373,935,936],{"xmlns":375},[377,937,938,953],{},[380,939,940,942,946,948,951],{},[458,941,461],{"stretchy":460},[383,943,945],{"mathvariant":944},"script","X",[458,947,898],{"separator":394},[383,949,950],{"mathvariant":944},"A",[458,952,468],{"stretchy":460},[387,954,955],{"encoding":389},"(\\mathcal X,\\mathcal A)",[363,957,959],{"className":958,"ariaHidden":394},[393],[363,960,962,965,968,973,976,979,982],{"className":961},[398],[363,963],{"className":964,"style":487},[402],[363,966,461],{"className":967},[494],[363,969,945],{"className":970,"style":972},[407,971],"mathcal","margin-right:0.1464em;",[363,974,898],{"className":975},[920],[363,977],{"className":978,"style":754},[505],[363,980,950],{"className":981},[407,971],[363,983,468],{"className":984},[501]," 上的两个概率分布，且 ",[363,987,989,1002],{"className":988,"translate":367},[366],[363,990,992],{"className":991},[371],[373,993,994],{"xmlns":375},[377,995,996,1000],{},[380,997,998],{},[383,999,554],{},[387,1001,554],{"encoding":389},[363,1003,1005],{"className":1004,"ariaHidden":394},[393],[363,1006,1008,1012],{"className":1007},[398],[363,1009],{"className":1010,"style":1011},[402],"height:0.6833em;",[363,1013,554],{"className":1014,"style":682},[407,408]," 关于 ",[363,1017,1019,1032],{"className":1018,"translate":367},[366],[363,1020,1022],{"className":1021},[371],[373,1023,1024],{"xmlns":375},[377,1025,1026,1030],{},[380,1027,1028],{},[383,1029,561],{},[387,1031,561],{"encoding":389},[363,1033,1035],{"className":1034,"ariaHidden":394},[393],[363,1036,1038,1041],{"className":1037},[398],[363,1039],{"className":1040,"style":913},[402],[363,1042,561],{"className":1043},[407,408]," 绝对连续（即 ",[363,1046,1048,1067],{"className":1047,"translate":367},[366],[363,1049,1051],{"className":1050},[371],[373,1052,1053],{"xmlns":375},[377,1054,1055,1064],{},[380,1056,1057,1059,1062],{},[383,1058,554],{},[458,1060,1061],{},"≪",[383,1063,561],{},[387,1065,1066],{"encoding":389},"P\\ll Q",[363,1068,1070,1089],{"className":1069,"ariaHidden":394},[393],[363,1071,1073,1077,1080,1083,1086],{"className":1072},[398],[363,1074],{"className":1075,"style":1076},[402],"height:0.7224em;vertical-align:-0.0391em;",[363,1078,554],{"className":1079,"style":682},[407,408],[363,1081],{"className":1082,"style":506},[505],[363,1084,1061],{"className":1085},[510],[363,1087],{"className":1088,"style":506},[505],[363,1090,1092,1095],{"className":1091},[398],[363,1093],{"className":1094,"style":913},[402],[363,1096,561],{"className":1097},[407,408],"），记",[363,1100,1102],{"className":1101,"translate":367},[528],[363,1103,1105,1149],{"className":1104,"translate":367},[366],[363,1106,1108],{"className":1107},[371],[373,1109,1110],{"xmlns":375,"display":537},[377,1111,1112,1146],{},[380,1113,1114,1117,1119,1122,1124,1126,1140,1142,1144],{},[383,1115,1116],{},"t",[458,1118,461],{"stretchy":460},[383,1120,1121],{},"x",[458,1123,468],{"stretchy":460},[458,1125,471],{},[586,1127,1128,1134],{},[380,1129,1130,1132],{},[383,1131,592],{},[383,1133,554],{},[380,1135,1136,1138],{},[383,1137,592],{},[383,1139,561],{},[458,1141,461],{"stretchy":460},[383,1143,1121],{},[458,1145,468],{"stretchy":460},[387,1147,1148],{"encoding":389},"t(x)=\\frac{dP}{dQ}(x)",[363,1150,1152,1179],{"className":1151,"ariaHidden":394},[393],[363,1153,1155,1158,1161,1164,1167,1170,1173,1176],{"className":1154},[398],[363,1156],{"className":1157,"style":487},[402],[363,1159,1116],{"className":1160},[407,408],[363,1162,461],{"className":1163},[494],[363,1165,1121],{"className":1166},[407,408],[363,1168,468],{"className":1169},[501],[363,1171],{"className":1172,"style":506},[505],[363,1174,471],{"className":1175},[510],[363,1177],{"className":1178,"style":506},[505],[363,1180,1182,1186,1254,1257,1260],{"className":1181},[398],[363,1183],{"className":1184,"style":1185},[402],"height:2.2519em;vertical-align:-0.8804em;",[363,1187,1189,1192,1251],{"className":1188},[407],[363,1190],{"className":1191},[494,789],[363,1193,1195],{"className":1194},[586],[363,1196,1198,1243],{"className":1197},[633,634],[363,1199,1201,1240],{"className":1200},[638],[363,1202,1204,1218,1226],{"className":1203,"style":802},[642],[363,1205,1206,1209],{"style":805},[363,1207],{"className":1208,"style":809},[650],[363,1210,1212,1215],{"className":1211},[407],[363,1213,592],{"className":1214},[407,408],[363,1216,561],{"className":1217},[407,408],[363,1219,1220,1223],{"style":821},[363,1221],{"className":1222,"style":809},[650],[363,1224],{"className":1225,"style":829},[828],[363,1227,1228,1231],{"style":832},[363,1229],{"className":1230,"style":809},[650],[363,1232,1234,1237],{"className":1233},[407],[363,1235,592],{"className":1236},[407,408],[363,1238,554],{"className":1239,"style":682},[407,408],[363,1241,666],{"className":1242},[665],[363,1244,1246],{"className":1245},[638],[363,1247,1249],{"className":1248,"style":854},[642],[363,1250],{},[363,1252],{"className":1253},[501,789],[363,1255,461],{"className":1256},[494],[363,1258,1121],{"className":1259},[407,408],[363,1261,468],{"className":1262},[501],[11,1264,1265,1266,1338],{},"为 Radon–Nikodym 导数（在离散情形就是概率质量之比，在密度存在时就是密度之比 ",[363,1267,1269,1301],{"className":1268,"translate":367},[366],[363,1270,1272],{"className":1271},[371],[373,1273,1274],{"xmlns":375},[377,1275,1276,1298],{},[380,1277,1278,1280,1282,1284,1286,1289,1292,1294,1296],{},[383,1279,11],{},[458,1281,461],{"stretchy":460},[383,1283,1121],{},[458,1285,468],{"stretchy":460},[383,1287,1288],{"mathvariant":557},"\u002F",[383,1290,1291],{},"q",[458,1293,461],{"stretchy":460},[383,1295,1121],{},[458,1297,468],{"stretchy":460},[387,1299,1300],{"encoding":389},"p(x)\u002Fq(x)",[363,1302,1304],{"className":1303,"ariaHidden":394},[393],[363,1305,1307,1310,1313,1316,1319,1322,1325,1329,1332,1335],{"className":1306},[398],[363,1308],{"className":1309,"style":487},[402],[363,1311,11],{"className":1312},[407,408],[363,1314,461],{"className":1315},[494],[363,1317,1121],{"className":1318},[407,408],[363,1320,468],{"className":1321},[501],[363,1323,1288],{"className":1324},[407],[363,1326,1291],{"className":1327,"style":1328},[407,408],"margin-right:0.0359em;",[363,1330,461],{"className":1331},[494],[363,1333,1121],{"className":1334},[407,408],[363,1336,468],{"className":1337},[501],"）。",[1340,1341,1343,1576,1983,2015,2595],"theorem",{"title":1342},"定义 1.1（f-散度）",[11,1344,1345,1346,1447,1448,1513,1514,1015,1542,1570,1571,1575],{},"给定一个凸函数 ",[363,1347,1349,1383],{"className":1348,"translate":367},[366],[363,1350,1352],{"className":1351},[371],[373,1353,1354],{"xmlns":375},[377,1355,1356,1380],{},[380,1357,1358,1360,1363,1365,1367,1369,1372,1374,1377],{},[383,1359,385],{},[458,1361,1362],{},":",[458,1364,578],{"stretchy":460},[463,1366,474],{},[458,1368,898],{"separator":394},[383,1370,1371],{"mathvariant":557},"∞",[458,1373,468],{"stretchy":460},[458,1375,1376],{},"→",[383,1378,1379],{"mathvariant":570},"R",[387,1381,1382],{"encoding":389},"f:[0,\\infty)\\to\\mathbb R",[363,1384,1386,1404,1437],{"className":1385,"ariaHidden":394},[393],[363,1387,1389,1392,1395,1398,1401],{"className":1388},[398],[363,1390],{"className":1391,"style":403},[402],[363,1393,385],{"className":1394,"style":409},[407,408],[363,1396],{"className":1397,"style":506},[505],[363,1399,1362],{"className":1400},[510],[363,1402],{"className":1403,"style":506},[505],[363,1405,1407,1410,1413,1416,1419,1422,1425,1428,1431,1434],{"className":1406},[398],[363,1408],{"className":1409,"style":487},[402],[363,1411,578],{"className":1412},[494],[363,1414,474],{"className":1415},[407],[363,1417,898],{"className":1418},[920],[363,1420],{"className":1421,"style":754},[505],[363,1423,1371],{"className":1424},[407],[363,1426,468],{"className":1427},[501],[363,1429],{"className":1430,"style":506},[505],[363,1432,1376],{"className":1433},[510],[363,1435],{"className":1436,"style":506},[505],[363,1438,1440,1444],{"className":1439},[398],[363,1441],{"className":1442,"style":1443},[402],"height:0.6889em;",[363,1445,1379],{"className":1446},[407,714],"，且满足 ",[363,1449,1451,1474],{"className":1450,"translate":367},[366],[363,1452,1454],{"className":1453},[371],[373,1455,1456],{"xmlns":375},[377,1457,1458,1472],{},[380,1459,1460,1462,1464,1466,1468,1470],{},[383,1461,385],{},[458,1463,461],{"stretchy":460},[463,1465,465],{},[458,1467,468],{"stretchy":460},[458,1469,471],{},[463,1471,474],{},[387,1473,477],{"encoding":389},[363,1475,1477,1504],{"className":1476,"ariaHidden":394},[393],[363,1478,1480,1483,1486,1489,1492,1495,1498,1501],{"className":1479},[398],[363,1481],{"className":1482,"style":487},[402],[363,1484,385],{"className":1485,"style":409},[407,408],[363,1487,461],{"className":1488},[494],[363,1490,465],{"className":1491},[407],[363,1493,468],{"className":1494},[501],[363,1496],{"className":1497,"style":506},[505],[363,1499,471],{"className":1500},[510],[363,1502],{"className":1503,"style":506},[505],[363,1505,1507,1510],{"className":1506},[398],[363,1508],{"className":1509,"style":520},[402],[363,1511,474],{"className":1512},[407],"，则 ",[363,1515,1517,1530],{"className":1516,"translate":367},[366],[363,1518,1520],{"className":1519},[371],[373,1521,1522],{"xmlns":375},[377,1523,1524,1528],{},[380,1525,1526],{},[383,1527,554],{},[387,1529,554],{"encoding":389},[363,1531,1533],{"className":1532,"ariaHidden":394},[393],[363,1534,1536,1539],{"className":1535},[398],[363,1537],{"className":1538,"style":1011},[402],[363,1540,554],{"className":1541,"style":682},[407,408],[363,1543,1545,1558],{"className":1544,"translate":367},[366],[363,1546,1548],{"className":1547},[371],[373,1549,1550],{"xmlns":375},[377,1551,1552,1556],{},[380,1553,1554],{},[383,1555,561],{},[387,1557,561],{"encoding":389},[363,1559,1561],{"className":1560,"ariaHidden":394},[393],[363,1562,1564,1567],{"className":1563},[398],[363,1565],{"className":1566,"style":913},[402],[363,1568,561],{"className":1569},[407,408]," 的 ",[1572,1573,1574],"strong",{},"f-散度"," 定义为",[363,1577,1579],{"className":1578,"translate":367},[528],[363,1580,1582,1689],{"className":1581,"translate":367},[366],[363,1583,1585],{"className":1584},[371],[373,1586,1587],{"xmlns":375,"display":537},[377,1588,1589,1686],{},[1590,1591,1595],"mtable",{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},"0.25em","right left","0em",[1596,1597,1598,1622],"mtr",{},[1599,1600,1601],"mtd",{},[1602,1603,1604],"mstyle",{"scriptlevel":474,"displaystyle":394},[380,1605,1606,1612,1614,1616,1618,1620],{},[543,1607,1608,1610],{},[383,1609,547],{},[383,1611,385],{},[458,1613,461],{"stretchy":460},[383,1615,554],{},[383,1617,558],{"mathvariant":557},[383,1619,561],{},[458,1621,468],{"stretchy":460},[1599,1623,1624],{},[1602,1625,1626],{"scriptlevel":474,"displaystyle":394},[380,1627,1628,1630,1632,1635,1637,1639,1641,1643,1647,1649,1652,1680,1682,1684],{},[380,1629],{},[458,1631,471],{},[458,1633,1634],{},"∫",[383,1636,1291],{},[458,1638,461],{"stretchy":460},[383,1640,1121],{},[458,1642,468],{"stretchy":460},[1644,1645,1646],"mtext",{}," ",[383,1648,385],{},[1644,1650,1651],{}," ⁣",[380,1653,1654,1656,1678],{},[458,1655,461],{"fence":394},[586,1657,1658,1668],{},[380,1659,1660,1662,1664,1666],{},[383,1661,11],{},[458,1663,461],{"stretchy":460},[383,1665,1121],{},[458,1667,468],{"stretchy":460},[380,1669,1670,1672,1674,1676],{},[383,1671,1291],{},[458,1673,461],{"stretchy":460},[383,1675,1121],{},[458,1677,468],{"stretchy":460},[458,1679,468],{"fence":394},[383,1681,592],{},[383,1683,1121],{},[458,1685,898],{"separator":394},[387,1687,1688],{"encoding":389},"\\begin{aligned}\nD_f(P\\|Q)\n&=\\int q(x)\\,\nf\\!\\left(\\frac{p(x)}{q(x)}\\right)dx,\n\\end{aligned}",[363,1690,1692],{"className":1691,"ariaHidden":394},[393],[363,1693,1695,1698],{"className":1694},[398],[363,1696],{"className":1697,"style":707},[402],[363,1699,1701],{"className":1700},[407],[363,1702,1704,1795],{"className":1703},[1590],[363,1705,1708],{"className":1706},[1707],"col-align-r",[363,1709,1711,1786],{"className":1710},[633,634],[363,1712,1714,1783],{"className":1713},[638],[363,1715,1718],{"className":1716,"style":1717},[642],"height:1.45em;",[363,1719,1721,1725],{"style":1720},"top:-3.45em;",[363,1722],{"className":1723,"style":1724},[650],"height:3.45em;",[363,1726,1728,1768,1771,1774,1777,1780],{"className":1727},[407],[363,1729,1731,1734],{"className":1730},[407],[363,1732,547],{"className":1733,"style":625},[407,408],[363,1735,1737],{"className":1736},[629],[363,1738,1740,1760],{"className":1739},[633,634],[363,1741,1743,1757],{"className":1742},[638],[363,1744,1746],{"className":1745,"style":643},[642],[363,1747,1748,1751],{"style":646},[363,1749],{"className":1750,"style":651},[650],[363,1752,1754],{"className":1753},[655,656,657,658],[363,1755,385],{"className":1756,"style":409},[407,408,658],[363,1758,666],{"className":1759},[665],[363,1761,1763],{"className":1762},[638],[363,1764,1766],{"className":1765,"style":673},[642],[363,1767],{},[363,1769,461],{"className":1770},[494],[363,1772,554],{"className":1773,"style":682},[407,408],[363,1775,558],{"className":1776},[407],[363,1778,561],{"className":1779},[407,408],[363,1781,468],{"className":1782},[501],[363,1784,666],{"className":1785},[665],[363,1787,1789],{"className":1788},[638],[363,1790,1793],{"className":1791,"style":1792},[642],"height:0.95em;",[363,1794],{},[363,1796,1799],{"className":1797},[1798],"col-align-l",[363,1800,1802,1975],{"className":1801},[633,634],[363,1803,1805,1972],{"className":1804},[638],[363,1806,1808],{"className":1807,"style":1717},[642],[363,1809,1810,1813],{"style":1720},[363,1811],{"className":1812,"style":1724},[650],[363,1814,1816,1819,1822,1825,1828,1835,1838,1841,1844,1847,1850,1853,1856,1860,1863,1960,1963,1966,1969],{"className":1815},[407],[363,1817],{"className":1818},[407],[363,1820],{"className":1821,"style":506},[505],[363,1823,471],{"className":1824},[510],[363,1826],{"className":1827,"style":506},[505],[363,1829,1634],{"className":1830,"style":1834},[1831,1832,1833],"mop","op-symbol","large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[363,1836],{"className":1837,"style":754},[505],[363,1839,1291],{"className":1840,"style":1328},[407,408],[363,1842,461],{"className":1843},[494],[363,1845,1121],{"className":1846},[407,408],[363,1848,468],{"className":1849},[501],[363,1851],{"className":1852,"style":754},[505],[363,1854,385],{"className":1855,"style":409},[407,408],[363,1857],{"className":1858,"style":1859},[505],"margin-right:-0.1667em;",[363,1861],{"className":1862,"style":754},[505],[363,1864,1866,1872,1954],{"className":1865},[758],[363,1867,1869],{"className":1868,"style":763},[494,762],[363,1870,461],{"className":1871},[767,657],[363,1873,1875,1878,1951],{"className":1874},[407],[363,1876],{"className":1877},[494,789],[363,1879,1881],{"className":1880},[586],[363,1882,1884,1942],{"className":1883},[633,634],[363,1885,1887,1939],{"className":1886},[638],[363,1888,1891,1911,1919],{"className":1889,"style":1890},[642],"height:1.427em;",[363,1892,1893,1896],{"style":805},[363,1894],{"className":1895,"style":809},[650],[363,1897,1899,1902,1905,1908],{"className":1898},[407],[363,1900,1291],{"className":1901,"style":1328},[407,408],[363,1903,461],{"className":1904},[494],[363,1906,1121],{"className":1907},[407,408],[363,1909,468],{"className":1910},[501],[363,1912,1913,1916],{"style":821},[363,1914],{"className":1915,"style":809},[650],[363,1917],{"className":1918,"style":829},[828],[363,1920,1921,1924],{"style":832},[363,1922],{"className":1923,"style":809},[650],[363,1925,1927,1930,1933,1936],{"className":1926},[407],[363,1928,11],{"className":1929},[407,408],[363,1931,461],{"className":1932},[494],[363,1934,1121],{"className":1935},[407,408],[363,1937,468],{"className":1938},[501],[363,1940,666],{"className":1941},[665],[363,1943,1945],{"className":1944},[638],[363,1946,1949],{"className":1947,"style":1948},[642],"height:0.936em;",[363,1950],{},[363,1952],{"className":1953},[501,789],[363,1955,1957],{"className":1956,"style":763},[501,762],[363,1958,468],{"className":1959},[767,657],[363,1961],{"className":1962,"style":754},[505],[363,1964,592],{"className":1965},[407,408],[363,1967,1121],{"className":1968},[407,408],[363,1970,898],{"className":1971},[920],[363,1973,666],{"className":1974},[665],[363,1976,1978],{"className":1977},[638],[363,1979,1981],{"className":1980,"style":1792},[642],[363,1982],{},[11,1984,1985,1986,2014],{},"更一般地写成关于 ",[363,1987,1989,2002],{"className":1988,"translate":367},[366],[363,1990,1992],{"className":1991},[371],[373,1993,1994],{"xmlns":375},[377,1995,1996,2000],{},[380,1997,1998],{},[383,1999,561],{},[387,2001,561],{"encoding":389},[363,2003,2005],{"className":2004,"ariaHidden":394},[393],[363,2006,2008,2011],{"className":2007},[398],[363,2009],{"className":2010,"style":913},[402],[363,2012,561],{"className":2013},[407,408]," 的期望形式",[363,2016,2018],{"className":2017,"translate":367},[528],[363,2019,2021,2155],{"className":2020,"translate":367},[366],[363,2022,2024],{"className":2023},[371],[373,2025,2026],{"xmlns":375,"display":537},[377,2027,2028,2152],{},[1590,2029,2030,2102],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,2031,2032,2054],{},[1599,2033,2034],{},[1602,2035,2036],{"scriptlevel":474,"displaystyle":394},[380,2037,2038,2044,2046,2048,2050,2052],{},[543,2039,2040,2042],{},[383,2041,547],{},[383,2043,385],{},[458,2045,461],{"stretchy":460},[383,2047,554],{},[383,2049,558],{"mathvariant":557},[383,2051,561],{},[458,2053,468],{"stretchy":460},[1599,2055,2056],{},[1602,2057,2058],{"scriptlevel":474,"displaystyle":394},[380,2059,2060,2062,2064,2070,2072],{},[380,2061],{},[458,2063,471],{},[543,2065,2066,2068],{},[383,2067,571],{"mathvariant":570},[383,2069,561],{},[1644,2071,1651],{},[380,2073,2074,2076,2078,2080,2100],{},[458,2075,578],{"fence":394},[383,2077,385],{},[1644,2079,1651],{},[380,2081,2082,2084,2098],{},[458,2083,461],{"fence":394},[586,2085,2086,2092],{},[380,2087,2088,2090],{},[383,2089,592],{},[383,2091,554],{},[380,2093,2094,2096],{},[383,2095,592],{},[383,2097,561],{},[458,2099,468],{"fence":394},[458,2101,605],{"fence":394},[1596,2103,2104,2110],{},[1599,2105,2106],{},[1602,2107,2108],{"scriptlevel":474,"displaystyle":394},[380,2109],{},[1599,2111,2112],{},[1602,2113,2114],{"scriptlevel":474,"displaystyle":394},[380,2115,2116,2118,2120,2122,2124,2126,2146,2148,2150],{},[380,2117],{},[458,2119,471],{},[458,2121,1634],{},[383,2123,385],{},[1644,2125,1651],{},[380,2127,2128,2130,2144],{},[458,2129,461],{"fence":394},[586,2131,2132,2138],{},[380,2133,2134,2136],{},[383,2135,592],{},[383,2137,554],{},[380,2139,2140,2142],{},[383,2141,592],{},[383,2143,561],{},[458,2145,468],{"fence":394},[383,2147,592],{},[383,2149,561],{},[458,2151,898],{"separator":394},[387,2153,2154],{"encoding":389},"\\begin{aligned}\nD_f(P\\|Q)\n&=\\mathbb E_Q\\!\\left[\nf\\!\\left(\\frac{dP}{dQ}\\right)\\right]\\\\\n&=\\int f\\!\\left(\\frac{dP}{dQ}\\right)dQ,\n\\end{aligned}",[363,2156,2158],{"className":2157,"ariaHidden":394},[393],[363,2159,2161,2165],{"className":2160},[398],[363,2162],{"className":2163,"style":2164},[402],"height:5.1001em;vertical-align:-2.3em;",[363,2166,2168],{"className":2167},[407],[363,2169,2171,2269],{"className":2170},[1590],[363,2172,2174],{"className":2173},[1707],[363,2175,2177,2260],{"className":2176},[633,634],[363,2178,2180,2257],{"className":2179},[638],[363,2181,2184,2248],{"className":2182,"style":2183},[642],"height:2.8em;",[363,2185,2187,2190],{"style":2186},"top:-4.8em;",[363,2188],{"className":2189,"style":1724},[650],[363,2191,2193,2233,2236,2239,2242,2245],{"className":2192},[407],[363,2194,2196,2199],{"className":2195},[407],[363,2197,547],{"className":2198,"style":625},[407,408],[363,2200,2202],{"className":2201},[629],[363,2203,2205,2225],{"className":2204},[633,634],[363,2206,2208,2222],{"className":2207},[638],[363,2209,2211],{"className":2210,"style":643},[642],[363,2212,2213,2216],{"style":646},[363,2214],{"className":2215,"style":651},[650],[363,2217,2219],{"className":2218},[655,656,657,658],[363,2220,385],{"className":2221,"style":409},[407,408,658],[363,2223,666],{"className":2224},[665],[363,2226,2228],{"className":2227},[638],[363,2229,2231],{"className":2230,"style":673},[642],[363,2232],{},[363,2234,461],{"className":2235},[494],[363,2237,554],{"className":2238,"style":682},[407,408],[363,2240,558],{"className":2241},[407],[363,2243,561],{"className":2244},[407,408],[363,2246,468],{"className":2247},[501],[363,2249,2251,2254],{"style":2250},"top:-2.1em;",[363,2252],{"className":2253,"style":1724},[650],[363,2255],{"className":2256},[407],[363,2258,666],{"className":2259},[665],[363,2261,2263],{"className":2262},[638],[363,2264,2267],{"className":2265,"style":2266},[642],"height:2.3em;",[363,2268],{},[363,2270,2272],{"className":2271},[1798],[363,2273,2275,2587],{"className":2274},[633,634],[363,2276,2278,2584],{"className":2277},[638],[363,2279,2281,2454],{"className":2280,"style":2183},[642],[363,2282,2283,2286],{"style":2186},[363,2284],{"className":2285,"style":1724},[650],[363,2287,2289,2292,2295,2298,2301,2341,2344,2347],{"className":2288},[407],[363,2290],{"className":2291},[407],[363,2293],{"className":2294,"style":506},[505],[363,2296,471],{"className":2297},[510],[363,2299],{"className":2300,"style":506},[505],[363,2302,2304,2307],{"className":2303},[407],[363,2305,571],{"className":2306},[407,714],[363,2308,2310],{"className":2309},[629],[363,2311,2313,2333],{"className":2312},[633,634],[363,2314,2316,2330],{"className":2315},[638],[363,2317,2319],{"className":2318,"style":727},[642],[363,2320,2321,2324],{"style":730},[363,2322],{"className":2323,"style":651},[650],[363,2325,2327],{"className":2326},[655,656,657,658],[363,2328,561],{"className":2329},[407,408,658],[363,2331,666],{"className":2332},[665],[363,2334,2336],{"className":2335},[638],[363,2337,2339],{"className":2338,"style":673},[642],[363,2340],{},[363,2342],{"className":2343,"style":1859},[505],[363,2345],{"className":2346,"style":754},[505],[363,2348,2350,2356,2359,2362,2365,2448],{"className":2349},[758],[363,2351,2353],{"className":2352,"style":763},[494,762],[363,2354,578],{"className":2355},[767,657],[363,2357,385],{"className":2358,"style":409},[407,408],[363,2360],{"className":2361,"style":1859},[505],[363,2363],{"className":2364,"style":754},[505],[363,2366,2368,2374,2442],{"className":2367},[758],[363,2369,2371],{"className":2370,"style":763},[494,762],[363,2372,461],{"className":2373},[767,657],[363,2375,2377,2380,2439],{"className":2376},[407],[363,2378],{"className":2379},[494,789],[363,2381,2383],{"className":2382},[586],[363,2384,2386,2431],{"className":2385},[633,634],[363,2387,2389,2428],{"className":2388},[638],[363,2390,2392,2406,2414],{"className":2391,"style":802},[642],[363,2393,2394,2397],{"style":805},[363,2395],{"className":2396,"style":809},[650],[363,2398,2400,2403],{"className":2399},[407],[363,2401,592],{"className":2402},[407,408],[363,2404,561],{"className":2405},[407,408],[363,2407,2408,2411],{"style":821},[363,2409],{"className":2410,"style":809},[650],[363,2412],{"className":2413,"style":829},[828],[363,2415,2416,2419],{"style":832},[363,2417],{"className":2418,"style":809},[650],[363,2420,2422,2425],{"className":2421},[407],[363,2423,592],{"className":2424},[407,408],[363,2426,554],{"className":2427,"style":682},[407,408],[363,2429,666],{"className":2430},[665],[363,2432,2434],{"className":2433},[638],[363,2435,2437],{"className":2436,"style":854},[642],[363,2438],{},[363,2440],{"className":2441},[501,789],[363,2443,2445],{"className":2444,"style":763},[501,762],[363,2446,468],{"className":2447},[767,657],[363,2449,2451],{"className":2450,"style":763},[501,762],[363,2452,605],{"className":2453},[767,657],[363,2455,2456,2459],{"style":2250},[363,2457],{"className":2458,"style":1724},[650],[363,2460,2462,2465,2468,2471,2474,2477,2480,2483,2486,2489,2572,2575,2578,2581],{"className":2461},[407],[363,2463],{"className":2464},[407],[363,2466],{"className":2467,"style":506},[505],[363,2469,471],{"className":2470},[510],[363,2472],{"className":2473,"style":506},[505],[363,2475,1634],{"className":2476,"style":1834},[1831,1832,1833],[363,2478],{"className":2479,"style":754},[505],[363,2481,385],{"className":2482,"style":409},[407,408],[363,2484],{"className":2485,"style":1859},[505],[363,2487],{"className":2488,"style":754},[505],[363,2490,2492,2498,2566],{"className":2491},[758],[363,2493,2495],{"className":2494,"style":763},[494,762],[363,2496,461],{"className":2497},[767,657],[363,2499,2501,2504,2563],{"className":2500},[407],[363,2502],{"className":2503},[494,789],[363,2505,2507],{"className":2506},[586],[363,2508,2510,2555],{"className":2509},[633,634],[363,2511,2513,2552],{"className":2512},[638],[363,2514,2516,2530,2538],{"className":2515,"style":802},[642],[363,2517,2518,2521],{"style":805},[363,2519],{"className":2520,"style":809},[650],[363,2522,2524,2527],{"className":2523},[407],[363,2525,592],{"className":2526},[407,408],[363,2528,561],{"className":2529},[407,408],[363,2531,2532,2535],{"style":821},[363,2533],{"className":2534,"style":809},[650],[363,2536],{"className":2537,"style":829},[828],[363,2539,2540,2543],{"style":832},[363,2541],{"className":2542,"style":809},[650],[363,2544,2546,2549],{"className":2545},[407],[363,2547,592],{"className":2548},[407,408],[363,2550,554],{"className":2551,"style":682},[407,408],[363,2553,666],{"className":2554},[665],[363,2556,2558],{"className":2557},[638],[363,2559,2561],{"className":2560,"style":854},[642],[363,2562],{},[363,2564],{"className":2565},[501,789],[363,2567,2569],{"className":2568,"style":763},[501,762],[363,2570,468],{"className":2571},[767,657],[363,2573],{"className":2574,"style":754},[505],[363,2576,592],{"className":2577},[407,408],[363,2579,561],{"className":2580},[407,408],[363,2582,898],{"className":2583},[920],[363,2585,666],{"className":2586},[665],[363,2588,2590],{"className":2589},[638],[363,2591,2593],{"className":2592,"style":2266},[642],[363,2594],{},[11,2596,2597,2598,2627,2628,2656],{},"其中 ",[363,2599,2601,2614],{"className":2600,"translate":367},[366],[363,2602,2604],{"className":2603},[371],[373,2605,2606],{"xmlns":375},[377,2607,2608,2612],{},[380,2609,2610],{},[383,2611,1291],{},[387,2613,1291],{"encoding":389},[363,2615,2617],{"className":2616,"ariaHidden":394},[393],[363,2618,2620,2624],{"className":2619},[398],[363,2621],{"className":2622,"style":2623},[402],"height:0.625em;vertical-align:-0.1944em;",[363,2625,1291],{"className":2626,"style":1328},[407,408]," 是 ",[363,2629,2631,2644],{"className":2630,"translate":367},[366],[363,2632,2634],{"className":2633},[371],[373,2635,2636],{"xmlns":375},[377,2637,2638,2642],{},[380,2639,2640],{},[383,2641,561],{},[387,2643,561],{"encoding":389},[363,2645,2647],{"className":2646,"ariaHidden":394},[393],[363,2648,2650,2653],{"className":2649},[398],[363,2651],{"className":2652,"style":913},[402],[363,2654,561],{"className":2655},[407,408]," 的密度。",[2658,2659,2661],"h3",{"id":2660},"_11-不依赖参考测度","1.1 不依赖参考测度",[11,2663,2664,2665,2696,2697,2727,2728,2756,2757,2785,2786,2954,2955,3092,3093,3230,3231,3295,3296,3501],{},"上面的定义里出现了「密度」，这会让读者误以为它依赖 Lebesgue 测度。其实 f-散度只依赖两个分布本身。取任一 ",[363,2666,2668,2683],{"className":2667,"translate":367},[366],[363,2669,2671],{"className":2670},[371],[373,2672,2673],{"xmlns":375},[377,2674,2675,2680],{},[380,2676,2677],{},[383,2678,2679],{},"σ",[387,2681,2682],{"encoding":389},"\\sigma",[363,2684,2686],{"className":2685,"ariaHidden":394},[393],[363,2687,2689,2693],{"className":2688},[398],[363,2690],{"className":2691,"style":2692},[402],"height:0.4306em;",[363,2694,2679],{"className":2695,"style":1328},[407,408],"-有限测度 ",[363,2698,2700,2715],{"className":2699,"translate":367},[366],[363,2701,2703],{"className":2702},[371],[373,2704,2705],{"xmlns":375},[377,2706,2707,2712],{},[380,2708,2709],{},[383,2710,2711],{},"μ",[387,2713,2714],{"encoding":389},"\\mu",[363,2716,2718],{"className":2717,"ariaHidden":394},[393],[363,2719,2721,2724],{"className":2720},[398],[363,2722],{"className":2723,"style":2623},[402],[363,2725,2711],{"className":2726},[407,408]," 同时控制 ",[363,2729,2731,2744],{"className":2730,"translate":367},[366],[363,2732,2734],{"className":2733},[371],[373,2735,2736],{"xmlns":375},[377,2737,2738,2742],{},[380,2739,2740],{},[383,2741,554],{},[387,2743,554],{"encoding":389},[363,2745,2747],{"className":2746,"ariaHidden":394},[393],[363,2748,2750,2753],{"className":2749},[398],[363,2751],{"className":2752,"style":1011},[402],[363,2754,554],{"className":2755,"style":682},[407,408]," 与 ",[363,2758,2760,2773],{"className":2759,"translate":367},[366],[363,2761,2763],{"className":2762},[371],[373,2764,2765],{"xmlns":375},[377,2766,2767,2771],{},[380,2768,2769],{},[383,2770,561],{},[387,2772,561],{"encoding":389},[363,2774,2776],{"className":2775,"ariaHidden":394},[393],[363,2777,2779,2782],{"className":2778},[398],[363,2780],{"className":2781,"style":913},[402],[363,2783,561],{"className":2784},[407,408],"（例如 ",[363,2787,2789,2825],{"className":2788,"translate":367},[366],[363,2790,2792],{"className":2791},[371],[373,2793,2794],{"xmlns":375},[377,2795,2796,2822],{},[380,2797,2798,2800,2802,2811,2813,2815,2818,2820],{},[383,2799,2711],{},[458,2801,471],{},[1602,2803,2804],{"scriptlevel":474,"displaystyle":460},[586,2805,2806,2808],{},[463,2807,465],{},[463,2809,2810],{},"2",[458,2812,461],{"stretchy":460},[383,2814,554],{},[458,2816,2817],{},"+",[383,2819,561],{},[458,2821,468],{"stretchy":460},[387,2823,2824],{"encoding":389},"\\mu=\\tfrac12(P+Q)",[363,2826,2828,2846,2942],{"className":2827,"ariaHidden":394},[393],[363,2829,2831,2834,2837,2840,2843],{"className":2830},[398],[363,2832],{"className":2833,"style":2623},[402],[363,2835,2711],{"className":2836},[407,408],[363,2838],{"className":2839,"style":506},[505],[363,2841,471],{"className":2842},[510],[363,2844],{"className":2845,"style":506},[505],[363,2847,2849,2853,2925,2928,2931,2935,2939],{"className":2848},[398],[363,2850],{"className":2851,"style":2852},[402],"height:1.1901em;vertical-align:-0.345em;",[363,2854,2856,2859,2922],{"className":2855},[407],[363,2857],{"className":2858},[494,789],[363,2860,2862],{"className":2861},[586],[363,2863,2865,2913],{"className":2864},[633,634],[363,2866,2868,2910],{"className":2867},[638],[363,2869,2872,2887,2895],{"className":2870,"style":2871},[642],"height:0.8451em;",[363,2873,2875,2878],{"style":2874},"top:-2.655em;",[363,2876],{"className":2877,"style":809},[650],[363,2879,2881],{"className":2880},[655,656,657,658],[363,2882,2884],{"className":2883},[407,658],[363,2885,2810],{"className":2886},[407,658],[363,2888,2889,2892],{"style":821},[363,2890],{"className":2891,"style":809},[650],[363,2893],{"className":2894,"style":829},[828],[363,2896,2898,2901],{"style":2897},"top:-3.394em;",[363,2899],{"className":2900,"style":809},[650],[363,2902,2904],{"className":2903},[655,656,657,658],[363,2905,2907],{"className":2906},[407,658],[363,2908,465],{"className":2909},[407,658],[363,2911,666],{"className":2912},[665],[363,2914,2916],{"className":2915},[638],[363,2917,2920],{"className":2918,"style":2919},[642],"height:0.345em;",[363,2921],{},[363,2923],{"className":2924},[501,789],[363,2926,461],{"className":2927},[494],[363,2929,554],{"className":2930,"style":682},[407,408],[363,2932],{"className":2933,"style":2934},[505],"margin-right:0.2222em;",[363,2936,2817],{"className":2937},[2938],"mbin",[363,2940],{"className":2941,"style":2934},[505],[363,2943,2945,2948,2951],{"className":2944},[398],[363,2946],{"className":2947,"style":487},[402],[363,2949,561],{"className":2950},[407,408],[363,2952,468],{"className":2953},[501],"），令 ",[363,2956,2958,2988],{"className":2957,"translate":367},[366],[363,2959,2961],{"className":2960},[371],[373,2962,2963],{"xmlns":375},[377,2964,2965,2985],{},[380,2966,2967,2969,2971],{},[383,2968,11],{},[458,2970,471],{},[586,2972,2973,2979],{},[380,2974,2975,2977],{},[383,2976,592],{},[383,2978,554],{},[380,2980,2981,2983],{},[383,2982,592],{},[383,2984,2711],{},[387,2986,2987],{"encoding":389},"p=\\frac{dP}{d\\mu}",[363,2989,2991,3009],{"className":2990,"ariaHidden":394},[393],[363,2992,2994,2997,3000,3003,3006],{"className":2993},[398],[363,2995],{"className":2996,"style":2623},[402],[363,2998,11],{"className":2999},[407,408],[363,3001],{"className":3002,"style":506},[505],[363,3004,471],{"className":3005},[510],[363,3007],{"className":3008,"style":506},[505],[363,3010,3012,3016],{"className":3011},[398],[363,3013],{"className":3014,"style":3015},[402],"height:1.3612em;vertical-align:-0.4811em;",[363,3017,3019,3022,3089],{"className":3018},[407],[363,3020],{"className":3021},[494,789],[363,3023,3025],{"className":3024},[586],[363,3026,3028,3080],{"className":3027},[633,634],[363,3029,3031,3077],{"className":3030},[638],[363,3032,3035,3052,3060],{"className":3033,"style":3034},[642],"height:0.8801em;",[363,3036,3037,3040],{"style":2874},[363,3038],{"className":3039,"style":809},[650],[363,3041,3043],{"className":3042},[655,656,657,658],[363,3044,3046,3049],{"className":3045},[407,658],[363,3047,592],{"className":3048},[407,408,658],[363,3050,2711],{"className":3051},[407,408,658],[363,3053,3054,3057],{"style":821},[363,3055],{"className":3056,"style":809},[650],[363,3058],{"className":3059,"style":829},[828],[363,3061,3062,3065],{"style":2897},[363,3063],{"className":3064,"style":809},[650],[363,3066,3068],{"className":3067},[655,656,657,658],[363,3069,3071,3074],{"className":3070},[407,658],[363,3072,592],{"className":3073},[407,408,658],[363,3075,554],{"className":3076,"style":682},[407,408,658],[363,3078,666],{"className":3079},[665],[363,3081,3083],{"className":3082},[638],[363,3084,3087],{"className":3085,"style":3086},[642],"height:0.4811em;",[363,3088],{},[363,3090],{"className":3091},[501,789],"，",[363,3094,3096,3126],{"className":3095,"translate":367},[366],[363,3097,3099],{"className":3098},[371],[373,3100,3101],{"xmlns":375},[377,3102,3103,3123],{},[380,3104,3105,3107,3109],{},[383,3106,1291],{},[458,3108,471],{},[586,3110,3111,3117],{},[380,3112,3113,3115],{},[383,3114,592],{},[383,3116,561],{},[380,3118,3119,3121],{},[383,3120,592],{},[383,3122,2711],{},[387,3124,3125],{"encoding":389},"q=\\frac{dQ}{d\\mu}",[363,3127,3129,3147],{"className":3128,"ariaHidden":394},[393],[363,3130,3132,3135,3138,3141,3144],{"className":3131},[398],[363,3133],{"className":3134,"style":2623},[402],[363,3136,1291],{"className":3137,"style":1328},[407,408],[363,3139],{"className":3140,"style":506},[505],[363,3142,471],{"className":3143},[510],[363,3145],{"className":3146,"style":506},[505],[363,3148,3150,3154],{"className":3149},[398],[363,3151],{"className":3152,"style":3153},[402],"height:1.4133em;vertical-align:-0.4811em;",[363,3155,3157,3160,3227],{"className":3156},[407],[363,3158],{"className":3159},[494,789],[363,3161,3163],{"className":3162},[586],[363,3164,3166,3219],{"className":3165},[633,634],[363,3167,3169,3216],{"className":3168},[638],[363,3170,3173,3190,3198],{"className":3171,"style":3172},[642],"height:0.9322em;",[363,3174,3175,3178],{"style":2874},[363,3176],{"className":3177,"style":809},[650],[363,3179,3181],{"className":3180},[655,656,657,658],[363,3182,3184,3187],{"className":3183},[407,658],[363,3185,592],{"className":3186},[407,408,658],[363,3188,2711],{"className":3189},[407,408,658],[363,3191,3192,3195],{"style":821},[363,3193],{"className":3194,"style":809},[650],[363,3196],{"className":3197,"style":829},[828],[363,3199,3201,3204],{"style":3200},"top:-3.4461em;",[363,3202],{"className":3203,"style":809},[650],[363,3205,3207],{"className":3206},[655,656,657,658],[363,3208,3210,3213],{"className":3209},[407,658],[363,3211,592],{"className":3212},[407,408,658],[363,3214,561],{"className":3215},[407,408,658],[363,3217,666],{"className":3218},[665],[363,3220,3222],{"className":3221},[638],[363,3223,3225],{"className":3224,"style":3086},[642],[363,3226],{},[363,3228],{"className":3229},[501,789],"。在集合 ",[363,3232,3234,3259],{"className":3233,"translate":367},[366],[363,3235,3237],{"className":3236},[371],[373,3238,3239],{"xmlns":375},[377,3240,3241,3256],{},[380,3242,3243,3246,3248,3251,3253],{},[458,3244,3245],{"stretchy":460},"{",[383,3247,1291],{},[458,3249,3250],{},">",[463,3252,474],{},[458,3254,3255],{"stretchy":460},"}",[387,3257,3258],{"encoding":389},"\\{q>0\\}",[363,3260,3262,3283],{"className":3261,"ariaHidden":394},[393],[363,3263,3265,3268,3271,3274,3277,3280],{"className":3264},[398],[363,3266],{"className":3267,"style":487},[402],[363,3269,3245],{"className":3270},[494],[363,3272,1291],{"className":3273,"style":1328},[407,408],[363,3275],{"className":3276,"style":506},[505],[363,3278,3250],{"className":3279},[510],[363,3281],{"className":3282,"style":506},[505],[363,3284,3286,3289,3292],{"className":3285},[398],[363,3287],{"className":3288,"style":487},[402],[363,3290,474],{"className":3291},[407],[363,3293,3255],{"className":3294},[501]," 上有 ",[363,3297,3299,3333],{"className":3298,"translate":367},[366],[363,3300,3302],{"className":3301},[371],[373,3303,3304],{"xmlns":375},[377,3305,3306,3330],{},[380,3307,3308,3322,3324],{},[586,3309,3310,3316],{},[380,3311,3312,3314],{},[383,3313,592],{},[383,3315,554],{},[380,3317,3318,3320],{},[383,3319,592],{},[383,3321,561],{},[458,3323,471],{},[586,3325,3326,3328],{},[383,3327,11],{},[383,3329,1291],{},[387,3331,3332],{"encoding":389},"\\frac{dP}{dQ}=\\frac{p}{q}",[363,3334,3336,3425],{"className":3335,"ariaHidden":394},[393],[363,3337,3339,3342,3416,3419,3422],{"className":3338},[398],[363,3340],{"className":3341,"style":3015},[402],[363,3343,3345,3348,3413],{"className":3344},[407],[363,3346],{"className":3347},[494,789],[363,3349,3351],{"className":3350},[586],[363,3352,3354,3405],{"className":3353},[633,634],[363,3355,3357,3402],{"className":3356},[638],[363,3358,3360,3377,3385],{"className":3359,"style":3034},[642],[363,3361,3362,3365],{"style":2874},[363,3363],{"className":3364,"style":809},[650],[363,3366,3368],{"className":3367},[655,656,657,658],[363,3369,3371,3374],{"className":3370},[407,658],[363,3372,592],{"className":3373},[407,408,658],[363,3375,561],{"className":3376},[407,408,658],[363,3378,3379,3382],{"style":821},[363,3380],{"className":3381,"style":809},[650],[363,3383],{"className":3384,"style":829},[828],[363,3386,3387,3390],{"style":2897},[363,3388],{"className":3389,"style":809},[650],[363,3391,3393],{"className":3392},[655,656,657,658],[363,3394,3396,3399],{"className":3395},[407,658],[363,3397,592],{"className":3398},[407,408,658],[363,3400,554],{"className":3401,"style":682},[407,408,658],[363,3403,666],{"className":3404},[665],[363,3406,3408],{"className":3407},[638],[363,3409,3411],{"className":3410,"style":3086},[642],[363,3412],{},[363,3414],{"className":3415},[501,789],[363,3417],{"className":3418,"style":506},[505],[363,3420,471],{"className":3421},[510],[363,3423],{"className":3424,"style":506},[505],[363,3426,3428,3432],{"className":3427},[398],[363,3429],{"className":3430,"style":3431},[402],"height:1.2286em;vertical-align:-0.4811em;",[363,3433,3435,3438,3498],{"className":3434},[407],[363,3436],{"className":3437},[494,789],[363,3439,3441],{"className":3440},[586],[363,3442,3444,3490],{"className":3443},[633,634],[363,3445,3447,3487],{"className":3446},[638],[363,3448,3451,3465,3473],{"className":3449,"style":3450},[642],"height:0.7475em;",[363,3452,3453,3456],{"style":2874},[363,3454],{"className":3455,"style":809},[650],[363,3457,3459],{"className":3458},[655,656,657,658],[363,3460,3462],{"className":3461},[407,658],[363,3463,1291],{"className":3464,"style":1328},[407,408,658],[363,3466,3467,3470],{"style":821},[363,3468],{"className":3469,"style":809},[650],[363,3471],{"className":3472,"style":829},[828],[363,3474,3475,3478],{"style":3200},[363,3476],{"className":3477,"style":809},[650],[363,3479,3481],{"className":3480},[655,656,657,658],[363,3482,3484],{"className":3483},[407,658],[363,3485,11],{"className":3486},[407,408,658],[363,3488,666],{"className":3489},[665],[363,3491,3493],{"className":3492},[638],[363,3494,3496],{"className":3495,"style":3086},[642],[363,3497],{},[363,3499],{"className":3500},[501,789],"，于是",[363,3503,3505],{"className":3504,"translate":367},[528],[363,3506,3508,3658],{"className":3507,"translate":367},[366],[363,3509,3511],{"className":3510},[371],[373,3512,3513],{"xmlns":375,"display":537},[377,3514,3515,3655],{},[1590,3516,3517,3591],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,3518,3519,3541],{},[1599,3520,3521],{},[1602,3522,3523],{"scriptlevel":474,"displaystyle":394},[380,3524,3525,3531,3533,3535,3537,3539],{},[543,3526,3527,3529],{},[383,3528,547],{},[383,3530,385],{},[458,3532,461],{"stretchy":460},[383,3534,554],{},[383,3536,558],{"mathvariant":557},[383,3538,561],{},[458,3540,468],{"stretchy":460},[1599,3542,3543],{},[1602,3544,3545],{"scriptlevel":474,"displaystyle":394},[380,3546,3547,3549,3551,3567,3569,3571,3583,3585,3587,3589],{},[380,3548],{},[458,3550,471],{},[543,3552,3553,3555],{},[458,3554,1634],{},[380,3556,3557,3559,3561,3563,3565],{},[458,3558,3245],{"stretchy":460},[383,3560,1291],{},[458,3562,3250],{},[463,3564,474],{},[458,3566,3255],{"stretchy":460},[383,3568,385],{},[1644,3570,1651],{},[380,3572,3573,3575,3581],{},[458,3574,461],{"fence":394},[586,3576,3577,3579],{},[383,3578,11],{},[383,3580,1291],{},[458,3582,468],{"fence":394},[383,3584,1291],{},[1644,3586,1646],{},[383,3588,592],{},[383,3590,2711],{},[1596,3592,3593,3599],{},[1599,3594,3595],{},[1602,3596,3597],{"scriptlevel":474,"displaystyle":394},[380,3598],{},[1599,3600,3601],{},[1602,3602,3603],{"scriptlevel":474,"displaystyle":394},[380,3604,3605,3607,3610,3612,3628,3630,3632,3644,3647,3649,3651,3653],{},[380,3606],{},[505,3608],{"width":3609},"2em",[458,3611,2817],{},[543,3613,3614,3616],{},[458,3615,1634],{},[380,3617,3618,3620,3622,3624,3626],{},[458,3619,3245],{"stretchy":460},[383,3621,1291],{},[458,3623,471],{},[463,3625,474],{},[458,3627,3255],{"stretchy":460},[383,3629,385],{},[1644,3631,1651],{},[380,3633,3634,3636,3642],{},[458,3635,461],{"fence":394},[586,3637,3638,3640],{},[383,3639,11],{},[463,3641,474],{},[458,3643,468],{"fence":394},[458,3645,3646],{},"⋅",[463,3648,474],{},[1644,3650,1646],{},[383,3652,592],{},[383,3654,2711],{},[387,3656,3657],{"encoding":389},"\\begin{aligned}\nD_f(P\\|Q)\n&=\\int_{\\{q>0\\}}\nf\\!\\left(\\frac{p}{q}\\right)q\\,d\\mu\\\\\n&\\qquad+\\int_{\\{q=0\\}}\nf\\!\\left(\\frac{p}{0}\\right)\\cdot 0\\,d\\mu\n\\end{aligned}",[363,3659,3661],{"className":3660,"ariaHidden":394},[393],[363,3662,3664,3668],{"className":3663},[398],[363,3665],{"className":3666,"style":3667},[402],"height:5.2839em;vertical-align:-2.392em;",[363,3669,3671],{"className":3670},[407],[363,3672,3674,3772],{"className":3673},[1590],[363,3675,3677],{"className":3676},[1707],[363,3678,3680,3763],{"className":3679},[633,634],[363,3681,3683,3760],{"className":3682},[638],[363,3684,3687,3751],{"className":3685,"style":3686},[642],"height:2.892em;",[363,3688,3690,3693],{"style":3689},"top:-4.892em;",[363,3691],{"className":3692,"style":1724},[650],[363,3694,3696,3736,3739,3742,3745,3748],{"className":3695},[407],[363,3697,3699,3702],{"className":3698},[407],[363,3700,547],{"className":3701,"style":625},[407,408],[363,3703,3705],{"className":3704},[629],[363,3706,3708,3728],{"className":3707},[633,634],[363,3709,3711,3725],{"className":3710},[638],[363,3712,3714],{"className":3713,"style":643},[642],[363,3715,3716,3719],{"style":646},[363,3717],{"className":3718,"style":651},[650],[363,3720,3722],{"className":3721},[655,656,657,658],[363,3723,385],{"className":3724,"style":409},[407,408,658],[363,3726,666],{"className":3727},[665],[363,3729,3731],{"className":3730},[638],[363,3732,3734],{"className":3733,"style":673},[642],[363,3735],{},[363,3737,461],{"className":3738},[494],[363,3740,554],{"className":3741,"style":682},[407,408],[363,3743,558],{"className":3744},[407],[363,3746,561],{"className":3747},[407,408],[363,3749,468],{"className":3750},[501],[363,3752,3754,3757],{"style":3753},"top:-2.145em;",[363,3755],{"className":3756,"style":1724},[650],[363,3758],{"className":3759},[407],[363,3761,666],{"className":3762},[665],[363,3764,3766],{"className":3765},[638],[363,3767,3770],{"className":3768,"style":3769},[642],"height:2.392em;",[363,3771],{},[363,3773,3775],{"className":3774},[1798],[363,3776,3778,4161],{"className":3777},[633,634],[363,3779,3781,4158],{"className":3780},[638],[363,3782,3784,3967],{"className":3783,"style":3686},[642],[363,3785,3786,3789],{"style":3689},[363,3787],{"className":3788,"style":1724},[650],[363,3790,3792,3795,3798,3801,3804,3862,3865,3868,3871,3874,3952,3955,3958,3961,3964],{"className":3791},[407],[363,3793],{"className":3794},[407],[363,3796],{"className":3797,"style":506},[505],[363,3799,471],{"className":3800},[510],[363,3802],{"className":3803,"style":506},[505],[363,3805,3807,3810],{"className":3806},[1831],[363,3808,1634],{"className":3809,"style":1834},[1831,1832,1833],[363,3811,3813],{"className":3812},[629],[363,3814,3816,3853],{"className":3815},[633,634],[363,3817,3819,3850],{"className":3818},[638],[363,3820,3823],{"className":3821,"style":3822},[642],"height:-0.3869em;",[363,3824,3826,3829],{"style":3825},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[363,3827],{"className":3828,"style":651},[650],[363,3830,3832],{"className":3831},[655,656,657,658],[363,3833,3835,3838,3841,3844,3847],{"className":3834},[407,658],[363,3836,3245],{"className":3837},[494,658],[363,3839,1291],{"className":3840,"style":1328},[407,408,658],[363,3842,3250],{"className":3843},[510,658],[363,3845,474],{"className":3846},[407,658],[363,3848,3255],{"className":3849},[501,658],[363,3851,666],{"className":3852},[665],[363,3854,3856],{"className":3855},[638],[363,3857,3860],{"className":3858,"style":3859},[642],"height:1.0869em;",[363,3861],{},[363,3863],{"className":3864,"style":754},[505],[363,3866,385],{"className":3867,"style":409},[407,408],[363,3869],{"className":3870,"style":1859},[505],[363,3872],{"className":3873,"style":754},[505],[363,3875,3877,3883,3946],{"className":3876},[758],[363,3878,3880],{"className":3879,"style":763},[494,762],[363,3881,461],{"className":3882},[767,657],[363,3884,3886,3889,3943],{"className":3885},[407],[363,3887],{"className":3888},[494,789],[363,3890,3892],{"className":3891},[586],[363,3893,3895,3935],{"className":3894},[633,634],[363,3896,3898,3932],{"className":3897},[638],[363,3899,3902,3913,3921],{"className":3900,"style":3901},[642],"height:1.1076em;",[363,3903,3904,3907],{"style":805},[363,3905],{"className":3906,"style":809},[650],[363,3908,3910],{"className":3909},[407],[363,3911,1291],{"className":3912,"style":1328},[407,408],[363,3914,3915,3918],{"style":821},[363,3916],{"className":3917,"style":809},[650],[363,3919],{"className":3920,"style":829},[828],[363,3922,3923,3926],{"style":832},[363,3924],{"className":3925,"style":809},[650],[363,3927,3929],{"className":3928},[407],[363,3930,11],{"className":3931},[407,408],[363,3933,666],{"className":3934},[665],[363,3936,3938],{"className":3937},[638],[363,3939,3941],{"className":3940,"style":854},[642],[363,3942],{},[363,3944],{"className":3945},[501,789],[363,3947,3949],{"className":3948,"style":763},[501,762],[363,3950,468],{"className":3951},[767,657],[363,3953],{"className":3954,"style":754},[505],[363,3956,1291],{"className":3957,"style":1328},[407,408],[363,3959],{"className":3960,"style":754},[505],[363,3962,592],{"className":3963},[407,408],[363,3965,2711],{"className":3966},[407,408],[363,3968,3969,3972],{"style":3753},[363,3970],{"className":3971,"style":1724},[650],[363,3973,3975,3978,3982,3985,3988,3991,4046,4049,4052,4055,4058,4137,4140,4143,4146,4149,4152,4155],{"className":3974},[407],[363,3976],{"className":3977},[407],[363,3979],{"className":3980,"style":3981},[505],"margin-right:2em;",[363,3983],{"className":3984,"style":2934},[505],[363,3986,2817],{"className":3987},[2938],[363,3989],{"className":3990,"style":2934},[505],[363,3992,3994,3997],{"className":3993},[1831],[363,3995,1634],{"className":3996,"style":1834},[1831,1832,1833],[363,3998,4000],{"className":3999},[629],[363,4001,4003,4038],{"className":4002},[633,634],[363,4004,4006,4035],{"className":4005},[638],[363,4007,4009],{"className":4008,"style":3822},[642],[363,4010,4011,4014],{"style":3825},[363,4012],{"className":4013,"style":651},[650],[363,4015,4017],{"className":4016},[655,656,657,658],[363,4018,4020,4023,4026,4029,4032],{"className":4019},[407,658],[363,4021,3245],{"className":4022},[494,658],[363,4024,1291],{"className":4025,"style":1328},[407,408,658],[363,4027,471],{"className":4028},[510,658],[363,4030,474],{"className":4031},[407,658],[363,4033,3255],{"className":4034},[501,658],[363,4036,666],{"className":4037},[665],[363,4039,4041],{"className":4040},[638],[363,4042,4044],{"className":4043,"style":3859},[642],[363,4045],{},[363,4047],{"className":4048,"style":754},[505],[363,4050,385],{"className":4051,"style":409},[407,408],[363,4053],{"className":4054,"style":1859},[505],[363,4056],{"className":4057,"style":754},[505],[363,4059,4061,4068,4131],{"className":4060},[758],[363,4062,4064],{"className":4063,"style":763},[494,762],[363,4065,461],{"className":4066},[767,4067],"size2",[363,4069,4071,4074,4128],{"className":4070},[407],[363,4072],{"className":4073},[494,789],[363,4075,4077],{"className":4076},[586],[363,4078,4080,4119],{"className":4079},[633,634],[363,4081,4083,4116],{"className":4082},[638],[363,4084,4086,4097,4105],{"className":4085,"style":3901},[642],[363,4087,4088,4091],{"style":805},[363,4089],{"className":4090,"style":809},[650],[363,4092,4094],{"className":4093},[407],[363,4095,474],{"className":4096},[407],[363,4098,4099,4102],{"style":821},[363,4100],{"className":4101,"style":809},[650],[363,4103],{"className":4104,"style":829},[828],[363,4106,4107,4110],{"style":832},[363,4108],{"className":4109,"style":809},[650],[363,4111,4113],{"className":4112},[407],[363,4114,11],{"className":4115},[407,408],[363,4117,666],{"className":4118},[665],[363,4120,4122],{"className":4121},[638],[363,4123,4126],{"className":4124,"style":4125},[642],"height:0.686em;",[363,4127],{},[363,4129],{"className":4130},[501,789],[363,4132,4134],{"className":4133,"style":763},[501,762],[363,4135,468],{"className":4136},[767,4067],[363,4138],{"className":4139,"style":2934},[505],[363,4141,3646],{"className":4142},[2938],[363,4144],{"className":4145,"style":2934},[505],[363,4147,474],{"className":4148},[407],[363,4150],{"className":4151,"style":754},[505],[363,4153,592],{"className":4154},[407,408],[363,4156,2711],{"className":4157},[407,408],[363,4159,666],{"className":4160},[665],[363,4162,4164],{"className":4163},[638],[363,4165,4167],{"className":4166,"style":3769},[642],[363,4168],{},[11,4170,4171,4172,4200,4201,4230,4231,4319,4320,4348,4349,4420,4421,4512,4513,4200,4541,4569,4570,4605],{},"第二项正是处理「支撑集不重叠」的地方。若 ",[363,4173,4175,4188],{"className":4174,"translate":367},[366],[363,4176,4178],{"className":4177},[371],[373,4179,4180],{"xmlns":375},[377,4181,4182,4186],{},[380,4183,4184],{},[383,4185,385],{},[387,4187,385],{"encoding":389},[363,4189,4191],{"className":4190,"ariaHidden":394},[393],[363,4192,4194,4197],{"className":4193},[398],[363,4195],{"className":4196,"style":403},[402],[363,4198,385],{"className":4199,"style":409},[407,408]," 在 ",[363,4202,4204,4218],{"className":4203,"translate":367},[366],[363,4205,4207],{"className":4206},[371],[373,4208,4209],{"xmlns":375},[377,4210,4211,4215],{},[380,4212,4213],{},[383,4214,1371],{"mathvariant":557},[387,4216,4217],{"encoding":389},"\\infty",[363,4219,4221],{"className":4220,"ariaHidden":394},[393],[363,4222,4224,4227],{"className":4223},[398],[363,4225],{"className":4226,"style":2692},[402],[363,4228,1371],{"className":4229},[407]," 处有界，可约定 ",[363,4232,4234,4262],{"className":4233,"translate":367},[366],[363,4235,4237],{"className":4236},[371],[373,4238,4239],{"xmlns":375},[377,4240,4241,4259],{},[380,4242,4243,4245,4247,4249,4251,4253,4255,4257],{},[463,4244,474],{},[458,4246,3646],{},[383,4248,385],{},[458,4250,461],{"stretchy":460},[383,4252,1371],{"mathvariant":557},[458,4254,468],{"stretchy":460},[458,4256,471],{},[463,4258,474],{},[387,4260,4261],{"encoding":389},"0\\cdot f(\\infty)=0",[363,4263,4265,4283,4310],{"className":4264,"ariaHidden":394},[393],[363,4266,4268,4271,4274,4277,4280],{"className":4267},[398],[363,4269],{"className":4270,"style":520},[402],[363,4272,474],{"className":4273},[407],[363,4275],{"className":4276,"style":2934},[505],[363,4278,3646],{"className":4279},[2938],[363,4281],{"className":4282,"style":2934},[505],[363,4284,4286,4289,4292,4295,4298,4301,4304,4307],{"className":4285},[398],[363,4287],{"className":4288,"style":487},[402],[363,4290,385],{"className":4291,"style":409},[407,408],[363,4293,461],{"className":4294},[494],[363,4296,1371],{"className":4297},[407],[363,4299,468],{"className":4300},[501],[363,4302],{"className":4303,"style":506},[505],[363,4305,471],{"className":4306},[510],[363,4308],{"className":4309,"style":506},[505],[363,4311,4313,4316],{"className":4312},[398],[363,4314],{"className":4315,"style":520},[402],[363,4317,474],{"className":4318},[407],"；若 ",[363,4321,4323,4336],{"className":4322,"translate":367},[366],[363,4324,4326],{"className":4325},[371],[373,4327,4328],{"xmlns":375},[377,4329,4330,4334],{},[380,4331,4332],{},[383,4333,385],{},[387,4335,385],{"encoding":389},[363,4337,4339],{"className":4338,"ariaHidden":394},[393],[363,4340,4342,4345],{"className":4341},[398],[363,4343],{"className":4344,"style":403},[402],[363,4346,385],{"className":4347,"style":409},[407,408]," 无界，则这一项是否发散决定了 ",[363,4350,4352,4370],{"className":4351,"translate":367},[366],[363,4353,4355],{"className":4354},[371],[373,4356,4357],{"xmlns":375},[377,4358,4359,4367],{},[380,4360,4361],{},[543,4362,4363,4365],{},[383,4364,547],{},[383,4366,385],{},[387,4368,4369],{"encoding":389},"D_f",[363,4371,4373],{"className":4372,"ariaHidden":394},[393],[363,4374,4376,4380],{"className":4375},[398],[363,4377],{"className":4378,"style":4379},[402],"height:0.9694em;vertical-align:-0.2861em;",[363,4381,4383,4386],{"className":4382},[407],[363,4384,547],{"className":4385,"style":625},[407,408],[363,4387,4389],{"className":4388},[629],[363,4390,4392,4412],{"className":4391},[633,634],[363,4393,4395,4409],{"className":4394},[638],[363,4396,4398],{"className":4397,"style":643},[642],[363,4399,4400,4403],{"style":646},[363,4401],{"className":4402,"style":651},[650],[363,4404,4406],{"className":4405},[655,656,657,658],[363,4407,385],{"className":4408,"style":409},[407,408,658],[363,4410,666],{"className":4411},[665],[363,4413,4415],{"className":4414},[638],[363,4416,4418],{"className":4417,"style":673},[642],[363,4419],{}," 是否有限。例如对 KL 的 ",[363,4422,4424,4456],{"className":4423,"translate":367},[366],[363,4425,4427],{"className":4426},[371],[373,4428,4429],{"xmlns":375},[377,4430,4431,4453],{},[380,4432,4433,4435,4437,4439,4441,4443,4445,4448,4451],{},[383,4434,385],{},[458,4436,461],{"stretchy":460},[383,4438,1116],{},[458,4440,468],{"stretchy":460},[458,4442,471],{},[383,4444,1116],{},[383,4446,4447],{},"log",[458,4449,4450],{},"⁡",[383,4452,1116],{},[387,4454,4455],{"encoding":389},"f(t)=t\\log t",[363,4457,4459,4486],{"className":4458,"ariaHidden":394},[393],[363,4460,4462,4465,4468,4471,4474,4477,4480,4483],{"className":4461},[398],[363,4463],{"className":4464,"style":487},[402],[363,4466,385],{"className":4467,"style":409},[407,408],[363,4469,461],{"className":4470},[494],[363,4472,1116],{"className":4473},[407,408],[363,4475,468],{"className":4476},[501],[363,4478],{"className":4479,"style":506},[505],[363,4481,471],{"className":4482},[510],[363,4484],{"className":4485,"style":506},[505],[363,4487,4489,4492,4495,4498,4506,4509],{"className":4488},[398],[363,4490],{"className":4491,"style":403},[402],[363,4493,1116],{"className":4494},[407,408],[363,4496],{"className":4497,"style":754},[505],[363,4499,4501,4502],{"className":4500},[1831],"lo",[363,4503,4505],{"style":4504},"margin-right:0.0139em;","g",[363,4507],{"className":4508,"style":754},[505],[363,4510,1116],{"className":4511},[407,408],"，当 ",[363,4514,4516,4529],{"className":4515,"translate":367},[366],[363,4517,4519],{"className":4518},[371],[373,4520,4521],{"xmlns":375},[377,4522,4523,4527],{},[380,4524,4525],{},[383,4526,554],{},[387,4528,554],{"encoding":389},[363,4530,4532],{"className":4531,"ariaHidden":394},[393],[363,4533,4535,4538],{"className":4534},[398],[363,4536],{"className":4537,"style":1011},[402],[363,4539,554],{"className":4540,"style":682},[407,408],[363,4542,4544,4557],{"className":4543,"translate":367},[366],[363,4545,4547],{"className":4546},[371],[373,4548,4549],{"xmlns":375},[377,4550,4551,4555],{},[380,4552,4553],{},[383,4554,561],{},[387,4556,561],{"encoding":389},[363,4558,4560],{"className":4559,"ariaHidden":394},[393],[363,4561,4563,4566],{"className":4562},[398],[363,4564],{"className":4565,"style":913},[402],[363,4567,561],{"className":4568},[407,408]," 的零测集上放质量时这一项为 ",[363,4571,4573,4589],{"className":4572,"translate":367},[366],[363,4574,4576],{"className":4575},[371],[373,4577,4578],{"xmlns":375},[377,4579,4580,4586],{},[380,4581,4582,4584],{},[458,4583,2817],{},[383,4585,1371],{"mathvariant":557},[387,4587,4588],{"encoding":389},"+\\infty",[363,4590,4592],{"className":4591,"ariaHidden":394},[393],[363,4593,4595,4599,4602],{"className":4594},[398],[363,4596],{"className":4597,"style":4598},[402],"height:0.6667em;vertical-align:-0.0833em;",[363,4600,2817],{"className":4601},[407],[363,4603,1371],{"className":4604},[407],"。因此约定：",[363,4607,4609],{"className":4608,"translate":367},[528],[363,4610,4612,4726],{"className":4611,"translate":367},[366],[363,4613,4615],{"className":4614},[371],[373,4616,4617],{"xmlns":375,"display":537},[377,4618,4619,4723],{},[380,4620,4621,4623,4626,4628,4631,4634,4636,4642,4644,4646,4648,4650,4652,4654],{},[383,4622,554],{},[458,4624,4625],{},"≪̸",[383,4627,561],{},[1644,4629,4630],{}," ",[458,4632,4633],{},"⟹",[1644,4635,4630],{},[543,4637,4638,4640],{},[383,4639,547],{},[383,4641,385],{},[458,4643,461],{"stretchy":460},[383,4645,554],{},[383,4647,558],{"mathvariant":557},[383,4649,561],{},[458,4651,468],{"stretchy":460},[458,4653,471],{},[380,4655,4656,4658],{},[458,4657,3245],{"fence":394},[1590,4659,4663,4698],{"rowspacing":4660,"columnalign":4661,"columnspacing":4662},"0.36em","left left","1em",[1596,4664,4665,4677],{},[1599,4666,4667],{},[1602,4668,4669],{"scriptlevel":474,"displaystyle":460},[380,4670,4671,4673,4675],{},[458,4672,2817],{},[383,4674,1371],{"mathvariant":557},[458,4676,898],{"separator":394},[1599,4678,4679],{},[1602,4680,4681],{"scriptlevel":474,"displaystyle":460},[380,4682,4683,4686,4688,4691,4693,4696],{},[1644,4684,4685],{},"若 ",[383,4687,385],{},[1644,4689,4690],{}," 在 ",[383,4692,1371],{"mathvariant":557},[1644,4694,4695],{}," 处增长",[458,4697,898],{"separator":394},[1596,4699,4700,4711],{},[1599,4701,4702],{},[1602,4703,4704],{"scriptlevel":474,"displaystyle":460},[380,4705,4706,4709],{},[1644,4707,4708],{},"有限极限值",[458,4710,898],{"separator":394},[1599,4712,4713],{},[1602,4714,4715],{"scriptlevel":474,"displaystyle":460},[380,4716,4717,4720],{},[1644,4718,4719],{},"否则",[383,4721,4722],{"mathvariant":557},".",[387,4724,4725],{"encoding":389},"P\\not\\ll Q\\ \\Longrightarrow\\\nD_f(P\\|Q)=\n\\begin{cases}\n+\\infty, & \\text{若 } f \\text{ 在 } \\infty\n\\text{ 处增长},\\\\[2pt]\n\\text{有限极限值}, & \\text{否则}.\n\\end{cases}",[363,4727,4729,4784,4808,4878],{"className":4728,"ariaHidden":394},[393],[363,4730,4732,4735,4738,4741,4774,4778,4781],{"className":4731},[398],[363,4733],{"className":4734,"style":403},[402],[363,4736,554],{"className":4737,"style":682},[407,408],[363,4739],{"className":4740,"style":506},[505],[363,4742,4744],{"className":4743},[510],[363,4745,4748],{"className":4746},[407,4747],"vbox",[363,4749,4752],{"className":4750},[4751],"thinbox",[363,4753,4756,4759,4770],{"className":4754},[4755],"rlap",[363,4757],{"className":4758,"style":403},[402],[363,4760,4763],{"className":4761},[4762],"inner",[363,4764,4766],{"className":4765},[407],[363,4767,4769],{"className":4768},[510],"",[363,4771],{"className":4772},[4773],"fix",[363,4775],{"className":4776},[505,4777],"nobreak",[363,4779,1061],{"className":4780},[510],[363,4782],{"className":4783,"style":506},[505],[363,4785,4787,4790,4793,4796,4799,4802,4805],{"className":4786},[398],[363,4788],{"className":4789,"style":913},[402],[363,4791,561],{"className":4792},[407,408],[363,4794,4630],{"className":4795},[505],[363,4797],{"className":4798,"style":506},[505],[363,4800,4633],{"className":4801},[510],[363,4803,4630],{"className":4804},[505],[363,4806],{"className":4807,"style":506},[505],[363,4809,4811,4814,4854,4857,4860,4863,4866,4869,4872,4875],{"className":4810},[398],[363,4812],{"className":4813,"style":618},[402],[363,4815,4817,4820],{"className":4816},[407],[363,4818,547],{"className":4819,"style":625},[407,408],[363,4821,4823],{"className":4822},[629],[363,4824,4826,4846],{"className":4825},[633,634],[363,4827,4829,4843],{"className":4828},[638],[363,4830,4832],{"className":4831,"style":643},[642],[363,4833,4834,4837],{"style":646},[363,4835],{"className":4836,"style":651},[650],[363,4838,4840],{"className":4839},[655,656,657,658],[363,4841,385],{"className":4842,"style":409},[407,408,658],[363,4844,666],{"className":4845},[665],[363,4847,4849],{"className":4848},[638],[363,4850,4852],{"className":4851,"style":673},[642],[363,4853],{},[363,4855,461],{"className":4856},[494],[363,4858,554],{"className":4859,"style":682},[407,408],[363,4861,558],{"className":4862},[407],[363,4864,561],{"className":4865},[407,408],[363,4867,468],{"className":4868},[501],[363,4870],{"className":4871,"style":506},[505],[363,4873,471],{"className":4874},[510],[363,4876],{"className":4877,"style":506},[505],[363,4879,4881,4885],{"className":4880},[398],[363,4882],{"className":4883,"style":4884},[402],"height:3.08em;vertical-align:-1.29em;",[363,4886,4888,4895,5060],{"className":4887},[758],[363,4889,4891],{"className":4890,"style":763},[494,762],[363,4892,3245],{"className":4893},[767,4894],"size4",[363,4896,4898],{"className":4897},[407],[363,4899,4901,4965,4970],{"className":4900},[1590],[363,4902,4904],{"className":4903},[1798],[363,4905,4907,4956],{"className":4906},[633,634],[363,4908,4910,4953],{"className":4909},[638],[363,4911,4914,4933],{"className":4912,"style":4913},[642],"height:1.79em;",[363,4915,4917,4921],{"style":4916},"top:-3.79em;",[363,4918],{"className":4919,"style":4920},[650],"height:3.008em;",[363,4922,4924,4927,4930],{"className":4923},[407],[363,4925,2817],{"className":4926},[407],[363,4928,1371],{"className":4929},[407],[363,4931,898],{"className":4932},[920],[363,4934,4936,4939],{"style":4935},"top:-2.15em;",[363,4937],{"className":4938,"style":4920},[650],[363,4940,4942,4950],{"className":4941},[407],[363,4943,4946],{"className":4944},[407,4945],"text",[363,4947,4708],{"className":4948},[407,4949],"cjk_fallback",[363,4951,898],{"className":4952},[920],[363,4954,666],{"className":4955},[665],[363,4957,4959],{"className":4958},[638],[363,4960,4963],{"className":4961,"style":4962},[642],"height:1.29em;",[363,4964],{},[363,4966],{"className":4967,"style":4969},[4968],"arraycolsep","width:1em;",[363,4971,4973],{"className":4972},[1798],[363,4974,4976,5052],{"className":4975},[633,634],[363,4977,4979,5049],{"className":4978},[638],[363,4980,4982,5032],{"className":4981,"style":4913},[642],[363,4983,4984,4987],{"style":4916},[363,4985],{"className":4986,"style":4920},[650],[363,4988,4990,5000,5003,5016,5019,5029],{"className":4989},[407],[363,4991,4993,4997],{"className":4992},[407,4945],[363,4994,4996],{"className":4995},[407,4949],"若",[363,4998,4630],{"className":4999},[407],[363,5001,385],{"className":5002,"style":409},[407,408],[363,5004,5006,5009,5013],{"className":5005},[407,4945],[363,5007,4630],{"className":5008},[407],[363,5010,5012],{"className":5011},[407,4949],"在",[363,5014,4630],{"className":5015},[407],[363,5017,1371],{"className":5018},[407],[363,5020,5022,5025],{"className":5021},[407,4945],[363,5023,4630],{"className":5024},[407],[363,5026,5028],{"className":5027},[407,4949],"处增长",[363,5030,898],{"className":5031},[920],[363,5033,5034,5037],{"style":4935},[363,5035],{"className":5036,"style":4920},[650],[363,5038,5040,5046],{"className":5039},[407],[363,5041,5043],{"className":5042},[407,4945],[363,5044,4719],{"className":5045},[407,4949],[363,5047,4722],{"className":5048},[407],[363,5050,666],{"className":5051},[665],[363,5053,5055],{"className":5054},[638],[363,5056,5058],{"className":5057,"style":4962},[642],[363,5059],{},[363,5061],{"className":5062},[501,789],[11,5064,5065,5066,4200,5094,5122,5123,5299,5300,5369,5370,5420,5421,5490,5491,5548],{},"其中「否则」指 ",[363,5067,5069,5082],{"className":5068,"translate":367},[366],[363,5070,5072],{"className":5071},[371],[373,5073,5074],{"xmlns":375},[377,5075,5076,5080],{},[380,5077,5078],{},[383,5079,385],{},[387,5081,385],{"encoding":389},[363,5083,5085],{"className":5084,"ariaHidden":394},[393],[363,5086,5088,5091],{"className":5087},[398],[363,5089],{"className":5090,"style":403},[402],[363,5092,385],{"className":5093,"style":409},[407,408],[363,5095,5097,5110],{"className":5096,"translate":367},[366],[363,5098,5100],{"className":5099},[371],[373,5101,5102],{"xmlns":375},[377,5103,5104,5108],{},[380,5105,5106],{},[383,5107,1371],{"mathvariant":557},[387,5109,4217],{"encoding":389},[363,5111,5113],{"className":5112,"ariaHidden":394},[393],[363,5114,5116,5119],{"className":5115},[398],[363,5117],{"className":5118,"style":2692},[402],[363,5120,1371],{"className":5121},[407]," 处有界（如 ",[363,5124,5126,5168],{"className":5125,"translate":367},[366],[363,5127,5129],{"className":5128},[371],[373,5130,5131],{"xmlns":375},[377,5132,5133,5165],{},[380,5134,5135,5137,5139,5141,5143,5145,5153,5156,5158,5161,5163],{},[383,5136,385],{},[458,5138,461],{"stretchy":460},[383,5140,1116],{},[458,5142,468],{"stretchy":460},[458,5144,471],{},[1602,5146,5147],{"scriptlevel":474,"displaystyle":460},[586,5148,5149,5151],{},[463,5150,465],{},[463,5152,2810],{},[458,5154,5155],{"stretchy":460},"∣",[383,5157,1116],{},[458,5159,5160],{},"−",[463,5162,465],{},[458,5164,5155],{"stretchy":460},[387,5166,5167],{"encoding":389},"f(t)=\\tfrac12\\lvert t-1\\rvert",[363,5169,5171,5198,5287],{"className":5170,"ariaHidden":394},[393],[363,5172,5174,5177,5180,5183,5186,5189,5192,5195],{"className":5173},[398],[363,5175],{"className":5176,"style":487},[402],[363,5178,385],{"className":5179,"style":409},[407,408],[363,5181,461],{"className":5182},[494],[363,5184,1116],{"className":5185},[407,408],[363,5187,468],{"className":5188},[501],[363,5190],{"className":5191,"style":506},[505],[363,5193,471],{"className":5194},[510],[363,5196],{"className":5197,"style":506},[505],[363,5199,5201,5204,5272,5275,5278,5281,5284],{"className":5200},[398],[363,5202],{"className":5203,"style":2852},[402],[363,5205,5207,5210,5269],{"className":5206},[407],[363,5208],{"className":5209},[494,789],[363,5211,5213],{"className":5212},[586],[363,5214,5216,5261],{"className":5215},[633,634],[363,5217,5219,5258],{"className":5218},[638],[363,5220,5222,5236,5244],{"className":5221,"style":2871},[642],[363,5223,5224,5227],{"style":2874},[363,5225],{"className":5226,"style":809},[650],[363,5228,5230],{"className":5229},[655,656,657,658],[363,5231,5233],{"className":5232},[407,658],[363,5234,2810],{"className":5235},[407,658],[363,5237,5238,5241],{"style":821},[363,5239],{"className":5240,"style":809},[650],[363,5242],{"className":5243,"style":829},[828],[363,5245,5246,5249],{"style":2897},[363,5247],{"className":5248,"style":809},[650],[363,5250,5252],{"className":5251},[655,656,657,658],[363,5253,5255],{"className":5254},[407,658],[363,5256,465],{"className":5257},[407,658],[363,5259,666],{"className":5260},[665],[363,5262,5264],{"className":5263},[638],[363,5265,5267],{"className":5266,"style":2919},[642],[363,5268],{},[363,5270],{"className":5271},[501,789],[363,5273,5155],{"className":5274},[494],[363,5276,1116],{"className":5277},[407,408],[363,5279],{"className":5280,"style":2934},[505],[363,5282,5160],{"className":5283},[2938],[363,5285],{"className":5286,"style":2934},[505],[363,5288,5290,5293,5296],{"className":5289},[398],[363,5291],{"className":5292,"style":487},[402],[363,5294,465],{"className":5295},[407],[363,5297,5155],{"className":5298},[501],"），此时 ",[363,5301,5303,5320],{"className":5302,"translate":367},[366],[363,5304,5306],{"className":5305},[371],[373,5307,5308],{"xmlns":375},[377,5309,5310,5318],{},[380,5311,5312],{},[543,5313,5314,5316],{},[383,5315,547],{},[383,5317,385],{},[387,5319,4369],{"encoding":389},[363,5321,5323],{"className":5322,"ariaHidden":394},[393],[363,5324,5326,5329],{"className":5325},[398],[363,5327],{"className":5328,"style":4379},[402],[363,5330,5332,5335],{"className":5331},[407],[363,5333,547],{"className":5334,"style":625},[407,408],[363,5336,5338],{"className":5337},[629],[363,5339,5341,5361],{"className":5340},[633,634],[363,5342,5344,5358],{"className":5343},[638],[363,5345,5347],{"className":5346,"style":643},[642],[363,5348,5349,5352],{"style":646},[363,5350],{"className":5351,"style":651},[650],[363,5353,5355],{"className":5354},[655,656,657,658],[363,5356,385],{"className":5357,"style":409},[407,408,658],[363,5359,666],{"className":5360},[665],[363,5362,5364],{"className":5363},[638],[363,5365,5367],{"className":5366,"style":673},[642],[363,5368],{}," 取有限极限值。下文如无特别说明，默认 ",[363,5371,5373,5390],{"className":5372,"translate":367},[366],[363,5374,5376],{"className":5375},[371],[373,5377,5378],{"xmlns":375},[377,5379,5380,5388],{},[380,5381,5382,5384,5386],{},[383,5383,554],{},[458,5385,1061],{},[383,5387,561],{},[387,5389,1066],{"encoding":389},[363,5391,5393,5411],{"className":5392,"ariaHidden":394},[393],[363,5394,5396,5399,5402,5405,5408],{"className":5395},[398],[363,5397],{"className":5398,"style":1076},[402],[363,5400,554],{"className":5401,"style":682},[407,408],[363,5403],{"className":5404,"style":506},[505],[363,5406,1061],{"className":5407},[510],[363,5409],{"className":5410,"style":506},[505],[363,5412,5414,5417],{"className":5413},[398],[363,5415],{"className":5416,"style":913},[402],[363,5418,561],{"className":5419},[407,408],"，并把 ",[363,5422,5424,5441],{"className":5423,"translate":367},[366],[363,5425,5427],{"className":5426},[371],[373,5428,5429],{"xmlns":375},[377,5430,5431,5439],{},[380,5432,5433],{},[543,5434,5435,5437],{},[383,5436,547],{},[383,5438,385],{},[387,5440,4369],{"encoding":389},[363,5442,5444],{"className":5443,"ariaHidden":394},[393],[363,5445,5447,5450],{"className":5446},[398],[363,5448],{"className":5449,"style":4379},[402],[363,5451,5453,5456],{"className":5452},[407],[363,5454,547],{"className":5455,"style":625},[407,408],[363,5457,5459],{"className":5458},[629],[363,5460,5462,5482],{"className":5461},[633,634],[363,5463,5465,5479],{"className":5464},[638],[363,5466,5468],{"className":5467,"style":643},[642],[363,5469,5470,5473],{"style":646},[363,5471],{"className":5472,"style":651},[650],[363,5474,5476],{"className":5475},[655,656,657,658],[363,5477,385],{"className":5478,"style":409},[407,408,658],[363,5480,666],{"className":5481},[665],[363,5483,5485],{"className":5484},[638],[363,5486,5488],{"className":5487,"style":673},[642],[363,5489],{}," 看成 ",[363,5492,5494,5518],{"className":5493,"translate":367},[366],[363,5495,5497],{"className":5496},[371],[373,5498,5499],{"xmlns":375},[377,5500,5501,5515],{},[380,5502,5503,5505,5507,5509,5511,5513],{},[458,5504,578],{"stretchy":460},[463,5506,474],{},[458,5508,898],{"separator":394},[458,5510,2817],{},[383,5512,1371],{"mathvariant":557},[458,5514,605],{"stretchy":460},[387,5516,5517],{"encoding":389},"[0,+\\infty]",[363,5519,5521],{"className":5520,"ariaHidden":394},[393],[363,5522,5524,5527,5530,5533,5536,5539,5542,5545],{"className":5523},[398],[363,5525],{"className":5526,"style":487},[402],[363,5528,578],{"className":5529},[494],[363,5531,474],{"className":5532},[407],[363,5534,898],{"className":5535},[920],[363,5537],{"className":5538,"style":754},[505],[363,5540,2817],{"className":5541},[407],[363,5543,1371],{"className":5544},[407],[363,5546,605],{"className":5547},[501]," 中的值。",[2658,5550,5552],{"id":5551},"_12-只依赖似然比","1.2 只依赖似然比",[11,5554,5555,5556,5651,5652,5724,5725,5802,5803,5831,5832,5874],{},"由定义立刻看出：",[363,5557,5559,5587],{"className":5558,"translate":367},[366],[363,5560,5562],{"className":5561},[371],[373,5563,5564],{"xmlns":375},[377,5565,5566,5584],{},[380,5567,5568,5574,5576,5578,5580,5582],{},[543,5569,5570,5572],{},[383,5571,547],{},[383,5573,385],{},[458,5575,461],{"stretchy":460},[383,5577,554],{},[383,5579,558],{"mathvariant":557},[383,5581,561],{},[458,5583,468],{"stretchy":460},[387,5585,5586],{"encoding":389},"D_f(P\\|Q)",[363,5588,5590],{"className":5589,"ariaHidden":394},[393],[363,5591,5593,5596,5636,5639,5642,5645,5648],{"className":5592},[398],[363,5594],{"className":5595,"style":618},[402],[363,5597,5599,5602],{"className":5598},[407],[363,5600,547],{"className":5601,"style":625},[407,408],[363,5603,5605],{"className":5604},[629],[363,5606,5608,5628],{"className":5607},[633,634],[363,5609,5611,5625],{"className":5610},[638],[363,5612,5614],{"className":5613,"style":643},[642],[363,5615,5616,5619],{"style":646},[363,5617],{"className":5618,"style":651},[650],[363,5620,5622],{"className":5621},[655,656,657,658],[363,5623,385],{"className":5624,"style":409},[407,408,658],[363,5626,666],{"className":5627},[665],[363,5629,5631],{"className":5630},[638],[363,5632,5634],{"className":5633,"style":673},[642],[363,5635],{},[363,5637,461],{"className":5638},[494],[363,5640,554],{"className":5641,"style":682},[407,408],[363,5643,558],{"className":5644},[407],[363,5646,561],{"className":5647},[407,408],[363,5649,468],{"className":5650},[501]," 只通过似然比 ",[363,5653,5655,5681],{"className":5654,"translate":367},[366],[363,5656,5658],{"className":5657},[371],[373,5659,5660],{"xmlns":375},[377,5661,5662,5678],{},[380,5663,5664,5666,5668,5670,5672,5674,5676],{},[383,5665,1116],{},[458,5667,471],{},[383,5669,592],{},[383,5671,554],{},[383,5673,1288],{"mathvariant":557},[383,5675,592],{},[383,5677,561],{},[387,5679,5680],{"encoding":389},"t=dP\u002FdQ",[363,5682,5684,5703],{"className":5683,"ariaHidden":394},[393],[363,5685,5687,5691,5694,5697,5700],{"className":5686},[398],[363,5688],{"className":5689,"style":5690},[402],"height:0.6151em;",[363,5692,1116],{"className":5693},[407,408],[363,5695],{"className":5696,"style":506},[505],[363,5698,471],{"className":5699},[510],[363,5701],{"className":5702,"style":506},[505],[363,5704,5706,5709,5712,5715,5718,5721],{"className":5705},[398],[363,5707],{"className":5708,"style":487},[402],[363,5710,592],{"className":5711},[407,408],[363,5713,554],{"className":5714,"style":682},[407,408],[363,5716,1288],{"className":5717},[407],[363,5719,592],{"className":5720},[407,408],[363,5722,561],{"className":5723},[407,408]," 起作用。也就是说，对任意可测映射 ",[363,5726,5728,5752],{"className":5727,"translate":367},[366],[363,5729,5731],{"className":5730},[371],[373,5732,5733],{"xmlns":375},[377,5734,5735,5749],{},[380,5736,5737,5740,5742,5744,5746],{},[383,5738,5739],{},"T",[458,5741,1362],{},[383,5743,945],{"mathvariant":944},[458,5745,1376],{},[383,5747,5748],{"mathvariant":944},"Y",[387,5750,5751],{"encoding":389},"T:\\mathcal X\\to\\mathcal Y",[363,5753,5755,5773,5791],{"className":5754,"ariaHidden":394},[393],[363,5756,5758,5761,5764,5767,5770],{"className":5757},[398],[363,5759],{"className":5760,"style":1011},[402],[363,5762,5739],{"className":5763,"style":682},[407,408],[363,5765],{"className":5766,"style":506},[505],[363,5768,1362],{"className":5769},[510],[363,5771],{"className":5772,"style":506},[505],[363,5774,5776,5779,5782,5785,5788],{"className":5775},[398],[363,5777],{"className":5778,"style":1011},[402],[363,5780,945],{"className":5781,"style":972},[407,971],[363,5783],{"className":5784,"style":506},[505],[363,5786,1376],{"className":5787},[510],[363,5789],{"className":5790,"style":506},[505],[363,5792,5794,5798],{"className":5793},[398],[363,5795],{"className":5796,"style":5797},[402],"height:0.7805em;vertical-align:-0.0972em;",[363,5799,5748],{"className":5800,"style":5801},[407,971],"margin-right:0.0822em;","，它是 ",[363,5804,5806,5819],{"className":5805,"translate":367},[366],[363,5807,5809],{"className":5808},[371],[373,5810,5811],{"xmlns":375},[377,5812,5813,5817],{},[380,5814,5815],{},[383,5816,1116],{},[387,5818,1116],{"encoding":389},[363,5820,5822],{"className":5821,"ariaHidden":394},[393],[363,5823,5825,5828],{"className":5824},[398],[363,5826],{"className":5827,"style":5690},[402],[363,5829,1116],{"className":5830},[407,408]," 的函数，而不是 ",[363,5833,5835,5853],{"className":5834,"translate":367},[366],[363,5836,5838],{"className":5837},[371],[373,5839,5840],{"xmlns":375},[377,5841,5842,5850],{},[380,5843,5844,5846,5848],{},[383,5845,11],{},[458,5847,898],{"separator":394},[383,5849,1291],{},[387,5851,5852],{"encoding":389},"p,q",[363,5854,5856],{"className":5855,"ariaHidden":394},[393],[363,5857,5859,5862,5865,5868,5871],{"className":5858},[398],[363,5860],{"className":5861,"style":2623},[402],[363,5863,11],{"className":5864},[407,408],[363,5866,898],{"className":5867},[920],[363,5869],{"className":5870,"style":754},[505],[363,5872,1291],{"className":5873,"style":1328},[407,408]," 各自的函数。",[11,5876,5877,5878,5917],{},"这一点是 f-散度「缺少几何」的根源，也是它与 Wasserstein 距离分道扬镳的地方（见第 6 节）：只要保持比值 ",[363,5879,5881,5899],{"className":5880,"translate":367},[366],[363,5882,5884],{"className":5883},[371],[373,5885,5886],{"xmlns":375},[377,5887,5888,5896],{},[380,5889,5890,5892,5894],{},[383,5891,11],{},[383,5893,1288],{"mathvariant":557},[383,5895,1291],{},[387,5897,5898],{"encoding":389},"p\u002Fq",[363,5900,5902],{"className":5901,"ariaHidden":394},[393],[363,5903,5905,5908,5911,5914],{"className":5904},[398],[363,5906],{"className":5907,"style":487},[402],[363,5909,11],{"className":5910},[407,408],[363,5912,1288],{"className":5913},[407],[363,5915,1291],{"className":5916,"style":1328},[407,408]," 不变，把两个分布同时「搬到别处」，f-散度的值完全不动。",[2658,5919,5921],{"id":5920},"_13-非单射与仿射自由度","1.3 非单射与仿射自由度",[11,5923,5924,5925,5992,5993,6057],{},"注意 ",[363,5926,5928,5950],{"className":5927,"translate":367},[366],[363,5929,5931],{"className":5930},[371],[373,5932,5933],{"xmlns":375},[377,5934,5935,5947],{},[380,5936,5937,5939,5941,5943,5945],{},[458,5938,1634],{},[383,5940,592],{},[383,5942,561],{},[458,5944,471],{},[463,5946,465],{},[387,5948,5949],{"encoding":389},"\\int dQ=1",[363,5951,5953,5983],{"className":5952,"ariaHidden":394},[393],[363,5954,5956,5960,5965,5968,5971,5974,5977,5980],{"className":5955},[398],[363,5957],{"className":5958,"style":5959},[402],"height:1.1111em;vertical-align:-0.3061em;",[363,5961,1634],{"className":5962,"style":5964},[1831,1832,5963],"small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[363,5966],{"className":5967,"style":754},[505],[363,5969,592],{"className":5970},[407,408],[363,5972,561],{"className":5973},[407,408],[363,5975],{"className":5976,"style":506},[505],[363,5978,471],{"className":5979},[510],[363,5981],{"className":5982,"style":506},[505],[363,5984,5986,5989],{"className":5985},[398],[363,5987],{"className":5988,"style":520},[402],[363,5990,465],{"className":5991},[407],"、",[363,5994,5996,6018],{"className":5995,"translate":367},[366],[363,5997,5999],{"className":5998},[371],[373,6000,6001],{"xmlns":375},[377,6002,6003,6015],{},[380,6004,6005,6007,6009,6011,6013],{},[458,6006,1634],{},[383,6008,592],{},[383,6010,554],{},[458,6012,471],{},[463,6014,465],{},[387,6016,6017],{"encoding":389},"\\int dP=1",[363,6019,6021,6048],{"className":6020,"ariaHidden":394},[393],[363,6022,6024,6027,6030,6033,6036,6039,6042,6045],{"className":6023},[398],[363,6025],{"className":6026,"style":5959},[402],[363,6028,1634],{"className":6029,"style":5964},[1831,1832,5963],[363,6031],{"className":6032,"style":754},[505],[363,6034,592],{"className":6035},[407,408],[363,6037,554],{"className":6038,"style":682},[407,408],[363,6040],{"className":6041,"style":506},[505],[363,6043,471],{"className":6044},[510],[363,6046],{"className":6047,"style":506},[505],[363,6049,6051,6054],{"className":6050},[398],[363,6052],{"className":6053,"style":520},[402],[363,6055,465],{"className":6056},[407],"，因此",[363,6059,6061],{"className":6060,"translate":367},[528],[363,6062,6064,6115],{"className":6063,"translate":367},[366],[363,6065,6067],{"className":6066},[371],[373,6068,6069],{"xmlns":375,"display":537},[377,6070,6071,6112],{},[380,6072,6073,6075,6077,6079,6081,6083,6085,6087,6089,6091,6093,6095,6097,6099,6101,6103,6105,6107,6109],{},[458,6074,1634],{},[458,6076,461],{"stretchy":460},[383,6078,1116],{},[458,6080,5160],{},[463,6082,465],{},[458,6084,468],{"stretchy":460},[1644,6086,1646],{},[383,6088,592],{},[383,6090,561],{},[458,6092,471],{},[458,6094,1634],{},[383,6096,592],{},[383,6098,554],{},[458,6100,5160],{},[458,6102,1634],{},[383,6104,592],{},[383,6106,561],{},[458,6108,471],{},[463,6110,6111],{},"0.",[387,6113,6114],{"encoding":389},"\\int (t-1)\\,dQ=\\int dP-\\int dQ=0 .",[363,6116,6118,6143,6173,6200,6227],{"className":6117,"ariaHidden":394},[393],[363,6119,6121,6125,6128,6131,6134,6137,6140],{"className":6120},[398],[363,6122],{"className":6123,"style":6124},[402],"height:2.2222em;vertical-align:-0.8622em;",[363,6126,1634],{"className":6127,"style":1834},[1831,1832,1833],[363,6129,461],{"className":6130},[494],[363,6132,1116],{"className":6133},[407,408],[363,6135],{"className":6136,"style":2934},[505],[363,6138,5160],{"className":6139},[2938],[363,6141],{"className":6142,"style":2934},[505],[363,6144,6146,6149,6152,6155,6158,6161,6164,6167,6170],{"className":6145},[398],[363,6147],{"className":6148,"style":487},[402],[363,6150,465],{"className":6151},[407],[363,6153,468],{"className":6154},[501],[363,6156],{"className":6157,"style":754},[505],[363,6159,592],{"className":6160},[407,408],[363,6162,561],{"className":6163},[407,408],[363,6165],{"className":6166,"style":506},[505],[363,6168,471],{"className":6169},[510],[363,6171],{"className":6172,"style":506},[505],[363,6174,6176,6179,6182,6185,6188,6191,6194,6197],{"className":6175},[398],[363,6177],{"className":6178,"style":6124},[402],[363,6180,1634],{"className":6181,"style":1834},[1831,1832,1833],[363,6183],{"className":6184,"style":754},[505],[363,6186,592],{"className":6187},[407,408],[363,6189,554],{"className":6190,"style":682},[407,408],[363,6192],{"className":6193,"style":2934},[505],[363,6195,5160],{"className":6196},[2938],[363,6198],{"className":6199,"style":2934},[505],[363,6201,6203,6206,6209,6212,6215,6218,6221,6224],{"className":6202},[398],[363,6204],{"className":6205,"style":6124},[402],[363,6207,1634],{"className":6208,"style":1834},[1831,1832,1833],[363,6210],{"className":6211,"style":754},[505],[363,6213,592],{"className":6214},[407,408],[363,6216,561],{"className":6217},[407,408],[363,6219],{"className":6220,"style":506},[505],[363,6222,471],{"className":6223},[510],[363,6225],{"className":6226,"style":506},[505],[363,6228,6230,6233],{"className":6229},[398],[363,6231],{"className":6232,"style":520},[402],[363,6234,6111],{"className":6235},[407],[11,6237,6238,6239,3092],{},"于是对任意常数 ",[363,6240,6242,6262],{"className":6241,"translate":367},[366],[363,6243,6245],{"className":6244},[371],[373,6246,6247],{"xmlns":375},[377,6248,6249,6259],{},[380,6250,6251,6254,6257],{},[383,6252,6253],{},"c",[458,6255,6256],{},"∈",[383,6258,1379],{"mathvariant":570},[387,6260,6261],{"encoding":389},"c\\in\\mathbb R",[363,6263,6265,6284],{"className":6264,"ariaHidden":394},[393],[363,6266,6268,6272,6275,6278,6281],{"className":6267},[398],[363,6269],{"className":6270,"style":6271},[402],"height:0.5782em;vertical-align:-0.0391em;",[363,6273,6253],{"className":6274},[407,408],[363,6276],{"className":6277,"style":506},[505],[363,6279,6256],{"className":6280},[510],[363,6282],{"className":6283,"style":506},[505],[363,6285,6287,6290],{"className":6286},[398],[363,6288],{"className":6289,"style":1443},[402],[363,6291,1379],{"className":6292},[407,714],[363,6294,6296],{"className":6295,"translate":367},[528],[363,6297,6299,6417],{"className":6298,"translate":367},[366],[363,6300,6302],{"className":6301},[371],[373,6303,6304],{"xmlns":375,"display":537},[377,6305,6306,6414],{},[380,6307,6308,6330,6332,6334,6336,6338,6340,6342,6348,6350,6352,6354,6356,6358,6360,6362,6394,6396,6402,6404,6406,6408,6410,6412],{},[543,6309,6310,6312],{},[383,6311,547],{},[380,6313,6314,6316,6318,6320,6322,6324,6326,6328],{},[383,6315,385],{},[458,6317,2817],{},[383,6319,6253],{},[458,6321,461],{"stretchy":460},[383,6323,1116],{},[458,6325,5160],{},[463,6327,465],{},[458,6329,468],{"stretchy":460},[458,6331,461],{"stretchy":460},[383,6333,554],{},[383,6335,558],{"mathvariant":557},[383,6337,561],{},[458,6339,468],{"stretchy":460},[458,6341,471],{},[543,6343,6344,6346],{},[383,6345,547],{},[383,6347,385],{},[458,6349,461],{"stretchy":460},[383,6351,554],{},[383,6353,558],{"mathvariant":557},[383,6355,561],{},[458,6357,468],{"stretchy":460},[458,6359,2817],{},[383,6361,6253],{},[6363,6364,6365,6388],"munder",{},[6363,6366,6367,6385],{},[380,6368,6369,6371,6373,6375,6377,6379,6381,6383],{},[458,6370,1634],{},[458,6372,461],{"stretchy":460},[383,6374,1116],{},[458,6376,5160],{},[463,6378,465],{},[458,6380,468],{"stretchy":460},[383,6382,592],{},[383,6384,561],{},[458,6386,6387],{"stretchy":394},"⏟",[380,6389,6390,6392],{},[458,6391,471],{},[463,6393,474],{},[458,6395,471],{},[543,6397,6398,6400],{},[383,6399,547],{},[383,6401,385],{},[458,6403,461],{"stretchy":460},[383,6405,554],{},[383,6407,558],{"mathvariant":557},[383,6409,561],{},[458,6411,468],{"stretchy":460},[383,6413,4722],{"mathvariant":557},[387,6415,6416],{"encoding":389},"D_{f+c(t-1)}(P\\|Q)\n=D_f(P\\|Q)+c\\underbrace{\\int(t-1)dQ}_{=0}\n=D_f(P\\|Q).",[363,6418,6420,6518,6588,6772],{"className":6419,"ariaHidden":394},[393],[363,6421,6423,6427,6494,6497,6500,6503,6506,6509,6512,6515],{"className":6422},[398],[363,6424],{"className":6425,"style":6426},[402],"height:1.1052em;vertical-align:-0.3552em;",[363,6428,6430,6433],{"className":6429},[407],[363,6431,547],{"className":6432,"style":625},[407,408],[363,6434,6436],{"className":6435},[629],[363,6437,6439,6485],{"className":6438},[633,634],[363,6440,6442,6482],{"className":6441},[638],[363,6443,6446],{"className":6444,"style":6445},[642],"height:0.3448em;",[363,6447,6449,6452],{"style":6448},"top:-2.5198em;margin-left:-0.0278em;margin-right:0.05em;",[363,6450],{"className":6451,"style":651},[650],[363,6453,6455],{"className":6454},[655,656,657,658],[363,6456,6458,6461,6464,6467,6470,6473,6476,6479],{"className":6457},[407,658],[363,6459,385],{"className":6460,"style":409},[407,408,658],[363,6462,2817],{"className":6463},[2938,658],[363,6465,6253],{"className":6466},[407,408,658],[363,6468,461],{"className":6469},[494,658],[363,6471,1116],{"className":6472},[407,408,658],[363,6474,5160],{"className":6475},[2938,658],[363,6477,465],{"className":6478},[407,658],[363,6480,468],{"className":6481},[501,658],[363,6483,666],{"className":6484},[665],[363,6486,6488],{"className":6487},[638],[363,6489,6492],{"className":6490,"style":6491},[642],"height:0.3552em;",[363,6493],{},[363,6495,461],{"className":6496},[494],[363,6498,554],{"className":6499,"style":682},[407,408],[363,6501,558],{"className":6502},[407],[363,6504,561],{"className":6505},[407,408],[363,6507,468],{"className":6508},[501],[363,6510],{"className":6511,"style":506},[505],[363,6513,471],{"className":6514},[510],[363,6516],{"className":6517,"style":506},[505],[363,6519,6521,6524,6564,6567,6570,6573,6576,6579,6582,6585],{"className":6520},[398],[363,6522],{"className":6523,"style":618},[402],[363,6525,6527,6530],{"className":6526},[407],[363,6528,547],{"className":6529,"style":625},[407,408],[363,6531,6533],{"className":6532},[629],[363,6534,6536,6556],{"className":6535},[633,634],[363,6537,6539,6553],{"className":6538},[638],[363,6540,6542],{"className":6541,"style":643},[642],[363,6543,6544,6547],{"style":646},[363,6545],{"className":6546,"style":651},[650],[363,6548,6550],{"className":6549},[655,656,657,658],[363,6551,385],{"className":6552,"style":409},[407,408,658],[363,6554,666],{"className":6555},[665],[363,6557,6559],{"className":6558},[638],[363,6560,6562],{"className":6561,"style":673},[642],[363,6563],{},[363,6565,461],{"className":6566},[494],[363,6568,554],{"className":6569,"style":682},[407,408],[363,6571,558],{"className":6572},[407],[363,6574,561],{"className":6575},[407,408],[363,6577,468],{"className":6578},[501],[363,6580],{"className":6581,"style":2934},[505],[363,6583,2817],{"className":6584},[2938],[363,6586],{"className":6587,"style":2934},[505],[363,6589,6591,6595,6598,6601,6763,6766,6769],{"className":6590},[398],[363,6592],{"className":6593,"style":6594},[402],"height:3.5214em;vertical-align:-2.1614em;",[363,6596,6253],{"className":6597},[407,408],[363,6599],{"className":6600,"style":754},[505],[363,6602,6604],{"className":6603},[758,6363],[363,6605,6607,6754],{"className":6606},[633,634],[363,6608,6610,6751],{"className":6609},[638],[363,6611,6614,6633],{"className":6612,"style":6613},[642],"height:1.36em;",[363,6615,6617,6621],{"style":6616},"top:-1.1986em;",[363,6618],{"className":6619,"style":6620},[650],"height:3.36em;",[363,6622,6624],{"className":6623},[655,656,657,658],[363,6625,6627,6630],{"className":6626},[407,658],[363,6628,471],{"className":6629},[510,658],[363,6631,474],{"className":6632},[407,658],[363,6634,6636,6639],{"style":6635},"top:-3.36em;",[363,6637],{"className":6638,"style":6620},[650],[363,6640,6642],{"className":6641},[758,6363],[363,6643,6645,6742],{"className":6644},[633,634],[363,6646,6648,6739],{"className":6647},[638],[363,6649,6651,6701],{"className":6650,"style":6613},[642],[363,6652,6656,6659],{"className":6653,"style":6655},[6654],"svg-align","top:-1.8498em;",[363,6657],{"className":6658,"style":6620},[650],[363,6660,6664,6681,6691],{"className":6661,"style":6663},[6662],"stretchy","height:0.548em;min-width:1.6em;",[363,6665,6669],{"className":6666,"style":6668},[6667],"brace-left","height:0.548em;",[6670,6671,6677],"svg",{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6676},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","0.548em","0 0 400000 548","xMinYMin slice",[6678,6679],"path",{"d":6680},"M0 6l6-6h17c12.688 0 19.313.3 20 1 4 4 7.313 8.3 10 13\n 35.313 51.3 80.813 93.8 136.5 127.5 55.688 33.7 117.188 55.8 184.5 66.5.688\n 0 2 .3 4 1 18.688 2.7 76 4.3 172 5h399450v120H429l-6-1c-124.688-8-235-61.7\n-331-161C60.687 138.7 32.312 99.3 7 54L0 41V6z",[363,6682,6685],{"className":6683,"style":6668},[6684],"brace-center",[6670,6686,6688],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6687},"xMidYMin slice",[6678,6689],{"d":6690},"M199572 214\nc100.7 8.3 195.3 44 280 108 55.3 42 101.7 93 139 153l9 14c2.7-4 5.7-8.7 9-14\n 53.3-86.7 123.7-153 211-199 66.7-36 137.3-56.3 212-62h199568v120H200432c-178.3\n 11.7-311.7 78.3-403 201-6 8-9.7 12-11 12-.7.7-6.7 1-18 1s-17.3-.3-18-1c-1.3 0\n-5-4-11-12-44.7-59.3-101.3-106.3-170-141s-145.3-54.3-229-60H0V214z",[363,6692,6695],{"className":6693,"style":6668},[6694],"brace-right",[6670,6696,6698],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6697},"xMaxYMin slice",[6678,6699],{"d":6700},"M399994 0l6 6v35l-6 11c-56 104-135.3 181.3-238 232-57.3\n 28.7-117 45-179 50H-300V214h399897c43.3-7 81-15 113-26 100.7-33 179.7-91 237\n-174 2.7-5 6-9 10-13 .7-1 7.3-1 20-1h17z",[363,6702,6703,6706],{"style":6635},[363,6704],{"className":6705,"style":6620},[650],[363,6707,6709,6712,6715,6718,6721,6724,6727,6730,6733,6736],{"className":6708},[407],[363,6710,1634],{"className":6711,"style":1834},[1831,1832,1833],[363,6713,461],{"className":6714},[494],[363,6716,1116],{"className":6717},[407,408],[363,6719],{"className":6720,"style":2934},[505],[363,6722,5160],{"className":6723},[2938],[363,6725],{"className":6726,"style":2934},[505],[363,6728,465],{"className":6729},[407],[363,6731,468],{"className":6732},[501],[363,6734,592],{"className":6735},[407,408],[363,6737,561],{"className":6738},[407,408],[363,6740,666],{"className":6741},[665],[363,6743,6745],{"className":6744},[638],[363,6746,6749],{"className":6747,"style":6748},[642],"height:1.5103em;",[363,6750],{},[363,6752,666],{"className":6753},[665],[363,6755,6757],{"className":6756},[638],[363,6758,6761],{"className":6759,"style":6760},[642],"height:2.1614em;",[363,6762],{},[363,6764],{"className":6765,"style":506},[505],[363,6767,471],{"className":6768},[510],[363,6770],{"className":6771,"style":506},[505],[363,6773,6775,6778,6818,6821,6824,6827,6830,6833],{"className":6774},[398],[363,6776],{"className":6777,"style":618},[402],[363,6779,6781,6784],{"className":6780},[407],[363,6782,547],{"className":6783,"style":625},[407,408],[363,6785,6787],{"className":6786},[629],[363,6788,6790,6810],{"className":6789},[633,634],[363,6791,6793,6807],{"className":6792},[638],[363,6794,6796],{"className":6795,"style":643},[642],[363,6797,6798,6801],{"style":646},[363,6799],{"className":6800,"style":651},[650],[363,6802,6804],{"className":6803},[655,656,657,658],[363,6805,385],{"className":6806,"style":409},[407,408,658],[363,6808,666],{"className":6809},[665],[363,6811,6813],{"className":6812},[638],[363,6814,6816],{"className":6815,"style":673},[642],[363,6817],{},[363,6819,461],{"className":6820},[494],[363,6822,554],{"className":6823,"style":682},[407,408],[363,6825,558],{"className":6826},[407],[363,6828,561],{"className":6829},[407,408],[363,6831,468],{"className":6832},[501],[363,6834,4722],{"className":6835},[407],[11,6837,6838,6841,6842,6911,6912,6940,6941,7007],{},[1572,6839,6840],{},"结论："," ",[363,6843,6845,6862],{"className":6844,"translate":367},[366],[363,6846,6848],{"className":6847},[371],[373,6849,6850],{"xmlns":375},[377,6851,6852,6860],{},[380,6853,6854],{},[543,6855,6856,6858],{},[383,6857,547],{},[383,6859,385],{},[387,6861,4369],{"encoding":389},[363,6863,6865],{"className":6864,"ariaHidden":394},[393],[363,6866,6868,6871],{"className":6867},[398],[363,6869],{"className":6870,"style":4379},[402],[363,6872,6874,6877],{"className":6873},[407],[363,6875,547],{"className":6876,"style":625},[407,408],[363,6878,6880],{"className":6879},[629],[363,6881,6883,6903],{"className":6882},[633,634],[363,6884,6886,6900],{"className":6885},[638],[363,6887,6889],{"className":6888,"style":643},[642],[363,6890,6891,6894],{"style":646},[363,6892],{"className":6893,"style":651},[650],[363,6895,6897],{"className":6896},[655,656,657,658],[363,6898,385],{"className":6899,"style":409},[407,408,658],[363,6901,666],{"className":6902},[665],[363,6904,6906],{"className":6905},[638],[363,6907,6909],{"className":6908,"style":673},[642],[363,6910],{}," 只依赖 ",[363,6913,6915,6928],{"className":6914,"translate":367},[366],[363,6916,6918],{"className":6917},[371],[373,6919,6920],{"xmlns":375},[377,6921,6922,6926],{},[380,6923,6924],{},[383,6925,385],{},[387,6927,385],{"encoding":389},[363,6929,6931],{"className":6930,"ariaHidden":394},[393],[363,6932,6934,6937],{"className":6933},[398],[363,6935],{"className":6936,"style":403},[402],[363,6938,385],{"className":6939,"style":409},[407,408]," 在「模去 ",[363,6942,6944,6968],{"className":6943,"translate":367},[366],[363,6945,6947],{"className":6946},[371],[373,6948,6949],{"xmlns":375},[377,6950,6951,6965],{},[380,6952,6953,6955,6957,6959,6961,6963],{},[383,6954,6253],{},[458,6956,461],{"stretchy":460},[383,6958,1116],{},[458,6960,5160],{},[463,6962,465],{},[458,6964,468],{"stretchy":460},[387,6966,6967],{"encoding":389},"c(t-1)",[363,6969,6971,6995],{"className":6970,"ariaHidden":394},[393],[363,6972,6974,6977,6980,6983,6986,6989,6992],{"className":6973},[398],[363,6975],{"className":6976,"style":487},[402],[363,6978,6253],{"className":6979},[407,408],[363,6981,461],{"className":6982},[494],[363,6984,1116],{"className":6985},[407,408],[363,6987],{"className":6988,"style":2934},[505],[363,6990,5160],{"className":6991},[2938],[363,6993],{"className":6994,"style":2934},[505],[363,6996,6998,7001,7004],{"className":6997},[398],[363,6999],{"className":7000,"style":487},[402],[363,7002,465],{"className":7003},[407],[363,7005,468],{"className":7006},[501],"」之后的等价类。两个常用规范化是：",[7009,7010,7011,7080],"ol",{},[7012,7013,7014,7079],"li",{},[363,7015,7017,7040],{"className":7016,"translate":367},[366],[363,7018,7020],{"className":7019},[371],[373,7021,7022],{"xmlns":375},[377,7023,7024,7038],{},[380,7025,7026,7028,7030,7032,7034,7036],{},[383,7027,385],{},[458,7029,461],{"stretchy":460},[463,7031,465],{},[458,7033,468],{"stretchy":460},[458,7035,471],{},[463,7037,474],{},[387,7039,477],{"encoding":389},[363,7041,7043,7070],{"className":7042,"ariaHidden":394},[393],[363,7044,7046,7049,7052,7055,7058,7061,7064,7067],{"className":7045},[398],[363,7047],{"className":7048,"style":487},[402],[363,7050,385],{"className":7051,"style":409},[407,408],[363,7053,461],{"className":7054},[494],[363,7056,465],{"className":7057},[407],[363,7059,468],{"className":7060},[501],[363,7062],{"className":7063,"style":506},[505],[363,7065,471],{"className":7066},[510],[363,7068],{"className":7069,"style":506},[505],[363,7071,7073,7076],{"className":7072},[398],[363,7074],{"className":7075,"style":520},[402],[363,7077,474],{"className":7078},[407],"（本文采用）；",[7012,7081,7082,7147,7148,7252,7253,3092,7464,7492],{},[363,7083,7085,7108],{"className":7084,"translate":367},[366],[363,7086,7088],{"className":7087},[371],[373,7089,7090],{"xmlns":375},[377,7091,7092,7106],{},[380,7093,7094,7096,7098,7100,7102,7104],{},[383,7095,385],{},[458,7097,461],{"stretchy":460},[463,7099,465],{},[458,7101,468],{"stretchy":460},[458,7103,471],{},[463,7105,474],{},[387,7107,477],{"encoding":389},[363,7109,7111,7138],{"className":7110,"ariaHidden":394},[393],[363,7112,7114,7117,7120,7123,7126,7129,7132,7135],{"className":7113},[398],[363,7115],{"className":7116,"style":487},[402],[363,7118,385],{"className":7119,"style":409},[407,408],[363,7121,461],{"className":7122},[494],[363,7124,465],{"className":7125},[407],[363,7127,468],{"className":7128},[501],[363,7130],{"className":7131,"style":506},[505],[363,7133,471],{"className":7134},[510],[363,7136],{"className":7137,"style":506},[505],[363,7139,7141,7144],{"className":7140},[398],[363,7142],{"className":7143,"style":520},[402],[363,7145,474],{"className":7146},[407]," 且 ",[363,7149,7151,7181],{"className":7150,"translate":367},[366],[363,7152,7154],{"className":7153},[371],[373,7155,7156],{"xmlns":375},[377,7157,7158,7178],{},[380,7159,7160,7168,7170,7172,7174,7176],{},[7161,7162,7163,7165],"msup",{},[383,7164,385],{},[458,7166,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},"′",[458,7169,461],{"stretchy":460},[463,7171,465],{},[458,7173,468],{"stretchy":460},[458,7175,471],{},[463,7177,474],{},[387,7179,7180],{"encoding":389},"f'(1)=0",[363,7182,7184,7243],{"className":7183,"ariaHidden":394},[393],[363,7185,7187,7191,7225,7228,7231,7234,7237,7240],{"className":7186},[398],[363,7188],{"className":7189,"style":7190},[402],"height:1.0019em;vertical-align:-0.25em;",[363,7192,7194,7197],{"className":7193},[407],[363,7195,385],{"className":7196,"style":409},[407,408],[363,7198,7200],{"className":7199},[629],[363,7201,7203],{"className":7202},[633],[363,7204,7206],{"className":7205},[638],[363,7207,7210],{"className":7208,"style":7209},[642],"height:0.7519em;",[363,7211,7213,7216],{"style":7212},"top:-3.063em;margin-right:0.05em;",[363,7214],{"className":7215,"style":651},[650],[363,7217,7219],{"className":7218},[655,656,657,658],[363,7220,7222],{"className":7221},[407,658],[363,7223,7167],{"className":7224},[407,658],[363,7226,461],{"className":7227},[494],[363,7229,465],{"className":7230},[407],[363,7232,468],{"className":7233},[501],[363,7235],{"className":7236,"style":506},[505],[363,7238,471],{"className":7239},[510],[363,7241],{"className":7242,"style":506},[505],[363,7244,7246,7249],{"className":7245},[398],[363,7247],{"className":7248,"style":520},[402],[363,7250,474],{"className":7251},[407],"——此时由凸性 ",[363,7254,7256,7315],{"className":7255,"translate":367},[366],[363,7257,7259],{"className":7258},[371],[373,7260,7261],{"xmlns":375},[377,7262,7263,7312],{},[380,7264,7265,7267,7269,7271,7273,7276,7278,7280,7282,7284,7286,7292,7294,7296,7298,7300,7302,7304,7306,7308,7310],{},[383,7266,385],{},[458,7268,461],{"stretchy":460},[383,7270,1116],{},[458,7272,468],{"stretchy":460},[458,7274,7275],{},"≥",[383,7277,385],{},[458,7279,461],{"stretchy":460},[463,7281,465],{},[458,7283,468],{"stretchy":460},[458,7285,2817],{},[7161,7287,7288,7290],{},[383,7289,385],{},[458,7291,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,7293,461],{"stretchy":460},[463,7295,465],{},[458,7297,468],{"stretchy":460},[458,7299,461],{"stretchy":460},[383,7301,1116],{},[458,7303,5160],{},[463,7305,465],{},[458,7307,468],{"stretchy":460},[458,7309,471],{},[463,7311,474],{},[387,7313,7314],{"encoding":389},"f(t)\\ge f(1)+f'(1)(t-1)=0",[363,7316,7318,7345,7372,7434,7455],{"className":7317,"ariaHidden":394},[393],[363,7319,7321,7324,7327,7330,7333,7336,7339,7342],{"className":7320},[398],[363,7322],{"className":7323,"style":487},[402],[363,7325,385],{"className":7326,"style":409},[407,408],[363,7328,461],{"className":7329},[494],[363,7331,1116],{"className":7332},[407,408],[363,7334,468],{"className":7335},[501],[363,7337],{"className":7338,"style":506},[505],[363,7340,7275],{"className":7341},[510],[363,7343],{"className":7344,"style":506},[505],[363,7346,7348,7351,7354,7357,7360,7363,7366,7369],{"className":7347},[398],[363,7349],{"className":7350,"style":487},[402],[363,7352,385],{"className":7353,"style":409},[407,408],[363,7355,461],{"className":7356},[494],[363,7358,465],{"className":7359},[407],[363,7361,468],{"className":7362},[501],[363,7364],{"className":7365,"style":2934},[505],[363,7367,2817],{"className":7368},[2938],[363,7370],{"className":7371,"style":2934},[505],[363,7373,7375,7378,7410,7413,7416,7419,7422,7425,7428,7431],{"className":7374},[398],[363,7376],{"className":7377,"style":7190},[402],[363,7379,7381,7384],{"className":7380},[407],[363,7382,385],{"className":7383,"style":409},[407,408],[363,7385,7387],{"className":7386},[629],[363,7388,7390],{"className":7389},[633],[363,7391,7393],{"className":7392},[638],[363,7394,7396],{"className":7395,"style":7209},[642],[363,7397,7398,7401],{"style":7212},[363,7399],{"className":7400,"style":651},[650],[363,7402,7404],{"className":7403},[655,656,657,658],[363,7405,7407],{"className":7406},[407,658],[363,7408,7167],{"className":7409},[407,658],[363,7411,461],{"className":7412},[494],[363,7414,465],{"className":7415},[407],[363,7417,468],{"className":7418},[501],[363,7420,461],{"className":7421},[494],[363,7423,1116],{"className":7424},[407,408],[363,7426],{"className":7427,"style":2934},[505],[363,7429,5160],{"className":7430},[2938],[363,7432],{"className":7433,"style":2934},[505],[363,7435,7437,7440,7443,7446,7449,7452],{"className":7436},[398],[363,7438],{"className":7439,"style":487},[402],[363,7441,465],{"className":7442},[407],[363,7444,468],{"className":7445},[501],[363,7447],{"className":7448,"style":506},[505],[363,7450,471],{"className":7451},[510],[363,7453],{"className":7454,"style":506},[505],[363,7456,7458,7461],{"className":7457},[398],[363,7459],{"className":7460,"style":520},[402],[363,7462,474],{"className":7463},[407],[363,7465,7467,7480],{"className":7466,"translate":367},[366],[363,7468,7470],{"className":7469},[371],[373,7471,7472],{"xmlns":375},[377,7473,7474,7478],{},[380,7475,7476],{},[383,7477,385],{},[387,7479,385],{"encoding":389},[363,7481,7483],{"className":7482,"ariaHidden":394},[393],[363,7484,7486,7489],{"className":7485},[398],[363,7487],{"className":7488,"style":403},[402],[363,7490,385],{"className":7491,"style":409},[407,408]," 在整个定义域上非负。",[11,7494,7495,7496,7581,7582,7635,7636,7705],{},"第 3 节里的 KL 的 ",[363,7497,7499,7528],{"className":7498,"translate":367},[366],[363,7500,7502],{"className":7501},[371],[373,7503,7504],{"xmlns":375},[377,7505,7506,7526],{},[380,7507,7508,7510,7512,7514,7516,7518,7520,7522,7524],{},[383,7509,385],{},[458,7511,461],{"stretchy":460},[383,7513,1116],{},[458,7515,468],{"stretchy":460},[458,7517,471],{},[383,7519,1116],{},[383,7521,4447],{},[458,7523,4450],{},[383,7525,1116],{},[387,7527,4455],{"encoding":389},[363,7529,7531,7558],{"className":7530,"ariaHidden":394},[393],[363,7532,7534,7537,7540,7543,7546,7549,7552,7555],{"className":7533},[398],[363,7535],{"className":7536,"style":487},[402],[363,7538,385],{"className":7539,"style":409},[407,408],[363,7541,461],{"className":7542},[494],[363,7544,1116],{"className":7545},[407,408],[363,7547,468],{"className":7548},[501],[363,7550],{"className":7551,"style":506},[505],[363,7553,471],{"className":7554},[510],[363,7556],{"className":7557,"style":506},[505],[363,7559,7561,7564,7567,7570,7575,7578],{"className":7560},[398],[363,7562],{"className":7563,"style":403},[402],[363,7565,1116],{"className":7566},[407,408],[363,7568],{"className":7569,"style":754},[505],[363,7571,4501,7573],{"className":7572},[1831],[363,7574,4505],{"style":4504},[363,7576],{"className":7577,"style":754},[505],[363,7579,1116],{"className":7580},[407,408]," 不满足第 2 条（它在 ",[363,7583,7585,7604],{"className":7584,"translate":367},[366],[363,7586,7588],{"className":7587},[371],[373,7589,7590],{"xmlns":375},[377,7591,7592,7601],{},[380,7593,7594,7596,7599],{},[383,7595,1116],{},[458,7597,7598],{},"\u003C",[463,7600,465],{},[387,7602,7603],{"encoding":389},"t\u003C1",[363,7605,7607,7626],{"className":7606,"ariaHidden":394},[393],[363,7608,7610,7614,7617,7620,7623],{"className":7609},[398],[363,7611],{"className":7612,"style":7613},[402],"height:0.6542em;vertical-align:-0.0391em;",[363,7615,1116],{"className":7616},[407,408],[363,7618],{"className":7619,"style":506},[505],[363,7621,7598],{"className":7622},[510],[363,7624],{"className":7625,"style":506},[505],[363,7627,7629,7632],{"className":7628},[398],[363,7630],{"className":7631,"style":520},[402],[363,7633,465],{"className":7634},[407]," 时取负值），但这无妨：",[363,7637,7639,7656],{"className":7638,"translate":367},[366],[363,7640,7642],{"className":7641},[371],[373,7643,7644],{"xmlns":375},[377,7645,7646,7654],{},[380,7647,7648],{},[543,7649,7650,7652],{},[383,7651,547],{},[383,7653,385],{},[387,7655,4369],{"encoding":389},[363,7657,7659],{"className":7658,"ariaHidden":394},[393],[363,7660,7662,7665],{"className":7661},[398],[363,7663],{"className":7664,"style":4379},[402],[363,7666,7668,7671],{"className":7667},[407],[363,7669,547],{"className":7670,"style":625},[407,408],[363,7672,7674],{"className":7673},[629],[363,7675,7677,7697],{"className":7676},[633,634],[363,7678,7680,7694],{"className":7679},[638],[363,7681,7683],{"className":7682,"style":643},[642],[363,7684,7685,7688],{"style":646},[363,7686],{"className":7687,"style":651},[650],[363,7689,7691],{"className":7690},[655,656,657,658],[363,7692,385],{"className":7693,"style":409},[407,408,658],[363,7695,666],{"className":7696},[665],[363,7698,7700],{"className":7699},[638],[363,7701,7703],{"className":7702,"style":673},[642],[363,7704],{}," 仍然非负（见 4.1），因为「逐点非负」从来不是 f-散度非负性的必要条件。",[2658,7707,7709],{"id":7708},"_14-等价书写形式","1.4 等价书写形式",[363,7711,7713],{"className":7712,"translate":367},[528],[363,7714,7716,7950],{"className":7715,"translate":367},[366],[363,7717,7719],{"className":7718},[371],[373,7720,7721],{"xmlns":375,"display":537},[377,7722,7723,7947],{},[1590,7724,7725,7797,7869],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,7726,7727,7749],{},[1599,7728,7729],{},[1602,7730,7731],{"scriptlevel":474,"displaystyle":394},[380,7732,7733,7739,7741,7743,7745,7747],{},[543,7734,7735,7737],{},[383,7736,547],{},[383,7738,385],{},[458,7740,461],{"stretchy":460},[383,7742,554],{},[383,7744,558],{"mathvariant":557},[383,7746,561],{},[458,7748,468],{"stretchy":460},[1599,7750,7751],{},[1602,7752,7753],{"scriptlevel":474,"displaystyle":394},[380,7754,7755,7757,7759,7765,7767],{},[380,7756],{},[458,7758,471],{},[543,7760,7761,7763],{},[383,7762,571],{"mathvariant":570},[383,7764,561],{},[1644,7766,1651],{},[380,7768,7769,7771,7773,7775,7795],{},[458,7770,578],{"fence":394},[383,7772,385],{},[1644,7774,1651],{},[380,7776,7777,7779,7793],{},[458,7778,461],{"fence":394},[586,7780,7781,7787],{},[380,7782,7783,7785],{},[383,7784,592],{},[383,7786,554],{},[380,7788,7789,7791],{},[383,7790,592],{},[383,7792,561],{},[458,7794,468],{"fence":394},[458,7796,605],{"fence":394},[1596,7798,7799,7805],{},[1599,7800,7801],{},[1602,7802,7803],{"scriptlevel":474,"displaystyle":394},[380,7804],{},[1599,7806,7807],{},[1602,7808,7809],{"scriptlevel":474,"displaystyle":394},[380,7810,7811,7813,7815,7821,7823],{},[380,7812],{},[458,7814,471],{},[543,7816,7817,7819],{},[383,7818,571],{"mathvariant":570},[383,7820,554],{},[1644,7822,1651],{},[380,7824,7825,7827,7841,7843,7845,7847,7867],{},[458,7826,578],{"fence":394},[586,7828,7829,7835],{},[380,7830,7831,7833],{},[383,7832,592],{},[383,7834,561],{},[380,7836,7837,7839],{},[383,7838,592],{},[383,7840,554],{},[1644,7842,1646],{},[383,7844,385],{},[1644,7846,1651],{},[380,7848,7849,7851,7865],{},[458,7850,461],{"fence":394},[586,7852,7853,7859],{},[380,7854,7855,7857],{},[383,7856,592],{},[383,7858,554],{},[380,7860,7861,7863],{},[383,7862,592],{},[383,7864,561],{},[458,7866,468],{"fence":394},[458,7868,605],{"fence":394},[1596,7870,7871,7877],{},[1599,7872,7873],{},[1602,7874,7875],{"scriptlevel":474,"displaystyle":394},[380,7876],{},[1599,7878,7879],{},[1602,7880,7881],{"scriptlevel":474,"displaystyle":394},[380,7882,7883,7885,7887,7893,7895,7945],{},[380,7884],{},[458,7886,471],{},[543,7888,7889,7891],{},[383,7890,571],{"mathvariant":570},[383,7892,554],{},[1644,7894,1651],{},[380,7896,7897,7899,7921,7923,7943],{},[458,7898,578],{"fence":394},[7900,7901,7902,7904,7918],"msubsup",{},[383,7903,385],{},[380,7905,7906,7909,7912,7915],{},[383,7907,7908],{},"s",[383,7910,7911],{},"k",[383,7913,7914],{},"e",[383,7916,7917],{},"w",[458,7919,7920],{"lspace":1594,"rspace":1594},"∗",[1644,7922,1651],{},[380,7924,7925,7927,7941],{},[458,7926,461],{"fence":394},[586,7928,7929,7935],{},[380,7930,7931,7933],{},[383,7932,592],{},[383,7934,561],{},[380,7936,7937,7939],{},[383,7938,592],{},[383,7940,554],{},[458,7942,468],{"fence":394},[458,7944,605],{"fence":394},[458,7946,898],{"separator":394},[387,7948,7949],{"encoding":389},"\\begin{aligned}\nD_f(P\\|Q)\n&=\\mathbb E_Q\\!\\left[\nf\\!\\left(\\frac{dP}{dQ}\\right)\\right]\\\\[2pt]\n&=\\mathbb E_P\\!\\left[\\frac{dQ}{dP}\\,\nf\\!\\left(\\frac{dP}{dQ}\\right)\\right]\\\\\n&=\\mathbb E_P\\!\\left[\nf^{*}_{skew}\\!\\left(\\frac{dQ}{dP}\\right)\\right],\n\\end{aligned}",[363,7951,7953],{"className":7952,"ariaHidden":394},[393],[363,7954,7956,7960],{"className":7955},[398],[363,7957],{"className":7958,"style":7959},[402],"height:7.8001em;vertical-align:-3.65em;",[363,7961,7963],{"className":7962},[407],[363,7964,7966,8072],{"className":7965},[1590],[363,7967,7969],{"className":7968},[1707],[363,7970,7972,8063],{"className":7971},[633,634],[363,7973,7975,8060],{"className":7974},[638],[363,7976,7979,8043,8051],{"className":7977,"style":7978},[642],"height:4.15em;",[363,7980,7982,7985],{"style":7981},"top:-6.15em;",[363,7983],{"className":7984,"style":1724},[650],[363,7986,7988,8028,8031,8034,8037,8040],{"className":7987},[407],[363,7989,7991,7994],{"className":7990},[407],[363,7992,547],{"className":7993,"style":625},[407,408],[363,7995,7997],{"className":7996},[629],[363,7998,8000,8020],{"className":7999},[633,634],[363,8001,8003,8017],{"className":8002},[638],[363,8004,8006],{"className":8005,"style":643},[642],[363,8007,8008,8011],{"style":646},[363,8009],{"className":8010,"style":651},[650],[363,8012,8014],{"className":8013},[655,656,657,658],[363,8015,385],{"className":8016,"style":409},[407,408,658],[363,8018,666],{"className":8019},[665],[363,8021,8023],{"className":8022},[638],[363,8024,8026],{"className":8025,"style":673},[642],[363,8027],{},[363,8029,461],{"className":8030},[494],[363,8032,554],{"className":8033,"style":682},[407,408],[363,8035,558],{"className":8036},[407],[363,8038,561],{"className":8039},[407,408],[363,8041,468],{"className":8042},[501],[363,8044,8045,8048],{"style":1720},[363,8046],{"className":8047,"style":1724},[650],[363,8049],{"className":8050},[407],[363,8052,8054,8057],{"style":8053},"top:-0.75em;",[363,8055],{"className":8056,"style":1724},[650],[363,8058],{"className":8059},[407],[363,8061,666],{"className":8062},[665],[363,8064,8066],{"className":8065},[638],[363,8067,8070],{"className":8068,"style":8069},[642],"height:3.65em;",[363,8071],{},[363,8073,8075],{"className":8074},[1798],[363,8076,8078,8753],{"className":8077},[633,634],[363,8079,8081,8750],{"className":8080},[638],[363,8082,8084,8257,8502],{"className":8083,"style":7978},[642],[363,8085,8086,8089],{"style":7981},[363,8087],{"className":8088,"style":1724},[650],[363,8090,8092,8095,8098,8101,8104,8144,8147,8150],{"className":8091},[407],[363,8093],{"className":8094},[407],[363,8096],{"className":8097,"style":506},[505],[363,8099,471],{"className":8100},[510],[363,8102],{"className":8103,"style":506},[505],[363,8105,8107,8110],{"className":8106},[407],[363,8108,571],{"className":8109},[407,714],[363,8111,8113],{"className":8112},[629],[363,8114,8116,8136],{"className":8115},[633,634],[363,8117,8119,8133],{"className":8118},[638],[363,8120,8122],{"className":8121,"style":727},[642],[363,8123,8124,8127],{"style":730},[363,8125],{"className":8126,"style":651},[650],[363,8128,8130],{"className":8129},[655,656,657,658],[363,8131,561],{"className":8132},[407,408,658],[363,8134,666],{"className":8135},[665],[363,8137,8139],{"className":8138},[638],[363,8140,8142],{"className":8141,"style":673},[642],[363,8143],{},[363,8145],{"className":8146,"style":1859},[505],[363,8148],{"className":8149,"style":754},[505],[363,8151,8153,8159,8162,8165,8168,8251],{"className":8152},[758],[363,8154,8156],{"className":8155,"style":763},[494,762],[363,8157,578],{"className":8158},[767,657],[363,8160,385],{"className":8161,"style":409},[407,408],[363,8163],{"className":8164,"style":1859},[505],[363,8166],{"className":8167,"style":754},[505],[363,8169,8171,8177,8245],{"className":8170},[758],[363,8172,8174],{"className":8173,"style":763},[494,762],[363,8175,461],{"className":8176},[767,657],[363,8178,8180,8183,8242],{"className":8179},[407],[363,8181],{"className":8182},[494,789],[363,8184,8186],{"className":8185},[586],[363,8187,8189,8234],{"className":8188},[633,634],[363,8190,8192,8231],{"className":8191},[638],[363,8193,8195,8209,8217],{"className":8194,"style":802},[642],[363,8196,8197,8200],{"style":805},[363,8198],{"className":8199,"style":809},[650],[363,8201,8203,8206],{"className":8202},[407],[363,8204,592],{"className":8205},[407,408],[363,8207,561],{"className":8208},[407,408],[363,8210,8211,8214],{"style":821},[363,8212],{"className":8213,"style":809},[650],[363,8215],{"className":8216,"style":829},[828],[363,8218,8219,8222],{"style":832},[363,8220],{"className":8221,"style":809},[650],[363,8223,8225,8228],{"className":8224},[407],[363,8226,592],{"className":8227},[407,408],[363,8229,554],{"className":8230,"style":682},[407,408],[363,8232,666],{"className":8233},[665],[363,8235,8237],{"className":8236},[638],[363,8238,8240],{"className":8239,"style":854},[642],[363,8241],{},[363,8243],{"className":8244},[501,789],[363,8246,8248],{"className":8247,"style":763},[501,762],[363,8249,468],{"className":8250},[767,657],[363,8252,8254],{"className":8253,"style":763},[501,762],[363,8255,605],{"className":8256},[767,657],[363,8258,8259,8262],{"style":1720},[363,8260],{"className":8261,"style":1724},[650],[363,8263,8265,8268,8271,8274,8277,8318,8321,8324],{"className":8264},[407],[363,8266],{"className":8267},[407],[363,8269],{"className":8270,"style":506},[505],[363,8272,471],{"className":8273},[510],[363,8275],{"className":8276,"style":506},[505],[363,8278,8280,8283],{"className":8279},[407],[363,8281,571],{"className":8282},[407,714],[363,8284,8286],{"className":8285},[629],[363,8287,8289,8309],{"className":8288},[633,634],[363,8290,8292,8306],{"className":8291},[638],[363,8293,8295],{"className":8294,"style":727},[642],[363,8296,8297,8300],{"style":730},[363,8298],{"className":8299,"style":651},[650],[363,8301,8303],{"className":8302},[655,656,657,658],[363,8304,554],{"className":8305,"style":682},[407,408,658],[363,8307,666],{"className":8308},[665],[363,8310,8312],{"className":8311},[638],[363,8313,8316],{"className":8314,"style":8315},[642],"height:0.15em;",[363,8317],{},[363,8319],{"className":8320,"style":1859},[505],[363,8322],{"className":8323,"style":754},[505],[363,8325,8327,8333,8401,8404,8407,8410,8413,8496],{"className":8326},[758],[363,8328,8330],{"className":8329,"style":763},[494,762],[363,8331,578],{"className":8332},[767,657],[363,8334,8336,8339,8398],{"className":8335},[407],[363,8337],{"className":8338},[494,789],[363,8340,8342],{"className":8341},[586],[363,8343,8345,8390],{"className":8344},[633,634],[363,8346,8348,8387],{"className":8347},[638],[363,8349,8351,8365,8373],{"className":8350,"style":802},[642],[363,8352,8353,8356],{"style":805},[363,8354],{"className":8355,"style":809},[650],[363,8357,8359,8362],{"className":8358},[407],[363,8360,592],{"className":8361},[407,408],[363,8363,554],{"className":8364,"style":682},[407,408],[363,8366,8367,8370],{"style":821},[363,8368],{"className":8369,"style":809},[650],[363,8371],{"className":8372,"style":829},[828],[363,8374,8375,8378],{"style":832},[363,8376],{"className":8377,"style":809},[650],[363,8379,8381,8384],{"className":8380},[407],[363,8382,592],{"className":8383},[407,408],[363,8385,561],{"className":8386},[407,408],[363,8388,666],{"className":8389},[665],[363,8391,8393],{"className":8392},[638],[363,8394,8396],{"className":8395,"style":4125},[642],[363,8397],{},[363,8399],{"className":8400},[501,789],[363,8402],{"className":8403,"style":754},[505],[363,8405,385],{"className":8406,"style":409},[407,408],[363,8408],{"className":8409,"style":1859},[505],[363,8411],{"className":8412,"style":754},[505],[363,8414,8416,8422,8490],{"className":8415},[758],[363,8417,8419],{"className":8418,"style":763},[494,762],[363,8420,461],{"className":8421},[767,657],[363,8423,8425,8428,8487],{"className":8424},[407],[363,8426],{"className":8427},[494,789],[363,8429,8431],{"className":8430},[586],[363,8432,8434,8479],{"className":8433},[633,634],[363,8435,8437,8476],{"className":8436},[638],[363,8438,8440,8454,8462],{"className":8439,"style":802},[642],[363,8441,8442,8445],{"style":805},[363,8443],{"className":8444,"style":809},[650],[363,8446,8448,8451],{"className":8447},[407],[363,8449,592],{"className":8450},[407,408],[363,8452,561],{"className":8453},[407,408],[363,8455,8456,8459],{"style":821},[363,8457],{"className":8458,"style":809},[650],[363,8460],{"className":8461,"style":829},[828],[363,8463,8464,8467],{"style":832},[363,8465],{"className":8466,"style":809},[650],[363,8468,8470,8473],{"className":8469},[407],[363,8471,592],{"className":8472},[407,408],[363,8474,554],{"className":8475,"style":682},[407,408],[363,8477,666],{"className":8478},[665],[363,8480,8482],{"className":8481},[638],[363,8483,8485],{"className":8484,"style":854},[642],[363,8486],{},[363,8488],{"className":8489},[501,789],[363,8491,8493],{"className":8492,"style":763},[501,762],[363,8494,468],{"className":8495},[767,657],[363,8497,8499],{"className":8498,"style":763},[501,762],[363,8500,605],{"className":8501},[767,657],[363,8503,8504,8507],{"style":8053},[363,8505],{"className":8506,"style":1724},[650],[363,8508,8510,8513,8516,8519,8522,8562,8565,8568,8744,8747],{"className":8509},[407],[363,8511],{"className":8512},[407],[363,8514],{"className":8515,"style":506},[505],[363,8517,471],{"className":8518},[510],[363,8520],{"className":8521,"style":506},[505],[363,8523,8525,8528],{"className":8524},[407],[363,8526,571],{"className":8527},[407,714],[363,8529,8531],{"className":8530},[629],[363,8532,8534,8554],{"className":8533},[633,634],[363,8535,8537,8551],{"className":8536},[638],[363,8538,8540],{"className":8539,"style":727},[642],[363,8541,8542,8545],{"style":730},[363,8543],{"className":8544,"style":651},[650],[363,8546,8548],{"className":8547},[655,656,657,658],[363,8549,554],{"className":8550,"style":682},[407,408,658],[363,8552,666],{"className":8553},[665],[363,8555,8557],{"className":8556},[638],[363,8558,8560],{"className":8559,"style":8315},[642],[363,8561],{},[363,8563],{"className":8564,"style":1859},[505],[363,8566],{"className":8567,"style":754},[505],[363,8569,8571,8577,8649,8652,8655,8738],{"className":8570},[758],[363,8572,8574],{"className":8573,"style":763},[494,762],[363,8575,578],{"className":8576},[767,657],[363,8578,8580,8583],{"className":8579},[407],[363,8581,385],{"className":8582,"style":409},[407,408],[363,8584,8586],{"className":8585},[629],[363,8587,8589,8640],{"className":8588},[633,634],[363,8590,8592,8637],{"className":8591},[638],[363,8593,8596,8622],{"className":8594,"style":8595},[642],"height:0.7387em;",[363,8597,8599,8602],{"style":8598},"top:-2.453em;margin-left:-0.1076em;margin-right:0.05em;",[363,8600],{"className":8601,"style":651},[650],[363,8603,8605],{"className":8604},[655,656,657,658],[363,8606,8608,8611,8615,8618],{"className":8607},[407,658],[363,8609,7908],{"className":8610},[407,408,658],[363,8612,7911],{"className":8613,"style":8614},[407,408,658],"margin-right:0.0315em;",[363,8616,7914],{"className":8617},[407,408,658],[363,8619,7917],{"className":8620,"style":8621},[407,408,658],"margin-right:0.0269em;",[363,8623,8625,8628],{"style":8624},"top:-3.113em;margin-right:0.05em;",[363,8626],{"className":8627,"style":651},[650],[363,8629,8631],{"className":8630},[655,656,657,658],[363,8632,8634],{"className":8633},[407,658],[363,8635,7920],{"className":8636},[407,658],[363,8638,666],{"className":8639},[665],[363,8641,8643],{"className":8642},[638],[363,8644,8647],{"className":8645,"style":8646},[642],"height:0.247em;",[363,8648],{},[363,8650],{"className":8651,"style":1859},[505],[363,8653],{"className":8654,"style":754},[505],[363,8656,8658,8664,8732],{"className":8657},[758],[363,8659,8661],{"className":8660,"style":763},[494,762],[363,8662,461],{"className":8663},[767,657],[363,8665,8667,8670,8729],{"className":8666},[407],[363,8668],{"className":8669},[494,789],[363,8671,8673],{"className":8672},[586],[363,8674,8676,8721],{"className":8675},[633,634],[363,8677,8679,8718],{"className":8678},[638],[363,8680,8682,8696,8704],{"className":8681,"style":802},[642],[363,8683,8684,8687],{"style":805},[363,8685],{"className":8686,"style":809},[650],[363,8688,8690,8693],{"className":8689},[407],[363,8691,592],{"className":8692},[407,408],[363,8694,554],{"className":8695,"style":682},[407,408],[363,8697,8698,8701],{"style":821},[363,8699],{"className":8700,"style":809},[650],[363,8702],{"className":8703,"style":829},[828],[363,8705,8706,8709],{"style":832},[363,8707],{"className":8708,"style":809},[650],[363,8710,8712,8715],{"className":8711},[407],[363,8713,592],{"className":8714},[407,408],[363,8716,561],{"className":8717},[407,408],[363,8719,666],{"className":8720},[665],[363,8722,8724],{"className":8723},[638],[363,8725,8727],{"className":8726,"style":4125},[642],[363,8728],{},[363,8730],{"className":8731},[501,789],[363,8733,8735],{"className":8734,"style":763},[501,762],[363,8736,468],{"className":8737},[767,657],[363,8739,8741],{"className":8740,"style":763},[501,762],[363,8742,605],{"className":8743},[767,657],[363,8745],{"className":8746,"style":754},[505],[363,8748,898],{"className":8749},[920],[363,8751,666],{"className":8752},[665],[363,8754,8756],{"className":8755},[638],[363,8757,8759],{"className":8758,"style":8069},[642],[363,8760],{},[11,8762,2597,8763,8943,8944,8985,8986,9014,9015,9095],{},[363,8764,8766,8818],{"className":8765,"translate":367},[366],[363,8767,8769],{"className":8768},[371],[373,8770,8771],{"xmlns":375},[377,8772,8773,8815],{},[380,8774,8775,8791,8793,8795,8797,8799,8801,8803,8805,8807,8809,8811,8813],{},[7900,8776,8777,8779,8789],{},[383,8778,385],{},[380,8780,8781,8783,8785,8787],{},[383,8782,7908],{},[383,8784,7911],{},[383,8786,7914],{},[383,8788,7917],{},[458,8790,7920],{"lspace":1594,"rspace":1594},[458,8792,461],{"stretchy":460},[383,8794,1116],{},[458,8796,468],{"stretchy":460},[458,8798,471],{},[383,8800,1116],{},[1644,8802,1646],{},[383,8804,385],{},[458,8806,461],{"stretchy":460},[463,8808,465],{},[383,8810,1288],{"mathvariant":557},[383,8812,1116],{},[458,8814,468],{"stretchy":460},[387,8816,8817],{"encoding":389},"f^{*}_{skew}(t)=t\\,f(1\u002Ft)",[363,8819,8821,8915],{"className":8820,"ariaHidden":394},[393],[363,8822,8824,8828,8897,8900,8903,8906,8909,8912],{"className":8823},[398],[363,8825],{"className":8826,"style":8827},[402],"height:1.0331em;vertical-align:-0.2831em;",[363,8829,8831,8834],{"className":8830},[407],[363,8832,385],{"className":8833,"style":409},[407,408],[363,8835,8837],{"className":8836},[629],[363,8838,8840,8888],{"className":8839},[633,634],[363,8841,8843,8885],{"className":8842},[638],[363,8844,8847,8871],{"className":8845,"style":8846},[642],"height:0.6887em;",[363,8848,8850,8853],{"style":8849},"top:-2.4169em;margin-left:-0.1076em;margin-right:0.05em;",[363,8851],{"className":8852,"style":651},[650],[363,8854,8856],{"className":8855},[655,656,657,658],[363,8857,8859,8862,8865,8868],{"className":8858},[407,658],[363,8860,7908],{"className":8861},[407,408,658],[363,8863,7911],{"className":8864,"style":8614},[407,408,658],[363,8866,7914],{"className":8867},[407,408,658],[363,8869,7917],{"className":8870,"style":8621},[407,408,658],[363,8872,8873,8876],{"style":7212},[363,8874],{"className":8875,"style":651},[650],[363,8877,8879],{"className":8878},[655,656,657,658],[363,8880,8882],{"className":8881},[407,658],[363,8883,7920],{"className":8884},[407,658],[363,8886,666],{"className":8887},[665],[363,8889,8891],{"className":8890},[638],[363,8892,8895],{"className":8893,"style":8894},[642],"height:0.2831em;",[363,8896],{},[363,8898,461],{"className":8899},[494],[363,8901,1116],{"className":8902},[407,408],[363,8904,468],{"className":8905},[501],[363,8907],{"className":8908,"style":506},[505],[363,8910,471],{"className":8911},[510],[363,8913],{"className":8914,"style":506},[505],[363,8916,8918,8921,8924,8927,8930,8933,8937,8940],{"className":8917},[398],[363,8919],{"className":8920,"style":487},[402],[363,8922,1116],{"className":8923},[407,408],[363,8925],{"className":8926,"style":754},[505],[363,8928,385],{"className":8929,"style":409},[407,408],[363,8931,461],{"className":8932},[494],[363,8934,8936],{"className":8935},[407],"1\u002F",[363,8938,1116],{"className":8939},[407,408],[363,8941,468],{"className":8942},[501]," 是后面 4.3 节的「斜共轭」。最后一个等式说明：交换 ",[363,8945,8947,8964],{"className":8946,"translate":367},[366],[363,8948,8950],{"className":8949},[371],[373,8951,8952],{"xmlns":375},[377,8953,8954,8962],{},[380,8955,8956,8958,8960],{},[383,8957,554],{},[458,8959,898],{"separator":394},[383,8961,561],{},[387,8963,903],{"encoding":389},[363,8965,8967],{"className":8966,"ariaHidden":394},[393],[363,8968,8970,8973,8976,8979,8982],{"className":8969},[398],[363,8971],{"className":8972,"style":913},[402],[363,8974,554],{"className":8975,"style":682},[407,408],[363,8977,898],{"className":8978},[920],[363,8980],{"className":8981,"style":754},[505],[363,8983,561],{"className":8984},[407,408]," 只是把 ",[363,8987,8989,9002],{"className":8988,"translate":367},[366],[363,8990,8992],{"className":8991},[371],[373,8993,8994],{"xmlns":375},[377,8995,8996,9000],{},[380,8997,8998],{},[383,8999,385],{},[387,9001,385],{"encoding":389},[363,9003,9005],{"className":9004,"ariaHidden":394},[393],[363,9006,9008,9011],{"className":9007},[398],[363,9009],{"className":9010,"style":403},[402],[363,9012,385],{"className":9013,"style":409},[407,408]," 换成 ",[363,9016,9018,9049],{"className":9017,"translate":367},[366],[363,9019,9021],{"className":9020},[371],[373,9022,9023],{"xmlns":375},[377,9024,9025,9046],{},[380,9026,9027,9029,9032,9034,9036,9038,9040,9042,9044],{},[383,9028,1116],{},[458,9030,9031],{},"↦",[383,9033,1116],{},[383,9035,385],{},[458,9037,461],{"stretchy":460},[463,9039,465],{},[383,9041,1288],{"mathvariant":557},[383,9043,1116],{},[458,9045,468],{"stretchy":460},[387,9047,9048],{"encoding":389},"t\\mapsto t f(1\u002Ft)",[363,9050,9052,9071],{"className":9051,"ariaHidden":394},[393],[363,9053,9055,9059,9062,9065,9068],{"className":9054},[398],[363,9056],{"className":9057,"style":9058},[402],"height:0.6261em;vertical-align:-0.011em;",[363,9060,1116],{"className":9061},[407,408],[363,9063],{"className":9064,"style":506},[505],[363,9066,9031],{"className":9067},[510],[363,9069],{"className":9070,"style":506},[505],[363,9072,9074,9077,9080,9083,9086,9089,9092],{"className":9073},[398],[363,9075],{"className":9076,"style":487},[402],[363,9078,1116],{"className":9079},[407,408],[363,9081,385],{"className":9082,"style":409},[407,408],[363,9084,461],{"className":9085},[494],[363,9087,8936],{"className":9088},[407],[363,9090,1116],{"className":9091},[407,408],[363,9093,468],{"className":9094},[501],"，这对推导「反向 KL」之类的对称性非常方便。",[18,9097,9099,9100,9128,9129],{"id":9098},"_2-为何-fff-凸且-f10f10f10","2. 为何 ",[363,9101,9103,9116],{"className":9102,"translate":367},[366],[363,9104,9106],{"className":9105},[371],[373,9107,9108],{"xmlns":375},[377,9109,9110,9114],{},[380,9111,9112],{},[383,9113,385],{},[387,9115,385],{"encoding":389},[363,9117,9119],{"className":9118,"ariaHidden":394},[393],[363,9120,9122,9125],{"className":9121},[398],[363,9123],{"className":9124,"style":403},[402],[363,9126,385],{"className":9127,"style":409},[407,408]," 凸且 ",[363,9130,9132,9155],{"className":9131,"translate":367},[366],[363,9133,9135],{"className":9134},[371],[373,9136,9137],{"xmlns":375},[377,9138,9139,9153],{},[380,9140,9141,9143,9145,9147,9149,9151],{},[383,9142,385],{},[458,9144,461],{"stretchy":460},[463,9146,465],{},[458,9148,468],{"stretchy":460},[458,9150,471],{},[463,9152,474],{},[387,9154,477],{"encoding":389},[363,9156,9158,9185],{"className":9157,"ariaHidden":394},[393],[363,9159,9161,9164,9167,9170,9173,9176,9179,9182],{"className":9160},[398],[363,9162],{"className":9163,"style":487},[402],[363,9165,385],{"className":9166,"style":409},[407,408],[363,9168,461],{"className":9169},[494],[363,9171,465],{"className":9172},[407],[363,9174,468],{"className":9175},[501],[363,9177],{"className":9178,"style":506},[505],[363,9180,471],{"className":9181},[510],[363,9183],{"className":9184,"style":506},[505],[363,9186,9188,9191],{"className":9187},[398],[363,9189],{"className":9190,"style":520},[402],[363,9192,474],{"className":9193},[407],[2658,9195,9197],{"id":9196},"_21-非负性与-jensen","2.1 非负性与 Jensen",[11,9199,881,9200,1513,9253,9297,9298,9367,9368,9438],{},[363,9201,9203,9222],{"className":9202,"translate":367},[366],[363,9204,9206],{"className":9205},[371],[373,9207,9208],{"xmlns":375},[377,9209,9210,9219],{},[380,9211,9212,9214,9217],{},[383,9213,945],{},[458,9215,9216],{},"∼",[383,9218,561],{},[387,9220,9221],{"encoding":389},"X\\sim Q",[363,9223,9225,9244],{"className":9224,"ariaHidden":394},[393],[363,9226,9228,9231,9235,9238,9241],{"className":9227},[398],[363,9229],{"className":9230,"style":1011},[402],[363,9232,945],{"className":9233,"style":9234},[407,408],"margin-right:0.0785em;",[363,9236],{"className":9237,"style":506},[505],[363,9239,9216],{"className":9240},[510],[363,9242],{"className":9243,"style":506},[505],[363,9245,9247,9250],{"className":9246},[398],[363,9248],{"className":9249,"style":913},[402],[363,9251,561],{"className":9252},[407,408],[363,9254,9256,9276],{"className":9255,"translate":367},[366],[363,9257,9259],{"className":9258},[371],[373,9260,9261],{"xmlns":375},[377,9262,9263,9273],{},[380,9264,9265,9267,9269,9271],{},[383,9266,385],{},[458,9268,461],{"stretchy":460},[383,9270,945],{},[458,9272,468],{"stretchy":460},[387,9274,9275],{"encoding":389},"f(X)",[363,9277,9279],{"className":9278,"ariaHidden":394},[393],[363,9280,9282,9285,9288,9291,9294],{"className":9281},[398],[363,9283],{"className":9284,"style":487},[402],[363,9286,385],{"className":9287,"style":409},[407,408],[363,9289,461],{"className":9290},[494],[363,9292,945],{"className":9293,"style":9234},[407,408],[363,9295,468],{"className":9296},[501]," 的期望就是 ",[363,9299,9301,9318],{"className":9300,"translate":367},[366],[363,9302,9304],{"className":9303},[371],[373,9305,9306],{"xmlns":375},[377,9307,9308,9316],{},[380,9309,9310],{},[543,9311,9312,9314],{},[383,9313,547],{},[383,9315,385],{},[387,9317,4369],{"encoding":389},[363,9319,9321],{"className":9320,"ariaHidden":394},[393],[363,9322,9324,9327],{"className":9323},[398],[363,9325],{"className":9326,"style":4379},[402],[363,9328,9330,9333],{"className":9329},[407],[363,9331,547],{"className":9332,"style":625},[407,408],[363,9334,9336],{"className":9335},[629],[363,9337,9339,9359],{"className":9338},[633,634],[363,9340,9342,9356],{"className":9341},[638],[363,9343,9345],{"className":9344,"style":643},[642],[363,9346,9347,9350],{"style":646},[363,9348],{"className":9349,"style":651},[650],[363,9351,9353],{"className":9352},[655,656,657,658],[363,9354,385],{"className":9355,"style":409},[407,408,658],[363,9357,666],{"className":9358},[665],[363,9360,9362],{"className":9361},[638],[363,9363,9365],{"className":9364,"style":673},[642],[363,9366],{},"。因为 ",[363,9369,9371,9396],{"className":9370,"translate":367},[366],[363,9372,9374],{"className":9373},[371],[373,9375,9376],{"xmlns":375},[377,9377,9378,9394],{},[380,9379,9380,9382,9384,9386,9388,9390,9392],{},[383,9381,1116],{},[458,9383,471],{},[383,9385,592],{},[383,9387,554],{},[383,9389,1288],{"mathvariant":557},[383,9391,592],{},[383,9393,561],{},[387,9395,5680],{"encoding":389},[363,9397,9399,9417],{"className":9398,"ariaHidden":394},[393],[363,9400,9402,9405,9408,9411,9414],{"className":9401},[398],[363,9403],{"className":9404,"style":5690},[402],[363,9406,1116],{"className":9407},[407,408],[363,9409],{"className":9410,"style":506},[505],[363,9412,471],{"className":9413},[510],[363,9415],{"className":9416,"style":506},[505],[363,9418,9420,9423,9426,9429,9432,9435],{"className":9419},[398],[363,9421],{"className":9422,"style":487},[402],[363,9424,592],{"className":9425},[407,408],[363,9427,554],{"className":9428,"style":682},[407,408],[363,9430,1288],{"className":9431},[407],[363,9433,592],{"className":9434},[407,408],[363,9436,561],{"className":9437},[407,408]," 满足",[363,9440,9442],{"className":9441,"translate":367},[528],[363,9443,9445,9507],{"className":9444,"translate":367},[366],[363,9446,9448],{"className":9447},[371],[373,9449,9450],{"xmlns":375,"display":537},[377,9451,9452,9504],{},[380,9453,9454,9460,9462,9464,9466,9468,9470,9484,9486,9488,9490,9492,9494,9496,9498,9500,9502],{},[543,9455,9456,9458],{},[383,9457,571],{"mathvariant":570},[383,9459,561],{},[458,9461,578],{"stretchy":460},[383,9463,1116],{},[458,9465,605],{"stretchy":460},[458,9467,471],{},[458,9469,1634],{},[586,9471,9472,9478],{},[380,9473,9474,9476],{},[383,9475,592],{},[383,9477,554],{},[380,9479,9480,9482],{},[383,9481,592],{},[383,9483,561],{},[1644,9485,1646],{},[383,9487,592],{},[383,9489,561],{},[458,9491,471],{},[458,9493,1634],{},[383,9495,592],{},[383,9497,554],{},[458,9499,471],{},[463,9501,465],{},[458,9503,898],{"separator":394},[387,9505,9506],{"encoding":389},"\\mathbb E_Q[t]=\\int \\frac{dP}{dQ}\\,dQ=\\int dP=1,",[363,9508,9510,9574,9672,9699],{"className":9509,"ariaHidden":394},[393],[363,9511,9513,9516,9556,9559,9562,9565,9568,9571],{"className":9512},[398],[363,9514],{"className":9515,"style":618},[402],[363,9517,9519,9522],{"className":9518},[407],[363,9520,571],{"className":9521},[407,714],[363,9523,9525],{"className":9524},[629],[363,9526,9528,9548],{"className":9527},[633,634],[363,9529,9531,9545],{"className":9530},[638],[363,9532,9534],{"className":9533,"style":727},[642],[363,9535,9536,9539],{"style":730},[363,9537],{"className":9538,"style":651},[650],[363,9540,9542],{"className":9541},[655,656,657,658],[363,9543,561],{"className":9544},[407,408,658],[363,9546,666],{"className":9547},[665],[363,9549,9551],{"className":9550},[638],[363,9552,9554],{"className":9553,"style":673},[642],[363,9555],{},[363,9557,578],{"className":9558},[494],[363,9560,1116],{"className":9561},[407,408],[363,9563,605],{"className":9564},[501],[363,9566],{"className":9567,"style":506},[505],[363,9569,471],{"className":9570},[510],[363,9572],{"className":9573,"style":506},[505],[363,9575,9577,9580,9583,9586,9654,9657,9660,9663,9666,9669],{"className":9576},[398],[363,9578],{"className":9579,"style":1185},[402],[363,9581,1634],{"className":9582,"style":1834},[1831,1832,1833],[363,9584],{"className":9585,"style":754},[505],[363,9587,9589,9592,9651],{"className":9588},[407],[363,9590],{"className":9591},[494,789],[363,9593,9595],{"className":9594},[586],[363,9596,9598,9643],{"className":9597},[633,634],[363,9599,9601,9640],{"className":9600},[638],[363,9602,9604,9618,9626],{"className":9603,"style":802},[642],[363,9605,9606,9609],{"style":805},[363,9607],{"className":9608,"style":809},[650],[363,9610,9612,9615],{"className":9611},[407],[363,9613,592],{"className":9614},[407,408],[363,9616,561],{"className":9617},[407,408],[363,9619,9620,9623],{"style":821},[363,9621],{"className":9622,"style":809},[650],[363,9624],{"className":9625,"style":829},[828],[363,9627,9628,9631],{"style":832},[363,9629],{"className":9630,"style":809},[650],[363,9632,9634,9637],{"className":9633},[407],[363,9635,592],{"className":9636},[407,408],[363,9638,554],{"className":9639,"style":682},[407,408],[363,9641,666],{"className":9642},[665],[363,9644,9646],{"className":9645},[638],[363,9647,9649],{"className":9648,"style":854},[642],[363,9650],{},[363,9652],{"className":9653},[501,789],[363,9655],{"className":9656,"style":754},[505],[363,9658,592],{"className":9659},[407,408],[363,9661,561],{"className":9662},[407,408],[363,9664],{"className":9665,"style":506},[505],[363,9667,471],{"className":9668},[510],[363,9670],{"className":9671,"style":506},[505],[363,9673,9675,9678,9681,9684,9687,9690,9693,9696],{"className":9674},[398],[363,9676],{"className":9677,"style":6124},[402],[363,9679,1634],{"className":9680,"style":1834},[1831,1832,1833],[363,9682],{"className":9683,"style":754},[505],[363,9685,592],{"className":9686},[407,408],[363,9688,554],{"className":9689,"style":682},[407,408],[363,9691],{"className":9692,"style":506},[505],[363,9694,471],{"className":9695},[510],[363,9697],{"className":9698,"style":506},[505],[363,9700,9702,9706,9709],{"className":9701},[398],[363,9703],{"className":9704,"style":9705},[402],"height:0.8389em;vertical-align:-0.1944em;",[363,9707,465],{"className":9708},[407],[363,9710,898],{"className":9711},[920],[11,9713,9714,9715,9743,9744,9747],{},"对凸函数 ",[363,9716,9718,9731],{"className":9717,"translate":367},[366],[363,9719,9721],{"className":9720},[371],[373,9722,9723],{"xmlns":375},[377,9724,9725,9729],{},[380,9726,9727],{},[383,9728,385],{},[387,9730,385],{"encoding":389},[363,9732,9734],{"className":9733,"ariaHidden":394},[393],[363,9735,9737,9740],{"className":9736},[398],[363,9738],{"className":9739,"style":403},[402],[363,9741,385],{"className":9742,"style":409},[407,408]," 用 ",[1572,9745,9746],{},"Jensen 不等式","：",[363,9749,9751],{"className":9750,"translate":367},[528],[363,9752,9754,9873],{"className":9753,"translate":367},[366],[363,9755,9757],{"className":9756},[371],[373,9758,9759],{"xmlns":375,"display":537},[377,9760,9761,9870],{},[1590,9762,9763,9840],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,9764,9765,9808],{},[1599,9766,9767],{},[1602,9768,9769],{"scriptlevel":474,"displaystyle":394},[380,9770,9771,9777,9779,9781,9783,9785,9787,9789,9795,9798,9800,9802,9804,9806],{},[543,9772,9773,9775],{},[383,9774,547],{},[383,9776,385],{},[458,9778,461],{"stretchy":460},[383,9780,554],{},[383,9782,558],{"mathvariant":557},[383,9784,561],{},[458,9786,468],{"stretchy":460},[458,9788,471],{},[543,9790,9791,9793],{},[383,9792,571],{"mathvariant":570},[383,9794,561],{},[458,9796,578],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},"1.2em",[383,9799,385],{},[458,9801,461],{"stretchy":460},[383,9803,1116],{},[458,9805,468],{"stretchy":460},[458,9807,605],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[1599,9809,9810],{},[1602,9811,9812],{"scriptlevel":474,"displaystyle":394},[380,9813,9814,9816,9818,9820,9822,9824,9826,9832,9834,9836,9838],{},[380,9815],{},[1644,9817,4630],{},[458,9819,7275],{},[1644,9821,4630],{},[383,9823,385],{},[458,9825,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[543,9827,9828,9830],{},[383,9829,571],{"mathvariant":570},[383,9831,561],{},[458,9833,578],{"stretchy":460},[383,9835,1116],{},[458,9837,605],{"stretchy":460},[458,9839,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[1596,9841,9842,9848],{},[1599,9843,9844],{},[1602,9845,9846],{"scriptlevel":474,"displaystyle":394},[380,9847],{},[1599,9849,9850],{},[1602,9851,9852],{"scriptlevel":474,"displaystyle":394},[380,9853,9854,9856,9858,9860,9862,9864,9866,9868],{},[380,9855],{},[458,9857,471],{},[383,9859,385],{},[458,9861,461],{"stretchy":460},[463,9863,465],{},[458,9865,468],{"stretchy":460},[458,9867,471],{},[463,9869,6111],{},[387,9871,9872],{"encoding":389},"\\begin{aligned}\nD_f(P\\|Q)=\\mathbb E_Q\\big[f(t)\\big]\n&\\ \\ge\\ f\\big(\\mathbb E_Q[t]\\big)\\\\[2pt]\n&=f(1)=0 .\n\\end{aligned}",[363,9874,9876],{"className":9875,"ariaHidden":394},[393],[363,9877,9879,9883],{"className":9878},[398],[363,9880],{"className":9881,"style":9882},[402],"height:2.91em;vertical-align:-1.205em;",[363,9884,9886],{"className":9885},[407],[363,9887,9889,10061],{"className":9888},[1590],[363,9890,9892],{"className":9891},[1707],[363,9893,9895,10052],{"className":9894},[633,634],[363,9896,9898,10049],{"className":9897},[638],[363,9899,9902,10040],{"className":9900,"style":9901},[642],"height:1.705em;",[363,9903,9905,9908],{"style":9904},"top:-3.855em;",[363,9906],{"className":9907,"style":809},[650],[363,9909,9911,9951,9954,9957,9960,9963,9966,9969,9972,9975,10015,10022,10025,10028,10031,10034],{"className":9910},[407],[363,9912,9914,9917],{"className":9913},[407],[363,9915,547],{"className":9916,"style":625},[407,408],[363,9918,9920],{"className":9919},[629],[363,9921,9923,9943],{"className":9922},[633,634],[363,9924,9926,9940],{"className":9925},[638],[363,9927,9929],{"className":9928,"style":643},[642],[363,9930,9931,9934],{"style":646},[363,9932],{"className":9933,"style":651},[650],[363,9935,9937],{"className":9936},[655,656,657,658],[363,9938,385],{"className":9939,"style":409},[407,408,658],[363,9941,666],{"className":9942},[665],[363,9944,9946],{"className":9945},[638],[363,9947,9949],{"className":9948,"style":673},[642],[363,9950],{},[363,9952,461],{"className":9953},[494],[363,9955,554],{"className":9956,"style":682},[407,408],[363,9958,558],{"className":9959},[407],[363,9961,561],{"className":9962},[407,408],[363,9964,468],{"className":9965},[501],[363,9967],{"className":9968,"style":506},[505],[363,9970,471],{"className":9971},[510],[363,9973],{"className":9974,"style":506},[505],[363,9976,9978,9981],{"className":9977},[407],[363,9979,571],{"className":9980},[407,714],[363,9982,9984],{"className":9983},[629],[363,9985,9987,10007],{"className":9986},[633,634],[363,9988,9990,10004],{"className":9989},[638],[363,9991,9993],{"className":9992,"style":727},[642],[363,9994,9995,9998],{"style":730},[363,9996],{"className":9997,"style":651},[650],[363,9999,10001],{"className":10000},[655,656,657,658],[363,10002,561],{"className":10003},[407,408,658],[363,10005,666],{"className":10006},[665],[363,10008,10010],{"className":10009},[638],[363,10011,10013],{"className":10012,"style":673},[642],[363,10014],{},[363,10016,10018],{"className":10017},[407],[363,10019,578],{"className":10020},[767,10021],"size1",[363,10023,385],{"className":10024,"style":409},[407,408],[363,10026,461],{"className":10027},[494],[363,10029,1116],{"className":10030},[407,408],[363,10032,468],{"className":10033},[501],[363,10035,10037],{"className":10036},[407],[363,10038,605],{"className":10039},[767,10021],[363,10041,10043,10046],{"style":10042},"top:-2.155em;",[363,10044],{"className":10045,"style":809},[650],[363,10047],{"className":10048},[407],[363,10050,666],{"className":10051},[665],[363,10053,10055],{"className":10054},[638],[363,10056,10059],{"className":10057,"style":10058},[642],"height:1.205em;",[363,10060],{},[363,10062,10064],{"className":10063},[1798],[363,10065,10067,10210],{"className":10066},[633,634],[363,10068,10070,10207],{"className":10069},[638],[363,10071,10073,10163],{"className":10072,"style":9901},[642],[363,10074,10075,10078],{"style":9904},[363,10076],{"className":10077,"style":809},[650],[363,10079,10081,10084,10087,10090,10093,10096,10099,10102,10108,10148,10151,10154,10157],{"className":10080},[407],[363,10082],{"className":10083},[407],[363,10085,4630],{"className":10086},[505],[363,10088],{"className":10089,"style":506},[505],[363,10091,7275],{"className":10092},[510],[363,10094,4630],{"className":10095},[505],[363,10097],{"className":10098,"style":506},[505],[363,10100,385],{"className":10101,"style":409},[407,408],[363,10103,10105],{"className":10104},[407],[363,10106,461],{"className":10107},[767,10021],[363,10109,10111,10114],{"className":10110},[407],[363,10112,571],{"className":10113},[407,714],[363,10115,10117],{"className":10116},[629],[363,10118,10120,10140],{"className":10119},[633,634],[363,10121,10123,10137],{"className":10122},[638],[363,10124,10126],{"className":10125,"style":727},[642],[363,10127,10128,10131],{"style":730},[363,10129],{"className":10130,"style":651},[650],[363,10132,10134],{"className":10133},[655,656,657,658],[363,10135,561],{"className":10136},[407,408,658],[363,10138,666],{"className":10139},[665],[363,10141,10143],{"className":10142},[638],[363,10144,10146],{"className":10145,"style":673},[642],[363,10147],{},[363,10149,578],{"className":10150},[494],[363,10152,1116],{"className":10153},[407,408],[363,10155,605],{"className":10156},[501],[363,10158,10160],{"className":10159},[407],[363,10161,468],{"className":10162},[767,10021],[363,10164,10165,10168],{"style":10042},[363,10166],{"className":10167,"style":809},[650],[363,10169,10171,10174,10177,10180,10183,10186,10189,10192,10195,10198,10201,10204],{"className":10170},[407],[363,10172],{"className":10173},[407],[363,10175],{"className":10176,"style":506},[505],[363,10178,471],{"className":10179},[510],[363,10181],{"className":10182,"style":506},[505],[363,10184,385],{"className":10185,"style":409},[407,408],[363,10187,461],{"className":10188},[494],[363,10190,465],{"className":10191},[407],[363,10193,468],{"className":10194},[501],[363,10196],{"className":10197,"style":506},[505],[363,10199,471],{"className":10200},[510],[363,10202],{"className":10203,"style":506},[505],[363,10205,6111],{"className":10206},[407],[363,10208,666],{"className":10209},[665],[363,10211,10213],{"className":10212},[638],[363,10214,10216],{"className":10215,"style":10058},[642],[363,10217],{},[11,10219,10220,10221,10249,10250,10278,10279,10372],{},"这就是非负性。",[363,10222,10224,10237],{"className":10223,"translate":367},[366],[363,10225,10227],{"className":10226},[371],[373,10228,10229],{"xmlns":375},[377,10230,10231,10235],{},[380,10232,10233],{},[383,10234,385],{},[387,10236,385],{"encoding":389},[363,10238,10240],{"className":10239,"ariaHidden":394},[393],[363,10241,10243,10246],{"className":10242},[398],[363,10244],{"className":10245,"style":403},[402],[363,10247,385],{"className":10248,"style":409},[407,408]," 的凸性是关键：若 ",[363,10251,10253,10266],{"className":10252,"translate":367},[366],[363,10254,10256],{"className":10255},[371],[373,10257,10258],{"xmlns":375},[377,10259,10260,10264],{},[380,10261,10262],{},[383,10263,385],{},[387,10265,385],{"encoding":389},[363,10267,10269],{"className":10268,"ariaHidden":394},[393],[363,10270,10272,10275],{"className":10271},[398],[363,10273],{"className":10274,"style":403},[402],[363,10276,385],{"className":10277,"style":409},[407,408]," 是凹函数，Jensen 方向反转，",[363,10280,10282,10305],{"className":10281,"translate":367},[366],[363,10283,10285],{"className":10284},[371],[373,10286,10287],{"xmlns":375},[377,10288,10289,10302],{},[380,10290,10291,10297,10300],{},[543,10292,10293,10295],{},[383,10294,547],{},[383,10296,385],{},[458,10298,10299],{},"≤",[463,10301,474],{},[387,10303,10304],{"encoding":389},"D_f\\le 0",[363,10306,10308,10363],{"className":10307,"ariaHidden":394},[393],[363,10309,10311,10314,10354,10357,10360],{"className":10310},[398],[363,10312],{"className":10313,"style":4379},[402],[363,10315,10317,10320],{"className":10316},[407],[363,10318,547],{"className":10319,"style":625},[407,408],[363,10321,10323],{"className":10322},[629],[363,10324,10326,10346],{"className":10325},[633,634],[363,10327,10329,10343],{"className":10328},[638],[363,10330,10332],{"className":10331,"style":643},[642],[363,10333,10334,10337],{"style":646},[363,10335],{"className":10336,"style":651},[650],[363,10338,10340],{"className":10339},[655,656,657,658],[363,10341,385],{"className":10342,"style":409},[407,408,658],[363,10344,666],{"className":10345},[665],[363,10347,10349],{"className":10348},[638],[363,10350,10352],{"className":10351,"style":673},[642],[363,10353],{},[363,10355],{"className":10356,"style":506},[505],[363,10358,10299],{"className":10359},[510],[363,10361],{"className":10362,"style":506},[505],[363,10364,10366,10369],{"className":10365},[398],[363,10367],{"className":10368,"style":520},[402],[363,10370,474],{"className":10371},[407],"，那就不是「散度」了。",[10374,10375,10376,10528],"ul",{},[7012,10377,10378,10409,10410,10527],{},[1572,10379,10380,10408],{},[363,10381,10383,10396],{"className":10382,"translate":367},[366],[363,10384,10386],{"className":10385},[371],[373,10387,10388],{"xmlns":375},[377,10389,10390,10394],{},[380,10391,10392],{},[383,10393,385],{},[387,10395,385],{"encoding":389},[363,10397,10399],{"className":10398,"ariaHidden":394},[393],[363,10400,10402,10405],{"className":10401},[398],[363,10403],{"className":10404,"style":403},[402],[363,10406,385],{"className":10407,"style":409},[407,408]," 凸","：保证 ",[363,10411,10413,10445],{"className":10412,"translate":367},[366],[363,10414,10416],{"className":10415},[371],[373,10417,10418],{"xmlns":375},[377,10419,10420,10442],{},[380,10421,10422,10428,10430,10432,10434,10436,10438,10440],{},[543,10423,10424,10426],{},[383,10425,547],{},[383,10427,385],{},[458,10429,461],{"stretchy":460},[383,10431,554],{},[383,10433,558],{"mathvariant":557},[383,10435,561],{},[458,10437,468],{"stretchy":460},[458,10439,7275],{},[463,10441,474],{},[387,10443,10444],{"encoding":389},"D_f(P\\|Q)\\ge 0",[363,10446,10448,10518],{"className":10447,"ariaHidden":394},[393],[363,10449,10451,10454,10494,10497,10500,10503,10506,10509,10512,10515],{"className":10450},[398],[363,10452],{"className":10453,"style":618},[402],[363,10455,10457,10460],{"className":10456},[407],[363,10458,547],{"className":10459,"style":625},[407,408],[363,10461,10463],{"className":10462},[629],[363,10464,10466,10486],{"className":10465},[633,634],[363,10467,10469,10483],{"className":10468},[638],[363,10470,10472],{"className":10471,"style":643},[642],[363,10473,10474,10477],{"style":646},[363,10475],{"className":10476,"style":651},[650],[363,10478,10480],{"className":10479},[655,656,657,658],[363,10481,385],{"className":10482,"style":409},[407,408,658],[363,10484,666],{"className":10485},[665],[363,10487,10489],{"className":10488},[638],[363,10490,10492],{"className":10491,"style":673},[642],[363,10493],{},[363,10495,461],{"className":10496},[494],[363,10498,554],{"className":10499,"style":682},[407,408],[363,10501,558],{"className":10502},[407],[363,10504,561],{"className":10505},[407,408],[363,10507,468],{"className":10508},[501],[363,10510],{"className":10511,"style":506},[505],[363,10513,7275],{"className":10514},[510],[363,10516],{"className":10517,"style":506},[505],[363,10519,10521,10524],{"className":10520},[398],[363,10522],{"className":10523,"style":520},[402],[363,10525,474],{"className":10526},[407],"。",[7012,10529,10530,10597,10598,10649,10650,10784,10785,10527],{},[1572,10531,10532],{},[363,10533,10535,10558],{"className":10534,"translate":367},[366],[363,10536,10538],{"className":10537},[371],[373,10539,10540],{"xmlns":375},[377,10541,10542,10556],{},[380,10543,10544,10546,10548,10550,10552,10554],{},[383,10545,385],{},[458,10547,461],{"stretchy":460},[463,10549,465],{},[458,10551,468],{"stretchy":460},[458,10553,471],{},[463,10555,474],{},[387,10557,477],{"encoding":389},[363,10559,10561,10588],{"className":10560,"ariaHidden":394},[393],[363,10562,10564,10567,10570,10573,10576,10579,10582,10585],{"className":10563},[398],[363,10565],{"className":10566,"style":487},[402],[363,10568,385],{"className":10569,"style":409},[407,408],[363,10571,461],{"className":10572},[494],[363,10574,465],{"className":10575},[407],[363,10577,468],{"className":10578},[501],[363,10580],{"className":10581,"style":506},[505],[363,10583,471],{"className":10584},[510],[363,10586],{"className":10587,"style":506},[505],[363,10589,10591,10594],{"className":10590},[398],[363,10592],{"className":10593,"style":520},[402],[363,10595,474],{"className":10596},[407],"：保证当 ",[363,10599,10601,10619],{"className":10600,"translate":367},[366],[363,10602,10604],{"className":10603},[371],[373,10605,10606],{"xmlns":375},[377,10607,10608,10616],{},[380,10609,10610,10612,10614],{},[383,10611,554],{},[458,10613,471],{},[383,10615,561],{},[387,10617,10618],{"encoding":389},"P=Q",[363,10620,10622,10640],{"className":10621,"ariaHidden":394},[393],[363,10623,10625,10628,10631,10634,10637],{"className":10624},[398],[363,10626],{"className":10627,"style":1011},[402],[363,10629,554],{"className":10630,"style":682},[407,408],[363,10632],{"className":10633,"style":506},[505],[363,10635,471],{"className":10636},[510],[363,10638],{"className":10639,"style":506},[505],[363,10641,10643,10646],{"className":10642},[398],[363,10644],{"className":10645,"style":913},[402],[363,10647,561],{"className":10648},[407,408]," 时，",[363,10651,10653,10683],{"className":10652,"translate":367},[366],[363,10654,10656],{"className":10655},[371],[373,10657,10658],{"xmlns":375},[377,10659,10660,10680],{},[380,10661,10662,10676,10678],{},[586,10663,10664,10670],{},[380,10665,10666,10668],{},[383,10667,592],{},[383,10669,554],{},[380,10671,10672,10674],{},[383,10673,592],{},[383,10675,561],{},[458,10677,471],{},[463,10679,465],{},[387,10681,10682],{"encoding":389},"\\frac{dP}{dQ}=1",[363,10684,10686,10775],{"className":10685,"ariaHidden":394},[393],[363,10687,10689,10692,10766,10769,10772],{"className":10688},[398],[363,10690],{"className":10691,"style":3015},[402],[363,10693,10695,10698,10763],{"className":10694},[407],[363,10696],{"className":10697},[494,789],[363,10699,10701],{"className":10700},[586],[363,10702,10704,10755],{"className":10703},[633,634],[363,10705,10707,10752],{"className":10706},[638],[363,10708,10710,10727,10735],{"className":10709,"style":3034},[642],[363,10711,10712,10715],{"style":2874},[363,10713],{"className":10714,"style":809},[650],[363,10716,10718],{"className":10717},[655,656,657,658],[363,10719,10721,10724],{"className":10720},[407,658],[363,10722,592],{"className":10723},[407,408,658],[363,10725,561],{"className":10726},[407,408,658],[363,10728,10729,10732],{"style":821},[363,10730],{"className":10731,"style":809},[650],[363,10733],{"className":10734,"style":829},[828],[363,10736,10737,10740],{"style":2897},[363,10738],{"className":10739,"style":809},[650],[363,10741,10743],{"className":10742},[655,656,657,658],[363,10744,10746,10749],{"className":10745},[407,658],[363,10747,592],{"className":10748},[407,408,658],[363,10750,554],{"className":10751,"style":682},[407,408,658],[363,10753,666],{"className":10754},[665],[363,10756,10758],{"className":10757},[638],[363,10759,10761],{"className":10760,"style":3086},[642],[363,10762],{},[363,10764],{"className":10765},[501,789],[363,10767],{"className":10768,"style":506},[505],[363,10770,471],{"className":10771},[510],[363,10773],{"className":10774,"style":506},[505],[363,10776,10778,10781],{"className":10777},[398],[363,10779],{"className":10780,"style":520},[402],[363,10782,465],{"className":10783},[407],"，从而 ",[363,10786,10788,10820],{"className":10787,"translate":367},[366],[363,10789,10791],{"className":10790},[371],[373,10792,10793],{"xmlns":375},[377,10794,10795,10817],{},[380,10796,10797,10803,10805,10807,10809,10811,10813,10815],{},[543,10798,10799,10801],{},[383,10800,547],{},[383,10802,385],{},[458,10804,461],{"stretchy":460},[383,10806,554],{},[383,10808,558],{"mathvariant":557},[383,10810,554],{},[458,10812,468],{"stretchy":460},[458,10814,471],{},[463,10816,474],{},[387,10818,10819],{"encoding":389},"D_f(P\\|P)=0",[363,10821,10823,10893],{"className":10822,"ariaHidden":394},[393],[363,10824,10826,10829,10869,10872,10875,10878,10881,10884,10887,10890],{"className":10825},[398],[363,10827],{"className":10828,"style":618},[402],[363,10830,10832,10835],{"className":10831},[407],[363,10833,547],{"className":10834,"style":625},[407,408],[363,10836,10838],{"className":10837},[629],[363,10839,10841,10861],{"className":10840},[633,634],[363,10842,10844,10858],{"className":10843},[638],[363,10845,10847],{"className":10846,"style":643},[642],[363,10848,10849,10852],{"style":646},[363,10850],{"className":10851,"style":651},[650],[363,10853,10855],{"className":10854},[655,656,657,658],[363,10856,385],{"className":10857,"style":409},[407,408,658],[363,10859,666],{"className":10860},[665],[363,10862,10864],{"className":10863},[638],[363,10865,10867],{"className":10866,"style":673},[642],[363,10868],{},[363,10870,461],{"className":10871},[494],[363,10873,554],{"className":10874,"style":682},[407,408],[363,10876,558],{"className":10877},[407],[363,10879,554],{"className":10880,"style":682},[407,408],[363,10882,468],{"className":10883},[501],[363,10885],{"className":10886,"style":506},[505],[363,10888,471],{"className":10889},[510],[363,10891],{"className":10892,"style":506},[505],[363,10894,10896,10899],{"className":10895},[398],[363,10897],{"className":10898,"style":520},[402],[363,10900,474],{"className":10901},[407],[11,10903,10904],{},"因此 f-散度天然具有非负性和「相同分布散度为零」的性质。",[2658,10906,10908],{"id":10907},"_22-凸性为何必需","2.2 凸性为何必需",[11,10910,10911,10912,10981,10982,11010],{},"有人会问：凸性是不是一个过强的技术条件？答案是否定的。若要求 ",[363,10913,10915,10932],{"className":10914,"translate":367},[366],[363,10916,10918],{"className":10917},[371],[373,10919,10920],{"xmlns":375},[377,10921,10922,10930],{},[380,10923,10924],{},[543,10925,10926,10928],{},[383,10927,547],{},[383,10929,385],{},[387,10931,4369],{"encoding":389},[363,10933,10935],{"className":10934,"ariaHidden":394},[393],[363,10936,10938,10941],{"className":10937},[398],[363,10939],{"className":10940,"style":4379},[402],[363,10942,10944,10947],{"className":10943},[407],[363,10945,547],{"className":10946,"style":625},[407,408],[363,10948,10950],{"className":10949},[629],[363,10951,10953,10973],{"className":10952},[633,634],[363,10954,10956,10970],{"className":10955},[638],[363,10957,10959],{"className":10958,"style":643},[642],[363,10960,10961,10964],{"style":646},[363,10962],{"className":10963,"style":651},[650],[363,10965,10967],{"className":10966},[655,656,657,658],[363,10968,385],{"className":10969,"style":409},[407,408,658],[363,10971,666],{"className":10972},[665],[363,10974,10976],{"className":10975},[638],[363,10977,10979],{"className":10978,"style":673},[642],[363,10980],{}," 对一切「随机变换」（马尔可夫核）单调不增（即第 4.5 节的数据处理不等式），那么 ",[363,10983,10985,10998],{"className":10984,"translate":367},[366],[363,10986,10988],{"className":10987},[371],[373,10989,10990],{"xmlns":375},[377,10991,10992,10996],{},[380,10993,10994],{},[383,10995,385],{},[387,10997,385],{"encoding":389},[363,10999,11001],{"className":11000,"ariaHidden":394},[393],[363,11002,11004,11007],{"className":11003},[398],[363,11005],{"className":11006,"style":403},[402],[363,11008,385],{"className":11009,"style":409},[407,408]," 必须凸。二元分布上就能看到这一点。",[1340,11012,11014],{"title":11013},"命题 2.1（Csiszár 刻画）",[11,11015,11016,11017,11212,11213,11254,11255,11283,11284,11312],{},"若数据处理不等式 ",[363,11018,11020,11071],{"className":11019,"translate":367},[366],[363,11021,11023],{"className":11022},[371],[373,11024,11025],{"xmlns":375},[377,11026,11027,11068],{},[380,11028,11029,11035,11037,11039,11042,11044,11046,11048,11050,11052,11058,11060,11062,11064,11066],{},[543,11030,11031,11033],{},[383,11032,547],{},[383,11034,385],{},[458,11036,461],{"stretchy":460},[383,11038,554],{},[383,11040,11041],{},"K",[383,11043,558],{"mathvariant":557},[383,11045,561],{},[383,11047,11041],{},[458,11049,468],{"stretchy":460},[458,11051,10299],{},[543,11053,11054,11056],{},[383,11055,547],{},[383,11057,385],{},[458,11059,461],{"stretchy":460},[383,11061,554],{},[383,11063,558],{"mathvariant":557},[383,11065,561],{},[458,11067,468],{"stretchy":460},[387,11069,11070],{"encoding":389},"D_f(PK\\|QK)\\le D_f(P\\|Q)",[363,11072,11074,11151],{"className":11073,"ariaHidden":394},[393],[363,11075,11077,11080,11120,11123,11126,11130,11133,11136,11139,11142,11145,11148],{"className":11076},[398],[363,11078],{"className":11079,"style":618},[402],[363,11081,11083,11086],{"className":11082},[407],[363,11084,547],{"className":11085,"style":625},[407,408],[363,11087,11089],{"className":11088},[629],[363,11090,11092,11112],{"className":11091},[633,634],[363,11093,11095,11109],{"className":11094},[638],[363,11096,11098],{"className":11097,"style":643},[642],[363,11099,11100,11103],{"style":646},[363,11101],{"className":11102,"style":651},[650],[363,11104,11106],{"className":11105},[655,656,657,658],[363,11107,385],{"className":11108,"style":409},[407,408,658],[363,11110,666],{"className":11111},[665],[363,11113,11115],{"className":11114},[638],[363,11116,11118],{"className":11117,"style":673},[642],[363,11119],{},[363,11121,461],{"className":11122},[494],[363,11124,554],{"className":11125,"style":682},[407,408],[363,11127,11041],{"className":11128,"style":11129},[407,408],"margin-right:0.0715em;",[363,11131,558],{"className":11132},[407],[363,11134,561],{"className":11135},[407,408],[363,11137,11041],{"className":11138,"style":11129},[407,408],[363,11140,468],{"className":11141},[501],[363,11143],{"className":11144,"style":506},[505],[363,11146,10299],{"className":11147},[510],[363,11149],{"className":11150,"style":506},[505],[363,11152,11154,11157,11197,11200,11203,11206,11209],{"className":11153},[398],[363,11155],{"className":11156,"style":618},[402],[363,11158,11160,11163],{"className":11159},[407],[363,11161,547],{"className":11162,"style":625},[407,408],[363,11164,11166],{"className":11165},[629],[363,11167,11169,11189],{"className":11168},[633,634],[363,11170,11172,11186],{"className":11171},[638],[363,11173,11175],{"className":11174,"style":643},[642],[363,11176,11177,11180],{"style":646},[363,11178],{"className":11179,"style":651},[650],[363,11181,11183],{"className":11182},[655,656,657,658],[363,11184,385],{"className":11185,"style":409},[407,408,658],[363,11187,666],{"className":11188},[665],[363,11190,11192],{"className":11191},[638],[363,11193,11195],{"className":11194,"style":673},[642],[363,11196],{},[363,11198,461],{"className":11199},[494],[363,11201,554],{"className":11202,"style":682},[407,408],[363,11204,558],{"className":11205},[407],[363,11207,561],{"className":11208},[407,408],[363,11210,468],{"className":11211},[501]," 对一切概率对 ",[363,11214,11216,11233],{"className":11215,"translate":367},[366],[363,11217,11219],{"className":11218},[371],[373,11220,11221],{"xmlns":375},[377,11222,11223,11231],{},[380,11224,11225,11227,11229],{},[383,11226,554],{},[458,11228,898],{"separator":394},[383,11230,561],{},[387,11232,903],{"encoding":389},[363,11234,11236],{"className":11235,"ariaHidden":394},[393],[363,11237,11239,11242,11245,11248,11251],{"className":11238},[398],[363,11240],{"className":11241,"style":913},[402],[363,11243,554],{"className":11244,"style":682},[407,408],[363,11246,898],{"className":11247},[920],[363,11249],{"className":11250,"style":754},[505],[363,11252,561],{"className":11253},[407,408]," 与一切马尔可夫核 ",[363,11256,11258,11271],{"className":11257,"translate":367},[366],[363,11259,11261],{"className":11260},[371],[373,11262,11263],{"xmlns":375},[377,11264,11265,11269],{},[380,11266,11267],{},[383,11268,11041],{},[387,11270,11041],{"encoding":389},[363,11272,11274],{"className":11273,"ariaHidden":394},[393],[363,11275,11277,11280],{"className":11276},[398],[363,11278],{"className":11279,"style":1011},[402],[363,11281,11041],{"className":11282,"style":11129},[407,408]," 成立，则 ",[363,11285,11287,11300],{"className":11286,"translate":367},[366],[363,11288,11290],{"className":11289},[371],[373,11291,11292],{"xmlns":375},[377,11293,11294,11298],{},[380,11295,11296],{},[383,11297,385],{},[387,11299,385],{"encoding":389},[363,11301,11303],{"className":11302,"ariaHidden":394},[393],[363,11304,11306,11309],{"className":11305},[398],[363,11307],{"className":11308,"style":403},[402],[363,11310,385],{"className":11311,"style":409},[407,408]," 凸。",[11,11314,11315],{},[1572,11316,11317],{},"证明（两步）。",[11,11319,11320,11407,11408,2627,11642,11671,11672,11748,11749,5992,11947,12144,12145,12282],{},[1572,11321,11322,11323,6841,11354,11406],{},"第一步：DPI ",[363,11324,11326,11341],{"className":11325,"translate":367},[366],[363,11327,11329],{"className":11328},[371],[373,11330,11331],{"xmlns":375},[377,11332,11333,11338],{},[380,11334,11335],{},[458,11336,11337],{},"⇒",[387,11339,11340],{"encoding":389},"\\Rightarrow",[363,11342,11344],{"className":11343,"ariaHidden":394},[393],[363,11345,11347,11351],{"className":11346},[398],[363,11348],{"className":11349,"style":11350},[402],"height:0.3669em;",[363,11352,11337],{"className":11353},[510],[363,11355,11357,11379],{"className":11356,"translate":367},[366],[363,11358,11360],{"className":11359},[371],[373,11361,11362],{"xmlns":375},[377,11363,11364,11376],{},[380,11365,11366,11368,11370,11372,11374],{},[458,11367,461],{"stretchy":460},[383,11369,554],{},[458,11371,898],{"separator":394},[383,11373,561],{},[458,11375,468],{"stretchy":460},[387,11377,11378],{"encoding":389},"(P,Q)",[363,11380,11382],{"className":11381,"ariaHidden":394},[393],[363,11383,11385,11388,11391,11394,11397,11400,11403],{"className":11384},[398],[363,11386],{"className":11387,"style":487},[402],[363,11389,461],{"className":11390},[494],[363,11392,554],{"className":11393,"style":682},[407,408],[363,11395,898],{"className":11396},[920],[363,11398],{"className":11399,"style":754},[505],[363,11401,561],{"className":11402},[407,408],[363,11404,468],{"className":11405},[501]," 联合凸。"," 设 ",[363,11409,11411,11453],{"className":11410,"translate":367},[366],[363,11412,11414],{"className":11413},[371],[373,11415,11416],{"xmlns":375},[377,11417,11418,11450],{},[380,11419,11420,11426,11428,11434,11436,11442,11444],{},[543,11421,11422,11424],{},[383,11423,554],{},[463,11425,465],{},[458,11427,898],{"separator":394},[543,11429,11430,11432],{},[383,11431,554],{},[463,11433,2810],{},[458,11435,898],{"separator":394},[543,11437,11438,11440],{},[383,11439,561],{},[463,11441,465],{},[458,11443,898],{"separator":394},[543,11445,11446,11448],{},[383,11447,561],{},[463,11449,2810],{},[387,11451,11452],{"encoding":389},"P_1,P_2,Q_1,Q_2",[363,11454,11456],{"className":11455,"ariaHidden":394},[393],[363,11457,11459,11462,11504,11507,11510,11550,11553,11556,11596,11599,11602],{"className":11458},[398],[363,11460],{"className":11461,"style":913},[402],[363,11463,11465,11468],{"className":11464},[407],[363,11466,554],{"className":11467,"style":682},[407,408],[363,11469,11471],{"className":11470},[629],[363,11472,11474,11496],{"className":11473},[633,634],[363,11475,11477,11493],{"className":11476},[638],[363,11478,11481],{"className":11479,"style":11480},[642],"height:0.3011em;",[363,11482,11484,11487],{"style":11483},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[363,11485],{"className":11486,"style":651},[650],[363,11488,11490],{"className":11489},[655,656,657,658],[363,11491,465],{"className":11492},[407,658],[363,11494,666],{"className":11495},[665],[363,11497,11499],{"className":11498},[638],[363,11500,11502],{"className":11501,"style":8315},[642],[363,11503],{},[363,11505,898],{"className":11506},[920],[363,11508],{"className":11509,"style":754},[505],[363,11511,11513,11516],{"className":11512},[407],[363,11514,554],{"className":11515,"style":682},[407,408],[363,11517,11519],{"className":11518},[629],[363,11520,11522,11542],{"className":11521},[633,634],[363,11523,11525,11539],{"className":11524},[638],[363,11526,11528],{"className":11527,"style":11480},[642],[363,11529,11530,11533],{"style":11483},[363,11531],{"className":11532,"style":651},[650],[363,11534,11536],{"className":11535},[655,656,657,658],[363,11537,2810],{"className":11538},[407,658],[363,11540,666],{"className":11541},[665],[363,11543,11545],{"className":11544},[638],[363,11546,11548],{"className":11547,"style":8315},[642],[363,11549],{},[363,11551,898],{"className":11552},[920],[363,11554],{"className":11555,"style":754},[505],[363,11557,11559,11562],{"className":11558},[407],[363,11560,561],{"className":11561},[407,408],[363,11563,11565],{"className":11564},[629],[363,11566,11568,11588],{"className":11567},[633,634],[363,11569,11571,11585],{"className":11570},[638],[363,11572,11574],{"className":11573,"style":11480},[642],[363,11575,11576,11579],{"style":730},[363,11577],{"className":11578,"style":651},[650],[363,11580,11582],{"className":11581},[655,656,657,658],[363,11583,465],{"className":11584},[407,658],[363,11586,666],{"className":11587},[665],[363,11589,11591],{"className":11590},[638],[363,11592,11594],{"className":11593,"style":8315},[642],[363,11595],{},[363,11597,898],{"className":11598},[920],[363,11600],{"className":11601,"style":754},[505],[363,11603,11605,11608],{"className":11604},[407],[363,11606,561],{"className":11607},[407,408],[363,11609,11611],{"className":11610},[629],[363,11612,11614,11634],{"className":11613},[633,634],[363,11615,11617,11631],{"className":11616},[638],[363,11618,11620],{"className":11619,"style":11480},[642],[363,11621,11622,11625],{"style":730},[363,11623],{"className":11624,"style":651},[650],[363,11626,11628],{"className":11627},[655,656,657,658],[363,11629,2810],{"className":11630},[407,658],[363,11632,666],{"className":11633},[665],[363,11635,11637],{"className":11636},[638],[363,11638,11640],{"className":11639,"style":8315},[642],[363,11641],{},[363,11643,11645,11659],{"className":11644,"translate":367},[366],[363,11646,11648],{"className":11647},[371],[373,11649,11650],{"xmlns":375},[377,11651,11652,11656],{},[380,11653,11654],{},[383,11655,945],{"mathvariant":944},[387,11657,11658],{"encoding":389},"\\mathcal X",[363,11660,11662],{"className":11661,"ariaHidden":394},[393],[363,11663,11665,11668],{"className":11664},[398],[363,11666],{"className":11667,"style":1011},[402],[363,11669,945],{"className":11670,"style":972},[407,971]," 上任给的四对分布，",[363,11673,11675,11702],{"className":11674,"translate":367},[366],[363,11676,11678],{"className":11677},[371],[373,11679,11680],{"xmlns":375},[377,11681,11682,11699],{},[380,11683,11684,11687,11689,11691,11693,11695,11697],{},[383,11685,11686],{},"λ",[458,11688,6256],{},[458,11690,461],{"stretchy":460},[463,11692,474],{},[458,11694,898],{"separator":394},[463,11696,465],{},[458,11698,468],{"stretchy":460},[387,11700,11701],{"encoding":389},"\\lambda\\in(0,1)",[363,11703,11705,11724],{"className":11704,"ariaHidden":394},[393],[363,11706,11708,11712,11715,11718,11721],{"className":11707},[398],[363,11709],{"className":11710,"style":11711},[402],"height:0.7335em;vertical-align:-0.0391em;",[363,11713,11686],{"className":11714},[407,408],[363,11716],{"className":11717,"style":506},[505],[363,11719,6256],{"className":11720},[510],[363,11722],{"className":11723,"style":506},[505],[363,11725,11727,11730,11733,11736,11739,11742,11745],{"className":11726},[398],[363,11728],{"className":11729,"style":487},[402],[363,11731,461],{"className":11732},[494],[363,11734,474],{"className":11735},[407],[363,11737,898],{"className":11738},[920],[363,11740],{"className":11741,"style":754},[505],[363,11743,465],{"className":11744},[407],[363,11746,468],{"className":11747},[501],"，记 ",[363,11750,11752,11794],{"className":11751,"translate":367},[366],[363,11753,11755],{"className":11754},[371],[373,11756,11757],{"xmlns":375},[377,11758,11759,11791],{},[380,11760,11761,11763,11765,11767,11773,11775,11777,11779,11781,11783,11785],{},[383,11762,554],{},[458,11764,471],{},[383,11766,11686],{},[543,11768,11769,11771],{},[383,11770,554],{},[463,11772,465],{},[458,11774,2817],{},[458,11776,461],{"stretchy":460},[463,11778,465],{},[458,11780,5160],{},[383,11782,11686],{},[458,11784,468],{"stretchy":460},[543,11786,11787,11789],{},[383,11788,554],{},[463,11790,2810],{},[387,11792,11793],{"encoding":389},"P=\\lambda P_1+(1-\\lambda)P_2",[363,11795,11797,11815,11874,11895],{"className":11796,"ariaHidden":394},[393],[363,11798,11800,11803,11806,11809,11812],{"className":11799},[398],[363,11801],{"className":11802,"style":1011},[402],[363,11804,554],{"className":11805,"style":682},[407,408],[363,11807],{"className":11808,"style":506},[505],[363,11810,471],{"className":11811},[510],[363,11813],{"className":11814,"style":506},[505],[363,11816,11818,11822,11825,11865,11868,11871],{"className":11817},[398],[363,11819],{"className":11820,"style":11821},[402],"height:0.8444em;vertical-align:-0.15em;",[363,11823,11686],{"className":11824},[407,408],[363,11826,11828,11831],{"className":11827},[407],[363,11829,554],{"className":11830,"style":682},[407,408],[363,11832,11834],{"className":11833},[629],[363,11835,11837,11857],{"className":11836},[633,634],[363,11838,11840,11854],{"className":11839},[638],[363,11841,11843],{"className":11842,"style":11480},[642],[363,11844,11845,11848],{"style":11483},[363,11846],{"className":11847,"style":651},[650],[363,11849,11851],{"className":11850},[655,656,657,658],[363,11852,465],{"className":11853},[407,658],[363,11855,666],{"className":11856},[665],[363,11858,11860],{"className":11859},[638],[363,11861,11863],{"className":11862,"style":8315},[642],[363,11864],{},[363,11866],{"className":11867,"style":2934},[505],[363,11869,2817],{"className":11870},[2938],[363,11872],{"className":11873,"style":2934},[505],[363,11875,11877,11880,11883,11886,11889,11892],{"className":11876},[398],[363,11878],{"className":11879,"style":487},[402],[363,11881,461],{"className":11882},[494],[363,11884,465],{"className":11885},[407],[363,11887],{"className":11888,"style":2934},[505],[363,11890,5160],{"className":11891},[2938],[363,11893],{"className":11894,"style":2934},[505],[363,11896,11898,11901,11904,11907],{"className":11897},[398],[363,11899],{"className":11900,"style":487},[402],[363,11902,11686],{"className":11903},[407,408],[363,11905,468],{"className":11906},[501],[363,11908,11910,11913],{"className":11909},[407],[363,11911,554],{"className":11912,"style":682},[407,408],[363,11914,11916],{"className":11915},[629],[363,11917,11919,11939],{"className":11918},[633,634],[363,11920,11922,11936],{"className":11921},[638],[363,11923,11925],{"className":11924,"style":11480},[642],[363,11926,11927,11930],{"style":11483},[363,11928],{"className":11929,"style":651},[650],[363,11931,11933],{"className":11932},[655,656,657,658],[363,11934,2810],{"className":11935},[407,658],[363,11937,666],{"className":11938},[665],[363,11940,11942],{"className":11941},[638],[363,11943,11945],{"className":11944,"style":8315},[642],[363,11946],{},[363,11948,11950,11992],{"className":11949,"translate":367},[366],[363,11951,11953],{"className":11952},[371],[373,11954,11955],{"xmlns":375},[377,11956,11957,11989],{},[380,11958,11959,11961,11963,11965,11971,11973,11975,11977,11979,11981,11983],{},[383,11960,561],{},[458,11962,471],{},[383,11964,11686],{},[543,11966,11967,11969],{},[383,11968,561],{},[463,11970,465],{},[458,11972,2817],{},[458,11974,461],{"stretchy":460},[463,11976,465],{},[458,11978,5160],{},[383,11980,11686],{},[458,11982,468],{"stretchy":460},[543,11984,11985,11987],{},[383,11986,561],{},[463,11988,2810],{},[387,11990,11991],{"encoding":389},"Q=\\lambda Q_1+(1-\\lambda)Q_2",[363,11993,11995,12013,12071,12092],{"className":11994,"ariaHidden":394},[393],[363,11996,11998,12001,12004,12007,12010],{"className":11997},[398],[363,11999],{"className":12000,"style":913},[402],[363,12002,561],{"className":12003},[407,408],[363,12005],{"className":12006,"style":506},[505],[363,12008,471],{"className":12009},[510],[363,12011],{"className":12012,"style":506},[505],[363,12014,12016,12019,12022,12062,12065,12068],{"className":12015},[398],[363,12017],{"className":12018,"style":403},[402],[363,12020,11686],{"className":12021},[407,408],[363,12023,12025,12028],{"className":12024},[407],[363,12026,561],{"className":12027},[407,408],[363,12029,12031],{"className":12030},[629],[363,12032,12034,12054],{"className":12033},[633,634],[363,12035,12037,12051],{"className":12036},[638],[363,12038,12040],{"className":12039,"style":11480},[642],[363,12041,12042,12045],{"style":730},[363,12043],{"className":12044,"style":651},[650],[363,12046,12048],{"className":12047},[655,656,657,658],[363,12049,465],{"className":12050},[407,658],[363,12052,666],{"className":12053},[665],[363,12055,12057],{"className":12056},[638],[363,12058,12060],{"className":12059,"style":8315},[642],[363,12061],{},[363,12063],{"className":12064,"style":2934},[505],[363,12066,2817],{"className":12067},[2938],[363,12069],{"className":12070,"style":2934},[505],[363,12072,12074,12077,12080,12083,12086,12089],{"className":12073},[398],[363,12075],{"className":12076,"style":487},[402],[363,12078,461],{"className":12079},[494],[363,12081,465],{"className":12082},[407],[363,12084],{"className":12085,"style":2934},[505],[363,12087,5160],{"className":12088},[2938],[363,12090],{"className":12091,"style":2934},[505],[363,12093,12095,12098,12101,12104],{"className":12094},[398],[363,12096],{"className":12097,"style":487},[402],[363,12099,11686],{"className":12100},[407,408],[363,12102,468],{"className":12103},[501],[363,12105,12107,12110],{"className":12106},[407],[363,12108,561],{"className":12109},[407,408],[363,12111,12113],{"className":12112},[629],[363,12114,12116,12136],{"className":12115},[633,634],[363,12117,12119,12133],{"className":12118},[638],[363,12120,12122],{"className":12121,"style":11480},[642],[363,12123,12124,12127],{"style":730},[363,12125],{"className":12126,"style":651},[650],[363,12128,12130],{"className":12129},[655,656,657,658],[363,12131,2810],{"className":12132},[407,658],[363,12134,666],{"className":12135},[665],[363,12137,12139],{"className":12138},[638],[363,12140,12142],{"className":12141,"style":8315},[642],[363,12143],{},"。构造扩大一倍的样本空间 ",[363,12146,12148,12185],{"className":12147,"translate":367},[366],[363,12149,12151],{"className":12150},[371],[373,12152,12153],{"xmlns":375},[377,12154,12155,12182],{},[380,12156,12157,12165,12167,12169,12171,12173,12175,12177,12180],{},[12158,12159,12160,12162],"mover",{"accent":394},[383,12161,945],{"mathvariant":944},[458,12163,12164],{},"~",[458,12166,471],{},[458,12168,3245],{"stretchy":460},[463,12170,465],{},[458,12172,898],{"separator":394},[463,12174,2810],{},[458,12176,3255],{"stretchy":460},[458,12178,12179],{},"×",[383,12181,945],{"mathvariant":944},[387,12183,12184],{"encoding":389},"\\tilde{\\mathcal X}=\\{1,2\\}\\times\\mathcal X",[363,12186,12188,12240,12273],{"className":12187,"ariaHidden":394},[393],[363,12189,12191,12195,12231,12234,12237],{"className":12190},[398],[363,12192],{"className":12193,"style":12194},[402],"height:0.9202em;",[363,12196,12199],{"className":12197},[407,12198],"accent",[363,12200,12202],{"className":12201},[633],[363,12203,12205],{"className":12204},[638],[363,12206,12208,12217],{"className":12207,"style":12194},[642],[363,12209,12211,12214],{"style":12210},"top:-3em;",[363,12212],{"className":12213,"style":809},[650],[363,12215,945],{"className":12216,"style":972},[407,971],[363,12218,12220,12223],{"style":12219},"top:-3.6023em;",[363,12221],{"className":12222,"style":809},[650],[363,12224,12228],{"className":12225,"style":12227},[12226],"accent-body","left:-0.1111em;",[363,12229,12164],{"className":12230},[407],[363,12232],{"className":12233,"style":506},[505],[363,12235,471],{"className":12236},[510],[363,12238],{"className":12239,"style":506},[505],[363,12241,12243,12246,12249,12252,12255,12258,12261,12264,12267,12270],{"className":12242},[398],[363,12244],{"className":12245,"style":487},[402],[363,12247,3245],{"className":12248},[494],[363,12250,465],{"className":12251},[407],[363,12253,898],{"className":12254},[920],[363,12256],{"className":12257,"style":754},[505],[363,12259,2810],{"className":12260},[407],[363,12262,3255],{"className":12263},[501],[363,12265],{"className":12266,"style":2934},[505],[363,12268,12179],{"className":12269},[2938],[363,12271],{"className":12272,"style":2934},[505],[363,12274,12276,12279],{"className":12275},[398],[363,12277],{"className":12278,"style":1011},[402],[363,12280,945],{"className":12281,"style":972},[407,971]," 及其上的两个分块分布：",[363,12284,12286],{"className":12285,"translate":367},[528],[363,12287,12289,12424],{"className":12288,"translate":367},[366],[363,12290,12292],{"className":12291},[371],[373,12293,12294],{"xmlns":375,"display":537},[377,12295,12296,12421],{},[380,12297,12298,12304,12306,12308,12311,12313,12315,12317,12319,12321,12327,12329,12335,12337,12339,12341,12343,12345,12351,12353,12355,12357,12359,12361,12363,12365,12367,12373,12375,12381,12383,12385,12387,12389,12391,12397,12399,12401,12403,12405,12411,12413,12415,12417,12419],{},[12158,12299,12300,12302],{"accent":394},[383,12301,554],{},[458,12303,12164],{},[458,12305,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,12307,461],{"stretchy":460},[383,12309,12310],{},"i",[458,12312,898],{"separator":394},[383,12314,1121],{},[458,12316,468],{"stretchy":460},[458,12318,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,12320,471],{},[543,12322,12323,12325],{},[383,12324,7917],{},[383,12326,12310],{},[1644,12328,1646],{},[543,12330,12331,12333],{},[383,12332,554],{},[383,12334,12310],{},[458,12336,461],{"stretchy":460},[383,12338,1121],{},[458,12340,468],{"stretchy":460},[458,12342,898],{"separator":394},[505,12344],{"width":3609},[12158,12346,12347,12349],{"accent":394},[383,12348,561],{},[458,12350,12164],{},[458,12352,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,12354,461],{"stretchy":460},[383,12356,12310],{},[458,12358,898],{"separator":394},[383,12360,1121],{},[458,12362,468],{"stretchy":460},[458,12364,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,12366,471],{},[543,12368,12369,12371],{},[383,12370,7917],{},[383,12372,12310],{},[1644,12374,1646],{},[543,12376,12377,12379],{},[383,12378,561],{},[383,12380,12310],{},[458,12382,461],{"stretchy":460},[383,12384,1121],{},[458,12386,468],{"stretchy":460},[458,12388,898],{"separator":394},[505,12390],{"width":3609},[543,12392,12393,12395],{},[383,12394,7917],{},[463,12396,465],{},[458,12398,471],{},[383,12400,11686],{},[458,12402,898],{"separator":394},[1644,12404,4630],{},[543,12406,12407,12409],{},[383,12408,7917],{},[463,12410,2810],{},[458,12412,471],{},[463,12414,465],{},[458,12416,5160],{},[383,12418,11686],{},[383,12420,4722],{"mathvariant":557},[387,12422,12423],{"encoding":389},"\\tilde P\\big((i,x)\\big)=w_i\\,P_i(x),\\qquad\n\\tilde Q\\big((i,x)\\big)=w_i\\,Q_i(x),\\qquad\nw_1=\\lambda,\\ w_2=1-\\lambda .",[363,12425,12427,12505,12696,12852,12919,12938],{"className":12426,"ariaHidden":394},[393],[363,12428,12430,12434,12466,12472,12475,12478,12481,12484,12487,12490,12496,12499,12502],{"className":12429},[398],[363,12431],{"className":12432,"style":12433},[402],"height:1.2702em;vertical-align:-0.35em;",[363,12435,12437],{"className":12436},[407,12198],[363,12438,12440],{"className":12439},[633],[363,12441,12443],{"className":12442},[638],[363,12444,12446,12454],{"className":12445,"style":12194},[642],[363,12447,12448,12451],{"style":12210},[363,12449],{"className":12450,"style":809},[650],[363,12452,554],{"className":12453,"style":682},[407,408],[363,12455,12456,12459],{"style":12219},[363,12457],{"className":12458,"style":809},[650],[363,12460,12463],{"className":12461,"style":12462},[12226],"left:-0.1667em;",[363,12464,12164],{"className":12465},[407],[363,12467,12469],{"className":12468},[407],[363,12470,461],{"className":12471},[767,10021],[363,12473,461],{"className":12474},[494],[363,12476,12310],{"className":12477},[407,408],[363,12479,898],{"className":12480},[920],[363,12482],{"className":12483,"style":754},[505],[363,12485,1121],{"className":12486},[407,408],[363,12488,468],{"className":12489},[501],[363,12491,12493],{"className":12492},[407],[363,12494,468],{"className":12495},[767,10021],[363,12497],{"className":12498,"style":506},[505],[363,12500,471],{"className":12501},[510],[363,12503],{"className":12504,"style":506},[505],[363,12506,12508,12511,12553,12556,12596,12599,12602,12605,12608,12611,12614,12657,12663,12666,12669,12672,12675,12678,12681,12687,12690,12693],{"className":12507},[398],[363,12509],{"className":12510,"style":12433},[402],[363,12512,12514,12517],{"className":12513},[407],[363,12515,7917],{"className":12516,"style":8621},[407,408],[363,12518,12520],{"className":12519},[629],[363,12521,12523,12545],{"className":12522},[633,634],[363,12524,12526,12542],{"className":12525},[638],[363,12527,12530],{"className":12528,"style":12529},[642],"height:0.3117em;",[363,12531,12533,12536],{"style":12532},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[363,12534],{"className":12535,"style":651},[650],[363,12537,12539],{"className":12538},[655,656,657,658],[363,12540,12310],{"className":12541},[407,408,658],[363,12543,666],{"className":12544},[665],[363,12546,12548],{"className":12547},[638],[363,12549,12551],{"className":12550,"style":8315},[642],[363,12552],{},[363,12554],{"className":12555,"style":754},[505],[363,12557,12559,12562],{"className":12558},[407],[363,12560,554],{"className":12561,"style":682},[407,408],[363,12563,12565],{"className":12564},[629],[363,12566,12568,12588],{"className":12567},[633,634],[363,12569,12571,12585],{"className":12570},[638],[363,12572,12574],{"className":12573,"style":12529},[642],[363,12575,12576,12579],{"style":11483},[363,12577],{"className":12578,"style":651},[650],[363,12580,12582],{"className":12581},[655,656,657,658],[363,12583,12310],{"className":12584},[407,408,658],[363,12586,666],{"className":12587},[665],[363,12589,12591],{"className":12590},[638],[363,12592,12594],{"className":12593,"style":8315},[642],[363,12595],{},[363,12597,461],{"className":12598},[494],[363,12600,1121],{"className":12601},[407,408],[363,12603,468],{"className":12604},[501],[363,12606,898],{"className":12607},[920],[363,12609],{"className":12610,"style":3981},[505],[363,12612],{"className":12613,"style":754},[505],[363,12615,12617],{"className":12616},[407,12198],[363,12618,12620,12648],{"className":12619},[633,634],[363,12621,12623,12645],{"className":12622},[638],[363,12624,12626,12634],{"className":12625,"style":12194},[642],[363,12627,12628,12631],{"style":12210},[363,12629],{"className":12630,"style":809},[650],[363,12632,561],{"className":12633},[407,408],[363,12635,12636,12639],{"style":12219},[363,12637],{"className":12638,"style":809},[650],[363,12640,12642],{"className":12641,"style":12462},[12226],[363,12643,12164],{"className":12644},[407],[363,12646,666],{"className":12647},[665],[363,12649,12651],{"className":12650},[638],[363,12652,12655],{"className":12653,"style":12654},[642],"height:0.1944em;",[363,12656],{},[363,12658,12660],{"className":12659},[407],[363,12661,461],{"className":12662},[767,10021],[363,12664,461],{"className":12665},[494],[363,12667,12310],{"className":12668},[407,408],[363,12670,898],{"className":12671},[920],[363,12673],{"className":12674,"style":754},[505],[363,12676,1121],{"className":12677},[407,408],[363,12679,468],{"className":12680},[501],[363,12682,12684],{"className":12683},[407],[363,12685,468],{"className":12686},[767,10021],[363,12688],{"className":12689,"style":506},[505],[363,12691,471],{"className":12692},[510],[363,12694],{"className":12695,"style":506},[505],[363,12697,12699,12702,12742,12745,12785,12788,12791,12794,12797,12800,12803,12843,12846,12849],{"className":12698},[398],[363,12700],{"className":12701,"style":487},[402],[363,12703,12705,12708],{"className":12704},[407],[363,12706,7917],{"className":12707,"style":8621},[407,408],[363,12709,12711],{"className":12710},[629],[363,12712,12714,12734],{"className":12713},[633,634],[363,12715,12717,12731],{"className":12716},[638],[363,12718,12720],{"className":12719,"style":12529},[642],[363,12721,12722,12725],{"style":12532},[363,12723],{"className":12724,"style":651},[650],[363,12726,12728],{"className":12727},[655,656,657,658],[363,12729,12310],{"className":12730},[407,408,658],[363,12732,666],{"className":12733},[665],[363,12735,12737],{"className":12736},[638],[363,12738,12740],{"className":12739,"style":8315},[642],[363,12741],{},[363,12743],{"className":12744,"style":754},[505],[363,12746,12748,12751],{"className":12747},[407],[363,12749,561],{"className":12750},[407,408],[363,12752,12754],{"className":12753},[629],[363,12755,12757,12777],{"className":12756},[633,634],[363,12758,12760,12774],{"className":12759},[638],[363,12761,12763],{"className":12762,"style":12529},[642],[363,12764,12765,12768],{"style":730},[363,12766],{"className":12767,"style":651},[650],[363,12769,12771],{"className":12770},[655,656,657,658],[363,12772,12310],{"className":12773},[407,408,658],[363,12775,666],{"className":12776},[665],[363,12778,12780],{"className":12779},[638],[363,12781,12783],{"className":12782,"style":8315},[642],[363,12784],{},[363,12786,461],{"className":12787},[494],[363,12789,1121],{"className":12790},[407,408],[363,12792,468],{"className":12793},[501],[363,12795,898],{"className":12796},[920],[363,12798],{"className":12799,"style":3981},[505],[363,12801],{"className":12802,"style":754},[505],[363,12804,12806,12809],{"className":12805},[407],[363,12807,7917],{"className":12808,"style":8621},[407,408],[363,12810,12812],{"className":12811},[629],[363,12813,12815,12835],{"className":12814},[633,634],[363,12816,12818,12832],{"className":12817},[638],[363,12819,12821],{"className":12820,"style":11480},[642],[363,12822,12823,12826],{"style":12532},[363,12824],{"className":12825,"style":651},[650],[363,12827,12829],{"className":12828},[655,656,657,658],[363,12830,465],{"className":12831},[407,658],[363,12833,666],{"className":12834},[665],[363,12836,12838],{"className":12837},[638],[363,12839,12841],{"className":12840,"style":8315},[642],[363,12842],{},[363,12844],{"className":12845,"style":506},[505],[363,12847,471],{"className":12848},[510],[363,12850],{"className":12851,"style":506},[505],[363,12853,12855,12858,12861,12864,12867,12870,12910,12913,12916],{"className":12854},[398],[363,12856],{"className":12857,"style":403},[402],[363,12859,11686],{"className":12860},[407,408],[363,12862,898],{"className":12863},[920],[363,12865,4630],{"className":12866},[505],[363,12868],{"className":12869,"style":754},[505],[363,12871,12873,12876],{"className":12872},[407],[363,12874,7917],{"className":12875,"style":8621},[407,408],[363,12877,12879],{"className":12878},[629],[363,12880,12882,12902],{"className":12881},[633,634],[363,12883,12885,12899],{"className":12884},[638],[363,12886,12888],{"className":12887,"style":11480},[642],[363,12889,12890,12893],{"style":12532},[363,12891],{"className":12892,"style":651},[650],[363,12894,12896],{"className":12895},[655,656,657,658],[363,12897,2810],{"className":12898},[407,658],[363,12900,666],{"className":12901},[665],[363,12903,12905],{"className":12904},[638],[363,12906,12908],{"className":12907,"style":8315},[642],[363,12909],{},[363,12911],{"className":12912,"style":506},[505],[363,12914,471],{"className":12915},[510],[363,12917],{"className":12918,"style":506},[505],[363,12920,12922,12926,12929,12932,12935],{"className":12921},[398],[363,12923],{"className":12924,"style":12925},[402],"height:0.7278em;vertical-align:-0.0833em;",[363,12927,465],{"className":12928},[407],[363,12930],{"className":12931,"style":2934},[505],[363,12933,5160],{"className":12934},[2938],[363,12936],{"className":12937,"style":2934},[505],[363,12939,12941,12945,12948],{"className":12940},[398],[363,12942],{"className":12943,"style":12944},[402],"height:0.6944em;",[363,12946,11686],{"className":12947},[407,408],[363,12949,4722],{"className":12950},[407],[11,12952,12953,12954,6841,12957,13058,13059,13087,13088,5992,13176,13276,13277,13690,13691,13762],{},"取",[1572,12955,12956],{},"确定性核",[363,12958,12960,12992],{"className":12959,"translate":367},[366],[363,12961,12963],{"className":12962},[371],[373,12964,12965],{"xmlns":375},[377,12966,12967,12989],{},[380,12968,12969,12971,12973,12975,12977,12979,12981,12983,12985,12987],{},[383,12970,11041],{},[458,12972,1362],{},[1644,12974,1646],{},[458,12976,461],{"stretchy":460},[383,12978,12310],{},[458,12980,898],{"separator":394},[383,12982,1121],{},[458,12984,468],{"stretchy":460},[458,12986,9031],{},[383,12988,1121],{},[387,12990,12991],{"encoding":389},"K:\\,(i,x)\\mapsto x",[363,12993,12995,13016,13049],{"className":12994,"ariaHidden":394},[393],[363,12996,12998,13001,13004,13007,13010,13013],{"className":12997},[398],[363,12999],{"className":13000,"style":1011},[402],[363,13002,11041],{"className":13003,"style":11129},[407,408],[363,13005],{"className":13006,"style":506},[505],[363,13008,1362],{"className":13009},[510],[363,13011],{"className":13012,"style":754},[505],[363,13014],{"className":13015,"style":506},[505],[363,13017,13019,13022,13025,13028,13031,13034,13037,13040,13043,13046],{"className":13018},[398],[363,13020],{"className":13021,"style":487},[402],[363,13023,461],{"className":13024},[494],[363,13026,12310],{"className":13027},[407,408],[363,13029,898],{"className":13030},[920],[363,13032],{"className":13033,"style":754},[505],[363,13035,1121],{"className":13036},[407,408],[363,13038,468],{"className":13039},[501],[363,13041],{"className":13042,"style":506},[505],[363,13044,9031],{"className":13045},[510],[363,13047],{"className":13048,"style":506},[505],[363,13050,13052,13055],{"className":13051},[398],[363,13053],{"className":13054,"style":2692},[402],[363,13056,1121],{"className":13057},[407,408],"（\"擦掉\"分量下标，只保留 ",[363,13060,13062,13075],{"className":13061,"translate":367},[366],[363,13063,13065],{"className":13064},[371],[373,13066,13067],{"xmlns":375},[377,13068,13069,13073],{},[380,13070,13071],{},[383,13072,1121],{},[387,13074,1121],{"encoding":389},[363,13076,13078],{"className":13077,"ariaHidden":394},[393],[363,13079,13081,13084],{"className":13080},[398],[363,13082],{"className":13083,"style":2692},[402],[363,13085,1121],{"className":13086},[407,408],"）。由分块结构立刻算出 ",[363,13089,13091,13115],{"className":13090,"translate":367},[366],[363,13092,13094],{"className":13093},[371],[373,13095,13096],{"xmlns":375},[377,13097,13098,13112],{},[380,13099,13100,13106,13108,13110],{},[12158,13101,13102,13104],{"accent":394},[383,13103,554],{},[458,13105,12164],{},[383,13107,11041],{},[458,13109,471],{},[383,13111,554],{},[387,13113,13114],{"encoding":389},"\\tilde PK=P",[363,13116,13118,13167],{"className":13117,"ariaHidden":394},[393],[363,13119,13121,13124,13155,13158,13161,13164],{"className":13120},[398],[363,13122],{"className":13123,"style":12194},[402],[363,13125,13127],{"className":13126},[407,12198],[363,13128,13130],{"className":13129},[633],[363,13131,13133],{"className":13132},[638],[363,13134,13136,13144],{"className":13135,"style":12194},[642],[363,13137,13138,13141],{"style":12210},[363,13139],{"className":13140,"style":809},[650],[363,13142,554],{"className":13143,"style":682},[407,408],[363,13145,13146,13149],{"style":12219},[363,13147],{"className":13148,"style":809},[650],[363,13150,13152],{"className":13151,"style":12462},[12226],[363,13153,12164],{"className":13154},[407],[363,13156,11041],{"className":13157,"style":11129},[407,408],[363,13159],{"className":13160,"style":506},[505],[363,13162,471],{"className":13163},[510],[363,13165],{"className":13166,"style":506},[505],[363,13168,13170,13173],{"className":13169},[398],[363,13171],{"className":13172,"style":1011},[402],[363,13174,554],{"className":13175,"style":682},[407,408],[363,13177,13179,13203],{"className":13178,"translate":367},[366],[363,13180,13182],{"className":13181},[371],[373,13183,13184],{"xmlns":375},[377,13185,13186,13200],{},[380,13187,13188,13194,13196,13198],{},[12158,13189,13190,13192],{"accent":394},[383,13191,561],{},[458,13193,12164],{},[383,13195,11041],{},[458,13197,471],{},[383,13199,561],{},[387,13201,13202],{"encoding":389},"\\tilde QK=Q",[363,13204,13206,13267],{"className":13205,"ariaHidden":394},[393],[363,13207,13209,13213,13255,13258,13261,13264],{"className":13208},[398],[363,13210],{"className":13211,"style":13212},[402],"height:1.1146em;vertical-align:-0.1944em;",[363,13214,13216],{"className":13215},[407,12198],[363,13217,13219,13247],{"className":13218},[633,634],[363,13220,13222,13244],{"className":13221},[638],[363,13223,13225,13233],{"className":13224,"style":12194},[642],[363,13226,13227,13230],{"style":12210},[363,13228],{"className":13229,"style":809},[650],[363,13231,561],{"className":13232},[407,408],[363,13234,13235,13238],{"style":12219},[363,13236],{"className":13237,"style":809},[650],[363,13239,13241],{"className":13240,"style":12462},[12226],[363,13242,12164],{"className":13243},[407],[363,13245,666],{"className":13246},[665],[363,13248,13250],{"className":13249},[638],[363,13251,13253],{"className":13252,"style":12654},[642],[363,13254],{},[363,13256,11041],{"className":13257,"style":11129},[407,408],[363,13259],{"className":13260,"style":506},[505],[363,13262,471],{"className":13263},[510],[363,13265],{"className":13266,"style":506},[505],[363,13268,13270,13273],{"className":13269},[398],[363,13271],{"className":13272,"style":913},[402],[363,13274,561],{"className":13275},[407,408],"，且似然比是分块恒定的：",[363,13278,13280,13358],{"className":13279,"translate":367},[366],[363,13281,13283],{"className":13282},[371],[373,13284,13285],{"xmlns":375},[377,13286,13287,13355],{},[380,13288,13289,13313,13315,13317,13319,13321,13323,13325,13349,13351,13353],{},[1602,13290,13291],{"scriptlevel":474,"displaystyle":394},[586,13292,13293,13303],{},[380,13294,13295,13297],{},[383,13296,592],{},[12158,13298,13299,13301],{"accent":394},[383,13300,554],{},[458,13302,12164],{},[380,13304,13305,13307],{},[383,13306,592],{},[12158,13308,13309,13311],{"accent":394},[383,13310,561],{},[458,13312,12164],{},[458,13314,461],{"stretchy":460},[383,13316,12310],{},[458,13318,898],{"separator":394},[383,13320,1121],{},[458,13322,468],{"stretchy":460},[458,13324,471],{},[1602,13326,13327],{"scriptlevel":474,"displaystyle":394},[586,13328,13329,13339],{},[380,13330,13331,13333],{},[383,13332,592],{},[543,13334,13335,13337],{},[383,13336,554],{},[383,13338,12310],{},[380,13340,13341,13343],{},[383,13342,592],{},[543,13344,13345,13347],{},[383,13346,561],{},[383,13348,12310],{},[458,13350,461],{"stretchy":460},[383,13352,1121],{},[458,13354,468],{"stretchy":460},[387,13356,13357],{"encoding":389},"\\dfrac{d\\tilde P}{d\\tilde Q}(i,x)=\\dfrac{dP_i}{dQ_i}(x)",[363,13359,13361,13533],{"className":13360,"ariaHidden":394},[393],[363,13362,13364,13368,13506,13509,13512,13515,13518,13521,13524,13527,13530],{"className":13363},[398],[363,13365],{"className":13366,"style":13367},[402],"height:2.6018em;vertical-align:-1.0046em;",[363,13369,13371,13374,13503],{"className":13370},[407],[363,13372],{"className":13373},[494,789],[363,13375,13377],{"className":13376},[586],[363,13378,13380,13494],{"className":13379},[633,634],[363,13381,13383,13491],{"className":13382},[638],[363,13384,13387,13441,13449],{"className":13385,"style":13386},[642],"height:1.5972em;",[363,13388,13390,13393],{"style":13389},"top:-2.1898em;",[363,13391],{"className":13392,"style":809},[650],[363,13394,13396,13399],{"className":13395},[407],[363,13397,592],{"className":13398},[407,408],[363,13400,13402],{"className":13401},[407,12198],[363,13403,13405,13433],{"className":13404},[633,634],[363,13406,13408,13430],{"className":13407},[638],[363,13409,13411,13419],{"className":13410,"style":12194},[642],[363,13412,13413,13416],{"style":12210},[363,13414],{"className":13415,"style":809},[650],[363,13417,561],{"className":13418},[407,408],[363,13420,13421,13424],{"style":12219},[363,13422],{"className":13423,"style":809},[650],[363,13425,13427],{"className":13426,"style":12462},[12226],[363,13428,12164],{"className":13429},[407],[363,13431,666],{"className":13432},[665],[363,13434,13436],{"className":13435},[638],[363,13437,13439],{"className":13438,"style":12654},[642],[363,13440],{},[363,13442,13443,13446],{"style":821},[363,13444],{"className":13445,"style":809},[650],[363,13447],{"className":13448,"style":829},[828],[363,13450,13451,13454],{"style":832},[363,13452],{"className":13453,"style":809},[650],[363,13455,13457,13460],{"className":13456},[407],[363,13458,592],{"className":13459},[407,408],[363,13461,13463],{"className":13462},[407,12198],[363,13464,13466],{"className":13465},[633],[363,13467,13469],{"className":13468},[638],[363,13470,13472,13480],{"className":13471,"style":12194},[642],[363,13473,13474,13477],{"style":12210},[363,13475],{"className":13476,"style":809},[650],[363,13478,554],{"className":13479,"style":682},[407,408],[363,13481,13482,13485],{"style":12219},[363,13483],{"className":13484,"style":809},[650],[363,13486,13488],{"className":13487,"style":12462},[12226],[363,13489,12164],{"className":13490},[407],[363,13492,666],{"className":13493},[665],[363,13495,13497],{"className":13496},[638],[363,13498,13501],{"className":13499,"style":13500},[642],"height:1.0046em;",[363,13502],{},[363,13504],{"className":13505},[501,789],[363,13507,461],{"className":13508},[494],[363,13510,12310],{"className":13511},[407,408],[363,13513,898],{"className":13514},[920],[363,13516],{"className":13517,"style":754},[505],[363,13519,1121],{"className":13520},[407,408],[363,13522,468],{"className":13523},[501],[363,13525],{"className":13526,"style":506},[505],[363,13528,471],{"className":13529},[510],[363,13531],{"className":13532,"style":506},[505],[363,13534,13536,13539,13681,13684,13687],{"className":13535},[398],[363,13537],{"className":13538,"style":1185},[402],[363,13540,13542,13545,13678],{"className":13541},[407],[363,13543],{"className":13544},[494,789],[363,13546,13548],{"className":13547},[586],[363,13549,13551,13670],{"className":13550},[633,634],[363,13552,13554,13667],{"className":13553},[638],[363,13555,13557,13608,13616],{"className":13556,"style":802},[642],[363,13558,13559,13562],{"style":805},[363,13560],{"className":13561,"style":809},[650],[363,13563,13565,13568],{"className":13564},[407],[363,13566,592],{"className":13567},[407,408],[363,13569,13571,13574],{"className":13570},[407],[363,13572,561],{"className":13573},[407,408],[363,13575,13577],{"className":13576},[629],[363,13578,13580,13600],{"className":13579},[633,634],[363,13581,13583,13597],{"className":13582},[638],[363,13584,13586],{"className":13585,"style":12529},[642],[363,13587,13588,13591],{"style":730},[363,13589],{"className":13590,"style":651},[650],[363,13592,13594],{"className":13593},[655,656,657,658],[363,13595,12310],{"className":13596},[407,408,658],[363,13598,666],{"className":13599},[665],[363,13601,13603],{"className":13602},[638],[363,13604,13606],{"className":13605,"style":8315},[642],[363,13607],{},[363,13609,13610,13613],{"style":821},[363,13611],{"className":13612,"style":809},[650],[363,13614],{"className":13615,"style":829},[828],[363,13617,13618,13621],{"style":832},[363,13619],{"className":13620,"style":809},[650],[363,13622,13624,13627],{"className":13623},[407],[363,13625,592],{"className":13626},[407,408],[363,13628,13630,13633],{"className":13629},[407],[363,13631,554],{"className":13632,"style":682},[407,408],[363,13634,13636],{"className":13635},[629],[363,13637,13639,13659],{"className":13638},[633,634],[363,13640,13642,13656],{"className":13641},[638],[363,13643,13645],{"className":13644,"style":12529},[642],[363,13646,13647,13650],{"style":11483},[363,13648],{"className":13649,"style":651},[650],[363,13651,13653],{"className":13652},[655,656,657,658],[363,13654,12310],{"className":13655},[407,408,658],[363,13657,666],{"className":13658},[665],[363,13660,13662],{"className":13661},[638],[363,13663,13665],{"className":13664,"style":8315},[642],[363,13666],{},[363,13668,666],{"className":13669},[665],[363,13671,13673],{"className":13672},[638],[363,13674,13676],{"className":13675,"style":854},[642],[363,13677],{},[363,13679],{"className":13680},[501,789],[363,13682,461],{"className":13683},[494],[363,13685,1121],{"className":13686},[407,408],[363,13688,468],{"className":13689},[501],"（权重 ",[363,13692,13694,13712],{"className":13693,"translate":367},[366],[363,13695,13697],{"className":13696},[371],[373,13698,13699],{"xmlns":375},[377,13700,13701,13709],{},[380,13702,13703],{},[543,13704,13705,13707],{},[383,13706,7917],{},[383,13708,12310],{},[387,13710,13711],{"encoding":389},"w_i",[363,13713,13715],{"className":13714,"ariaHidden":394},[393],[363,13716,13718,13722],{"className":13717},[398],[363,13719],{"className":13720,"style":13721},[402],"height:0.5806em;vertical-align:-0.15em;",[363,13723,13725,13728],{"className":13724},[407],[363,13726,7917],{"className":13727,"style":8621},[407,408],[363,13729,13731],{"className":13730},[629],[363,13732,13734,13754],{"className":13733},[633,634],[363,13735,13737,13751],{"className":13736},[638],[363,13738,13740],{"className":13739,"style":12529},[642],[363,13741,13742,13745],{"style":12532},[363,13743],{"className":13744,"style":651},[650],[363,13746,13748],{"className":13747},[655,656,657,658],[363,13749,12310],{"className":13750},[407,408,658],[363,13752,666],{"className":13753},[665],[363,13755,13757],{"className":13756},[638],[363,13758,13760],{"className":13759,"style":8315},[642],[363,13761],{}," 在分子分母中约去）。代入定义：",[363,13764,13766],{"className":13765,"translate":367},[528],[363,13767,13769,13912],{"className":13768,"translate":367},[366],[363,13770,13772],{"className":13771},[371],[373,13773,13774],{"xmlns":375,"display":537},[377,13775,13776,13909],{},[380,13777,13778,13784,13786,13792,13794,13800,13802,13804,13811,13817,13819,13825,13827,13833,13835,13841,13843,13845,13847,13853,13855,13861,13863,13869,13871,13873,13875,13877,13879,13881,13883,13889,13891,13897,13899,13905,13907],{},[543,13779,13780,13782],{},[383,13781,547],{},[383,13783,385],{},[458,13785,461],{"stretchy":460},[12158,13787,13788,13790],{"accent":394},[383,13789,554],{},[458,13791,12164],{},[383,13793,558],{"mathvariant":557},[12158,13795,13796,13798],{"accent":394},[383,13797,561],{},[458,13799,12164],{},[458,13801,468],{"stretchy":460},[458,13803,471],{},[6363,13805,13806,13809],{},[458,13807,13808],{},"∑",[383,13810,12310],{},[543,13812,13813,13815],{},[383,13814,7917],{},[383,13816,12310],{},[1644,13818,1646],{},[543,13820,13821,13823],{},[383,13822,547],{},[383,13824,385],{},[458,13826,461],{"stretchy":460},[543,13828,13829,13831],{},[383,13830,554],{},[383,13832,12310],{},[383,13834,558],{"mathvariant":557},[543,13836,13837,13839],{},[383,13838,561],{},[383,13840,12310],{},[458,13842,468],{"stretchy":460},[458,13844,471],{},[383,13846,11686],{},[543,13848,13849,13851],{},[383,13850,547],{},[383,13852,385],{},[458,13854,461],{"stretchy":460},[543,13856,13857,13859],{},[383,13858,554],{},[463,13860,465],{},[383,13862,558],{"mathvariant":557},[543,13864,13865,13867],{},[383,13866,561],{},[463,13868,465],{},[458,13870,468],{"stretchy":460},[458,13872,2817],{},[458,13874,461],{"stretchy":460},[463,13876,465],{},[458,13878,5160],{},[383,13880,11686],{},[458,13882,468],{"stretchy":460},[543,13884,13885,13887],{},[383,13886,547],{},[383,13888,385],{},[458,13890,461],{"stretchy":460},[543,13892,13893,13895],{},[383,13894,554],{},[463,13896,2810],{},[383,13898,558],{"mathvariant":557},[543,13900,13901,13903],{},[383,13902,561],{},[463,13904,2810],{},[458,13906,468],{"stretchy":460},[383,13908,4722],{"mathvariant":557},[387,13910,13911],{"encoding":389},"D_f(\\tilde P\\|\\tilde Q)\n=\\sum_i w_i\\,D_f(P_i\\|Q_i)\n=\\lambda D_f(P_1\\|Q_1)+(1-\\lambda)D_f(P_2\\|Q_2).",[363,13913,13915,14053,14294,14441,14462],{"className":13914,"ariaHidden":394},[393],[363,13916,13918,13922,13962,13965,13996,13999,14041,14044,14047,14050],{"className":13917},[398],[363,13919],{"className":13920,"style":13921},[402],"height:1.2063em;vertical-align:-0.2861em;",[363,13923,13925,13928],{"className":13924},[407],[363,13926,547],{"className":13927,"style":625},[407,408],[363,13929,13931],{"className":13930},[629],[363,13932,13934,13954],{"className":13933},[633,634],[363,13935,13937,13951],{"className":13936},[638],[363,13938,13940],{"className":13939,"style":643},[642],[363,13941,13942,13945],{"style":646},[363,13943],{"className":13944,"style":651},[650],[363,13946,13948],{"className":13947},[655,656,657,658],[363,13949,385],{"className":13950,"style":409},[407,408,658],[363,13952,666],{"className":13953},[665],[363,13955,13957],{"className":13956},[638],[363,13958,13960],{"className":13959,"style":673},[642],[363,13961],{},[363,13963,461],{"className":13964},[494],[363,13966,13968],{"className":13967},[407,12198],[363,13969,13971],{"className":13970},[633],[363,13972,13974],{"className":13973},[638],[363,13975,13977,13985],{"className":13976,"style":12194},[642],[363,13978,13979,13982],{"style":12210},[363,13980],{"className":13981,"style":809},[650],[363,13983,554],{"className":13984,"style":682},[407,408],[363,13986,13987,13990],{"style":12219},[363,13988],{"className":13989,"style":809},[650],[363,13991,13993],{"className":13992,"style":12462},[12226],[363,13994,12164],{"className":13995},[407],[363,13997,558],{"className":13998},[407],[363,14000,14002],{"className":14001},[407,12198],[363,14003,14005,14033],{"className":14004},[633,634],[363,14006,14008,14030],{"className":14007},[638],[363,14009,14011,14019],{"className":14010,"style":12194},[642],[363,14012,14013,14016],{"style":12210},[363,14014],{"className":14015,"style":809},[650],[363,14017,561],{"className":14018},[407,408],[363,14020,14021,14024],{"style":12219},[363,14022],{"className":14023,"style":809},[650],[363,14025,14027],{"className":14026,"style":12462},[12226],[363,14028,12164],{"className":14029},[407],[363,14031,666],{"className":14032},[665],[363,14034,14036],{"className":14035},[638],[363,14037,14039],{"className":14038,"style":12654},[642],[363,14040],{},[363,14042,468],{"className":14043},[501],[363,14045],{"className":14046,"style":506},[505],[363,14048,471],{"className":14049},[510],[363,14051],{"className":14052,"style":506},[505],[363,14054,14056,14060,14110,14113,14153,14156,14196,14199,14239,14242,14282,14285,14288,14291],{"className":14055},[398],[363,14057],{"className":14058,"style":14059},[402],"height:2.3277em;vertical-align:-1.2777em;",[363,14061,14064],{"className":14062},[1831,14063],"op-limits",[363,14065,14067,14101],{"className":14066},[633,634],[363,14068,14070,14098],{"className":14069},[638],[363,14071,14074,14087],{"className":14072,"style":14073},[642],"height:1.05em;",[363,14075,14077,14081],{"style":14076},"top:-1.8723em;margin-left:0em;",[363,14078],{"className":14079,"style":14080},[650],"height:3.05em;",[363,14082,14084],{"className":14083},[655,656,657,658],[363,14085,12310],{"className":14086},[407,408,658],[363,14088,14090,14093],{"style":14089},"top:-3.05em;",[363,14091],{"className":14092,"style":14080},[650],[363,14094,14095],{},[363,14096,13808],{"className":14097},[1831,1832,1833],[363,14099,666],{"className":14100},[665],[363,14102,14104],{"className":14103},[638],[363,14105,14108],{"className":14106,"style":14107},[642],"height:1.2777em;",[363,14109],{},[363,14111],{"className":14112,"style":754},[505],[363,14114,14116,14119],{"className":14115},[407],[363,14117,7917],{"className":14118,"style":8621},[407,408],[363,14120,14122],{"className":14121},[629],[363,14123,14125,14145],{"className":14124},[633,634],[363,14126,14128,14142],{"className":14127},[638],[363,14129,14131],{"className":14130,"style":12529},[642],[363,14132,14133,14136],{"style":12532},[363,14134],{"className":14135,"style":651},[650],[363,14137,14139],{"className":14138},[655,656,657,658],[363,14140,12310],{"className":14141},[407,408,658],[363,14143,666],{"className":14144},[665],[363,14146,14148],{"className":14147},[638],[363,14149,14151],{"className":14150,"style":8315},[642],[363,14152],{},[363,14154],{"className":14155,"style":754},[505],[363,14157,14159,14162],{"className":14158},[407],[363,14160,547],{"className":14161,"style":625},[407,408],[363,14163,14165],{"className":14164},[629],[363,14166,14168,14188],{"className":14167},[633,634],[363,14169,14171,14185],{"className":14170},[638],[363,14172,14174],{"className":14173,"style":643},[642],[363,14175,14176,14179],{"style":646},[363,14177],{"className":14178,"style":651},[650],[363,14180,14182],{"className":14181},[655,656,657,658],[363,14183,385],{"className":14184,"style":409},[407,408,658],[363,14186,666],{"className":14187},[665],[363,14189,14191],{"className":14190},[638],[363,14192,14194],{"className":14193,"style":673},[642],[363,14195],{},[363,14197,461],{"className":14198},[494],[363,14200,14202,14205],{"className":14201},[407],[363,14203,554],{"className":14204,"style":682},[407,408],[363,14206,14208],{"className":14207},[629],[363,14209,14211,14231],{"className":14210},[633,634],[363,14212,14214,14228],{"className":14213},[638],[363,14215,14217],{"className":14216,"style":12529},[642],[363,14218,14219,14222],{"style":11483},[363,14220],{"className":14221,"style":651},[650],[363,14223,14225],{"className":14224},[655,656,657,658],[363,14226,12310],{"className":14227},[407,408,658],[363,14229,666],{"className":14230},[665],[363,14232,14234],{"className":14233},[638],[363,14235,14237],{"className":14236,"style":8315},[642],[363,14238],{},[363,14240,558],{"className":14241},[407],[363,14243,14245,14248],{"className":14244},[407],[363,14246,561],{"className":14247},[407,408],[363,14249,14251],{"className":14250},[629],[363,14252,14254,14274],{"className":14253},[633,634],[363,14255,14257,14271],{"className":14256},[638],[363,14258,14260],{"className":14259,"style":12529},[642],[363,14261,14262,14265],{"style":730},[363,14263],{"className":14264,"style":651},[650],[363,14266,14268],{"className":14267},[655,656,657,658],[363,14269,12310],{"className":14270},[407,408,658],[363,14272,666],{"className":14273},[665],[363,14275,14277],{"className":14276},[638],[363,14278,14280],{"className":14279,"style":8315},[642],[363,14281],{},[363,14283,468],{"className":14284},[501],[363,14286],{"className":14287,"style":506},[505],[363,14289,471],{"className":14290},[510],[363,14292],{"className":14293,"style":506},[505],[363,14295,14297,14300,14303,14343,14346,14386,14389,14429,14432,14435,14438],{"className":14296},[398],[363,14298],{"className":14299,"style":618},[402],[363,14301,11686],{"className":14302},[407,408],[363,14304,14306,14309],{"className":14305},[407],[363,14307,547],{"className":14308,"style":625},[407,408],[363,14310,14312],{"className":14311},[629],[363,14313,14315,14335],{"className":14314},[633,634],[363,14316,14318,14332],{"className":14317},[638],[363,14319,14321],{"className":14320,"style":643},[642],[363,14322,14323,14326],{"style":646},[363,14324],{"className":14325,"style":651},[650],[363,14327,14329],{"className":14328},[655,656,657,658],[363,14330,385],{"className":14331,"style":409},[407,408,658],[363,14333,666],{"className":14334},[665],[363,14336,14338],{"className":14337},[638],[363,14339,14341],{"className":14340,"style":673},[642],[363,14342],{},[363,14344,461],{"className":14345},[494],[363,14347,14349,14352],{"className":14348},[407],[363,14350,554],{"className":14351,"style":682},[407,408],[363,14353,14355],{"className":14354},[629],[363,14356,14358,14378],{"className":14357},[633,634],[363,14359,14361,14375],{"className":14360},[638],[363,14362,14364],{"className":14363,"style":11480},[642],[363,14365,14366,14369],{"style":11483},[363,14367],{"className":14368,"style":651},[650],[363,14370,14372],{"className":14371},[655,656,657,658],[363,14373,465],{"className":14374},[407,658],[363,14376,666],{"className":14377},[665],[363,14379,14381],{"className":14380},[638],[363,14382,14384],{"className":14383,"style":8315},[642],[363,14385],{},[363,14387,558],{"className":14388},[407],[363,14390,14392,14395],{"className":14391},[407],[363,14393,561],{"className":14394},[407,408],[363,14396,14398],{"className":14397},[629],[363,14399,14401,14421],{"className":14400},[633,634],[363,14402,14404,14418],{"className":14403},[638],[363,14405,14407],{"className":14406,"style":11480},[642],[363,14408,14409,14412],{"style":730},[363,14410],{"className":14411,"style":651},[650],[363,14413,14415],{"className":14414},[655,656,657,658],[363,14416,465],{"className":14417},[407,658],[363,14419,666],{"className":14420},[665],[363,14422,14424],{"className":14423},[638],[363,14425,14427],{"className":14426,"style":8315},[642],[363,14428],{},[363,14430,468],{"className":14431},[501],[363,14433],{"className":14434,"style":2934},[505],[363,14436,2817],{"className":14437},[2938],[363,14439],{"className":14440,"style":2934},[505],[363,14442,14444,14447,14450,14453,14456,14459],{"className":14443},[398],[363,14445],{"className":14446,"style":487},[402],[363,14448,461],{"className":14449},[494],[363,14451,465],{"className":14452},[407],[363,14454],{"className":14455,"style":2934},[505],[363,14457,5160],{"className":14458},[2938],[363,14460],{"className":14461,"style":2934},[505],[363,14463,14465,14468,14471,14474,14514,14517,14557,14560,14600,14603],{"className":14464},[398],[363,14466],{"className":14467,"style":618},[402],[363,14469,11686],{"className":14470},[407,408],[363,14472,468],{"className":14473},[501],[363,14475,14477,14480],{"className":14476},[407],[363,14478,547],{"className":14479,"style":625},[407,408],[363,14481,14483],{"className":14482},[629],[363,14484,14486,14506],{"className":14485},[633,634],[363,14487,14489,14503],{"className":14488},[638],[363,14490,14492],{"className":14491,"style":643},[642],[363,14493,14494,14497],{"style":646},[363,14495],{"className":14496,"style":651},[650],[363,14498,14500],{"className":14499},[655,656,657,658],[363,14501,385],{"className":14502,"style":409},[407,408,658],[363,14504,666],{"className":14505},[665],[363,14507,14509],{"className":14508},[638],[363,14510,14512],{"className":14511,"style":673},[642],[363,14513],{},[363,14515,461],{"className":14516},[494],[363,14518,14520,14523],{"className":14519},[407],[363,14521,554],{"className":14522,"style":682},[407,408],[363,14524,14526],{"className":14525},[629],[363,14527,14529,14549],{"className":14528},[633,634],[363,14530,14532,14546],{"className":14531},[638],[363,14533,14535],{"className":14534,"style":11480},[642],[363,14536,14537,14540],{"style":11483},[363,14538],{"className":14539,"style":651},[650],[363,14541,14543],{"className":14542},[655,656,657,658],[363,14544,2810],{"className":14545},[407,658],[363,14547,666],{"className":14548},[665],[363,14550,14552],{"className":14551},[638],[363,14553,14555],{"className":14554,"style":8315},[642],[363,14556],{},[363,14558,558],{"className":14559},[407],[363,14561,14563,14566],{"className":14562},[407],[363,14564,561],{"className":14565},[407,408],[363,14567,14569],{"className":14568},[629],[363,14570,14572,14592],{"className":14571},[633,634],[363,14573,14575,14589],{"className":14574},[638],[363,14576,14578],{"className":14577,"style":11480},[642],[363,14579,14580,14583],{"style":730},[363,14581],{"className":14582,"style":651},[650],[363,14584,14586],{"className":14585},[655,656,657,658],[363,14587,2810],{"className":14588},[407,658],[363,14590,666],{"className":14591},[665],[363,14593,14595],{"className":14594},[638],[363,14596,14598],{"className":14597,"style":8315},[642],[363,14599],{},[363,14601,468],{"className":14602},[501],[363,14604,4722],{"className":14605},[407],[11,14607,14608,14609,14737],{},"对 ",[363,14610,14612,14642],{"className":14611,"translate":367},[366],[363,14613,14615],{"className":14614},[371],[373,14616,14617],{"xmlns":375},[377,14618,14619,14639],{},[380,14620,14621,14623,14629,14631,14637],{},[458,14622,461],{"stretchy":460},[12158,14624,14625,14627],{"accent":394},[383,14626,554],{},[458,14628,12164],{},[458,14630,898],{"separator":394},[12158,14632,14633,14635],{"accent":394},[383,14634,561],{},[458,14636,12164],{},[458,14638,468],{"stretchy":460},[387,14640,14641],{"encoding":389},"(\\tilde P,\\tilde Q)",[363,14643,14645],{"className":14644,"ariaHidden":394},[393],[363,14646,14648,14652,14655,14686,14689,14692,14734],{"className":14647},[398],[363,14649],{"className":14650,"style":14651},[402],"height:1.1702em;vertical-align:-0.25em;",[363,14653,461],{"className":14654},[494],[363,14656,14658],{"className":14657},[407,12198],[363,14659,14661],{"className":14660},[633],[363,14662,14664],{"className":14663},[638],[363,14665,14667,14675],{"className":14666,"style":12194},[642],[363,14668,14669,14672],{"style":12210},[363,14670],{"className":14671,"style":809},[650],[363,14673,554],{"className":14674,"style":682},[407,408],[363,14676,14677,14680],{"style":12219},[363,14678],{"className":14679,"style":809},[650],[363,14681,14683],{"className":14682,"style":12462},[12226],[363,14684,12164],{"className":14685},[407],[363,14687,898],{"className":14688},[920],[363,14690],{"className":14691,"style":754},[505],[363,14693,14695],{"className":14694},[407,12198],[363,14696,14698,14726],{"className":14697},[633,634],[363,14699,14701,14723],{"className":14700},[638],[363,14702,14704,14712],{"className":14703,"style":12194},[642],[363,14705,14706,14709],{"style":12210},[363,14707],{"className":14708,"style":809},[650],[363,14710,561],{"className":14711},[407,408],[363,14713,14714,14717],{"style":12219},[363,14715],{"className":14716,"style":809},[650],[363,14718,14720],{"className":14719,"style":12462},[12226],[363,14721,12164],{"className":14722},[407],[363,14724,666],{"className":14725},[665],[363,14727,14729],{"className":14728},[638],[363,14730,14732],{"className":14731,"style":12654},[642],[363,14733],{},[363,14735,468],{"className":14736},[501]," 使用 DPI，即得到联合凸性：",[363,14739,14741],{"className":14740,"translate":367},[528],[363,14742,14744,14924],{"className":14743,"translate":367},[366],[363,14745,14747],{"className":14746},[371],[373,14748,14749],{"xmlns":375,"display":537},[377,14750,14751,14921],{},[1590,14752,14753,14837],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,14754,14755,14761],{},[1599,14756,14757],{},[1602,14758,14759],{"scriptlevel":474,"displaystyle":394},[380,14760],{},[1599,14762,14763],{},[1602,14764,14765],{"scriptlevel":474,"displaystyle":394},[380,14766,14767,14769,14775,14777,14779,14785,14787,14789,14791,14793,14795,14797,14803,14805,14807,14809,14811,14817,14819,14821,14823,14825,14827,14829,14835],{},[380,14768],{},[543,14770,14771,14773],{},[383,14772,547],{},[383,14774,385],{},[458,14776,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,14778,11686],{},[543,14780,14781,14783],{},[383,14782,554],{},[463,14784,465],{},[458,14786,2817],{},[458,14788,461],{"stretchy":460},[463,14790,465],{},[458,14792,5160],{},[383,14794,11686],{},[458,14796,468],{"stretchy":460},[543,14798,14799,14801],{},[383,14800,554],{},[463,14802,2810],{},[1644,14804,1646],{},[458,14806,558],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[1644,14808,1646],{},[383,14810,11686],{},[543,14812,14813,14815],{},[383,14814,561],{},[463,14816,465],{},[458,14818,2817],{},[458,14820,461],{"stretchy":460},[463,14822,465],{},[458,14824,5160],{},[383,14826,11686],{},[458,14828,468],{"stretchy":460},[543,14830,14831,14833],{},[383,14832,561],{},[463,14834,2810],{},[458,14836,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[1596,14838,14839,14845],{},[1599,14840,14841],{},[1602,14842,14843],{"scriptlevel":474,"displaystyle":394},[380,14844],{},[1599,14846,14847],{},[1602,14848,14849],{"scriptlevel":474,"displaystyle":394},[380,14850,14851,14853,14855,14857,14859,14865,14867,14873,14875,14881,14883,14885,14887,14889,14891,14893,14895,14901,14903,14909,14911,14917,14919],{},[380,14852],{},[505,14854],{"width":3609},[458,14856,10299],{},[383,14858,11686],{},[543,14860,14861,14863],{},[383,14862,547],{},[383,14864,385],{},[458,14866,461],{"stretchy":460},[543,14868,14869,14871],{},[383,14870,554],{},[463,14872,465],{},[383,14874,558],{"mathvariant":557},[543,14876,14877,14879],{},[383,14878,561],{},[463,14880,465],{},[458,14882,468],{"stretchy":460},[458,14884,2817],{},[458,14886,461],{"stretchy":460},[463,14888,465],{},[458,14890,5160],{},[383,14892,11686],{},[458,14894,468],{"stretchy":460},[543,14896,14897,14899],{},[383,14898,547],{},[383,14900,385],{},[458,14902,461],{"stretchy":460},[543,14904,14905,14907],{},[383,14906,554],{},[463,14908,2810],{},[383,14910,558],{"mathvariant":557},[543,14912,14913,14915],{},[383,14914,561],{},[463,14916,2810],{},[458,14918,468],{"stretchy":460},[383,14920,4722],{"mathvariant":557},[387,14922,14923],{"encoding":389},"\\begin{aligned}\n&D_f\\big(\\lambda P_1+(1-\\lambda)P_2\n\\,\\big\\|\\,\\lambda Q_1+(1-\\lambda)Q_2\\big)\\\\\n&\\qquad\\le \\lambda D_f(P_1\\|Q_1)\n+(1-\\lambda)D_f(P_2\\|Q_2).\n\\end{aligned}",[363,14925,14927],{"className":14926,"ariaHidden":394},[393],[363,14928,14930,14934],{"className":14929},[398],[363,14931],{"className":14932,"style":14933},[402],"height:2.71em;vertical-align:-1.105em;",[363,14935,14937],{"className":14936},[407],[363,14938,14940,14984],{"className":14939},[1590],[363,14941,14943],{"className":14942},[1707],[363,14944,14946,14975],{"className":14945},[633,634],[363,14947,14949,14972],{"className":14948},[638],[363,14950,14953,14963],{"className":14951,"style":14952},[642],"height:1.605em;",[363,14954,14956,14960],{"style":14955},"top:-3.605em;",[363,14957],{"className":14958,"style":14959},[650],"height:2.85em;",[363,14961],{"className":14962},[407],[363,14964,14966,14969],{"style":14965},"top:-2.105em;",[363,14967],{"className":14968,"style":14959},[650],[363,14970],{"className":14971},[407],[363,14973,666],{"className":14974},[665],[363,14976,14978],{"className":14977},[638],[363,14979,14982],{"className":14980,"style":14981},[642],"height:1.105em;",[363,14983],{},[363,14985,14987],{"className":14986},[1798],[363,14988,14990,15659],{"className":14989},[633,634],[363,14991,14993,15656],{"className":14992},[638],[363,14994,14996,15338],{"className":14995,"style":14952},[642],[363,14997,14999,15002],{"style":14998},"top:-3.755em;",[363,15000],{"className":15001,"style":809},[650],[363,15003,15005,15008,15048,15054,15057,15097,15100,15103,15106,15109,15112,15115,15118,15121,15124,15127,15167,15170,15216,15219,15222,15262,15265,15268,15271,15274,15277,15280,15283,15286,15289,15292,15332],{"className":15004},[407],[363,15006],{"className":15007},[407],[363,15009,15011,15014],{"className":15010},[407],[363,15012,547],{"className":15013,"style":625},[407,408],[363,15015,15017],{"className":15016},[629],[363,15018,15020,15040],{"className":15019},[633,634],[363,15021,15023,15037],{"className":15022},[638],[363,15024,15026],{"className":15025,"style":643},[642],[363,15027,15028,15031],{"style":646},[363,15029],{"className":15030,"style":651},[650],[363,15032,15034],{"className":15033},[655,656,657,658],[363,15035,385],{"className":15036,"style":409},[407,408,658],[363,15038,666],{"className":15039},[665],[363,15041,15043],{"className":15042},[638],[363,15044,15046],{"className":15045,"style":673},[642],[363,15047],{},[363,15049,15051],{"className":15050},[407],[363,15052,461],{"className":15053},[767,10021],[363,15055,11686],{"className":15056},[407,408],[363,15058,15060,15063],{"className":15059},[407],[363,15061,554],{"className":15062,"style":682},[407,408],[363,15064,15066],{"className":15065},[629],[363,15067,15069,15089],{"className":15068},[633,634],[363,15070,15072,15086],{"className":15071},[638],[363,15073,15075],{"className":15074,"style":11480},[642],[363,15076,15077,15080],{"style":11483},[363,15078],{"className":15079,"style":651},[650],[363,15081,15083],{"className":15082},[655,656,657,658],[363,15084,465],{"className":15085},[407,658],[363,15087,666],{"className":15088},[665],[363,15090,15092],{"className":15091},[638],[363,15093,15095],{"className":15094,"style":8315},[642],[363,15096],{},[363,15098],{"className":15099,"style":2934},[505],[363,15101,2817],{"className":15102},[2938],[363,15104],{"className":15105,"style":2934},[505],[363,15107,461],{"className":15108},[494],[363,15110,465],{"className":15111},[407],[363,15113],{"className":15114,"style":2934},[505],[363,15116,5160],{"className":15117},[2938],[363,15119],{"className":15120,"style":2934},[505],[363,15122,11686],{"className":15123},[407,408],[363,15125,468],{"className":15126},[501],[363,15128,15130,15133],{"className":15129},[407],[363,15131,554],{"className":15132,"style":682},[407,408],[363,15134,15136],{"className":15135},[629],[363,15137,15139,15159],{"className":15138},[633,634],[363,15140,15142,15156],{"className":15141},[638],[363,15143,15145],{"className":15144,"style":11480},[642],[363,15146,15147,15150],{"style":11483},[363,15148],{"className":15149,"style":651},[650],[363,15151,15153],{"className":15152},[655,656,657,658],[363,15154,2810],{"className":15155},[407,658],[363,15157,666],{"className":15158},[665],[363,15160,15162],{"className":15161},[638],[363,15163,15165],{"className":15164,"style":8315},[642],[363,15166],{},[363,15168],{"className":15169,"style":754},[505],[363,15171,15173],{"className":15172},[407],[363,15174,15177],{"className":15175},[767,15176],"mult",[363,15178,15180,15207],{"className":15179},[633,634],[363,15181,15183,15204],{"className":15182},[638],[363,15184,15187],{"className":15185,"style":15186},[642],"height:0.85em;",[363,15188,15190,15194],{"style":15189},"top:-2.85em;",[363,15191],{"className":15192,"style":15193},[650],"height:3.2em;",[363,15195,15197],{"style":15196},"width:0.556em;height:1.2em;",[6670,15198,15201],{"xmlns":6672,"width":15199,"height":9797,"viewBox":15200},"0.556em","0 0 556 1200",[6678,15202],{"d":15203},"M145 15 v585 v0 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v0 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v0 v585 h43z\nM367 15 v585 v0 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v0 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M410 15 H367 v585 v0 v585 h43z",[363,15205,666],{"className":15206},[665],[363,15208,15210],{"className":15209},[638],[363,15211,15214],{"className":15212,"style":15213},[642],"height:0.35em;",[363,15215],{},[363,15217],{"className":15218,"style":754},[505],[363,15220,11686],{"className":15221},[407,408],[363,15223,15225,15228],{"className":15224},[407],[363,15226,561],{"className":15227},[407,408],[363,15229,15231],{"className":15230},[629],[363,15232,15234,15254],{"className":15233},[633,634],[363,15235,15237,15251],{"className":15236},[638],[363,15238,15240],{"className":15239,"style":11480},[642],[363,15241,15242,15245],{"style":730},[363,15243],{"className":15244,"style":651},[650],[363,15246,15248],{"className":15247},[655,656,657,658],[363,15249,465],{"className":15250},[407,658],[363,15252,666],{"className":15253},[665],[363,15255,15257],{"className":15256},[638],[363,15258,15260],{"className":15259,"style":8315},[642],[363,15261],{},[363,15263],{"className":15264,"style":2934},[505],[363,15266,2817],{"className":15267},[2938],[363,15269],{"className":15270,"style":2934},[505],[363,15272,461],{"className":15273},[494],[363,15275,465],{"className":15276},[407],[363,15278],{"className":15279,"style":2934},[505],[363,15281,5160],{"className":15282},[2938],[363,15284],{"className":15285,"style":2934},[505],[363,15287,11686],{"className":15288},[407,408],[363,15290,468],{"className":15291},[501],[363,15293,15295,15298],{"className":15294},[407],[363,15296,561],{"className":15297},[407,408],[363,15299,15301],{"className":15300},[629],[363,15302,15304,15324],{"className":15303},[633,634],[363,15305,15307,15321],{"className":15306},[638],[363,15308,15310],{"className":15309,"style":11480},[642],[363,15311,15312,15315],{"style":730},[363,15313],{"className":15314,"style":651},[650],[363,15316,15318],{"className":15317},[655,656,657,658],[363,15319,2810],{"className":15320},[407,658],[363,15322,666],{"className":15323},[665],[363,15325,15327],{"className":15326},[638],[363,15328,15330],{"className":15329,"style":8315},[642],[363,15331],{},[363,15333,15335],{"className":15334},[407],[363,15336,468],{"className":15337},[767,10021],[363,15339,15341,15344],{"style":15340},"top:-2.255em;",[363,15342],{"className":15343,"style":809},[650],[363,15345,15347,15350,15353,15356,15359,15362,15365,15405,15408,15448,15451,15491,15494,15497,15500,15503,15506,15509,15512,15515,15518,15521,15524,15564,15567,15607,15610,15650,15653],{"className":15346},[407],[363,15348],{"className":15349},[407],[363,15351],{"className":15352,"style":3981},[505],[363,15354],{"className":15355,"style":506},[505],[363,15357,10299],{"className":15358},[510],[363,15360],{"className":15361,"style":506},[505],[363,15363,11686],{"className":15364},[407,408],[363,15366,15368,15371],{"className":15367},[407],[363,15369,547],{"className":15370,"style":625},[407,408],[363,15372,15374],{"className":15373},[629],[363,15375,15377,15397],{"className":15376},[633,634],[363,15378,15380,15394],{"className":15379},[638],[363,15381,15383],{"className":15382,"style":643},[642],[363,15384,15385,15388],{"style":646},[363,15386],{"className":15387,"style":651},[650],[363,15389,15391],{"className":15390},[655,656,657,658],[363,15392,385],{"className":15393,"style":409},[407,408,658],[363,15395,666],{"className":15396},[665],[363,15398,15400],{"className":15399},[638],[363,15401,15403],{"className":15402,"style":673},[642],[363,15404],{},[363,15406,461],{"className":15407},[494],[363,15409,15411,15414],{"className":15410},[407],[363,15412,554],{"className":15413,"style":682},[407,408],[363,15415,15417],{"className":15416},[629],[363,15418,15420,15440],{"className":15419},[633,634],[363,15421,15423,15437],{"className":15422},[638],[363,15424,15426],{"className":15425,"style":11480},[642],[363,15427,15428,15431],{"style":11483},[363,15429],{"className":15430,"style":651},[650],[363,15432,15434],{"className":15433},[655,656,657,658],[363,15435,465],{"className":15436},[407,658],[363,15438,666],{"className":15439},[665],[363,15441,15443],{"className":15442},[638],[363,15444,15446],{"className":15445,"style":8315},[642],[363,15447],{},[363,15449,558],{"className":15450},[407],[363,15452,15454,15457],{"className":15453},[407],[363,15455,561],{"className":15456},[407,408],[363,15458,15460],{"className":15459},[629],[363,15461,15463,15483],{"className":15462},[633,634],[363,15464,15466,15480],{"className":15465},[638],[363,15467,15469],{"className":15468,"style":11480},[642],[363,15470,15471,15474],{"style":730},[363,15472],{"className":15473,"style":651},[650],[363,15475,15477],{"className":15476},[655,656,657,658],[363,15478,465],{"className":15479},[407,658],[363,15481,666],{"className":15482},[665],[363,15484,15486],{"className":15485},[638],[363,15487,15489],{"className":15488,"style":8315},[642],[363,15490],{},[363,15492,468],{"className":15493},[501],[363,15495],{"className":15496,"style":2934},[505],[363,15498,2817],{"className":15499},[2938],[363,15501],{"className":15502,"style":2934},[505],[363,15504,461],{"className":15505},[494],[363,15507,465],{"className":15508},[407],[363,15510],{"className":15511,"style":2934},[505],[363,15513,5160],{"className":15514},[2938],[363,15516],{"className":15517,"style":2934},[505],[363,15519,11686],{"className":15520},[407,408],[363,15522,468],{"className":15523},[501],[363,15525,15527,15530],{"className":15526},[407],[363,15528,547],{"className":15529,"style":625},[407,408],[363,15531,15533],{"className":15532},[629],[363,15534,15536,15556],{"className":15535},[633,634],[363,15537,15539,15553],{"className":15538},[638],[363,15540,15542],{"className":15541,"style":643},[642],[363,15543,15544,15547],{"style":646},[363,15545],{"className":15546,"style":651},[650],[363,15548,15550],{"className":15549},[655,656,657,658],[363,15551,385],{"className":15552,"style":409},[407,408,658],[363,15554,666],{"className":15555},[665],[363,15557,15559],{"className":15558},[638],[363,15560,15562],{"className":15561,"style":673},[642],[363,15563],{},[363,15565,461],{"className":15566},[494],[363,15568,15570,15573],{"className":15569},[407],[363,15571,554],{"className":15572,"style":682},[407,408],[363,15574,15576],{"className":15575},[629],[363,15577,15579,15599],{"className":15578},[633,634],[363,15580,15582,15596],{"className":15581},[638],[363,15583,15585],{"className":15584,"style":11480},[642],[363,15586,15587,15590],{"style":11483},[363,15588],{"className":15589,"style":651},[650],[363,15591,15593],{"className":15592},[655,656,657,658],[363,15594,2810],{"className":15595},[407,658],[363,15597,666],{"className":15598},[665],[363,15600,15602],{"className":15601},[638],[363,15603,15605],{"className":15604,"style":8315},[642],[363,15606],{},[363,15608,558],{"className":15609},[407],[363,15611,15613,15616],{"className":15612},[407],[363,15614,561],{"className":15615},[407,408],[363,15617,15619],{"className":15618},[629],[363,15620,15622,15642],{"className":15621},[633,634],[363,15623,15625,15639],{"className":15624},[638],[363,15626,15628],{"className":15627,"style":11480},[642],[363,15629,15630,15633],{"style":730},[363,15631],{"className":15632,"style":651},[650],[363,15634,15636],{"className":15635},[655,656,657,658],[363,15637,2810],{"className":15638},[407,658],[363,15640,666],{"className":15641},[665],[363,15643,15645],{"className":15644},[638],[363,15646,15648],{"className":15647,"style":8315},[642],[363,15649],{},[363,15651,468],{"className":15652},[501],[363,15654,4722],{"className":15655},[407],[363,15657,666],{"className":15658},[665],[363,15660,15662],{"className":15661},[638],[363,15663,15665],{"className":15664,"style":14981},[642],[363,15666],{},[11,15668,15669,15728,15729,2756,15795,15868,15869,15985,15986,16038,16039,16142,16143,16217],{},[1572,15670,15671,15672,6841,15700,11312],{},"第二步：联合凸 ",[363,15673,15675,15688],{"className":15674,"translate":367},[366],[363,15676,15678],{"className":15677},[371],[373,15679,15680],{"xmlns":375},[377,15681,15682,15686],{},[380,15683,15684],{},[458,15685,11337],{},[387,15687,11340],{"encoding":389},[363,15689,15691],{"className":15690,"ariaHidden":394},[393],[363,15692,15694,15697],{"className":15693},[398],[363,15695],{"className":15696,"style":11350},[402],[363,15698,11337],{"className":15699},[510],[363,15701,15703,15716],{"className":15702,"translate":367},[366],[363,15704,15706],{"className":15705},[371],[373,15707,15708],{"xmlns":375},[377,15709,15710,15714],{},[380,15711,15712],{},[383,15713,385],{},[387,15715,385],{"encoding":389},[363,15717,15719],{"className":15718,"ariaHidden":394},[393],[363,15720,15722,15725],{"className":15721},[398],[363,15723],{"className":15724,"style":403},[402],[363,15726,385],{"className":15727,"style":409},[407,408]," 固定 ",[363,15730,15732,15755],{"className":15731,"translate":367},[366],[363,15733,15735],{"className":15734},[371],[373,15736,15737],{"xmlns":375},[377,15738,15739,15752],{},[380,15740,15741,15743,15745,15748,15750],{},[383,15742,7908],{},[458,15744,898],{"separator":394},[383,15746,15747],{},"u",[458,15749,7275],{},[463,15751,474],{},[387,15753,15754],{"encoding":389},"s,u\\ge0",[363,15756,15758,15786],{"className":15757,"ariaHidden":394},[393],[363,15759,15761,15765,15768,15771,15774,15777,15780,15783],{"className":15760},[398],[363,15762],{"className":15763,"style":15764},[402],"height:0.8304em;vertical-align:-0.1944em;",[363,15766,7908],{"className":15767},[407,408],[363,15769,898],{"className":15770},[920],[363,15772],{"className":15773,"style":754},[505],[363,15775,15747],{"className":15776},[407,408],[363,15778],{"className":15779,"style":506},[505],[363,15781,7275],{"className":15782},[510],[363,15784],{"className":15785,"style":506},[505],[363,15787,15789,15792],{"className":15788},[398],[363,15790],{"className":15791,"style":520},[402],[363,15793,474],{"className":15794},[407],[363,15796,15798,15823],{"className":15797,"translate":367},[366],[363,15799,15801],{"className":15800},[371],[373,15802,15803],{"xmlns":375},[377,15804,15805,15821],{},[380,15806,15807,15809,15811,15813,15815,15817,15819],{},[383,15808,11686],{},[458,15810,6256],{},[458,15812,461],{"stretchy":460},[463,15814,474],{},[458,15816,898],{"separator":394},[463,15818,465],{},[458,15820,468],{"stretchy":460},[387,15822,11701],{"encoding":389},[363,15824,15826,15844],{"className":15825,"ariaHidden":394},[393],[363,15827,15829,15832,15835,15838,15841],{"className":15828},[398],[363,15830],{"className":15831,"style":11711},[402],[363,15833,11686],{"className":15834},[407,408],[363,15836],{"className":15837,"style":506},[505],[363,15839,6256],{"className":15840},[510],[363,15842],{"className":15843,"style":506},[505],[363,15845,15847,15850,15853,15856,15859,15862,15865],{"className":15846},[398],[363,15848],{"className":15849,"style":487},[402],[363,15851,461],{"className":15852},[494],[363,15854,474],{"className":15855},[407],[363,15857,898],{"className":15858},[920],[363,15860],{"className":15861,"style":754},[505],[363,15863,465],{"className":15864},[407],[363,15866,468],{"className":15867},[501],"，记目标值 ",[363,15870,15872,15906],{"className":15871,"translate":367},[366],[363,15873,15875],{"className":15874},[371],[373,15876,15877],{"xmlns":375},[377,15878,15879,15903],{},[380,15880,15881,15883,15885,15887,15889,15891,15893,15895,15897,15899,15901],{},[383,15882,7917],{},[458,15884,471],{},[383,15886,11686],{},[383,15888,7908],{},[458,15890,2817],{},[458,15892,461],{"stretchy":460},[463,15894,465],{},[458,15896,5160],{},[383,15898,11686],{},[458,15900,468],{"stretchy":460},[383,15902,15747],{},[387,15904,15905],{"encoding":389},"w=\\lambda s+(1-\\lambda)u",[363,15907,15909,15927,15949,15970],{"className":15908,"ariaHidden":394},[393],[363,15910,15912,15915,15918,15921,15924],{"className":15911},[398],[363,15913],{"className":15914,"style":2692},[402],[363,15916,7917],{"className":15917,"style":8621},[407,408],[363,15919],{"className":15920,"style":506},[505],[363,15922,471],{"className":15923},[510],[363,15925],{"className":15926,"style":506},[505],[363,15928,15930,15934,15937,15940,15943,15946],{"className":15929},[398],[363,15931],{"className":15932,"style":15933},[402],"height:0.7778em;vertical-align:-0.0833em;",[363,15935,11686],{"className":15936},[407,408],[363,15938,7908],{"className":15939},[407,408],[363,15941],{"className":15942,"style":2934},[505],[363,15944,2817],{"className":15945},[2938],[363,15947],{"className":15948,"style":2934},[505],[363,15950,15952,15955,15958,15961,15964,15967],{"className":15951},[398],[363,15953],{"className":15954,"style":487},[402],[363,15956,461],{"className":15957},[494],[363,15959,465],{"className":15960},[407],[363,15962],{"className":15963,"style":2934},[505],[363,15965,5160],{"className":15966},[2938],[363,15968],{"className":15969,"style":2934},[505],[363,15971,15973,15976,15979,15982],{"className":15972},[398],[363,15974],{"className":15975,"style":487},[402],[363,15977,11686],{"className":15978},[407,408],[363,15980,468],{"className":15981},[501],[363,15983,15747],{"className":15984},[407,408],"。在两点空间 ",[363,15987,15989,16011],{"className":15988,"translate":367},[366],[363,15990,15992],{"className":15991},[371],[373,15993,15994],{"xmlns":375},[377,15995,15996,16008],{},[380,15997,15998,16000,16002,16004,16006],{},[458,15999,3245],{"stretchy":460},[463,16001,465],{},[458,16003,898],{"separator":394},[463,16005,2810],{},[458,16007,3255],{"stretchy":460},[387,16009,16010],{"encoding":389},"\\{1,2\\}",[363,16012,16014],{"className":16013,"ariaHidden":394},[393],[363,16015,16017,16020,16023,16026,16029,16032,16035],{"className":16016},[398],[363,16018],{"className":16019,"style":487},[402],[363,16021,3245],{"className":16022},[494],[363,16024,465],{"className":16025},[407],[363,16027,898],{"className":16028},[920],[363,16030],{"className":16031,"style":754},[505],[363,16033,2810],{"className":16034},[407],[363,16036,3255],{"className":16037},[501]," 上取同一个底分布 ",[363,16040,16042,16075],{"className":16041,"translate":367},[366],[363,16043,16045],{"className":16044},[371],[373,16046,16047],{"xmlns":375},[377,16048,16049,16072],{},[380,16050,16051,16053,16055,16057,16060,16062,16064,16066,16068,16070],{},[383,16052,561],{},[458,16054,471],{},[458,16056,461],{"stretchy":460},[383,16058,16059],{},"δ",[458,16061,898],{"separator":394},[1644,16063,1646],{},[463,16065,465],{},[458,16067,5160],{},[383,16069,16059],{},[458,16071,468],{"stretchy":460},[387,16073,16074],{"encoding":389},"Q=(\\delta,\\,1-\\delta)",[363,16076,16078,16096,16130],{"className":16077,"ariaHidden":394},[393],[363,16079,16081,16084,16087,16090,16093],{"className":16080},[398],[363,16082],{"className":16083,"style":913},[402],[363,16085,561],{"className":16086},[407,408],[363,16088],{"className":16089,"style":506},[505],[363,16091,471],{"className":16092},[510],[363,16094],{"className":16095,"style":506},[505],[363,16097,16099,16102,16105,16109,16112,16115,16118,16121,16124,16127],{"className":16098},[398],[363,16100],{"className":16101,"style":487},[402],[363,16103,461],{"className":16104},[494],[363,16106,16059],{"className":16107,"style":16108},[407,408],"margin-right:0.0379em;",[363,16110,898],{"className":16111},[920],[363,16113],{"className":16114,"style":754},[505],[363,16116],{"className":16117,"style":754},[505],[363,16119,465],{"className":16120},[407],[363,16122],{"className":16123,"style":2934},[505],[363,16125,5160],{"className":16126},[2938],[363,16128],{"className":16129,"style":2934},[505],[363,16131,16133,16136,16139],{"className":16132},[398],[363,16134],{"className":16135,"style":487},[402],[363,16137,16059],{"className":16138,"style":16108},[407,408],[363,16140,468],{"className":16141},[501],"（",[363,16144,16146,16172],{"className":16145,"translate":367},[366],[363,16147,16149],{"className":16148},[371],[373,16150,16151],{"xmlns":375},[377,16152,16153,16169],{},[380,16154,16155,16157,16159,16161,16163,16165,16167],{},[383,16156,16059],{},[458,16158,6256],{},[458,16160,461],{"stretchy":460},[463,16162,474],{},[458,16164,898],{"separator":394},[463,16166,465],{},[458,16168,468],{"stretchy":460},[387,16170,16171],{"encoding":389},"\\delta\\in(0,1)",[363,16173,16175,16193],{"className":16174,"ariaHidden":394},[393],[363,16176,16178,16181,16184,16187,16190],{"className":16177},[398],[363,16179],{"className":16180,"style":11711},[402],[363,16182,16059],{"className":16183,"style":16108},[407,408],[363,16185],{"className":16186,"style":506},[505],[363,16188,6256],{"className":16189},[510],[363,16191],{"className":16192,"style":506},[505],[363,16194,16196,16199,16202,16205,16208,16211,16214],{"className":16195},[398],[363,16197],{"className":16198,"style":487},[402],[363,16200,461],{"className":16201},[494],[363,16203,474],{"className":16204},[407],[363,16206,898],{"className":16207},[920],[363,16209],{"className":16210,"style":754},[505],[363,16212,465],{"className":16213},[407],[363,16215,468],{"className":16216},[501]," 充分小），并取似然比在第一坐标上为常数的分布：",[363,16219,16221],{"className":16220,"translate":367},[528],[363,16222,16224,16299],{"className":16223,"translate":367},[366],[363,16225,16227],{"className":16226},[371],[373,16228,16229],{"xmlns":375,"display":537},[377,16230,16231,16296],{},[380,16232,16233,16239,16241,16243,16245,16247,16249,16252,16254,16256,16258,16260,16262,16264,16266,16272,16274,16276,16278,16280,16282,16284,16286,16288,16290,16292,16294],{},[543,16234,16235,16237],{},[383,16236,554],{},[463,16238,465],{},[458,16240,471],{},[458,16242,461],{"stretchy":460},[383,16244,7908],{},[383,16246,16059],{},[458,16248,898],{"separator":394},[1644,16250,16251],{},"  ",[463,16253,465],{},[458,16255,5160],{},[383,16257,7908],{},[383,16259,16059],{},[458,16261,468],{"stretchy":460},[458,16263,898],{"separator":394},[505,16265],{"width":3609},[543,16267,16268,16270],{},[383,16269,554],{},[463,16271,2810],{},[458,16273,471],{},[458,16275,461],{"stretchy":460},[383,16277,15747],{},[383,16279,16059],{},[458,16281,898],{"separator":394},[1644,16283,16251],{},[463,16285,465],{},[458,16287,5160],{},[383,16289,15747],{},[383,16291,16059],{},[458,16293,468],{"stretchy":460},[458,16295,898],{"separator":394},[387,16297,16298],{"encoding":389},"P_1=(s\\delta,\\;1-s\\delta),\\qquad\nP_2=(u\\delta,\\;1-u\\delta),",[363,16300,16302,16358,16392,16462,16498],{"className":16301,"ariaHidden":394},[393],[363,16303,16305,16309,16349,16352,16355],{"className":16304},[398],[363,16306],{"className":16307,"style":16308},[402],"height:0.8333em;vertical-align:-0.15em;",[363,16310,16312,16315],{"className":16311},[407],[363,16313,554],{"className":16314,"style":682},[407,408],[363,16316,16318],{"className":16317},[629],[363,16319,16321,16341],{"className":16320},[633,634],[363,16322,16324,16338],{"className":16323},[638],[363,16325,16327],{"className":16326,"style":11480},[642],[363,16328,16329,16332],{"style":11483},[363,16330],{"className":16331,"style":651},[650],[363,16333,16335],{"className":16334},[655,656,657,658],[363,16336,465],{"className":16337},[407,658],[363,16339,666],{"className":16340},[665],[363,16342,16344],{"className":16343},[638],[363,16345,16347],{"className":16346,"style":8315},[642],[363,16348],{},[363,16350],{"className":16351,"style":506},[505],[363,16353,471],{"className":16354},[510],[363,16356],{"className":16357,"style":506},[505],[363,16359,16361,16364,16367,16371,16374,16377,16380,16383,16386,16389],{"className":16360},[398],[363,16362],{"className":16363,"style":487},[402],[363,16365,461],{"className":16366},[494],[363,16368,16370],{"className":16369,"style":16108},[407,408],"sδ",[363,16372,898],{"className":16373},[920],[363,16375],{"className":16376,"style":506},[505],[363,16378],{"className":16379,"style":754},[505],[363,16381,465],{"className":16382},[407],[363,16384],{"className":16385,"style":2934},[505],[363,16387,5160],{"className":16388},[2938],[363,16390],{"className":16391,"style":2934},[505],[363,16393,16395,16398,16401,16404,16407,16410,16413,16453,16456,16459],{"className":16394},[398],[363,16396],{"className":16397,"style":487},[402],[363,16399,16370],{"className":16400,"style":16108},[407,408],[363,16402,468],{"className":16403},[501],[363,16405,898],{"className":16406},[920],[363,16408],{"className":16409,"style":3981},[505],[363,16411],{"className":16412,"style":754},[505],[363,16414,16416,16419],{"className":16415},[407],[363,16417,554],{"className":16418,"style":682},[407,408],[363,16420,16422],{"className":16421},[629],[363,16423,16425,16445],{"className":16424},[633,634],[363,16426,16428,16442],{"className":16427},[638],[363,16429,16431],{"className":16430,"style":11480},[642],[363,16432,16433,16436],{"style":11483},[363,16434],{"className":16435,"style":651},[650],[363,16437,16439],{"className":16438},[655,656,657,658],[363,16440,2810],{"className":16441},[407,658],[363,16443,666],{"className":16444},[665],[363,16446,16448],{"className":16447},[638],[363,16449,16451],{"className":16450,"style":8315},[642],[363,16452],{},[363,16454],{"className":16455,"style":506},[505],[363,16457,471],{"className":16458},[510],[363,16460],{"className":16461,"style":506},[505],[363,16463,16465,16468,16471,16474,16477,16480,16483,16486,16489,16492,16495],{"className":16464},[398],[363,16466],{"className":16467,"style":487},[402],[363,16469,461],{"className":16470},[494],[363,16472,15747],{"className":16473},[407,408],[363,16475,16059],{"className":16476,"style":16108},[407,408],[363,16478,898],{"className":16479},[920],[363,16481],{"className":16482,"style":506},[505],[363,16484],{"className":16485,"style":754},[505],[363,16487,465],{"className":16488},[407],[363,16490],{"className":16491,"style":2934},[505],[363,16493,5160],{"className":16494},[2938],[363,16496],{"className":16497,"style":2934},[505],[363,16499,16501,16504,16507,16510,16513],{"className":16500},[398],[363,16502],{"className":16503,"style":487},[402],[363,16505,15747],{"className":16506},[407,408],[363,16508,16059],{"className":16509,"style":16108},[407,408],[363,16511,468],{"className":16512},[501],[363,16514,898],{"className":16515},[920],[11,16517,16142,16518,16547,16548,16590,16591,2756,16619,16782,16783,16812,16813,3092],{},[363,16519,16521,16535],{"className":16520,"translate":367},[366],[363,16522,16524],{"className":16523},[371],[373,16525,16526],{"xmlns":375},[377,16527,16528,16532],{},[380,16529,16530],{},[383,16531,16059],{},[387,16533,16534],{"encoding":389},"\\delta",[363,16536,16538],{"className":16537,"ariaHidden":394},[393],[363,16539,16541,16544],{"className":16540},[398],[363,16542],{"className":16543,"style":12944},[402],[363,16545,16059],{"className":16546,"style":16108},[407,408]," 足够小时这都是合法概率分布；",[363,16549,16551,16569],{"className":16550,"translate":367},[366],[363,16552,16554],{"className":16553},[371],[373,16555,16556],{"xmlns":375},[377,16557,16558,16566],{},[380,16559,16560,16562,16564],{},[463,16561,474],{},[458,16563,898],{"separator":394},[463,16565,465],{},[387,16567,16568],{"encoding":389},"0,1",[363,16570,16572],{"className":16571,"ariaHidden":394},[393],[363,16573,16575,16578,16581,16584,16587],{"className":16574},[398],[363,16576],{"className":16577,"style":9705},[402],[363,16579,474],{"className":16580},[407],[363,16582,898],{"className":16583},[920],[363,16585],{"className":16586,"style":754},[505],[363,16588,465],{"className":16589},[407]," 两点上的似然比分别为 ",[363,16592,16594,16607],{"className":16593,"translate":367},[366],[363,16595,16597],{"className":16596},[371],[373,16598,16599],{"xmlns":375},[377,16600,16601,16605],{},[380,16602,16603],{},[383,16604,7908],{},[387,16606,7908],{"encoding":389},[363,16608,16610],{"className":16609,"ariaHidden":394},[393],[363,16611,16613,16616],{"className":16612},[398],[363,16614],{"className":16615,"style":2692},[402],[363,16617,7908],{"className":16618},[407,408],[363,16620,16622,16664],{"className":16621,"translate":367},[366],[363,16623,16625],{"className":16624},[371],[373,16626,16627],{"xmlns":375},[377,16628,16629,16661],{},[380,16630,16631,16633,16635,16637,16639,16641],{},[383,16632,4505],{},[458,16634,461],{"stretchy":460},[383,16636,7908],{},[458,16638,468],{"stretchy":460},[458,16640,471],{},[586,16642,16643,16653],{},[380,16644,16645,16647,16649,16651],{},[463,16646,465],{},[458,16648,5160],{},[383,16650,7908],{},[383,16652,16059],{},[380,16654,16655,16657,16659],{},[463,16656,465],{},[458,16658,5160],{},[383,16660,16059],{},[387,16662,16663],{"encoding":389},"g(s)=\\frac{1-s\\delta}{1-\\delta}",[363,16665,16667,16694],{"className":16666,"ariaHidden":394},[393],[363,16668,16670,16673,16676,16679,16682,16685,16688,16691],{"className":16669},[398],[363,16671],{"className":16672,"style":487},[402],[363,16674,4505],{"className":16675,"style":1328},[407,408],[363,16677,461],{"className":16678},[494],[363,16680,7908],{"className":16681},[407,408],[363,16683,468],{"className":16684},[501],[363,16686],{"className":16687,"style":506},[505],[363,16689,471],{"className":16690},[510],[363,16692],{"className":16693,"style":506},[505],[363,16695,16697,16701],{"className":16696},[398],[363,16698],{"className":16699,"style":16700},[402],"height:1.2834em;vertical-align:-0.4033em;",[363,16702,16704,16707,16779],{"className":16703},[407],[363,16705],{"className":16706},[494,789],[363,16708,16710],{"className":16709},[586],[363,16711,16713,16770],{"className":16712},[633,634],[363,16714,16716,16767],{"className":16715},[638],[363,16717,16719,16739,16747],{"className":16718,"style":3034},[642],[363,16720,16721,16724],{"style":2874},[363,16722],{"className":16723,"style":809},[650],[363,16725,16727],{"className":16726},[655,656,657,658],[363,16728,16730,16733,16736],{"className":16729},[407,658],[363,16731,465],{"className":16732},[407,658],[363,16734,5160],{"className":16735},[2938,658],[363,16737,16059],{"className":16738,"style":16108},[407,408,658],[363,16740,16741,16744],{"style":821},[363,16742],{"className":16743,"style":809},[650],[363,16745],{"className":16746,"style":829},[828],[363,16748,16749,16752],{"style":2897},[363,16750],{"className":16751,"style":809},[650],[363,16753,16755],{"className":16754},[655,656,657,658],[363,16756,16758,16761,16764],{"className":16757},[407,658],[363,16759,465],{"className":16760},[407,658],[363,16762,5160],{"className":16763},[2938,658],[363,16765,16370],{"className":16766,"style":16108},[407,408,658],[363,16768,666],{"className":16769},[665],[363,16771,16773],{"className":16772},[638],[363,16774,16777],{"className":16775,"style":16776},[642],"height:0.4033em;",[363,16778],{},[363,16780],{"className":16781},[501,789],"）。于是一般公式给出：对任何第一坐标似然比为常值 ",[363,16784,16786,16800],{"className":16785,"translate":367},[366],[363,16787,16789],{"className":16788},[371],[373,16790,16791],{"xmlns":375},[377,16792,16793,16798],{},[380,16794,16795],{},[383,16796,16797],{},"r",[387,16799,16797],{"encoding":389},[363,16801,16803],{"className":16802,"ariaHidden":394},[393],[363,16804,16806,16809],{"className":16805},[398],[363,16807],{"className":16808,"style":2692},[402],[363,16810,16797],{"className":16811,"style":625},[407,408]," 的分布 ",[363,16814,16816,16836],{"className":16815,"translate":367},[366],[363,16817,16819],{"className":16818},[371],[373,16820,16821],{"xmlns":375},[377,16822,16823,16833],{},[380,16824,16825,16827,16829,16831],{},[383,16826,554],{},[458,16828,461],{"stretchy":460},[383,16830,16797],{},[458,16832,468],{"stretchy":460},[387,16834,16835],{"encoding":389},"P(r)",[363,16837,16839],{"className":16838,"ariaHidden":394},[393],[363,16840,16842,16845,16848,16851,16854],{"className":16841},[398],[363,16843],{"className":16844,"style":487},[402],[363,16846,554],{"className":16847,"style":682},[407,408],[363,16849,461],{"className":16850},[494],[363,16852,16797],{"className":16853,"style":625},[407,408],[363,16855,468],{"className":16856},[501],[363,16858,16860],{"className":16859,"translate":367},[528],[363,16861,16863,16995],{"className":16862,"translate":367},[366],[363,16864,16866],{"className":16865},[371],[373,16867,16868],{"xmlns":375,"display":537},[377,16869,16870,16992],{},[1590,16871,16872,16928],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,16873,16874,16906],{},[1599,16875,16876],{},[1602,16877,16878],{"scriptlevel":474,"displaystyle":394},[380,16879,16880,16886,16888,16890,16892,16894,16896,16898,16900,16902,16904],{},[543,16881,16882,16884],{},[383,16883,547],{},[383,16885,385],{},[458,16887,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,16889,554],{},[458,16891,461],{"stretchy":460},[383,16893,16797],{},[458,16895,468],{"stretchy":460},[1644,16897,1646],{},[458,16899,558],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[1644,16901,1646],{},[383,16903,561],{},[458,16905,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[1599,16907,16908],{},[1602,16909,16910],{"scriptlevel":474,"displaystyle":394},[380,16911,16912,16914,16916,16918,16920,16922,16924,16926],{},[380,16913],{},[458,16915,471],{},[383,16917,16059],{},[1644,16919,1646],{},[383,16921,385],{},[458,16923,461],{"stretchy":460},[383,16925,16797],{},[458,16927,468],{"stretchy":460},[1596,16929,16930,16936],{},[1599,16931,16932],{},[1602,16933,16934],{"scriptlevel":474,"displaystyle":394},[380,16935],{},[1599,16937,16938],{},[1602,16939,16940],{"scriptlevel":474,"displaystyle":394},[380,16941,16942,16944,16946,16948,16950,16952,16954,16956,16958,16960,16962,16964,16990],{},[380,16943],{},[505,16945],{"width":3609},[458,16947,2817],{},[458,16949,461],{"stretchy":460},[463,16951,465],{},[458,16953,5160],{},[383,16955,16059],{},[458,16957,468],{"stretchy":460},[1644,16959,1646],{},[383,16961,385],{},[1644,16963,1651],{},[380,16965,16966,16968,16988],{},[458,16967,461],{"fence":394},[586,16969,16970,16980],{},[380,16971,16972,16974,16976,16978],{},[463,16973,465],{},[458,16975,5160],{},[383,16977,16797],{},[383,16979,16059],{},[380,16981,16982,16984,16986],{},[463,16983,465],{},[458,16985,5160],{},[383,16987,16059],{},[458,16989,468],{"fence":394},[383,16991,4722],{"mathvariant":557},[387,16993,16994],{"encoding":389},"\\begin{aligned}\nD_f\\big(P(r)\\,\\big\\|\\,Q\\big)\n&=\\delta\\,f(r)\\\\\n&\\qquad +(1-\\delta)\\,\nf\\!\\left(\\frac{1-r\\delta}{1-\\delta}\\right).\n\\end{aligned}",[363,16996,16998],{"className":16997,"ariaHidden":394},[393],[363,16999,17001,17005],{"className":17000},[398],[363,17002],{"className":17003,"style":17004},[402],"height:3.91em;vertical-align:-1.705em;",[363,17006,17008],{"className":17007},[407],[363,17009,17011,17163],{"className":17010},[1590],[363,17012,17014],{"className":17013},[1707],[363,17015,17017,17155],{"className":17016},[633,634],[363,17018,17020,17152],{"className":17019},[638],[363,17021,17024,17143],{"className":17022,"style":17023},[642],"height:2.205em;",[363,17025,17027,17030],{"style":17026},"top:-4.805em;",[363,17028],{"className":17029,"style":1724},[650],[363,17031,17033,17073,17079,17082,17085,17088,17091,17094,17131,17134,17137],{"className":17032},[407],[363,17034,17036,17039],{"className":17035},[407],[363,17037,547],{"className":17038,"style":625},[407,408],[363,17040,17042],{"className":17041},[629],[363,17043,17045,17065],{"className":17044},[633,634],[363,17046,17048,17062],{"className":17047},[638],[363,17049,17051],{"className":17050,"style":643},[642],[363,17052,17053,17056],{"style":646},[363,17054],{"className":17055,"style":651},[650],[363,17057,17059],{"className":17058},[655,656,657,658],[363,17060,385],{"className":17061,"style":409},[407,408,658],[363,17063,666],{"className":17064},[665],[363,17066,17068],{"className":17067},[638],[363,17069,17071],{"className":17070,"style":673},[642],[363,17072],{},[363,17074,17076],{"className":17075},[407],[363,17077,461],{"className":17078},[767,10021],[363,17080,554],{"className":17081,"style":682},[407,408],[363,17083,461],{"className":17084},[494],[363,17086,16797],{"className":17087,"style":625},[407,408],[363,17089,468],{"className":17090},[501],[363,17092],{"className":17093,"style":754},[505],[363,17095,17097],{"className":17096},[407],[363,17098,17100],{"className":17099},[767,15176],[363,17101,17103,17123],{"className":17102},[633,634],[363,17104,17106,17120],{"className":17105},[638],[363,17107,17109],{"className":17108,"style":15186},[642],[363,17110,17111,17114],{"style":15189},[363,17112],{"className":17113,"style":15193},[650],[363,17115,17116],{"style":15196},[6670,17117,17118],{"xmlns":6672,"width":15199,"height":9797,"viewBox":15200},[6678,17119],{"d":15203},[363,17121,666],{"className":17122},[665],[363,17124,17126],{"className":17125},[638],[363,17127,17129],{"className":17128,"style":15213},[642],[363,17130],{},[363,17132],{"className":17133,"style":754},[505],[363,17135,561],{"className":17136},[407,408],[363,17138,17140],{"className":17139},[407],[363,17141,468],{"className":17142},[767,10021],[363,17144,17146,17149],{"style":17145},"top:-2.695em;",[363,17147],{"className":17148,"style":1724},[650],[363,17150],{"className":17151},[407],[363,17153,666],{"className":17154},[665],[363,17156,17158],{"className":17157},[638],[363,17159,17161],{"className":17160,"style":9901},[642],[363,17162],{},[363,17164,17166],{"className":17165},[1798],[363,17167,17169,17383],{"className":17168},[633,634],[363,17170,17172,17380],{"className":17171},[638],[363,17173,17175,17213],{"className":17174,"style":17023},[642],[363,17176,17177,17180],{"style":17026},[363,17178],{"className":17179,"style":1724},[650],[363,17181,17183,17186,17189,17192,17195,17198,17201,17204,17207,17210],{"className":17182},[407],[363,17184],{"className":17185},[407],[363,17187],{"className":17188,"style":506},[505],[363,17190,471],{"className":17191},[510],[363,17193],{"className":17194,"style":506},[505],[363,17196,16059],{"className":17197,"style":16108},[407,408],[363,17199],{"className":17200,"style":754},[505],[363,17202,385],{"className":17203,"style":409},[407,408],[363,17205,461],{"className":17206},[494],[363,17208,16797],{"className":17209,"style":625},[407,408],[363,17211,468],{"className":17212},[501],[363,17214,17215,17218],{"style":17145},[363,17216],{"className":17217,"style":1724},[650],[363,17219,17221,17224,17227,17230,17233,17236,17239,17242,17245,17248,17251,17254,17257,17260,17263,17266,17269,17374,17377],{"className":17220},[407],[363,17222],{"className":17223},[407],[363,17225],{"className":17226,"style":3981},[505],[363,17228],{"className":17229,"style":2934},[505],[363,17231,2817],{"className":17232},[2938],[363,17234],{"className":17235,"style":2934},[505],[363,17237,461],{"className":17238},[494],[363,17240,465],{"className":17241},[407],[363,17243],{"className":17244,"style":2934},[505],[363,17246,5160],{"className":17247},[2938],[363,17249],{"className":17250,"style":2934},[505],[363,17252,16059],{"className":17253,"style":16108},[407,408],[363,17255,468],{"className":17256},[501],[363,17258],{"className":17259,"style":754},[505],[363,17261,385],{"className":17262,"style":409},[407,408],[363,17264],{"className":17265,"style":1859},[505],[363,17267],{"className":17268,"style":754},[505],[363,17270,17272,17278,17368],{"className":17271},[758],[363,17273,17275],{"className":17274,"style":763},[494,762],[363,17276,461],{"className":17277},[767,657],[363,17279,17281,17284,17365],{"className":17280},[407],[363,17282],{"className":17283},[494,789],[363,17285,17287],{"className":17286},[586],[363,17288,17290,17356],{"className":17289},[633,634],[363,17291,17293,17353],{"className":17292},[638],[363,17294,17296,17319,17327],{"className":17295,"style":802},[642],[363,17297,17298,17301],{"style":805},[363,17299],{"className":17300,"style":809},[650],[363,17302,17304,17307,17310,17313,17316],{"className":17303},[407],[363,17305,465],{"className":17306},[407],[363,17308],{"className":17309,"style":2934},[505],[363,17311,5160],{"className":17312},[2938],[363,17314],{"className":17315,"style":2934},[505],[363,17317,16059],{"className":17318,"style":16108},[407,408],[363,17320,17321,17324],{"style":821},[363,17322],{"className":17323,"style":809},[650],[363,17325],{"className":17326,"style":829},[828],[363,17328,17329,17332],{"style":832},[363,17330],{"className":17331,"style":809},[650],[363,17333,17335,17338,17341,17344,17347,17350],{"className":17334},[407],[363,17336,465],{"className":17337},[407],[363,17339],{"className":17340,"style":2934},[505],[363,17342,5160],{"className":17343},[2938],[363,17345],{"className":17346,"style":2934},[505],[363,17348,16797],{"className":17349,"style":625},[407,408],[363,17351,16059],{"className":17352,"style":16108},[407,408],[363,17354,666],{"className":17355},[665],[363,17357,17359],{"className":17358},[638],[363,17360,17363],{"className":17361,"style":17362},[642],"height:0.7693em;",[363,17364],{},[363,17366],{"className":17367},[501,789],[363,17369,17371],{"className":17370,"style":763},[501,762],[363,17372,468],{"className":17373},[767,657],[363,17375],{"className":17376,"style":754},[505],[363,17378,4722],{"className":17379},[407],[363,17381,666],{"className":17382},[665],[363,17384,17386],{"className":17385},[638],[363,17387,17389],{"className":17388,"style":9901},[642],[363,17390],{},[11,17392,17393,17394,5992,17445,17496,17497,17548,17549,17664,17665,6841,17668,17696],{},"把 ",[363,17395,17397,17415],{"className":17396,"translate":367},[366],[363,17398,17400],{"className":17399},[371],[373,17401,17402],{"xmlns":375},[377,17403,17404,17412],{},[380,17405,17406,17408,17410],{},[383,17407,16797],{},[458,17409,471],{},[383,17411,7908],{},[387,17413,17414],{"encoding":389},"r=s",[363,17416,17418,17436],{"className":17417,"ariaHidden":394},[393],[363,17419,17421,17424,17427,17430,17433],{"className":17420},[398],[363,17422],{"className":17423,"style":2692},[402],[363,17425,16797],{"className":17426,"style":625},[407,408],[363,17428],{"className":17429,"style":506},[505],[363,17431,471],{"className":17432},[510],[363,17434],{"className":17435,"style":506},[505],[363,17437,17439,17442],{"className":17438},[398],[363,17440],{"className":17441,"style":2692},[402],[363,17443,7908],{"className":17444},[407,408],[363,17446,17448,17466],{"className":17447,"translate":367},[366],[363,17449,17451],{"className":17450},[371],[373,17452,17453],{"xmlns":375},[377,17454,17455,17463],{},[380,17456,17457,17459,17461],{},[383,17458,16797],{},[458,17460,471],{},[383,17462,15747],{},[387,17464,17465],{"encoding":389},"r=u",[363,17467,17469,17487],{"className":17468,"ariaHidden":394},[393],[363,17470,17472,17475,17478,17481,17484],{"className":17471},[398],[363,17473],{"className":17474,"style":2692},[402],[363,17476,16797],{"className":17477,"style":625},[407,408],[363,17479],{"className":17480,"style":506},[505],[363,17482,471],{"className":17483},[510],[363,17485],{"className":17486,"style":506},[505],[363,17488,17490,17493],{"className":17489},[398],[363,17491],{"className":17492,"style":2692},[402],[363,17494,15747],{"className":17495},[407,408],"、以及混合后的 ",[363,17498,17500,17518],{"className":17499,"translate":367},[366],[363,17501,17503],{"className":17502},[371],[373,17504,17505],{"xmlns":375},[377,17506,17507,17515],{},[380,17508,17509,17511,17513],{},[383,17510,16797],{},[458,17512,471],{},[383,17514,7917],{},[387,17516,17517],{"encoding":389},"r=w",[363,17519,17521,17539],{"className":17520,"ariaHidden":394},[393],[363,17522,17524,17527,17530,17533,17536],{"className":17523},[398],[363,17525],{"className":17526,"style":2692},[402],[363,17528,16797],{"className":17529,"style":625},[407,408],[363,17531],{"className":17532,"style":506},[505],[363,17534,471],{"className":17535},[510],[363,17537],{"className":17538,"style":506},[505],[363,17540,17542,17545],{"className":17541},[398],[363,17543],{"className":17544,"style":2692},[402],[363,17546,7917],{"className":17547,"style":8621},[407,408],"（混合后第一坐标似然比恰为 ",[363,17550,17552,17586],{"className":17551,"translate":367},[366],[363,17553,17555],{"className":17554},[371],[373,17556,17557],{"xmlns":375},[377,17558,17559,17583],{},[380,17560,17561,17563,17565,17567,17569,17571,17573,17575,17577,17579,17581],{},[383,17562,11686],{},[383,17564,7908],{},[458,17566,2817],{},[458,17568,461],{"stretchy":460},[463,17570,465],{},[458,17572,5160],{},[383,17574,11686],{},[458,17576,468],{"stretchy":460},[383,17578,15747],{},[458,17580,471],{},[383,17582,7917],{},[387,17584,17585],{"encoding":389},"\\lambda s+(1-\\lambda)u=w",[363,17587,17589,17610,17631,17655],{"className":17588,"ariaHidden":394},[393],[363,17590,17592,17595,17598,17601,17604,17607],{"className":17591},[398],[363,17593],{"className":17594,"style":15933},[402],[363,17596,11686],{"className":17597},[407,408],[363,17599,7908],{"className":17600},[407,408],[363,17602],{"className":17603,"style":2934},[505],[363,17605,2817],{"className":17606},[2938],[363,17608],{"className":17609,"style":2934},[505],[363,17611,17613,17616,17619,17622,17625,17628],{"className":17612},[398],[363,17614],{"className":17615,"style":487},[402],[363,17617,461],{"className":17618},[494],[363,17620,465],{"className":17621},[407],[363,17623],{"className":17624,"style":2934},[505],[363,17626,5160],{"className":17627},[2938],[363,17629],{"className":17630,"style":2934},[505],[363,17632,17634,17637,17640,17643,17646,17649,17652],{"className":17633},[398],[363,17635],{"className":17636,"style":487},[402],[363,17638,11686],{"className":17639},[407,408],[363,17641,468],{"className":17642},[501],[363,17644,15747],{"className":17645},[407,408],[363,17647],{"className":17648,"style":506},[505],[363,17650,471],{"className":17651},[510],[363,17653],{"className":17654,"style":506},[505],[363,17656,17658,17661],{"className":17657},[398],[363,17659],{"className":17660,"style":2692},[402],[363,17662,7917],{"className":17663,"style":8621},[407,408],"，因为两个分布在",[1572,17666,17667],{},"同一个",[363,17669,17671,17684],{"className":17670,"translate":367},[366],[363,17672,17674],{"className":17673},[371],[373,17675,17676],{"xmlns":375},[377,17677,17678,17682],{},[380,17679,17680],{},[383,17681,561],{},[387,17683,561],{"encoding":389},[363,17685,17687],{"className":17686,"ariaHidden":394},[393],[363,17688,17690,17693],{"className":17689},[398],[363,17691],{"className":17692,"style":913},[402],[363,17694,561],{"className":17695},[407,408]," 下混合，比值线性）代入第一步的联合凸性：",[363,17698,17700],{"className":17699,"translate":367},[528],[363,17701,17703,17900],{"className":17702,"translate":367},[366],[363,17704,17706],{"className":17705},[371],[373,17707,17708],{"xmlns":375,"display":537},[377,17709,17710,17897],{},[1590,17711,17712,17764,17825],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,17713,17714,17720],{},[1599,17715,17716],{},[1602,17717,17718],{"scriptlevel":474,"displaystyle":394},[380,17719],{},[1599,17721,17722],{},[1602,17723,17724],{"scriptlevel":474,"displaystyle":394},[380,17725,17726,17728,17730,17732,17734,17736,17738,17740,17742,17744,17746,17748,17750,17752,17754,17756,17758,17760,17762],{},[380,17727],{},[383,17729,16059],{},[383,17731,385],{},[458,17733,461],{"stretchy":460},[383,17735,7917],{},[458,17737,468],{"stretchy":460},[458,17739,2817],{},[458,17741,461],{"stretchy":460},[463,17743,465],{},[458,17745,5160],{},[383,17747,16059],{},[458,17749,468],{"stretchy":460},[383,17751,385],{},[458,17753,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,17755,4505],{},[458,17757,461],{"stretchy":460},[383,17759,7917],{},[458,17761,468],{"stretchy":460},[458,17763,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[1596,17765,17766,17772],{},[1599,17767,17768],{},[1602,17769,17770],{"scriptlevel":474,"displaystyle":394},[380,17771],{},[1599,17773,17774],{},[1602,17775,17776],{"scriptlevel":474,"displaystyle":394},[380,17777,17778,17780,17782,17784,17787,17789,17791,17793,17795,17797,17799,17801,17803,17805,17807,17809,17811,17813,17815,17817,17819,17821,17823],{},[380,17779],{},[458,17781,10299],{},[383,17783,11686],{},[458,17785,578],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},"1.8em",[383,17788,16059],{},[383,17790,385],{},[458,17792,461],{"stretchy":460},[383,17794,7908],{},[458,17796,468],{"stretchy":460},[458,17798,2817],{},[458,17800,461],{"stretchy":460},[463,17802,465],{},[458,17804,5160],{},[383,17806,16059],{},[458,17808,468],{"stretchy":460},[383,17810,385],{},[458,17812,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,17814,4505],{},[458,17816,461],{"stretchy":460},[383,17818,7908],{},[458,17820,468],{"stretchy":460},[458,17822,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,17824,605],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[1596,17826,17827,17833],{},[1599,17828,17829],{},[1602,17830,17831],{"scriptlevel":474,"displaystyle":394},[380,17832],{},[1599,17834,17835],{},[1602,17836,17837],{"scriptlevel":474,"displaystyle":394},[380,17838,17839,17841,17843,17845,17847,17849,17851,17853,17855,17857,17859,17861,17863,17865,17867,17869,17871,17873,17875,17877,17879,17881,17883,17885,17887,17889,17891,17893,17895],{},[380,17840],{},[505,17842],{"width":3609},[458,17844,2817],{},[458,17846,461],{"stretchy":460},[463,17848,465],{},[458,17850,5160],{},[383,17852,11686],{},[458,17854,468],{"stretchy":460},[458,17856,578],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[383,17858,16059],{},[383,17860,385],{},[458,17862,461],{"stretchy":460},[383,17864,15747],{},[458,17866,468],{"stretchy":460},[458,17868,2817],{},[458,17870,461],{"stretchy":460},[463,17872,465],{},[458,17874,5160],{},[383,17876,16059],{},[458,17878,468],{"stretchy":460},[383,17880,385],{},[458,17882,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,17884,4505],{},[458,17886,461],{"stretchy":460},[383,17888,15747],{},[458,17890,468],{"stretchy":460},[458,17892,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,17894,605],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[458,17896,898],{"separator":394},[387,17898,17899],{"encoding":389},"\\begin{aligned}\n&\\delta f(w)+(1-\\delta)f\\big(g(w)\\big)\\\\\n&\\le \\lambda\\Big[\\delta f(s)\n+(1-\\delta)f\\big(g(s)\\big)\\Big]\\\\\n&\\qquad+(1-\\lambda)\\Big[\\delta f(u)\n+(1-\\delta)f\\big(g(u)\\big)\\Big],\n\\end{aligned}",[363,17901,17903],{"className":17902,"ariaHidden":394},[393],[363,17904,17906,17910],{"className":17905},[398],[363,17907],{"className":17908,"style":17909},[402],"height:5.41em;vertical-align:-2.455em;",[363,17911,17913],{"className":17912},[407],[363,17914,17916,17969],{"className":17915},[1590],[363,17917,17919],{"className":17918},[1707],[363,17920,17922,17960],{"className":17921},[633,634],[363,17923,17925,17957],{"className":17924},[638],[363,17926,17929,17939,17948],{"className":17927,"style":17928},[642],"height:2.955em;",[363,17930,17932,17936],{"style":17931},"top:-5.255em;",[363,17933],{"className":17934,"style":17935},[650],"height:3.15em;",[363,17937],{"className":17938},[407],[363,17940,17942,17945],{"style":17941},"top:-3.445em;",[363,17943],{"className":17944,"style":17935},[650],[363,17946],{"className":17947},[407],[363,17949,17951,17954],{"style":17950},"top:-1.345em;",[363,17952],{"className":17953,"style":17935},[650],[363,17955],{"className":17956},[407],[363,17958,666],{"className":17959},[665],[363,17961,17963],{"className":17962},[638],[363,17964,17967],{"className":17965,"style":17966},[642],"height:2.455em;",[363,17968],{},[363,17970,17972],{"className":17971},[1798],[363,17973,17975,18305],{"className":17974},[633,634],[363,17976,17978,18302],{"className":17977},[638],[363,17979,17981,18064,18171],{"className":17980,"style":17928},[642],[363,17982,17983,17986],{"style":17931},[363,17984],{"className":17985,"style":17935},[650],[363,17987,17989,17992,17995,17998,18001,18004,18007,18010,18013,18016,18019,18022,18025,18028,18031,18034,18037,18040,18046,18049,18052,18055,18058],{"className":17988},[407],[363,17990],{"className":17991},[407],[363,17993,16059],{"className":17994,"style":16108},[407,408],[363,17996,385],{"className":17997,"style":409},[407,408],[363,17999,461],{"className":18000},[494],[363,18002,7917],{"className":18003,"style":8621},[407,408],[363,18005,468],{"className":18006},[501],[363,18008],{"className":18009,"style":2934},[505],[363,18011,2817],{"className":18012},[2938],[363,18014],{"className":18015,"style":2934},[505],[363,18017,461],{"className":18018},[494],[363,18020,465],{"className":18021},[407],[363,18023],{"className":18024,"style":2934},[505],[363,18026,5160],{"className":18027},[2938],[363,18029],{"className":18030,"style":2934},[505],[363,18032,16059],{"className":18033,"style":16108},[407,408],[363,18035,468],{"className":18036},[501],[363,18038,385],{"className":18039,"style":409},[407,408],[363,18041,18043],{"className":18042},[407],[363,18044,461],{"className":18045},[767,10021],[363,18047,4505],{"className":18048,"style":1328},[407,408],[363,18050,461],{"className":18051},[494],[363,18053,7917],{"className":18054,"style":8621},[407,408],[363,18056,468],{"className":18057},[501],[363,18059,18061],{"className":18060},[407],[363,18062,468],{"className":18063},[767,10021],[363,18065,18066,18069],{"style":17941},[363,18067],{"className":18068,"style":17935},[650],[363,18070,18072,18075,18078,18081,18084,18087,18093,18096,18099,18102,18105,18108,18111,18114,18117,18120,18123,18126,18129,18132,18135,18138,18141,18147,18150,18153,18156,18159,18165],{"className":18071},[407],[363,18073],{"className":18074},[407],[363,18076],{"className":18077,"style":506},[505],[363,18079,10299],{"className":18080},[510],[363,18082],{"className":18083,"style":506},[505],[363,18085,11686],{"className":18086},[407,408],[363,18088,18090],{"className":18089},[407],[363,18091,578],{"className":18092},[767,4067],[363,18094,16059],{"className":18095,"style":16108},[407,408],[363,18097,385],{"className":18098,"style":409},[407,408],[363,18100,461],{"className":18101},[494],[363,18103,7908],{"className":18104},[407,408],[363,18106,468],{"className":18107},[501],[363,18109],{"className":18110,"style":2934},[505],[363,18112,2817],{"className":18113},[2938],[363,18115],{"className":18116,"style":2934},[505],[363,18118,461],{"className":18119},[494],[363,18121,465],{"className":18122},[407],[363,18124],{"className":18125,"style":2934},[505],[363,18127,5160],{"className":18128},[2938],[363,18130],{"className":18131,"style":2934},[505],[363,18133,16059],{"className":18134,"style":16108},[407,408],[363,18136,468],{"className":18137},[501],[363,18139,385],{"className":18140,"style":409},[407,408],[363,18142,18144],{"className":18143},[407],[363,18145,461],{"className":18146},[767,10021],[363,18148,4505],{"className":18149,"style":1328},[407,408],[363,18151,461],{"className":18152},[494],[363,18154,7908],{"className":18155},[407,408],[363,18157,468],{"className":18158},[501],[363,18160,18162],{"className":18161},[407],[363,18163,468],{"className":18164},[767,10021],[363,18166,18168],{"className":18167},[407],[363,18169,605],{"className":18170},[767,4067],[363,18172,18173,18176],{"style":17950},[363,18174],{"className":18175,"style":17935},[650],[363,18177,18179,18182,18185,18188,18191,18194,18197,18200,18203,18206,18209,18212,18215,18221,18224,18227,18230,18233,18236,18239,18242,18245,18248,18251,18254,18257,18260,18263,18266,18269,18275,18278,18281,18284,18287,18293,18299],{"className":18178},[407],[363,18180],{"className":18181},[407],[363,18183],{"className":18184,"style":3981},[505],[363,18186],{"className":18187,"style":2934},[505],[363,18189,2817],{"className":18190},[2938],[363,18192],{"className":18193,"style":2934},[505],[363,18195,461],{"className":18196},[494],[363,18198,465],{"className":18199},[407],[363,18201],{"className":18202,"style":2934},[505],[363,18204,5160],{"className":18205},[2938],[363,18207],{"className":18208,"style":2934},[505],[363,18210,11686],{"className":18211},[407,408],[363,18213,468],{"className":18214},[501],[363,18216,18218],{"className":18217},[407],[363,18219,578],{"className":18220},[767,4067],[363,18222,16059],{"className":18223,"style":16108},[407,408],[363,18225,385],{"className":18226,"style":409},[407,408],[363,18228,461],{"className":18229},[494],[363,18231,15747],{"className":18232},[407,408],[363,18234,468],{"className":18235},[501],[363,18237],{"className":18238,"style":2934},[505],[363,18240,2817],{"className":18241},[2938],[363,18243],{"className":18244,"style":2934},[505],[363,18246,461],{"className":18247},[494],[363,18249,465],{"className":18250},[407],[363,18252],{"className":18253,"style":2934},[505],[363,18255,5160],{"className":18256},[2938],[363,18258],{"className":18259,"style":2934},[505],[363,18261,16059],{"className":18262,"style":16108},[407,408],[363,18264,468],{"className":18265},[501],[363,18267,385],{"className":18268,"style":409},[407,408],[363,18270,18272],{"className":18271},[407],[363,18273,461],{"className":18274},[767,10021],[363,18276,4505],{"className":18277,"style":1328},[407,408],[363,18279,461],{"className":18280},[494],[363,18282,15747],{"className":18283},[407,408],[363,18285,468],{"className":18286},[501],[363,18288,18290],{"className":18289},[407],[363,18291,468],{"className":18292},[767,10021],[363,18294,18296],{"className":18295},[407],[363,18297,605],{"className":18298},[767,4067],[363,18300,898],{"className":18301},[920],[363,18303,666],{"className":18304},[665],[363,18306,18308],{"className":18307},[638],[363,18309,18311],{"className":18310,"style":17966},[642],[363,18312],{},[11,18314,2597,18315,18488,18489,18517,18518,18678,18679,4200,18707,18735,18736,18977,18978,19055,19056,19238,19239,19309,19310,3092,19338,19395,19396,19424],{},[363,18316,18318,18362],{"className":18317,"translate":367},[366],[363,18319,18321],{"className":18320},[371],[373,18322,18323],{"xmlns":375},[377,18324,18325,18359],{},[380,18326,18327,18329,18331,18333,18335,18337],{},[383,18328,4505],{},[458,18330,461],{"stretchy":460},[383,18332,16797],{},[458,18334,468],{"stretchy":460},[458,18336,471],{},[1602,18338,18339],{"scriptlevel":474,"displaystyle":394},[586,18340,18341,18351],{},[380,18342,18343,18345,18347,18349],{},[463,18344,465],{},[458,18346,5160],{},[383,18348,16797],{},[383,18350,16059],{},[380,18352,18353,18355,18357],{},[463,18354,465],{},[458,18356,5160],{},[383,18358,16059],{},[387,18360,18361],{"encoding":389},"g(r)=\\dfrac{1-r\\delta}{1-\\delta}",[363,18363,18365,18392],{"className":18364,"ariaHidden":394},[393],[363,18366,18368,18371,18374,18377,18380,18383,18386,18389],{"className":18367},[398],[363,18369],{"className":18370,"style":487},[402],[363,18372,4505],{"className":18373,"style":1328},[407,408],[363,18375,461],{"className":18376},[494],[363,18378,16797],{"className":18379,"style":625},[407,408],[363,18381,468],{"className":18382},[501],[363,18384],{"className":18385,"style":506},[505],[363,18387,471],{"className":18388},[510],[363,18390],{"className":18391,"style":506},[505],[363,18393,18395,18399],{"className":18394},[398],[363,18396],{"className":18397,"style":18398},[402],"height:2.1408em;vertical-align:-0.7693em;",[363,18400,18402,18405,18485],{"className":18401},[407],[363,18403],{"className":18404},[494,789],[363,18406,18408],{"className":18407},[586],[363,18409,18411,18477],{"className":18410},[633,634],[363,18412,18414,18474],{"className":18413},[638],[363,18415,18417,18440,18448],{"className":18416,"style":802},[642],[363,18418,18419,18422],{"style":805},[363,18420],{"className":18421,"style":809},[650],[363,18423,18425,18428,18431,18434,18437],{"className":18424},[407],[363,18426,465],{"className":18427},[407],[363,18429],{"className":18430,"style":2934},[505],[363,18432,5160],{"className":18433},[2938],[363,18435],{"className":18436,"style":2934},[505],[363,18438,16059],{"className":18439,"style":16108},[407,408],[363,18441,18442,18445],{"style":821},[363,18443],{"className":18444,"style":809},[650],[363,18446],{"className":18447,"style":829},[828],[363,18449,18450,18453],{"style":832},[363,18451],{"className":18452,"style":809},[650],[363,18454,18456,18459,18462,18465,18468,18471],{"className":18455},[407],[363,18457,465],{"className":18458},[407],[363,18460],{"className":18461,"style":2934},[505],[363,18463,5160],{"className":18464},[2938],[363,18466],{"className":18467,"style":2934},[505],[363,18469,16797],{"className":18470,"style":625},[407,408],[363,18472,16059],{"className":18473,"style":16108},[407,408],[363,18475,666],{"className":18476},[665],[363,18478,18480],{"className":18479},[638],[363,18481,18483],{"className":18482,"style":17362},[642],[363,18484],{},[363,18486],{"className":18487},[501,789],"。注意 ",[363,18490,18492,18505],{"className":18491,"translate":367},[366],[363,18493,18495],{"className":18494},[371],[373,18496,18497],{"xmlns":375},[377,18498,18499,18503],{},[380,18500,18501],{},[383,18502,4505],{},[387,18504,4505],{"encoding":389},[363,18506,18508],{"className":18507,"ariaHidden":394},[393],[363,18509,18511,18514],{"className":18510},[398],[363,18512],{"className":18513,"style":2623},[402],[363,18515,4505],{"className":18516,"style":1328},[407,408]," 是仿射函数且 ",[363,18519,18521,18573],{"className":18520,"translate":367},[366],[363,18522,18524],{"className":18523},[371],[373,18525,18526],{"xmlns":375},[377,18527,18528,18570],{},[380,18529,18530,18532,18534,18536,18538,18540,18542,18544,18546,18548,18550,18552,18554,18556,18558,18560,18562,18564,18566,18568],{},[383,18531,4505],{},[458,18533,461],{"stretchy":460},[383,18535,7917],{},[458,18537,468],{"stretchy":460},[458,18539,471],{},[383,18541,11686],{},[383,18543,4505],{},[458,18545,461],{"stretchy":460},[383,18547,7908],{},[458,18549,468],{"stretchy":460},[458,18551,2817],{},[458,18553,461],{"stretchy":460},[463,18555,465],{},[458,18557,5160],{},[383,18559,11686],{},[458,18561,468],{"stretchy":460},[383,18563,4505],{},[458,18565,461],{"stretchy":460},[383,18567,15747],{},[458,18569,468],{"stretchy":460},[387,18571,18572],{"encoding":389},"g(w)=\\lambda g(s)+(1-\\lambda)g(u)",[363,18574,18576,18603,18633,18654],{"className":18575,"ariaHidden":394},[393],[363,18577,18579,18582,18585,18588,18591,18594,18597,18600],{"className":18578},[398],[363,18580],{"className":18581,"style":487},[402],[363,18583,4505],{"className":18584,"style":1328},[407,408],[363,18586,461],{"className":18587},[494],[363,18589,7917],{"className":18590,"style":8621},[407,408],[363,18592,468],{"className":18593},[501],[363,18595],{"className":18596,"style":506},[505],[363,18598,471],{"className":18599},[510],[363,18601],{"className":18602,"style":506},[505],[363,18604,18606,18609,18612,18615,18618,18621,18624,18627,18630],{"className":18605},[398],[363,18607],{"className":18608,"style":487},[402],[363,18610,11686],{"className":18611},[407,408],[363,18613,4505],{"className":18614,"style":1328},[407,408],[363,18616,461],{"className":18617},[494],[363,18619,7908],{"className":18620},[407,408],[363,18622,468],{"className":18623},[501],[363,18625],{"className":18626,"style":2934},[505],[363,18628,2817],{"className":18629},[2938],[363,18631],{"className":18632,"style":2934},[505],[363,18634,18636,18639,18642,18645,18648,18651],{"className":18635},[398],[363,18637],{"className":18638,"style":487},[402],[363,18640,461],{"className":18641},[494],[363,18643,465],{"className":18644},[407],[363,18646],{"className":18647,"style":2934},[505],[363,18649,5160],{"className":18650},[2938],[363,18652],{"className":18653,"style":2934},[505],[363,18655,18657,18660,18663,18666,18669,18672,18675],{"className":18656},[398],[363,18658],{"className":18659,"style":487},[402],[363,18661,11686],{"className":18662},[407,408],[363,18664,468],{"className":18665},[501],[363,18667,4505],{"className":18668,"style":1328},[407,408],[363,18670,461],{"className":18671},[494],[363,18673,15747],{"className":18674},[407,408],[363,18676,468],{"className":18677},[501],"，用 ",[363,18680,18682,18695],{"className":18681,"translate":367},[366],[363,18683,18685],{"className":18684},[371],[373,18686,18687],{"xmlns":375},[377,18688,18689,18693],{},[380,18690,18691],{},[383,18692,385],{},[387,18694,385],{"encoding":389},[363,18696,18698],{"className":18697,"ariaHidden":394},[393],[363,18699,18701,18704],{"className":18700},[398],[363,18702],{"className":18703,"style":403},[402],[363,18705,385],{"className":18706,"style":409},[407,408],[363,18708,18710,18723],{"className":18709,"translate":367},[366],[363,18711,18713],{"className":18712},[371],[373,18714,18715],{"xmlns":375},[377,18716,18717,18721],{},[380,18718,18719],{},[463,18720,465],{},[387,18722,465],{"encoding":389},[363,18724,18726],{"className":18725,"ariaHidden":394},[393],[363,18727,18729,18732],{"className":18728},[398],[363,18730],{"className":18731,"style":520},[402],[363,18733,465],{"className":18734},[407]," 处的支撑线（凸函数在可微点处 ",[363,18737,18739,18805],{"className":18738,"translate":367},[366],[363,18740,18742],{"className":18741},[371],[373,18743,18744],{"xmlns":375},[377,18745,18746,18802],{},[380,18747,18748,18750,18752,18754,18756,18758,18760,18762,18764,18766,18768,18774,18776,18778,18780,18782,18784,18786,18788,18790,18796,18798,18800],{},[383,18749,385],{},[458,18751,461],{"stretchy":460},[383,18753,1116],{},[458,18755,468],{"stretchy":460},[458,18757,7275],{},[383,18759,385],{},[458,18761,461],{"stretchy":460},[463,18763,465],{},[458,18765,468],{"stretchy":460},[458,18767,2817],{},[7161,18769,18770,18772],{},[383,18771,385],{},[458,18773,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,18775,461],{"stretchy":460},[463,18777,465],{},[458,18779,468],{"stretchy":460},[458,18781,461],{"stretchy":460},[383,18783,1116],{},[458,18785,5160],{},[463,18787,465],{},[458,18789,468],{"stretchy":460},[7161,18791,18792,18794],{},[383,18793,385],{},[458,18795,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,18797,461],{"stretchy":460},[463,18799,465],{},[458,18801,468],{"stretchy":460},[387,18803,18804],{"encoding":389},"f(t)\\ge f(1)+f'(1)(t-1)f'(1)",[363,18806,18808,18835,18862,18924],{"className":18807,"ariaHidden":394},[393],[363,18809,18811,18814,18817,18820,18823,18826,18829,18832],{"className":18810},[398],[363,18812],{"className":18813,"style":487},[402],[363,18815,385],{"className":18816,"style":409},[407,408],[363,18818,461],{"className":18819},[494],[363,18821,1116],{"className":18822},[407,408],[363,18824,468],{"className":18825},[501],[363,18827],{"className":18828,"style":506},[505],[363,18830,7275],{"className":18831},[510],[363,18833],{"className":18834,"style":506},[505],[363,18836,18838,18841,18844,18847,18850,18853,18856,18859],{"className":18837},[398],[363,18839],{"className":18840,"style":487},[402],[363,18842,385],{"className":18843,"style":409},[407,408],[363,18845,461],{"className":18846},[494],[363,18848,465],{"className":18849},[407],[363,18851,468],{"className":18852},[501],[363,18854],{"className":18855,"style":2934},[505],[363,18857,2817],{"className":18858},[2938],[363,18860],{"className":18861,"style":2934},[505],[363,18863,18865,18868,18900,18903,18906,18909,18912,18915,18918,18921],{"className":18864},[398],[363,18866],{"className":18867,"style":7190},[402],[363,18869,18871,18874],{"className":18870},[407],[363,18872,385],{"className":18873,"style":409},[407,408],[363,18875,18877],{"className":18876},[629],[363,18878,18880],{"className":18879},[633],[363,18881,18883],{"className":18882},[638],[363,18884,18886],{"className":18885,"style":7209},[642],[363,18887,18888,18891],{"style":7212},[363,18889],{"className":18890,"style":651},[650],[363,18892,18894],{"className":18893},[655,656,657,658],[363,18895,18897],{"className":18896},[407,658],[363,18898,7167],{"className":18899},[407,658],[363,18901,461],{"className":18902},[494],[363,18904,465],{"className":18905},[407],[363,18907,468],{"className":18908},[501],[363,18910,461],{"className":18911},[494],[363,18913,1116],{"className":18914},[407,408],[363,18916],{"className":18917,"style":2934},[505],[363,18919,5160],{"className":18920},[2938],[363,18922],{"className":18923,"style":2934},[505],[363,18925,18927,18930,18933,18936,18968,18971,18974],{"className":18926},[398],[363,18928],{"className":18929,"style":7190},[402],[363,18931,465],{"className":18932},[407],[363,18934,468],{"className":18935},[501],[363,18937,18939,18942],{"className":18938},[407],[363,18940,385],{"className":18941,"style":409},[407,408],[363,18943,18945],{"className":18944},[629],[363,18946,18948],{"className":18947},[633],[363,18949,18951],{"className":18950},[638],[363,18952,18954],{"className":18953,"style":7209},[642],[363,18955,18956,18959],{"style":7212},[363,18957],{"className":18958,"style":651},[650],[363,18960,18962],{"className":18961},[655,656,657,658],[363,18963,18965],{"className":18964},[407,658],[363,18966,7167],{"className":18967},[407,658],[363,18969,461],{"className":18970},[494],[363,18972,465],{"className":18973},[407],[363,18975,468],{"className":18976},[501],"，此处只需次梯度 ",[363,18979,18981,19005],{"className":18980,"translate":367},[366],[363,18982,18984],{"className":18983},[371],[373,18985,18986],{"xmlns":375},[377,18987,18988,19002],{},[380,18989,18990,18996,18998,19000],{},[7161,18991,18992,18994],{},[383,18993,385],{},[458,18995,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,18997,461],{"stretchy":460},[463,18999,465],{},[458,19001,468],{"stretchy":460},[387,19003,19004],{"encoding":389},"f'(1)",[363,19006,19008],{"className":19007,"ariaHidden":394},[393],[363,19009,19011,19014,19046,19049,19052],{"className":19010},[398],[363,19012],{"className":19013,"style":7190},[402],[363,19015,19017,19020],{"className":19016},[407],[363,19018,385],{"className":19019,"style":409},[407,408],[363,19021,19023],{"className":19022},[629],[363,19024,19026],{"className":19025},[633],[363,19027,19029],{"className":19028},[638],[363,19030,19032],{"className":19031,"style":7209},[642],[363,19033,19034,19037],{"style":7212},[363,19035],{"className":19036,"style":651},[650],[363,19038,19040],{"className":19039},[655,656,657,658],[363,19041,19043],{"className":19042},[407,658],[363,19044,7167],{"className":19045},[407,658],[363,19047,461],{"className":19048},[494],[363,19050,465],{"className":19051},[407],[363,19053,468],{"className":19054},[501],"，即 ",[363,19057,19059,19107],{"className":19058,"translate":367},[366],[363,19060,19062],{"className":19061},[371],[373,19063,19064],{"xmlns":375},[377,19065,19066,19104],{},[380,19067,19068,19070,19072,19074,19076,19078,19080,19082,19084,19086,19088,19094,19096,19098,19100,19102],{},[383,19069,385],{},[458,19071,461],{"stretchy":460},[383,19073,1116],{},[458,19075,468],{"stretchy":460},[458,19077,7275],{},[383,19079,385],{},[458,19081,461],{"stretchy":460},[463,19083,465],{},[458,19085,468],{"stretchy":460},[458,19087,2817],{},[543,19089,19090,19092],{},[383,19091,4505],{},[463,19093,465],{},[458,19095,461],{"stretchy":460},[383,19097,1116],{},[458,19099,5160],{},[463,19101,465],{},[458,19103,468],{"stretchy":460},[387,19105,19106],{"encoding":389},"f(t)\\ge f(1)+g_1(t-1)",[363,19108,19110,19137,19164,19226],{"className":19109,"ariaHidden":394},[393],[363,19111,19113,19116,19119,19122,19125,19128,19131,19134],{"className":19112},[398],[363,19114],{"className":19115,"style":487},[402],[363,19117,385],{"className":19118,"style":409},[407,408],[363,19120,461],{"className":19121},[494],[363,19123,1116],{"className":19124},[407,408],[363,19126,468],{"className":19127},[501],[363,19129],{"className":19130,"style":506},[505],[363,19132,7275],{"className":19133},[510],[363,19135],{"className":19136,"style":506},[505],[363,19138,19140,19143,19146,19149,19152,19155,19158,19161],{"className":19139},[398],[363,19141],{"className":19142,"style":487},[402],[363,19144,385],{"className":19145,"style":409},[407,408],[363,19147,461],{"className":19148},[494],[363,19150,465],{"className":19151},[407],[363,19153,468],{"className":19154},[501],[363,19156],{"className":19157,"style":2934},[505],[363,19159,2817],{"className":19160},[2938],[363,19162],{"className":19163,"style":2934},[505],[363,19165,19167,19170,19211,19214,19217,19220,19223],{"className":19166},[398],[363,19168],{"className":19169,"style":487},[402],[363,19171,19173,19176],{"className":19172},[407],[363,19174,4505],{"className":19175,"style":1328},[407,408],[363,19177,19179],{"className":19178},[629],[363,19180,19182,19203],{"className":19181},[633,634],[363,19183,19185,19200],{"className":19184},[638],[363,19186,19188],{"className":19187,"style":11480},[642],[363,19189,19191,19194],{"style":19190},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[363,19192],{"className":19193,"style":651},[650],[363,19195,19197],{"className":19196},[655,656,657,658],[363,19198,465],{"className":19199},[407,658],[363,19201,666],{"className":19202},[665],[363,19204,19206],{"className":19205},[638],[363,19207,19209],{"className":19208,"style":8315},[642],[363,19210],{},[363,19212,461],{"className":19213},[494],[363,19215,1116],{"className":19216},[407,408],[363,19218],{"className":19219,"style":2934},[505],[363,19221,5160],{"className":19222},[2938],[363,19224],{"className":19225,"style":2934},[505],[363,19227,19229,19232,19235],{"className":19228},[398],[363,19230],{"className":19231,"style":487},[402],[363,19233,465],{"className":19234},[407],[363,19236,468],{"className":19237},[501]," 对任一次梯度 ",[363,19240,19242,19260],{"className":19241,"translate":367},[366],[363,19243,19245],{"className":19244},[371],[373,19246,19247],{"xmlns":375},[377,19248,19249,19257],{},[380,19250,19251],{},[543,19252,19253,19255],{},[383,19254,4505],{},[463,19256,465],{},[387,19258,19259],{"encoding":389},"g_1",[363,19261,19263],{"className":19262,"ariaHidden":394},[393],[363,19264,19266,19269],{"className":19265},[398],[363,19267],{"className":19268,"style":2623},[402],[363,19270,19272,19275],{"className":19271},[407],[363,19273,4505],{"className":19274,"style":1328},[407,408],[363,19276,19278],{"className":19277},[629],[363,19279,19281,19301],{"className":19280},[633,634],[363,19282,19284,19298],{"className":19283},[638],[363,19285,19287],{"className":19286,"style":11480},[642],[363,19288,19289,19292],{"style":19190},[363,19290],{"className":19291,"style":651},[650],[363,19293,19295],{"className":19294},[655,656,657,658],[363,19296,465],{"className":19297},[407,658],[363,19299,666],{"className":19300},[665],[363,19302,19304],{"className":19303},[638],[363,19305,19307],{"className":19306,"style":8315},[642],[363,19308],{},"）处理非主项：对凸的 ",[363,19311,19313,19326],{"className":19312,"translate":367},[366],[363,19314,19316],{"className":19315},[371],[373,19317,19318],{"xmlns":375},[377,19319,19320,19324],{},[380,19321,19322],{},[383,19323,385],{},[387,19325,385],{"encoding":389},[363,19327,19329],{"className":19328,"ariaHidden":394},[393],[363,19330,19332,19335],{"className":19331},[398],[363,19333],{"className":19334,"style":403},[402],[363,19336,385],{"className":19337,"style":409},[407,408],[363,19339,19341,19367],{"className":19340,"translate":367},[366],[363,19342,19344],{"className":19343},[371],[373,19345,19346],{"xmlns":375},[377,19347,19348,19364],{},[380,19349,19350,19352,19354,19356,19358,19360,19362],{},[383,19351,385],{},[458,19353,461],{"stretchy":460},[383,19355,4505],{},[458,19357,461],{"stretchy":460},[383,19359,16797],{},[458,19361,468],{"stretchy":460},[458,19363,468],{"stretchy":460},[387,19365,19366],{"encoding":389},"f(g(r))",[363,19368,19370],{"className":19369,"ariaHidden":394},[393],[363,19371,19373,19376,19379,19382,19385,19388,19391],{"className":19372},[398],[363,19374],{"className":19375,"style":487},[402],[363,19377,385],{"className":19378,"style":409},[407,408],[363,19380,461],{"className":19381},[494],[363,19383,4505],{"className":19384,"style":1328},[407,408],[363,19386,461],{"className":19387},[494],[363,19389,16797],{"className":19390,"style":625},[407,408],[363,19392,19394],{"className":19393},[501],"))"," 中关于 ",[363,19397,19399,19412],{"className":19398,"translate":367},[366],[363,19400,19402],{"className":19401},[371],[373,19403,19404],{"xmlns":375},[377,19405,19406,19410],{},[380,19407,19408],{},[383,19409,16797],{},[387,19411,16797],{"encoding":389},[363,19413,19415],{"className":19414,"ariaHidden":394},[393],[363,19416,19418,19421],{"className":19417},[398],[363,19419],{"className":19420,"style":2692},[402],[363,19422,16797],{"className":19423,"style":625},[407,408]," 的\"非主项\"部分为",[363,19426,19428],{"className":19427,"translate":367},[528],[363,19429,19431,19636],{"className":19430,"translate":367},[366],[363,19432,19434],{"className":19433},[371],[373,19435,19436],{"xmlns":375,"display":537},[377,19437,19438,19633],{},[1590,19439,19440,19504,19579],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,19441,19442,19462],{},[1599,19443,19444],{},[1602,19445,19446],{"scriptlevel":474,"displaystyle":394},[380,19447,19448,19450,19452,19454,19456,19458,19460],{},[383,19449,385],{},[458,19451,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,19453,4505],{},[458,19455,461],{"stretchy":460},[383,19457,16797],{},[458,19459,468],{"stretchy":460},[458,19461,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[1599,19463,19464],{},[1602,19465,19466],{"scriptlevel":474,"displaystyle":394},[380,19467,19468,19470,19472,19474,19476,19478,19480,19482,19502],{},[380,19469],{},[458,19471,471],{},[383,19473,385],{},[458,19475,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[463,19477,465],{},[458,19479,2817],{},[383,19481,16059],{},[1602,19483,19484],{"scriptlevel":474,"displaystyle":460},[586,19485,19486,19494],{},[380,19487,19488,19490,19492],{},[463,19489,465],{},[458,19491,5160],{},[383,19493,16797],{},[380,19495,19496,19498,19500],{},[463,19497,465],{},[458,19499,5160],{},[383,19501,16059],{},[458,19503,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[1596,19505,19506,19512],{},[1599,19507,19508],{},[1602,19509,19510],{"scriptlevel":474,"displaystyle":394},[380,19511],{},[1599,19513,19514],{},[1602,19515,19516],{"scriptlevel":474,"displaystyle":394},[380,19517,19518,19520,19522,19524,19526,19528,19530,19532,19538,19540,19542,19544,19564,19566,19569,19571,19577],{},[380,19519],{},[458,19521,471],{},[383,19523,385],{},[458,19525,461],{"stretchy":460},[463,19527,465],{},[458,19529,468],{"stretchy":460},[458,19531,2817],{},[543,19533,19534,19536],{},[383,19535,4505],{},[463,19537,465],{},[458,19539,3646],{},[383,19541,16059],{},[1644,19543,1646],{},[1602,19545,19546],{"scriptlevel":474,"displaystyle":460},[586,19547,19548,19556],{},[380,19549,19550,19552,19554],{},[463,19551,465],{},[458,19553,5160],{},[383,19555,16797],{},[380,19557,19558,19560,19562],{},[463,19559,465],{},[458,19561,5160],{},[383,19563,16059],{},[458,19565,2817],{},[383,19567,19568],{},"O",[458,19570,461],{"stretchy":460},[7161,19572,19573,19575],{},[383,19574,16059],{},[463,19576,2810],{},[458,19578,468],{"stretchy":460},[1596,19580,19581,19587],{},[1599,19582,19583],{},[1602,19584,19585],{"scriptlevel":474,"displaystyle":394},[380,19586],{},[1599,19588,19589],{},[1602,19590,19591],{"scriptlevel":474,"displaystyle":394},[380,19592,19593,19595,19597,19603,19605,19607,19609,19611,19613,19615,19617,19619,19621,19623,19629,19631],{},[380,19594],{},[458,19596,471],{},[543,19598,19599,19601],{},[383,19600,4505],{},[463,19602,465],{},[1644,19604,1646],{},[383,19606,16059],{},[458,19608,461],{"stretchy":460},[463,19610,465],{},[458,19612,5160],{},[383,19614,16797],{},[458,19616,468],{"stretchy":460},[458,19618,2817],{},[383,19620,19568],{},[458,19622,461],{"stretchy":460},[7161,19624,19625,19627],{},[383,19626,16059],{},[463,19628,2810],{},[458,19630,468],{"stretchy":460},[458,19632,898],{"separator":394},[387,19634,19635],{"encoding":389},"\\begin{aligned}\nf\\big(g(r)\\big)\n&=f\\big(1+\\delta\\tfrac{1-r}{1-\\delta}\\big)\\\\\n&= f(1)+g_1\\cdot\\delta\\,\\tfrac{1-r}{1-\\delta}\n+O(\\delta^2)\\\\\n&= g_1\\,\\delta(1-r)+O(\\delta^2),\n\\end{aligned}",[363,19637,19639],{"className":19638,"ariaHidden":394},[393],[363,19640,19642,19646],{"className":19641},[398],[363,19643],{"className":19644,"style":19645},[402],"height:4.3449em;vertical-align:-1.9224em;",[363,19647,19649],{"className":19648},[407],[363,19650,19652,19731],{"className":19651},[1590],[363,19653,19655],{"className":19654},[1707],[363,19656,19658,19722],{"className":19657},[633,634],[363,19659,19661,19719],{"className":19660},[638],[363,19662,19665,19701,19710],{"className":19663,"style":19664},[642],"height:2.4224em;",[363,19666,19668,19671],{"style":19667},"top:-4.5724em;",[363,19669],{"className":19670,"style":809},[650],[363,19672,19674,19677,19683,19686,19689,19692,19695],{"className":19673},[407],[363,19675,385],{"className":19676,"style":409},[407,408],[363,19678,19680],{"className":19679},[407],[363,19681,461],{"className":19682},[767,10021],[363,19684,4505],{"className":19685,"style":1328},[407,408],[363,19687,461],{"className":19688},[494],[363,19690,16797],{"className":19691,"style":625},[407,408],[363,19693,468],{"className":19694},[501],[363,19696,19698],{"className":19697},[407],[363,19699,468],{"className":19700},[767,10021],[363,19702,19704,19707],{"style":19703},"top:-3.005em;",[363,19705],{"className":19706,"style":809},[650],[363,19708],{"className":19709},[407],[363,19711,19713,19716],{"style":19712},"top:-1.4376em;",[363,19714],{"className":19715,"style":809},[650],[363,19717],{"className":19718},[407],[363,19720,666],{"className":19721},[665],[363,19723,19725],{"className":19724},[638],[363,19726,19729],{"className":19727,"style":19728},[642],"height:1.9224em;",[363,19730],{},[363,19732,19734],{"className":19733},[1798],[363,19735,19737,20237],{"className":19736},[633,634],[363,19738,19740,20234],{"className":19739},[638],[363,19741,19743,19873,20097],{"className":19742,"style":19664},[642],[363,19744,19745,19748],{"style":19667},[363,19746],{"className":19747,"style":809},[650],[363,19749,19751,19754,19757,19760,19763,19766,19772,19775,19778,19781,19784,19787,19867],{"className":19750},[407],[363,19752],{"className":19753},[407],[363,19755],{"className":19756,"style":506},[505],[363,19758,471],{"className":19759},[510],[363,19761],{"className":19762,"style":506},[505],[363,19764,385],{"className":19765,"style":409},[407,408],[363,19767,19769],{"className":19768},[407],[363,19770,461],{"className":19771},[767,10021],[363,19773,465],{"className":19774},[407],[363,19776],{"className":19777,"style":2934},[505],[363,19779,2817],{"className":19780},[2938],[363,19782],{"className":19783,"style":2934},[505],[363,19785,16059],{"className":19786,"style":16108},[407,408],[363,19788,19790,19793,19864],{"className":19789},[407],[363,19791],{"className":19792},[494,789],[363,19794,19796],{"className":19795},[586],[363,19797,19799,19856],{"className":19798},[633,634],[363,19800,19802,19853],{"className":19801},[638],[363,19803,19805,19825,19833],{"className":19804,"style":2871},[642],[363,19806,19807,19810],{"style":2874},[363,19808],{"className":19809,"style":809},[650],[363,19811,19813],{"className":19812},[655,656,657,658],[363,19814,19816,19819,19822],{"className":19815},[407,658],[363,19817,465],{"className":19818},[407,658],[363,19820,5160],{"className":19821},[2938,658],[363,19823,16059],{"className":19824,"style":16108},[407,408,658],[363,19826,19827,19830],{"style":821},[363,19828],{"className":19829,"style":809},[650],[363,19831],{"className":19832,"style":829},[828],[363,19834,19835,19838],{"style":2897},[363,19836],{"className":19837,"style":809},[650],[363,19839,19841],{"className":19840},[655,656,657,658],[363,19842,19844,19847,19850],{"className":19843},[407,658],[363,19845,465],{"className":19846},[407,658],[363,19848,5160],{"className":19849},[2938,658],[363,19851,16797],{"className":19852,"style":625},[407,408,658],[363,19854,666],{"className":19855},[665],[363,19857,19859],{"className":19858},[638],[363,19860,19862],{"className":19861,"style":16776},[642],[363,19863],{},[363,19865],{"className":19866},[501,789],[363,19868,19870],{"className":19869},[407],[363,19871,468],{"className":19872},[767,10021],[363,19874,19875,19878],{"style":19703},[363,19876],{"className":19877,"style":809},[650],[363,19879,19881,19884,19887,19890,19893,19896,19899,19902,19905,19908,19911,19914,19954,19957,19960,19963,19966,19969,20049,20052,20055,20058,20061,20064,20094],{"className":19880},[407],[363,19882],{"className":19883},[407],[363,19885],{"className":19886,"style":506},[505],[363,19888,471],{"className":19889},[510],[363,19891],{"className":19892,"style":506},[505],[363,19894,385],{"className":19895,"style":409},[407,408],[363,19897,461],{"className":19898},[494],[363,19900,465],{"className":19901},[407],[363,19903,468],{"className":19904},[501],[363,19906],{"className":19907,"style":2934},[505],[363,19909,2817],{"className":19910},[2938],[363,19912],{"className":19913,"style":2934},[505],[363,19915,19917,19920],{"className":19916},[407],[363,19918,4505],{"className":19919,"style":1328},[407,408],[363,19921,19923],{"className":19922},[629],[363,19924,19926,19946],{"className":19925},[633,634],[363,19927,19929,19943],{"className":19928},[638],[363,19930,19932],{"className":19931,"style":11480},[642],[363,19933,19934,19937],{"style":19190},[363,19935],{"className":19936,"style":651},[650],[363,19938,19940],{"className":19939},[655,656,657,658],[363,19941,465],{"className":19942},[407,658],[363,19944,666],{"className":19945},[665],[363,19947,19949],{"className":19948},[638],[363,19950,19952],{"className":19951,"style":8315},[642],[363,19953],{},[363,19955],{"className":19956,"style":2934},[505],[363,19958,3646],{"className":19959},[2938],[363,19961],{"className":19962,"style":2934},[505],[363,19964,16059],{"className":19965,"style":16108},[407,408],[363,19967],{"className":19968,"style":754},[505],[363,19970,19972,19975,20046],{"className":19971},[407],[363,19973],{"className":19974},[494,789],[363,19976,19978],{"className":19977},[586],[363,19979,19981,20038],{"className":19980},[633,634],[363,19982,19984,20035],{"className":19983},[638],[363,19985,19987,20007,20015],{"className":19986,"style":2871},[642],[363,19988,19989,19992],{"style":2874},[363,19990],{"className":19991,"style":809},[650],[363,19993,19995],{"className":19994},[655,656,657,658],[363,19996,19998,20001,20004],{"className":19997},[407,658],[363,19999,465],{"className":20000},[407,658],[363,20002,5160],{"className":20003},[2938,658],[363,20005,16059],{"className":20006,"style":16108},[407,408,658],[363,20008,20009,20012],{"style":821},[363,20010],{"className":20011,"style":809},[650],[363,20013],{"className":20014,"style":829},[828],[363,20016,20017,20020],{"style":2897},[363,20018],{"className":20019,"style":809},[650],[363,20021,20023],{"className":20022},[655,656,657,658],[363,20024,20026,20029,20032],{"className":20025},[407,658],[363,20027,465],{"className":20028},[407,658],[363,20030,5160],{"className":20031},[2938,658],[363,20033,16797],{"className":20034,"style":625},[407,408,658],[363,20036,666],{"className":20037},[665],[363,20039,20041],{"className":20040},[638],[363,20042,20044],{"className":20043,"style":16776},[642],[363,20045],{},[363,20047],{"className":20048},[501,789],[363,20050],{"className":20051,"style":2934},[505],[363,20053,2817],{"className":20054},[2938],[363,20056],{"className":20057,"style":2934},[505],[363,20059,19568],{"className":20060,"style":625},[407,408],[363,20062,461],{"className":20063},[494],[363,20065,20067,20070],{"className":20066},[407],[363,20068,16059],{"className":20069,"style":16108},[407,408],[363,20071,20073],{"className":20072},[629],[363,20074,20076],{"className":20075},[633],[363,20077,20079],{"className":20078},[638],[363,20080,20083],{"className":20081,"style":20082},[642],"height:0.8641em;",[363,20084,20085,20088],{"style":8624},[363,20086],{"className":20087,"style":651},[650],[363,20089,20091],{"className":20090},[655,656,657,658],[363,20092,2810],{"className":20093},[407,658],[363,20095,468],{"className":20096},[501],[363,20098,20099,20102],{"style":19712},[363,20100],{"className":20101,"style":809},[650],[363,20103,20105,20108,20111,20114,20117,20157,20160,20163,20166,20169,20172,20175,20178,20181,20184,20187,20190,20193,20196,20199,20228,20231],{"className":20104},[407],[363,20106],{"className":20107},[407],[363,20109],{"className":20110,"style":506},[505],[363,20112,471],{"className":20113},[510],[363,20115],{"className":20116,"style":506},[505],[363,20118,20120,20123],{"className":20119},[407],[363,20121,4505],{"className":20122,"style":1328},[407,408],[363,20124,20126],{"className":20125},[629],[363,20127,20129,20149],{"className":20128},[633,634],[363,20130,20132,20146],{"className":20131},[638],[363,20133,20135],{"className":20134,"style":11480},[642],[363,20136,20137,20140],{"style":19190},[363,20138],{"className":20139,"style":651},[650],[363,20141,20143],{"className":20142},[655,656,657,658],[363,20144,465],{"className":20145},[407,658],[363,20147,666],{"className":20148},[665],[363,20150,20152],{"className":20151},[638],[363,20153,20155],{"className":20154,"style":8315},[642],[363,20156],{},[363,20158],{"className":20159,"style":754},[505],[363,20161,16059],{"className":20162,"style":16108},[407,408],[363,20164,461],{"className":20165},[494],[363,20167,465],{"className":20168},[407],[363,20170],{"className":20171,"style":2934},[505],[363,20173,5160],{"className":20174},[2938],[363,20176],{"className":20177,"style":2934},[505],[363,20179,16797],{"className":20180,"style":625},[407,408],[363,20182,468],{"className":20183},[501],[363,20185],{"className":20186,"style":2934},[505],[363,20188,2817],{"className":20189},[2938],[363,20191],{"className":20192,"style":2934},[505],[363,20194,19568],{"className":20195,"style":625},[407,408],[363,20197,461],{"className":20198},[494],[363,20200,20202,20205],{"className":20201},[407],[363,20203,16059],{"className":20204,"style":16108},[407,408],[363,20206,20208],{"className":20207},[629],[363,20209,20211],{"className":20210},[633],[363,20212,20214],{"className":20213},[638],[363,20215,20217],{"className":20216,"style":20082},[642],[363,20218,20219,20222],{"style":8624},[363,20220],{"className":20221,"style":651},[650],[363,20223,20225],{"className":20224},[655,656,657,658],[363,20226,2810],{"className":20227},[407,658],[363,20229,468],{"className":20230},[501],[363,20232,898],{"className":20233},[920],[363,20235,666],{"className":20236},[665],[363,20238,20240],{"className":20239},[638],[363,20241,20243],{"className":20242,"style":19728},[642],[363,20244],{},[11,20246,20247,20248,20313,20314,20390,20391,20419,20420,7147,20523,20551,20552,20601,20602,2756,20738,20787],{},"（用了 ",[363,20249,20251,20274],{"className":20250,"translate":367},[366],[363,20252,20254],{"className":20253},[371],[373,20255,20256],{"xmlns":375},[377,20257,20258,20272],{},[380,20259,20260,20262,20264,20266,20268,20270],{},[383,20261,385],{},[458,20263,461],{"stretchy":460},[463,20265,465],{},[458,20267,468],{"stretchy":460},[458,20269,471],{},[463,20271,474],{},[387,20273,477],{"encoding":389},[363,20275,20277,20304],{"className":20276,"ariaHidden":394},[393],[363,20278,20280,20283,20286,20289,20292,20295,20298,20301],{"className":20279},[398],[363,20281],{"className":20282,"style":487},[402],[363,20284,385],{"className":20285,"style":409},[407,408],[363,20287,461],{"className":20288},[494],[363,20290,465],{"className":20291},[407],[363,20293,468],{"className":20294},[501],[363,20296],{"className":20297,"style":506},[505],[363,20299,471],{"className":20300},[510],[363,20302],{"className":20303,"style":506},[505],[363,20305,20307,20310],{"className":20306},[398],[363,20308],{"className":20309,"style":520},[402],[363,20311,474],{"className":20312},[407],"；",[363,20315,20317,20341],{"className":20316,"translate":367},[366],[363,20318,20320],{"className":20319},[371],[373,20321,20322],{"xmlns":375},[377,20323,20324,20338],{},[380,20325,20326,20328,20330,20336],{},[383,20327,19568],{},[458,20329,461],{"stretchy":460},[7161,20331,20332,20334],{},[383,20333,16059],{},[463,20335,2810],{},[458,20337,468],{"stretchy":460},[387,20339,20340],{"encoding":389},"O(\\delta^2)",[363,20342,20344],{"className":20343,"ariaHidden":394},[393],[363,20345,20347,20351,20354,20357,20387],{"className":20346},[398],[363,20348],{"className":20349,"style":20350},[402],"height:1.0641em;vertical-align:-0.25em;",[363,20352,19568],{"className":20353,"style":625},[407,408],[363,20355,461],{"className":20356},[494],[363,20358,20360,20363],{"className":20359},[407],[363,20361,16059],{"className":20362,"style":16108},[407,408],[363,20364,20366],{"className":20365},[629],[363,20367,20369],{"className":20368},[633],[363,20370,20372],{"className":20371},[638],[363,20373,20376],{"className":20374,"style":20375},[642],"height:0.8141em;",[363,20377,20378,20381],{"style":7212},[363,20379],{"className":20380,"style":651},[650],[363,20382,20384],{"className":20383},[655,656,657,658],[363,20385,2810],{"className":20386},[407,658],[363,20388,468],{"className":20389},[501]," 项在 ",[363,20392,20394,20407],{"className":20393,"translate":367},[366],[363,20395,20397],{"className":20396},[371],[373,20398,20399],{"xmlns":375},[377,20400,20401,20405],{},[380,20402,20403],{},[383,20404,16797],{},[387,20406,16797],{"encoding":389},[363,20408,20410],{"className":20409,"ariaHidden":394},[393],[363,20411,20413,20416],{"className":20412},[398],[363,20414],{"className":20415,"style":2692},[402],[363,20417,16797],{"className":20418,"style":625},[407,408]," 变化时一致有界，因为 ",[363,20421,20423,20457],{"className":20422,"translate":367},[366],[363,20424,20426],{"className":20425},[371],[373,20427,20428],{"xmlns":375},[377,20429,20430,20454],{},[380,20431,20432,20434,20436,20438,20440,20442,20444,20446,20448,20450,20452],{},[383,20433,4505],{},[458,20435,461],{"stretchy":460},[383,20437,16797],{},[458,20439,468],{"stretchy":460},[458,20441,471],{},[463,20443,465],{},[458,20445,2817],{},[383,20447,19568],{},[458,20449,461],{"stretchy":460},[383,20451,16059],{},[458,20453,468],{"stretchy":460},[387,20455,20456],{"encoding":389},"g(r)=1+O(\\delta)",[363,20458,20460,20487,20505],{"className":20459,"ariaHidden":394},[393],[363,20461,20463,20466,20469,20472,20475,20478,20481,20484],{"className":20462},[398],[363,20464],{"className":20465,"style":487},[402],[363,20467,4505],{"className":20468,"style":1328},[407,408],[363,20470,461],{"className":20471},[494],[363,20473,16797],{"className":20474,"style":625},[407,408],[363,20476,468],{"className":20477},[501],[363,20479],{"className":20480,"style":506},[505],[363,20482,471],{"className":20483},[510],[363,20485],{"className":20486,"style":506},[505],[363,20488,20490,20493,20496,20499,20502],{"className":20489},[398],[363,20491],{"className":20492,"style":12925},[402],[363,20494,465],{"className":20495},[407],[363,20497],{"className":20498,"style":2934},[505],[363,20500,2817],{"className":20501},[2938],[363,20503],{"className":20504,"style":2934},[505],[363,20506,20508,20511,20514,20517,20520],{"className":20507},[398],[363,20509],{"className":20510,"style":487},[402],[363,20512,19568],{"className":20513,"style":625},[407,408],[363,20515,461],{"className":20516},[494],[363,20518,16059],{"className":20519,"style":16108},[407,408],[363,20521,468],{"className":20522},[501],[363,20524,20526,20539],{"className":20525,"translate":367},[366],[363,20527,20529],{"className":20528},[371],[373,20530,20531],{"xmlns":375},[377,20532,20533,20537],{},[380,20534,20535],{},[383,20536,385],{},[387,20538,385],{"encoding":389},[363,20540,20542],{"className":20541,"ariaHidden":394},[393],[363,20543,20545,20548],{"className":20544},[398],[363,20546],{"className":20547,"style":403},[402],[363,20549,385],{"className":20550,"style":409},[407,408]," 连续）。代回不等式：两边的主项（",[363,20553,20555,20577],{"className":20554,"translate":367},[366],[363,20556,20558],{"className":20557},[371],[373,20559,20560],{"xmlns":375},[377,20561,20562,20574],{},[380,20563,20564,20566,20568,20570,20572],{},[383,20565,16059],{},[383,20567,385],{},[458,20569,461],{"stretchy":460},[458,20571,3646],{},[458,20573,468],{"stretchy":460},[387,20575,20576],{"encoding":389},"\\delta f(\\cdot)",[363,20578,20580],{"className":20579,"ariaHidden":394},[393],[363,20581,20583,20586,20589,20592,20595,20598],{"className":20582},[398],[363,20584],{"className":20585,"style":487},[402],[363,20587,16059],{"className":20588,"style":16108},[407,408],[363,20590,385],{"className":20591,"style":409},[407,408],[363,20593,461],{"className":20594},[494],[363,20596,3646],{"className":20597},[407],[363,20599,468],{"className":20600},[501]," 部分）正是 ",[363,20603,20605,20653],{"className":20604,"translate":367},[366],[363,20606,20608],{"className":20607},[371],[373,20609,20610],{"xmlns":375},[377,20611,20612,20650],{},[380,20613,20614,20616,20618,20620,20622,20624,20626,20628,20630,20632,20634,20636,20638,20640,20642,20644,20646,20648],{},[383,20615,16059],{},[458,20617,578],{"stretchy":460},[383,20619,11686],{},[383,20621,385],{},[458,20623,461],{"stretchy":460},[383,20625,7908],{},[458,20627,468],{"stretchy":460},[458,20629,2817],{},[458,20631,461],{"stretchy":460},[463,20633,465],{},[458,20635,5160],{},[383,20637,11686],{},[458,20639,468],{"stretchy":460},[383,20641,385],{},[458,20643,461],{"stretchy":460},[383,20645,15747],{},[458,20647,468],{"stretchy":460},[458,20649,605],{"stretchy":460},[387,20651,20652],{"encoding":389},"\\delta[\\lambda f(s)+(1-\\lambda)f(u)]",[363,20654,20656,20692,20713],{"className":20655,"ariaHidden":394},[393],[363,20657,20659,20662,20665,20668,20671,20674,20677,20680,20683,20686,20689],{"className":20658},[398],[363,20660],{"className":20661,"style":487},[402],[363,20663,16059],{"className":20664,"style":16108},[407,408],[363,20666,578],{"className":20667},[494],[363,20669,11686],{"className":20670},[407,408],[363,20672,385],{"className":20673,"style":409},[407,408],[363,20675,461],{"className":20676},[494],[363,20678,7908],{"className":20679},[407,408],[363,20681,468],{"className":20682},[501],[363,20684],{"className":20685,"style":2934},[505],[363,20687,2817],{"className":20688},[2938],[363,20690],{"className":20691,"style":2934},[505],[363,20693,20695,20698,20701,20704,20707,20710],{"className":20694},[398],[363,20696],{"className":20697,"style":487},[402],[363,20699,461],{"className":20700},[494],[363,20702,465],{"className":20703},[407],[363,20705],{"className":20706,"style":2934},[505],[363,20708,5160],{"className":20709},[2938],[363,20711],{"className":20712,"style":2934},[505],[363,20714,20716,20719,20722,20725,20728,20731,20734],{"className":20715},[398],[363,20717],{"className":20718,"style":487},[402],[363,20720,11686],{"className":20721},[407,408],[363,20723,468],{"className":20724},[501],[363,20726,385],{"className":20727,"style":409},[407,408],[363,20729,461],{"className":20730},[494],[363,20732,15747],{"className":20733},[407,408],[363,20735,20737],{"className":20736},[501],")]",[363,20739,20741,20763],{"className":20740,"translate":367},[366],[363,20742,20744],{"className":20743},[371],[373,20745,20746],{"xmlns":375},[377,20747,20748,20760],{},[380,20749,20750,20752,20754,20756,20758],{},[383,20751,16059],{},[383,20753,385],{},[458,20755,461],{"stretchy":460},[383,20757,7917],{},[458,20759,468],{"stretchy":460},[387,20761,20762],{"encoding":389},"\\delta f(w)",[363,20764,20766],{"className":20765,"ariaHidden":394},[393],[363,20767,20769,20772,20775,20778,20781,20784],{"className":20768},[398],[363,20770],{"className":20771,"style":487},[402],[363,20773,16059],{"className":20774,"style":16108},[407,408],[363,20776,385],{"className":20777,"style":409},[407,408],[363,20779,461],{"className":20780},[494],[363,20782,7917],{"className":20783,"style":8621},[407,408],[363,20785,468],{"className":20786},[501],"；非主项部分",[363,20789,20791],{"className":20790,"translate":367},[528],[363,20792,20794,20880],{"className":20793,"translate":367},[366],[363,20795,20797],{"className":20796},[371],[373,20798,20799],{"xmlns":375,"display":537},[377,20800,20801,20877],{},[380,20802,20803,20805,20807,20809,20811,20813,20815,20821,20823,20825,20827,20829,20831,20833,20835,20837,20839,20841,20843,20845,20847,20849,20851,20853,20855,20857,20859,20861,20863,20865,20867,20869,20871,20873,20875],{},[458,20804,461],{"stretchy":460},[463,20806,465],{},[458,20808,5160],{},[383,20810,16059],{},[458,20812,468],{"stretchy":460},[1644,20814,1646],{},[543,20816,20817,20819],{},[383,20818,4505],{},[463,20820,465],{},[383,20822,16059],{},[458,20824,578],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,20826,11686],{},[458,20828,461],{"stretchy":460},[463,20830,465],{},[458,20832,5160],{},[383,20834,7908],{},[458,20836,468],{"stretchy":460},[458,20838,2817],{},[458,20840,461],{"stretchy":460},[463,20842,465],{},[458,20844,5160],{},[383,20846,11686],{},[458,20848,468],{"stretchy":460},[458,20850,461],{"stretchy":460},[463,20852,465],{},[458,20854,5160],{},[383,20856,15747],{},[458,20858,468],{"stretchy":460},[458,20860,5160],{},[458,20862,461],{"stretchy":460},[463,20864,465],{},[458,20866,5160],{},[383,20868,7917],{},[458,20870,468],{"stretchy":460},[458,20872,605],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,20874,471],{},[463,20876,474],{},[387,20878,20879],{"encoding":389},"(1-\\delta)\\,g_1\\delta\\big[\\lambda(1-s)\n+(1-\\lambda)(1-u)-(1-w)\\big]=0",[363,20881,20883,20904,20987,21008,21029,21056,21077,21098,21125],{"className":20882,"ariaHidden":394},[393],[363,20884,20886,20889,20892,20895,20898,20901],{"className":20885},[398],[363,20887],{"className":20888,"style":487},[402],[363,20890,461],{"className":20891},[494],[363,20893,465],{"className":20894},[407],[363,20896],{"className":20897,"style":2934},[505],[363,20899,5160],{"className":20900},[2938],[363,20902],{"className":20903,"style":2934},[505],[363,20905,20907,20911,20914,20917,20920,20960,20963,20969,20972,20975,20978,20981,20984],{"className":20906},[398],[363,20908],{"className":20909,"style":20910},[402],"height:1.2em;vertical-align:-0.35em;",[363,20912,16059],{"className":20913,"style":16108},[407,408],[363,20915,468],{"className":20916},[501],[363,20918],{"className":20919,"style":754},[505],[363,20921,20923,20926],{"className":20922},[407],[363,20924,4505],{"className":20925,"style":1328},[407,408],[363,20927,20929],{"className":20928},[629],[363,20930,20932,20952],{"className":20931},[633,634],[363,20933,20935,20949],{"className":20934},[638],[363,20936,20938],{"className":20937,"style":11480},[642],[363,20939,20940,20943],{"style":19190},[363,20941],{"className":20942,"style":651},[650],[363,20944,20946],{"className":20945},[655,656,657,658],[363,20947,465],{"className":20948},[407,658],[363,20950,666],{"className":20951},[665],[363,20953,20955],{"className":20954},[638],[363,20956,20958],{"className":20957,"style":8315},[642],[363,20959],{},[363,20961,16059],{"className":20962,"style":16108},[407,408],[363,20964,20966],{"className":20965},[407],[363,20967,578],{"className":20968},[767,10021],[363,20970,11686],{"className":20971},[407,408],[363,20973,461],{"className":20974},[494],[363,20976,465],{"className":20977},[407],[363,20979],{"className":20980,"style":2934},[505],[363,20982,5160],{"className":20983},[2938],[363,20985],{"className":20986,"style":2934},[505],[363,20988,20990,20993,20996,20999,21002,21005],{"className":20989},[398],[363,20991],{"className":20992,"style":487},[402],[363,20994,7908],{"className":20995},[407,408],[363,20997,468],{"className":20998},[501],[363,21000],{"className":21001,"style":2934},[505],[363,21003,2817],{"className":21004},[2938],[363,21006],{"className":21007,"style":2934},[505],[363,21009,21011,21014,21017,21020,21023,21026],{"className":21010},[398],[363,21012],{"className":21013,"style":487},[402],[363,21015,461],{"className":21016},[494],[363,21018,465],{"className":21019},[407],[363,21021],{"className":21022,"style":2934},[505],[363,21024,5160],{"className":21025},[2938],[363,21027],{"className":21028,"style":2934},[505],[363,21030,21032,21035,21038,21041,21044,21047,21050,21053],{"className":21031},[398],[363,21033],{"className":21034,"style":487},[402],[363,21036,11686],{"className":21037},[407,408],[363,21039,468],{"className":21040},[501],[363,21042,461],{"className":21043},[494],[363,21045,465],{"className":21046},[407],[363,21048],{"className":21049,"style":2934},[505],[363,21051,5160],{"className":21052},[2938],[363,21054],{"className":21055,"style":2934},[505],[363,21057,21059,21062,21065,21068,21071,21074],{"className":21058},[398],[363,21060],{"className":21061,"style":487},[402],[363,21063,15747],{"className":21064},[407,408],[363,21066,468],{"className":21067},[501],[363,21069],{"className":21070,"style":2934},[505],[363,21072,5160],{"className":21073},[2938],[363,21075],{"className":21076,"style":2934},[505],[363,21078,21080,21083,21086,21089,21092,21095],{"className":21079},[398],[363,21081],{"className":21082,"style":487},[402],[363,21084,461],{"className":21085},[494],[363,21087,465],{"className":21088},[407],[363,21090],{"className":21091,"style":2934},[505],[363,21093,5160],{"className":21094},[2938],[363,21096],{"className":21097,"style":2934},[505],[363,21099,21101,21104,21107,21110,21116,21119,21122],{"className":21100},[398],[363,21102],{"className":21103,"style":20910},[402],[363,21105,7917],{"className":21106,"style":8621},[407,408],[363,21108,468],{"className":21109},[501],[363,21111,21113],{"className":21112},[407],[363,21114,605],{"className":21115},[767,10021],[363,21117],{"className":21118,"style":506},[505],[363,21120,471],{"className":21121},[510],[363,21123],{"className":21124,"style":506},[505],[363,21126,21128,21131],{"className":21127},[398],[363,21129],{"className":21130,"style":520},[402],[363,21132,474],{"className":21133},[407],[11,21135,21136,21137,21251,21252,21303,21304,21386],{},"（方括号内恰为 0，因为 ",[363,21138,21140,21173],{"className":21139,"translate":367},[366],[363,21141,21143],{"className":21142},[371],[373,21144,21145],{"xmlns":375},[377,21146,21147,21171],{},[380,21148,21149,21151,21153,21155,21157,21159,21161,21163,21165,21167,21169],{},[383,21150,7917],{},[458,21152,471],{},[383,21154,11686],{},[383,21156,7908],{},[458,21158,2817],{},[458,21160,461],{"stretchy":460},[463,21162,465],{},[458,21164,5160],{},[383,21166,11686],{},[458,21168,468],{"stretchy":460},[383,21170,15747],{},[387,21172,15905],{"encoding":389},[363,21174,21176,21194,21215,21236],{"className":21175,"ariaHidden":394},[393],[363,21177,21179,21182,21185,21188,21191],{"className":21178},[398],[363,21180],{"className":21181,"style":2692},[402],[363,21183,7917],{"className":21184,"style":8621},[407,408],[363,21186],{"className":21187,"style":506},[505],[363,21189,471],{"className":21190},[510],[363,21192],{"className":21193,"style":506},[505],[363,21195,21197,21200,21203,21206,21209,21212],{"className":21196},[398],[363,21198],{"className":21199,"style":15933},[402],[363,21201,11686],{"className":21202},[407,408],[363,21204,7908],{"className":21205},[407,408],[363,21207],{"className":21208,"style":2934},[505],[363,21210,2817],{"className":21211},[2938],[363,21213],{"className":21214,"style":2934},[505],[363,21216,21218,21221,21224,21227,21230,21233],{"className":21217},[398],[363,21219],{"className":21220,"style":487},[402],[363,21222,461],{"className":21223},[494],[363,21225,465],{"className":21226},[407],[363,21228],{"className":21229,"style":2934},[505],[363,21231,5160],{"className":21232},[2938],[363,21234],{"className":21235,"style":2934},[505],[363,21237,21239,21242,21245,21248],{"className":21238},[398],[363,21240],{"className":21241,"style":487},[402],[363,21243,11686],{"className":21244},[407,408],[363,21246,468],{"className":21247},[501],[363,21249,15747],{"className":21250},[407,408],"）。于是不等式两边同除以 ",[363,21253,21255,21273],{"className":21254,"translate":367},[366],[363,21256,21258],{"className":21257},[371],[373,21259,21260],{"xmlns":375},[377,21261,21262,21270],{},[380,21263,21264,21266,21268],{},[383,21265,16059],{},[458,21267,3250],{},[463,21269,474],{},[387,21271,21272],{"encoding":389},"\\delta>0",[363,21274,21276,21294],{"className":21275,"ariaHidden":394},[393],[363,21277,21279,21282,21285,21288,21291],{"className":21278},[398],[363,21280],{"className":21281,"style":11711},[402],[363,21283,16059],{"className":21284,"style":16108},[407,408],[363,21286],{"className":21287,"style":506},[505],[363,21289,3250],{"className":21290},[510],[363,21292],{"className":21293,"style":506},[505],[363,21295,21297,21300],{"className":21296},[398],[363,21298],{"className":21299,"style":520},[402],[363,21301,474],{"className":21302},[407],"，令 ",[363,21305,21307,21329],{"className":21306,"translate":367},[366],[363,21308,21310],{"className":21309},[371],[373,21311,21312],{"xmlns":375},[377,21313,21314,21326],{},[380,21315,21316,21318,21320],{},[383,21317,16059],{},[458,21319,1376],{},[7161,21321,21322,21324],{},[463,21323,474],{},[458,21325,2817],{},[387,21327,21328],{"encoding":389},"\\delta\\to0^+",[363,21330,21332,21350],{"className":21331,"ariaHidden":394},[393],[363,21333,21335,21338,21341,21344,21347],{"className":21334},[398],[363,21336],{"className":21337,"style":12944},[402],[363,21339,16059],{"className":21340,"style":16108},[407,408],[363,21342],{"className":21343,"style":506},[505],[363,21345,1376],{"className":21346},[510],[363,21348],{"className":21349,"style":506},[505],[363,21351,21353,21357],{"className":21352},[398],[363,21354],{"className":21355,"style":21356},[402],"height:0.7713em;",[363,21358,21360,21363],{"className":21359},[407],[363,21361,474],{"className":21362},[407],[363,21364,21366],{"className":21365},[629],[363,21367,21369],{"className":21368},[633],[363,21370,21372],{"className":21371},[638],[363,21373,21375],{"className":21374,"style":21356},[642],[363,21376,21377,21380],{"style":7212},[363,21378],{"className":21379,"style":651},[650],[363,21381,21383],{"className":21382},[655,656,657,658],[363,21384,2817],{"className":21385},[2938,658],"，得",[363,21388,21390],{"className":21389,"translate":367},[528],[363,21391,21393,21463],{"className":21392,"translate":367},[366],[363,21394,21396],{"className":21395},[371],[373,21397,21398],{"xmlns":375,"display":537},[377,21399,21400,21460],{},[380,21401,21402,21404,21406,21408,21410,21412,21414,21416,21418,21420,21422,21424,21426,21428,21430,21432,21434,21436,21438,21440,21442,21444,21446,21448,21450,21452,21454,21456,21458],{},[383,21403,385],{},[458,21405,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,21407,11686],{},[383,21409,7908],{},[458,21411,2817],{},[458,21413,461],{"stretchy":460},[463,21415,465],{},[458,21417,5160],{},[383,21419,11686],{},[458,21421,468],{"stretchy":460},[383,21423,15747],{},[458,21425,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,21427,10299],{},[383,21429,11686],{},[383,21431,385],{},[458,21433,461],{"stretchy":460},[383,21435,7908],{},[458,21437,468],{"stretchy":460},[458,21439,2817],{},[458,21441,461],{"stretchy":460},[463,21443,465],{},[458,21445,5160],{},[383,21447,11686],{},[458,21449,468],{"stretchy":460},[383,21451,385],{},[458,21453,461],{"stretchy":460},[383,21455,15747],{},[458,21457,468],{"stretchy":460},[458,21459,898],{"separator":394},[387,21461,21462],{"encoding":389},"f\\big(\\lambda s+(1-\\lambda)u\\big)\n\\le\\lambda f(s)+(1-\\lambda)f(u),",[363,21464,21466,21496,21517,21547,21577,21598],{"className":21465,"ariaHidden":394},[393],[363,21467,21469,21472,21475,21481,21484,21487,21490,21493],{"className":21468},[398],[363,21470],{"className":21471,"style":20910},[402],[363,21473,385],{"className":21474,"style":409},[407,408],[363,21476,21478],{"className":21477},[407],[363,21479,461],{"className":21480},[767,10021],[363,21482,11686],{"className":21483},[407,408],[363,21485,7908],{"className":21486},[407,408],[363,21488],{"className":21489,"style":2934},[505],[363,21491,2817],{"className":21492},[2938],[363,21494],{"className":21495,"style":2934},[505],[363,21497,21499,21502,21505,21508,21511,21514],{"className":21498},[398],[363,21500],{"className":21501,"style":487},[402],[363,21503,461],{"className":21504},[494],[363,21506,465],{"className":21507},[407],[363,21509],{"className":21510,"style":2934},[505],[363,21512,5160],{"className":21513},[2938],[363,21515],{"className":21516,"style":2934},[505],[363,21518,21520,21523,21526,21529,21532,21538,21541,21544],{"className":21519},[398],[363,21521],{"className":21522,"style":20910},[402],[363,21524,11686],{"className":21525},[407,408],[363,21527,468],{"className":21528},[501],[363,21530,15747],{"className":21531},[407,408],[363,21533,21535],{"className":21534},[407],[363,21536,468],{"className":21537},[767,10021],[363,21539],{"className":21540,"style":506},[505],[363,21542,10299],{"className":21543},[510],[363,21545],{"className":21546,"style":506},[505],[363,21548,21550,21553,21556,21559,21562,21565,21568,21571,21574],{"className":21549},[398],[363,21551],{"className":21552,"style":487},[402],[363,21554,11686],{"className":21555},[407,408],[363,21557,385],{"className":21558,"style":409},[407,408],[363,21560,461],{"className":21561},[494],[363,21563,7908],{"className":21564},[407,408],[363,21566,468],{"className":21567},[501],[363,21569],{"className":21570,"style":2934},[505],[363,21572,2817],{"className":21573},[2938],[363,21575],{"className":21576,"style":2934},[505],[363,21578,21580,21583,21586,21589,21592,21595],{"className":21579},[398],[363,21581],{"className":21582,"style":487},[402],[363,21584,461],{"className":21585},[494],[363,21587,465],{"className":21588},[407],[363,21590],{"className":21591,"style":2934},[505],[363,21593,5160],{"className":21594},[2938],[363,21596],{"className":21597,"style":2934},[505],[363,21599,21601,21604,21607,21610,21613,21616,21619,21622],{"className":21600},[398],[363,21602],{"className":21603,"style":487},[402],[363,21605,11686],{"className":21606},[407,408],[363,21608,468],{"className":21609},[501],[363,21611,385],{"className":21612,"style":409},[407,408],[363,21614,461],{"className":21615},[494],[363,21617,15747],{"className":21618},[407,408],[363,21620,468],{"className":21621},[501],[363,21623,898],{"className":21624},[920],[11,21626,21627,21628,11312],{},"即 ",[363,21629,21631,21644],{"className":21630,"translate":367},[366],[363,21632,21634],{"className":21633},[371],[373,21635,21636],{"xmlns":375},[377,21637,21638,21642],{},[380,21639,21640],{},[383,21641,385],{},[387,21643,385],{"encoding":389},[363,21645,21647],{"className":21646,"ariaHidden":394},[393],[363,21648,21650,21653],{"className":21649},[398],[363,21651],{"className":21652,"style":403},[402],[363,21654,385],{"className":21655,"style":409},[407,408],[11,21657,21658,21659,21662,21663,21691,21692,21722,21723,21751],{},"所以\"凸\"与\"数据处理\"是同一件事的两面。这也是 f-散度族成为\"一切满足数据处理不等式的最一般散度\"的原因：它不是一堆例子的偶然汇总，而是一个有刻画定理支撑的完整族。换句话说，Csiszár–Ali–Silvey 定理给出一个完整的",[1572,21660,21661],{},"刻画","：凸函数 ",[363,21664,21666,21679],{"className":21665,"translate":367},[366],[363,21667,21669],{"className":21668},[371],[373,21670,21671],{"xmlns":375},[377,21672,21673,21677],{},[380,21674,21675],{},[383,21676,385],{},[387,21678,385],{"encoding":389},[363,21680,21682],{"className":21681,"ariaHidden":394},[393],[363,21683,21685,21688],{"className":21684},[398],[363,21686],{"className":21687,"style":403},[402],[363,21689,385],{"className":21690,"style":409},[407,408],"（模去仿射项）",[363,21693,21695,21710],{"className":21694,"translate":367},[366],[363,21696,21698],{"className":21697},[371],[373,21699,21700],{"xmlns":375},[377,21701,21702,21707],{},[380,21703,21704],{},[458,21705,21706],{},"↔",[387,21708,21709],{"encoding":389},"\\leftrightarrow",[363,21711,21713],{"className":21712,"ariaHidden":394},[393],[363,21714,21716,21719],{"className":21715},[398],[363,21717],{"className":21718,"style":11350},[402],[363,21720,21706],{"className":21721},[510]," 联合凸泛函 ",[363,21724,21726,21739],{"className":21725,"translate":367},[366],[363,21727,21729],{"className":21728},[371],[373,21730,21731],{"xmlns":375},[377,21732,21733,21737],{},[380,21734,21735],{},[458,21736,21706],{},[387,21738,21709],{"encoding":389},[363,21740,21742],{"className":21741,"ariaHidden":394},[393],[363,21743,21745,21748],{"className":21744},[398],[363,21746],{"className":21747,"style":11350},[402],[363,21749,21706],{"className":21750},[510]," 满足数据处理不等式的分布差异度量，三者一一对应。",[18,21753,21755],{"id":21754},"_3-常见散度","3. 常见散度",[11,21757,21758,21759,21787],{},"不同的 ",[363,21760,21762,21775],{"className":21761,"translate":367},[366],[363,21763,21765],{"className":21764},[371],[373,21766,21767],{"xmlns":375},[377,21768,21769,21773],{},[380,21770,21771],{},[383,21772,385],{},[387,21774,385],{"encoding":389},[363,21776,21778],{"className":21777,"ariaHidden":394},[393],[363,21779,21781,21784],{"className":21780},[398],[363,21782],{"className":21783,"style":403},[402],[363,21785,385],{"className":21786,"style":409},[407,408]," 对应不同的散度。KL、JS、全变差、卡方、Hellinger、Wasserstein、MMD 等散度，表面上都是「衡量两个分布差多少」，但它们的根本区别可以归结为几个维度：",[11,21789,21790],{},"它们对「差异」的定义方式不同，对「支撑集不重叠」的处理不同，对「几何\u002F度量结构」的利用不同，因而导出的拓扑、梯度行为和优化性质也不同。",[11,21792,21793],{},"可以把不同散度的区别归纳为五个核心问题：",[7009,21795,21796,21799,21802,21805,21808],{},[7012,21797,21798],{},"差异定义在什么量上？是密度比值、密度差、累积分布差，还是搬运质量？",[7012,21800,21801],{},"是否对称？",[7012,21803,21804],{},"是否有界？",[7012,21806,21807],{},"是否利用样本空间的几何结构？",[7012,21809,21810],{},"诱导的拓扑强弱如何？",[11,21812,21813],{},"这五点决定了散度在理论性质和实际优化中的行为差异。下面逐个把常用散度「代入模板」并验算。",[2658,21815,21817],{"id":21816},"_31-kl-散度","3.1 KL 散度",[11,21819,21820],{},"取：",[363,21822,21824],{"className":21823,"translate":367},[528],[363,21825,21827,21856],{"className":21826,"translate":367},[366],[363,21828,21830],{"className":21829},[371],[373,21831,21832],{"xmlns":375,"display":537},[377,21833,21834,21854],{},[380,21835,21836,21838,21840,21842,21844,21846,21848,21850,21852],{},[383,21837,385],{},[458,21839,461],{"stretchy":460},[383,21841,1116],{},[458,21843,468],{"stretchy":460},[458,21845,471],{},[383,21847,1116],{},[383,21849,4447],{},[458,21851,4450],{},[383,21853,1116],{},[387,21855,4455],{"encoding":389},[363,21857,21859,21886],{"className":21858,"ariaHidden":394},[393],[363,21860,21862,21865,21868,21871,21874,21877,21880,21883],{"className":21861},[398],[363,21863],{"className":21864,"style":487},[402],[363,21866,385],{"className":21867,"style":409},[407,408],[363,21869,461],{"className":21870},[494],[363,21872,1116],{"className":21873},[407,408],[363,21875,468],{"className":21876},[501],[363,21878],{"className":21879,"style":506},[505],[363,21881,471],{"className":21882},[510],[363,21884],{"className":21885,"style":506},[505],[363,21887,21889,21892,21895,21898,21903,21906],{"className":21888},[398],[363,21890],{"className":21891,"style":403},[402],[363,21893,1116],{"className":21894},[407,408],[363,21896],{"className":21897,"style":754},[505],[363,21899,4501,21901],{"className":21900},[1831],[363,21902,4505],{"style":4504},[363,21904],{"className":21905,"style":754},[505],[363,21907,1116],{"className":21908},[407,408],[11,21910,21911,21912,21945,21946,3092,22011,22144],{},"（下面 ",[363,21913,21915,21931],{"className":21914,"translate":367},[366],[363,21916,21918],{"className":21917},[371],[373,21919,21920],{"xmlns":375},[377,21921,21922,21928],{},[380,21923,21924,21926],{},[383,21925,4447],{},[458,21927,4450],{},[387,21929,21930],{"encoding":389},"\\log",[363,21932,21934],{"className":21933,"ariaHidden":394},[393],[363,21935,21937,21940],{"className":21936},[398],[363,21938],{"className":21939,"style":403},[402],[363,21941,4501,21943],{"className":21942},[1831],[363,21944,4505],{"style":4504}," 均为自然对数。）则 ",[363,21947,21949,21972],{"className":21948,"translate":367},[366],[363,21950,21952],{"className":21951},[371],[373,21953,21954],{"xmlns":375},[377,21955,21956,21970],{},[380,21957,21958,21960,21962,21964,21966,21968],{},[383,21959,385],{},[458,21961,461],{"stretchy":460},[463,21963,465],{},[458,21965,468],{"stretchy":460},[458,21967,471],{},[463,21969,474],{},[387,21971,477],{"encoding":389},[363,21973,21975,22002],{"className":21974,"ariaHidden":394},[393],[363,21976,21978,21981,21984,21987,21990,21993,21996,21999],{"className":21977},[398],[363,21979],{"className":21980,"style":487},[402],[363,21982,385],{"className":21983,"style":409},[407,408],[363,21985,461],{"className":21986},[494],[363,21988,465],{"className":21989},[407],[363,21991,468],{"className":21992},[501],[363,21994],{"className":21995,"style":506},[505],[363,21997,471],{"className":21998},[510],[363,22000],{"className":22001,"style":506},[505],[363,22003,22005,22008],{"className":22004},[398],[363,22006],{"className":22007,"style":520},[402],[363,22009,474],{"className":22010},[407],[363,22012,22014,22054],{"className":22013,"translate":367},[366],[363,22015,22017],{"className":22016},[371],[373,22018,22019],{"xmlns":375},[377,22020,22021,22051],{},[380,22022,22023,22033,22035,22037,22039,22041,22043,22045,22047,22049],{},[7161,22024,22025,22027],{},[383,22026,385],{},[380,22028,22029,22031],{},[458,22030,7167],{"mathvariant":557},[458,22032,7167],{"mathvariant":557},[458,22034,461],{"stretchy":460},[383,22036,1116],{},[458,22038,468],{"stretchy":460},[458,22040,471],{},[463,22042,465],{},[383,22044,1288],{"mathvariant":557},[383,22046,1116],{},[458,22048,3250],{},[463,22050,474],{},[387,22052,22053],{"encoding":389},"f''(t)=1\u002Ft>0",[363,22055,22057,22114,22135],{"className":22056,"ariaHidden":394},[393],[363,22058,22060,22063,22096,22099,22102,22105,22108,22111],{"className":22059},[398],[363,22061],{"className":22062,"style":7190},[402],[363,22064,22066,22069],{"className":22065},[407],[363,22067,385],{"className":22068,"style":409},[407,408],[363,22070,22072],{"className":22071},[629],[363,22073,22075],{"className":22074},[633],[363,22076,22078],{"className":22077},[638],[363,22079,22081],{"className":22080,"style":7209},[642],[363,22082,22083,22086],{"style":7212},[363,22084],{"className":22085,"style":651},[650],[363,22087,22089],{"className":22088},[655,656,657,658],[363,22090,22092],{"className":22091},[407,658],[363,22093,22095],{"className":22094},[407,658],"′′",[363,22097,461],{"className":22098},[494],[363,22100,1116],{"className":22101},[407,408],[363,22103,468],{"className":22104},[501],[363,22106],{"className":22107,"style":506},[505],[363,22109,471],{"className":22110},[510],[363,22112],{"className":22113,"style":506},[505],[363,22115,22117,22120,22123,22126,22129,22132],{"className":22116},[398],[363,22118],{"className":22119,"style":487},[402],[363,22121,8936],{"className":22122},[407],[363,22124,1116],{"className":22125},[407,408],[363,22127],{"className":22128,"style":506},[505],[363,22130,3250],{"className":22131},[510],[363,22133],{"className":22134,"style":506},[505],[363,22136,22138,22141],{"className":22137},[398],[363,22139],{"className":22140,"style":520},[402],[363,22142,474],{"className":22143},[407]," 凸。代入模板：",[363,22146,22148],{"className":22147,"translate":367},[528],[363,22149,22151,22254],{"className":22150,"translate":367},[366],[363,22152,22154],{"className":22153},[371],[373,22155,22156],{"xmlns":375,"display":537},[377,22157,22158,22251],{},[380,22159,22160,22166,22168,22170,22172,22174,22176,22178,22180,22182,22184,22190,22192,22194,22200,22202,22204,22206,22208,22210,22212,22214,22216,22222,22224,22226,22228,22230,22241,22243,22245,22247,22249],{},[543,22161,22162,22164],{},[383,22163,547],{},[383,22165,385],{},[458,22167,461],{"stretchy":460},[383,22169,554],{},[383,22171,558],{"mathvariant":557},[383,22173,561],{},[458,22175,468],{"stretchy":460},[458,22177,471],{},[458,22179,1634],{},[383,22181,1291],{},[458,22183,3646],{},[586,22185,22186,22188],{},[383,22187,11],{},[383,22189,1291],{},[383,22191,4447],{},[458,22193,4450],{},[586,22195,22196,22198],{},[383,22197,11],{},[383,22199,1291],{},[1644,22201,1646],{},[383,22203,592],{},[383,22205,1121],{},[458,22207,471],{},[458,22209,1634],{},[383,22211,11],{},[383,22213,4447],{},[458,22215,4450],{},[586,22217,22218,22220],{},[383,22219,11],{},[383,22221,1291],{},[1644,22223,1646],{},[383,22225,592],{},[383,22227,1121],{},[458,22229,471],{},[543,22231,22232,22234],{},[383,22233,547],{},[380,22235,22236,22238],{},[383,22237,11041],{},[383,22239,22240],{},"L",[458,22242,461],{"stretchy":460},[383,22244,554],{},[383,22246,558],{"mathvariant":557},[383,22248,561],{},[458,22250,468],{"stretchy":460},[387,22252,22253],{"encoding":389},"D_f(P\\|Q)\n=\\int q\\cdot \\frac{p}{q}\\log\\frac{p}{q}\\,dx\n=\\int p\\log\\frac{p}{q}\\,dx\n=D_{KL}(P\\|Q)",[363,22255,22257,22327,22351,22511,22618],{"className":22256,"ariaHidden":394},[393],[363,22258,22260,22263,22303,22306,22309,22312,22315,22318,22321,22324],{"className":22259},[398],[363,22261],{"className":22262,"style":618},[402],[363,22264,22266,22269],{"className":22265},[407],[363,22267,547],{"className":22268,"style":625},[407,408],[363,22270,22272],{"className":22271},[629],[363,22273,22275,22295],{"className":22274},[633,634],[363,22276,22278,22292],{"className":22277},[638],[363,22279,22281],{"className":22280,"style":643},[642],[363,22282,22283,22286],{"style":646},[363,22284],{"className":22285,"style":651},[650],[363,22287,22289],{"className":22288},[655,656,657,658],[363,22290,385],{"className":22291,"style":409},[407,408,658],[363,22293,666],{"className":22294},[665],[363,22296,22298],{"className":22297},[638],[363,22299,22301],{"className":22300,"style":673},[642],[363,22302],{},[363,22304,461],{"className":22305},[494],[363,22307,554],{"className":22308,"style":682},[407,408],[363,22310,558],{"className":22311},[407],[363,22313,561],{"className":22314},[407,408],[363,22316,468],{"className":22317},[501],[363,22319],{"className":22320,"style":506},[505],[363,22322,471],{"className":22323},[510],[363,22325],{"className":22326,"style":506},[505],[363,22328,22330,22333,22336,22339,22342,22345,22348],{"className":22329},[398],[363,22331],{"className":22332,"style":6124},[402],[363,22334,1634],{"className":22335,"style":1834},[1831,1832,1833],[363,22337],{"className":22338,"style":754},[505],[363,22340,1291],{"className":22341,"style":1328},[407,408],[363,22343],{"className":22344,"style":2934},[505],[363,22346,3646],{"className":22347},[2938],[363,22349],{"className":22350,"style":2934},[505],[363,22352,22354,22358,22420,22423,22428,22431,22493,22496,22499,22502,22505,22508],{"className":22353},[398],[363,22355],{"className":22356,"style":22357},[402],"height:1.988em;vertical-align:-0.8804em;",[363,22359,22361,22364,22417],{"className":22360},[407],[363,22362],{"className":22363},[494,789],[363,22365,22367],{"className":22366},[586],[363,22368,22370,22409],{"className":22369},[633,634],[363,22371,22373,22406],{"className":22372},[638],[363,22374,22376,22387,22395],{"className":22375,"style":3901},[642],[363,22377,22378,22381],{"style":805},[363,22379],{"className":22380,"style":809},[650],[363,22382,22384],{"className":22383},[407],[363,22385,1291],{"className":22386,"style":1328},[407,408],[363,22388,22389,22392],{"style":821},[363,22390],{"className":22391,"style":809},[650],[363,22393],{"className":22394,"style":829},[828],[363,22396,22397,22400],{"style":832},[363,22398],{"className":22399,"style":809},[650],[363,22401,22403],{"className":22402},[407],[363,22404,11],{"className":22405},[407,408],[363,22407,666],{"className":22408},[665],[363,22410,22412],{"className":22411},[638],[363,22413,22415],{"className":22414,"style":854},[642],[363,22416],{},[363,22418],{"className":22419},[501,789],[363,22421],{"className":22422,"style":754},[505],[363,22424,4501,22426],{"className":22425},[1831],[363,22427,4505],{"style":4504},[363,22429],{"className":22430,"style":754},[505],[363,22432,22434,22437,22490],{"className":22433},[407],[363,22435],{"className":22436},[494,789],[363,22438,22440],{"className":22439},[586],[363,22441,22443,22482],{"className":22442},[633,634],[363,22444,22446,22479],{"className":22445},[638],[363,22447,22449,22460,22468],{"className":22448,"style":3901},[642],[363,22450,22451,22454],{"style":805},[363,22452],{"className":22453,"style":809},[650],[363,22455,22457],{"className":22456},[407],[363,22458,1291],{"className":22459,"style":1328},[407,408],[363,22461,22462,22465],{"style":821},[363,22463],{"className":22464,"style":809},[650],[363,22466],{"className":22467,"style":829},[828],[363,22469,22470,22473],{"style":832},[363,22471],{"className":22472,"style":809},[650],[363,22474,22476],{"className":22475},[407],[363,22477,11],{"className":22478},[407,408],[363,22480,666],{"className":22481},[665],[363,22483,22485],{"className":22484},[638],[363,22486,22488],{"className":22487,"style":854},[642],[363,22489],{},[363,22491],{"className":22492},[501,789],[363,22494],{"className":22495,"style":754},[505],[363,22497,592],{"className":22498},[407,408],[363,22500,1121],{"className":22501},[407,408],[363,22503],{"className":22504,"style":506},[505],[363,22506,471],{"className":22507},[510],[363,22509],{"className":22510,"style":506},[505],[363,22512,22514,22518,22521,22524,22527,22530,22535,22538,22600,22603,22606,22609,22612,22615],{"className":22513},[398],[363,22515],{"className":22516,"style":22517},[402],"height:2.2404em;vertical-align:-0.8804em;",[363,22519,1634],{"className":22520,"style":1834},[1831,1832,1833],[363,22522],{"className":22523,"style":754},[505],[363,22525,11],{"className":22526},[407,408],[363,22528],{"className":22529,"style":754},[505],[363,22531,4501,22533],{"className":22532},[1831],[363,22534,4505],{"style":4504},[363,22536],{"className":22537,"style":754},[505],[363,22539,22541,22544,22597],{"className":22540},[407],[363,22542],{"className":22543},[494,789],[363,22545,22547],{"className":22546},[586],[363,22548,22550,22589],{"className":22549},[633,634],[363,22551,22553,22586],{"className":22552},[638],[363,22554,22556,22567,22575],{"className":22555,"style":3901},[642],[363,22557,22558,22561],{"style":805},[363,22559],{"className":22560,"style":809},[650],[363,22562,22564],{"className":22563},[407],[363,22565,1291],{"className":22566,"style":1328},[407,408],[363,22568,22569,22572],{"style":821},[363,22570],{"className":22571,"style":809},[650],[363,22573],{"className":22574,"style":829},[828],[363,22576,22577,22580],{"style":832},[363,22578],{"className":22579,"style":809},[650],[363,22581,22583],{"className":22582},[407],[363,22584,11],{"className":22585},[407,408],[363,22587,666],{"className":22588},[665],[363,22590,22592],{"className":22591},[638],[363,22593,22595],{"className":22594,"style":854},[642],[363,22596],{},[363,22598],{"className":22599},[501,789],[363,22601],{"className":22602,"style":754},[505],[363,22604,592],{"className":22605},[407,408],[363,22607,1121],{"className":22608},[407,408],[363,22610],{"className":22611,"style":506},[505],[363,22613,471],{"className":22614},[510],[363,22616],{"className":22617,"style":506},[505],[363,22619,22621,22624,22670,22673,22676,22679,22682],{"className":22620},[398],[363,22622],{"className":22623,"style":487},[402],[363,22625,22627,22630],{"className":22626},[407],[363,22628,547],{"className":22629,"style":625},[407,408],[363,22631,22633],{"className":22632},[629],[363,22634,22636,22662],{"className":22635},[633,634],[363,22637,22639,22659],{"className":22638},[638],[363,22640,22642],{"className":22641,"style":727},[642],[363,22643,22644,22647],{"style":646},[363,22645],{"className":22646,"style":651},[650],[363,22648,22650],{"className":22649},[655,656,657,658],[363,22651,22653,22656],{"className":22652},[407,658],[363,22654,11041],{"className":22655,"style":11129},[407,408,658],[363,22657,22240],{"className":22658},[407,408,658],[363,22660,666],{"className":22661},[665],[363,22663,22665],{"className":22664},[638],[363,22666,22668],{"className":22667,"style":8315},[642],[363,22669],{},[363,22671,461],{"className":22672},[494],[363,22674,554],{"className":22675,"style":682},[407,408],[363,22677,558],{"className":22678},[407],[363,22680,561],{"className":22681},[407,408],[363,22683,468],{"className":22684},[501],[11,22686,22687,22688,22793,22794,9747],{},"反向 KL 散度 ",[363,22689,22691,22723],{"className":22690,"translate":367},[366],[363,22692,22694],{"className":22693},[371],[373,22695,22696],{"xmlns":375},[377,22697,22698,22720],{},[380,22699,22700,22710,22712,22714,22716,22718],{},[543,22701,22702,22704],{},[383,22703,547],{},[380,22705,22706,22708],{},[383,22707,11041],{},[383,22709,22240],{},[458,22711,461],{"stretchy":460},[383,22713,561],{},[383,22715,558],{"mathvariant":557},[383,22717,554],{},[458,22719,468],{"stretchy":460},[387,22721,22722],{"encoding":389},"D_{KL}(Q\\|P)",[363,22724,22726],{"className":22725,"ariaHidden":394},[393],[363,22727,22729,22732,22778,22781,22784,22787,22790],{"className":22728},[398],[363,22730],{"className":22731,"style":487},[402],[363,22733,22735,22738],{"className":22734},[407],[363,22736,547],{"className":22737,"style":625},[407,408],[363,22739,22741],{"className":22740},[629],[363,22742,22744,22770],{"className":22743},[633,634],[363,22745,22747,22767],{"className":22746},[638],[363,22748,22750],{"className":22749,"style":727},[642],[363,22751,22752,22755],{"style":646},[363,22753],{"className":22754,"style":651},[650],[363,22756,22758],{"className":22757},[655,656,657,658],[363,22759,22761,22764],{"className":22760},[407,658],[363,22762,11041],{"className":22763,"style":11129},[407,408,658],[363,22765,22240],{"className":22766},[407,408,658],[363,22768,666],{"className":22769},[665],[363,22771,22773],{"className":22772},[638],[363,22774,22776],{"className":22775,"style":8315},[642],[363,22777],{},[363,22779,461],{"className":22780},[494],[363,22782,561],{"className":22783},[407,408],[363,22785,558],{"className":22786},[407],[363,22788,554],{"className":22789,"style":682},[407,408],[363,22791,468],{"className":22792},[501]," 对应斜共轭 ",[363,22795,22797,22823],{"className":22796,"translate":367},[366],[363,22798,22800],{"className":22799},[371],[373,22801,22802],{"xmlns":375},[377,22803,22804,22820],{},[380,22805,22806,22808,22810,22812,22814,22816,22818],{},[383,22807,1116],{},[383,22809,385],{},[458,22811,461],{"stretchy":460},[463,22813,465],{},[383,22815,1288],{"mathvariant":557},[383,22817,1116],{},[458,22819,468],{"stretchy":460},[387,22821,22822],{"encoding":389},"t f(1\u002Ft)",[363,22824,22826],{"className":22825,"ariaHidden":394},[393],[363,22827,22829,22832,22835,22838,22841,22844,22847],{"className":22828},[398],[363,22830],{"className":22831,"style":487},[402],[363,22833,1116],{"className":22834},[407,408],[363,22836,385],{"className":22837,"style":409},[407,408],[363,22839,461],{"className":22840},[494],[363,22842,8936],{"className":22843},[407],[363,22845,1116],{"className":22846},[407,408],[363,22848,468],{"className":22849},[501],[363,22851,22853],{"className":22852,"translate":367},[528],[363,22854,22856,22978],{"className":22855,"translate":367},[366],[363,22857,22859],{"className":22858},[371],[373,22860,22861],{"xmlns":375,"display":537},[377,22862,22863,22975],{},[1590,22864,22865,22899],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,22866,22867,22881],{},[1599,22868,22869],{},[1602,22870,22871],{"scriptlevel":474,"displaystyle":394},[380,22872,22873,22875,22877,22879],{},[383,22874,385],{},[458,22876,461],{"stretchy":460},[383,22878,1116],{},[458,22880,468],{"stretchy":460},[1599,22882,22883],{},[1602,22884,22885],{"scriptlevel":474,"displaystyle":394},[380,22886,22887,22889,22891,22893,22895,22897],{},[380,22888],{},[458,22890,471],{},[383,22892,1116],{},[383,22894,4447],{},[458,22896,4450],{},[383,22898,1116],{},[1596,22900,22901,22907],{},[1599,22902,22903],{},[1602,22904,22905],{"scriptlevel":474,"displaystyle":394},[380,22906],{},[1599,22908,22909],{},[1602,22910,22911],{"scriptlevel":474,"displaystyle":394},[380,22912,22913,22915,22917,22919,22935,22937,22939,22941,22943,22945,22947,22953,22955,22957,22963,22965,22967,22969,22971,22973],{},[380,22914],{},[458,22916,4633],{},[1644,22918,4630],{},[7900,22920,22921,22923,22933],{},[383,22922,385],{},[380,22924,22925,22927,22929,22931],{},[383,22926,7908],{},[383,22928,7911],{},[383,22930,7914],{},[383,22932,7917],{},[458,22934,7920],{"lspace":1594,"rspace":1594},[458,22936,461],{"stretchy":460},[383,22938,1116],{},[458,22940,468],{"stretchy":460},[458,22942,471],{},[383,22944,1116],{},[458,22946,3646],{},[586,22948,22949,22951],{},[463,22950,465],{},[383,22952,1116],{},[383,22954,4447],{},[458,22956,4450],{},[586,22958,22959,22961],{},[463,22960,465],{},[383,22962,1116],{},[458,22964,471],{},[458,22966,5160],{},[383,22968,4447],{},[458,22970,4450],{},[383,22972,1116],{},[458,22974,898],{"separator":394},[387,22976,22977],{"encoding":389},"\\begin{aligned}\nf(t)&=t\\log t\\\\[2pt]\n&\\Longrightarrow\\ f^{*}_{skew}(t)\n=t\\cdot\\frac1t\\log\\frac1t=-\\log t,\n\\end{aligned}",[363,22979,22981],{"className":22980,"ariaHidden":394},[393],[363,22982,22984,22988],{"className":22983},[398],[363,22985],{"className":22986,"style":22987},[402],"height:3.7074em;vertical-align:-1.6037em;",[363,22989,22991],{"className":22990},[407],[363,22992,22994,23050],{"className":22993},[1590],[363,22995,22997],{"className":22996},[1707],[363,22998,23000,23041],{"className":22999},[633,634],[363,23001,23003,23038],{"className":23002},[638],[363,23004,23007,23029],{"className":23005,"style":23006},[642],"height:2.1037em;",[363,23008,23010,23014],{"style":23009},"top:-4.5852em;",[363,23011],{"className":23012,"style":23013},[650],"height:3.3214em;",[363,23015,23017,23020,23023,23026],{"className":23016},[407],[363,23018,385],{"className":23019,"style":409},[407,408],[363,23021,461],{"className":23022},[494],[363,23024,1116],{"className":23025},[407,408],[363,23027,468],{"className":23028},[501],[363,23030,23032,23035],{"style":23031},"top:-2.4037em;",[363,23033],{"className":23034,"style":23013},[650],[363,23036],{"className":23037},[407],[363,23039,666],{"className":23040},[665],[363,23042,23044],{"className":23043},[638],[363,23045,23048],{"className":23046,"style":23047},[642],"height:1.6037em;",[363,23049],{},[363,23051,23053],{"className":23052},[1798],[363,23054,23056,23386],{"className":23055},[633,634],[363,23057,23059,23383],{"className":23058},[638],[363,23060,23062,23099],{"className":23061,"style":23006},[642],[363,23063,23064,23067],{"style":23009},[363,23065],{"className":23066,"style":23013},[650],[363,23068,23070,23073,23076,23079,23082,23085,23088,23093,23096],{"className":23069},[407],[363,23071],{"className":23072},[407],[363,23074],{"className":23075,"style":506},[505],[363,23077,471],{"className":23078},[510],[363,23080],{"className":23081,"style":506},[505],[363,23083,1116],{"className":23084},[407,408],[363,23086],{"className":23087,"style":754},[505],[363,23089,4501,23091],{"className":23090},[1831],[363,23092,4505],{"style":4504},[363,23094],{"className":23095,"style":754},[505],[363,23097,1116],{"className":23098},[407,408],[363,23100,23101,23104],{"style":23031},[363,23102],{"className":23103,"style":23013},[650],[363,23105,23107,23110,23113,23116,23119,23122,23188,23191,23194,23197,23200,23203,23206,23209,23212,23215,23218,23281,23284,23289,23292,23354,23357,23360,23363,23366,23369,23374,23377,23380],{"className":23106},[407],[363,23108],{"className":23109},[407],[363,23111],{"className":23112,"style":506},[505],[363,23114,4633],{"className":23115},[510],[363,23117,4630],{"className":23118},[505],[363,23120],{"className":23121,"style":506},[505],[363,23123,23125,23128],{"className":23124},[407],[363,23126,385],{"className":23127,"style":409},[407,408],[363,23129,23131],{"className":23130},[629],[363,23132,23134,23180],{"className":23133},[633,634],[363,23135,23137,23177],{"className":23136},[638],[363,23138,23140,23163],{"className":23139,"style":8595},[642],[363,23141,23142,23145],{"style":8598},[363,23143],{"className":23144,"style":651},[650],[363,23146,23148],{"className":23147},[655,656,657,658],[363,23149,23151,23154,23157,23160],{"className":23150},[407,658],[363,23152,7908],{"className":23153},[407,408,658],[363,23155,7911],{"className":23156,"style":8614},[407,408,658],[363,23158,7914],{"className":23159},[407,408,658],[363,23161,7917],{"className":23162,"style":8621},[407,408,658],[363,23164,23165,23168],{"style":8624},[363,23166],{"className":23167,"style":651},[650],[363,23169,23171],{"className":23170},[655,656,657,658],[363,23172,23174],{"className":23173},[407,658],[363,23175,7920],{"className":23176},[407,658],[363,23178,666],{"className":23179},[665],[363,23181,23183],{"className":23182},[638],[363,23184,23186],{"className":23185,"style":8646},[642],[363,23187],{},[363,23189,461],{"className":23190},[494],[363,23192,1116],{"className":23193},[407,408],[363,23195,468],{"className":23196},[501],[363,23198],{"className":23199,"style":506},[505],[363,23201,471],{"className":23202},[510],[363,23204],{"className":23205,"style":506},[505],[363,23207,1116],{"className":23208},[407,408],[363,23210],{"className":23211,"style":2934},[505],[363,23213,3646],{"className":23214},[2938],[363,23216],{"className":23217,"style":2934},[505],[363,23219,23221,23224,23278],{"className":23220},[407],[363,23222],{"className":23223},[494,789],[363,23225,23227],{"className":23226},[586],[363,23228,23230,23270],{"className":23229},[633,634],[363,23231,23233,23267],{"className":23232},[638],[363,23234,23237,23248,23256],{"className":23235,"style":23236},[642],"height:1.3214em;",[363,23238,23239,23242],{"style":805},[363,23240],{"className":23241,"style":809},[650],[363,23243,23245],{"className":23244},[407],[363,23246,1116],{"className":23247},[407,408],[363,23249,23250,23253],{"style":821},[363,23251],{"className":23252,"style":809},[650],[363,23254],{"className":23255,"style":829},[828],[363,23257,23258,23261],{"style":832},[363,23259],{"className":23260,"style":809},[650],[363,23262,23264],{"className":23263},[407],[363,23265,465],{"className":23266},[407],[363,23268,666],{"className":23269},[665],[363,23271,23273],{"className":23272},[638],[363,23274,23276],{"className":23275,"style":4125},[642],[363,23277],{},[363,23279],{"className":23280},[501,789],[363,23282],{"className":23283,"style":754},[505],[363,23285,4501,23287],{"className":23286},[1831],[363,23288,4505],{"style":4504},[363,23290],{"className":23291,"style":754},[505],[363,23293,23295,23298,23351],{"className":23294},[407],[363,23296],{"className":23297},[494,789],[363,23299,23301],{"className":23300},[586],[363,23302,23304,23343],{"className":23303},[633,634],[363,23305,23307,23340],{"className":23306},[638],[363,23308,23310,23321,23329],{"className":23309,"style":23236},[642],[363,23311,23312,23315],{"style":805},[363,23313],{"className":23314,"style":809},[650],[363,23316,23318],{"className":23317},[407],[363,23319,1116],{"className":23320},[407,408],[363,23322,23323,23326],{"style":821},[363,23324],{"className":23325,"style":809},[650],[363,23327],{"className":23328,"style":829},[828],[363,23330,23331,23334],{"style":832},[363,23332],{"className":23333,"style":809},[650],[363,23335,23337],{"className":23336},[407],[363,23338,465],{"className":23339},[407],[363,23341,666],{"className":23342},[665],[363,23344,23346],{"className":23345},[638],[363,23347,23349],{"className":23348,"style":4125},[642],[363,23350],{},[363,23352],{"className":23353},[501,789],[363,23355],{"className":23356,"style":506},[505],[363,23358,471],{"className":23359},[510],[363,23361],{"className":23362,"style":506},[505],[363,23364,5160],{"className":23365},[407],[363,23367],{"className":23368,"style":754},[505],[363,23370,4501,23372],{"className":23371},[1831],[363,23373,4505],{"style":4504},[363,23375],{"className":23376,"style":754},[505],[363,23378,1116],{"className":23379},[407,408],[363,23381,898],{"className":23382},[920],[363,23384,666],{"className":23385},[665],[363,23387,23389],{"className":23388},[638],[363,23390,23392],{"className":23391,"style":23047},[642],[363,23393],{},[11,23395,23396],{},"所以",[363,23398,23400],{"className":23399,"translate":367},[528],[363,23401,23403,23479],{"className":23402,"translate":367},[366],[363,23404,23406],{"className":23405},[371],[373,23407,23408],{"xmlns":375,"display":537},[377,23409,23410,23476],{},[380,23411,23412,23414,23416,23418,23420,23422,23424,23426,23428,23430,23432,23434,23436,23442,23444,23446,23448,23450,23452,23454,23464,23466,23468,23470,23472,23474],{},[383,23413,385],{},[458,23415,461],{"stretchy":460},[383,23417,1116],{},[458,23419,468],{"stretchy":460},[458,23421,471],{},[458,23423,5160],{},[383,23425,4447],{},[458,23427,4450],{},[383,23429,1116],{},[1644,23431,4630],{},[458,23433,4633],{},[1644,23435,4630],{},[543,23437,23438,23440],{},[383,23439,547],{},[383,23441,385],{},[458,23443,461],{"stretchy":460},[383,23445,554],{},[383,23447,558],{"mathvariant":557},[383,23449,561],{},[458,23451,468],{"stretchy":460},[458,23453,471],{},[543,23455,23456,23458],{},[383,23457,547],{},[380,23459,23460,23462],{},[383,23461,11041],{},[383,23463,22240],{},[458,23465,461],{"stretchy":460},[383,23467,561],{},[383,23469,558],{"mathvariant":557},[383,23471,554],{},[458,23473,468],{"stretchy":460},[383,23475,4722],{"mathvariant":557},[387,23477,23478],{"encoding":389},"f(t)=-\\log t\n\\ \\Longrightarrow\\ D_f(P\\|Q)=D_{KL}(Q\\|P).",[363,23480,23482,23509,23547,23617],{"className":23481,"ariaHidden":394},[393],[363,23483,23485,23488,23491,23494,23497,23500,23503,23506],{"className":23484},[398],[363,23486],{"className":23487,"style":487},[402],[363,23489,385],{"className":23490,"style":409},[407,408],[363,23492,461],{"className":23493},[494],[363,23495,1116],{"className":23496},[407,408],[363,23498,468],{"className":23499},[501],[363,23501],{"className":23502,"style":506},[505],[363,23504,471],{"className":23505},[510],[363,23507],{"className":23508,"style":506},[505],[363,23510,23512,23515,23518,23521,23526,23529,23532,23535,23538,23541,23544],{"className":23511},[398],[363,23513],{"className":23514,"style":403},[402],[363,23516,5160],{"className":23517},[407],[363,23519],{"className":23520,"style":754},[505],[363,23522,4501,23524],{"className":23523},[1831],[363,23525,4505],{"style":4504},[363,23527],{"className":23528,"style":754},[505],[363,23530,1116],{"className":23531},[407,408],[363,23533,4630],{"className":23534},[505],[363,23536],{"className":23537,"style":506},[505],[363,23539,4633],{"className":23540},[510],[363,23542,4630],{"className":23543},[505],[363,23545],{"className":23546,"style":506},[505],[363,23548,23550,23553,23593,23596,23599,23602,23605,23608,23611,23614],{"className":23549},[398],[363,23551],{"className":23552,"style":618},[402],[363,23554,23556,23559],{"className":23555},[407],[363,23557,547],{"className":23558,"style":625},[407,408],[363,23560,23562],{"className":23561},[629],[363,23563,23565,23585],{"className":23564},[633,634],[363,23566,23568,23582],{"className":23567},[638],[363,23569,23571],{"className":23570,"style":643},[642],[363,23572,23573,23576],{"style":646},[363,23574],{"className":23575,"style":651},[650],[363,23577,23579],{"className":23578},[655,656,657,658],[363,23580,385],{"className":23581,"style":409},[407,408,658],[363,23583,666],{"className":23584},[665],[363,23586,23588],{"className":23587},[638],[363,23589,23591],{"className":23590,"style":673},[642],[363,23592],{},[363,23594,461],{"className":23595},[494],[363,23597,554],{"className":23598,"style":682},[407,408],[363,23600,558],{"className":23601},[407],[363,23603,561],{"className":23604},[407,408],[363,23606,468],{"className":23607},[501],[363,23609],{"className":23610,"style":506},[505],[363,23612,471],{"className":23613},[510],[363,23615],{"className":23616,"style":506},[505],[363,23618,23620,23623,23669,23672,23675,23678,23681,23684],{"className":23619},[398],[363,23621],{"className":23622,"style":487},[402],[363,23624,23626,23629],{"className":23625},[407],[363,23627,547],{"className":23628,"style":625},[407,408],[363,23630,23632],{"className":23631},[629],[363,23633,23635,23661],{"className":23634},[633,634],[363,23636,23638,23658],{"className":23637},[638],[363,23639,23641],{"className":23640,"style":727},[642],[363,23642,23643,23646],{"style":646},[363,23644],{"className":23645,"style":651},[650],[363,23647,23649],{"className":23648},[655,656,657,658],[363,23650,23652,23655],{"className":23651},[407,658],[363,23653,11041],{"className":23654,"style":11129},[407,408,658],[363,23656,22240],{"className":23657},[407,408,658],[363,23659,666],{"className":23660},[665],[363,23662,23664],{"className":23663},[638],[363,23665,23667],{"className":23666,"style":8315},[642],[363,23668],{},[363,23670,461],{"className":23671},[494],[363,23673,561],{"className":23674},[407,408],[363,23676,558],{"className":23677},[407],[363,23679,554],{"className":23680,"style":682},[407,408],[363,23682,468],{"className":23683},[501],[363,23685,4722],{"className":23686},[407],[11,23688,23689,23692,23693,23811,23812,23877,23878,23971],{},[1572,23690,23691],{},"对称化：Jeffreys 散度。"," 取 ",[363,23694,23696,23734],{"className":23695,"translate":367},[366],[363,23697,23699],{"className":23698},[371],[373,23700,23701],{"xmlns":375},[377,23702,23703,23731],{},[380,23704,23705,23707,23709,23711,23713,23715,23717,23719,23721,23723,23725,23727,23729],{},[383,23706,385],{},[458,23708,461],{"stretchy":460},[383,23710,1116],{},[458,23712,468],{"stretchy":460},[458,23714,471],{},[458,23716,461],{"stretchy":460},[383,23718,1116],{},[458,23720,5160],{},[463,23722,465],{},[458,23724,468],{"stretchy":460},[383,23726,4447],{},[458,23728,4450],{},[383,23730,1116],{},[387,23732,23733],{"encoding":389},"f(t)=(t-1)\\log t",[363,23735,23737,23764,23785],{"className":23736,"ariaHidden":394},[393],[363,23738,23740,23743,23746,23749,23752,23755,23758,23761],{"className":23739},[398],[363,23741],{"className":23742,"style":487},[402],[363,23744,385],{"className":23745,"style":409},[407,408],[363,23747,461],{"className":23748},[494],[363,23750,1116],{"className":23751},[407,408],[363,23753,468],{"className":23754},[501],[363,23756],{"className":23757,"style":506},[505],[363,23759,471],{"className":23760},[510],[363,23762],{"className":23763,"style":506},[505],[363,23765,23767,23770,23773,23776,23779,23782],{"className":23766},[398],[363,23768],{"className":23769,"style":487},[402],[363,23771,461],{"className":23772},[494],[363,23774,1116],{"className":23775},[407,408],[363,23777],{"className":23778,"style":2934},[505],[363,23780,5160],{"className":23781},[2938],[363,23783],{"className":23784,"style":2934},[505],[363,23786,23788,23791,23794,23797,23800,23805,23808],{"className":23787},[398],[363,23789],{"className":23790,"style":487},[402],[363,23792,465],{"className":23793},[407],[363,23795,468],{"className":23796},[501],[363,23798],{"className":23799,"style":754},[505],[363,23801,4501,23803],{"className":23802},[1831],[363,23804,4505],{"style":4504},[363,23806],{"className":23807,"style":754},[505],[363,23809,1116],{"className":23810},[407,408],"（它满足 ",[363,23813,23815,23838],{"className":23814,"translate":367},[366],[363,23816,23818],{"className":23817},[371],[373,23819,23820],{"xmlns":375},[377,23821,23822,23836],{},[380,23823,23824,23826,23828,23830,23832,23834],{},[383,23825,385],{},[458,23827,461],{"stretchy":460},[463,23829,465],{},[458,23831,468],{"stretchy":460},[458,23833,471],{},[463,23835,474],{},[387,23837,477],{"encoding":389},[363,23839,23841,23868],{"className":23840,"ariaHidden":394},[393],[363,23842,23844,23847,23850,23853,23856,23859,23862,23865],{"className":23843},[398],[363,23845],{"className":23846,"style":487},[402],[363,23848,385],{"className":23849,"style":409},[407,408],[363,23851,461],{"className":23852},[494],[363,23854,465],{"className":23855},[407],[363,23857,468],{"className":23858},[501],[363,23860],{"className":23861,"style":506},[505],[363,23863,471],{"className":23864},[510],[363,23866],{"className":23867,"style":506},[505],[363,23869,23871,23874],{"className":23870},[398],[363,23872],{"className":23873,"style":520},[402],[363,23875,474],{"className":23876},[407],"，且 ",[363,23879,23881,23917],{"className":23880,"translate":367},[366],[363,23882,23884],{"className":23883},[371],[373,23885,23886],{"xmlns":375},[377,23887,23888,23914],{},[380,23889,23890,23892,23894,23896,23898,23900,23902,23904,23906,23908,23910,23912],{},[383,23891,1116],{},[383,23893,385],{},[458,23895,461],{"stretchy":460},[463,23897,465],{},[383,23899,1288],{"mathvariant":557},[383,23901,1116],{},[458,23903,468],{"stretchy":460},[458,23905,471],{},[383,23907,385],{},[458,23909,461],{"stretchy":460},[383,23911,1116],{},[458,23913,468],{"stretchy":460},[387,23915,23916],{"encoding":389},"t f(1\u002Ft)=f(t)",[363,23918,23920,23953],{"className":23919,"ariaHidden":394},[393],[363,23921,23923,23926,23929,23932,23935,23938,23941,23944,23947,23950],{"className":23922},[398],[363,23924],{"className":23925,"style":487},[402],[363,23927,1116],{"className":23928},[407,408],[363,23930,385],{"className":23931,"style":409},[407,408],[363,23933,461],{"className":23934},[494],[363,23936,8936],{"className":23937},[407],[363,23939,1116],{"className":23940},[407,408],[363,23942,468],{"className":23943},[501],[363,23945],{"className":23946,"style":506},[505],[363,23948,471],{"className":23949},[510],[363,23951],{"className":23952,"style":506},[505],[363,23954,23956,23959,23962,23965,23968],{"className":23955},[398],[363,23957],{"className":23958,"style":487},[402],[363,23960,385],{"className":23961,"style":409},[407,408],[363,23963,461],{"className":23964},[494],[363,23966,1116],{"className":23967},[407,408],[363,23969,468],{"className":23970},[501],"），则",[363,23973,23975],{"className":23974,"translate":367},[528],[363,23976,23978,24106],{"className":23977,"translate":367},[366],[363,23979,23981],{"className":23980},[371],[373,23982,23983],{"xmlns":375,"display":537},[377,23984,23985,24103],{},[380,23986,23987,23993,23995,23997,23999,24001,24003,24005,24007,24009,24011,24013,24015,24017,24019,24021,24027,24029,24031,24033,24036,24038,24048,24050,24052,24054,24056,24058,24060,24070,24072,24074,24076,24078,24080,24082,24084,24091,24093,24095,24097,24099,24101],{},[543,23988,23989,23991],{},[383,23990,547],{},[383,23992,385],{},[458,23994,461],{"stretchy":460},[383,23996,554],{},[383,23998,558],{"mathvariant":557},[383,24000,561],{},[458,24002,468],{"stretchy":460},[458,24004,471],{},[458,24006,1634],{},[458,24008,461],{"stretchy":460},[383,24010,11],{},[458,24012,5160],{},[383,24014,1291],{},[458,24016,468],{"stretchy":460},[383,24018,4447],{},[458,24020,4450],{},[586,24022,24023,24025],{},[383,24024,11],{},[383,24026,1291],{},[1644,24028,1646],{},[383,24030,592],{},[383,24032,1121],{},[505,24034],{"linebreak":24035},"newline",[458,24037,471],{},[543,24039,24040,24042],{},[383,24041,547],{},[380,24043,24044,24046],{},[383,24045,11041],{},[383,24047,22240],{},[458,24049,461],{"stretchy":460},[383,24051,554],{},[383,24053,558],{"mathvariant":557},[383,24055,561],{},[458,24057,468],{"stretchy":460},[458,24059,2817],{},[543,24061,24062,24064],{},[383,24063,547],{},[380,24065,24066,24068],{},[383,24067,11041],{},[383,24069,22240],{},[458,24071,461],{"stretchy":460},[383,24073,561],{},[383,24075,558],{"mathvariant":557},[383,24077,554],{},[458,24079,468],{"stretchy":460},[458,24081,471],{},[458,24083,1362],{},[543,24085,24086,24088],{},[383,24087,547],{},[383,24089,24090],{},"J",[458,24092,461],{"stretchy":460},[383,24094,554],{},[458,24096,898],{"separator":394},[383,24098,561],{},[458,24100,468],{"stretchy":460},[458,24102,898],{"separator":394},[387,24104,24105],{"encoding":389},"D_f(P\\|Q)=\\int (p-q)\\log\\frac{p}{q}\\,dx \\\\\n=D_{KL}(P\\|Q)+D_{KL}(Q\\|P)=:D_J(P,Q),",[363,24107,24109,24179,24203,24297,24300,24312,24388,24465],{"className":24108,"ariaHidden":394},[393],[363,24110,24112,24115,24155,24158,24161,24164,24167,24170,24173,24176],{"className":24111},[398],[363,24113],{"className":24114,"style":618},[402],[363,24116,24118,24121],{"className":24117},[407],[363,24119,547],{"className":24120,"style":625},[407,408],[363,24122,24124],{"className":24123},[629],[363,24125,24127,24147],{"className":24126},[633,634],[363,24128,24130,24144],{"className":24129},[638],[363,24131,24133],{"className":24132,"style":643},[642],[363,24134,24135,24138],{"style":646},[363,24136],{"className":24137,"style":651},[650],[363,24139,24141],{"className":24140},[655,656,657,658],[363,24142,385],{"className":24143,"style":409},[407,408,658],[363,24145,666],{"className":24146},[665],[363,24148,24150],{"className":24149},[638],[363,24151,24153],{"className":24152,"style":673},[642],[363,24154],{},[363,24156,461],{"className":24157},[494],[363,24159,554],{"className":24160,"style":682},[407,408],[363,24162,558],{"className":24163},[407],[363,24165,561],{"className":24166},[407,408],[363,24168,468],{"className":24169},[501],[363,24171],{"className":24172,"style":506},[505],[363,24174,471],{"className":24175},[510],[363,24177],{"className":24178,"style":506},[505],[363,24180,24182,24185,24188,24191,24194,24197,24200],{"className":24181},[398],[363,24183],{"className":24184,"style":6124},[402],[363,24186,1634],{"className":24187,"style":1834},[1831,1832,1833],[363,24189,461],{"className":24190},[494],[363,24192,11],{"className":24193},[407,408],[363,24195],{"className":24196,"style":2934},[505],[363,24198,5160],{"className":24199},[2938],[363,24201],{"className":24202,"style":2934},[505],[363,24204,24206,24209,24212,24215,24218,24223,24226,24288,24291,24294],{"className":24205},[398],[363,24207],{"className":24208,"style":22357},[402],[363,24210,1291],{"className":24211,"style":1328},[407,408],[363,24213,468],{"className":24214},[501],[363,24216],{"className":24217,"style":754},[505],[363,24219,4501,24221],{"className":24220},[1831],[363,24222,4505],{"style":4504},[363,24224],{"className":24225,"style":754},[505],[363,24227,24229,24232,24285],{"className":24228},[407],[363,24230],{"className":24231},[494,789],[363,24233,24235],{"className":24234},[586],[363,24236,24238,24277],{"className":24237},[633,634],[363,24239,24241,24274],{"className":24240},[638],[363,24242,24244,24255,24263],{"className":24243,"style":3901},[642],[363,24245,24246,24249],{"style":805},[363,24247],{"className":24248,"style":809},[650],[363,24250,24252],{"className":24251},[407],[363,24253,1291],{"className":24254,"style":1328},[407,408],[363,24256,24257,24260],{"style":821},[363,24258],{"className":24259,"style":809},[650],[363,24261],{"className":24262,"style":829},[828],[363,24264,24265,24268],{"style":832},[363,24266],{"className":24267,"style":809},[650],[363,24269,24271],{"className":24270},[407],[363,24272,11],{"className":24273},[407,408],[363,24275,666],{"className":24276},[665],[363,24278,24280],{"className":24279},[638],[363,24281,24283],{"className":24282,"style":854},[642],[363,24284],{},[363,24286],{"className":24287},[501,789],[363,24289],{"className":24290,"style":754},[505],[363,24292,592],{"className":24293},[407,408],[363,24295,1121],{"className":24296},[407,408],[363,24298],{"className":24299},[505,24035],[363,24301,24303,24306,24309],{"className":24302},[398],[363,24304],{"className":24305,"style":11350},[402],[363,24307,471],{"className":24308},[510],[363,24310],{"className":24311,"style":506},[505],[363,24313,24315,24318,24364,24367,24370,24373,24376,24379,24382,24385],{"className":24314},[398],[363,24316],{"className":24317,"style":487},[402],[363,24319,24321,24324],{"className":24320},[407],[363,24322,547],{"className":24323,"style":625},[407,408],[363,24325,24327],{"className":24326},[629],[363,24328,24330,24356],{"className":24329},[633,634],[363,24331,24333,24353],{"className":24332},[638],[363,24334,24336],{"className":24335,"style":727},[642],[363,24337,24338,24341],{"style":646},[363,24339],{"className":24340,"style":651},[650],[363,24342,24344],{"className":24343},[655,656,657,658],[363,24345,24347,24350],{"className":24346},[407,658],[363,24348,11041],{"className":24349,"style":11129},[407,408,658],[363,24351,22240],{"className":24352},[407,408,658],[363,24354,666],{"className":24355},[665],[363,24357,24359],{"className":24358},[638],[363,24360,24362],{"className":24361,"style":8315},[642],[363,24363],{},[363,24365,461],{"className":24366},[494],[363,24368,554],{"className":24369,"style":682},[407,408],[363,24371,558],{"className":24372},[407],[363,24374,561],{"className":24375},[407,408],[363,24377,468],{"className":24378},[501],[363,24380],{"className":24381,"style":2934},[505],[363,24383,2817],{"className":24384},[2938],[363,24386],{"className":24387,"style":2934},[505],[363,24389,24391,24394,24440,24443,24446,24449,24452,24455,24458,24462],{"className":24390},[398],[363,24392],{"className":24393,"style":487},[402],[363,24395,24397,24400],{"className":24396},[407],[363,24398,547],{"className":24399,"style":625},[407,408],[363,24401,24403],{"className":24402},[629],[363,24404,24406,24432],{"className":24405},[633,634],[363,24407,24409,24429],{"className":24408},[638],[363,24410,24412],{"className":24411,"style":727},[642],[363,24413,24414,24417],{"style":646},[363,24415],{"className":24416,"style":651},[650],[363,24418,24420],{"className":24419},[655,656,657,658],[363,24421,24423,24426],{"className":24422},[407,658],[363,24424,11041],{"className":24425,"style":11129},[407,408,658],[363,24427,22240],{"className":24428},[407,408,658],[363,24430,666],{"className":24431},[665],[363,24433,24435],{"className":24434},[638],[363,24436,24438],{"className":24437,"style":8315},[642],[363,24439],{},[363,24441,461],{"className":24442},[494],[363,24444,561],{"className":24445},[407,408],[363,24447,558],{"className":24448},[407],[363,24450,554],{"className":24451,"style":682},[407,408],[363,24453,468],{"className":24454},[501],[363,24456],{"className":24457,"style":506},[505],[363,24459,24461],{"className":24460},[510],"=:",[363,24463],{"className":24464,"style":506},[505],[363,24466,24468,24471,24512,24515,24518,24521,24524,24527,24530],{"className":24467},[398],[363,24469],{"className":24470,"style":487},[402],[363,24472,24474,24477],{"className":24473},[407],[363,24475,547],{"className":24476,"style":625},[407,408],[363,24478,24480],{"className":24479},[629],[363,24481,24483,24504],{"className":24482},[633,634],[363,24484,24486,24501],{"className":24485},[638],[363,24487,24489],{"className":24488,"style":727},[642],[363,24490,24491,24494],{"style":646},[363,24492],{"className":24493,"style":651},[650],[363,24495,24497],{"className":24496},[655,656,657,658],[363,24498,24090],{"className":24499,"style":24500},[407,408,658],"margin-right:0.0962em;",[363,24502,666],{"className":24503},[665],[363,24505,24507],{"className":24506},[638],[363,24508,24510],{"className":24509,"style":8315},[642],[363,24511],{},[363,24513,461],{"className":24514},[494],[363,24516,554],{"className":24517,"style":682},[407,408],[363,24519,898],{"className":24520},[920],[363,24522],{"className":24523,"style":754},[505],[363,24525,561],{"className":24526},[407,408],[363,24528,468],{"className":24529},[501],[363,24531,898],{"className":24532},[920],[11,24534,24535],{},"这是 KL 的两向之和，也是一个人为构造的对称 f-散度。",[11,24537,24538,24541,24542,24545,24546,24574,24575,24603,24604,24632,24633,24665,24666,24771,24772,24800,24801,24829,24830,24833],{},[1572,24539,24540],{},"意义。"," KL 是最基础的散度，等价于信息论中的",[1572,24543,24544],{},"相对熵","：若真实分布是 ",[363,24547,24549,24562],{"className":24548,"translate":367},[366],[363,24550,24552],{"className":24551},[371],[373,24553,24554],{"xmlns":375},[377,24555,24556,24560],{},[380,24557,24558],{},[383,24559,554],{},[387,24561,554],{"encoding":389},[363,24563,24565],{"className":24564,"ariaHidden":394},[393],[363,24566,24568,24571],{"className":24567},[398],[363,24569],{"className":24570,"style":1011},[402],[363,24572,554],{"className":24573,"style":682},[407,408],"、而用 ",[363,24576,24578,24591],{"className":24577,"translate":367},[366],[363,24579,24581],{"className":24580},[371],[373,24582,24583],{"xmlns":375},[377,24584,24585,24589],{},[380,24586,24587],{},[383,24588,561],{},[387,24590,561],{"encoding":389},[363,24592,24594],{"className":24593,"ariaHidden":394},[393],[363,24595,24597,24600],{"className":24596},[398],[363,24598],{"className":24599,"style":913},[402],[363,24601,561],{"className":24602},[407,408]," 去编码来自 ",[363,24605,24607,24620],{"className":24606,"translate":367},[366],[363,24608,24610],{"className":24609},[371],[373,24611,24612],{"xmlns":375},[377,24613,24614,24618],{},[380,24615,24616],{},[383,24617,554],{},[387,24619,554],{"encoding":389},[363,24621,24623],{"className":24622,"ariaHidden":394},[393],[363,24624,24626,24629],{"className":24625},[398],[363,24627],{"className":24628,"style":1011},[402],[363,24630,554],{"className":24631,"style":682},[407,408]," 的样本，那么 ",[363,24634,24636,24651],{"className":24635,"translate":367},[366],[363,24637,24639],{"className":24638},[371],[373,24640,24641],{"xmlns":375},[377,24642,24643,24649],{},[380,24644,24645,24647],{},[383,24646,4447],{},[458,24648,4450],{},[387,24650,21930],{"encoding":389},[363,24652,24654],{"className":24653,"ariaHidden":394},[393],[363,24655,24657,24660],{"className":24656},[398],[363,24658],{"className":24659,"style":403},[402],[363,24661,4501,24663],{"className":24662},[1831],[363,24664,4505],{"style":4504}," 以 2 为底时 ",[363,24667,24669,24701],{"className":24668,"translate":367},[366],[363,24670,24672],{"className":24671},[371],[373,24673,24674],{"xmlns":375},[377,24675,24676,24698],{},[380,24677,24678,24688,24690,24692,24694,24696],{},[543,24679,24680,24682],{},[383,24681,547],{},[380,24683,24684,24686],{},[383,24685,11041],{},[383,24687,22240],{},[458,24689,461],{"stretchy":460},[383,24691,554],{},[383,24693,558],{"mathvariant":557},[383,24695,561],{},[458,24697,468],{"stretchy":460},[387,24699,24700],{"encoding":389},"D_{KL}(P\\|Q)",[363,24702,24704],{"className":24703,"ariaHidden":394},[393],[363,24705,24707,24710,24756,24759,24762,24765,24768],{"className":24706},[398],[363,24708],{"className":24709,"style":487},[402],[363,24711,24713,24716],{"className":24712},[407],[363,24714,547],{"className":24715,"style":625},[407,408],[363,24717,24719],{"className":24718},[629],[363,24720,24722,24748],{"className":24721},[633,634],[363,24723,24725,24745],{"className":24724},[638],[363,24726,24728],{"className":24727,"style":727},[642],[363,24729,24730,24733],{"style":646},[363,24731],{"className":24732,"style":651},[650],[363,24734,24736],{"className":24735},[655,656,657,658],[363,24737,24739,24742],{"className":24738},[407,658],[363,24740,11041],{"className":24741,"style":11129},[407,408,658],[363,24743,22240],{"className":24744},[407,408,658],[363,24746,666],{"className":24747},[665],[363,24749,24751],{"className":24750},[638],[363,24752,24754],{"className":24753,"style":8315},[642],[363,24755],{},[363,24757,461],{"className":24758},[494],[363,24760,554],{"className":24761,"style":682},[407,408],[363,24763,558],{"className":24764},[407],[363,24766,561],{"className":24767},[407,408],[363,24769,468],{"className":24770},[501]," 正是用 ",[363,24773,24775,24788],{"className":24774,"translate":367},[366],[363,24776,24778],{"className":24777},[371],[373,24779,24780],{"xmlns":375},[377,24781,24782,24786],{},[380,24783,24784],{},[383,24785,561],{},[387,24787,561],{"encoding":389},[363,24789,24791],{"className":24790,"ariaHidden":394},[393],[363,24792,24794,24797],{"className":24793},[398],[363,24795],{"className":24796,"style":913},[402],[363,24798,561],{"className":24799},[407,408]," 编码比用 ",[363,24802,24804,24817],{"className":24803,"translate":367},[366],[363,24805,24807],{"className":24806},[371],[373,24808,24809],{"xmlns":375},[377,24810,24811,24815],{},[380,24812,24813],{},[383,24814,554],{},[387,24816,554],{"encoding":389},[363,24818,24820],{"className":24819,"ariaHidden":394},[393],[363,24821,24823,24826],{"className":24822},[398],[363,24824],{"className":24825,"style":1011},[402],[363,24827,554],{"className":24828,"style":682},[407,408]," 编码",[1572,24831,24832],{},"多付出的比特数","，即",[363,24835,24837],{"className":24836,"translate":367},[528],[363,24838,24840,24982],{"className":24839,"translate":367},[366],[363,24841,24843],{"className":24842},[371],[373,24844,24845],{"xmlns":375,"display":537},[377,24846,24847,24979],{},[1590,24848,24849,24922],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,24850,24851,24877],{},[1599,24852,24853],{},[1602,24854,24855],{"scriptlevel":474,"displaystyle":394},[380,24856,24857,24867,24869,24871,24873,24875],{},[543,24858,24859,24861],{},[383,24860,547],{},[380,24862,24863,24865],{},[383,24864,11041],{},[383,24866,22240],{},[458,24868,461],{"stretchy":460},[383,24870,554],{},[383,24872,558],{"mathvariant":557},[383,24874,561],{},[458,24876,468],{"stretchy":460},[1599,24878,24879],{},[1602,24880,24881],{"scriptlevel":474,"displaystyle":394},[380,24882,24883,24885,24887],{},[380,24884],{},[458,24886,471],{},[6363,24888,24889,24919],{},[6363,24890,24891,24917],{},[380,24892,24893,24899,24901,24903,24905,24907,24909,24911,24913,24915],{},[543,24894,24895,24897],{},[383,24896,571],{"mathvariant":570},[383,24898,554],{},[458,24900,578],{"stretchy":460},[458,24902,5160],{},[383,24904,4447],{},[458,24906,4450],{},[383,24908,1291],{},[458,24910,461],{"stretchy":460},[383,24912,945],{},[458,24914,468],{"stretchy":460},[458,24916,605],{"stretchy":460},[458,24918,6387],{"stretchy":394},[1644,24920,24921],{},"交叉熵",[1596,24923,24924,24930],{},[1599,24925,24926],{},[1602,24927,24928],{"scriptlevel":474,"displaystyle":394},[380,24929],{},[1599,24931,24932],{},[1602,24933,24934],{"scriptlevel":474,"displaystyle":394},[380,24935,24936,24938,24940,24942,24977],{},[380,24937],{},[505,24939],{"width":3609},[458,24941,5160],{},[6363,24943,24944,24974],{},[6363,24945,24946,24972],{},[380,24947,24948,24954,24956,24958,24960,24962,24964,24966,24968,24970],{},[543,24949,24950,24952],{},[383,24951,571],{"mathvariant":570},[383,24953,554],{},[458,24955,578],{"stretchy":460},[458,24957,5160],{},[383,24959,4447],{},[458,24961,4450],{},[383,24963,11],{},[458,24965,461],{"stretchy":460},[383,24967,945],{},[458,24969,468],{"stretchy":460},[458,24971,605],{"stretchy":460},[458,24973,6387],{"stretchy":394},[1644,24975,24976],{},"熵",[383,24978,4722],{"mathvariant":557},[387,24980,24981],{"encoding":389},"\\begin{aligned}\nD_{KL}(P\\|Q)\n&=\\underbrace{\\mathbb E_P[-\\log q(X)]}\n_{\\text{交叉熵}}\\\\[2pt]\n&\\qquad-\\underbrace{\\mathbb E_P[-\\log p(X)]}\n_{\\text{熵}} .\n\\end{aligned}",[363,24983,24985],{"className":24984,"ariaHidden":394},[393],[363,24986,24988,24992],{"className":24987},[398],[363,24989],{"className":24990,"style":24991},[402],"height:5.1327em;vertical-align:-2.3163em;",[363,24993,24995],{"className":24994},[407],[363,24996,24998,25102],{"className":24997},[1590],[363,24999,25001],{"className":25000},[1707],[363,25002,25004,25093],{"className":25003},[633,634],[363,25005,25007,25090],{"className":25006},[638],[363,25008,25011,25081],{"className":25009,"style":25010},[642],"height:2.8163em;",[363,25012,25014,25017],{"style":25013},"top:-4.9763em;",[363,25015],{"className":25016,"style":809},[650],[363,25018,25020,25066,25069,25072,25075,25078],{"className":25019},[407],[363,25021,25023,25026],{"className":25022},[407],[363,25024,547],{"className":25025,"style":625},[407,408],[363,25027,25029],{"className":25028},[629],[363,25030,25032,25058],{"className":25031},[633,634],[363,25033,25035,25055],{"className":25034},[638],[363,25036,25038],{"className":25037,"style":727},[642],[363,25039,25040,25043],{"style":646},[363,25041],{"className":25042,"style":651},[650],[363,25044,25046],{"className":25045},[655,656,657,658],[363,25047,25049,25052],{"className":25048},[407,658],[363,25050,11041],{"className":25051,"style":11129},[407,408,658],[363,25053,22240],{"className":25054},[407,408,658],[363,25056,666],{"className":25057},[665],[363,25059,25061],{"className":25060},[638],[363,25062,25064],{"className":25063,"style":8315},[642],[363,25065],{},[363,25067,461],{"className":25068},[494],[363,25070,554],{"className":25071,"style":682},[407,408],[363,25073,558],{"className":25074},[407],[363,25076,561],{"className":25077},[407,408],[363,25079,468],{"className":25080},[501],[363,25082,25084,25087],{"style":25083},"top:-2.26em;",[363,25085],{"className":25086,"style":809},[650],[363,25088],{"className":25089},[407],[363,25091,666],{"className":25092},[665],[363,25094,25096],{"className":25095},[638],[363,25097,25100],{"className":25098,"style":25099},[642],"height:2.3163em;",[363,25101],{},[363,25103,25105],{"className":25104},[1798],[363,25106,25108,25521],{"className":25107},[633,634],[363,25109,25111,25518],{"className":25110},[638],[363,25112,25114,25314],{"className":25113,"style":25010},[642],[363,25115,25116,25119],{"style":25013},[363,25117],{"className":25118,"style":809},[650],[363,25120,25122,25125,25128,25131,25134],{"className":25121},[407],[363,25123],{"className":25124},[407],[363,25126],{"className":25127,"style":506},[505],[363,25129,471],{"className":25130},[510],[363,25132],{"className":25133,"style":506},[505],[363,25135,25137],{"className":25136},[758,6363],[363,25138,25140,25305],{"className":25139},[633,634],[363,25141,25143,25302],{"className":25142},[638],[363,25144,25147,25165],{"className":25145,"style":25146},[642],"height:0.75em;",[363,25148,25150,25153],{"style":25149},"top:-1.4237em;",[363,25151],{"className":25152,"style":809},[650],[363,25154,25156],{"className":25155},[655,656,657,658],[363,25157,25159],{"className":25158},[407,658],[363,25160,25162],{"className":25161},[407,4945,658],[363,25163,24921],{"className":25164},[407,4949,658],[363,25166,25167,25170],{"style":12210},[363,25168],{"className":25169,"style":809},[650],[363,25171,25173],{"className":25172},[758,6363],[363,25174,25176,25293],{"className":25175},[633,634],[363,25177,25179,25290],{"className":25178},[638],[363,25180,25182,25213],{"className":25181,"style":25146},[642],[363,25183,25186,25189],{"className":25184,"style":25185},[6654],"top:-2.102em;",[363,25187],{"className":25188,"style":809},[650],[363,25190,25192,25199,25206],{"className":25191,"style":6663},[6662],[363,25193,25195],{"className":25194,"style":6668},[6667],[6670,25196,25197],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6676},[6678,25198],{"d":6680},[363,25200,25202],{"className":25201,"style":6668},[6684],[6670,25203,25204],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6687},[6678,25205],{"d":6690},[363,25207,25209],{"className":25208,"style":6668},[6694],[6670,25210,25211],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6697},[6678,25212],{"d":6700},[363,25214,25215,25218],{"style":12210},[363,25216],{"className":25217,"style":809},[650],[363,25219,25221,25261,25264,25267,25270,25275,25278,25281,25284,25287],{"className":25220},[407],[363,25222,25224,25227],{"className":25223},[407],[363,25225,571],{"className":25226},[407,714],[363,25228,25230],{"className":25229},[629],[363,25231,25233,25253],{"className":25232},[633,634],[363,25234,25236,25250],{"className":25235},[638],[363,25237,25239],{"className":25238,"style":727},[642],[363,25240,25241,25244],{"style":730},[363,25242],{"className":25243,"style":651},[650],[363,25245,25247],{"className":25246},[655,656,657,658],[363,25248,554],{"className":25249,"style":682},[407,408,658],[363,25251,666],{"className":25252},[665],[363,25254,25256],{"className":25255},[638],[363,25257,25259],{"className":25258,"style":8315},[642],[363,25260],{},[363,25262,578],{"className":25263},[494],[363,25265,5160],{"className":25266},[407],[363,25268],{"className":25269,"style":754},[505],[363,25271,4501,25273],{"className":25272},[1831],[363,25274,4505],{"style":4504},[363,25276],{"className":25277,"style":754},[505],[363,25279,1291],{"className":25280,"style":1328},[407,408],[363,25282,461],{"className":25283},[494],[363,25285,945],{"className":25286,"style":9234},[407,408],[363,25288,20737],{"className":25289},[501],[363,25291,666],{"className":25292},[665],[363,25294,25296],{"className":25295},[638],[363,25297,25300],{"className":25298,"style":25299},[642],"height:0.898em;",[363,25301],{},[363,25303,666],{"className":25304},[665],[363,25306,25308],{"className":25307},[638],[363,25309,25312],{"className":25310,"style":25311},[642],"height:1.5763em;",[363,25313],{},[363,25315,25316,25319],{"style":25083},[363,25317],{"className":25318,"style":809},[650],[363,25320,25322,25325,25328,25331,25334,25337,25512,25515],{"className":25321},[407],[363,25323],{"className":25324},[407],[363,25326],{"className":25327,"style":3981},[505],[363,25329],{"className":25330,"style":2934},[505],[363,25332,5160],{"className":25333},[2938],[363,25335],{"className":25336,"style":2934},[505],[363,25338,25340],{"className":25339},[758,6363],[363,25341,25343,25504],{"className":25342},[633,634],[363,25344,25346,25501],{"className":25345},[638],[363,25347,25349,25366],{"className":25348,"style":25146},[642],[363,25350,25351,25354],{"style":25149},[363,25352],{"className":25353,"style":809},[650],[363,25355,25357],{"className":25356},[655,656,657,658],[363,25358,25360],{"className":25359},[407,658],[363,25361,25363],{"className":25362},[407,4945,658],[363,25364,24976],{"className":25365},[407,4949,658],[363,25367,25368,25371],{"style":12210},[363,25369],{"className":25370,"style":809},[650],[363,25372,25374],{"className":25373},[758,6363],[363,25375,25377,25493],{"className":25376},[633,634],[363,25378,25380,25490],{"className":25379},[638],[363,25381,25383,25413],{"className":25382,"style":25146},[642],[363,25384,25386,25389],{"className":25385,"style":25185},[6654],[363,25387],{"className":25388,"style":809},[650],[363,25390,25392,25399,25406],{"className":25391,"style":6663},[6662],[363,25393,25395],{"className":25394,"style":6668},[6667],[6670,25396,25397],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6676},[6678,25398],{"d":6680},[363,25400,25402],{"className":25401,"style":6668},[6684],[6670,25403,25404],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6687},[6678,25405],{"d":6690},[363,25407,25409],{"className":25408,"style":6668},[6694],[6670,25410,25411],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6697},[6678,25412],{"d":6700},[363,25414,25415,25418],{"style":12210},[363,25416],{"className":25417,"style":809},[650],[363,25419,25421,25461,25464,25467,25470,25475,25478,25481,25484,25487],{"className":25420},[407],[363,25422,25424,25427],{"className":25423},[407],[363,25425,571],{"className":25426},[407,714],[363,25428,25430],{"className":25429},[629],[363,25431,25433,25453],{"className":25432},[633,634],[363,25434,25436,25450],{"className":25435},[638],[363,25437,25439],{"className":25438,"style":727},[642],[363,25440,25441,25444],{"style":730},[363,25442],{"className":25443,"style":651},[650],[363,25445,25447],{"className":25446},[655,656,657,658],[363,25448,554],{"className":25449,"style":682},[407,408,658],[363,25451,666],{"className":25452},[665],[363,25454,25456],{"className":25455},[638],[363,25457,25459],{"className":25458,"style":8315},[642],[363,25460],{},[363,25462,578],{"className":25463},[494],[363,25465,5160],{"className":25466},[407],[363,25468],{"className":25469,"style":754},[505],[363,25471,4501,25473],{"className":25472},[1831],[363,25474,4505],{"style":4504},[363,25476],{"className":25477,"style":754},[505],[363,25479,11],{"className":25480},[407,408],[363,25482,461],{"className":25483},[494],[363,25485,945],{"className":25486,"style":9234},[407,408],[363,25488,20737],{"className":25489},[501],[363,25491,666],{"className":25492},[665],[363,25494,25496],{"className":25495},[638],[363,25497,25499],{"className":25498,"style":25299},[642],[363,25500],{},[363,25502,666],{"className":25503},[665],[363,25505,25507],{"className":25506},[638],[363,25508,25510],{"className":25509,"style":25311},[642],[363,25511],{},[363,25513],{"className":25514,"style":754},[505],[363,25516,4722],{"className":25517},[407],[363,25519,666],{"className":25520},[665],[363,25522,25524],{"className":25523},[638],[363,25525,25527],{"className":25526,"style":25099},[642],[363,25528],{},[11,25530,25531,25532,25636,25637,4200,25665,25693,25694,25697,25698,25726,25727,25831,25832,4200,25860,25888,25889,25892],{},"在统计中它是最大似然估计的对数似然比的期望，决定了 Stein 引理里第二类错误的最优指数，也是 AIC\u002FBIC 这类模型选择的基石；在机器学习中它是最大似然训练、变分推断与知识蒸馏的目标。它的不对称性带来两种相反的行为：",[363,25533,25535,25566],{"className":25534,"translate":367},[366],[363,25536,25538],{"className":25537},[371],[373,25539,25540],{"xmlns":375},[377,25541,25542,25564],{},[380,25543,25544,25554,25556,25558,25560,25562],{},[543,25545,25546,25548],{},[383,25547,547],{},[380,25549,25550,25552],{},[383,25551,11041],{},[383,25553,22240],{},[458,25555,461],{"stretchy":460},[383,25557,554],{},[383,25559,558],{"mathvariant":557},[383,25561,561],{},[458,25563,468],{"stretchy":460},[387,25565,24700],{"encoding":389},[363,25567,25569],{"className":25568,"ariaHidden":394},[393],[363,25570,25572,25575,25621,25624,25627,25630,25633],{"className":25571},[398],[363,25573],{"className":25574,"style":487},[402],[363,25576,25578,25581],{"className":25577},[407],[363,25579,547],{"className":25580,"style":625},[407,408],[363,25582,25584],{"className":25583},[629],[363,25585,25587,25613],{"className":25586},[633,634],[363,25588,25590,25610],{"className":25589},[638],[363,25591,25593],{"className":25592,"style":727},[642],[363,25594,25595,25598],{"style":646},[363,25596],{"className":25597,"style":651},[650],[363,25599,25601],{"className":25600},[655,656,657,658],[363,25602,25604,25607],{"className":25603},[407,658],[363,25605,11041],{"className":25606,"style":11129},[407,408,658],[363,25608,22240],{"className":25609},[407,408,658],[363,25611,666],{"className":25612},[665],[363,25614,25616],{"className":25615},[638],[363,25617,25619],{"className":25618,"style":8315},[642],[363,25620],{},[363,25622,461],{"className":25623},[494],[363,25625,554],{"className":25626,"style":682},[407,408],[363,25628,558],{"className":25629},[407],[363,25631,561],{"className":25632},[407,408],[363,25634,468],{"className":25635},[501]," 要求 ",[363,25638,25640,25653],{"className":25639,"translate":367},[366],[363,25641,25643],{"className":25642},[371],[373,25644,25645],{"xmlns":375},[377,25646,25647,25651],{},[380,25648,25649],{},[383,25650,561],{},[387,25652,561],{"encoding":389},[363,25654,25656],{"className":25655,"ariaHidden":394},[393],[363,25657,25659,25662],{"className":25658},[398],[363,25660],{"className":25661,"style":913},[402],[363,25663,561],{"className":25664},[407,408],[363,25666,25668,25681],{"className":25667,"translate":367},[366],[363,25669,25671],{"className":25670},[371],[373,25672,25673],{"xmlns":375},[377,25674,25675,25679],{},[380,25676,25677],{},[383,25678,554],{},[387,25680,554],{"encoding":389},[363,25682,25684],{"className":25683,"ariaHidden":394},[393],[363,25685,25687,25690],{"className":25686},[398],[363,25688],{"className":25689,"style":1011},[402],[363,25691,554],{"className":25692,"style":682},[407,408]," 有质量处不为零（",[1572,25695,25696],{},"零回避","，mass-covering，倾向覆盖 ",[363,25699,25701,25714],{"className":25700,"translate":367},[366],[363,25702,25704],{"className":25703},[371],[373,25705,25706],{"xmlns":375},[377,25707,25708,25712],{},[380,25709,25710],{},[383,25711,554],{},[387,25713,554],{"encoding":389},[363,25715,25717],{"className":25716,"ariaHidden":394},[393],[363,25718,25720,25723],{"className":25719},[398],[363,25721],{"className":25722,"style":1011},[402],[363,25724,554],{"className":25725,"style":682},[407,408]," 的每一个模式），而 ",[363,25728,25730,25761],{"className":25729,"translate":367},[366],[363,25731,25733],{"className":25732},[371],[373,25734,25735],{"xmlns":375},[377,25736,25737,25759],{},[380,25738,25739,25749,25751,25753,25755,25757],{},[543,25740,25741,25743],{},[383,25742,547],{},[380,25744,25745,25747],{},[383,25746,11041],{},[383,25748,22240],{},[458,25750,461],{"stretchy":460},[383,25752,561],{},[383,25754,558],{"mathvariant":557},[383,25756,554],{},[458,25758,468],{"stretchy":460},[387,25760,22722],{"encoding":389},[363,25762,25764],{"className":25763,"ariaHidden":394},[393],[363,25765,25767,25770,25816,25819,25822,25825,25828],{"className":25766},[398],[363,25768],{"className":25769,"style":487},[402],[363,25771,25773,25776],{"className":25772},[407],[363,25774,547],{"className":25775,"style":625},[407,408],[363,25777,25779],{"className":25778},[629],[363,25780,25782,25808],{"className":25781},[633,634],[363,25783,25785,25805],{"className":25784},[638],[363,25786,25788],{"className":25787,"style":727},[642],[363,25789,25790,25793],{"style":646},[363,25791],{"className":25792,"style":651},[650],[363,25794,25796],{"className":25795},[655,656,657,658],[363,25797,25799,25802],{"className":25798},[407,658],[363,25800,11041],{"className":25801,"style":11129},[407,408,658],[363,25803,22240],{"className":25804},[407,408,658],[363,25806,666],{"className":25807},[665],[363,25809,25811],{"className":25810},[638],[363,25812,25814],{"className":25813,"style":8315},[642],[363,25815],{},[363,25817,461],{"className":25818},[494],[363,25820,561],{"className":25821},[407,408],[363,25823,558],{"className":25824},[407],[363,25826,554],{"className":25827,"style":682},[407,408],[363,25829,468],{"className":25830},[501]," 会把 ",[363,25833,25835,25848],{"className":25834,"translate":367},[366],[363,25836,25838],{"className":25837},[371],[373,25839,25840],{"xmlns":375},[377,25841,25842,25846],{},[380,25843,25844],{},[383,25845,561],{},[387,25847,561],{"encoding":389},[363,25849,25851],{"className":25850,"ariaHidden":394},[393],[363,25852,25854,25857],{"className":25853},[398],[363,25855],{"className":25856,"style":913},[402],[363,25858,561],{"className":25859},[407,408],[363,25861,25863,25876],{"className":25862,"translate":367},[366],[363,25864,25866],{"className":25865},[371],[373,25867,25868],{"xmlns":375},[377,25869,25870,25874],{},[380,25871,25872],{},[383,25873,554],{},[387,25875,554],{"encoding":389},[363,25877,25879],{"className":25878,"ariaHidden":394},[393],[363,25880,25882,25885],{"className":25881},[398],[363,25883],{"className":25884,"style":1011},[402],[363,25886,554],{"className":25887,"style":682},[407,408]," 为零处压到零（",[1572,25890,25891],{},"零强制","，mode-seeking，倾向锁定单一模式）。GAN 的模式崩塌与变分推断的均值场近似，本质都由这一不对称性决定。",[2658,25894,25896],{"id":25895},"_32-js-散度","3.2 JS 散度",[11,25898,25899,25900,9747],{},"先回顾 JS 散度的定义，令 ",[363,25901,25903,25936],{"className":25902,"translate":367},[366],[363,25904,25906],{"className":25905},[371],[373,25907,25908],{"xmlns":375},[377,25909,25910,25933],{},[380,25911,25912,25915,25917,25923,25925,25927,25929,25931],{},[383,25913,25914],{},"M",[458,25916,471],{},[586,25918,25919,25921],{},[463,25920,465],{},[463,25922,2810],{},[458,25924,461],{"stretchy":460},[383,25926,554],{},[458,25928,2817],{},[383,25930,561],{},[458,25932,468],{"stretchy":460},[387,25934,25935],{"encoding":389},"M=\\frac12(P+Q)",[363,25937,25939,25958,26047],{"className":25938,"ariaHidden":394},[393],[363,25940,25942,25945,25949,25952,25955],{"className":25941},[398],[363,25943],{"className":25944,"style":1011},[402],[363,25946,25914],{"className":25947,"style":25948},[407,408],"margin-right:0.109em;",[363,25950],{"className":25951,"style":506},[505],[363,25953,471],{"className":25954},[510],[363,25956],{"className":25957,"style":506},[505],[363,25959,25961,25964,26032,26035,26038,26041,26044],{"className":25960},[398],[363,25962],{"className":25963,"style":2852},[402],[363,25965,25967,25970,26029],{"className":25966},[407],[363,25968],{"className":25969},[494,789],[363,25971,25973],{"className":25972},[586],[363,25974,25976,26021],{"className":25975},[633,634],[363,25977,25979,26018],{"className":25978},[638],[363,25980,25982,25996,26004],{"className":25981,"style":2871},[642],[363,25983,25984,25987],{"style":2874},[363,25985],{"className":25986,"style":809},[650],[363,25988,25990],{"className":25989},[655,656,657,658],[363,25991,25993],{"className":25992},[407,658],[363,25994,2810],{"className":25995},[407,658],[363,25997,25998,26001],{"style":821},[363,25999],{"className":26000,"style":809},[650],[363,26002],{"className":26003,"style":829},[828],[363,26005,26006,26009],{"style":2897},[363,26007],{"className":26008,"style":809},[650],[363,26010,26012],{"className":26011},[655,656,657,658],[363,26013,26015],{"className":26014},[407,658],[363,26016,465],{"className":26017},[407,658],[363,26019,666],{"className":26020},[665],[363,26022,26024],{"className":26023},[638],[363,26025,26027],{"className":26026,"style":2919},[642],[363,26028],{},[363,26030],{"className":26031},[501,789],[363,26033,461],{"className":26034},[494],[363,26036,554],{"className":26037,"style":682},[407,408],[363,26039],{"className":26040,"style":2934},[505],[363,26042,2817],{"className":26043},[2938],[363,26045],{"className":26046,"style":2934},[505],[363,26048,26050,26053,26056],{"className":26049},[398],[363,26051],{"className":26052,"style":487},[402],[363,26054,561],{"className":26055},[407,408],[363,26057,468],{"className":26058},[501],[363,26060,26062],{"className":26061,"translate":367},[528],[363,26063,26065,26164],{"className":26064,"translate":367},[366],[363,26066,26068],{"className":26067},[371],[373,26069,26070],{"xmlns":375,"display":537},[377,26071,26072,26161],{},[380,26073,26074,26085,26087,26089,26091,26093,26095,26097,26103,26113,26115,26127,26129,26135,26145,26147,26159],{},[543,26075,26076,26078],{},[383,26077,547],{},[380,26079,26080,26082],{},[383,26081,24090],{},[383,26083,26084],{},"S",[458,26086,461],{"stretchy":460},[383,26088,554],{},[383,26090,558],{"mathvariant":557},[383,26092,561],{},[458,26094,468],{"stretchy":460},[458,26096,471],{},[586,26098,26099,26101],{},[463,26100,465],{},[463,26102,2810],{},[543,26104,26105,26107],{},[383,26106,547],{},[380,26108,26109,26111],{},[383,26110,11041],{},[383,26112,22240],{},[1644,26114,1651],{},[380,26116,26117,26119,26121,26123,26125],{},[458,26118,461],{"fence":394},[383,26120,554],{},[383,26122,558],{"mathvariant":557},[383,26124,25914],{},[458,26126,468],{"fence":394},[458,26128,2817],{},[586,26130,26131,26133],{},[463,26132,465],{},[463,26134,2810],{},[543,26136,26137,26139],{},[383,26138,547],{},[380,26140,26141,26143],{},[383,26142,11041],{},[383,26144,22240],{},[1644,26146,1651],{},[380,26148,26149,26151,26153,26155,26157],{},[458,26150,461],{"fence":394},[383,26152,561],{},[383,26154,558],{"mathvariant":557},[383,26156,25914],{},[458,26158,468],{"fence":394},[383,26160,4722],{"mathvariant":557},[387,26162,26163],{"encoding":389},"D_{JS}(P\\|Q)=\\frac12 D_{KL}\\!\\left(P\\|M\\right)\n+\\frac12 D_{KL}\\!\\left(Q\\|M\\right).",[363,26165,26167,26244,26392],{"className":26166,"ariaHidden":394},[393],[363,26168,26170,26173,26220,26223,26226,26229,26232,26235,26238,26241],{"className":26169},[398],[363,26171],{"className":26172,"style":487},[402],[363,26174,26176,26179],{"className":26175},[407],[363,26177,547],{"className":26178,"style":625},[407,408],[363,26180,26182],{"className":26181},[629],[363,26183,26185,26212],{"className":26184},[633,634],[363,26186,26188,26209],{"className":26187},[638],[363,26189,26191],{"className":26190,"style":727},[642],[363,26192,26193,26196],{"style":646},[363,26194],{"className":26195,"style":651},[650],[363,26197,26199],{"className":26198},[655,656,657,658],[363,26200,26202,26205],{"className":26201},[407,658],[363,26203,24090],{"className":26204,"style":24500},[407,408,658],[363,26206,26084],{"className":26207,"style":26208},[407,408,658],"margin-right:0.0576em;",[363,26210,666],{"className":26211},[665],[363,26213,26215],{"className":26214},[638],[363,26216,26218],{"className":26217,"style":8315},[642],[363,26219],{},[363,26221,461],{"className":26222},[494],[363,26224,554],{"className":26225,"style":682},[407,408],[363,26227,558],{"className":26228},[407],[363,26230,561],{"className":26231},[407,408],[363,26233,468],{"className":26234},[501],[363,26236],{"className":26237,"style":506},[505],[363,26239,471],{"className":26240},[510],[363,26242],{"className":26243,"style":506},[505],[363,26245,26247,26251,26313,26359,26362,26365,26383,26386,26389],{"className":26246},[398],[363,26248],{"className":26249,"style":26250},[402],"height:2.0074em;vertical-align:-0.686em;",[363,26252,26254,26257,26310],{"className":26253},[407],[363,26255],{"className":26256},[494,789],[363,26258,26260],{"className":26259},[586],[363,26261,26263,26302],{"className":26262},[633,634],[363,26264,26266,26299],{"className":26265},[638],[363,26267,26269,26280,26288],{"className":26268,"style":23236},[642],[363,26270,26271,26274],{"style":805},[363,26272],{"className":26273,"style":809},[650],[363,26275,26277],{"className":26276},[407],[363,26278,2810],{"className":26279},[407],[363,26281,26282,26285],{"style":821},[363,26283],{"className":26284,"style":809},[650],[363,26286],{"className":26287,"style":829},[828],[363,26289,26290,26293],{"style":832},[363,26291],{"className":26292,"style":809},[650],[363,26294,26296],{"className":26295},[407],[363,26297,465],{"className":26298},[407],[363,26300,666],{"className":26301},[665],[363,26303,26305],{"className":26304},[638],[363,26306,26308],{"className":26307,"style":4125},[642],[363,26309],{},[363,26311],{"className":26312},[501,789],[363,26314,26316,26319],{"className":26315},[407],[363,26317,547],{"className":26318,"style":625},[407,408],[363,26320,26322],{"className":26321},[629],[363,26323,26325,26351],{"className":26324},[633,634],[363,26326,26328,26348],{"className":26327},[638],[363,26329,26331],{"className":26330,"style":727},[642],[363,26332,26333,26336],{"style":646},[363,26334],{"className":26335,"style":651},[650],[363,26337,26339],{"className":26338},[655,656,657,658],[363,26340,26342,26345],{"className":26341},[407,658],[363,26343,11041],{"className":26344,"style":11129},[407,408,658],[363,26346,22240],{"className":26347},[407,408,658],[363,26349,666],{"className":26350},[665],[363,26352,26354],{"className":26353},[638],[363,26355,26357],{"className":26356,"style":8315},[642],[363,26358],{},[363,26360],{"className":26361,"style":1859},[505],[363,26363],{"className":26364,"style":754},[505],[363,26366,26368,26371,26374,26377,26380],{"className":26367},[758],[363,26369,461],{"className":26370,"style":763},[494,762],[363,26372,554],{"className":26373,"style":682},[407,408],[363,26375,558],{"className":26376},[407],[363,26378,25914],{"className":26379,"style":25948},[407,408],[363,26381,468],{"className":26382,"style":763},[501,762],[363,26384],{"className":26385,"style":2934},[505],[363,26387,2817],{"className":26388},[2938],[363,26390],{"className":26391,"style":2934},[505],[363,26393,26395,26398,26460,26506,26509,26512,26530,26533],{"className":26394},[398],[363,26396],{"className":26397,"style":26250},[402],[363,26399,26401,26404,26457],{"className":26400},[407],[363,26402],{"className":26403},[494,789],[363,26405,26407],{"className":26406},[586],[363,26408,26410,26449],{"className":26409},[633,634],[363,26411,26413,26446],{"className":26412},[638],[363,26414,26416,26427,26435],{"className":26415,"style":23236},[642],[363,26417,26418,26421],{"style":805},[363,26419],{"className":26420,"style":809},[650],[363,26422,26424],{"className":26423},[407],[363,26425,2810],{"className":26426},[407],[363,26428,26429,26432],{"style":821},[363,26430],{"className":26431,"style":809},[650],[363,26433],{"className":26434,"style":829},[828],[363,26436,26437,26440],{"style":832},[363,26438],{"className":26439,"style":809},[650],[363,26441,26443],{"className":26442},[407],[363,26444,465],{"className":26445},[407],[363,26447,666],{"className":26448},[665],[363,26450,26452],{"className":26451},[638],[363,26453,26455],{"className":26454,"style":4125},[642],[363,26456],{},[363,26458],{"className":26459},[501,789],[363,26461,26463,26466],{"className":26462},[407],[363,26464,547],{"className":26465,"style":625},[407,408],[363,26467,26469],{"className":26468},[629],[363,26470,26472,26498],{"className":26471},[633,634],[363,26473,26475,26495],{"className":26474},[638],[363,26476,26478],{"className":26477,"style":727},[642],[363,26479,26480,26483],{"style":646},[363,26481],{"className":26482,"style":651},[650],[363,26484,26486],{"className":26485},[655,656,657,658],[363,26487,26489,26492],{"className":26488},[407,658],[363,26490,11041],{"className":26491,"style":11129},[407,408,658],[363,26493,22240],{"className":26494},[407,408,658],[363,26496,666],{"className":26497},[665],[363,26499,26501],{"className":26500},[638],[363,26502,26504],{"className":26503,"style":8315},[642],[363,26505],{},[363,26507],{"className":26508,"style":1859},[505],[363,26510],{"className":26511,"style":754},[505],[363,26513,26515,26518,26521,26524,26527],{"className":26514},[758],[363,26516,461],{"className":26517,"style":763},[494,762],[363,26519,561],{"className":26520},[407,408],[363,26522,558],{"className":26523},[407],[363,26525,25914],{"className":26526,"style":25948},[407,408],[363,26528,468],{"className":26529,"style":763},[501,762],[363,26531],{"className":26532,"style":754},[505],[363,26534,4722],{"className":26535},[407],[11,26537,26538,26541,26542,26570,26571,26626,26627,26655,26656,26807],{},[1572,26539,26540],{},"它是单个 f-散度。"," 这一点很容易被误解。我们直接构造 ",[363,26543,26545,26558],{"className":26544,"translate":367},[366],[363,26546,26548],{"className":26547},[371],[373,26549,26550],{"xmlns":375},[377,26551,26552,26556],{},[380,26553,26554],{},[383,26555,385],{},[387,26557,385],{"encoding":389},[363,26559,26561],{"className":26560,"ariaHidden":394},[393],[363,26562,26564,26567],{"className":26563},[398],[363,26565],{"className":26566,"style":403},[402],[363,26568,385],{"className":26569,"style":409},[407,408],"：代入 ",[363,26572,26574,26594],{"className":26573,"translate":367},[366],[363,26575,26577],{"className":26576},[371],[373,26578,26579],{"xmlns":375},[377,26580,26581,26591],{},[380,26582,26583,26585,26587,26589],{},[383,26584,11],{},[458,26586,471],{},[383,26588,1116],{},[383,26590,1291],{},[387,26592,26593],{"encoding":389},"p=tq",[363,26595,26597,26615],{"className":26596,"ariaHidden":394},[393],[363,26598,26600,26603,26606,26609,26612],{"className":26599},[398],[363,26601],{"className":26602,"style":2623},[402],[363,26604,11],{"className":26605},[407,408],[363,26607],{"className":26608,"style":506},[505],[363,26610,471],{"className":26611},[510],[363,26613],{"className":26614,"style":506},[505],[363,26616,26618,26622],{"className":26617},[398],[363,26619],{"className":26620,"style":26621},[402],"height:0.8095em;vertical-align:-0.1944em;",[363,26623,26625],{"className":26624,"style":1328},[407,408],"tq","，于是 ",[363,26628,26630,26643],{"className":26629,"translate":367},[366],[363,26631,26633],{"className":26632},[371],[373,26634,26635],{"xmlns":375},[377,26636,26637,26641],{},[380,26638,26639],{},[383,26640,25914],{},[387,26642,25914],{"encoding":389},[363,26644,26646],{"className":26645,"ariaHidden":394},[393],[363,26647,26649,26652],{"className":26648},[398],[363,26650],{"className":26651,"style":1011},[402],[363,26653,25914],{"className":26654,"style":25948},[407,408]," 的密度为 ",[363,26657,26659,26694],{"className":26658,"translate":367},[366],[363,26660,26662],{"className":26661},[371],[373,26663,26664],{"xmlns":375},[377,26665,26666,26691],{},[380,26667,26668,26671,26673],{},[383,26669,26670],{},"m",[458,26672,471],{},[586,26674,26675,26689],{},[380,26676,26677,26679,26681,26683,26685,26687],{},[458,26678,461],{"stretchy":460},[383,26680,1116],{},[458,26682,2817],{},[463,26684,465],{},[458,26686,468],{"stretchy":460},[383,26688,1291],{},[463,26690,2810],{},[387,26692,26693],{"encoding":389},"m=\\frac{(t+1)q}{2}",[363,26695,26697,26715],{"className":26696,"ariaHidden":394},[393],[363,26698,26700,26703,26706,26709,26712],{"className":26699},[398],[363,26701],{"className":26702,"style":2692},[402],[363,26704,26670],{"className":26705},[407,408],[363,26707],{"className":26708,"style":506},[505],[363,26710,471],{"className":26711},[510],[363,26713],{"className":26714,"style":506},[505],[363,26716,26718,26722],{"className":26717},[398],[363,26719],{"className":26720,"style":26721},[402],"height:1.355em;vertical-align:-0.345em;",[363,26723,26725,26728,26804],{"className":26724},[407],[363,26726],{"className":26727},[494,789],[363,26729,26731],{"className":26730},[586],[363,26732,26734,26796],{"className":26733},[633,634],[363,26735,26737,26793],{"className":26736},[638],[363,26738,26741,26755,26763],{"className":26739,"style":26740},[642],"height:1.01em;",[363,26742,26743,26746],{"style":2874},[363,26744],{"className":26745,"style":809},[650],[363,26747,26749],{"className":26748},[655,656,657,658],[363,26750,26752],{"className":26751},[407,658],[363,26753,2810],{"className":26754},[407,658],[363,26756,26757,26760],{"style":821},[363,26758],{"className":26759,"style":809},[650],[363,26761],{"className":26762,"style":829},[828],[363,26764,26766,26769],{"style":26765},"top:-3.485em;",[363,26767],{"className":26768,"style":809},[650],[363,26770,26772],{"className":26771},[655,656,657,658],[363,26773,26775,26778,26781,26784,26787,26790],{"className":26774},[407,658],[363,26776,461],{"className":26777},[494,658],[363,26779,1116],{"className":26780},[407,408,658],[363,26782,2817],{"className":26783},[2938,658],[363,26785,465],{"className":26786},[407,658],[363,26788,468],{"className":26789},[501,658],[363,26791,1291],{"className":26792,"style":1328},[407,408,658],[363,26794,666],{"className":26795},[665],[363,26797,26799],{"className":26798},[638],[363,26800,26802],{"className":26801,"style":2919},[642],[363,26803],{},[363,26805],{"className":26806},[501,789],"，逐项算：",[363,26809,26811],{"className":26810,"translate":367},[528],[363,26812,26814,26876],{"className":26813,"translate":367},[366],[363,26815,26817],{"className":26816},[371],[373,26818,26819],{"xmlns":375,"display":537},[377,26820,26821,26873],{},[380,26822,26823,26829,26831,26847,26849,26851,26857,26859,26871],{},[586,26824,26825,26827],{},[383,26826,11],{},[383,26828,26670],{},[458,26830,471],{},[586,26832,26833,26839],{},[380,26834,26835,26837],{},[463,26836,2810],{},[383,26838,1116],{},[380,26840,26841,26843,26845],{},[383,26842,1116],{},[458,26844,2817],{},[463,26846,465],{},[458,26848,898],{"separator":394},[505,26850],{"width":3609},[586,26852,26853,26855],{},[383,26854,1291],{},[383,26856,26670],{},[458,26858,471],{},[586,26860,26861,26863],{},[463,26862,2810],{},[380,26864,26865,26867,26869],{},[383,26866,1116],{},[458,26868,2817],{},[463,26870,465],{},[458,26872,898],{"separator":394},[387,26874,26875],{"encoding":389},"\\frac{p}{m}=\\frac{2t}{t+1},\\qquad\n\\frac{q}{m}=\\frac{2}{t+1},",[363,26877,26879,26957,27121],{"className":26878,"ariaHidden":394},[393],[363,26880,26882,26886,26948,26951,26954],{"className":26881},[398],[363,26883],{"className":26884,"style":26885},[402],"height:1.7936em;vertical-align:-0.686em;",[363,26887,26889,26892,26945],{"className":26888},[407],[363,26890],{"className":26891},[494,789],[363,26893,26895],{"className":26894},[586],[363,26896,26898,26937],{"className":26897},[633,634],[363,26899,26901,26934],{"className":26900},[638],[363,26902,26904,26915,26923],{"className":26903,"style":3901},[642],[363,26905,26906,26909],{"style":805},[363,26907],{"className":26908,"style":809},[650],[363,26910,26912],{"className":26911},[407],[363,26913,26670],{"className":26914},[407,408],[363,26916,26917,26920],{"style":821},[363,26918],{"className":26919,"style":809},[650],[363,26921],{"className":26922,"style":829},[828],[363,26924,26925,26928],{"style":832},[363,26926],{"className":26927,"style":809},[650],[363,26929,26931],{"className":26930},[407],[363,26932,11],{"className":26933},[407,408],[363,26935,666],{"className":26936},[665],[363,26938,26940],{"className":26939},[638],[363,26941,26943],{"className":26942,"style":4125},[642],[363,26944],{},[363,26946],{"className":26947},[501,789],[363,26949],{"className":26950,"style":506},[505],[363,26952,471],{"className":26953},[510],[363,26955],{"className":26956,"style":506},[505],[363,26958,26960,26964,27041,27044,27047,27050,27112,27115,27118],{"className":26959},[398],[363,26961],{"className":26962,"style":26963},[402],"height:2.0908em;vertical-align:-0.7693em;",[363,26965,26967,26970,27038],{"className":26966},[407],[363,26968],{"className":26969},[494,789],[363,26971,26973],{"className":26972},[586],[363,26974,26976,27030],{"className":26975},[633,634],[363,26977,26979,27027],{"className":26978},[638],[363,26980,26982,27005,27013],{"className":26981,"style":23236},[642],[363,26983,26984,26987],{"style":805},[363,26985],{"className":26986,"style":809},[650],[363,26988,26990,26993,26996,26999,27002],{"className":26989},[407],[363,26991,1116],{"className":26992},[407,408],[363,26994],{"className":26995,"style":2934},[505],[363,26997,2817],{"className":26998},[2938],[363,27000],{"className":27001,"style":2934},[505],[363,27003,465],{"className":27004},[407],[363,27006,27007,27010],{"style":821},[363,27008],{"className":27009,"style":809},[650],[363,27011],{"className":27012,"style":829},[828],[363,27014,27015,27018],{"style":832},[363,27016],{"className":27017,"style":809},[650],[363,27019,27021,27024],{"className":27020},[407],[363,27022,2810],{"className":27023},[407],[363,27025,1116],{"className":27026},[407,408],[363,27028,666],{"className":27029},[665],[363,27031,27033],{"className":27032},[638],[363,27034,27036],{"className":27035,"style":17362},[642],[363,27037],{},[363,27039],{"className":27040},[501,789],[363,27042,898],{"className":27043},[920],[363,27045],{"className":27046,"style":3981},[505],[363,27048],{"className":27049,"style":754},[505],[363,27051,27053,27056,27109],{"className":27052},[407],[363,27054],{"className":27055},[494,789],[363,27057,27059],{"className":27058},[586],[363,27060,27062,27101],{"className":27061},[633,634],[363,27063,27065,27098],{"className":27064},[638],[363,27066,27068,27079,27087],{"className":27067,"style":3901},[642],[363,27069,27070,27073],{"style":805},[363,27071],{"className":27072,"style":809},[650],[363,27074,27076],{"className":27075},[407],[363,27077,26670],{"className":27078},[407,408],[363,27080,27081,27084],{"style":821},[363,27082],{"className":27083,"style":809},[650],[363,27085],{"className":27086,"style":829},[828],[363,27088,27089,27092],{"style":832},[363,27090],{"className":27091,"style":809},[650],[363,27093,27095],{"className":27094},[407],[363,27096,1291],{"className":27097,"style":1328},[407,408],[363,27099,666],{"className":27100},[665],[363,27102,27104],{"className":27103},[638],[363,27105,27107],{"className":27106,"style":4125},[642],[363,27108],{},[363,27110],{"className":27111},[501,789],[363,27113],{"className":27114,"style":506},[505],[363,27116,471],{"className":27117},[510],[363,27119],{"className":27120,"style":506},[505],[363,27122,27124,27127,27201],{"className":27123},[398],[363,27125],{"className":27126,"style":26963},[402],[363,27128,27130,27133,27198],{"className":27129},[407],[363,27131],{"className":27132},[494,789],[363,27134,27136],{"className":27135},[586],[363,27137,27139,27190],{"className":27138},[633,634],[363,27140,27142,27187],{"className":27141},[638],[363,27143,27145,27168,27176],{"className":27144,"style":23236},[642],[363,27146,27147,27150],{"style":805},[363,27148],{"className":27149,"style":809},[650],[363,27151,27153,27156,27159,27162,27165],{"className":27152},[407],[363,27154,1116],{"className":27155},[407,408],[363,27157],{"className":27158,"style":2934},[505],[363,27160,2817],{"className":27161},[2938],[363,27163],{"className":27164,"style":2934},[505],[363,27166,465],{"className":27167},[407],[363,27169,27170,27173],{"style":821},[363,27171],{"className":27172,"style":809},[650],[363,27174],{"className":27175,"style":829},[828],[363,27177,27178,27181],{"style":832},[363,27179],{"className":27180,"style":809},[650],[363,27182,27184],{"className":27183},[407],[363,27185,2810],{"className":27186},[407],[363,27188,666],{"className":27189},[665],[363,27191,27193],{"className":27192},[638],[363,27194,27196],{"className":27195,"style":17362},[642],[363,27197],{},[363,27199],{"className":27200},[501,789],[363,27202,898],{"className":27203},[920],[363,27205,27207],{"className":27206,"translate":367},[528],[363,27208,27210,27350],{"className":27209,"translate":367},[366],[363,27211,27213],{"className":27212},[371],[373,27214,27215],{"xmlns":375,"display":537},[377,27216,27217,27347],{},[1590,27218,27219,27299],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,27220,27221,27247],{},[1599,27222,27223],{},[1602,27224,27225],{"scriptlevel":474,"displaystyle":394},[380,27226,27227,27237,27239,27241,27243,27245],{},[543,27228,27229,27231],{},[383,27230,547],{},[380,27232,27233,27235],{},[383,27234,24090],{},[383,27236,26084],{},[458,27238,461],{"stretchy":460},[383,27240,554],{},[383,27242,558],{"mathvariant":557},[383,27244,561],{},[458,27246,468],{"stretchy":460},[1599,27248,27249],{},[1602,27250,27251],{"scriptlevel":474,"displaystyle":394},[380,27252,27253,27255,27257,27263,27265,27267,27269,27271,27277,27279,27285,27287,27289,27291,27293],{},[380,27254],{},[458,27256,471],{},[586,27258,27259,27261],{},[463,27260,465],{},[463,27262,2810],{},[458,27264,1634],{},[383,27266,11],{},[383,27268,4447],{},[458,27270,4450],{},[586,27272,27273,27275],{},[383,27274,11],{},[383,27276,26670],{},[458,27278,2817],{},[586,27280,27281,27283],{},[463,27282,465],{},[463,27284,2810],{},[458,27286,1634],{},[383,27288,1291],{},[383,27290,4447],{},[458,27292,4450],{},[586,27294,27295,27297],{},[383,27296,1291],{},[383,27298,26670],{},[1596,27300,27301,27307],{},[1599,27302,27303],{},[1602,27304,27305],{"scriptlevel":474,"displaystyle":394},[380,27306],{},[1599,27308,27309],{},[1602,27310,27311],{"scriptlevel":474,"displaystyle":394},[380,27312,27313,27315,27317,27319,27321,27323,27333,27335,27337,27339,27341,27343,27345],{},[380,27314],{},[458,27316,471],{},[458,27318,1634],{},[383,27320,1291],{},[1644,27322,1646],{},[543,27324,27325,27327],{},[383,27326,385],{},[380,27328,27329,27331],{},[383,27330,24090],{},[383,27332,26084],{},[458,27334,461],{"stretchy":460},[383,27336,1116],{},[458,27338,468],{"stretchy":460},[1644,27340,1646],{},[383,27342,592],{},[383,27344,1121],{},[458,27346,898],{"separator":394},[387,27348,27349],{"encoding":389},"\\begin{aligned}\nD_{JS}(P\\|Q)\n&=\\frac12\\int p\\log\\frac{p}{m}\n+\\frac12\\int q\\log\\frac{q}{m}\\\\[2pt]\n&=\\int q\\,f_{JS}(t)\\,dx,\n\\end{aligned}",[363,27351,27353],{"className":27352,"ariaHidden":394},[393],[363,27354,27356,27360],{"className":27355},[398],[363,27357],{"className":27358,"style":27359},[402],"height:4.7445em;vertical-align:-2.1223em;",[363,27361,27363],{"className":27362},[407],[363,27364,27366,27469],{"className":27365},[1590],[363,27367,27369],{"className":27368},[1707],[363,27370,27372,27460],{"className":27371},[633,634],[363,27373,27375,27457],{"className":27374},[638],[363,27376,27379,27449],{"className":27377,"style":27378},[642],"height:2.6223em;",[363,27380,27382,27385],{"style":27381},"top:-4.6223em;",[363,27383],{"className":27384,"style":6620},[650],[363,27386,27388,27434,27437,27440,27443,27446],{"className":27387},[407],[363,27389,27391,27394],{"className":27390},[407],[363,27392,547],{"className":27393,"style":625},[407,408],[363,27395,27397],{"className":27396},[629],[363,27398,27400,27426],{"className":27399},[633,634],[363,27401,27403,27423],{"className":27402},[638],[363,27404,27406],{"className":27405,"style":727},[642],[363,27407,27408,27411],{"style":646},[363,27409],{"className":27410,"style":651},[650],[363,27412,27414],{"className":27413},[655,656,657,658],[363,27415,27417,27420],{"className":27416},[407,658],[363,27418,24090],{"className":27419,"style":24500},[407,408,658],[363,27421,26084],{"className":27422,"style":26208},[407,408,658],[363,27424,666],{"className":27425},[665],[363,27427,27429],{"className":27428},[638],[363,27430,27432],{"className":27431,"style":8315},[642],[363,27433],{},[363,27435,461],{"className":27436},[494],[363,27438,554],{"className":27439,"style":682},[407,408],[363,27441,558],{"className":27442},[407],[363,27444,561],{"className":27445},[407,408],[363,27447,468],{"className":27448},[501],[363,27450,27451,27454],{"style":2250},[363,27452],{"className":27453,"style":6620},[650],[363,27455],{"className":27456},[407],[363,27458,666],{"className":27459},[665],[363,27461,27463],{"className":27462},[638],[363,27464,27467],{"className":27465,"style":27466},[642],"height:2.1223em;",[363,27468],{},[363,27470,27472],{"className":27471},[1798],[363,27473,27475,27907],{"className":27474},[633,634],[363,27476,27478,27904],{"className":27477},[638],[363,27479,27481,27804],{"className":27480,"style":27378},[642],[363,27482,27483,27486],{"style":27381},[363,27484],{"className":27485,"style":6620},[650],[363,27487,27489,27492,27495,27498,27501,27563,27566,27569,27572,27575,27578,27583,27586,27648,27651,27654,27657,27719,27722,27725,27728,27731,27734,27739,27742],{"className":27488},[407],[363,27490],{"className":27491},[407],[363,27493],{"className":27494,"style":506},[505],[363,27496,471],{"className":27497},[510],[363,27499],{"className":27500,"style":506},[505],[363,27502,27504,27507,27560],{"className":27503},[407],[363,27505],{"className":27506},[494,789],[363,27508,27510],{"className":27509},[586],[363,27511,27513,27552],{"className":27512},[633,634],[363,27514,27516,27549],{"className":27515},[638],[363,27517,27519,27530,27538],{"className":27518,"style":23236},[642],[363,27520,27521,27524],{"style":805},[363,27522],{"className":27523,"style":809},[650],[363,27525,27527],{"className":27526},[407],[363,27528,2810],{"className":27529},[407],[363,27531,27532,27535],{"style":821},[363,27533],{"className":27534,"style":809},[650],[363,27536],{"className":27537,"style":829},[828],[363,27539,27540,27543],{"style":832},[363,27541],{"className":27542,"style":809},[650],[363,27544,27546],{"className":27545},[407],[363,27547,465],{"className":27548},[407],[363,27550,666],{"className":27551},[665],[363,27553,27555],{"className":27554},[638],[363,27556,27558],{"className":27557,"style":4125},[642],[363,27559],{},[363,27561],{"className":27562},[501,789],[363,27564],{"className":27565,"style":754},[505],[363,27567,1634],{"className":27568,"style":1834},[1831,1832,1833],[363,27570],{"className":27571,"style":754},[505],[363,27573,11],{"className":27574},[407,408],[363,27576],{"className":27577,"style":754},[505],[363,27579,4501,27581],{"className":27580},[1831],[363,27582,4505],{"style":4504},[363,27584],{"className":27585,"style":754},[505],[363,27587,27589,27592,27645],{"className":27588},[407],[363,27590],{"className":27591},[494,789],[363,27593,27595],{"className":27594},[586],[363,27596,27598,27637],{"className":27597},[633,634],[363,27599,27601,27634],{"className":27600},[638],[363,27602,27604,27615,27623],{"className":27603,"style":3901},[642],[363,27605,27606,27609],{"style":805},[363,27607],{"className":27608,"style":809},[650],[363,27610,27612],{"className":27611},[407],[363,27613,26670],{"className":27614},[407,408],[363,27616,27617,27620],{"style":821},[363,27618],{"className":27619,"style":809},[650],[363,27621],{"className":27622,"style":829},[828],[363,27624,27625,27628],{"style":832},[363,27626],{"className":27627,"style":809},[650],[363,27629,27631],{"className":27630},[407],[363,27632,11],{"className":27633},[407,408],[363,27635,666],{"className":27636},[665],[363,27638,27640],{"className":27639},[638],[363,27641,27643],{"className":27642,"style":4125},[642],[363,27644],{},[363,27646],{"className":27647},[501,789],[363,27649],{"className":27650,"style":2934},[505],[363,27652,2817],{"className":27653},[2938],[363,27655],{"className":27656,"style":2934},[505],[363,27658,27660,27663,27716],{"className":27659},[407],[363,27661],{"className":27662},[494,789],[363,27664,27666],{"className":27665},[586],[363,27667,27669,27708],{"className":27668},[633,634],[363,27670,27672,27705],{"className":27671},[638],[363,27673,27675,27686,27694],{"className":27674,"style":23236},[642],[363,27676,27677,27680],{"style":805},[363,27678],{"className":27679,"style":809},[650],[363,27681,27683],{"className":27682},[407],[363,27684,2810],{"className":27685},[407],[363,27687,27688,27691],{"style":821},[363,27689],{"className":27690,"style":809},[650],[363,27692],{"className":27693,"style":829},[828],[363,27695,27696,27699],{"style":832},[363,27697],{"className":27698,"style":809},[650],[363,27700,27702],{"className":27701},[407],[363,27703,465],{"className":27704},[407],[363,27706,666],{"className":27707},[665],[363,27709,27711],{"className":27710},[638],[363,27712,27714],{"className":27713,"style":4125},[642],[363,27715],{},[363,27717],{"className":27718},[501,789],[363,27720],{"className":27721,"style":754},[505],[363,27723,1634],{"className":27724,"style":1834},[1831,1832,1833],[363,27726],{"className":27727,"style":754},[505],[363,27729,1291],{"className":27730,"style":1328},[407,408],[363,27732],{"className":27733,"style":754},[505],[363,27735,4501,27737],{"className":27736},[1831],[363,27738,4505],{"style":4504},[363,27740],{"className":27741,"style":754},[505],[363,27743,27745,27748,27801],{"className":27744},[407],[363,27746],{"className":27747},[494,789],[363,27749,27751],{"className":27750},[586],[363,27752,27754,27793],{"className":27753},[633,634],[363,27755,27757,27790],{"className":27756},[638],[363,27758,27760,27771,27779],{"className":27759,"style":3901},[642],[363,27761,27762,27765],{"style":805},[363,27763],{"className":27764,"style":809},[650],[363,27766,27768],{"className":27767},[407],[363,27769,26670],{"className":27770},[407,408],[363,27772,27773,27776],{"style":821},[363,27774],{"className":27775,"style":809},[650],[363,27777],{"className":27778,"style":829},[828],[363,27780,27781,27784],{"style":832},[363,27782],{"className":27783,"style":809},[650],[363,27785,27787],{"className":27786},[407],[363,27788,1291],{"className":27789,"style":1328},[407,408],[363,27791,666],{"className":27792},[665],[363,27794,27796],{"className":27795},[638],[363,27797,27799],{"className":27798,"style":4125},[642],[363,27800],{},[363,27802],{"className":27803},[501,789],[363,27805,27806,27809],{"style":2250},[363,27807],{"className":27808,"style":6620},[650],[363,27810,27812,27815,27818,27821,27824,27827,27830,27833,27836,27883,27886,27889,27892,27895,27898,27901],{"className":27811},[407],[363,27813],{"className":27814},[407],[363,27816],{"className":27817,"style":506},[505],[363,27819,471],{"className":27820},[510],[363,27822],{"className":27823,"style":506},[505],[363,27825,1634],{"className":27826,"style":1834},[1831,1832,1833],[363,27828],{"className":27829,"style":754},[505],[363,27831,1291],{"className":27832,"style":1328},[407,408],[363,27834],{"className":27835,"style":754},[505],[363,27837,27839,27842],{"className":27838},[407],[363,27840,385],{"className":27841,"style":409},[407,408],[363,27843,27845],{"className":27844},[629],[363,27846,27848,27875],{"className":27847},[633,634],[363,27849,27851,27872],{"className":27850},[638],[363,27852,27854],{"className":27853,"style":727},[642],[363,27855,27857,27860],{"style":27856},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[363,27858],{"className":27859,"style":651},[650],[363,27861,27863],{"className":27862},[655,656,657,658],[363,27864,27866,27869],{"className":27865},[407,658],[363,27867,24090],{"className":27868,"style":24500},[407,408,658],[363,27870,26084],{"className":27871,"style":26208},[407,408,658],[363,27873,666],{"className":27874},[665],[363,27876,27878],{"className":27877},[638],[363,27879,27881],{"className":27880,"style":8315},[642],[363,27882],{},[363,27884,461],{"className":27885},[494],[363,27887,1116],{"className":27888},[407,408],[363,27890,468],{"className":27891},[501],[363,27893],{"className":27894,"style":754},[505],[363,27896,592],{"className":27897},[407,408],[363,27899,1121],{"className":27900},[407,408],[363,27902,898],{"className":27903},[920],[363,27905,666],{"className":27906},[665],[363,27908,27910],{"className":27909},[638],[363,27911,27913],{"className":27912,"style":27466},[642],[363,27914],{},[11,27916,27917],{},"其中",[363,27919,27921],{"className":27920,"translate":367},[528],[363,27922,27924,28008],{"className":27923,"translate":367},[366],[363,27925,27927],{"className":27926},[371],[373,27928,27929],{"xmlns":375,"display":537},[377,27930,27931,28005],{},[380,27932,27933,27943,27945,27947,27949,27951,27957,28003],{},[543,27934,27935,27937],{},[383,27936,385],{},[380,27938,27939,27941],{},[383,27940,24090],{},[383,27942,26084],{},[458,27944,461],{"stretchy":460},[383,27946,1116],{},[458,27948,468],{"stretchy":460},[458,27950,471],{},[586,27952,27953,27955],{},[463,27954,465],{},[463,27956,2810],{},[380,27958,27959,27961,27963,27965,27967,27983,27985,27987,27989,28001],{},[458,27960,578],{"fence":394},[383,27962,1116],{},[383,27964,4447],{},[458,27966,4450],{},[586,27968,27969,27975],{},[380,27970,27971,27973],{},[463,27972,2810],{},[383,27974,1116],{},[380,27976,27977,27979,27981],{},[383,27978,1116],{},[458,27980,2817],{},[463,27982,465],{},[458,27984,2817],{},[383,27986,4447],{},[458,27988,4450],{},[586,27990,27991,27993],{},[463,27992,2810],{},[380,27994,27995,27997,27999],{},[383,27996,1116],{},[458,27998,2817],{},[463,28000,465],{},[458,28002,605],{"fence":394},[383,28004,4722],{"mathvariant":557},[387,28006,28007],{"encoding":389},"f_{JS}(t)=\\frac12\\left[\nt\\log\\frac{2t}{t+1}+\\log\\frac{2}{t+1}\\right].",[363,28009,28011,28081],{"className":28010,"ariaHidden":394},[393],[363,28012,28014,28017,28063,28066,28069,28072,28075,28078],{"className":28013},[398],[363,28015],{"className":28016,"style":487},[402],[363,28018,28020,28023],{"className":28019},[407],[363,28021,385],{"className":28022,"style":409},[407,408],[363,28024,28026],{"className":28025},[629],[363,28027,28029,28055],{"className":28028},[633,634],[363,28030,28032,28052],{"className":28031},[638],[363,28033,28035],{"className":28034,"style":727},[642],[363,28036,28037,28040],{"style":27856},[363,28038],{"className":28039,"style":651},[650],[363,28041,28043],{"className":28042},[655,656,657,658],[363,28044,28046,28049],{"className":28045},[407,658],[363,28047,24090],{"className":28048,"style":24500},[407,408,658],[363,28050,26084],{"className":28051,"style":26208},[407,408,658],[363,28053,666],{"className":28054},[665],[363,28056,28058],{"className":28057},[638],[363,28059,28061],{"className":28060,"style":8315},[642],[363,28062],{},[363,28064,461],{"className":28065},[494],[363,28067,1116],{"className":28068},[407,408],[363,28070,468],{"className":28071},[501],[363,28073],{"className":28074,"style":506},[505],[363,28076,471],{"className":28077},[510],[363,28079],{"className":28080,"style":506},[505],[363,28082,28084,28087,28149,28152,28349,28352],{"className":28083},[398],[363,28085],{"className":28086,"style":707},[402],[363,28088,28090,28093,28146],{"className":28089},[407],[363,28091],{"className":28092},[494,789],[363,28094,28096],{"className":28095},[586],[363,28097,28099,28138],{"className":28098},[633,634],[363,28100,28102,28135],{"className":28101},[638],[363,28103,28105,28116,28124],{"className":28104,"style":23236},[642],[363,28106,28107,28110],{"style":805},[363,28108],{"className":28109,"style":809},[650],[363,28111,28113],{"className":28112},[407],[363,28114,2810],{"className":28115},[407],[363,28117,28118,28121],{"style":821},[363,28119],{"className":28120,"style":809},[650],[363,28122],{"className":28123,"style":829},[828],[363,28125,28126,28129],{"style":832},[363,28127],{"className":28128,"style":809},[650],[363,28130,28132],{"className":28131},[407],[363,28133,465],{"className":28134},[407],[363,28136,666],{"className":28137},[665],[363,28139,28141],{"className":28140},[638],[363,28142,28144],{"className":28143,"style":4125},[642],[363,28145],{},[363,28147],{"className":28148},[501,789],[363,28150],{"className":28151,"style":754},[505],[363,28153,28155,28161,28164,28167,28172,28175,28252,28255,28258,28261,28266,28269,28343],{"className":28154},[758],[363,28156,28158],{"className":28157,"style":763},[494,762],[363,28159,578],{"className":28160},[767,657],[363,28162,1116],{"className":28163},[407,408],[363,28165],{"className":28166,"style":754},[505],[363,28168,4501,28170],{"className":28169},[1831],[363,28171,4505],{"style":4504},[363,28173],{"className":28174,"style":754},[505],[363,28176,28178,28181,28249],{"className":28177},[407],[363,28179],{"className":28180},[494,789],[363,28182,28184],{"className":28183},[586],[363,28185,28187,28241],{"className":28186},[633,634],[363,28188,28190,28238],{"className":28189},[638],[363,28191,28193,28216,28224],{"className":28192,"style":23236},[642],[363,28194,28195,28198],{"style":805},[363,28196],{"className":28197,"style":809},[650],[363,28199,28201,28204,28207,28210,28213],{"className":28200},[407],[363,28202,1116],{"className":28203},[407,408],[363,28205],{"className":28206,"style":2934},[505],[363,28208,2817],{"className":28209},[2938],[363,28211],{"className":28212,"style":2934},[505],[363,28214,465],{"className":28215},[407],[363,28217,28218,28221],{"style":821},[363,28219],{"className":28220,"style":809},[650],[363,28222],{"className":28223,"style":829},[828],[363,28225,28226,28229],{"style":832},[363,28227],{"className":28228,"style":809},[650],[363,28230,28232,28235],{"className":28231},[407],[363,28233,2810],{"className":28234},[407],[363,28236,1116],{"className":28237},[407,408],[363,28239,666],{"className":28240},[665],[363,28242,28244],{"className":28243},[638],[363,28245,28247],{"className":28246,"style":17362},[642],[363,28248],{},[363,28250],{"className":28251},[501,789],[363,28253],{"className":28254,"style":2934},[505],[363,28256,2817],{"className":28257},[2938],[363,28259],{"className":28260,"style":2934},[505],[363,28262,4501,28264],{"className":28263},[1831],[363,28265,4505],{"style":4504},[363,28267],{"className":28268,"style":754},[505],[363,28270,28272,28275,28340],{"className":28271},[407],[363,28273],{"className":28274},[494,789],[363,28276,28278],{"className":28277},[586],[363,28279,28281,28332],{"className":28280},[633,634],[363,28282,28284,28329],{"className":28283},[638],[363,28285,28287,28310,28318],{"className":28286,"style":23236},[642],[363,28288,28289,28292],{"style":805},[363,28290],{"className":28291,"style":809},[650],[363,28293,28295,28298,28301,28304,28307],{"className":28294},[407],[363,28296,1116],{"className":28297},[407,408],[363,28299],{"className":28300,"style":2934},[505],[363,28302,2817],{"className":28303},[2938],[363,28305],{"className":28306,"style":2934},[505],[363,28308,465],{"className":28309},[407],[363,28311,28312,28315],{"style":821},[363,28313],{"className":28314,"style":809},[650],[363,28316],{"className":28317,"style":829},[828],[363,28319,28320,28323],{"style":832},[363,28321],{"className":28322,"style":809},[650],[363,28324,28326],{"className":28325},[407],[363,28327,2810],{"className":28328},[407],[363,28330,666],{"className":28331},[665],[363,28333,28335],{"className":28334},[638],[363,28336,28338],{"className":28337,"style":17362},[642],[363,28339],{},[363,28341],{"className":28342},[501,789],[363,28344,28346],{"className":28345,"style":763},[501,762],[363,28347,605],{"className":28348},[767,657],[363,28350],{"className":28351,"style":754},[505],[363,28353,4722],{"className":28354},[407],[11,28356,28357],{},"整理得",[363,28359,28361],{"className":28360,"translate":367},[528],[363,28362,28364,28456],{"className":28363,"translate":367},[366],[363,28365,28367],{"className":28366},[371],[373,28368,28369],{"xmlns":375,"display":537},[377,28370,28371,28453],{},[380,28372,28373],{},[28374,28375,28377],"menclose",{"notation":28376},"box",[1602,28378,28379],{"scriptlevel":474,"displaystyle":460},[1602,28380,28381],{"scriptlevel":474,"displaystyle":460},[1602,28382,28383],{"scriptlevel":474,"displaystyle":394},[380,28384,28385,28387,28397,28399,28401,28403,28405,28411,28413,28415,28417,28419,28421,28423,28425,28427,28429,28431,28433,28435,28437,28449,28451],{},[1644,28386,16251],{},[543,28388,28389,28391],{},[383,28390,385],{},[380,28392,28393,28395],{},[383,28394,24090],{},[383,28396,26084],{},[458,28398,461],{"stretchy":460},[383,28400,1116],{},[458,28402,468],{"stretchy":460},[458,28404,471],{},[586,28406,28407,28409],{},[463,28408,465],{},[463,28410,2810],{},[458,28412,578],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[383,28414,1116],{},[383,28416,4447],{},[458,28418,4450],{},[383,28420,1116],{},[458,28422,5160],{},[458,28424,461],{"stretchy":460},[383,28426,1116],{},[458,28428,2817],{},[463,28430,465],{},[458,28432,468],{"stretchy":460},[383,28434,4447],{},[458,28436,4450],{},[586,28438,28439,28447],{},[380,28440,28441,28443,28445],{},[383,28442,1116],{},[458,28444,2817],{},[463,28446,465],{},[463,28448,2810],{},[458,28450,605],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[1644,28452,16251],{},[387,28454,28455],{"encoding":389},"\\boxed{\\;\nf_{JS}(t)=\\frac12\\Big[\nt\\log t-(t+1)\\log\\frac{t+1}{2}\\Big]\n\\;}",[363,28457,28459],{"className":28458,"ariaHidden":394},[393],[363,28460,28462,28466],{"className":28461},[398],[363,28463],{"className":28464,"style":28465},[402],"height:2.6874em;vertical-align:-1.026em;",[363,28467,28469],{"className":28468},[407],[363,28470,28472,28786],{"className":28471},[633,634],[363,28473,28475,28783],{"className":28474},[638],[363,28476,28479,28772],{"className":28477,"style":28478},[642],"height:1.6614em;",[363,28480,28482,28486],{"style":28481},"top:-4.6874em;",[363,28483],{"className":28484,"style":28485},[650],"height:4.6874em;",[363,28487,28490],{"className":28488},[28489],"boxpad",[363,28491,28493],{"className":28492},[407],[363,28494,28496,28499,28545,28548,28551,28554,28557,28560,28563,28625,28631,28634,28637,28642,28645,28648,28651,28654,28657,28660,28663,28666,28669,28672,28675,28678,28681,28686,28689,28763,28769],{"className":28495},[407],[363,28497],{"className":28498,"style":506},[505],[363,28500,28502,28505],{"className":28501},[407],[363,28503,385],{"className":28504,"style":409},[407,408],[363,28506,28508],{"className":28507},[629],[363,28509,28511,28537],{"className":28510},[633,634],[363,28512,28514,28534],{"className":28513},[638],[363,28515,28517],{"className":28516,"style":727},[642],[363,28518,28519,28522],{"style":27856},[363,28520],{"className":28521,"style":651},[650],[363,28523,28525],{"className":28524},[655,656,657,658],[363,28526,28528,28531],{"className":28527},[407,658],[363,28529,24090],{"className":28530,"style":24500},[407,408,658],[363,28532,26084],{"className":28533,"style":26208},[407,408,658],[363,28535,666],{"className":28536},[665],[363,28538,28540],{"className":28539},[638],[363,28541,28543],{"className":28542,"style":8315},[642],[363,28544],{},[363,28546,461],{"className":28547},[494],[363,28549,1116],{"className":28550},[407,408],[363,28552,468],{"className":28553},[501],[363,28555],{"className":28556,"style":506},[505],[363,28558,471],{"className":28559},[510],[363,28561],{"className":28562,"style":506},[505],[363,28564,28566,28569,28622],{"className":28565},[407],[363,28567],{"className":28568},[494,789],[363,28570,28572],{"className":28571},[586],[363,28573,28575,28614],{"className":28574},[633,634],[363,28576,28578,28611],{"className":28577},[638],[363,28579,28581,28592,28600],{"className":28580,"style":23236},[642],[363,28582,28583,28586],{"style":805},[363,28584],{"className":28585,"style":809},[650],[363,28587,28589],{"className":28588},[407],[363,28590,2810],{"className":28591},[407],[363,28593,28594,28597],{"style":821},[363,28595],{"className":28596,"style":809},[650],[363,28598],{"className":28599,"style":829},[828],[363,28601,28602,28605],{"style":832},[363,28603],{"className":28604,"style":809},[650],[363,28606,28608],{"className":28607},[407],[363,28609,465],{"className":28610},[407],[363,28612,666],{"className":28613},[665],[363,28615,28617],{"className":28616},[638],[363,28618,28620],{"className":28619,"style":4125},[642],[363,28621],{},[363,28623],{"className":28624},[501,789],[363,28626,28628],{"className":28627},[407],[363,28629,578],{"className":28630},[767,4067],[363,28632,1116],{"className":28633},[407,408],[363,28635],{"className":28636,"style":754},[505],[363,28638,4501,28640],{"className":28639},[1831],[363,28641,4505],{"style":4504},[363,28643],{"className":28644,"style":754},[505],[363,28646,1116],{"className":28647},[407,408],[363,28649],{"className":28650,"style":2934},[505],[363,28652,5160],{"className":28653},[2938],[363,28655],{"className":28656,"style":2934},[505],[363,28658,461],{"className":28659},[494],[363,28661,1116],{"className":28662},[407,408],[363,28664],{"className":28665,"style":2934},[505],[363,28667,2817],{"className":28668},[2938],[363,28670],{"className":28671,"style":2934},[505],[363,28673,465],{"className":28674},[407],[363,28676,468],{"className":28677},[501],[363,28679],{"className":28680,"style":754},[505],[363,28682,4501,28684],{"className":28683},[1831],[363,28685,4505],{"style":4504},[363,28687],{"className":28688,"style":754},[505],[363,28690,28692,28695,28760],{"className":28691},[407],[363,28693],{"className":28694},[494,789],[363,28696,28698],{"className":28697},[586],[363,28699,28701,28752],{"className":28700},[633,634],[363,28702,28704,28749],{"className":28703},[638],[363,28705,28707,28718,28726],{"className":28706,"style":23236},[642],[363,28708,28709,28712],{"style":805},[363,28710],{"className":28711,"style":809},[650],[363,28713,28715],{"className":28714},[407],[363,28716,2810],{"className":28717},[407],[363,28719,28720,28723],{"style":821},[363,28721],{"className":28722,"style":809},[650],[363,28724],{"className":28725,"style":829},[828],[363,28727,28728,28731],{"style":832},[363,28729],{"className":28730,"style":809},[650],[363,28732,28734,28737,28740,28743,28746],{"className":28733},[407],[363,28735,1116],{"className":28736},[407,408],[363,28738],{"className":28739,"style":2934},[505],[363,28741,2817],{"className":28742},[2938],[363,28744],{"className":28745,"style":2934},[505],[363,28747,465],{"className":28748},[407],[363,28750,666],{"className":28751},[665],[363,28753,28755],{"className":28754},[638],[363,28756,28758],{"className":28757,"style":4125},[642],[363,28759],{},[363,28761],{"className":28762},[501,789],[363,28764,28766],{"className":28765},[407],[363,28767,605],{"className":28768},[767,4067],[363,28770],{"className":28771,"style":506},[505],[363,28773,28775,28778],{"style":28774},"top:-3.6614em;",[363,28776],{"className":28777,"style":28485},[650],[363,28779],{"className":28780,"style":28782},[6662,28781],"fbox","height:2.6874em;border-style:solid;border-width:0.04em;",[363,28784,666],{"className":28785},[665],[363,28787,28789],{"className":28788},[638],[363,28790,28793],{"className":28791,"style":28792},[642],"height:1.026em;",[363,28794],{},[11,28796,28797,28798,29063],{},"它满足 ",[363,28799,28801,28857],{"className":28800,"translate":367},[366],[363,28802,28804],{"className":28803},[371],[373,28805,28806],{"xmlns":375},[377,28807,28808,28854],{},[380,28809,28810,28820,28822,28824,28826,28828,28834,28836,28838,28840,28842,28844,28846,28848,28850,28852],{},[543,28811,28812,28814],{},[383,28813,385],{},[380,28815,28816,28818],{},[383,28817,24090],{},[383,28819,26084],{},[458,28821,461],{"stretchy":460},[463,28823,465],{},[458,28825,468],{"stretchy":460},[458,28827,471],{},[586,28829,28830,28832],{},[463,28831,465],{},[463,28833,2810],{},[458,28835,578],{"stretchy":460},[463,28837,474],{},[458,28839,5160],{},[463,28841,2810],{},[383,28843,4447],{},[458,28845,4450],{},[463,28847,465],{},[458,28849,605],{"stretchy":460},[458,28851,471],{},[463,28853,474],{},[387,28855,28856],{"encoding":389},"f_{JS}(1)=\\frac12[0-2\\log1]=0",[363,28858,28860,28930,29019,29054],{"className":28859,"ariaHidden":394},[393],[363,28861,28863,28866,28912,28915,28918,28921,28924,28927],{"className":28862},[398],[363,28864],{"className":28865,"style":487},[402],[363,28867,28869,28872],{"className":28868},[407],[363,28870,385],{"className":28871,"style":409},[407,408],[363,28873,28875],{"className":28874},[629],[363,28876,28878,28904],{"className":28877},[633,634],[363,28879,28881,28901],{"className":28880},[638],[363,28882,28884],{"className":28883,"style":727},[642],[363,28885,28886,28889],{"style":27856},[363,28887],{"className":28888,"style":651},[650],[363,28890,28892],{"className":28891},[655,656,657,658],[363,28893,28895,28898],{"className":28894},[407,658],[363,28896,24090],{"className":28897,"style":24500},[407,408,658],[363,28899,26084],{"className":28900,"style":26208},[407,408,658],[363,28902,666],{"className":28903},[665],[363,28905,28907],{"className":28906},[638],[363,28908,28910],{"className":28909,"style":8315},[642],[363,28911],{},[363,28913,461],{"className":28914},[494],[363,28916,465],{"className":28917},[407],[363,28919,468],{"className":28920},[501],[363,28922],{"className":28923,"style":506},[505],[363,28925,471],{"className":28926},[510],[363,28928],{"className":28929,"style":506},[505],[363,28931,28933,28936,29004,29007,29010,29013,29016],{"className":28932},[398],[363,28934],{"className":28935,"style":2852},[402],[363,28937,28939,28942,29001],{"className":28938},[407],[363,28940],{"className":28941},[494,789],[363,28943,28945],{"className":28944},[586],[363,28946,28948,28993],{"className":28947},[633,634],[363,28949,28951,28990],{"className":28950},[638],[363,28952,28954,28968,28976],{"className":28953,"style":2871},[642],[363,28955,28956,28959],{"style":2874},[363,28957],{"className":28958,"style":809},[650],[363,28960,28962],{"className":28961},[655,656,657,658],[363,28963,28965],{"className":28964},[407,658],[363,28966,2810],{"className":28967},[407,658],[363,28969,28970,28973],{"style":821},[363,28971],{"className":28972,"style":809},[650],[363,28974],{"className":28975,"style":829},[828],[363,28977,28978,28981],{"style":2897},[363,28979],{"className":28980,"style":809},[650],[363,28982,28984],{"className":28983},[655,656,657,658],[363,28985,28987],{"className":28986},[407,658],[363,28988,465],{"className":28989},[407,658],[363,28991,666],{"className":28992},[665],[363,28994,28996],{"className":28995},[638],[363,28997,28999],{"className":28998,"style":2919},[642],[363,29000],{},[363,29002],{"className":29003},[501,789],[363,29005,578],{"className":29006},[494],[363,29008,474],{"className":29009},[407],[363,29011],{"className":29012,"style":2934},[505],[363,29014,5160],{"className":29015},[2938],[363,29017],{"className":29018,"style":2934},[505],[363,29020,29022,29025,29028,29031,29036,29039,29042,29045,29048,29051],{"className":29021},[398],[363,29023],{"className":29024,"style":487},[402],[363,29026,2810],{"className":29027},[407],[363,29029],{"className":29030,"style":754},[505],[363,29032,4501,29034],{"className":29033},[1831],[363,29035,4505],{"style":4504},[363,29037],{"className":29038,"style":754},[505],[363,29040,465],{"className":29041},[407],[363,29043,605],{"className":29044},[501],[363,29046],{"className":29047,"style":506},[505],[363,29049,471],{"className":29050},[510],[363,29052],{"className":29053,"style":506},[505],[363,29055,29057,29060],{"className":29056},[398],[363,29058],{"className":29059,"style":520},[402],[363,29061,474],{"className":29062},[407],"，且",[363,29065,29067],{"className":29066,"translate":367},[528],[363,29068,29070,29262],{"className":29069,"translate":367},[366],[363,29071,29073],{"className":29072},[371],[373,29074,29075],{"xmlns":375,"display":537},[377,29076,29077,29259],{},[1590,29078,29079,29143,29213],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,29080,29081,29105],{},[1599,29082,29083],{},[1602,29084,29085],{"scriptlevel":474,"displaystyle":394},[380,29086,29087,29099,29101,29103],{},[7900,29088,29089,29091,29097],{},[383,29090,385],{},[380,29092,29093,29095],{},[383,29094,24090],{},[383,29096,26084],{},[458,29098,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,29100,461],{"stretchy":460},[383,29102,1116],{},[458,29104,468],{"stretchy":460},[1599,29106,29107],{},[1602,29108,29109],{"scriptlevel":474,"displaystyle":394},[380,29110,29111,29113,29115,29121,29123,29125,29141],{},[380,29112],{},[458,29114,471],{},[586,29116,29117,29119],{},[463,29118,465],{},[463,29120,2810],{},[383,29122,4447],{},[458,29124,4450],{},[586,29126,29127,29133],{},[380,29128,29129,29131],{},[463,29130,2810],{},[383,29132,1116],{},[380,29134,29135,29137,29139],{},[383,29136,1116],{},[458,29138,2817],{},[463,29140,465],{},[458,29142,898],{"separator":394},[1596,29144,29145,29173],{},[1599,29146,29147],{},[1602,29148,29149],{"scriptlevel":474,"displaystyle":394},[380,29150,29151,29167,29169,29171],{},[7900,29152,29153,29155,29161],{},[383,29154,385],{},[380,29156,29157,29159],{},[383,29158,24090],{},[383,29160,26084],{},[380,29162,29163,29165],{},[458,29164,7167],{"mathvariant":557},[458,29166,7167],{"mathvariant":557},[458,29168,461],{"stretchy":460},[383,29170,1116],{},[458,29172,468],{"stretchy":460},[1599,29174,29175],{},[1602,29176,29177],{"scriptlevel":474,"displaystyle":394},[380,29178,29179,29181,29183,29189,29191,29197,29199,29211],{},[380,29180],{},[458,29182,471],{},[586,29184,29185,29187],{},[463,29186,465],{},[463,29188,2810],{},[458,29190,461],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[586,29192,29193,29195],{},[463,29194,465],{},[383,29196,1116],{},[458,29198,5160],{},[586,29200,29201,29203],{},[463,29202,465],{},[380,29204,29205,29207,29209],{},[383,29206,1116],{},[458,29208,2817],{},[463,29210,465],{},[458,29212,468],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[1596,29214,29215,29221],{},[1599,29216,29217],{},[1602,29218,29219],{"scriptlevel":474,"displaystyle":394},[380,29220],{},[1599,29222,29223],{},[1602,29224,29225],{"scriptlevel":474,"displaystyle":394},[380,29226,29227,29229,29231,29233,29253,29255,29257],{},[380,29228],{},[505,29230],{"width":3609},[458,29232,471],{},[586,29234,29235,29237],{},[463,29236,465],{},[380,29238,29239,29241,29243,29245,29247,29249,29251],{},[463,29240,2810],{},[383,29242,1116],{},[458,29244,461],{"stretchy":460},[383,29246,1116],{},[458,29248,2817],{},[463,29250,465],{},[458,29252,468],{"stretchy":460},[458,29254,3250],{},[463,29256,474],{},[458,29258,898],{"separator":394},[387,29260,29261],{"encoding":389},"\\begin{aligned}\nf_{JS}'(t)&=\\frac12\\log\\frac{2t}{t+1},\\\\[2pt]\nf_{JS}''(t)&=\\frac12\\Big(\n\\frac1t-\\frac1{t+1}\\Big)\\\\\n&\\qquad=\\frac{1}{2t(t+1)}>0,\n\\end{aligned}",[363,29263,29265],{"className":29264,"ariaHidden":394},[393],[363,29266,29268,29272],{"className":29267},[398],[363,29269],{"className":29270,"style":29271},[402],"height:7.039em;vertical-align:-3.2695em;",[363,29273,29275],{"className":29274},[407],[363,29276,29278,29469],{"className":29277},[1590],[363,29279,29281],{"className":29280},[1707],[363,29282,29284,29460],{"className":29283},[633,634],[363,29285,29287,29457],{"className":29286},[638],[363,29288,29291,29370,29448],{"className":29289,"style":29290},[642],"height:3.7695em;",[363,29292,29294,29297],{"style":29293},"top:-5.7695em;",[363,29295],{"className":29296,"style":23013},[650],[363,29298,29300,29361,29364,29367],{"className":29299},[407],[363,29301,29303,29306],{"className":29302},[407],[363,29304,385],{"className":29305,"style":409},[407,408],[363,29307,29309],{"className":29308},[629],[363,29310,29312,29353],{"className":29311},[633,634],[363,29313,29315,29350],{"className":29314},[638],[363,29316,29319,29336],{"className":29317,"style":29318},[642],"height:0.8019em;",[363,29320,29321,29324],{"style":8598},[363,29322],{"className":29323,"style":651},[650],[363,29325,29327],{"className":29326},[655,656,657,658],[363,29328,29330,29333],{"className":29329},[407,658],[363,29331,24090],{"className":29332,"style":24500},[407,408,658],[363,29334,26084],{"className":29335,"style":26208},[407,408,658],[363,29337,29338,29341],{"style":8624},[363,29339],{"className":29340,"style":651},[650],[363,29342,29344],{"className":29343},[655,656,657,658],[363,29345,29347],{"className":29346},[407,658],[363,29348,7167],{"className":29349},[407,658],[363,29351,666],{"className":29352},[665],[363,29354,29356],{"className":29355},[638],[363,29357,29359],{"className":29358,"style":8646},[642],[363,29360],{},[363,29362,461],{"className":29363},[494],[363,29365,1116],{"className":29366},[407,408],[363,29368,468],{"className":29369},[501],[363,29371,29373,29376],{"style":29372},"top:-3.3787em;",[363,29374],{"className":29375,"style":23013},[650],[363,29377,29379,29439,29442,29445],{"className":29378},[407],[363,29380,29382,29385],{"className":29381},[407],[363,29383,385],{"className":29384,"style":409},[407,408],[363,29386,29388],{"className":29387},[629],[363,29389,29391,29431],{"className":29390},[633,634],[363,29392,29394,29428],{"className":29393},[638],[363,29395,29397,29414],{"className":29396,"style":29318},[642],[363,29398,29399,29402],{"style":8598},[363,29400],{"className":29401,"style":651},[650],[363,29403,29405],{"className":29404},[655,656,657,658],[363,29406,29408,29411],{"className":29407},[407,658],[363,29409,24090],{"className":29410,"style":24500},[407,408,658],[363,29412,26084],{"className":29413,"style":26208},[407,408,658],[363,29415,29416,29419],{"style":8624},[363,29417],{"className":29418,"style":651},[650],[363,29420,29422],{"className":29421},[655,656,657,658],[363,29423,29425],{"className":29424},[407,658],[363,29426,22095],{"className":29427},[407,658],[363,29429,666],{"className":29430},[665],[363,29432,29434],{"className":29433},[638],[363,29435,29437],{"className":29436,"style":8646},[642],[363,29438],{},[363,29440,461],{"className":29441},[494],[363,29443,1116],{"className":29444},[407,408],[363,29446,468],{"className":29447},[501],[363,29449,29451,29454],{"style":29450},"top:-0.9879em;",[363,29452],{"className":29453,"style":23013},[650],[363,29455],{"className":29456},[407],[363,29458,666],{"className":29459},[665],[363,29461,29463],{"className":29462},[638],[363,29464,29467],{"className":29465,"style":29466},[642],"height:3.2695em;",[363,29468],{},[363,29470,29472],{"className":29471},[1798],[363,29473,29475,30020],{"className":29474},[633,634],[363,29476,29478,30017],{"className":29477},[638],[363,29479,29481,29654,29893],{"className":29480,"style":29290},[642],[363,29482,29483,29486],{"style":29293},[363,29484],{"className":29485,"style":23013},[650],[363,29487,29489,29492,29495,29498,29501,29563,29566,29571,29574,29651],{"className":29488},[407],[363,29490],{"className":29491},[407],[363,29493],{"className":29494,"style":506},[505],[363,29496,471],{"className":29497},[510],[363,29499],{"className":29500,"style":506},[505],[363,29502,29504,29507,29560],{"className":29503},[407],[363,29505],{"className":29506},[494,789],[363,29508,29510],{"className":29509},[586],[363,29511,29513,29552],{"className":29512},[633,634],[363,29514,29516,29549],{"className":29515},[638],[363,29517,29519,29530,29538],{"className":29518,"style":23236},[642],[363,29520,29521,29524],{"style":805},[363,29522],{"className":29523,"style":809},[650],[363,29525,29527],{"className":29526},[407],[363,29528,2810],{"className":29529},[407],[363,29531,29532,29535],{"style":821},[363,29533],{"className":29534,"style":809},[650],[363,29536],{"className":29537,"style":829},[828],[363,29539,29540,29543],{"style":832},[363,29541],{"className":29542,"style":809},[650],[363,29544,29546],{"className":29545},[407],[363,29547,465],{"className":29548},[407],[363,29550,666],{"className":29551},[665],[363,29553,29555],{"className":29554},[638],[363,29556,29558],{"className":29557,"style":4125},[642],[363,29559],{},[363,29561],{"className":29562},[501,789],[363,29564],{"className":29565,"style":754},[505],[363,29567,4501,29569],{"className":29568},[1831],[363,29570,4505],{"style":4504},[363,29572],{"className":29573,"style":754},[505],[363,29575,29577,29580,29648],{"className":29576},[407],[363,29578],{"className":29579},[494,789],[363,29581,29583],{"className":29582},[586],[363,29584,29586,29640],{"className":29585},[633,634],[363,29587,29589,29637],{"className":29588},[638],[363,29590,29592,29615,29623],{"className":29591,"style":23236},[642],[363,29593,29594,29597],{"style":805},[363,29595],{"className":29596,"style":809},[650],[363,29598,29600,29603,29606,29609,29612],{"className":29599},[407],[363,29601,1116],{"className":29602},[407,408],[363,29604],{"className":29605,"style":2934},[505],[363,29607,2817],{"className":29608},[2938],[363,29610],{"className":29611,"style":2934},[505],[363,29613,465],{"className":29614},[407],[363,29616,29617,29620],{"style":821},[363,29618],{"className":29619,"style":809},[650],[363,29621],{"className":29622,"style":829},[828],[363,29624,29625,29628],{"style":832},[363,29626],{"className":29627,"style":809},[650],[363,29629,29631,29634],{"className":29630},[407],[363,29632,2810],{"className":29633},[407],[363,29635,1116],{"className":29636},[407,408],[363,29638,666],{"className":29639},[665],[363,29641,29643],{"className":29642},[638],[363,29644,29646],{"className":29645,"style":17362},[642],[363,29647],{},[363,29649],{"className":29650},[501,789],[363,29652,898],{"className":29653},[920],[363,29655,29656,29659],{"style":29372},[363,29657],{"className":29658,"style":23013},[650],[363,29660,29662,29665,29668,29671,29674,29736,29742,29804,29807,29810,29813,29887],{"className":29661},[407],[363,29663],{"className":29664},[407],[363,29666],{"className":29667,"style":506},[505],[363,29669,471],{"className":29670},[510],[363,29672],{"className":29673,"style":506},[505],[363,29675,29677,29680,29733],{"className":29676},[407],[363,29678],{"className":29679},[494,789],[363,29681,29683],{"className":29682},[586],[363,29684,29686,29725],{"className":29685},[633,634],[363,29687,29689,29722],{"className":29688},[638],[363,29690,29692,29703,29711],{"className":29691,"style":23236},[642],[363,29693,29694,29697],{"style":805},[363,29695],{"className":29696,"style":809},[650],[363,29698,29700],{"className":29699},[407],[363,29701,2810],{"className":29702},[407],[363,29704,29705,29708],{"style":821},[363,29706],{"className":29707,"style":809},[650],[363,29709],{"className":29710,"style":829},[828],[363,29712,29713,29716],{"style":832},[363,29714],{"className":29715,"style":809},[650],[363,29717,29719],{"className":29718},[407],[363,29720,465],{"className":29721},[407],[363,29723,666],{"className":29724},[665],[363,29726,29728],{"className":29727},[638],[363,29729,29731],{"className":29730,"style":4125},[642],[363,29732],{},[363,29734],{"className":29735},[501,789],[363,29737,29739],{"className":29738},[407],[363,29740,461],{"className":29741},[767,4067],[363,29743,29745,29748,29801],{"className":29744},[407],[363,29746],{"className":29747},[494,789],[363,29749,29751],{"className":29750},[586],[363,29752,29754,29793],{"className":29753},[633,634],[363,29755,29757,29790],{"className":29756},[638],[363,29758,29760,29771,29779],{"className":29759,"style":23236},[642],[363,29761,29762,29765],{"style":805},[363,29763],{"className":29764,"style":809},[650],[363,29766,29768],{"className":29767},[407],[363,29769,1116],{"className":29770},[407,408],[363,29772,29773,29776],{"style":821},[363,29774],{"className":29775,"style":809},[650],[363,29777],{"className":29778,"style":829},[828],[363,29780,29781,29784],{"style":832},[363,29782],{"className":29783,"style":809},[650],[363,29785,29787],{"className":29786},[407],[363,29788,465],{"className":29789},[407],[363,29791,666],{"className":29792},[665],[363,29794,29796],{"className":29795},[638],[363,29797,29799],{"className":29798,"style":4125},[642],[363,29800],{},[363,29802],{"className":29803},[501,789],[363,29805],{"className":29806,"style":2934},[505],[363,29808,5160],{"className":29809},[2938],[363,29811],{"className":29812,"style":2934},[505],[363,29814,29816,29819,29884],{"className":29815},[407],[363,29817],{"className":29818},[494,789],[363,29820,29822],{"className":29821},[586],[363,29823,29825,29876],{"className":29824},[633,634],[363,29826,29828,29873],{"className":29827},[638],[363,29829,29831,29854,29862],{"className":29830,"style":23236},[642],[363,29832,29833,29836],{"style":805},[363,29834],{"className":29835,"style":809},[650],[363,29837,29839,29842,29845,29848,29851],{"className":29838},[407],[363,29840,1116],{"className":29841},[407,408],[363,29843],{"className":29844,"style":2934},[505],[363,29846,2817],{"className":29847},[2938],[363,29849],{"className":29850,"style":2934},[505],[363,29852,465],{"className":29853},[407],[363,29855,29856,29859],{"style":821},[363,29857],{"className":29858,"style":809},[650],[363,29860],{"className":29861,"style":829},[828],[363,29863,29864,29867],{"style":832},[363,29865],{"className":29866,"style":809},[650],[363,29868,29870],{"className":29869},[407],[363,29871,465],{"className":29872},[407],[363,29874,666],{"className":29875},[665],[363,29877,29879],{"className":29878},[638],[363,29880,29882],{"className":29881,"style":17362},[642],[363,29883],{},[363,29885],{"className":29886},[501,789],[363,29888,29890],{"className":29889},[407],[363,29891,468],{"className":29892},[767,4067],[363,29894,29895,29898],{"style":29450},[363,29896],{"className":29897,"style":23013},[650],[363,29899,29901,29904,29907,29910,29913,29916,30002,30005,30008,30011,30014],{"className":29900},[407],[363,29902],{"className":29903},[407],[363,29905],{"className":29906,"style":3981},[505],[363,29908],{"className":29909,"style":506},[505],[363,29911,471],{"className":29912},[510],[363,29914],{"className":29915,"style":506},[505],[363,29917,29919,29922,29999],{"className":29918},[407],[363,29920],{"className":29921},[494,789],[363,29923,29925],{"className":29924},[586],[363,29926,29928,29991],{"className":29927},[633,634],[363,29929,29931,29988],{"className":29930},[638],[363,29932,29934,29969,29977],{"className":29933,"style":23236},[642],[363,29935,29936,29939],{"style":805},[363,29937],{"className":29938,"style":809},[650],[363,29940,29942,29945,29948,29951,29954,29957,29960,29963,29966],{"className":29941},[407],[363,29943,2810],{"className":29944},[407],[363,29946,1116],{"className":29947},[407,408],[363,29949,461],{"className":29950},[494],[363,29952,1116],{"className":29953},[407,408],[363,29955],{"className":29956,"style":2934},[505],[363,29958,2817],{"className":29959},[2938],[363,29961],{"className":29962,"style":2934},[505],[363,29964,465],{"className":29965},[407],[363,29967,468],{"className":29968},[501],[363,29970,29971,29974],{"style":821},[363,29972],{"className":29973,"style":809},[650],[363,29975],{"className":29976,"style":829},[828],[363,29978,29979,29982],{"style":832},[363,29980],{"className":29981,"style":809},[650],[363,29983,29985],{"className":29984},[407],[363,29986,465],{"className":29987},[407],[363,29989,666],{"className":29990},[665],[363,29992,29994],{"className":29993},[638],[363,29995,29997],{"className":29996,"style":1948},[642],[363,29998],{},[363,30000],{"className":30001},[501,789],[363,30003],{"className":30004,"style":506},[505],[363,30006,3250],{"className":30007},[510],[363,30009],{"className":30010,"style":506},[505],[363,30012,474],{"className":30013},[407],[363,30015,898],{"className":30016},[920],[363,30018,666],{"className":30019},[665],[363,30021,30023],{"className":30022},[638],[363,30024,30026],{"className":30025,"style":29466},[642],[363,30027],{},[11,30029,30030,30031,6841,30034,30229,30230,30280],{},"故凸；并且",[1572,30032,30033],{},"对称",[363,30035,30037,30089],{"className":30036,"translate":367},[366],[363,30038,30040],{"className":30039},[371],[373,30041,30042],{"xmlns":375},[377,30043,30044,30086],{},[380,30045,30046,30048,30058,30060,30062,30064,30066,30068,30070,30080,30082,30084],{},[383,30047,1116],{},[543,30049,30050,30052],{},[383,30051,385],{},[380,30053,30054,30056],{},[383,30055,24090],{},[383,30057,26084],{},[458,30059,461],{"stretchy":460},[463,30061,465],{},[383,30063,1288],{"mathvariant":557},[383,30065,1116],{},[458,30067,468],{"stretchy":460},[458,30069,471],{},[543,30071,30072,30074],{},[383,30073,385],{},[380,30075,30076,30078],{},[383,30077,24090],{},[383,30079,26084],{},[458,30081,461],{"stretchy":460},[383,30083,1116],{},[458,30085,468],{"stretchy":460},[387,30087,30088],{"encoding":389},"t f_{JS}(1\u002Ft)=f_{JS}(t)",[363,30090,30092,30168],{"className":30091,"ariaHidden":394},[393],[363,30093,30095,30098,30101,30147,30150,30153,30156,30159,30162,30165],{"className":30094},[398],[363,30096],{"className":30097,"style":487},[402],[363,30099,1116],{"className":30100},[407,408],[363,30102,30104,30107],{"className":30103},[407],[363,30105,385],{"className":30106,"style":409},[407,408],[363,30108,30110],{"className":30109},[629],[363,30111,30113,30139],{"className":30112},[633,634],[363,30114,30116,30136],{"className":30115},[638],[363,30117,30119],{"className":30118,"style":727},[642],[363,30120,30121,30124],{"style":27856},[363,30122],{"className":30123,"style":651},[650],[363,30125,30127],{"className":30126},[655,656,657,658],[363,30128,30130,30133],{"className":30129},[407,658],[363,30131,24090],{"className":30132,"style":24500},[407,408,658],[363,30134,26084],{"className":30135,"style":26208},[407,408,658],[363,30137,666],{"className":30138},[665],[363,30140,30142],{"className":30141},[638],[363,30143,30145],{"className":30144,"style":8315},[642],[363,30146],{},[363,30148,461],{"className":30149},[494],[363,30151,8936],{"className":30152},[407],[363,30154,1116],{"className":30155},[407,408],[363,30157,468],{"className":30158},[501],[363,30160],{"className":30161,"style":506},[505],[363,30163,471],{"className":30164},[510],[363,30166],{"className":30167,"style":506},[505],[363,30169,30171,30174,30220,30223,30226],{"className":30170},[398],[363,30172],{"className":30173,"style":487},[402],[363,30175,30177,30180],{"className":30176},[407],[363,30178,385],{"className":30179,"style":409},[407,408],[363,30181,30183],{"className":30182},[629],[363,30184,30186,30212],{"className":30185},[633,634],[363,30187,30189,30209],{"className":30188},[638],[363,30190,30192],{"className":30191,"style":727},[642],[363,30193,30194,30197],{"style":27856},[363,30195],{"className":30196,"style":651},[650],[363,30198,30200],{"className":30199},[655,656,657,658],[363,30201,30203,30206],{"className":30202},[407,658],[363,30204,24090],{"className":30205,"style":24500},[407,408,658],[363,30207,26084],{"className":30208,"style":26208},[407,408,658],[363,30210,666],{"className":30211},[665],[363,30213,30215],{"className":30214},[638],[363,30216,30218],{"className":30217,"style":8315},[642],[363,30219],{},[363,30221,461],{"className":30222},[494],[363,30224,1116],{"className":30225},[407,408],[363,30227,468],{"className":30228},[501],"。因此当 ",[363,30231,30233,30250],{"className":30232,"translate":367},[366],[363,30234,30236],{"className":30235},[371],[373,30237,30238],{"xmlns":375},[377,30239,30240,30248],{},[380,30241,30242,30244,30246],{},[383,30243,554],{},[458,30245,1061],{},[383,30247,561],{},[387,30249,1066],{"encoding":389},[363,30251,30253,30271],{"className":30252,"ariaHidden":394},[393],[363,30254,30256,30259,30262,30265,30268],{"className":30255},[398],[363,30257],{"className":30258,"style":1076},[402],[363,30260,554],{"className":30261,"style":682},[407,408],[363,30263],{"className":30264,"style":506},[505],[363,30266,1061],{"className":30267},[510],[363,30269],{"className":30270,"style":506},[505],[363,30272,30274,30277],{"className":30273},[398],[363,30275],{"className":30276,"style":913},[402],[363,30278,561],{"className":30279},[407,408]," 时",[363,30282,30284],{"className":30283,"translate":367},[528],[363,30285,30287,30415],{"className":30286,"translate":367},[366],[363,30288,30290],{"className":30289},[371],[373,30291,30292],{"xmlns":375,"display":537},[377,30293,30294,30412],{},[380,30295,30296,30306,30308,30310,30312,30314,30316,30318,30332,30334,30336,30338,30340,30342,30344,30350,30356,30358,30360,30362,30364,30366,30368,30374,30380,30382,30384,30386,30388,30390,30392,30394,30396,30398,30400,30402,30404,30406,30408,30410],{},[543,30297,30298,30300],{},[383,30299,547],{},[380,30301,30302,30304],{},[383,30303,24090],{},[383,30305,26084],{},[458,30307,461],{"stretchy":460},[383,30309,554],{},[383,30311,558],{"mathvariant":557},[383,30313,561],{},[458,30315,468],{"stretchy":460},[458,30317,471],{},[543,30319,30320,30322],{},[383,30321,547],{},[543,30323,30324,30326],{},[383,30325,385],{},[380,30327,30328,30330],{},[383,30329,24090],{},[383,30331,26084],{},[458,30333,461],{"stretchy":460},[383,30335,554],{},[383,30337,558],{"mathvariant":557},[383,30339,561],{},[458,30341,468],{"stretchy":460},[458,30343,471],{},[586,30345,30346,30348],{},[463,30347,465],{},[463,30349,2810],{},[543,30351,30352,30354],{},[383,30353,547],{},[383,30355,385],{},[458,30357,461],{"stretchy":460},[383,30359,554],{},[383,30361,558],{"mathvariant":557},[383,30363,25914],{},[458,30365,468],{"stretchy":460},[458,30367,2817],{},[586,30369,30370,30372],{},[463,30371,465],{},[463,30373,2810],{},[543,30375,30376,30378],{},[383,30377,547],{},[383,30379,385],{},[458,30381,461],{"stretchy":460},[383,30383,561],{},[383,30385,558],{"mathvariant":557},[383,30387,25914],{},[458,30389,468],{"stretchy":460},[458,30391,898],{"separator":394},[505,30393],{"width":3609},[458,30395,461],{"stretchy":460},[383,30397,385],{},[458,30399,471],{},[383,30401,1116],{},[383,30403,4447],{},[458,30405,4450],{},[383,30407,1116],{},[458,30409,468],{"stretchy":460},[458,30411,898],{"separator":394},[387,30413,30414],{"encoding":389},"D_{JS}(P\\|Q)=D_{f_{JS}}(P\\|Q)\n=\\frac12D_f(P\\|M)\n+\\frac12D_f(Q\\|M),\\qquad(f=t\\log t),",[363,30416,30418,30494,30614,30746,30893],{"className":30417,"ariaHidden":394},[393],[363,30419,30421,30424,30470,30473,30476,30479,30482,30485,30488,30491],{"className":30420},[398],[363,30422],{"className":30423,"style":487},[402],[363,30425,30427,30430],{"className":30426},[407],[363,30428,547],{"className":30429,"style":625},[407,408],[363,30431,30433],{"className":30432},[629],[363,30434,30436,30462],{"className":30435},[633,634],[363,30437,30439,30459],{"className":30438},[638],[363,30440,30442],{"className":30441,"style":727},[642],[363,30443,30444,30447],{"style":646},[363,30445],{"className":30446,"style":651},[650],[363,30448,30450],{"className":30449},[655,656,657,658],[363,30451,30453,30456],{"className":30452},[407,658],[363,30454,24090],{"className":30455,"style":24500},[407,408,658],[363,30457,26084],{"className":30458,"style":26208},[407,408,658],[363,30460,666],{"className":30461},[665],[363,30463,30465],{"className":30464},[638],[363,30466,30468],{"className":30467,"style":8315},[642],[363,30469],{},[363,30471,461],{"className":30472},[494],[363,30474,554],{"className":30475,"style":682},[407,408],[363,30477,558],{"className":30478},[407],[363,30480,561],{"className":30481},[407,408],[363,30483,468],{"className":30484},[501],[363,30486],{"className":30487,"style":506},[505],[363,30489,471],{"className":30490},[510],[363,30492],{"className":30493,"style":506},[505],[363,30495,30497,30500,30590,30593,30596,30599,30602,30605,30608,30611],{"className":30496},[398],[363,30498],{"className":30499,"style":618},[402],[363,30501,30503,30506],{"className":30502},[407],[363,30504,547],{"className":30505,"style":625},[407,408],[363,30507,30509],{"className":30508},[629],[363,30510,30512,30582],{"className":30511},[633,634],[363,30513,30515,30579],{"className":30514},[638],[363,30516,30518],{"className":30517,"style":643},[642],[363,30519,30520,30523],{"style":646},[363,30521],{"className":30522,"style":651},[650],[363,30524,30526],{"className":30525},[655,656,657,658],[363,30527,30529],{"className":30528},[407,658],[363,30530,30532,30535],{"className":30531},[407,658],[363,30533,385],{"className":30534,"style":409},[407,408,658],[363,30536,30538],{"className":30537},[629],[363,30539,30541,30570],{"className":30540},[633,634],[363,30542,30544,30567],{"className":30543},[638],[363,30545,30547],{"className":30546,"style":6445},[642],[363,30548,30550,30554],{"style":30549},"top:-2.3567em;margin-left:-0.1076em;margin-right:0.0714em;",[363,30551],{"className":30552,"style":30553},[650],"height:2.5em;",[363,30555,30558],{"className":30556},[655,30557,10021,658],"reset-size3",[363,30559,30561,30564],{"className":30560},[407,658],[363,30562,24090],{"className":30563,"style":24500},[407,408,658],[363,30565,26084],{"className":30566,"style":26208},[407,408,658],[363,30568,666],{"className":30569},[665],[363,30571,30573],{"className":30572},[638],[363,30574,30577],{"className":30575,"style":30576},[642],"height:0.1433em;",[363,30578],{},[363,30580,666],{"className":30581},[665],[363,30583,30585],{"className":30584},[638],[363,30586,30588],{"className":30587,"style":673},[642],[363,30589],{},[363,30591,461],{"className":30592},[494],[363,30594,554],{"className":30595,"style":682},[407,408],[363,30597,558],{"className":30598},[407],[363,30600,561],{"className":30601},[407,408],[363,30603,468],{"className":30604},[501],[363,30606],{"className":30607,"style":506},[505],[363,30609,471],{"className":30610},[510],[363,30612],{"className":30613,"style":506},[505],[363,30615,30617,30620,30682,30722,30725,30728,30731,30734,30737,30740,30743],{"className":30616},[398],[363,30618],{"className":30619,"style":26250},[402],[363,30621,30623,30626,30679],{"className":30622},[407],[363,30624],{"className":30625},[494,789],[363,30627,30629],{"className":30628},[586],[363,30630,30632,30671],{"className":30631},[633,634],[363,30633,30635,30668],{"className":30634},[638],[363,30636,30638,30649,30657],{"className":30637,"style":23236},[642],[363,30639,30640,30643],{"style":805},[363,30641],{"className":30642,"style":809},[650],[363,30644,30646],{"className":30645},[407],[363,30647,2810],{"className":30648},[407],[363,30650,30651,30654],{"style":821},[363,30652],{"className":30653,"style":809},[650],[363,30655],{"className":30656,"style":829},[828],[363,30658,30659,30662],{"style":832},[363,30660],{"className":30661,"style":809},[650],[363,30663,30665],{"className":30664},[407],[363,30666,465],{"className":30667},[407],[363,30669,666],{"className":30670},[665],[363,30672,30674],{"className":30673},[638],[363,30675,30677],{"className":30676,"style":4125},[642],[363,30678],{},[363,30680],{"className":30681},[501,789],[363,30683,30685,30688],{"className":30684},[407],[363,30686,547],{"className":30687,"style":625},[407,408],[363,30689,30691],{"className":30690},[629],[363,30692,30694,30714],{"className":30693},[633,634],[363,30695,30697,30711],{"className":30696},[638],[363,30698,30700],{"className":30699,"style":643},[642],[363,30701,30702,30705],{"style":646},[363,30703],{"className":30704,"style":651},[650],[363,30706,30708],{"className":30707},[655,656,657,658],[363,30709,385],{"className":30710,"style":409},[407,408,658],[363,30712,666],{"className":30713},[665],[363,30715,30717],{"className":30716},[638],[363,30718,30720],{"className":30719,"style":673},[642],[363,30721],{},[363,30723,461],{"className":30724},[494],[363,30726,554],{"className":30727,"style":682},[407,408],[363,30729,558],{"className":30730},[407],[363,30732,25914],{"className":30733,"style":25948},[407,408],[363,30735,468],{"className":30736},[501],[363,30738],{"className":30739,"style":2934},[505],[363,30741,2817],{"className":30742},[2938],[363,30744],{"className":30745,"style":2934},[505],[363,30747,30749,30752,30814,30854,30857,30860,30863,30866,30869,30872,30875,30878,30881,30884,30887,30890],{"className":30748},[398],[363,30750],{"className":30751,"style":26250},[402],[363,30753,30755,30758,30811],{"className":30754},[407],[363,30756],{"className":30757},[494,789],[363,30759,30761],{"className":30760},[586],[363,30762,30764,30803],{"className":30763},[633,634],[363,30765,30767,30800],{"className":30766},[638],[363,30768,30770,30781,30789],{"className":30769,"style":23236},[642],[363,30771,30772,30775],{"style":805},[363,30773],{"className":30774,"style":809},[650],[363,30776,30778],{"className":30777},[407],[363,30779,2810],{"className":30780},[407],[363,30782,30783,30786],{"style":821},[363,30784],{"className":30785,"style":809},[650],[363,30787],{"className":30788,"style":829},[828],[363,30790,30791,30794],{"style":832},[363,30792],{"className":30793,"style":809},[650],[363,30795,30797],{"className":30796},[407],[363,30798,465],{"className":30799},[407],[363,30801,666],{"className":30802},[665],[363,30804,30806],{"className":30805},[638],[363,30807,30809],{"className":30808,"style":4125},[642],[363,30810],{},[363,30812],{"className":30813},[501,789],[363,30815,30817,30820],{"className":30816},[407],[363,30818,547],{"className":30819,"style":625},[407,408],[363,30821,30823],{"className":30822},[629],[363,30824,30826,30846],{"className":30825},[633,634],[363,30827,30829,30843],{"className":30828},[638],[363,30830,30832],{"className":30831,"style":643},[642],[363,30833,30834,30837],{"style":646},[363,30835],{"className":30836,"style":651},[650],[363,30838,30840],{"className":30839},[655,656,657,658],[363,30841,385],{"className":30842,"style":409},[407,408,658],[363,30844,666],{"className":30845},[665],[363,30847,30849],{"className":30848},[638],[363,30850,30852],{"className":30851,"style":673},[642],[363,30853],{},[363,30855,461],{"className":30856},[494],[363,30858,561],{"className":30859},[407,408],[363,30861,558],{"className":30862},[407],[363,30864,25914],{"className":30865,"style":25948},[407,408],[363,30867,468],{"className":30868},[501],[363,30870,898],{"className":30871},[920],[363,30873],{"className":30874,"style":3981},[505],[363,30876],{"className":30877,"style":754},[505],[363,30879,461],{"className":30880},[494],[363,30882,385],{"className":30883,"style":409},[407,408],[363,30885],{"className":30886,"style":506},[505],[363,30888,471],{"className":30889},[510],[363,30891],{"className":30892,"style":506},[505],[363,30894,30896,30899,30902,30905,30910,30913,30916,30919],{"className":30895},[398],[363,30897],{"className":30898,"style":487},[402],[363,30900,1116],{"className":30901},[407,408],[363,30903],{"className":30904,"style":754},[505],[363,30906,4501,30908],{"className":30907},[1831],[363,30909,4505],{"style":4504},[363,30911],{"className":30912,"style":754},[505],[363,30914,1116],{"className":30915},[407,408],[363,30917,468],{"className":30918},[501],[363,30920,898],{"className":30921},[920],[11,30923,30924,30925,30953,30954,31023,31024,31159],{},"两种写法完全一致：JS 既是「两个 f-散度（相对 ",[363,30926,30928,30941],{"className":30927,"translate":367},[366],[363,30929,30931],{"className":30930},[371],[373,30932,30933],{"xmlns":375},[377,30934,30935,30939],{},[380,30936,30937],{},[383,30938,25914],{},[387,30940,25914],{"encoding":389},[363,30942,30944],{"className":30943,"ariaHidden":394},[393],[363,30945,30947,30950],{"className":30946},[398],[363,30948],{"className":30949,"style":1011},[402],[363,30951,25914],{"className":30952,"style":25948},[407,408],"）的平均」，也是「一个对称 f-散度」。原文「不是单一 ",[363,30955,30957,30974],{"className":30956,"translate":367},[366],[363,30958,30960],{"className":30959},[371],[373,30961,30962],{"xmlns":375},[377,30963,30964,30972],{},[380,30965,30966],{},[543,30967,30968,30970],{},[383,30969,547],{},[383,30971,385],{},[387,30973,4369],{"encoding":389},[363,30975,30977],{"className":30976,"ariaHidden":394},[393],[363,30978,30980,30983],{"className":30979},[398],[363,30981],{"className":30982,"style":4379},[402],[363,30984,30986,30989],{"className":30985},[407],[363,30987,547],{"className":30988,"style":625},[407,408],[363,30990,30992],{"className":30991},[629],[363,30993,30995,31015],{"className":30994},[633,634],[363,30996,30998,31012],{"className":30997},[638],[363,30999,31001],{"className":31000,"style":643},[642],[363,31002,31003,31006],{"style":646},[363,31004],{"className":31005,"style":651},[650],[363,31007,31009],{"className":31008},[655,656,657,658],[363,31010,385],{"className":31011,"style":409},[407,408,658],[363,31013,666],{"className":31014},[665],[363,31016,31018],{"className":31017},[638],[363,31019,31021],{"className":31020,"style":673},[642],[363,31022],{},"」的说法可修正为：",[1572,31025,31026,31027,31077,31078,31158],{},"在 ",[363,31028,31030,31047],{"className":31029,"translate":367},[366],[363,31031,31033],{"className":31032},[371],[373,31034,31035],{"xmlns":375},[377,31036,31037,31045],{},[380,31038,31039,31041,31043],{},[383,31040,554],{},[458,31042,1061],{},[383,31044,561],{},[387,31046,1066],{"encoding":389},[363,31048,31050,31068],{"className":31049,"ariaHidden":394},[393],[363,31051,31053,31056,31059,31062,31065],{"className":31052},[398],[363,31054],{"className":31055,"style":1076},[402],[363,31057,554],{"className":31058,"style":682},[407,408],[363,31060],{"className":31061,"style":506},[505],[363,31063,1061],{"className":31064},[510],[363,31066],{"className":31067,"style":506},[505],[363,31069,31071,31074],{"className":31070},[398],[363,31072],{"className":31073,"style":913},[402],[363,31075,561],{"className":31076},[407,408]," 时它是单一 ",[363,31079,31081,31103],{"className":31080,"translate":367},[366],[363,31082,31084],{"className":31083},[371],[373,31085,31086],{"xmlns":375},[377,31087,31088,31100],{},[380,31089,31090],{},[543,31091,31092,31094],{},[383,31093,385],{},[380,31095,31096,31098],{},[383,31097,24090],{},[383,31099,26084],{},[387,31101,31102],{"encoding":389},"f_{JS}",[363,31104,31106],{"className":31105,"ariaHidden":394},[393],[363,31107,31109,31112],{"className":31108},[398],[363,31110],{"className":31111,"style":403},[402],[363,31113,31115,31118],{"className":31114},[407],[363,31116,385],{"className":31117,"style":409},[407,408],[363,31119,31121],{"className":31120},[629],[363,31122,31124,31150],{"className":31123},[633,634],[363,31125,31127,31147],{"className":31126},[638],[363,31128,31130],{"className":31129,"style":727},[642],[363,31131,31132,31135],{"style":27856},[363,31133],{"className":31134,"style":651},[650],[363,31136,31138],{"className":31137},[655,656,657,658],[363,31139,31141,31144],{"className":31140},[407,658],[363,31142,24090],{"className":31143,"style":24500},[407,408,658],[363,31145,26084],{"className":31146,"style":26208},[407,408,658],[363,31148,666],{"className":31149},[665],[363,31151,31153],{"className":31152},[638],[363,31154,31156],{"className":31155,"style":8315},[642],[363,31157],{}," 的 f-散度","；一般情形则用下面的双变量形式。",[11,31161,31162,31165,31166,31207,31208,31323,31324,31327],{},[1572,31163,31164],{},"一般情形的双变量形式."," 当 ",[363,31167,31169,31186],{"className":31168,"translate":367},[366],[363,31170,31172],{"className":31171},[371],[373,31173,31174],{"xmlns":375},[377,31175,31176,31184],{},[380,31177,31178,31180,31182],{},[383,31179,554],{},[458,31181,898],{"separator":394},[383,31183,561],{},[387,31185,903],{"encoding":389},[363,31187,31189],{"className":31188,"ariaHidden":394},[393],[363,31190,31192,31195,31198,31201,31204],{"className":31191},[398],[363,31193],{"className":31194,"style":913},[402],[363,31196,554],{"className":31197,"style":682},[407,408],[363,31199,898],{"className":31200},[920],[363,31202],{"className":31203,"style":754},[505],[363,31205,561],{"className":31206},[407,408]," 支撑集可能分离时，",[363,31209,31211,31247],{"className":31210,"translate":367},[366],[363,31212,31214],{"className":31213},[371],[373,31215,31216],{"xmlns":375},[377,31217,31218,31244],{},[380,31219,31220,31222,31224,31226,31236,31238,31240,31242],{},[458,31221,461],{"stretchy":460},[383,31223,1116],{},[458,31225,898],{"separator":394},[543,31227,31228,31230],{},[383,31229,385],{},[380,31231,31232,31234],{},[383,31233,24090],{},[383,31235,26084],{},[458,31237,461],{"stretchy":460},[383,31239,1116],{},[458,31241,468],{"stretchy":460},[458,31243,468],{"stretchy":460},[387,31245,31246],{"encoding":389},"(t,f_{JS}(t))",[363,31248,31250],{"className":31249,"ariaHidden":394},[393],[363,31251,31253,31256,31259,31262,31265,31268,31314,31317,31320],{"className":31252},[398],[363,31254],{"className":31255,"style":487},[402],[363,31257,461],{"className":31258},[494],[363,31260,1116],{"className":31261},[407,408],[363,31263,898],{"className":31264},[920],[363,31266],{"className":31267,"style":754},[505],[363,31269,31271,31274],{"className":31270},[407],[363,31272,385],{"className":31273,"style":409},[407,408],[363,31275,31277],{"className":31276},[629],[363,31278,31280,31306],{"className":31279},[633,634],[363,31281,31283,31303],{"className":31282},[638],[363,31284,31286],{"className":31285,"style":727},[642],[363,31287,31288,31291],{"style":27856},[363,31289],{"className":31290,"style":651},[650],[363,31292,31294],{"className":31293},[655,656,657,658],[363,31295,31297,31300],{"className":31296},[407,658],[363,31298,24090],{"className":31299,"style":24500},[407,408,658],[363,31301,26084],{"className":31302,"style":26208},[407,408,658],[363,31304,666],{"className":31305},[665],[363,31307,31309],{"className":31308},[638],[363,31310,31312],{"className":31311,"style":8315},[642],[363,31313],{},[363,31315,461],{"className":31316},[494],[363,31318,1116],{"className":31319},[407,408],[363,31321,19394],{"className":31322},[501]," 的写法会漏掉奇异项。此时把 JS 写成 Csiszár 的",[1572,31325,31326],{},"双变量（齐次、联合凸）泛函","最稳妥：",[363,31329,31331],{"className":31330,"translate":367},[528],[363,31332,31334,31391],{"className":31333,"translate":367},[366],[363,31335,31337],{"className":31336},[371],[373,31338,31339],{"xmlns":375,"display":537},[377,31340,31341,31388],{},[380,31342,31343,31353,31355,31357,31359,31361,31363,31365,31367,31370,31372,31374,31376,31378,31380,31382,31384,31386],{},[543,31344,31345,31347],{},[383,31346,547],{},[380,31348,31349,31351],{},[383,31350,24090],{},[383,31352,26084],{},[458,31354,461],{"stretchy":460},[383,31356,554],{},[383,31358,558],{"mathvariant":557},[383,31360,561],{},[458,31362,468],{"stretchy":460},[458,31364,471],{},[458,31366,1634],{},[383,31368,31369],{},"φ",[458,31371,461],{"stretchy":460},[383,31373,11],{},[458,31375,898],{"separator":394},[383,31377,1291],{},[458,31379,468],{"stretchy":460},[1644,31381,1646],{},[383,31383,592],{},[383,31385,2711],{},[458,31387,898],{"separator":394},[387,31389,31390],{"encoding":389},"D_{JS}(P\\|Q)=\\int \\varphi(p,q)\\,d\\mu,",[363,31392,31394,31470],{"className":31393,"ariaHidden":394},[393],[363,31395,31397,31400,31446,31449,31452,31455,31458,31461,31464,31467],{"className":31396},[398],[363,31398],{"className":31399,"style":487},[402],[363,31401,31403,31406],{"className":31402},[407],[363,31404,547],{"className":31405,"style":625},[407,408],[363,31407,31409],{"className":31408},[629],[363,31410,31412,31438],{"className":31411},[633,634],[363,31413,31415,31435],{"className":31414},[638],[363,31416,31418],{"className":31417,"style":727},[642],[363,31419,31420,31423],{"style":646},[363,31421],{"className":31422,"style":651},[650],[363,31424,31426],{"className":31425},[655,656,657,658],[363,31427,31429,31432],{"className":31428},[407,658],[363,31430,24090],{"className":31431,"style":24500},[407,408,658],[363,31433,26084],{"className":31434,"style":26208},[407,408,658],[363,31436,666],{"className":31437},[665],[363,31439,31441],{"className":31440},[638],[363,31442,31444],{"className":31443,"style":8315},[642],[363,31445],{},[363,31447,461],{"className":31448},[494],[363,31450,554],{"className":31451,"style":682},[407,408],[363,31453,558],{"className":31454},[407],[363,31456,561],{"className":31457},[407,408],[363,31459,468],{"className":31460},[501],[363,31462],{"className":31463,"style":506},[505],[363,31465,471],{"className":31466},[510],[363,31468],{"className":31469,"style":506},[505],[363,31471,31473,31476,31479,31482,31485,31488,31491,31494,31497,31500,31503,31506,31509,31512],{"className":31472},[398],[363,31474],{"className":31475,"style":6124},[402],[363,31477,1634],{"className":31478,"style":1834},[1831,1832,1833],[363,31480],{"className":31481,"style":754},[505],[363,31483,31369],{"className":31484},[407,408],[363,31486,461],{"className":31487},[494],[363,31489,11],{"className":31490},[407,408],[363,31492,898],{"className":31493},[920],[363,31495],{"className":31496,"style":754},[505],[363,31498,1291],{"className":31499,"style":1328},[407,408],[363,31501,468],{"className":31502},[501],[363,31504],{"className":31505,"style":754},[505],[363,31507,592],{"className":31508},[407,408],[363,31510,2711],{"className":31511},[407,408],[363,31513,898],{"className":31514},[920],[363,31516,31518],{"className":31517,"translate":367},[528],[363,31519,31521,31605],{"className":31520,"translate":367},[366],[363,31522,31524],{"className":31523},[371],[373,31525,31526],{"xmlns":375,"display":537},[377,31527,31528,31602],{},[380,31529,31530,31532,31534,31536,31538,31540,31542,31544,31550,31552,31554,31556,31558,31574,31576,31578,31580,31582,31598,31600],{},[383,31531,31369],{},[458,31533,461],{"stretchy":460},[383,31535,11],{},[458,31537,898],{"separator":394},[383,31539,1291],{},[458,31541,468],{"stretchy":460},[458,31543,471],{},[586,31545,31546,31548],{},[463,31547,465],{},[463,31549,2810],{},[458,31551,578],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[383,31553,11],{},[383,31555,4447],{},[458,31557,4450],{},[586,31559,31560,31566],{},[380,31561,31562,31564],{},[463,31563,2810],{},[383,31565,11],{},[380,31567,31568,31570,31572],{},[383,31569,11],{},[458,31571,2817],{},[383,31573,1291],{},[458,31575,2817],{},[383,31577,1291],{},[383,31579,4447],{},[458,31581,4450],{},[586,31583,31584,31590],{},[380,31585,31586,31588],{},[463,31587,2810],{},[383,31589,1291],{},[380,31591,31592,31594,31596],{},[383,31593,11],{},[458,31595,2817],{},[383,31597,1291],{},[458,31599,605],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[458,31601,898],{"separator":394},[387,31603,31604],{"encoding":389},"\\varphi(p,q)=\\frac12\\Big[\np\\log\\frac{2p}{p+q}+q\\log\\frac{2q}{p+q}\\Big],",[363,31606,31608,31644,31819],{"className":31607,"ariaHidden":394},[393],[363,31609,31611,31614,31617,31620,31623,31626,31629,31632,31635,31638,31641],{"className":31610},[398],[363,31612],{"className":31613,"style":487},[402],[363,31615,31369],{"className":31616},[407,408],[363,31618,461],{"className":31619},[494],[363,31621,11],{"className":31622},[407,408],[363,31624,898],{"className":31625},[920],[363,31627],{"className":31628,"style":754},[505],[363,31630,1291],{"className":31631,"style":1328},[407,408],[363,31633,468],{"className":31634},[501],[363,31636],{"className":31637,"style":506},[505],[363,31639,471],{"className":31640},[510],[363,31642],{"className":31643,"style":506},[505],[363,31645,31647,31651,31713,31719,31722,31725,31730,31733,31810,31813,31816],{"className":31646},[398],[363,31648],{"className":31649,"style":31650},[402],"height:2.2019em;vertical-align:-0.8804em;",[363,31652,31654,31657,31710],{"className":31653},[407],[363,31655],{"className":31656},[494,789],[363,31658,31660],{"className":31659},[586],[363,31661,31663,31702],{"className":31662},[633,634],[363,31664,31666,31699],{"className":31665},[638],[363,31667,31669,31680,31688],{"className":31668,"style":23236},[642],[363,31670,31671,31674],{"style":805},[363,31672],{"className":31673,"style":809},[650],[363,31675,31677],{"className":31676},[407],[363,31678,2810],{"className":31679},[407],[363,31681,31682,31685],{"style":821},[363,31683],{"className":31684,"style":809},[650],[363,31686],{"className":31687,"style":829},[828],[363,31689,31690,31693],{"style":832},[363,31691],{"className":31692,"style":809},[650],[363,31694,31696],{"className":31695},[407],[363,31697,465],{"className":31698},[407],[363,31700,666],{"className":31701},[665],[363,31703,31705],{"className":31704},[638],[363,31706,31708],{"className":31707,"style":4125},[642],[363,31709],{},[363,31711],{"className":31712},[501,789],[363,31714,31716],{"className":31715},[407],[363,31717,578],{"className":31718},[767,4067],[363,31720,11],{"className":31721},[407,408],[363,31723],{"className":31724,"style":754},[505],[363,31726,4501,31728],{"className":31727},[1831],[363,31729,4505],{"style":4504},[363,31731],{"className":31732,"style":754},[505],[363,31734,31736,31739,31807],{"className":31735},[407],[363,31737],{"className":31738},[494,789],[363,31740,31742],{"className":31741},[586],[363,31743,31745,31799],{"className":31744},[633,634],[363,31746,31748,31796],{"className":31747},[638],[363,31749,31751,31774,31782],{"className":31750,"style":23236},[642],[363,31752,31753,31756],{"style":805},[363,31754],{"className":31755,"style":809},[650],[363,31757,31759,31762,31765,31768,31771],{"className":31758},[407],[363,31760,11],{"className":31761},[407,408],[363,31763],{"className":31764,"style":2934},[505],[363,31766,2817],{"className":31767},[2938],[363,31769],{"className":31770,"style":2934},[505],[363,31772,1291],{"className":31773,"style":1328},[407,408],[363,31775,31776,31779],{"style":821},[363,31777],{"className":31778,"style":809},[650],[363,31780],{"className":31781,"style":829},[828],[363,31783,31784,31787],{"style":832},[363,31785],{"className":31786,"style":809},[650],[363,31788,31790,31793],{"className":31789},[407],[363,31791,2810],{"className":31792},[407],[363,31794,11],{"className":31795},[407,408],[363,31797,666],{"className":31798},[665],[363,31800,31802],{"className":31801},[638],[363,31803,31805],{"className":31804,"style":854},[642],[363,31806],{},[363,31808],{"className":31809},[501,789],[363,31811],{"className":31812,"style":2934},[505],[363,31814,2817],{"className":31815},[2938],[363,31817],{"className":31818,"style":2934},[505],[363,31820,31822,31825,31828,31831,31836,31839,31916,31922],{"className":31821},[398],[363,31823],{"className":31824,"style":31650},[402],[363,31826,1291],{"className":31827,"style":1328},[407,408],[363,31829],{"className":31830,"style":754},[505],[363,31832,4501,31834],{"className":31833},[1831],[363,31835,4505],{"style":4504},[363,31837],{"className":31838,"style":754},[505],[363,31840,31842,31845,31913],{"className":31841},[407],[363,31843],{"className":31844},[494,789],[363,31846,31848],{"className":31847},[586],[363,31849,31851,31905],{"className":31850},[633,634],[363,31852,31854,31902],{"className":31853},[638],[363,31855,31857,31880,31888],{"className":31856,"style":23236},[642],[363,31858,31859,31862],{"style":805},[363,31860],{"className":31861,"style":809},[650],[363,31863,31865,31868,31871,31874,31877],{"className":31864},[407],[363,31866,11],{"className":31867},[407,408],[363,31869],{"className":31870,"style":2934},[505],[363,31872,2817],{"className":31873},[2938],[363,31875],{"className":31876,"style":2934},[505],[363,31878,1291],{"className":31879,"style":1328},[407,408],[363,31881,31882,31885],{"style":821},[363,31883],{"className":31884,"style":809},[650],[363,31886],{"className":31887,"style":829},[828],[363,31889,31890,31893],{"style":832},[363,31891],{"className":31892,"style":809},[650],[363,31894,31896,31899],{"className":31895},[407],[363,31897,2810],{"className":31898},[407],[363,31900,1291],{"className":31901,"style":1328},[407,408],[363,31903,666],{"className":31904},[665],[363,31906,31908],{"className":31907},[638],[363,31909,31911],{"className":31910,"style":854},[642],[363,31912],{},[363,31914],{"className":31915},[501,789],[363,31917,31919],{"className":31918},[407],[363,31920,605],{"className":31921},[767,4067],[363,31923,898],{"className":31924},[920],[11,31926,31927,1015,31956,32008,32009,32061,32062,32219,32220,32306,32307,32430],{},[363,31928,31930,31944],{"className":31929,"translate":367},[366],[363,31931,31933],{"className":31932},[371],[373,31934,31935],{"xmlns":375},[377,31936,31937,31941],{},[380,31938,31939],{},[383,31940,31369],{},[387,31942,31943],{"encoding":389},"\\varphi",[363,31945,31947],{"className":31946,"ariaHidden":394},[393],[363,31948,31950,31953],{"className":31949},[398],[363,31951],{"className":31952,"style":2623},[402],[363,31954,31369],{"className":31955},[407,408],[363,31957,31959,31981],{"className":31958,"translate":367},[366],[363,31960,31962],{"className":31961},[371],[373,31963,31964],{"xmlns":375},[377,31965,31966,31978],{},[380,31967,31968,31970,31972,31974,31976],{},[458,31969,461],{"stretchy":460},[383,31971,11],{},[458,31973,898],{"separator":394},[383,31975,1291],{},[458,31977,468],{"stretchy":460},[387,31979,31980],{"encoding":389},"(p,q)",[363,31982,31984],{"className":31983,"ariaHidden":394},[393],[363,31985,31987,31990,31993,31996,31999,32002,32005],{"className":31986},[398],[363,31988],{"className":31989,"style":487},[402],[363,31991,461],{"className":31992},[494],[363,31994,11],{"className":31995},[407,408],[363,31997,898],{"className":31998},[920],[363,32000],{"className":32001,"style":754},[505],[363,32003,1291],{"className":32004,"style":1328},[407,408],[363,32006,468],{"className":32007},[501]," 联合凸且一次齐次。在 ",[363,32010,32012,32030],{"className":32011,"translate":367},[366],[363,32013,32015],{"className":32014},[371],[373,32016,32017],{"xmlns":375},[377,32018,32019,32027],{},[380,32020,32021,32023,32025],{},[383,32022,1291],{},[458,32024,3250],{},[463,32026,474],{},[387,32028,32029],{"encoding":389},"q>0",[363,32031,32033,32052],{"className":32032,"ariaHidden":394},[393],[363,32034,32036,32040,32043,32046,32049],{"className":32035},[398],[363,32037],{"className":32038,"style":32039},[402],"height:0.7335em;vertical-align:-0.1944em;",[363,32041,1291],{"className":32042,"style":1328},[407,408],[363,32044],{"className":32045,"style":506},[505],[363,32047,3250],{"className":32048},[510],[363,32050],{"className":32051,"style":506},[505],[363,32053,32055,32058],{"className":32054},[398],[363,32056],{"className":32057,"style":520},[402],[363,32059,474],{"className":32060},[407]," 处 ",[363,32063,32065,32113],{"className":32064,"translate":367},[366],[363,32066,32068],{"className":32067},[371],[373,32069,32070],{"xmlns":375},[377,32071,32072,32110],{},[380,32073,32074,32076,32078,32080,32082,32084,32086,32088,32090,32092,32094,32104,32106,32108],{},[383,32075,31369],{},[458,32077,461],{"stretchy":460},[383,32079,1116],{},[383,32081,1291],{},[458,32083,898],{"separator":394},[383,32085,1291],{},[458,32087,468],{"stretchy":460},[458,32089,471],{},[383,32091,1291],{},[1644,32093,1646],{},[543,32095,32096,32098],{},[383,32097,385],{},[380,32099,32100,32102],{},[383,32101,24090],{},[383,32103,26084],{},[458,32105,461],{"stretchy":460},[383,32107,1116],{},[458,32109,468],{"stretchy":460},[387,32111,32112],{"encoding":389},"\\varphi(tq,q)=q\\,f_{JS}(t)",[363,32114,32116,32152],{"className":32115,"ariaHidden":394},[393],[363,32117,32119,32122,32125,32128,32131,32134,32137,32140,32143,32146,32149],{"className":32118},[398],[363,32120],{"className":32121,"style":487},[402],[363,32123,31369],{"className":32124},[407,408],[363,32126,461],{"className":32127},[494],[363,32129,26625],{"className":32130,"style":1328},[407,408],[363,32132,898],{"className":32133},[920],[363,32135],{"className":32136,"style":754},[505],[363,32138,1291],{"className":32139,"style":1328},[407,408],[363,32141,468],{"className":32142},[501],[363,32144],{"className":32145,"style":506},[505],[363,32147,471],{"className":32148},[510],[363,32150],{"className":32151,"style":506},[505],[363,32153,32155,32158,32161,32164,32210,32213,32216],{"className":32154},[398],[363,32156],{"className":32157,"style":487},[402],[363,32159,1291],{"className":32160,"style":1328},[407,408],[363,32162],{"className":32163,"style":754},[505],[363,32165,32167,32170],{"className":32166},[407],[363,32168,385],{"className":32169,"style":409},[407,408],[363,32171,32173],{"className":32172},[629],[363,32174,32176,32202],{"className":32175},[633,634],[363,32177,32179,32199],{"className":32178},[638],[363,32180,32182],{"className":32181,"style":727},[642],[363,32183,32184,32187],{"style":27856},[363,32185],{"className":32186,"style":651},[650],[363,32188,32190],{"className":32189},[655,656,657,658],[363,32191,32193,32196],{"className":32192},[407,658],[363,32194,24090],{"className":32195,"style":24500},[407,408,658],[363,32197,26084],{"className":32198,"style":26208},[407,408,658],[363,32200,666],{"className":32201},[665],[363,32203,32205],{"className":32204},[638],[363,32206,32208],{"className":32207,"style":8315},[642],[363,32209],{},[363,32211,461],{"className":32212},[494],[363,32214,1116],{"className":32215},[407,408],[363,32217,468],{"className":32218},[501],"，两者一致；在 ",[363,32221,32223,32249],{"className":32222,"translate":367},[366],[363,32224,32226],{"className":32225},[371],[373,32227,32228],{"xmlns":375},[377,32229,32230,32246],{},[380,32231,32232,32234,32236,32238,32240,32242,32244],{},[383,32233,1291],{},[458,32235,471],{},[463,32237,474],{},[458,32239,898],{"separator":394},[383,32241,11],{},[458,32243,3250],{},[463,32245,474],{},[387,32247,32248],{"encoding":389},"q=0,p>0",[363,32250,32252,32270,32297],{"className":32251,"ariaHidden":394},[393],[363,32253,32255,32258,32261,32264,32267],{"className":32254},[398],[363,32256],{"className":32257,"style":2623},[402],[363,32259,1291],{"className":32260,"style":1328},[407,408],[363,32262],{"className":32263,"style":506},[505],[363,32265,471],{"className":32266},[510],[363,32268],{"className":32269,"style":506},[505],[363,32271,32273,32276,32279,32282,32285,32288,32291,32294],{"className":32272},[398],[363,32274],{"className":32275,"style":9705},[402],[363,32277,474],{"className":32278},[407],[363,32280,898],{"className":32281},[920],[363,32283],{"className":32284,"style":754},[505],[363,32286,11],{"className":32287},[407,408],[363,32289],{"className":32290,"style":506},[505],[363,32292,3250],{"className":32293},[510],[363,32295],{"className":32296,"style":506},[505],[363,32298,32300,32303],{"className":32299},[398],[363,32301],{"className":32302,"style":520},[402],[363,32304,474],{"className":32305},[407]," 处奇异项 ",[363,32308,32310,32336],{"className":32309,"translate":367},[366],[363,32311,32313],{"className":32312},[371],[373,32314,32315],{"xmlns":375},[377,32316,32317,32333],{},[380,32318,32319,32325,32327,32329,32331],{},[586,32320,32321,32323],{},[463,32322,465],{},[463,32324,2810],{},[383,32326,11],{},[383,32328,4447],{},[458,32330,4450],{},[463,32332,2810],{},[387,32334,32335],{"encoding":389},"\\frac12 p\\log 2",[363,32337,32339],{"className":32338,"ariaHidden":394},[393],[363,32340,32342,32345,32413,32416,32419,32424,32427],{"className":32341},[398],[363,32343],{"className":32344,"style":2852},[402],[363,32346,32348,32351,32410],{"className":32347},[407],[363,32349],{"className":32350},[494,789],[363,32352,32354],{"className":32353},[586],[363,32355,32357,32402],{"className":32356},[633,634],[363,32358,32360,32399],{"className":32359},[638],[363,32361,32363,32377,32385],{"className":32362,"style":2871},[642],[363,32364,32365,32368],{"style":2874},[363,32366],{"className":32367,"style":809},[650],[363,32369,32371],{"className":32370},[655,656,657,658],[363,32372,32374],{"className":32373},[407,658],[363,32375,2810],{"className":32376},[407,658],[363,32378,32379,32382],{"style":821},[363,32380],{"className":32381,"style":809},[650],[363,32383],{"className":32384,"style":829},[828],[363,32386,32387,32390],{"style":2897},[363,32388],{"className":32389,"style":809},[650],[363,32391,32393],{"className":32392},[655,656,657,658],[363,32394,32396],{"className":32395},[407,658],[363,32397,465],{"className":32398},[407,658],[363,32400,666],{"className":32401},[665],[363,32403,32405],{"className":32404},[638],[363,32406,32408],{"className":32407,"style":2919},[642],[363,32409],{},[363,32411],{"className":32412},[501,789],[363,32414,11],{"className":32415},[407,408],[363,32417],{"className":32418,"style":754},[505],[363,32420,4501,32422],{"className":32421},[1831],[363,32423,4505],{"style":4504},[363,32425],{"className":32426,"style":754},[505],[363,32428,2810],{"className":32429},[407]," 会被保留下来（这正是 1.1 节讨论的「支撑不重叠」约定）。",[11,32432,32433,32436,32437,32516,32517,16142,32520,32571,32572,32805,32806,32834,32835,32863,32864,33052,33053,33148],{},[1572,32434,32435],{},"有界性。"," 注意 ",[363,32438,32440,32461],{"className":32439,"translate":367},[366],[363,32441,32443],{"className":32442},[371],[373,32444,32445],{"xmlns":375},[377,32446,32447,32459],{},[380,32448,32449],{},[543,32450,32451,32453],{},[383,32452,385],{},[380,32454,32455,32457],{},[383,32456,24090],{},[383,32458,26084],{},[387,32460,31102],{"encoding":389},[363,32462,32464],{"className":32463,"ariaHidden":394},[393],[363,32465,32467,32470],{"className":32466},[398],[363,32468],{"className":32469,"style":403},[402],[363,32471,32473,32476],{"className":32472},[407],[363,32474,385],{"className":32475,"style":409},[407,408],[363,32477,32479],{"className":32478},[629],[363,32480,32482,32508],{"className":32481},[633,634],[363,32483,32485,32505],{"className":32484},[638],[363,32486,32488],{"className":32487,"style":727},[642],[363,32489,32490,32493],{"style":27856},[363,32491],{"className":32492,"style":651},[650],[363,32494,32496],{"className":32495},[655,656,657,658],[363,32497,32499,32502],{"className":32498},[407,658],[363,32500,24090],{"className":32501,"style":24500},[407,408,658],[363,32503,26084],{"className":32504,"style":26208},[407,408,658],[363,32506,666],{"className":32507},[665],[363,32509,32511],{"className":32510},[638],[363,32512,32514],{"className":32513,"style":8315},[642],[363,32515],{}," 逐点",[1572,32518,32519],{},"无界",[363,32521,32523,32541],{"className":32522,"translate":367},[366],[363,32524,32526],{"className":32525},[371],[373,32527,32528],{"xmlns":375},[377,32529,32530,32538],{},[380,32531,32532,32534,32536],{},[383,32533,1116],{},[458,32535,1376],{},[383,32537,1371],{"mathvariant":557},[387,32539,32540],{"encoding":389},"t\\to\\infty",[363,32542,32544,32562],{"className":32543,"ariaHidden":394},[393],[363,32545,32547,32550,32553,32556,32559],{"className":32546},[398],[363,32548],{"className":32549,"style":5690},[402],[363,32551,1116],{"className":32552},[407,408],[363,32554],{"className":32555,"style":506},[505],[363,32557,1376],{"className":32558},[510],[363,32560],{"className":32561,"style":506},[505],[363,32563,32565,32568],{"className":32564},[398],[363,32566],{"className":32567,"style":2692},[402],[363,32569,1371],{"className":32570},[407]," 时 ",[363,32573,32575,32623],{"className":32574,"translate":367},[366],[363,32576,32578],{"className":32577},[371],[373,32579,32580],{"xmlns":375},[377,32581,32582,32620],{},[380,32583,32584,32594,32596,32598,32600,32602,32608,32610,32612,32614,32616,32618],{},[543,32585,32586,32588],{},[383,32587,385],{},[380,32589,32590,32592],{},[383,32591,24090],{},[383,32593,26084],{},[458,32595,461],{"stretchy":460},[383,32597,1116],{},[458,32599,468],{"stretchy":460},[458,32601,9216],{},[586,32603,32604,32606],{},[463,32605,465],{},[463,32607,2810],{},[383,32609,1116],{},[383,32611,4447],{},[458,32613,4450],{},[463,32615,2810],{},[458,32617,1376],{},[383,32619,1371],{"mathvariant":557},[387,32621,32622],{"encoding":389},"f_{JS}(t)\\sim\\frac12 t\\log 2\\to\\infty",[363,32624,32626,32696,32796],{"className":32625,"ariaHidden":394},[393],[363,32627,32629,32632,32678,32681,32684,32687,32690,32693],{"className":32628},[398],[363,32630],{"className":32631,"style":487},[402],[363,32633,32635,32638],{"className":32634},[407],[363,32636,385],{"className":32637,"style":409},[407,408],[363,32639,32641],{"className":32640},[629],[363,32642,32644,32670],{"className":32643},[633,634],[363,32645,32647,32667],{"className":32646},[638],[363,32648,32650],{"className":32649,"style":727},[642],[363,32651,32652,32655],{"style":27856},[363,32653],{"className":32654,"style":651},[650],[363,32656,32658],{"className":32657},[655,656,657,658],[363,32659,32661,32664],{"className":32660},[407,658],[363,32662,24090],{"className":32663,"style":24500},[407,408,658],[363,32665,26084],{"className":32666,"style":26208},[407,408,658],[363,32668,666],{"className":32669},[665],[363,32671,32673],{"className":32672},[638],[363,32674,32676],{"className":32675,"style":8315},[642],[363,32677],{},[363,32679,461],{"className":32680},[494],[363,32682,1116],{"className":32683},[407,408],[363,32685,468],{"className":32686},[501],[363,32688],{"className":32689,"style":506},[505],[363,32691,9216],{"className":32692},[510],[363,32694],{"className":32695,"style":506},[505],[363,32697,32699,32702,32770,32773,32776,32781,32784,32787,32790,32793],{"className":32698},[398],[363,32700],{"className":32701,"style":2852},[402],[363,32703,32705,32708,32767],{"className":32704},[407],[363,32706],{"className":32707},[494,789],[363,32709,32711],{"className":32710},[586],[363,32712,32714,32759],{"className":32713},[633,634],[363,32715,32717,32756],{"className":32716},[638],[363,32718,32720,32734,32742],{"className":32719,"style":2871},[642],[363,32721,32722,32725],{"style":2874},[363,32723],{"className":32724,"style":809},[650],[363,32726,32728],{"className":32727},[655,656,657,658],[363,32729,32731],{"className":32730},[407,658],[363,32732,2810],{"className":32733},[407,658],[363,32735,32736,32739],{"style":821},[363,32737],{"className":32738,"style":809},[650],[363,32740],{"className":32741,"style":829},[828],[363,32743,32744,32747],{"style":2897},[363,32745],{"className":32746,"style":809},[650],[363,32748,32750],{"className":32749},[655,656,657,658],[363,32751,32753],{"className":32752},[407,658],[363,32754,465],{"className":32755},[407,658],[363,32757,666],{"className":32758},[665],[363,32760,32762],{"className":32761},[638],[363,32763,32765],{"className":32764,"style":2919},[642],[363,32766],{},[363,32768],{"className":32769},[501,789],[363,32771,1116],{"className":32772},[407,408],[363,32774],{"className":32775,"style":754},[505],[363,32777,4501,32779],{"className":32778},[1831],[363,32780,4505],{"style":4504},[363,32782],{"className":32783,"style":754},[505],[363,32785,2810],{"className":32786},[407],[363,32788],{"className":32789,"style":506},[505],[363,32791,1376],{"className":32792},[510],[363,32794],{"className":32795,"style":506},[505],[363,32797,32799,32802],{"className":32798},[398],[363,32800],{"className":32801,"style":2692},[402],[363,32803,1371],{"className":32804},[407],"），但积分有界，因为 ",[363,32807,32809,32822],{"className":32808,"translate":367},[366],[363,32810,32812],{"className":32811},[371],[373,32813,32814],{"xmlns":375},[377,32815,32816,32820],{},[380,32817,32818],{},[383,32819,1116],{},[387,32821,1116],{"encoding":389},[363,32823,32825],{"className":32824,"ariaHidden":394},[393],[363,32826,32828,32831],{"className":32827},[398],[363,32829],{"className":32830,"style":5690},[402],[363,32832,1116],{"className":32833},[407,408]," 大的地方 ",[363,32836,32838,32851],{"className":32837,"translate":367},[366],[363,32839,32841],{"className":32840},[371],[373,32842,32843],{"xmlns":375},[377,32844,32845,32849],{},[380,32846,32847],{},[383,32848,1291],{},[387,32850,1291],{"encoding":389},[363,32852,32854],{"className":32853,"ariaHidden":394},[393],[363,32855,32857,32860],{"className":32856},[398],[363,32858],{"className":32859,"style":2623},[402],[363,32861,1291],{"className":32862,"style":1328},[407,408]," 小、权重趋于 0。严格地用两 KL 形式：",[363,32865,32867,32925],{"className":32866,"translate":367},[366],[363,32868,32870],{"className":32869},[371],[373,32871,32872],{"xmlns":375},[377,32873,32874,32922],{},[380,32875,32876,32878,32880,32882,32884,32886,32888,32890,32892,32894,32896,32898,32904,32906,32908,32910,32912,32914,32916,32918,32920],{},[463,32877,2810],{},[383,32879,11],{},[383,32881,1288],{"mathvariant":557},[458,32883,461],{"stretchy":460},[383,32885,11],{},[458,32887,2817],{},[383,32889,1291],{},[458,32891,468],{"stretchy":460},[458,32893,10299],{},[463,32895,2810],{},[458,32897,11337],{},[380,32899,32900,32902],{},[383,32901,11041],{"mathvariant":557},[383,32903,22240],{"mathvariant":557},[458,32905,461],{"stretchy":460},[383,32907,554],{},[383,32909,558],{"mathvariant":557},[383,32911,25914],{},[458,32913,468],{"stretchy":460},[458,32915,10299],{},[383,32917,4447],{},[458,32919,4450],{},[463,32921,2810],{},[387,32923,32924],{"encoding":389},"2p\u002F(p+q)\\le 2\\Rightarrow \\mathrm{KL}(P\\|M)\\le\\log2",[363,32926,32928,32958,32979,32997,33035],{"className":32927,"ariaHidden":394},[393],[363,32929,32931,32934,32937,32940,32943,32946,32949,32952,32955],{"className":32930},[398],[363,32932],{"className":32933,"style":487},[402],[363,32935,2810],{"className":32936},[407],[363,32938,11],{"className":32939},[407,408],[363,32941,1288],{"className":32942},[407],[363,32944,461],{"className":32945},[494],[363,32947,11],{"className":32948},[407,408],[363,32950],{"className":32951,"style":2934},[505],[363,32953,2817],{"className":32954},[2938],[363,32956],{"className":32957,"style":2934},[505],[363,32959,32961,32964,32967,32970,32973,32976],{"className":32960},[398],[363,32962],{"className":32963,"style":487},[402],[363,32965,1291],{"className":32966,"style":1328},[407,408],[363,32968,468],{"className":32969},[501],[363,32971],{"className":32972,"style":506},[505],[363,32974,10299],{"className":32975},[510],[363,32977],{"className":32978,"style":506},[505],[363,32980,32982,32985,32988,32991,32994],{"className":32981},[398],[363,32983],{"className":32984,"style":520},[402],[363,32986,2810],{"className":32987},[407],[363,32989],{"className":32990,"style":506},[505],[363,32992,11337],{"className":32993},[510],[363,32995],{"className":32996,"style":506},[505],[363,32998,33000,33003,33011,33014,33017,33020,33023,33026,33029,33032],{"className":32999},[398],[363,33001],{"className":33002,"style":487},[402],[363,33004,33006],{"className":33005},[407],[363,33007,33010],{"className":33008},[407,33009],"mathrm","KL",[363,33012,461],{"className":33013},[494],[363,33015,554],{"className":33016,"style":682},[407,408],[363,33018,558],{"className":33019},[407],[363,33021,25914],{"className":33022,"style":25948},[407,408],[363,33024,468],{"className":33025},[501],[363,33027],{"className":33028,"style":506},[505],[363,33030,10299],{"className":33031},[510],[363,33033],{"className":33034,"style":506},[505],[363,33036,33038,33041,33046,33049],{"className":33037},[398],[363,33039],{"className":33040,"style":403},[402],[363,33042,4501,33044],{"className":33043},[1831],[363,33045,4505],{"style":4504},[363,33047],{"className":33048,"style":754},[505],[363,33050,2810],{"className":33051},[407],"，同理 ",[363,33054,33056,33092],{"className":33055,"translate":367},[366],[363,33057,33059],{"className":33058},[371],[373,33060,33061],{"xmlns":375},[377,33062,33063,33089],{},[380,33064,33065,33071,33073,33075,33077,33079,33081,33083,33085,33087],{},[380,33066,33067,33069],{},[383,33068,11041],{"mathvariant":557},[383,33070,22240],{"mathvariant":557},[458,33072,461],{"stretchy":460},[383,33074,561],{},[383,33076,558],{"mathvariant":557},[383,33078,25914],{},[458,33080,468],{"stretchy":460},[458,33082,10299],{},[383,33084,4447],{},[458,33086,4450],{},[463,33088,2810],{},[387,33090,33091],{"encoding":389},"\\mathrm{KL}(Q\\|M)\\le\\log2",[363,33093,33095,33131],{"className":33094,"ariaHidden":394},[393],[363,33096,33098,33101,33107,33110,33113,33116,33119,33122,33125,33128],{"className":33097},[398],[363,33099],{"className":33100,"style":487},[402],[363,33102,33104],{"className":33103},[407],[363,33105,33010],{"className":33106},[407,33009],[363,33108,461],{"className":33109},[494],[363,33111,561],{"className":33112},[407,408],[363,33114,558],{"className":33115},[407],[363,33117,25914],{"className":33118,"style":25948},[407,408],[363,33120,468],{"className":33121},[501],[363,33123],{"className":33124,"style":506},[505],[363,33126,10299],{"className":33127},[510],[363,33129],{"className":33130,"style":506},[505],[363,33132,33134,33137,33142,33145],{"className":33133},[398],[363,33135],{"className":33136,"style":403},[402],[363,33138,4501,33140],{"className":33139},[1831],[363,33141,4505],{"style":4504},[363,33143],{"className":33144,"style":754},[505],[363,33146,2810],{"className":33147},[407],"，故",[363,33150,33152],{"className":33151,"translate":367},[528],[363,33153,33155,33313],{"className":33154,"translate":367},[366],[363,33156,33158],{"className":33157},[371],[373,33159,33160],{"xmlns":375,"display":537},[377,33161,33162,33310],{},[1590,33163,33164,33252],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,33165,33166,33196],{},[1599,33167,33168],{},[1602,33169,33170],{"scriptlevel":474,"displaystyle":394},[380,33171,33172,33174,33176,33186,33188,33190,33192,33194],{},[463,33173,474],{},[458,33175,10299],{},[543,33177,33178,33180],{},[383,33179,547],{},[380,33181,33182,33184],{},[383,33183,24090],{},[383,33185,26084],{},[458,33187,461],{"stretchy":460},[383,33189,554],{},[383,33191,558],{"mathvariant":557},[383,33193,561],{},[458,33195,468],{"stretchy":460},[1599,33197,33198],{},[1602,33199,33200],{"scriptlevel":474,"displaystyle":394},[380,33201,33202,33204,33206,33212,33218,33220,33222,33224,33226,33228,33230,33236,33242,33244,33246,33248,33250],{},[380,33203],{},[458,33205,471],{},[586,33207,33208,33210],{},[463,33209,465],{},[463,33211,2810],{},[380,33213,33214,33216],{},[383,33215,11041],{"mathvariant":557},[383,33217,22240],{"mathvariant":557},[458,33219,461],{"stretchy":460},[383,33221,554],{},[383,33223,558],{"mathvariant":557},[383,33225,25914],{},[458,33227,468],{"stretchy":460},[458,33229,2817],{},[586,33231,33232,33234],{},[463,33233,465],{},[463,33235,2810],{},[380,33237,33238,33240],{},[383,33239,11041],{"mathvariant":557},[383,33241,22240],{"mathvariant":557},[458,33243,461],{"stretchy":460},[383,33245,561],{},[383,33247,558],{"mathvariant":557},[383,33249,25914],{},[458,33251,468],{"stretchy":460},[1596,33253,33254,33260],{},[1599,33255,33256],{},[1602,33257,33258],{"scriptlevel":474,"displaystyle":394},[380,33259],{},[1599,33261,33262],{},[1602,33263,33264],{"scriptlevel":474,"displaystyle":394},[380,33265,33266,33268,33270,33276,33278,33280,33282,33284,33290,33292,33294,33296,33298,33300,33302,33304,33307],{},[380,33267],{},[458,33269,10299],{},[586,33271,33272,33274],{},[463,33273,465],{},[463,33275,2810],{},[383,33277,4447],{},[458,33279,4450],{},[463,33281,2810],{},[458,33283,2817],{},[586,33285,33286,33288],{},[463,33287,465],{},[463,33289,2810],{},[383,33291,4447],{},[458,33293,4450],{},[463,33295,2810],{},[458,33297,471],{},[383,33299,4447],{},[458,33301,4450],{},[463,33303,2810],{},[458,33305,33306],{},"≈",[463,33308,33309],{},"0.693.",[387,33311,33312],{"encoding":389},"\\begin{aligned}\n0\\le D_{JS}(P\\|Q)\n&=\\frac12\\mathrm{KL}(P\\|M)\n+\\frac12\\mathrm{KL}(Q\\|M)\\\\[2pt]\n&\\le \\frac12\\log 2+\\frac12\\log 2\n=\\log 2\\approx 0.693 .\n\\end{aligned}",[363,33314,33316],{"className":33315,"ariaHidden":394},[393],[363,33317,33319,33323],{"className":33318},[398],[363,33320],{"className":33321,"style":33322},[402],"height:4.3149em;vertical-align:-1.9074em;",[363,33324,33326],{"className":33325},[407],[363,33327,33329,33444],{"className":33328},[1590],[363,33330,33332],{"className":33331},[1707],[363,33333,33335,33435],{"className":33334},[633,634],[363,33336,33338,33432],{"className":33337},[638],[363,33339,33342,33424],{"className":33340,"style":33341},[642],"height:2.4074em;",[363,33343,33345,33348],{"style":33344},"top:-4.4074em;",[363,33346],{"className":33347,"style":23013},[650],[363,33349,33351,33354,33357,33360,33363,33409,33412,33415,33418,33421],{"className":33350},[407],[363,33352,474],{"className":33353},[407],[363,33355],{"className":33356,"style":506},[505],[363,33358,10299],{"className":33359},[510],[363,33361],{"className":33362,"style":506},[505],[363,33364,33366,33369],{"className":33365},[407],[363,33367,547],{"className":33368,"style":625},[407,408],[363,33370,33372],{"className":33371},[629],[363,33373,33375,33401],{"className":33374},[633,634],[363,33376,33378,33398],{"className":33377},[638],[363,33379,33381],{"className":33380,"style":727},[642],[363,33382,33383,33386],{"style":646},[363,33384],{"className":33385,"style":651},[650],[363,33387,33389],{"className":33388},[655,656,657,658],[363,33390,33392,33395],{"className":33391},[407,658],[363,33393,24090],{"className":33394,"style":24500},[407,408,658],[363,33396,26084],{"className":33397,"style":26208},[407,408,658],[363,33399,666],{"className":33400},[665],[363,33402,33404],{"className":33403},[638],[363,33405,33407],{"className":33406,"style":8315},[642],[363,33408],{},[363,33410,461],{"className":33411},[494],[363,33413,554],{"className":33414,"style":682},[407,408],[363,33416,558],{"className":33417},[407],[363,33419,561],{"className":33420},[407,408],[363,33422,468],{"className":33423},[501],[363,33425,33426,33429],{"style":2250},[363,33427],{"className":33428,"style":23013},[650],[363,33430],{"className":33431},[407],[363,33433,666],{"className":33434},[665],[363,33436,33438],{"className":33437},[638],[363,33439,33442],{"className":33440,"style":33441},[642],"height:1.9074em;",[363,33443],{},[363,33445,33447],{"className":33446},[1798],[363,33448,33450,33867],{"className":33449},[633,634],[363,33451,33453,33864],{"className":33452},[638],[363,33454,33456,33651],{"className":33455,"style":33341},[642],[363,33457,33458,33461],{"style":33344},[363,33459],{"className":33460,"style":23013},[650],[363,33462,33464,33467,33470,33473,33476,33538,33544,33547,33550,33553,33556,33559,33562,33565,33568,33630,33636,33639,33642,33645,33648],{"className":33463},[407],[363,33465],{"className":33466},[407],[363,33468],{"className":33469,"style":506},[505],[363,33471,471],{"className":33472},[510],[363,33474],{"className":33475,"style":506},[505],[363,33477,33479,33482,33535],{"className":33478},[407],[363,33480],{"className":33481},[494,789],[363,33483,33485],{"className":33484},[586],[363,33486,33488,33527],{"className":33487},[633,634],[363,33489,33491,33524],{"className":33490},[638],[363,33492,33494,33505,33513],{"className":33493,"style":23236},[642],[363,33495,33496,33499],{"style":805},[363,33497],{"className":33498,"style":809},[650],[363,33500,33502],{"className":33501},[407],[363,33503,2810],{"className":33504},[407],[363,33506,33507,33510],{"style":821},[363,33508],{"className":33509,"style":809},[650],[363,33511],{"className":33512,"style":829},[828],[363,33514,33515,33518],{"style":832},[363,33516],{"className":33517,"style":809},[650],[363,33519,33521],{"className":33520},[407],[363,33522,465],{"className":33523},[407],[363,33525,666],{"className":33526},[665],[363,33528,33530],{"className":33529},[638],[363,33531,33533],{"className":33532,"style":4125},[642],[363,33534],{},[363,33536],{"className":33537},[501,789],[363,33539,33541],{"className":33540},[407],[363,33542,33010],{"className":33543},[407,33009],[363,33545,461],{"className":33546},[494],[363,33548,554],{"className":33549,"style":682},[407,408],[363,33551,558],{"className":33552},[407],[363,33554,25914],{"className":33555,"style":25948},[407,408],[363,33557,468],{"className":33558},[501],[363,33560],{"className":33561,"style":2934},[505],[363,33563,2817],{"className":33564},[2938],[363,33566],{"className":33567,"style":2934},[505],[363,33569,33571,33574,33627],{"className":33570},[407],[363,33572],{"className":33573},[494,789],[363,33575,33577],{"className":33576},[586],[363,33578,33580,33619],{"className":33579},[633,634],[363,33581,33583,33616],{"className":33582},[638],[363,33584,33586,33597,33605],{"className":33585,"style":23236},[642],[363,33587,33588,33591],{"style":805},[363,33589],{"className":33590,"style":809},[650],[363,33592,33594],{"className":33593},[407],[363,33595,2810],{"className":33596},[407],[363,33598,33599,33602],{"style":821},[363,33600],{"className":33601,"style":809},[650],[363,33603],{"className":33604,"style":829},[828],[363,33606,33607,33610],{"style":832},[363,33608],{"className":33609,"style":809},[650],[363,33611,33613],{"className":33612},[407],[363,33614,465],{"className":33615},[407],[363,33617,666],{"className":33618},[665],[363,33620,33622],{"className":33621},[638],[363,33623,33625],{"className":33624,"style":4125},[642],[363,33626],{},[363,33628],{"className":33629},[501,789],[363,33631,33633],{"className":33632},[407],[363,33634,33010],{"className":33635},[407,33009],[363,33637,461],{"className":33638},[494],[363,33640,561],{"className":33641},[407,408],[363,33643,558],{"className":33644},[407],[363,33646,25914],{"className":33647,"style":25948},[407,408],[363,33649,468],{"className":33650},[501],[363,33652,33653,33656],{"style":2250},[363,33654],{"className":33655,"style":23013},[650],[363,33657,33659,33662,33665,33668,33671,33733,33736,33741,33744,33747,33750,33753,33756,33818,33821,33826,33829,33832,33835,33838,33841,33846,33849,33852,33855,33858,33861],{"className":33658},[407],[363,33660],{"className":33661},[407],[363,33663],{"className":33664,"style":506},[505],[363,33666,10299],{"className":33667},[510],[363,33669],{"className":33670,"style":506},[505],[363,33672,33674,33677,33730],{"className":33673},[407],[363,33675],{"className":33676},[494,789],[363,33678,33680],{"className":33679},[586],[363,33681,33683,33722],{"className":33682},[633,634],[363,33684,33686,33719],{"className":33685},[638],[363,33687,33689,33700,33708],{"className":33688,"style":23236},[642],[363,33690,33691,33694],{"style":805},[363,33692],{"className":33693,"style":809},[650],[363,33695,33697],{"className":33696},[407],[363,33698,2810],{"className":33699},[407],[363,33701,33702,33705],{"style":821},[363,33703],{"className":33704,"style":809},[650],[363,33706],{"className":33707,"style":829},[828],[363,33709,33710,33713],{"style":832},[363,33711],{"className":33712,"style":809},[650],[363,33714,33716],{"className":33715},[407],[363,33717,465],{"className":33718},[407],[363,33720,666],{"className":33721},[665],[363,33723,33725],{"className":33724},[638],[363,33726,33728],{"className":33727,"style":4125},[642],[363,33729],{},[363,33731],{"className":33732},[501,789],[363,33734],{"className":33735,"style":754},[505],[363,33737,4501,33739],{"className":33738},[1831],[363,33740,4505],{"style":4504},[363,33742],{"className":33743,"style":754},[505],[363,33745,2810],{"className":33746},[407],[363,33748],{"className":33749,"style":2934},[505],[363,33751,2817],{"className":33752},[2938],[363,33754],{"className":33755,"style":2934},[505],[363,33757,33759,33762,33815],{"className":33758},[407],[363,33760],{"className":33761},[494,789],[363,33763,33765],{"className":33764},[586],[363,33766,33768,33807],{"className":33767},[633,634],[363,33769,33771,33804],{"className":33770},[638],[363,33772,33774,33785,33793],{"className":33773,"style":23236},[642],[363,33775,33776,33779],{"style":805},[363,33777],{"className":33778,"style":809},[650],[363,33780,33782],{"className":33781},[407],[363,33783,2810],{"className":33784},[407],[363,33786,33787,33790],{"style":821},[363,33788],{"className":33789,"style":809},[650],[363,33791],{"className":33792,"style":829},[828],[363,33794,33795,33798],{"style":832},[363,33796],{"className":33797,"style":809},[650],[363,33799,33801],{"className":33800},[407],[363,33802,465],{"className":33803},[407],[363,33805,666],{"className":33806},[665],[363,33808,33810],{"className":33809},[638],[363,33811,33813],{"className":33812,"style":4125},[642],[363,33814],{},[363,33816],{"className":33817},[501,789],[363,33819],{"className":33820,"style":754},[505],[363,33822,4501,33824],{"className":33823},[1831],[363,33825,4505],{"style":4504},[363,33827],{"className":33828,"style":754},[505],[363,33830,2810],{"className":33831},[407],[363,33833],{"className":33834,"style":506},[505],[363,33836,471],{"className":33837},[510],[363,33839],{"className":33840,"style":506},[505],[363,33842,4501,33844],{"className":33843},[1831],[363,33845,4505],{"style":4504},[363,33847],{"className":33848,"style":754},[505],[363,33850,2810],{"className":33851},[407],[363,33853],{"className":33854,"style":506},[505],[363,33856,33306],{"className":33857},[510],[363,33859],{"className":33860,"style":506},[505],[363,33862,33309],{"className":33863},[407],[363,33865,666],{"className":33866},[665],[363,33868,33870],{"className":33869},[638],[363,33871,33873],{"className":33872,"style":33441},[642],[363,33874],{},[11,33876,33877,33878,33930],{},"等号成立当且仅当 ",[363,33879,33881,33900],{"className":33880,"translate":367},[366],[363,33882,33884],{"className":33883},[371],[373,33885,33886],{"xmlns":375},[377,33887,33888,33897],{},[380,33889,33890,33892,33895],{},[383,33891,554],{},[458,33893,33894],{},"⊥",[383,33896,561],{},[387,33898,33899],{"encoding":389},"P\\perp Q",[363,33901,33903,33921],{"className":33902,"ariaHidden":394},[393],[363,33904,33906,33909,33912,33915,33918],{"className":33905},[398],[363,33907],{"className":33908,"style":12944},[402],[363,33910,554],{"className":33911,"style":682},[407,408],[363,33913],{"className":33914,"style":506},[505],[363,33916,33894],{"className":33917},[510],[363,33919],{"className":33920,"style":506},[505],[363,33922,33924,33927],{"className":33923},[398],[363,33925],{"className":33926,"style":913},[402],[363,33928,561],{"className":33929},[407,408],"（支撑集不重叠）。有界是 JS 相对 KL 的最大优点（梯度消失则是它最大的缺点，二者互为因果）。",[11,33932,33933,33935,33936,33965,33966,33999,34000,34028,34029,34057,34058,34086,34087,34115,34116,2756,34144,34172,34173,9747],{},[1572,33934,24540],{}," JS 有一个很直观的信息论解释：先掷一枚公平硬币 ",[363,33937,33939,33953],{"className":33938,"translate":367},[366],[363,33940,33942],{"className":33941},[371],[373,33943,33944],{"xmlns":375},[377,33945,33946,33951],{},[380,33947,33948],{},[383,33949,33950],{},"Z",[387,33952,33950],{"encoding":389},[363,33954,33956],{"className":33955,"ariaHidden":394},[393],[363,33957,33959,33962],{"className":33958},[398],[363,33960],{"className":33961,"style":1011},[402],[363,33963,33950],{"className":33964,"style":11129},[407,408],"（正反面各 ",[363,33967,33969,33987],{"className":33968,"translate":367},[366],[363,33970,33972],{"className":33971},[371],[373,33973,33974],{"xmlns":375},[377,33975,33976,33984],{},[380,33977,33978,33980,33982],{},[463,33979,465],{},[383,33981,1288],{"mathvariant":557},[463,33983,2810],{},[387,33985,33986],{"encoding":389},"1\u002F2",[363,33988,33990],{"className":33989,"ariaHidden":394},[393],[363,33991,33993,33996],{"className":33992},[398],[363,33994],{"className":33995,"style":487},[402],[363,33997,33986],{"className":33998},[407],"），正面时从 ",[363,34001,34003,34016],{"className":34002,"translate":367},[366],[363,34004,34006],{"className":34005},[371],[373,34007,34008],{"xmlns":375},[377,34009,34010,34014],{},[380,34011,34012],{},[383,34013,554],{},[387,34015,554],{"encoding":389},[363,34017,34019],{"className":34018,"ariaHidden":394},[393],[363,34020,34022,34025],{"className":34021},[398],[363,34023],{"className":34024,"style":1011},[402],[363,34026,554],{"className":34027,"style":682},[407,408]," 取样、反面时从 ",[363,34030,34032,34045],{"className":34031,"translate":367},[366],[363,34033,34035],{"className":34034},[371],[373,34036,34037],{"xmlns":375},[377,34038,34039,34043],{},[380,34040,34041],{},[383,34042,561],{},[387,34044,561],{"encoding":389},[363,34046,34048],{"className":34047,"ariaHidden":394},[393],[363,34049,34051,34054],{"className":34050},[398],[363,34052],{"className":34053,"style":913},[402],[363,34055,561],{"className":34056},[407,408]," 取样，得到观测 ",[363,34059,34061,34074],{"className":34060,"translate":367},[366],[363,34062,34064],{"className":34063},[371],[373,34065,34066],{"xmlns":375},[377,34067,34068,34072],{},[380,34069,34070],{},[383,34071,945],{},[387,34073,945],{"encoding":389},[363,34075,34077],{"className":34076,"ariaHidden":394},[393],[363,34078,34080,34083],{"className":34079},[398],[363,34081],{"className":34082,"style":1011},[402],[363,34084,945],{"className":34085,"style":9234},[407,408],"；则 JS 正是「看一眼 ",[363,34088,34090,34103],{"className":34089,"translate":367},[366],[363,34091,34093],{"className":34092},[371],[373,34094,34095],{"xmlns":375},[377,34096,34097,34101],{},[380,34098,34099],{},[383,34100,945],{},[387,34102,945],{"encoding":389},[363,34104,34106],{"className":34105,"ariaHidden":394},[393],[363,34107,34109,34112],{"className":34108},[398],[363,34110],{"className":34111,"style":1011},[402],[363,34113,945],{"className":34114,"style":9234},[407,408]," 能否判断硬币正反」所蕴含的信息量，即 ",[363,34117,34119,34132],{"className":34118,"translate":367},[366],[363,34120,34122],{"className":34121},[371],[373,34123,34124],{"xmlns":375},[377,34125,34126,34130],{},[380,34127,34128],{},[383,34129,33950],{},[387,34131,33950],{"encoding":389},[363,34133,34135],{"className":34134,"ariaHidden":394},[393],[363,34136,34138,34141],{"className":34137},[398],[363,34139],{"className":34140,"style":1011},[402],[363,34142,33950],{"className":34143,"style":11129},[407,408],[363,34145,34147,34160],{"className":34146,"translate":367},[366],[363,34148,34150],{"className":34149},[371],[373,34151,34152],{"xmlns":375},[377,34153,34154,34158],{},[380,34155,34156],{},[383,34157,945],{},[387,34159,945],{"encoding":389},[363,34161,34163],{"className":34162,"ariaHidden":394},[393],[363,34164,34166,34169],{"className":34165},[398],[363,34167],{"className":34168,"style":1011},[402],[363,34170,945],{"className":34171,"style":9234},[407,408]," 的",[1572,34174,34175],{},"互信息",[363,34177,34179],{"className":34178,"translate":367},[528],[363,34180,34182,34261],{"className":34181,"translate":367},[366],[363,34183,34185],{"className":34184},[371],[373,34186,34187],{"xmlns":375,"display":537},[377,34188,34189,34258],{},[380,34190,34191,34201,34203,34205,34207,34209,34211,34213,34216,34218,34220,34223,34225,34227,34229,34232,34234,34236,34238,34240,34242,34244,34246,34248,34250,34252,34254,34256],{},[543,34192,34193,34195],{},[383,34194,547],{},[380,34196,34197,34199],{},[383,34198,24090],{},[383,34200,26084],{},[458,34202,461],{"stretchy":460},[383,34204,554],{},[383,34206,558],{"mathvariant":557},[383,34208,561],{},[458,34210,468],{"stretchy":460},[458,34212,471],{},[383,34214,34215],{},"I",[458,34217,461],{"stretchy":460},[383,34219,33950],{},[458,34221,34222],{"separator":394},";",[383,34224,945],{},[458,34226,468],{"stretchy":460},[458,34228,471],{},[383,34230,34231],{},"H",[458,34233,461],{"stretchy":460},[383,34235,945],{},[458,34237,468],{"stretchy":460},[458,34239,5160],{},[383,34241,34231],{},[458,34243,461],{"stretchy":460},[383,34245,945],{},[1644,34247,1646],{},[383,34249,5155],{"mathvariant":557},[1644,34251,1646],{},[383,34253,33950],{},[458,34255,468],{"stretchy":460},[383,34257,4722],{"mathvariant":557},[387,34259,34260],{"encoding":389},"D_{JS}(P\\|Q)=I(Z;X)=H(X)-H(X\\,|\\,Z).",[363,34262,34264,34340,34376,34404],{"className":34263,"ariaHidden":394},[393],[363,34265,34267,34270,34316,34319,34322,34325,34328,34331,34334,34337],{"className":34266},[398],[363,34268],{"className":34269,"style":487},[402],[363,34271,34273,34276],{"className":34272},[407],[363,34274,547],{"className":34275,"style":625},[407,408],[363,34277,34279],{"className":34278},[629],[363,34280,34282,34308],{"className":34281},[633,634],[363,34283,34285,34305],{"className":34284},[638],[363,34286,34288],{"className":34287,"style":727},[642],[363,34289,34290,34293],{"style":646},[363,34291],{"className":34292,"style":651},[650],[363,34294,34296],{"className":34295},[655,656,657,658],[363,34297,34299,34302],{"className":34298},[407,658],[363,34300,24090],{"className":34301,"style":24500},[407,408,658],[363,34303,26084],{"className":34304,"style":26208},[407,408,658],[363,34306,666],{"className":34307},[665],[363,34309,34311],{"className":34310},[638],[363,34312,34314],{"className":34313,"style":8315},[642],[363,34315],{},[363,34317,461],{"className":34318},[494],[363,34320,554],{"className":34321,"style":682},[407,408],[363,34323,558],{"className":34324},[407],[363,34326,561],{"className":34327},[407,408],[363,34329,468],{"className":34330},[501],[363,34332],{"className":34333,"style":506},[505],[363,34335,471],{"className":34336},[510],[363,34338],{"className":34339,"style":506},[505],[363,34341,34343,34346,34349,34352,34355,34358,34361,34364,34367,34370,34373],{"className":34342},[398],[363,34344],{"className":34345,"style":487},[402],[363,34347,34215],{"className":34348,"style":9234},[407,408],[363,34350,461],{"className":34351},[494],[363,34353,33950],{"className":34354,"style":11129},[407,408],[363,34356,34222],{"className":34357},[920],[363,34359],{"className":34360,"style":754},[505],[363,34362,945],{"className":34363,"style":9234},[407,408],[363,34365,468],{"className":34366},[501],[363,34368],{"className":34369,"style":506},[505],[363,34371,471],{"className":34372},[510],[363,34374],{"className":34375,"style":506},[505],[363,34377,34379,34382,34386,34389,34392,34395,34398,34401],{"className":34378},[398],[363,34380],{"className":34381,"style":487},[402],[363,34383,34231],{"className":34384,"style":34385},[407,408],"margin-right:0.0813em;",[363,34387,461],{"className":34388},[494],[363,34390,945],{"className":34391,"style":9234},[407,408],[363,34393,468],{"className":34394},[501],[363,34396],{"className":34397,"style":2934},[505],[363,34399,5160],{"className":34400},[2938],[363,34402],{"className":34403,"style":2934},[505],[363,34405,34407,34410,34413,34416,34419,34422,34425,34428,34431,34434],{"className":34406},[398],[363,34408],{"className":34409,"style":487},[402],[363,34411,34231],{"className":34412,"style":34385},[407,408],[363,34414,461],{"className":34415},[494],[363,34417,945],{"className":34418,"style":9234},[407,408],[363,34420],{"className":34421,"style":754},[505],[363,34423,5155],{"className":34424},[407],[363,34426],{"className":34427,"style":754},[505],[363,34429,33950],{"className":34430,"style":11129},[407,408],[363,34432,468],{"className":34433},[501],[363,34435,4722],{"className":34436},[407],[11,34438,34439,34440,34468,34469,34501,34502,34630,34631,34672,34673,34811,34812,34853],{},"由于 ",[363,34441,34443,34456],{"className":34442,"translate":367},[366],[363,34444,34446],{"className":34445},[371],[373,34447,34448],{"xmlns":375},[377,34449,34450,34454],{},[380,34451,34452],{},[383,34453,33950],{},[387,34455,33950],{"encoding":389},[363,34457,34459],{"className":34458,"ariaHidden":394},[393],[363,34460,34462,34465],{"className":34461},[398],[363,34463],{"className":34464,"style":1011},[402],[363,34466,33950],{"className":34467,"style":11129},[407,408]," 是概率 ",[363,34470,34472,34489],{"className":34471,"translate":367},[366],[363,34473,34475],{"className":34474},[371],[373,34476,34477],{"xmlns":375},[377,34478,34479,34487],{},[380,34480,34481,34483,34485],{},[463,34482,465],{},[383,34484,1288],{"mathvariant":557},[463,34486,2810],{},[387,34488,33986],{"encoding":389},[363,34490,34492],{"className":34491,"ariaHidden":394},[393],[363,34493,34495,34498],{"className":34494},[398],[363,34496],{"className":34497,"style":487},[402],[363,34499,33986],{"className":34500},[407]," 的伯努利变量，",[363,34503,34505,34547],{"className":34504,"translate":367},[366],[363,34506,34508],{"className":34507},[371],[373,34509,34510],{"xmlns":375},[377,34511,34512,34544],{},[380,34513,34514,34516,34518,34520,34522,34524,34526,34528,34530,34532,34534,34536,34538,34540,34542],{},[383,34515,34215],{},[458,34517,461],{"stretchy":460},[383,34519,33950],{},[458,34521,34222],{"separator":394},[383,34523,945],{},[458,34525,468],{"stretchy":460},[458,34527,10299],{},[383,34529,34231],{},[458,34531,461],{"stretchy":460},[383,34533,33950],{},[458,34535,468],{"stretchy":460},[458,34537,471],{},[383,34539,4447],{},[458,34541,4450],{},[463,34543,2810],{},[387,34545,34546],{"encoding":389},"I(Z;X)\\le H(Z)=\\log 2",[363,34548,34550,34586,34613],{"className":34549,"ariaHidden":394},[393],[363,34551,34553,34556,34559,34562,34565,34568,34571,34574,34577,34580,34583],{"className":34552},[398],[363,34554],{"className":34555,"style":487},[402],[363,34557,34215],{"className":34558,"style":9234},[407,408],[363,34560,461],{"className":34561},[494],[363,34563,33950],{"className":34564,"style":11129},[407,408],[363,34566,34222],{"className":34567},[920],[363,34569],{"className":34570,"style":754},[505],[363,34572,945],{"className":34573,"style":9234},[407,408],[363,34575,468],{"className":34576},[501],[363,34578],{"className":34579,"style":506},[505],[363,34581,10299],{"className":34582},[510],[363,34584],{"className":34585,"style":506},[505],[363,34587,34589,34592,34595,34598,34601,34604,34607,34610],{"className":34588},[398],[363,34590],{"className":34591,"style":487},[402],[363,34593,34231],{"className":34594,"style":34385},[407,408],[363,34596,461],{"className":34597},[494],[363,34599,33950],{"className":34600,"style":11129},[407,408],[363,34602,468],{"className":34603},[501],[363,34605],{"className":34606,"style":506},[505],[363,34608,471],{"className":34609},[510],[363,34611],{"className":34612,"style":506},[505],[363,34614,34616,34619,34624,34627],{"className":34615},[398],[363,34617],{"className":34618,"style":403},[402],[363,34620,4501,34622],{"className":34621},[1831],[363,34623,4505],{"style":4504},[363,34625],{"className":34626,"style":754},[505],[363,34628,2810],{"className":34629},[407],"，有界性由此而来，",[363,34632,34634,34652],{"className":34633,"translate":367},[366],[363,34635,34637],{"className":34636},[371],[373,34638,34639],{"xmlns":375},[377,34640,34641,34649],{},[380,34642,34643,34645,34647],{},[383,34644,4447],{},[458,34646,4450],{},[463,34648,2810],{},[387,34650,34651],{"encoding":389},"\\log 2",[363,34653,34655],{"className":34654,"ariaHidden":394},[393],[363,34656,34658,34661,34666,34669],{"className":34657},[398],[363,34659],{"className":34660,"style":403},[402],[363,34662,4501,34664],{"className":34663},[1831],[363,34665,4505],{"style":4504},[363,34667],{"className":34668,"style":754},[505],[363,34670,2810],{"className":34671},[407]," 恰好对应「最多只能获得 1 比特」这一直觉。JS 对称、有界且 ",[363,34674,34676,34701],{"className":34675,"translate":367},[366],[363,34677,34679],{"className":34678},[371],[373,34680,34681],{"xmlns":375},[377,34682,34683,34698],{},[380,34684,34685],{},[34686,34687,34688],"msqrt",{},[543,34689,34690,34692],{},[383,34691,547],{},[380,34693,34694,34696],{},[383,34695,24090],{},[383,34697,26084],{},[387,34699,34700],{"encoding":389},"\\sqrt{D_{JS}}",[363,34702,34704],{"className":34703,"ariaHidden":394},[393],[363,34705,34707,34711],{"className":34706},[398],[363,34708],{"className":34709,"style":34710},[402],"height:1.04em;vertical-align:-0.1883em;",[363,34712,34715],{"className":34713},[407,34714],"sqrt",[363,34716,34718,34802],{"className":34717},[633,634],[363,34719,34721,34799],{"className":34720},[638],[363,34722,34725,34781],{"className":34723,"style":34724},[642],"height:0.8517em;",[363,34726,34728,34731],{"className":34727,"style":12210},[6654],[363,34729],{"className":34730,"style":809},[650],[363,34732,34735],{"className":34733,"style":34734},[407],"padding-left:0.833em;",[363,34736,34738,34741],{"className":34737},[407],[363,34739,547],{"className":34740,"style":625},[407,408],[363,34742,34744],{"className":34743},[629],[363,34745,34747,34773],{"className":34746},[633,634],[363,34748,34750,34770],{"className":34749},[638],[363,34751,34753],{"className":34752,"style":727},[642],[363,34754,34755,34758],{"style":646},[363,34756],{"className":34757,"style":651},[650],[363,34759,34761],{"className":34760},[655,656,657,658],[363,34762,34764,34767],{"className":34763},[407,658],[363,34765,24090],{"className":34766,"style":24500},[407,408,658],[363,34768,26084],{"className":34769,"style":26208},[407,408,658],[363,34771,666],{"className":34772},[665],[363,34774,34776],{"className":34775},[638],[363,34777,34779],{"className":34778,"style":8315},[642],[363,34780],{},[363,34782,34784,34787],{"style":34783},"top:-2.8117em;",[363,34785],{"className":34786,"style":809},[650],[363,34788,34792],{"className":34789,"style":34791},[34790],"hide-tail","min-width:0.853em;height:1.08em;",[6670,34793,34796],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},"1.08em","0 0 400000 1080",[6678,34797],{"d":34798},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[363,34800,666],{"className":34801},[665],[363,34803,34805],{"className":34804},[638],[363,34806,34809],{"className":34807,"style":34808},[642],"height:0.1883em;",[363,34810],{}," 仍是度量，因此在文本\u002F分布聚类、模型比较与原始 GAN 目标里被广泛使用；代价同样来自「有界」与上面这个混合结构——真差异越大 JS 越接近饱和的 ",[363,34813,34815,34833],{"className":34814,"translate":367},[366],[363,34816,34818],{"className":34817},[371],[373,34819,34820],{"xmlns":375},[377,34821,34822,34830],{},[380,34823,34824,34826,34828],{},[383,34825,4447],{},[458,34827,4450],{},[463,34829,2810],{},[387,34831,34832],{"encoding":389},"\\log2",[363,34834,34836],{"className":34835,"ariaHidden":394},[393],[363,34837,34839,34842,34847,34850],{"className":34838},[398],[363,34840],{"className":34841,"style":403},[402],[363,34843,4501,34845],{"className":34844},[1831],[363,34846,4505],{"style":4504},[363,34848],{"className":34849,"style":754},[505],[363,34851,2810],{"className":34852},[407],"，梯度随之消失，这正是 WGAN 等替代方案的动机。",[2658,34855,34857],{"id":34856},"_33-全变差","3.3 全变差",[11,34859,21820],{},[363,34861,34863],{"className":34862,"translate":367},[528],[363,34864,34866,34904],{"className":34865,"translate":367},[366],[363,34867,34869],{"className":34868},[371],[373,34870,34871],{"xmlns":375,"display":537},[377,34872,34873,34901],{},[380,34874,34875,34877,34879,34881,34883,34885,34891,34893,34895,34897,34899],{},[383,34876,385],{},[458,34878,461],{"stretchy":460},[383,34880,1116],{},[458,34882,468],{"stretchy":460},[458,34884,471],{},[586,34886,34887,34889],{},[463,34888,465],{},[463,34890,2810],{},[383,34892,5155],{"mathvariant":557},[383,34894,1116],{},[458,34896,5160],{},[463,34898,465],{},[383,34900,5155],{"mathvariant":557},[387,34902,34903],{"encoding":389},"f(t)=\\frac12|t-1|",[363,34905,34907,34934,35017],{"className":34906,"ariaHidden":394},[393],[363,34908,34910,34913,34916,34919,34922,34925,34928,34931],{"className":34909},[398],[363,34911],{"className":34912,"style":487},[402],[363,34914,385],{"className":34915,"style":409},[407,408],[363,34917,461],{"className":34918},[494],[363,34920,1116],{"className":34921},[407,408],[363,34923,468],{"className":34924},[501],[363,34926],{"className":34927,"style":506},[505],[363,34929,471],{"className":34930},[510],[363,34932],{"className":34933,"style":506},[505],[363,34935,34937,34940,35002,35005,35008,35011,35014],{"className":34936},[398],[363,34938],{"className":34939,"style":26250},[402],[363,34941,34943,34946,34999],{"className":34942},[407],[363,34944],{"className":34945},[494,789],[363,34947,34949],{"className":34948},[586],[363,34950,34952,34991],{"className":34951},[633,634],[363,34953,34955,34988],{"className":34954},[638],[363,34956,34958,34969,34977],{"className":34957,"style":23236},[642],[363,34959,34960,34963],{"style":805},[363,34961],{"className":34962,"style":809},[650],[363,34964,34966],{"className":34965},[407],[363,34967,2810],{"className":34968},[407],[363,34970,34971,34974],{"style":821},[363,34972],{"className":34973,"style":809},[650],[363,34975],{"className":34976,"style":829},[828],[363,34978,34979,34982],{"style":832},[363,34980],{"className":34981,"style":809},[650],[363,34983,34985],{"className":34984},[407],[363,34986,465],{"className":34987},[407],[363,34989,666],{"className":34990},[665],[363,34992,34994],{"className":34993},[638],[363,34995,34997],{"className":34996,"style":4125},[642],[363,34998],{},[363,35000],{"className":35001},[501,789],[363,35003,5155],{"className":35004},[407],[363,35006,1116],{"className":35007},[407,408],[363,35009],{"className":35010,"style":2934},[505],[363,35012,5160],{"className":35013},[2938],[363,35015],{"className":35016,"style":2934},[505],[363,35018,35020,35023],{"className":35019},[398],[363,35021],{"className":35022,"style":487},[402],[363,35024,35026],{"className":35025},[407],"1∣",[11,35028,35029,35030,35095],{},"则 ",[363,35031,35033,35056],{"className":35032,"translate":367},[366],[363,35034,35036],{"className":35035},[371],[373,35037,35038],{"xmlns":375},[377,35039,35040,35054],{},[380,35041,35042,35044,35046,35048,35050,35052],{},[383,35043,385],{},[458,35045,461],{"stretchy":460},[463,35047,465],{},[458,35049,468],{"stretchy":460},[458,35051,471],{},[463,35053,474],{},[387,35055,477],{"encoding":389},[363,35057,35059,35086],{"className":35058,"ariaHidden":394},[393],[363,35060,35062,35065,35068,35071,35074,35077,35080,35083],{"className":35061},[398],[363,35063],{"className":35064,"style":487},[402],[363,35066,385],{"className":35067,"style":409},[407,408],[363,35069,461],{"className":35070},[494],[363,35072,465],{"className":35073},[407],[363,35075,468],{"className":35076},[501],[363,35078],{"className":35079,"style":506},[505],[363,35081,471],{"className":35082},[510],[363,35084],{"className":35085,"style":506},[505],[363,35087,35089,35092],{"className":35088},[398],[363,35090],{"className":35091,"style":520},[402],[363,35093,474],{"className":35094},[407]," 且凸（绝对值是凸函数），代入：",[363,35097,35099],{"className":35098,"translate":367},[528],[363,35100,35102,35213],{"className":35101,"translate":367},[366],[363,35103,35105],{"className":35104},[371],[373,35106,35107],{"xmlns":375,"display":537},[377,35108,35109,35210],{},[380,35110,35111,35117,35119,35121,35123,35125,35127,35129,35135,35137,35139,35155,35157,35159,35161,35167,35169,35171,35173,35175,35177,35179,35181,35183,35185,35187,35198,35200,35202,35204,35206,35208],{},[543,35112,35113,35115],{},[383,35114,547],{},[383,35116,385],{},[458,35118,461],{"stretchy":460},[383,35120,554],{},[383,35122,558],{"mathvariant":557},[383,35124,561],{},[458,35126,468],{"stretchy":460},[458,35128,471],{},[586,35130,35131,35133],{},[463,35132,465],{},[463,35134,2810],{},[458,35136,1634],{},[383,35138,1291],{},[380,35140,35141,35143,35149,35151,35153],{},[458,35142,5155],{"fence":394},[586,35144,35145,35147],{},[383,35146,11],{},[383,35148,1291],{},[458,35150,5160],{},[463,35152,465],{},[458,35154,5155],{"fence":394},[383,35156,592],{},[383,35158,1121],{},[458,35160,471],{},[586,35162,35163,35165],{},[463,35164,465],{},[463,35166,2810],{},[458,35168,1634],{},[383,35170,5155],{"mathvariant":557},[383,35172,11],{},[458,35174,5160],{},[383,35176,1291],{},[383,35178,5155],{"mathvariant":557},[1644,35180,1646],{},[383,35182,592],{},[383,35184,1121],{},[458,35186,471],{},[543,35188,35189,35191],{},[383,35190,547],{},[380,35192,35193,35195],{},[383,35194,5739],{},[383,35196,35197],{},"V",[458,35199,461],{"stretchy":460},[383,35201,554],{},[383,35203,558],{"mathvariant":557},[383,35205,561],{},[458,35207,468],{"stretchy":460},[383,35209,4722],{"mathvariant":557},[387,35211,35212],{"encoding":389},"D_f(P\\|Q)\n=\\frac12\\int q\\left|\\frac{p}{q}-1\\right|dx\n=\\frac12\\int |p-q|\\,dx\n=D_{TV}(P\\|Q).",[363,35214,35216,35286,35544,35636,35666],{"className":35215,"ariaHidden":394},[393],[363,35217,35219,35222,35262,35265,35268,35271,35274,35277,35280,35283],{"className":35218},[398],[363,35220],{"className":35221,"style":618},[402],[363,35223,35225,35228],{"className":35224},[407],[363,35226,547],{"className":35227,"style":625},[407,408],[363,35229,35231],{"className":35230},[629],[363,35232,35234,35254],{"className":35233},[633,634],[363,35235,35237,35251],{"className":35236},[638],[363,35238,35240],{"className":35239,"style":643},[642],[363,35241,35242,35245],{"style":646},[363,35243],{"className":35244,"style":651},[650],[363,35246,35248],{"className":35247},[655,656,657,658],[363,35249,385],{"className":35250,"style":409},[407,408,658],[363,35252,666],{"className":35253},[665],[363,35255,35257],{"className":35256},[638],[363,35258,35260],{"className":35259,"style":673},[642],[363,35261],{},[363,35263,461],{"className":35264},[494],[363,35266,554],{"className":35267,"style":682},[407,408],[363,35269,558],{"className":35270},[407],[363,35272,561],{"className":35273},[407,408],[363,35275,468],{"className":35276},[501],[363,35278],{"className":35279,"style":506},[505],[363,35281,471],{"className":35282},[510],[363,35284],{"className":35285,"style":506},[505],[363,35287,35289,35292,35354,35357,35360,35363,35366,35369,35526,35529,35532,35535,35538,35541],{"className":35288},[398],[363,35290],{"className":35291,"style":707},[402],[363,35293,35295,35298,35351],{"className":35294},[407],[363,35296],{"className":35297},[494,789],[363,35299,35301],{"className":35300},[586],[363,35302,35304,35343],{"className":35303},[633,634],[363,35305,35307,35340],{"className":35306},[638],[363,35308,35310,35321,35329],{"className":35309,"style":23236},[642],[363,35311,35312,35315],{"style":805},[363,35313],{"className":35314,"style":809},[650],[363,35316,35318],{"className":35317},[407],[363,35319,2810],{"className":35320},[407],[363,35322,35323,35326],{"style":821},[363,35324],{"className":35325,"style":809},[650],[363,35327],{"className":35328,"style":829},[828],[363,35330,35331,35334],{"style":832},[363,35332],{"className":35333,"style":809},[650],[363,35335,35337],{"className":35336},[407],[363,35338,465],{"className":35339},[407],[363,35341,666],{"className":35342},[665],[363,35344,35346],{"className":35345},[638],[363,35347,35349],{"className":35348,"style":4125},[642],[363,35350],{},[363,35352],{"className":35353},[501,789],[363,35355],{"className":35356,"style":754},[505],[363,35358,1634],{"className":35359,"style":1834},[1831,1832,1833],[363,35361],{"className":35362,"style":754},[505],[363,35364,1291],{"className":35365,"style":1328},[407,408],[363,35367],{"className":35368,"style":754},[505],[363,35370,35372,35415,35477,35480,35483,35486,35489],{"className":35371},[758],[363,35373,35375],{"className":35374},[494],[363,35376,35378],{"className":35377},[767,15176],[363,35379,35381,35407],{"className":35380},[633,634],[363,35382,35384,35404],{"className":35383},[638],[363,35385,35387],{"className":35386,"style":1717},[642],[363,35388,35389,35393],{"style":1720},[363,35390],{"className":35391,"style":35392},[650],"height:4.4em;",[363,35394,35396],{"style":35395},"width:0.333em;height:2.4em;",[6670,35397,35401],{"xmlns":6672,"width":35398,"height":35399,"viewBox":35400},"0.333em","2.4em","0 0 333 2400",[6678,35402],{"d":35403},"M145 15 v585 v1200 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v-1200 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v1200 v585 h43z",[363,35405,666],{"className":35406},[665],[363,35408,35410],{"className":35409},[638],[363,35411,35413],{"className":35412,"style":1792},[642],[363,35414],{},[363,35416,35418,35421,35474],{"className":35417},[407],[363,35419],{"className":35420},[494,789],[363,35422,35424],{"className":35423},[586],[363,35425,35427,35466],{"className":35426},[633,634],[363,35428,35430,35463],{"className":35429},[638],[363,35431,35433,35444,35452],{"className":35432,"style":3901},[642],[363,35434,35435,35438],{"style":805},[363,35436],{"className":35437,"style":809},[650],[363,35439,35441],{"className":35440},[407],[363,35442,1291],{"className":35443,"style":1328},[407,408],[363,35445,35446,35449],{"style":821},[363,35447],{"className":35448,"style":809},[650],[363,35450],{"className":35451,"style":829},[828],[363,35453,35454,35457],{"style":832},[363,35455],{"className":35456,"style":809},[650],[363,35458,35460],{"className":35459},[407],[363,35461,11],{"className":35462},[407,408],[363,35464,666],{"className":35465},[665],[363,35467,35469],{"className":35468},[638],[363,35470,35472],{"className":35471,"style":854},[642],[363,35473],{},[363,35475],{"className":35476},[501,789],[363,35478],{"className":35479,"style":2934},[505],[363,35481,5160],{"className":35482},[2938],[363,35484],{"className":35485,"style":2934},[505],[363,35487,465],{"className":35488},[407],[363,35490,35492],{"className":35491},[501],[363,35493,35495],{"className":35494},[767,15176],[363,35496,35498,35518],{"className":35497},[633,634],[363,35499,35501,35515],{"className":35500},[638],[363,35502,35504],{"className":35503,"style":1717},[642],[363,35505,35506,35509],{"style":1720},[363,35507],{"className":35508,"style":35392},[650],[363,35510,35511],{"style":35395},[6670,35512,35513],{"xmlns":6672,"width":35398,"height":35399,"viewBox":35400},[6678,35514],{"d":35403},[363,35516,666],{"className":35517},[665],[363,35519,35521],{"className":35520},[638],[363,35522,35524],{"className":35523,"style":1792},[642],[363,35525],{},[363,35527],{"className":35528,"style":754},[505],[363,35530,592],{"className":35531},[407,408],[363,35533,1121],{"className":35534},[407,408],[363,35536],{"className":35537,"style":506},[505],[363,35539,471],{"className":35540},[510],[363,35542],{"className":35543,"style":506},[505],[363,35545,35547,35550,35612,35615,35618,35621,35624,35627,35630,35633],{"className":35546},[398],[363,35548],{"className":35549,"style":6124},[402],[363,35551,35553,35556,35609],{"className":35552},[407],[363,35554],{"className":35555},[494,789],[363,35557,35559],{"className":35558},[586],[363,35560,35562,35601],{"className":35561},[633,634],[363,35563,35565,35598],{"className":35564},[638],[363,35566,35568,35579,35587],{"className":35567,"style":23236},[642],[363,35569,35570,35573],{"style":805},[363,35571],{"className":35572,"style":809},[650],[363,35574,35576],{"className":35575},[407],[363,35577,2810],{"className":35578},[407],[363,35580,35581,35584],{"style":821},[363,35582],{"className":35583,"style":809},[650],[363,35585],{"className":35586,"style":829},[828],[363,35588,35589,35592],{"style":832},[363,35590],{"className":35591,"style":809},[650],[363,35593,35595],{"className":35594},[407],[363,35596,465],{"className":35597},[407],[363,35599,666],{"className":35600},[665],[363,35602,35604],{"className":35603},[638],[363,35605,35607],{"className":35606,"style":4125},[642],[363,35608],{},[363,35610],{"className":35611},[501,789],[363,35613],{"className":35614,"style":754},[505],[363,35616,1634],{"className":35617,"style":1834},[1831,1832,1833],[363,35619],{"className":35620,"style":754},[505],[363,35622,5155],{"className":35623},[407],[363,35625,11],{"className":35626},[407,408],[363,35628],{"className":35629,"style":2934},[505],[363,35631,5160],{"className":35632},[2938],[363,35634],{"className":35635,"style":2934},[505],[363,35637,35639,35642,35645,35648,35651,35654,35657,35660,35663],{"className":35638},[398],[363,35640],{"className":35641,"style":487},[402],[363,35643,1291],{"className":35644,"style":1328},[407,408],[363,35646,5155],{"className":35647},[407],[363,35649],{"className":35650,"style":754},[505],[363,35652,592],{"className":35653},[407,408],[363,35655,1121],{"className":35656},[407,408],[363,35658],{"className":35659,"style":506},[505],[363,35661,471],{"className":35662},[510],[363,35664],{"className":35665,"style":506},[505],[363,35667,35669,35672,35718,35721,35724,35727,35730,35733],{"className":35668},[398],[363,35670],{"className":35671,"style":487},[402],[363,35673,35675,35678],{"className":35674},[407],[363,35676,547],{"className":35677,"style":625},[407,408],[363,35679,35681],{"className":35680},[629],[363,35682,35684,35710],{"className":35683},[633,634],[363,35685,35687,35707],{"className":35686},[638],[363,35688,35690],{"className":35689,"style":727},[642],[363,35691,35692,35695],{"style":646},[363,35693],{"className":35694,"style":651},[650],[363,35696,35698],{"className":35697},[655,656,657,658],[363,35699,35701,35704],{"className":35700},[407,658],[363,35702,5739],{"className":35703,"style":682},[407,408,658],[363,35705,35197],{"className":35706,"style":2934},[407,408,658],[363,35708,666],{"className":35709},[665],[363,35711,35713],{"className":35712},[638],[363,35714,35716],{"className":35715,"style":8315},[642],[363,35717],{},[363,35719,461],{"className":35720},[494],[363,35722,554],{"className":35723,"style":682},[407,408],[363,35725,558],{"className":35726},[407],[363,35728,561],{"className":35729},[407,408],[363,35731,468],{"className":35732},[501],[363,35734,4722],{"className":35735},[407],[11,35737,35738,35739,36004,36005,36130],{},"一般测度上 ",[363,35740,35742,35815],{"className":35741,"translate":367},[366],[363,35743,35745],{"className":35744},[371],[373,35746,35747],{"xmlns":375},[377,35748,35749,35812],{},[380,35750,35751,35761,35763,35765,35767,35769,35771,35773,35790,35792,35794,35796,35798,35800,35802,35804,35806,35808,35810],{},[543,35752,35753,35755],{},[383,35754,547],{},[380,35756,35757,35759],{},[383,35758,5739],{},[383,35760,35197],{},[458,35762,461],{"stretchy":460},[383,35764,554],{},[458,35766,898],{"separator":394},[383,35768,561],{},[458,35770,468],{"stretchy":460},[458,35772,471],{},[543,35774,35775,35782],{},[380,35776,35777,35780],{},[383,35778,35779],{},"sup",[458,35781,4450],{},[380,35783,35784,35786,35788],{},[383,35785,950],{},[458,35787,6256],{},[383,35789,950],{"mathvariant":944},[383,35791,5155],{"mathvariant":557},[383,35793,554],{},[458,35795,461],{"stretchy":460},[383,35797,950],{},[458,35799,468],{"stretchy":460},[458,35801,5160],{},[383,35803,561],{},[458,35805,461],{"stretchy":460},[383,35807,950],{},[458,35809,468],{"stretchy":460},[383,35811,5155],{"mathvariant":557},[387,35813,35814],{"encoding":389},"D_{TV}(P,Q)=\\sup_{A\\in\\mathcal A}|P(A)-Q(A)|",[363,35816,35818,35897,35983],{"className":35817,"ariaHidden":394},[393],[363,35819,35821,35824,35870,35873,35876,35879,35882,35885,35888,35891,35894],{"className":35820},[398],[363,35822],{"className":35823,"style":487},[402],[363,35825,35827,35830],{"className":35826},[407],[363,35828,547],{"className":35829,"style":625},[407,408],[363,35831,35833],{"className":35832},[629],[363,35834,35836,35862],{"className":35835},[633,634],[363,35837,35839,35859],{"className":35838},[638],[363,35840,35842],{"className":35841,"style":727},[642],[363,35843,35844,35847],{"style":646},[363,35845],{"className":35846,"style":651},[650],[363,35848,35850],{"className":35849},[655,656,657,658],[363,35851,35853,35856],{"className":35852},[407,658],[363,35854,5739],{"className":35855,"style":682},[407,408,658],[363,35857,35197],{"className":35858,"style":2934},[407,408,658],[363,35860,666],{"className":35861},[665],[363,35863,35865],{"className":35864},[638],[363,35866,35868],{"className":35867,"style":8315},[642],[363,35869],{},[363,35871,461],{"className":35872},[494],[363,35874,554],{"className":35875,"style":682},[407,408],[363,35877,898],{"className":35878},[920],[363,35880],{"className":35881,"style":754},[505],[363,35883,561],{"className":35884},[407,408],[363,35886,468],{"className":35887},[501],[363,35889],{"className":35890,"style":506},[505],[363,35892,471],{"className":35893},[510],[363,35895],{"className":35896,"style":506},[505],[363,35898,35900,35904,35956,35959,35962,35965,35968,35971,35974,35977,35980],{"className":35899},[398],[363,35901],{"className":35902,"style":35903},[402],"height:1.0215em;vertical-align:-0.2715em;",[363,35905,35907,35910],{"className":35906},[1831],[363,35908,35779],{"className":35909},[1831],[363,35911,35913],{"className":35912},[629],[363,35914,35916,35947],{"className":35915},[633,634],[363,35917,35919,35944],{"className":35918},[638],[363,35920,35923],{"className":35921,"style":35922},[642],"height:0.2342em;",[363,35924,35926,35929],{"style":35925},"top:-2.4559em;margin-right:0.05em;",[363,35927],{"className":35928,"style":651},[650],[363,35930,35932],{"className":35931},[655,656,657,658],[363,35933,35935,35938,35941],{"className":35934},[407,658],[363,35936,950],{"className":35937},[407,408,658],[363,35939,6256],{"className":35940},[510,658],[363,35942,950],{"className":35943},[407,971,658],[363,35945,666],{"className":35946},[665],[363,35948,35950],{"className":35949},[638],[363,35951,35954],{"className":35952,"style":35953},[642],"height:0.2715em;",[363,35955],{},[363,35957],{"className":35958,"style":754},[505],[363,35960,5155],{"className":35961},[407],[363,35963,554],{"className":35964,"style":682},[407,408],[363,35966,461],{"className":35967},[494],[363,35969,950],{"className":35970},[407,408],[363,35972,468],{"className":35973},[501],[363,35975],{"className":35976,"style":2934},[505],[363,35978,5160],{"className":35979},[2938],[363,35981],{"className":35982,"style":2934},[505],[363,35984,35986,35989,35992,35995,35998,36001],{"className":35985},[398],[363,35987],{"className":35988,"style":487},[402],[363,35990,561],{"className":35991},[407,408],[363,35993,461],{"className":35994},[494],[363,35996,950],{"className":35997},[407,408],[363,35999,468],{"className":36000},[501],[363,36002,5155],{"className":36003},[407],"；两个表达式相等（这是全变差的对偶刻画）。注意 ",[363,36006,36008,36042],{"className":36007,"translate":367},[366],[363,36009,36011],{"className":36010},[371],[373,36012,36013],{"xmlns":375},[377,36014,36015,36039],{},[380,36016,36017,36027,36029,36031,36033,36035,36037],{},[543,36018,36019,36021],{},[383,36020,547],{},[380,36022,36023,36025],{},[383,36024,5739],{},[383,36026,35197],{},[458,36028,6256],{},[458,36030,578],{"stretchy":460},[463,36032,474],{},[458,36034,898],{"separator":394},[463,36036,465],{},[458,36038,605],{"stretchy":460},[387,36040,36041],{"encoding":389},"D_{TV}\\in[0,1]",[363,36043,36045,36106],{"className":36044,"ariaHidden":394},[393],[363,36046,36048,36051,36097,36100,36103],{"className":36047},[398],[363,36049],{"className":36050,"style":16308},[402],[363,36052,36054,36057],{"className":36053},[407],[363,36055,547],{"className":36056,"style":625},[407,408],[363,36058,36060],{"className":36059},[629],[363,36061,36063,36089],{"className":36062},[633,634],[363,36064,36066,36086],{"className":36065},[638],[363,36067,36069],{"className":36068,"style":727},[642],[363,36070,36071,36074],{"style":646},[363,36072],{"className":36073,"style":651},[650],[363,36075,36077],{"className":36076},[655,656,657,658],[363,36078,36080,36083],{"className":36079},[407,658],[363,36081,5739],{"className":36082,"style":682},[407,408,658],[363,36084,35197],{"className":36085,"style":2934},[407,408,658],[363,36087,666],{"className":36088},[665],[363,36090,36092],{"className":36091},[638],[363,36093,36095],{"className":36094,"style":8315},[642],[363,36096],{},[363,36098],{"className":36099,"style":506},[505],[363,36101,6256],{"className":36102},[510],[363,36104],{"className":36105,"style":506},[505],[363,36107,36109,36112,36115,36118,36121,36124,36127],{"className":36108},[398],[363,36110],{"className":36111,"style":487},[402],[363,36113,578],{"className":36114},[494],[363,36116,474],{"className":36117},[407],[363,36119,898],{"className":36120},[920],[363,36122],{"className":36123,"style":754},[505],[363,36125,465],{"className":36126},[407],[363,36128,605],{"className":36129},[501],"，总有界。",[11,36132,36133,9747,36136,36522],{},[1572,36134,36135],{},"斜共轭",[363,36137,36139,36203],{"className":36138,"translate":367},[366],[363,36140,36142],{"className":36141},[371],[373,36143,36144],{"xmlns":375},[377,36145,36146,36200],{},[380,36147,36148,36150,36152,36158,36160,36166,36168,36170,36172,36174,36180,36182,36184,36186,36188,36190,36192,36194,36196,36198],{},[383,36149,1116],{},[458,36151,3646],{},[586,36153,36154,36156],{},[463,36155,465],{},[463,36157,2810],{},[383,36159,5155],{"mathvariant":557},[586,36161,36162,36164],{},[463,36163,465],{},[383,36165,1116],{},[458,36167,5160],{},[463,36169,465],{},[383,36171,5155],{"mathvariant":557},[458,36173,471],{},[586,36175,36176,36178],{},[463,36177,465],{},[463,36179,2810],{},[383,36181,5155],{"mathvariant":557},[463,36183,465],{},[458,36185,5160],{},[383,36187,1116],{},[383,36189,5155],{"mathvariant":557},[458,36191,471],{},[383,36193,385],{},[458,36195,461],{"stretchy":460},[383,36197,1116],{},[458,36199,468],{"stretchy":460},[387,36201,36202],{"encoding":389},"t\\cdot\\frac12|\\frac1t-1|=\\frac12|1-t|=f(t)",[363,36204,36206,36224,36378,36396,36483,36504],{"className":36205,"ariaHidden":394},[393],[363,36207,36209,36212,36215,36218,36221],{"className":36208},[398],[363,36210],{"className":36211,"style":5690},[402],[363,36213,1116],{"className":36214},[407,408],[363,36216],{"className":36217,"style":2934},[505],[363,36219,3646],{"className":36220},[2938],[363,36222],{"className":36223,"style":2934},[505],[363,36225,36227,36230,36298,36301,36369,36372,36375],{"className":36226},[398],[363,36228],{"className":36229,"style":2852},[402],[363,36231,36233,36236,36295],{"className":36232},[407],[363,36234],{"className":36235},[494,789],[363,36237,36239],{"className":36238},[586],[363,36240,36242,36287],{"className":36241},[633,634],[363,36243,36245,36284],{"className":36244},[638],[363,36246,36248,36262,36270],{"className":36247,"style":2871},[642],[363,36249,36250,36253],{"style":2874},[363,36251],{"className":36252,"style":809},[650],[363,36254,36256],{"className":36255},[655,656,657,658],[363,36257,36259],{"className":36258},[407,658],[363,36260,2810],{"className":36261},[407,658],[363,36263,36264,36267],{"style":821},[363,36265],{"className":36266,"style":809},[650],[363,36268],{"className":36269,"style":829},[828],[363,36271,36272,36275],{"style":2897},[363,36273],{"className":36274,"style":809},[650],[363,36276,36278],{"className":36277},[655,656,657,658],[363,36279,36281],{"className":36280},[407,658],[363,36282,465],{"className":36283},[407,658],[363,36285,666],{"className":36286},[665],[363,36288,36290],{"className":36289},[638],[363,36291,36293],{"className":36292,"style":2919},[642],[363,36294],{},[363,36296],{"className":36297},[501,789],[363,36299,5155],{"className":36300},[407],[363,36302,36304,36307,36366],{"className":36303},[407],[363,36305],{"className":36306},[494,789],[363,36308,36310],{"className":36309},[586],[363,36311,36313,36358],{"className":36312},[633,634],[363,36314,36316,36355],{"className":36315},[638],[363,36317,36319,36333,36341],{"className":36318,"style":2871},[642],[363,36320,36321,36324],{"style":2874},[363,36322],{"className":36323,"style":809},[650],[363,36325,36327],{"className":36326},[655,656,657,658],[363,36328,36330],{"className":36329},[407,658],[363,36331,1116],{"className":36332},[407,408,658],[363,36334,36335,36338],{"style":821},[363,36336],{"className":36337,"style":809},[650],[363,36339],{"className":36340,"style":829},[828],[363,36342,36343,36346],{"style":2897},[363,36344],{"className":36345,"style":809},[650],[363,36347,36349],{"className":36348},[655,656,657,658],[363,36350,36352],{"className":36351},[407,658],[363,36353,465],{"className":36354},[407,658],[363,36356,666],{"className":36357},[665],[363,36359,36361],{"className":36360},[638],[363,36362,36364],{"className":36363,"style":2919},[642],[363,36365],{},[363,36367],{"className":36368},[501,789],[363,36370],{"className":36371,"style":2934},[505],[363,36373,5160],{"className":36374},[2938],[363,36376],{"className":36377,"style":2934},[505],[363,36379,36381,36384,36387,36390,36393],{"className":36380},[398],[363,36382],{"className":36383,"style":487},[402],[363,36385,35026],{"className":36386},[407],[363,36388],{"className":36389,"style":506},[505],[363,36391,471],{"className":36392},[510],[363,36394],{"className":36395,"style":506},[505],[363,36397,36399,36402,36470,36474,36477,36480],{"className":36398},[398],[363,36400],{"className":36401,"style":2852},[402],[363,36403,36405,36408,36467],{"className":36404},[407],[363,36406],{"className":36407},[494,789],[363,36409,36411],{"className":36410},[586],[363,36412,36414,36459],{"className":36413},[633,634],[363,36415,36417,36456],{"className":36416},[638],[363,36418,36420,36434,36442],{"className":36419,"style":2871},[642],[363,36421,36422,36425],{"style":2874},[363,36423],{"className":36424,"style":809},[650],[363,36426,36428],{"className":36427},[655,656,657,658],[363,36429,36431],{"className":36430},[407,658],[363,36432,2810],{"className":36433},[407,658],[363,36435,36436,36439],{"style":821},[363,36437],{"className":36438,"style":809},[650],[363,36440],{"className":36441,"style":829},[828],[363,36443,36444,36447],{"style":2897},[363,36445],{"className":36446,"style":809},[650],[363,36448,36450],{"className":36449},[655,656,657,658],[363,36451,36453],{"className":36452},[407,658],[363,36454,465],{"className":36455},[407,658],[363,36457,666],{"className":36458},[665],[363,36460,36462],{"className":36461},[638],[363,36463,36465],{"className":36464,"style":2919},[642],[363,36466],{},[363,36468],{"className":36469},[501,789],[363,36471,36473],{"className":36472},[407],"∣1",[363,36475],{"className":36476,"style":2934},[505],[363,36478,5160],{"className":36479},[2938],[363,36481],{"className":36482,"style":2934},[505],[363,36484,36486,36489,36492,36495,36498,36501],{"className":36485},[398],[363,36487],{"className":36488,"style":487},[402],[363,36490,1116],{"className":36491},[407,408],[363,36493,5155],{"className":36494},[407],[363,36496],{"className":36497,"style":506},[505],[363,36499,471],{"className":36500},[510],[363,36502],{"className":36503,"style":506},[505],[363,36505,36507,36510,36513,36516,36519],{"className":36506},[398],[363,36508],{"className":36509,"style":487},[402],[363,36511,385],{"className":36512,"style":409},[407,408],[363,36514,461],{"className":36515},[494],[363,36517,1116],{"className":36518},[407,408],[363,36520,468],{"className":36521},[501],"，所以 TV 是对称的。",[11,36524,36525,36527,36528,36531],{},[1572,36526,24540],{}," 全变差是概率测度空间上真正的",[1572,36529,36530],{},"度量","（对称、满足三角不等式），它等于两个分布在一件事上能给出的最大概率差：",[363,36533,36535],{"className":36534,"translate":367},[528],[363,36536,36538,36612],{"className":36537,"translate":367},[366],[363,36539,36541],{"className":36540},[371],[373,36542,36543],{"xmlns":375,"display":537},[377,36544,36545,36609],{},[380,36546,36547,36557,36559,36561,36563,36565,36567,36569,36585,36587,36589,36591,36593,36595,36597,36599,36601,36603,36605,36607],{},[543,36548,36549,36551],{},[383,36550,547],{},[380,36552,36553,36555],{},[383,36554,5739],{},[383,36556,35197],{},[458,36558,461],{"stretchy":460},[383,36560,554],{},[458,36562,898],{"separator":394},[383,36564,561],{},[458,36566,468],{"stretchy":460},[458,36568,471],{},[6363,36570,36571,36577],{},[380,36572,36573,36575],{},[383,36574,35779],{},[458,36576,4450],{},[380,36578,36579,36581,36583],{},[383,36580,950],{},[458,36582,6256],{},[383,36584,950],{"mathvariant":944},[458,36586,5155],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,36588,554],{},[458,36590,461],{"stretchy":460},[383,36592,950],{},[458,36594,468],{"stretchy":460},[458,36596,5160],{},[383,36598,561],{},[458,36600,461],{"stretchy":460},[383,36602,950],{},[458,36604,468],{"stretchy":460},[458,36606,5155],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,36608,4722],{"mathvariant":557},[387,36610,36611],{"encoding":389},"D_{TV}(P,Q)\n=\\sup_{A\\in\\mathcal A}\\big|P(A)-Q(A)\\big| .",[363,36613,36615,36694,36820],{"className":36614,"ariaHidden":394},[393],[363,36616,36618,36621,36667,36670,36673,36676,36679,36682,36685,36688,36691],{"className":36617},[398],[363,36619],{"className":36620,"style":487},[402],[363,36622,36624,36627],{"className":36623},[407],[363,36625,547],{"className":36626,"style":625},[407,408],[363,36628,36630],{"className":36629},[629],[363,36631,36633,36659],{"className":36632},[633,634],[363,36634,36636,36656],{"className":36635},[638],[363,36637,36639],{"className":36638,"style":727},[642],[363,36640,36641,36644],{"style":646},[363,36642],{"className":36643,"style":651},[650],[363,36645,36647],{"className":36646},[655,656,657,658],[363,36648,36650,36653],{"className":36649},[407,658],[363,36651,5739],{"className":36652,"style":682},[407,408,658],[363,36654,35197],{"className":36655,"style":2934},[407,408,658],[363,36657,666],{"className":36658},[665],[363,36660,36662],{"className":36661},[638],[363,36663,36665],{"className":36664,"style":8315},[642],[363,36666],{},[363,36668,461],{"className":36669},[494],[363,36671,554],{"className":36672,"style":682},[407,408],[363,36674,898],{"className":36675},[920],[363,36677],{"className":36678,"style":754},[505],[363,36680,561],{"className":36681},[407,408],[363,36683,468],{"className":36684},[501],[363,36686],{"className":36687,"style":506},[505],[363,36689,471],{"className":36690},[510],[363,36692],{"className":36693,"style":506},[505],[363,36695,36697,36701,36756,36759,36799,36802,36805,36808,36811,36814,36817],{"className":36696},[398],[363,36698],{"className":36699,"style":36700},[402],"height:1.8161em;vertical-align:-0.9661em;",[363,36702,36704],{"className":36703},[1831,14063],[363,36705,36707,36747],{"className":36706},[633,634],[363,36708,36710,36744],{"className":36709},[638],[363,36711,36713,36734],{"className":36712,"style":2692},[642],[363,36714,36716,36719],{"style":36715},"top:-2.1612em;margin-left:0em;",[363,36717],{"className":36718,"style":809},[650],[363,36720,36722],{"className":36721},[655,656,657,658],[363,36723,36725,36728,36731],{"className":36724},[407,658],[363,36726,950],{"className":36727},[407,408,658],[363,36729,6256],{"className":36730},[510,658],[363,36732,950],{"className":36733},[407,971,658],[363,36735,36736,36739],{"style":12210},[363,36737],{"className":36738,"style":809},[650],[363,36740,36741],{},[363,36742,35779],{"className":36743},[1831],[363,36745,666],{"className":36746},[665],[363,36748,36750],{"className":36749},[638],[363,36751,36754],{"className":36752,"style":36753},[642],"height:0.9661em;",[363,36755],{},[363,36757],{"className":36758,"style":754},[505],[363,36760,36762],{"className":36761},[407],[363,36763,36765],{"className":36764},[767,15176],[363,36766,36768,36791],{"className":36767},[633,634],[363,36769,36771,36788],{"className":36770},[638],[363,36772,36774],{"className":36773,"style":15186},[642],[363,36775,36776,36779],{"style":15189},[363,36777],{"className":36778,"style":15193},[650],[363,36780,36782],{"style":36781},"width:0.333em;height:1.2em;",[6670,36783,36785],{"xmlns":6672,"width":35398,"height":9797,"viewBox":36784},"0 0 333 1200",[6678,36786],{"d":36787},"M145 15 v585 v0 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v0 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v0 v585 h43z",[363,36789,666],{"className":36790},[665],[363,36792,36794],{"className":36793},[638],[363,36795,36797],{"className":36796,"style":15213},[642],[363,36798],{},[363,36800,554],{"className":36801,"style":682},[407,408],[363,36803,461],{"className":36804},[494],[363,36806,950],{"className":36807},[407,408],[363,36809,468],{"className":36810},[501],[363,36812],{"className":36813,"style":2934},[505],[363,36815,5160],{"className":36816},[2938],[363,36818],{"className":36819,"style":2934},[505],[363,36821,36823,36826,36829,36832,36835,36838,36875],{"className":36822},[398],[363,36824],{"className":36825,"style":20910},[402],[363,36827,561],{"className":36828},[407,408],[363,36830,461],{"className":36831},[494],[363,36833,950],{"className":36834},[407,408],[363,36836,468],{"className":36837},[501],[363,36839,36841],{"className":36840},[407],[363,36842,36844],{"className":36843},[767,15176],[363,36845,36847,36867],{"className":36846},[633,634],[363,36848,36850,36864],{"className":36849},[638],[363,36851,36853],{"className":36852,"style":15186},[642],[363,36854,36855,36858],{"style":15189},[363,36856],{"className":36857,"style":15193},[650],[363,36859,36860],{"style":36781},[6670,36861,36862],{"xmlns":6672,"width":35398,"height":9797,"viewBox":36784},[6678,36863],{"d":36787},[363,36865,666],{"className":36866},[665],[363,36868,36870],{"className":36869},[638],[363,36871,36873],{"className":36872,"style":15213},[642],[363,36874],{},[363,36876,4722],{"className":36877},[407],[11,36879,36880,36881,2756,36909,36937,36938,37132,37133,37136,37137,37189,37190,37492],{},"它还有一个判决论解释：在等先验下用最优检验区分 ",[363,36882,36884,36897],{"className":36883,"translate":367},[366],[363,36885,36887],{"className":36886},[371],[373,36888,36889],{"xmlns":375},[377,36890,36891,36895],{},[380,36892,36893],{},[383,36894,554],{},[387,36896,554],{"encoding":389},[363,36898,36900],{"className":36899,"ariaHidden":394},[393],[363,36901,36903,36906],{"className":36902},[398],[363,36904],{"className":36905,"style":1011},[402],[363,36907,554],{"className":36908,"style":682},[407,408],[363,36910,36912,36925],{"className":36911,"translate":367},[366],[363,36913,36915],{"className":36914},[371],[373,36916,36917],{"xmlns":375},[377,36918,36919,36923],{},[380,36920,36921],{},[383,36922,561],{},[387,36924,561],{"encoding":389},[363,36926,36928],{"className":36927,"ariaHidden":394},[393],[363,36929,36931,36934],{"className":36930},[398],[363,36932],{"className":36933,"style":913},[402],[363,36935,561],{"className":36936},[407,408]," 时，最小平均错误率为 ",[363,36939,36941,36979],{"className":36940,"translate":367},[366],[363,36942,36944],{"className":36943},[371],[373,36945,36946],{"xmlns":375},[377,36947,36948,36976],{},[380,36949,36950,36958,36960,36962,36964,36974],{},[1602,36951,36952],{"scriptlevel":474,"displaystyle":460},[586,36953,36954,36956],{},[463,36955,465],{},[463,36957,2810],{},[458,36959,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[463,36961,465],{},[458,36963,5160],{},[543,36965,36966,36968],{},[383,36967,547],{},[380,36969,36970,36972],{},[383,36971,5739],{},[383,36973,35197],{},[458,36975,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[387,36977,36978],{"encoding":389},"\\tfrac12\\big(1-D_{TV}\\big)",[363,36980,36982,37074],{"className":36981,"ariaHidden":394},[393],[363,36983,36985,36988,37056,37062,37065,37068,37071],{"className":36984},[398],[363,36986],{"className":36987,"style":20910},[402],[363,36989,36991,36994,37053],{"className":36990},[407],[363,36992],{"className":36993},[494,789],[363,36995,36997],{"className":36996},[586],[363,36998,37000,37045],{"className":36999},[633,634],[363,37001,37003,37042],{"className":37002},[638],[363,37004,37006,37020,37028],{"className":37005,"style":2871},[642],[363,37007,37008,37011],{"style":2874},[363,37009],{"className":37010,"style":809},[650],[363,37012,37014],{"className":37013},[655,656,657,658],[363,37015,37017],{"className":37016},[407,658],[363,37018,2810],{"className":37019},[407,658],[363,37021,37022,37025],{"style":821},[363,37023],{"className":37024,"style":809},[650],[363,37026],{"className":37027,"style":829},[828],[363,37029,37030,37033],{"style":2897},[363,37031],{"className":37032,"style":809},[650],[363,37034,37036],{"className":37035},[655,656,657,658],[363,37037,37039],{"className":37038},[407,658],[363,37040,465],{"className":37041},[407,658],[363,37043,666],{"className":37044},[665],[363,37046,37048],{"className":37047},[638],[363,37049,37051],{"className":37050,"style":2919},[642],[363,37052],{},[363,37054],{"className":37055},[501,789],[363,37057,37059],{"className":37058},[407],[363,37060,461],{"className":37061},[767,10021],[363,37063,465],{"className":37064},[407],[363,37066],{"className":37067,"style":2934},[505],[363,37069,5160],{"className":37070},[2938],[363,37072],{"className":37073,"style":2934},[505],[363,37075,37077,37080,37126],{"className":37076},[398],[363,37078],{"className":37079,"style":20910},[402],[363,37081,37083,37086],{"className":37082},[407],[363,37084,547],{"className":37085,"style":625},[407,408],[363,37087,37089],{"className":37088},[629],[363,37090,37092,37118],{"className":37091},[633,634],[363,37093,37095,37115],{"className":37094},[638],[363,37096,37098],{"className":37097,"style":727},[642],[363,37099,37100,37103],{"style":646},[363,37101],{"className":37102,"style":651},[650],[363,37104,37106],{"className":37105},[655,656,657,658],[363,37107,37109,37112],{"className":37108},[407,658],[363,37110,5739],{"className":37111,"style":682},[407,408,658],[363,37113,35197],{"className":37114,"style":2934},[407,408,658],[363,37116,666],{"className":37117},[665],[363,37119,37121],{"className":37120},[638],[363,37122,37124],{"className":37123,"style":8315},[642],[363,37125],{},[363,37127,37129],{"className":37128},[407],[363,37130,468],{"className":37131},[767,10021],"，因此 TV 直接度量了",[1572,37134,37135],{},"可分性","，「TV 小」就等于「几乎分不开」。TV 是这里所有 f-散度中最「弱」的标尺（总在 ",[363,37138,37140,37162],{"className":37139,"translate":367},[366],[363,37141,37143],{"className":37142},[371],[373,37144,37145],{"xmlns":375},[377,37146,37147,37159],{},[380,37148,37149,37151,37153,37155,37157],{},[458,37150,578],{"stretchy":460},[463,37152,474],{},[458,37154,898],{"separator":394},[463,37156,465],{},[458,37158,605],{"stretchy":460},[387,37160,37161],{"encoding":389},"[0,1]",[363,37163,37165],{"className":37164,"ariaHidden":394},[393],[363,37166,37168,37171,37174,37177,37180,37183,37186],{"className":37167},[398],[363,37169],{"className":37170,"style":487},[402],[363,37172,578],{"className":37173},[494],[363,37175,474],{"className":37176},[407],[363,37178,898],{"className":37179},[920],[363,37181],{"className":37182,"style":754},[505],[363,37184,465],{"className":37185},[407],[363,37187,605],{"className":37188},[501]," 内），但按 Csiszár 定理它与 KL 诱导同一个拓扑，所以常常已经够用；在一维实直线上它退化为 Kolmogorov 距离 ",[363,37191,37193,37258],{"className":37192,"translate":367},[366],[363,37194,37196],{"className":37195},[371],[373,37197,37198],{"xmlns":375},[377,37199,37200,37255],{},[380,37201,37202,37212,37214,37224,37226,37233,37235,37237,37239,37241,37247,37249,37251,37253],{},[543,37203,37204,37206],{},[383,37205,547],{},[380,37207,37208,37210],{},[383,37209,5739],{},[383,37211,35197],{},[458,37213,471],{},[543,37215,37216,37222],{},[380,37217,37218,37220],{},[383,37219,35779],{},[458,37221,4450],{},[383,37223,1121],{},[383,37225,5155],{"mathvariant":557},[543,37227,37228,37231],{},[383,37229,37230],{},"F",[383,37232,554],{},[458,37234,461],{"stretchy":460},[383,37236,1121],{},[458,37238,468],{"stretchy":460},[458,37240,5160],{},[543,37242,37243,37245],{},[383,37244,37230],{},[383,37246,561],{},[458,37248,461],{"stretchy":460},[383,37250,1121],{},[458,37252,468],{"stretchy":460},[383,37254,5155],{"mathvariant":557},[387,37256,37257],{"encoding":389},"D_{TV}=\\sup_x|F_P(x)-F_Q(x)|",[363,37259,37261,37322,37434],{"className":37260,"ariaHidden":394},[393],[363,37262,37264,37267,37313,37316,37319],{"className":37263},[398],[363,37265],{"className":37266,"style":16308},[402],[363,37268,37270,37273],{"className":37269},[407],[363,37271,547],{"className":37272,"style":625},[407,408],[363,37274,37276],{"className":37275},[629],[363,37277,37279,37305],{"className":37278},[633,634],[363,37280,37282,37302],{"className":37281},[638],[363,37283,37285],{"className":37284,"style":727},[642],[363,37286,37287,37290],{"style":646},[363,37288],{"className":37289,"style":651},[650],[363,37291,37293],{"className":37292},[655,656,657,658],[363,37294,37296,37299],{"className":37295},[407,658],[363,37297,5739],{"className":37298,"style":682},[407,408,658],[363,37300,35197],{"className":37301,"style":2934},[407,408,658],[363,37303,666],{"className":37304},[665],[363,37306,37308],{"className":37307},[638],[363,37309,37311],{"className":37310,"style":8315},[642],[363,37312],{},[363,37314],{"className":37315,"style":506},[505],[363,37317,471],{"className":37318},[510],[363,37320],{"className":37321,"style":506},[505],[363,37323,37325,37328,37370,37373,37376,37416,37419,37422,37425,37428,37431],{"className":37324},[398],[363,37326],{"className":37327,"style":487},[402],[363,37329,37331,37334],{"className":37330},[1831],[363,37332,35779],{"className":37333},[1831],[363,37335,37337],{"className":37336},[629],[363,37338,37340,37361],{"className":37339},[633,634],[363,37341,37343,37358],{"className":37342},[638],[363,37344,37347],{"className":37345,"style":37346},[642],"height:0.0573em;",[363,37348,37349,37352],{"style":35925},[363,37350],{"className":37351,"style":651},[650],[363,37353,37355],{"className":37354},[655,656,657,658],[363,37356,1121],{"className":37357},[407,408,658],[363,37359,666],{"className":37360},[665],[363,37362,37364],{"className":37363},[638],[363,37365,37368],{"className":37366,"style":37367},[642],"height:0.2441em;",[363,37369],{},[363,37371],{"className":37372,"style":754},[505],[363,37374,5155],{"className":37375},[407],[363,37377,37379,37382],{"className":37378},[407],[363,37380,37230],{"className":37381,"style":682},[407,408],[363,37383,37385],{"className":37384},[629],[363,37386,37388,37408],{"className":37387},[633,634],[363,37389,37391,37405],{"className":37390},[638],[363,37392,37394],{"className":37393,"style":727},[642],[363,37395,37396,37399],{"style":11483},[363,37397],{"className":37398,"style":651},[650],[363,37400,37402],{"className":37401},[655,656,657,658],[363,37403,554],{"className":37404,"style":682},[407,408,658],[363,37406,666],{"className":37407},[665],[363,37409,37411],{"className":37410},[638],[363,37412,37414],{"className":37413,"style":8315},[642],[363,37415],{},[363,37417,461],{"className":37418},[494],[363,37420,1121],{"className":37421},[407,408],[363,37423,468],{"className":37424},[501],[363,37426],{"className":37427,"style":2934},[505],[363,37429,5160],{"className":37430},[2938],[363,37432],{"className":37433,"style":2934},[505],[363,37435,37437,37440,37480,37483,37486,37489],{"className":37436},[398],[363,37438],{"className":37439,"style":618},[402],[363,37441,37443,37446],{"className":37442},[407],[363,37444,37230],{"className":37445,"style":682},[407,408],[363,37447,37449],{"className":37448},[629],[363,37450,37452,37472],{"className":37451},[633,634],[363,37453,37455,37469],{"className":37454},[638],[363,37456,37458],{"className":37457,"style":727},[642],[363,37459,37460,37463],{"style":11483},[363,37461],{"className":37462,"style":651},[650],[363,37464,37466],{"className":37465},[655,656,657,658],[363,37467,561],{"className":37468},[407,408,658],[363,37470,666],{"className":37471},[665],[363,37473,37475],{"className":37474},[638],[363,37476,37478],{"className":37477,"style":673},[642],[363,37479],{},[363,37481,461],{"className":37482},[494],[363,37484,1121],{"className":37485},[407,408],[363,37487,468],{"className":37488},[501],[363,37490,5155],{"className":37491},[407],"。马尔可夫链的混合时间、耦合构造与统计距离（total variation distance）都以它为核心。",[2658,37494,37496],{"id":37495},"_34-卡方散度","3.4 卡方散度",[11,37498,21820],{},[363,37500,37502],{"className":37501,"translate":367},[528],[363,37503,37505,37541],{"className":37504,"translate":367},[366],[363,37506,37508],{"className":37507},[371],[373,37509,37510],{"xmlns":375,"display":537},[377,37511,37512,37538],{},[380,37513,37514,37516,37518,37520,37522,37524,37526,37528,37530,37532],{},[383,37515,385],{},[458,37517,461],{"stretchy":460},[383,37519,1116],{},[458,37521,468],{"stretchy":460},[458,37523,471],{},[458,37525,461],{"stretchy":460},[383,37527,1116],{},[458,37529,5160],{},[463,37531,465],{},[7161,37533,37534,37536],{},[458,37535,468],{"stretchy":460},[463,37537,2810],{},[387,37539,37540],{"encoding":389},"f(t)=(t-1)^2",[363,37542,37544,37571,37592],{"className":37543,"ariaHidden":394},[393],[363,37545,37547,37550,37553,37556,37559,37562,37565,37568],{"className":37546},[398],[363,37548],{"className":37549,"style":487},[402],[363,37551,385],{"className":37552,"style":409},[407,408],[363,37554,461],{"className":37555},[494],[363,37557,1116],{"className":37558},[407,408],[363,37560,468],{"className":37561},[501],[363,37563],{"className":37564,"style":506},[505],[363,37566,471],{"className":37567},[510],[363,37569],{"className":37570,"style":506},[505],[363,37572,37574,37577,37580,37583,37586,37589],{"className":37573},[398],[363,37575],{"className":37576,"style":487},[402],[363,37578,461],{"className":37579},[494],[363,37581,1116],{"className":37582},[407,408],[363,37584],{"className":37585,"style":2934},[505],[363,37587,5160],{"className":37588},[2938],[363,37590],{"className":37591,"style":2934},[505],[363,37593,37595,37599,37602],{"className":37594},[398],[363,37596],{"className":37597,"style":37598},[402],"height:1.1141em;vertical-align:-0.25em;",[363,37600,465],{"className":37601},[407],[363,37603,37605,37608],{"className":37604},[501],[363,37606,468],{"className":37607},[501],[363,37609,37611],{"className":37610},[629],[363,37612,37614],{"className":37613},[633],[363,37615,37617],{"className":37616},[638],[363,37618,37620],{"className":37619,"style":20082},[642],[363,37621,37622,37625],{"style":8624},[363,37623],{"className":37624,"style":651},[650],[363,37626,37628],{"className":37627},[655,656,657,658],[363,37629,2810],{"className":37630},[407,658],[11,37632,35029,37633,37698],{},[363,37634,37636,37659],{"className":37635,"translate":367},[366],[363,37637,37639],{"className":37638},[371],[373,37640,37641],{"xmlns":375},[377,37642,37643,37657],{},[380,37644,37645,37647,37649,37651,37653,37655],{},[383,37646,385],{},[458,37648,461],{"stretchy":460},[463,37650,465],{},[458,37652,468],{"stretchy":460},[458,37654,471],{},[463,37656,474],{},[387,37658,477],{"encoding":389},[363,37660,37662,37689],{"className":37661,"ariaHidden":394},[393],[363,37663,37665,37668,37671,37674,37677,37680,37683,37686],{"className":37664},[398],[363,37666],{"className":37667,"style":487},[402],[363,37669,385],{"className":37670,"style":409},[407,408],[363,37672,461],{"className":37673},[494],[363,37675,465],{"className":37676},[407],[363,37678,468],{"className":37679},[501],[363,37681],{"className":37682,"style":506},[505],[363,37684,471],{"className":37685},[510],[363,37687],{"className":37688,"style":506},[505],[363,37690,37692,37695],{"className":37691},[398],[363,37693],{"className":37694,"style":520},[402],[363,37696,474],{"className":37697},[407],"、凸，代入：",[363,37700,37702],{"className":37701,"translate":367},[528],[363,37703,37705,37812],{"className":37704,"translate":367},[366],[363,37706,37708],{"className":37707},[371],[373,37709,37710],{"xmlns":375,"display":537},[377,37711,37712,37809],{},[380,37713,37714,37720,37722,37724,37726,37728,37730,37732,37734,37736,37756,37758,37760,37762,37764,37784,37786,37788,37790,37792,37799,37801,37803,37805,37807],{},[543,37715,37716,37718],{},[383,37717,547],{},[383,37719,385],{},[458,37721,461],{"stretchy":460},[383,37723,554],{},[383,37725,558],{"mathvariant":557},[383,37727,561],{},[458,37729,468],{"stretchy":460},[458,37731,471],{},[458,37733,1634],{},[383,37735,1291],{},[7161,37737,37738,37754],{},[380,37739,37740,37742,37748,37750,37752],{},[458,37741,461],{"fence":394},[586,37743,37744,37746],{},[383,37745,11],{},[383,37747,1291],{},[458,37749,5160],{},[463,37751,465],{},[458,37753,468],{"fence":394},[463,37755,2810],{},[383,37757,592],{},[383,37759,1121],{},[458,37761,471],{},[458,37763,1634],{},[586,37765,37766,37782],{},[380,37767,37768,37770,37772,37774,37776],{},[458,37769,461],{"stretchy":460},[383,37771,11],{},[458,37773,5160],{},[383,37775,1291],{},[7161,37777,37778,37780],{},[458,37779,468],{"stretchy":460},[463,37781,2810],{},[383,37783,1291],{},[1644,37785,1646],{},[383,37787,592],{},[383,37789,1121],{},[458,37791,471],{},[7161,37793,37794,37797],{},[383,37795,37796],{},"χ",[463,37798,2810],{},[458,37800,461],{"stretchy":460},[383,37802,554],{},[383,37804,558],{"mathvariant":557},[383,37806,561],{},[458,37808,468],{"stretchy":460},[387,37810,37811],{"encoding":389},"D_f(P\\|Q)=\\int q\\left(\\frac{p}{q}-1\\right)^2dx\n=\\int \\frac{(p-q)^2}{q}\\,dx\n=\\chi^2(P\\|Q)",[363,37813,37815,37885,38039,38177],{"className":37814,"ariaHidden":394},[393],[363,37816,37818,37821,37861,37864,37867,37870,37873,37876,37879,37882],{"className":37817},[398],[363,37819],{"className":37820,"style":618},[402],[363,37822,37824,37827],{"className":37823},[407],[363,37825,547],{"className":37826,"style":625},[407,408],[363,37828,37830],{"className":37829},[629],[363,37831,37833,37853],{"className":37832},[633,634],[363,37834,37836,37850],{"className":37835},[638],[363,37837,37839],{"className":37838,"style":643},[642],[363,37840,37841,37844],{"style":646},[363,37842],{"className":37843,"style":651},[650],[363,37845,37847],{"className":37846},[655,656,657,658],[363,37848,385],{"className":37849,"style":409},[407,408,658],[363,37851,666],{"className":37852},[665],[363,37854,37856],{"className":37855},[638],[363,37857,37859],{"className":37858,"style":673},[642],[363,37860],{},[363,37862,461],{"className":37863},[494],[363,37865,554],{"className":37866,"style":682},[407,408],[363,37868,558],{"className":37869},[407],[363,37871,561],{"className":37872},[407,408],[363,37874,468],{"className":37875},[501],[363,37877],{"className":37878,"style":506},[505],[363,37880,471],{"className":37881},[510],[363,37883],{"className":37884,"style":506},[505],[363,37886,37888,37892,37895,37898,37901,37904,38021,38024,38027,38030,38033,38036],{"className":37887},[398],[363,37889],{"className":37890,"style":37891},[402],"height:2.604em;vertical-align:-0.95em;",[363,37893,1634],{"className":37894,"style":1834},[1831,1832,1833],[363,37896],{"className":37897,"style":754},[505],[363,37899,1291],{"className":37900,"style":1328},[407,408],[363,37902],{"className":37903,"style":754},[505],[363,37905,37907,37996],{"className":37906},[758],[363,37908,37910,37916,37978,37981,37984,37987,37990],{"className":37909},[758],[363,37911,37913],{"className":37912,"style":763},[494,762],[363,37914,461],{"className":37915},[767,657],[363,37917,37919,37922,37975],{"className":37918},[407],[363,37920],{"className":37921},[494,789],[363,37923,37925],{"className":37924},[586],[363,37926,37928,37967],{"className":37927},[633,634],[363,37929,37931,37964],{"className":37930},[638],[363,37932,37934,37945,37953],{"className":37933,"style":3901},[642],[363,37935,37936,37939],{"style":805},[363,37937],{"className":37938,"style":809},[650],[363,37940,37942],{"className":37941},[407],[363,37943,1291],{"className":37944,"style":1328},[407,408],[363,37946,37947,37950],{"style":821},[363,37948],{"className":37949,"style":809},[650],[363,37951],{"className":37952,"style":829},[828],[363,37954,37955,37958],{"style":832},[363,37956],{"className":37957,"style":809},[650],[363,37959,37961],{"className":37960},[407],[363,37962,11],{"className":37963},[407,408],[363,37965,666],{"className":37966},[665],[363,37968,37970],{"className":37969},[638],[363,37971,37973],{"className":37972,"style":854},[642],[363,37974],{},[363,37976],{"className":37977},[501,789],[363,37979],{"className":37980,"style":2934},[505],[363,37982,5160],{"className":37983},[2938],[363,37985],{"className":37986,"style":2934},[505],[363,37988,465],{"className":37989},[407],[363,37991,37993],{"className":37992,"style":763},[501,762],[363,37994,468],{"className":37995},[767,657],[363,37997,37999],{"className":37998},[629],[363,38000,38002],{"className":38001},[633],[363,38003,38005],{"className":38004},[638],[363,38006,38009],{"className":38007,"style":38008},[642],"height:1.654em;",[363,38010,38012,38015],{"style":38011},"top:-3.9029em;margin-right:0.05em;",[363,38013],{"className":38014,"style":651},[650],[363,38016,38018],{"className":38017},[655,656,657,658],[363,38019,2810],{"className":38020},[407,658],[363,38022],{"className":38023,"style":754},[505],[363,38025,592],{"className":38026},[407,408],[363,38028,1121],{"className":38029},[407,408],[363,38031],{"className":38032,"style":506},[505],[363,38034,471],{"className":38035},[510],[363,38037],{"className":38038,"style":506},[505],[363,38040,38042,38046,38049,38052,38159,38162,38165,38168,38171,38174],{"className":38041},[398],[363,38043],{"className":38044,"style":38045},[402],"height:2.3715em;vertical-align:-0.8804em;",[363,38047,1634],{"className":38048,"style":1834},[1831,1832,1833],[363,38050],{"className":38051,"style":754},[505],[363,38053,38055,38058,38156],{"className":38054},[407],[363,38056],{"className":38057},[494,789],[363,38059,38061],{"className":38060},[586],[363,38062,38064,38148],{"className":38063},[633,634],[363,38065,38067,38145],{"className":38066},[638],[363,38068,38071,38082,38090],{"className":38069,"style":38070},[642],"height:1.4911em;",[363,38072,38073,38076],{"style":805},[363,38074],{"className":38075,"style":809},[650],[363,38077,38079],{"className":38078},[407],[363,38080,1291],{"className":38081,"style":1328},[407,408],[363,38083,38084,38087],{"style":821},[363,38085],{"className":38086,"style":809},[650],[363,38088],{"className":38089,"style":829},[828],[363,38091,38092,38095],{"style":832},[363,38093],{"className":38094,"style":809},[650],[363,38096,38098,38101,38104,38107,38110,38113,38116],{"className":38097},[407],[363,38099,461],{"className":38100},[494],[363,38102,11],{"className":38103},[407,408],[363,38105],{"className":38106,"style":2934},[505],[363,38108,5160],{"className":38109},[2938],[363,38111],{"className":38112,"style":2934},[505],[363,38114,1291],{"className":38115,"style":1328},[407,408],[363,38117,38119,38122],{"className":38118},[501],[363,38120,468],{"className":38121},[501],[363,38123,38125],{"className":38124},[629],[363,38126,38128],{"className":38127},[633],[363,38129,38131],{"className":38130},[638],[363,38132,38134],{"className":38133,"style":20375},[642],[363,38135,38136,38139],{"style":7212},[363,38137],{"className":38138,"style":651},[650],[363,38140,38142],{"className":38141},[655,656,657,658],[363,38143,2810],{"className":38144},[407,658],[363,38146,666],{"className":38147},[665],[363,38149,38151],{"className":38150},[638],[363,38152,38154],{"className":38153,"style":854},[642],[363,38155],{},[363,38157],{"className":38158},[501,789],[363,38160],{"className":38161,"style":754},[505],[363,38163,592],{"className":38164},[407,408],[363,38166,1121],{"className":38167},[407,408],[363,38169],{"className":38170,"style":506},[505],[363,38172,471],{"className":38173},[510],[363,38175],{"className":38176,"style":506},[505],[363,38178,38180,38183,38212,38215,38218,38221,38224],{"className":38179},[398],[363,38181],{"className":38182,"style":37598},[402],[363,38184,38186,38189],{"className":38185},[407],[363,38187,37796],{"className":38188},[407,408],[363,38190,38192],{"className":38191},[629],[363,38193,38195],{"className":38194},[633],[363,38196,38198],{"className":38197},[638],[363,38199,38201],{"className":38200,"style":20082},[642],[363,38202,38203,38206],{"style":8624},[363,38204],{"className":38205,"style":651},[650],[363,38207,38209],{"className":38208},[655,656,657,658],[363,38210,2810],{"className":38211},[407,658],[363,38213,461],{"className":38214},[494],[363,38216,554],{"className":38217,"style":682},[407,408],[363,38219,558],{"className":38220},[407],[363,38222,561],{"className":38223},[407,408],[363,38225,468],{"className":38226},[501],[11,38228,38229,38230,38233],{},"这是",[1572,38231,38232],{},"皮尔逊（Pearson）卡方散度","。它非对称、无界。其斜共轭是",[363,38235,38237],{"className":38236,"translate":367},[528],[363,38238,38240,38316],{"className":38239,"translate":367},[366],[363,38241,38243],{"className":38242},[371],[373,38244,38245],{"xmlns":375,"display":537},[377,38246,38247,38313],{},[380,38248,38249,38251,38253,38255,38257,38259,38261,38263,38265,38267,38269,38289,38291,38311],{},[383,38250,1116],{},[1644,38252,1646],{},[383,38254,385],{},[458,38256,461],{"stretchy":460},[463,38258,465],{},[383,38260,1288],{"mathvariant":557},[383,38262,1116],{},[458,38264,468],{"stretchy":460},[458,38266,471],{},[383,38268,1116],{},[7161,38270,38271,38287],{},[380,38272,38273,38275,38281,38283,38285],{},[458,38274,461],{"fence":394},[586,38276,38277,38279],{},[463,38278,465],{},[383,38280,1116],{},[458,38282,5160],{},[463,38284,465],{},[458,38286,468],{"fence":394},[463,38288,2810],{},[458,38290,471],{},[586,38292,38293,38309],{},[380,38294,38295,38297,38299,38301,38303],{},[458,38296,461],{"stretchy":460},[383,38298,1116],{},[458,38300,5160],{},[463,38302,465],{},[7161,38304,38305,38307],{},[458,38306,468],{"stretchy":460},[463,38308,2810],{},[383,38310,1116],{},[458,38312,898],{"separator":394},[387,38314,38315],{"encoding":389},"t\\,f(1\u002Ft)=t\\left(\\frac1t-1\\right)^2\n=\\frac{(t-1)^2}{t},",[363,38317,38319,38355,38491],{"className":38318,"ariaHidden":394},[393],[363,38320,38322,38325,38328,38331,38334,38337,38340,38343,38346,38349,38352],{"className":38321},[398],[363,38323],{"className":38324,"style":487},[402],[363,38326,1116],{"className":38327},[407,408],[363,38329],{"className":38330,"style":754},[505],[363,38332,385],{"className":38333,"style":409},[407,408],[363,38335,461],{"className":38336},[494],[363,38338,8936],{"className":38339},[407],[363,38341,1116],{"className":38342},[407,408],[363,38344,468],{"className":38345},[501],[363,38347],{"className":38348,"style":506},[505],[363,38350,471],{"className":38351},[510],[363,38353],{"className":38354,"style":506},[505],[363,38356,38358,38361,38364,38367,38482,38485,38488],{"className":38357},[398],[363,38359],{"className":38360,"style":37891},[402],[363,38362,1116],{"className":38363},[407,408],[363,38365],{"className":38366,"style":754},[505],[363,38368,38370,38459],{"className":38369},[758],[363,38371,38373,38379,38441,38444,38447,38450,38453],{"className":38372},[758],[363,38374,38376],{"className":38375,"style":763},[494,762],[363,38377,461],{"className":38378},[767,657],[363,38380,38382,38385,38438],{"className":38381},[407],[363,38383],{"className":38384},[494,789],[363,38386,38388],{"className":38387},[586],[363,38389,38391,38430],{"className":38390},[633,634],[363,38392,38394,38427],{"className":38393},[638],[363,38395,38397,38408,38416],{"className":38396,"style":23236},[642],[363,38398,38399,38402],{"style":805},[363,38400],{"className":38401,"style":809},[650],[363,38403,38405],{"className":38404},[407],[363,38406,1116],{"className":38407},[407,408],[363,38409,38410,38413],{"style":821},[363,38411],{"className":38412,"style":809},[650],[363,38414],{"className":38415,"style":829},[828],[363,38417,38418,38421],{"style":832},[363,38419],{"className":38420,"style":809},[650],[363,38422,38424],{"className":38423},[407],[363,38425,465],{"className":38426},[407],[363,38428,666],{"className":38429},[665],[363,38431,38433],{"className":38432},[638],[363,38434,38436],{"className":38435,"style":4125},[642],[363,38437],{},[363,38439],{"className":38440},[501,789],[363,38442],{"className":38443,"style":2934},[505],[363,38445,5160],{"className":38446},[2938],[363,38448],{"className":38449,"style":2934},[505],[363,38451,465],{"className":38452},[407],[363,38454,38456],{"className":38455,"style":763},[501,762],[363,38457,468],{"className":38458},[767,657],[363,38460,38462],{"className":38461},[629],[363,38463,38465],{"className":38464},[633],[363,38466,38468],{"className":38467},[638],[363,38469,38471],{"className":38470,"style":38008},[642],[363,38472,38473,38476],{"style":38011},[363,38474],{"className":38475,"style":651},[650],[363,38477,38479],{"className":38478},[655,656,657,658],[363,38480,2810],{"className":38481},[407,658],[363,38483],{"className":38484,"style":506},[505],[363,38486,471],{"className":38487},[510],[363,38489],{"className":38490,"style":506},[505],[363,38492,38494,38498,38604],{"className":38493},[398],[363,38495],{"className":38496,"style":38497},[402],"height:2.1771em;vertical-align:-0.686em;",[363,38499,38501,38504,38601],{"className":38500},[407],[363,38502],{"className":38503},[494,789],[363,38505,38507],{"className":38506},[586],[363,38508,38510,38593],{"className":38509},[633,634],[363,38511,38513,38590],{"className":38512},[638],[363,38514,38516,38527,38535],{"className":38515,"style":38070},[642],[363,38517,38518,38521],{"style":805},[363,38519],{"className":38520,"style":809},[650],[363,38522,38524],{"className":38523},[407],[363,38525,1116],{"className":38526},[407,408],[363,38528,38529,38532],{"style":821},[363,38530],{"className":38531,"style":809},[650],[363,38533],{"className":38534,"style":829},[828],[363,38536,38537,38540],{"style":832},[363,38538],{"className":38539,"style":809},[650],[363,38541,38543,38546,38549,38552,38555,38558,38561],{"className":38542},[407],[363,38544,461],{"className":38545},[494],[363,38547,1116],{"className":38548},[407,408],[363,38550],{"className":38551,"style":2934},[505],[363,38553,5160],{"className":38554},[2938],[363,38556],{"className":38557,"style":2934},[505],[363,38559,465],{"className":38560},[407],[363,38562,38564,38567],{"className":38563},[501],[363,38565,468],{"className":38566},[501],[363,38568,38570],{"className":38569},[629],[363,38571,38573],{"className":38572},[633],[363,38574,38576],{"className":38575},[638],[363,38577,38579],{"className":38578,"style":20375},[642],[363,38580,38581,38584],{"style":7212},[363,38582],{"className":38583,"style":651},[650],[363,38585,38587],{"className":38586},[655,656,657,658],[363,38588,2810],{"className":38589},[407,658],[363,38591,666],{"className":38592},[665],[363,38594,38596],{"className":38595},[638],[363,38597,38599],{"className":38598,"style":4125},[642],[363,38600],{},[363,38602],{"className":38603},[501,789],[363,38605,898],{"className":38606},[920],[11,38608,38609,38610,6841,38613,19055,38895,38979],{},"对应 ",[1572,38611,38612],{},"Neyman 卡方散度",[363,38614,38616,38677],{"className":38615,"translate":367},[366],[363,38617,38619],{"className":38618},[371],[373,38620,38621],{"xmlns":375},[377,38622,38623,38674],{},[380,38624,38625,38634,38636,38638,38640,38642,38644,38646,38648,38668,38670,38672],{},[7900,38626,38627,38629,38632],{},[383,38628,37796],{},[383,38630,38631],{},"N",[463,38633,2810],{},[458,38635,461],{"stretchy":460},[383,38637,554],{},[383,38639,558],{"mathvariant":557},[383,38641,561],{},[458,38643,468],{"stretchy":460},[458,38645,471],{},[458,38647,1634],{},[586,38649,38650,38666],{},[380,38651,38652,38654,38656,38658,38660],{},[458,38653,461],{"stretchy":460},[383,38655,1291],{},[458,38657,5160],{},[383,38659,11],{},[7161,38661,38662,38664],{},[458,38663,468],{"stretchy":460},[463,38665,2810],{},[383,38667,11],{},[1644,38669,1646],{},[383,38671,592],{},[383,38673,1121],{},[387,38675,38676],{"encoding":389},"\\chi_N^2(P\\|Q)=\\int\\frac{(q-p)^2}{p}\\,dx",[363,38678,38680,38764],{"className":38679,"ariaHidden":394},[393],[363,38681,38683,38687,38740,38743,38746,38749,38752,38755,38758,38761],{"className":38682},[398],[363,38684],{"className":38685,"style":38686},[402],"height:1.0894em;vertical-align:-0.2753em;",[363,38688,38690,38693],{"className":38689},[407],[363,38691,37796],{"className":38692},[407,408],[363,38694,38696],{"className":38695},[629],[363,38697,38699,38731],{"className":38698},[633,634],[363,38700,38702,38728],{"className":38701},[638],[363,38703,38705,38717],{"className":38704,"style":20375},[642],[363,38706,38708,38711],{"style":38707},"top:-2.4247em;margin-left:0em;margin-right:0.05em;",[363,38709],{"className":38710,"style":651},[650],[363,38712,38714],{"className":38713},[655,656,657,658],[363,38715,38631],{"className":38716,"style":25948},[407,408,658],[363,38718,38719,38722],{"style":7212},[363,38720],{"className":38721,"style":651},[650],[363,38723,38725],{"className":38724},[655,656,657,658],[363,38726,2810],{"className":38727},[407,658],[363,38729,666],{"className":38730},[665],[363,38732,38734],{"className":38733},[638],[363,38735,38738],{"className":38736,"style":38737},[642],"height:0.2753em;",[363,38739],{},[363,38741,461],{"className":38742},[494],[363,38744,554],{"className":38745,"style":682},[407,408],[363,38747,558],{"className":38748},[407],[363,38750,561],{"className":38751},[407,408],[363,38753,468],{"className":38754},[501],[363,38756],{"className":38757,"style":506},[505],[363,38759,471],{"className":38760},[510],[363,38762],{"className":38763,"style":506},[505],[363,38765,38767,38771,38774,38777,38886,38889,38892],{"className":38766},[398],[363,38768],{"className":38769,"style":38770},[402],"height:1.59em;vertical-align:-0.4811em;",[363,38772,1634],{"className":38773,"style":5964},[1831,1832,5963],[363,38775],{"className":38776,"style":754},[505],[363,38778,38780,38783,38883],{"className":38779},[407],[363,38781],{"className":38782},[494,789],[363,38784,38786],{"className":38785},[586],[363,38787,38789,38875],{"className":38788},[633,634],[363,38790,38792,38872],{"className":38791},[638],[363,38793,38796,38810,38818],{"className":38794,"style":38795},[642],"height:1.1089em;",[363,38797,38798,38801],{"style":2874},[363,38799],{"className":38800,"style":809},[650],[363,38802,38804],{"className":38803},[655,656,657,658],[363,38805,38807],{"className":38806},[407,658],[363,38808,11],{"className":38809},[407,408,658],[363,38811,38812,38815],{"style":821},[363,38813],{"className":38814,"style":809},[650],[363,38816],{"className":38817,"style":829},[828],[363,38819,38820,38823],{"style":26765},[363,38821],{"className":38822,"style":809},[650],[363,38824,38826],{"className":38825},[655,656,657,658],[363,38827,38829,38832,38835,38838,38841],{"className":38828},[407,658],[363,38830,461],{"className":38831},[494,658],[363,38833,1291],{"className":38834,"style":1328},[407,408,658],[363,38836,5160],{"className":38837},[2938,658],[363,38839,11],{"className":38840},[407,408,658],[363,38842,38844,38847],{"className":38843},[501,658],[363,38845,468],{"className":38846},[501,658],[363,38848,38850],{"className":38849},[629],[363,38851,38853],{"className":38852},[633],[363,38854,38856],{"className":38855},[638],[363,38857,38860],{"className":38858,"style":38859},[642],"height:0.8913em;",[363,38861,38863,38866],{"style":38862},"top:-2.931em;margin-right:0.0714em;",[363,38864],{"className":38865,"style":30553},[650],[363,38867,38869],{"className":38868},[655,30557,10021,658],[363,38870,2810],{"className":38871},[407,658],[363,38873,666],{"className":38874},[665],[363,38876,38878],{"className":38877},[638],[363,38879,38881],{"className":38880,"style":3086},[642],[363,38882],{},[363,38884],{"className":38885},[501,789],[363,38887],{"className":38888,"style":754},[505],[363,38890,592],{"className":38891},[407,408],[363,38893,1121],{"className":38894},[407,408],[363,38896,38898,38926],{"className":38897,"translate":367},[366],[363,38899,38901],{"className":38900},[371],[373,38902,38903],{"xmlns":375},[377,38904,38905,38923],{},[380,38906,38907,38913,38915,38917,38919,38921],{},[7161,38908,38909,38911],{},[383,38910,37796],{},[463,38912,2810],{},[458,38914,461],{"stretchy":460},[383,38916,561],{},[383,38918,558],{"mathvariant":557},[383,38920,554],{},[458,38922,468],{"stretchy":460},[387,38924,38925],{"encoding":389},"\\chi^2(Q\\|P)",[363,38927,38929],{"className":38928,"ariaHidden":394},[393],[363,38930,38932,38935,38964,38967,38970,38973,38976],{"className":38931},[398],[363,38933],{"className":38934,"style":20350},[402],[363,38936,38938,38941],{"className":38937},[407],[363,38939,37796],{"className":38940},[407,408],[363,38942,38944],{"className":38943},[629],[363,38945,38947],{"className":38946},[633],[363,38948,38950],{"className":38949},[638],[363,38951,38953],{"className":38952,"style":20375},[642],[363,38954,38955,38958],{"style":7212},[363,38956],{"className":38957,"style":651},[650],[363,38959,38961],{"className":38960},[655,656,657,658],[363,38962,2810],{"className":38963},[407,658],[363,38965,461],{"className":38966},[494],[363,38968,561],{"className":38969},[407,408],[363,38971,558],{"className":38972},[407],[363,38974,554],{"className":38975,"style":682},[407,408],[363,38977,468],{"className":38978},[501],"：皮尔逊卡方的\"反向兄弟\"。",[11,38981,38982,38983,39132,39133,39295,39296,39611,39612,39850,39851,39932],{},"卡方散度的重要性在于它是「二阶」散度：小偏差下（",[363,38984,38986,39016],{"className":38985,"translate":367},[366],[363,38987,38989],{"className":38988},[371],[373,38990,38991],{"xmlns":375},[377,38992,38993,39013],{},[380,38994,38995,39001,39003,39005,39007,39010],{},[586,38996,38997,38999],{},[383,38998,11],{},[383,39000,1291],{},[458,39002,471],{},[463,39004,465],{},[458,39006,2817],{},[383,39008,39009],{},"ε",[383,39011,39012],{},"h",[387,39014,39015],{"encoding":389},"\\frac{p}{q}=1+\\varepsilon h",[363,39017,39019,39102,39120],{"className":39018,"ariaHidden":394},[393],[363,39020,39022,39025,39093,39096,39099],{"className":39021},[398],[363,39023],{"className":39024,"style":3431},[402],[363,39026,39028,39031,39090],{"className":39027},[407],[363,39029],{"className":39030},[494,789],[363,39032,39034],{"className":39033},[586],[363,39035,39037,39082],{"className":39036},[633,634],[363,39038,39040,39079],{"className":39039},[638],[363,39041,39043,39057,39065],{"className":39042,"style":3450},[642],[363,39044,39045,39048],{"style":2874},[363,39046],{"className":39047,"style":809},[650],[363,39049,39051],{"className":39050},[655,656,657,658],[363,39052,39054],{"className":39053},[407,658],[363,39055,1291],{"className":39056,"style":1328},[407,408,658],[363,39058,39059,39062],{"style":821},[363,39060],{"className":39061,"style":809},[650],[363,39063],{"className":39064,"style":829},[828],[363,39066,39067,39070],{"style":3200},[363,39068],{"className":39069,"style":809},[650],[363,39071,39073],{"className":39072},[655,656,657,658],[363,39074,39076],{"className":39075},[407,658],[363,39077,11],{"className":39078},[407,408,658],[363,39080,666],{"className":39081},[665],[363,39083,39085],{"className":39084},[638],[363,39086,39088],{"className":39087,"style":3086},[642],[363,39089],{},[363,39091],{"className":39092},[501,789],[363,39094],{"className":39095,"style":506},[505],[363,39097,471],{"className":39098},[510],[363,39100],{"className":39101,"style":506},[505],[363,39103,39105,39108,39111,39114,39117],{"className":39104},[398],[363,39106],{"className":39107,"style":12925},[402],[363,39109,465],{"className":39110},[407],[363,39112],{"className":39113,"style":2934},[505],[363,39115,2817],{"className":39116},[2938],[363,39118],{"className":39119,"style":2934},[505],[363,39121,39123,39126,39129],{"className":39122},[398],[363,39124],{"className":39125,"style":12944},[402],[363,39127,39009],{"className":39128},[407,408],[363,39130,39012],{"className":39131},[407,408]," 展开）有 ",[363,39134,39136,39168],{"className":39135,"translate":367},[366],[363,39137,39139],{"className":39138},[371],[373,39140,39141],{"xmlns":375},[377,39142,39143,39165],{},[380,39144,39145,39151,39153,39159],{},[380,39146,39147,39149],{},[383,39148,11041],{"mathvariant":557},[383,39150,22240],{"mathvariant":557},[458,39152,33306],{},[586,39154,39155,39157],{},[463,39156,465],{},[463,39158,2810],{},[7161,39160,39161,39163],{},[383,39162,37796],{},[463,39164,2810],{},[387,39166,39167],{"encoding":389},"\\mathrm{KL}\\approx\\frac12\\chi^2",[363,39169,39171,39192],{"className":39170,"ariaHidden":394},[393],[363,39172,39174,39177,39183,39186,39189],{"className":39173},[398],[363,39175],{"className":39176,"style":1011},[402],[363,39178,39180],{"className":39179},[407],[363,39181,33010],{"className":39182},[407,33009],[363,39184],{"className":39185,"style":506},[505],[363,39187,33306],{"className":39188},[510],[363,39190],{"className":39191,"style":506},[505],[363,39193,39195,39198,39266],{"className":39194},[398],[363,39196],{"className":39197,"style":2852},[402],[363,39199,39201,39204,39263],{"className":39200},[407],[363,39202],{"className":39203},[494,789],[363,39205,39207],{"className":39206},[586],[363,39208,39210,39255],{"className":39209},[633,634],[363,39211,39213,39252],{"className":39212},[638],[363,39214,39216,39230,39238],{"className":39215,"style":2871},[642],[363,39217,39218,39221],{"style":2874},[363,39219],{"className":39220,"style":809},[650],[363,39222,39224],{"className":39223},[655,656,657,658],[363,39225,39227],{"className":39226},[407,658],[363,39228,2810],{"className":39229},[407,658],[363,39231,39232,39235],{"style":821},[363,39233],{"className":39234,"style":809},[650],[363,39236],{"className":39237,"style":829},[828],[363,39239,39240,39243],{"style":2897},[363,39241],{"className":39242,"style":809},[650],[363,39244,39246],{"className":39245},[655,656,657,658],[363,39247,39249],{"className":39248},[407,658],[363,39250,465],{"className":39251},[407,658],[363,39253,666],{"className":39254},[665],[363,39256,39258],{"className":39257},[638],[363,39259,39261],{"className":39260,"style":2919},[642],[363,39262],{},[363,39264],{"className":39265},[501,789],[363,39267,39269,39272],{"className":39268},[407],[363,39270,37796],{"className":39271},[407,408],[363,39273,39275],{"className":39274},[629],[363,39276,39278],{"className":39277},[633],[363,39279,39281],{"className":39280},[638],[363,39282,39284],{"className":39283,"style":20375},[642],[363,39285,39286,39289],{"style":7212},[363,39287],{"className":39288,"style":651},[650],[363,39290,39292],{"className":39291},[655,656,657,658],[363,39293,2810],{"className":39294},[407,658],"、本文约定的 ",[363,39297,39299,39346],{"className":39298,"translate":367},[366],[363,39300,39302],{"className":39301},[371],[373,39303,39304],{"xmlns":375},[377,39305,39306,39343],{},[380,39307,39308,39310,39312,39316,39318,39322,39328,39330,39337],{},[458,39309,1634],{},[458,39311,461],{"stretchy":460},[34686,39313,39314],{},[383,39315,11],{},[458,39317,5160],{},[34686,39319,39320],{},[383,39321,1291],{},[7161,39323,39324,39326],{},[458,39325,468],{"stretchy":460},[463,39327,2810],{},[458,39329,33306],{},[586,39331,39332,39334],{},[463,39333,465],{},[463,39335,39336],{},"4",[7161,39338,39339,39341],{},[383,39340,37796],{},[463,39342,2810],{},[387,39344,39345],{"encoding":389},"\\int(\\sqrt p-\\sqrt q)^2\\approx\\frac14\\chi^2",[363,39347,39349,39418,39508],{"className":39348,"ariaHidden":394},[393],[363,39350,39352,39356,39359,39362,39409,39412,39415],{"className":39351},[398],[363,39353],{"className":39354,"style":39355},[402],"height:1.1419em;vertical-align:-0.3369em;",[363,39357,1634],{"className":39358,"style":5964},[1831,1832,5963],[363,39360,461],{"className":39361},[494],[363,39363,39365],{"className":39364},[407,34714],[363,39366,39368,39400],{"className":39367},[633,634],[363,39369,39371,39397],{"className":39370},[638],[363,39372,39375,39384],{"className":39373,"style":39374},[642],"height:0.7031em;",[363,39376,39378,39381],{"className":39377,"style":12210},[6654],[363,39379],{"className":39380,"style":809},[650],[363,39382,11],{"className":39383,"style":34734},[407,408],[363,39385,39387,39390],{"style":39386},"top:-2.6631em;",[363,39388],{"className":39389,"style":809},[650],[363,39391,39393],{"className":39392,"style":34791},[34790],[6670,39394,39395],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,39396],{"d":34798},[363,39398,666],{"className":39399},[665],[363,39401,39403],{"className":39402},[638],[363,39404,39407],{"className":39405,"style":39406},[642],"height:0.3369em;",[363,39408],{},[363,39410],{"className":39411,"style":2934},[505],[363,39413,5160],{"className":39414},[2938],[363,39416],{"className":39417,"style":2934},[505],[363,39419,39421,39425,39470,39499,39502,39505],{"className":39420},[398],[363,39422],{"className":39423,"style":39424},[402],"height:1.151em;vertical-align:-0.3369em;",[363,39426,39428],{"className":39427},[407,34714],[363,39429,39431,39462],{"className":39430},[633,634],[363,39432,39434,39459],{"className":39433},[638],[363,39435,39437,39447],{"className":39436,"style":39374},[642],[363,39438,39440,39443],{"className":39439,"style":12210},[6654],[363,39441],{"className":39442,"style":809},[650],[363,39444,1291],{"className":39445,"style":39446},[407,408],"margin-right:0.0359em;padding-left:0.833em;",[363,39448,39449,39452],{"style":39386},[363,39450],{"className":39451,"style":809},[650],[363,39453,39455],{"className":39454,"style":34791},[34790],[6670,39456,39457],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,39458],{"d":34798},[363,39460,666],{"className":39461},[665],[363,39463,39465],{"className":39464},[638],[363,39466,39468],{"className":39467,"style":39406},[642],[363,39469],{},[363,39471,39473,39476],{"className":39472},[501],[363,39474,468],{"className":39475},[501],[363,39477,39479],{"className":39478},[629],[363,39480,39482],{"className":39481},[633],[363,39483,39485],{"className":39484},[638],[363,39486,39488],{"className":39487,"style":20375},[642],[363,39489,39490,39493],{"style":7212},[363,39491],{"className":39492,"style":651},[650],[363,39494,39496],{"className":39495},[655,656,657,658],[363,39497,2810],{"className":39498},[407,658],[363,39500],{"className":39501,"style":506},[505],[363,39503,33306],{"className":39504},[510],[363,39506],{"className":39507,"style":506},[505],[363,39509,39511,39514,39582],{"className":39510},[398],[363,39512],{"className":39513,"style":2852},[402],[363,39515,39517,39520,39579],{"className":39516},[407],[363,39518],{"className":39519},[494,789],[363,39521,39523],{"className":39522},[586],[363,39524,39526,39571],{"className":39525},[633,634],[363,39527,39529,39568],{"className":39528},[638],[363,39530,39532,39546,39554],{"className":39531,"style":2871},[642],[363,39533,39534,39537],{"style":2874},[363,39535],{"className":39536,"style":809},[650],[363,39538,39540],{"className":39539},[655,656,657,658],[363,39541,39543],{"className":39542},[407,658],[363,39544,39336],{"className":39545},[407,658],[363,39547,39548,39551],{"style":821},[363,39549],{"className":39550,"style":809},[650],[363,39552],{"className":39553,"style":829},[828],[363,39555,39556,39559],{"style":2897},[363,39557],{"className":39558,"style":809},[650],[363,39560,39562],{"className":39561},[655,656,657,658],[363,39563,39565],{"className":39564},[407,658],[363,39566,465],{"className":39567},[407,658],[363,39569,666],{"className":39570},[665],[363,39572,39574],{"className":39573},[638],[363,39575,39577],{"className":39576,"style":2919},[642],[363,39578],{},[363,39580],{"className":39581},[501,789],[363,39583,39585,39588],{"className":39584},[407],[363,39586,37796],{"className":39587},[407,408],[363,39589,39591],{"className":39590},[629],[363,39592,39594],{"className":39593},[633],[363,39595,39597],{"className":39596},[638],[363,39598,39600],{"className":39599,"style":20375},[642],[363,39601,39602,39605],{"style":7212},[363,39603],{"className":39604,"style":651},[650],[363,39606,39608],{"className":39607},[655,656,657,658],[363,39609,2810],{"className":39610},[407,658],"、Bhattacharyya 约定的 ",[363,39613,39615,39660],{"className":39614,"translate":367},[366],[363,39616,39618],{"className":39617},[371],[373,39619,39620],{"xmlns":375},[377,39621,39622,39657],{},[380,39623,39624,39630,39632,39634,39636,39639,39642,39644,39651],{},[7161,39625,39626,39628],{},[383,39627,34231],{},[463,39629,2810],{},[458,39631,471],{},[463,39633,465],{},[458,39635,5160],{},[383,39637,39638],{},"B",[383,39640,39641],{},"C",[458,39643,33306],{},[586,39645,39646,39648],{},[463,39647,465],{},[463,39649,39650],{},"8",[7161,39652,39653,39655],{},[383,39654,37796],{},[463,39656,2810],{},[387,39658,39659],{"encoding":389},"H^2=1-BC\\approx\\frac18\\chi^2",[363,39661,39663,39707,39725,39747],{"className":39662,"ariaHidden":394},[393],[363,39664,39666,39669,39698,39701,39704],{"className":39665},[398],[363,39667],{"className":39668,"style":20375},[402],[363,39670,39672,39675],{"className":39671},[407],[363,39673,34231],{"className":39674,"style":34385},[407,408],[363,39676,39678],{"className":39677},[629],[363,39679,39681],{"className":39680},[633],[363,39682,39684],{"className":39683},[638],[363,39685,39687],{"className":39686,"style":20375},[642],[363,39688,39689,39692],{"style":7212},[363,39690],{"className":39691,"style":651},[650],[363,39693,39695],{"className":39694},[655,656,657,658],[363,39696,2810],{"className":39697},[407,658],[363,39699],{"className":39700,"style":506},[505],[363,39702,471],{"className":39703},[510],[363,39705],{"className":39706,"style":506},[505],[363,39708,39710,39713,39716,39719,39722],{"className":39709},[398],[363,39711],{"className":39712,"style":12925},[402],[363,39714,465],{"className":39715},[407],[363,39717],{"className":39718,"style":2934},[505],[363,39720,5160],{"className":39721},[2938],[363,39723],{"className":39724,"style":2934},[505],[363,39726,39728,39731,39735,39738,39741,39744],{"className":39727},[398],[363,39729],{"className":39730,"style":1011},[402],[363,39732,39638],{"className":39733,"style":39734},[407,408],"margin-right:0.0502em;",[363,39736,39641],{"className":39737,"style":11129},[407,408],[363,39739],{"className":39740,"style":506},[505],[363,39742,33306],{"className":39743},[510],[363,39745],{"className":39746,"style":506},[505],[363,39748,39750,39753,39821],{"className":39749},[398],[363,39751],{"className":39752,"style":2852},[402],[363,39754,39756,39759,39818],{"className":39755},[407],[363,39757],{"className":39758},[494,789],[363,39760,39762],{"className":39761},[586],[363,39763,39765,39810],{"className":39764},[633,634],[363,39766,39768,39807],{"className":39767},[638],[363,39769,39771,39785,39793],{"className":39770,"style":2871},[642],[363,39772,39773,39776],{"style":2874},[363,39774],{"className":39775,"style":809},[650],[363,39777,39779],{"className":39778},[655,656,657,658],[363,39780,39782],{"className":39781},[407,658],[363,39783,39650],{"className":39784},[407,658],[363,39786,39787,39790],{"style":821},[363,39788],{"className":39789,"style":809},[650],[363,39791],{"className":39792,"style":829},[828],[363,39794,39795,39798],{"style":2897},[363,39796],{"className":39797,"style":809},[650],[363,39799,39801],{"className":39800},[655,656,657,658],[363,39802,39804],{"className":39803},[407,658],[363,39805,465],{"className":39806},[407,658],[363,39808,666],{"className":39809},[665],[363,39811,39813],{"className":39812},[638],[363,39814,39816],{"className":39815,"style":2919},[642],[363,39817],{},[363,39819],{"className":39820},[501,789],[363,39822,39824,39827],{"className":39823},[407],[363,39825,37796],{"className":39826},[407,408],[363,39828,39830],{"className":39829},[629],[363,39831,39833],{"className":39832},[633],[363,39834,39836],{"className":39835},[638],[363,39837,39839],{"className":39838,"style":20375},[642],[363,39840,39841,39844],{"style":7212},[363,39842],{"className":39843,"style":651},[650],[363,39845,39847],{"className":39846},[655,656,657,658],[363,39848,2810],{"className":39849},[407,658],"（见 4.6 节的局部展开），因此它是所有 f-散度在局部的「公因子」——只是在 ",[363,39852,39854,39882],{"className":39853,"translate":367},[366],[363,39855,39857],{"className":39856},[371],[373,39858,39859],{"xmlns":375},[377,39860,39861,39879],{},[380,39862,39863,39873,39875,39877],{},[7161,39864,39865,39867],{},[383,39866,385],{},[380,39868,39869,39871],{},[458,39870,7167],{"mathvariant":557},[458,39872,7167],{"mathvariant":557},[458,39874,461],{"stretchy":460},[463,39876,465],{},[458,39878,468],{"stretchy":460},[387,39880,39881],{"encoding":389},"f''(1)",[363,39883,39885],{"className":39884,"ariaHidden":394},[393],[363,39886,39888,39891,39923,39926,39929],{"className":39887},[398],[363,39889],{"className":39890,"style":7190},[402],[363,39892,39894,39897],{"className":39893},[407],[363,39895,385],{"className":39896,"style":409},[407,408],[363,39898,39900],{"className":39899},[629],[363,39901,39903],{"className":39902},[633],[363,39904,39906],{"className":39905},[638],[363,39907,39909],{"className":39908,"style":7209},[642],[363,39910,39911,39914],{"style":7212},[363,39912],{"className":39913,"style":651},[650],[363,39915,39917],{"className":39916},[655,656,657,658],[363,39918,39920],{"className":39919},[407,658],[363,39921,22095],{"className":39922},[407,658],[363,39924,461],{"className":39925},[494],[363,39927,465],{"className":39928},[407],[363,39930,468],{"className":39931},[501]," 意义下的「单位」不同。",[11,39934,39935,39937,39938,40270,40271,40299,40300,3092,40328,40412,40413,40441,40442,40470,40471,40499,40500,40528,40529,40557,40558,40561,40562,40720,40721,40781],{},[1572,39936,24540],{}," 卡方散度是 Pearson 拟合优度统计量 ",[363,39939,39941,39991],{"className":39940,"translate":367},[366],[363,39942,39944],{"className":39943},[371],[373,39945,39946],{"xmlns":375},[377,39947,39948,39988],{},[380,39949,39950,39956],{},[543,39951,39952,39954],{},[458,39953,13808],{},[383,39955,12310],{},[586,39957,39958,39982],{},[380,39959,39960,39962,39968,39970,39976],{},[458,39961,461],{"stretchy":460},[543,39963,39964,39966],{},[383,39965,19568],{},[383,39967,12310],{},[458,39969,5160],{},[543,39971,39972,39974],{},[383,39973,571],{},[383,39975,12310],{},[7161,39977,39978,39980],{},[458,39979,468],{"stretchy":460},[463,39981,2810],{},[543,39983,39984,39986],{},[383,39985,571],{},[383,39987,12310],{},[387,39989,39990],{"encoding":389},"\\sum_i\\frac{(O_i-E_i)^2}{E_i}",[363,39992,39994],{"className":39993,"ariaHidden":394},[393],[363,39995,39997,40001,40045,40048],{"className":39996},[398],[363,39998],{"className":39999,"style":40000},[402],"height:1.554em;vertical-align:-0.4451em;",[363,40002,40004,40008],{"className":40003},[1831],[363,40005,13808],{"className":40006,"style":40007},[1831,1832,5963],"position:relative;top:0em;",[363,40009,40011],{"className":40010},[629],[363,40012,40014,40036],{"className":40013},[633,634],[363,40015,40017,40033],{"className":40016},[638],[363,40018,40021],{"className":40019,"style":40020},[642],"height:0.162em;",[363,40022,40024,40027],{"style":40023},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[363,40025],{"className":40026,"style":651},[650],[363,40028,40030],{"className":40029},[655,656,657,658],[363,40031,12310],{"className":40032},[407,408,658],[363,40034,666],{"className":40035},[665],[363,40037,40039],{"className":40038},[638],[363,40040,40043],{"className":40041,"style":40042},[642],"height:0.2997em;",[363,40044],{},[363,40046],{"className":40047,"style":754},[505],[363,40049,40051,40054,40267],{"className":40050},[407],[363,40052],{"className":40053},[494,789],[363,40055,40057],{"className":40056},[586],[363,40058,40060,40258],{"className":40059},[633,634],[363,40061,40063,40255],{"className":40062},[638],[363,40064,40066,40120,40128],{"className":40065,"style":38795},[642],[363,40067,40068,40071],{"style":2874},[363,40069],{"className":40070,"style":809},[650],[363,40072,40074],{"className":40073},[655,656,657,658],[363,40075,40077],{"className":40076},[407,658],[363,40078,40080,40083],{"className":40079},[407,658],[363,40081,571],{"className":40082,"style":26208},[407,408,658],[363,40084,40086],{"className":40085},[629],[363,40087,40089,40111],{"className":40088},[633,634],[363,40090,40092,40108],{"className":40091},[638],[363,40093,40096],{"className":40094,"style":40095},[642],"height:0.3281em;",[363,40097,40099,40102],{"style":40098},"top:-2.357em;margin-left:-0.0576em;margin-right:0.0714em;",[363,40100],{"className":40101,"style":30553},[650],[363,40103,40105],{"className":40104},[655,30557,10021,658],[363,40106,12310],{"className":40107},[407,408,658],[363,40109,666],{"className":40110},[665],[363,40112,40114],{"className":40113},[638],[363,40115,40118],{"className":40116,"style":40117},[642],"height:0.143em;",[363,40119],{},[363,40121,40122,40125],{"style":821},[363,40123],{"className":40124,"style":809},[650],[363,40126],{"className":40127,"style":829},[828],[363,40129,40130,40133],{"style":26765},[363,40131],{"className":40132,"style":809},[650],[363,40134,40136],{"className":40135},[655,656,657,658],[363,40137,40139,40142,40183,40186,40226],{"className":40138},[407,658],[363,40140,461],{"className":40141},[494,658],[363,40143,40145,40148],{"className":40144},[407,658],[363,40146,19568],{"className":40147,"style":625},[407,408,658],[363,40149,40151],{"className":40150},[629],[363,40152,40154,40175],{"className":40153},[633,634],[363,40155,40157,40172],{"className":40156},[638],[363,40158,40160],{"className":40159,"style":40095},[642],[363,40161,40163,40166],{"style":40162},"top:-2.357em;margin-left:-0.0278em;margin-right:0.0714em;",[363,40164],{"className":40165,"style":30553},[650],[363,40167,40169],{"className":40168},[655,30557,10021,658],[363,40170,12310],{"className":40171},[407,408,658],[363,40173,666],{"className":40174},[665],[363,40176,40178],{"className":40177},[638],[363,40179,40181],{"className":40180,"style":40117},[642],[363,40182],{},[363,40184,5160],{"className":40185},[2938,658],[363,40187,40189,40192],{"className":40188},[407,658],[363,40190,571],{"className":40191,"style":26208},[407,408,658],[363,40193,40195],{"className":40194},[629],[363,40196,40198,40218],{"className":40197},[633,634],[363,40199,40201,40215],{"className":40200},[638],[363,40202,40204],{"className":40203,"style":40095},[642],[363,40205,40206,40209],{"style":40098},[363,40207],{"className":40208,"style":30553},[650],[363,40210,40212],{"className":40211},[655,30557,10021,658],[363,40213,12310],{"className":40214},[407,408,658],[363,40216,666],{"className":40217},[665],[363,40219,40221],{"className":40220},[638],[363,40222,40224],{"className":40223,"style":40117},[642],[363,40225],{},[363,40227,40229,40232],{"className":40228},[501,658],[363,40230,468],{"className":40231},[501,658],[363,40233,40235],{"className":40234},[629],[363,40236,40238],{"className":40237},[633],[363,40239,40241],{"className":40240},[638],[363,40242,40244],{"className":40243,"style":38859},[642],[363,40245,40246,40249],{"style":38862},[363,40247],{"className":40248,"style":30553},[650],[363,40250,40252],{"className":40251},[655,30557,10021,658],[363,40253,2810],{"className":40254},[407,658],[363,40256,666],{"className":40257},[665],[363,40259,40261],{"className":40260},[638],[363,40262,40265],{"className":40263,"style":40264},[642],"height:0.4451em;",[363,40266],{},[363,40268],{"className":40269},[501,789]," 的总体（无限样本）版本：把观测频率看作 ",[363,40272,40274,40287],{"className":40273,"translate":367},[366],[363,40275,40277],{"className":40276},[371],[373,40278,40279],{"xmlns":375},[377,40280,40281,40285],{},[380,40282,40283],{},[383,40284,554],{},[387,40286,554],{"encoding":389},[363,40288,40290],{"className":40289,"ariaHidden":394},[393],[363,40291,40293,40296],{"className":40292},[398],[363,40294],{"className":40295,"style":1011},[402],[363,40297,554],{"className":40298,"style":682},[407,408],"、期望频率看作 ",[363,40301,40303,40316],{"className":40302,"translate":367},[366],[363,40304,40306],{"className":40305},[371],[373,40307,40308],{"xmlns":375},[377,40309,40310,40314],{},[380,40311,40312],{},[383,40313,561],{},[387,40315,561],{"encoding":389},[363,40317,40319],{"className":40318,"ariaHidden":394},[393],[363,40320,40322,40325],{"className":40321},[398],[363,40323],{"className":40324,"style":913},[402],[363,40326,561],{"className":40327},[407,408],[363,40329,40331,40359],{"className":40330,"translate":367},[366],[363,40332,40334],{"className":40333},[371],[373,40335,40336],{"xmlns":375},[377,40337,40338,40356],{},[380,40339,40340,40346,40348,40350,40352,40354],{},[7161,40341,40342,40344],{},[383,40343,37796],{},[463,40345,2810],{},[458,40347,461],{"stretchy":460},[383,40349,554],{},[383,40351,558],{"mathvariant":557},[383,40353,561],{},[458,40355,468],{"stretchy":460},[387,40357,40358],{"encoding":389},"\\chi^2(P\\|Q)",[363,40360,40362],{"className":40361,"ariaHidden":394},[393],[363,40363,40365,40368,40397,40400,40403,40406,40409],{"className":40364},[398],[363,40366],{"className":40367,"style":20350},[402],[363,40369,40371,40374],{"className":40370},[407],[363,40372,37796],{"className":40373},[407,408],[363,40375,40377],{"className":40376},[629],[363,40378,40380],{"className":40379},[633],[363,40381,40383],{"className":40382},[638],[363,40384,40386],{"className":40385,"style":20375},[642],[363,40387,40388,40391],{"style":7212},[363,40389],{"className":40390,"style":651},[650],[363,40392,40394],{"className":40393},[655,656,657,658],[363,40395,2810],{"className":40396},[407,658],[363,40398,461],{"className":40399},[494],[363,40401,554],{"className":40402,"style":682},[407,408],[363,40404,558],{"className":40405},[407],[363,40407,561],{"className":40408},[407,408],[363,40410,468],{"className":40411},[501]," 就是「",[363,40414,40416,40429],{"className":40415,"translate":367},[366],[363,40417,40419],{"className":40418},[371],[373,40420,40421],{"xmlns":375},[377,40422,40423,40427],{},[380,40424,40425],{},[383,40426,554],{},[387,40428,554],{"encoding":389},[363,40430,40432],{"className":40431,"ariaHidden":394},[393],[363,40433,40435,40438],{"className":40434},[398],[363,40436],{"className":40437,"style":1011},[402],[363,40439,554],{"className":40440,"style":682},[407,408]," 是否来自 ",[363,40443,40445,40458],{"className":40444,"translate":367},[366],[363,40446,40448],{"className":40447},[371],[373,40449,40450],{"xmlns":375},[377,40451,40452,40456],{},[380,40453,40454],{},[383,40455,561],{},[387,40457,561],{"encoding":389},[363,40459,40461],{"className":40460,"ariaHidden":394},[393],[363,40462,40464,40467],{"className":40463},[398],[363,40465],{"className":40466,"style":913},[402],[363,40468,561],{"className":40469},[407,408],"」的标准化偏差，因此它是独立性检验、拟合优度检验与特征选择的自然尺度。它的分母 ",[363,40472,40474,40487],{"className":40473,"translate":367},[366],[363,40475,40477],{"className":40476},[371],[373,40478,40479],{"xmlns":375},[377,40480,40481,40485],{},[380,40482,40483],{},[383,40484,1291],{},[387,40486,1291],{"encoding":389},[363,40488,40490],{"className":40489,"ariaHidden":394},[393],[363,40491,40493,40496],{"className":40492},[398],[363,40494],{"className":40495,"style":2623},[402],[363,40497,1291],{"className":40498,"style":1328},[407,408]," 使它对「",[363,40501,40503,40516],{"className":40502,"translate":367},[366],[363,40504,40506],{"className":40505},[371],[373,40507,40508],{"xmlns":375},[377,40509,40510,40514],{},[380,40511,40512],{},[383,40513,561],{},[387,40515,561],{"encoding":389},[363,40517,40519],{"className":40518,"ariaHidden":394},[393],[363,40520,40522,40525],{"className":40521},[398],[363,40523],{"className":40524,"style":913},[402],[363,40526,561],{"className":40527},[407,408]," 很小而 ",[363,40530,40532,40545],{"className":40531,"translate":367},[366],[363,40533,40535],{"className":40534},[371],[373,40536,40537],{"xmlns":375},[377,40538,40539,40543],{},[380,40540,40541],{},[383,40542,554],{},[387,40544,554],{"encoding":389},[363,40546,40548],{"className":40547,"ariaHidden":394},[393],[363,40549,40551,40554],{"className":40550},[398],[363,40552],{"className":40553,"style":1011},[402],[363,40555,554],{"className":40556,"style":682},[407,408]," 不小」的稀有区域极度敏感（",[1572,40559,40560],{},"尾部敏感","）：这既是它能捕捉稀有事件的优点，也是它容易被少量异常值带偏的缺点。在 f-GAN 家族里它对应最小二乘 GAN（LSGAN）：因为 ",[363,40563,40565,40606],{"className":40564,"translate":367},[366],[363,40566,40568],{"className":40567},[371],[373,40569,40570],{"xmlns":375},[377,40571,40572,40603],{},[380,40573,40574,40580,40582,40585,40587,40589,40591,40593,40599,40601],{},[7161,40575,40576,40578],{},[383,40577,385],{},[458,40579,7920],{},[458,40581,461],{"stretchy":460},[383,40583,40584],{},"y",[458,40586,468],{"stretchy":460},[458,40588,471],{},[383,40590,40584],{},[458,40592,2817],{},[7161,40594,40595,40597],{},[383,40596,40584],{},[463,40598,2810],{},[383,40600,1288],{"mathvariant":557},[463,40602,39336],{},[387,40604,40605],{"encoding":389},"f^*(y)=y+y^2\u002F4",[363,40607,40609,40662,40681],{"className":40608,"ariaHidden":394},[393],[363,40610,40612,40615,40644,40647,40650,40653,40656,40659],{"className":40611},[398],[363,40613],{"className":40614,"style":487},[402],[363,40616,40618,40621],{"className":40617},[407],[363,40619,385],{"className":40620,"style":409},[407,408],[363,40622,40624],{"className":40623},[629],[363,40625,40627],{"className":40626},[633],[363,40628,40630],{"className":40629},[638],[363,40631,40633],{"className":40632,"style":8846},[642],[363,40634,40635,40638],{"style":7212},[363,40636],{"className":40637,"style":651},[650],[363,40639,40641],{"className":40640},[655,656,657,658],[363,40642,7920],{"className":40643},[2938,658],[363,40645,461],{"className":40646},[494],[363,40648,40584],{"className":40649,"style":1328},[407,408],[363,40651,468],{"className":40652},[501],[363,40654],{"className":40655,"style":506},[505],[363,40657,471],{"className":40658},[510],[363,40660],{"className":40661,"style":506},[505],[363,40663,40665,40669,40672,40675,40678],{"className":40664},[398],[363,40666],{"className":40667,"style":40668},[402],"height:0.7778em;vertical-align:-0.1944em;",[363,40670,40584],{"className":40671,"style":1328},[407,408],[363,40673],{"className":40674,"style":2934},[505],[363,40676,2817],{"className":40677},[2938],[363,40679],{"className":40680,"style":2934},[505],[363,40682,40684,40687,40716],{"className":40683},[398],[363,40685],{"className":40686,"style":20350},[402],[363,40688,40690,40693],{"className":40689},[407],[363,40691,40584],{"className":40692,"style":1328},[407,408],[363,40694,40696],{"className":40695},[629],[363,40697,40699],{"className":40698},[633],[363,40700,40702],{"className":40701},[638],[363,40703,40705],{"className":40704,"style":20375},[642],[363,40706,40707,40710],{"style":7212},[363,40708],{"className":40709,"style":651},[650],[363,40711,40713],{"className":40712},[655,656,657,658],[363,40714,2810],{"className":40715},[407,658],[363,40717,40719],{"className":40718},[407],"\u002F4"," 是二次的，判别器梯度不会像 JS 那样饱和；在鲁棒统计与核方法中，",[363,40722,40724,40742],{"className":40723,"translate":367},[366],[363,40725,40727],{"className":40726},[371],[373,40728,40729],{"xmlns":375},[377,40730,40731,40739],{},[380,40732,40733],{},[7161,40734,40735,40737],{},[383,40736,37796],{},[463,40738,2810],{},[387,40740,40741],{"encoding":389},"\\chi^2",[363,40743,40745],{"className":40744,"ariaHidden":394},[393],[363,40746,40748,40752],{"className":40747},[398],[363,40749],{"className":40750,"style":40751},[402],"height:1.0085em;vertical-align:-0.1944em;",[363,40753,40755,40758],{"className":40754},[407],[363,40756,37796],{"className":40757},[407,408],[363,40759,40761],{"className":40760},[629],[363,40762,40764],{"className":40763},[633],[363,40765,40767],{"className":40766},[638],[363,40768,40770],{"className":40769,"style":20375},[642],[363,40771,40772,40775],{"style":7212},[363,40773],{"className":40774,"style":651},[650],[363,40776,40778],{"className":40777},[655,656,657,658],[363,40779,2810],{"className":40780},[407,658]," 距离还给出了带权核的另一种「局部」相似度。",[2658,40783,40785],{"id":40784},"_35-hellinger-平方","3.5 Hellinger 平方",[11,40787,21820],{},[363,40789,40791],{"className":40790,"translate":367},[528],[363,40792,40794,40832],{"className":40793,"translate":367},[366],[363,40795,40797],{"className":40796},[371],[373,40798,40799],{"xmlns":375,"display":537},[377,40800,40801,40829],{},[380,40802,40803,40805,40807,40809,40811,40813,40815,40819,40821,40823],{},[383,40804,385],{},[458,40806,461],{"stretchy":460},[383,40808,1116],{},[458,40810,468],{"stretchy":460},[458,40812,471],{},[458,40814,461],{"stretchy":460},[34686,40816,40817],{},[383,40818,1116],{},[458,40820,5160],{},[463,40822,465],{},[7161,40824,40825,40827],{},[458,40826,468],{"stretchy":460},[463,40828,2810],{},[387,40830,40831],{"encoding":389},"f(t)=(\\sqrt{t}-1)^2",[363,40833,40835,40862,40931],{"className":40834,"ariaHidden":394},[393],[363,40836,40838,40841,40844,40847,40850,40853,40856,40859],{"className":40837},[398],[363,40839],{"className":40840,"style":487},[402],[363,40842,385],{"className":40843,"style":409},[407,408],[363,40845,461],{"className":40846},[494],[363,40848,1116],{"className":40849},[407,408],[363,40851,468],{"className":40852},[501],[363,40854],{"className":40855,"style":506},[505],[363,40857,471],{"className":40858},[510],[363,40860],{"className":40861,"style":506},[505],[363,40863,40865,40869,40872,40922,40925,40928],{"className":40864},[398],[363,40866],{"className":40867,"style":40868},[402],"height:1.1914em;vertical-align:-0.25em;",[363,40870,461],{"className":40871},[494],[363,40873,40875],{"className":40874},[407,34714],[363,40876,40878,40913],{"className":40877},[633,634],[363,40879,40881,40910],{"className":40880},[638],[363,40882,40885,40897],{"className":40883,"style":40884},[642],"height:0.9414em;",[363,40886,40888,40891],{"className":40887,"style":12210},[6654],[363,40889],{"className":40890,"style":809},[650],[363,40892,40894],{"className":40893,"style":34734},[407],[363,40895,1116],{"className":40896},[407,408],[363,40898,40900,40903],{"style":40899},"top:-2.9014em;",[363,40901],{"className":40902,"style":809},[650],[363,40904,40906],{"className":40905,"style":34791},[34790],[6670,40907,40908],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,40909],{"d":34798},[363,40911,666],{"className":40912},[665],[363,40914,40916],{"className":40915},[638],[363,40917,40920],{"className":40918,"style":40919},[642],"height:0.0986em;",[363,40921],{},[363,40923],{"className":40924,"style":2934},[505],[363,40926,5160],{"className":40927},[2938],[363,40929],{"className":40930,"style":2934},[505],[363,40932,40934,40937,40940],{"className":40933},[398],[363,40935],{"className":40936,"style":37598},[402],[363,40938,465],{"className":40939},[407],[363,40941,40943,40946],{"className":40942},[501],[363,40944,468],{"className":40945},[501],[363,40947,40949],{"className":40948},[629],[363,40950,40952],{"className":40951},[633],[363,40953,40955],{"className":40954},[638],[363,40956,40958],{"className":40957,"style":20082},[642],[363,40959,40960,40963],{"style":8624},[363,40961],{"className":40962,"style":651},[650],[363,40964,40966],{"className":40965},[655,656,657,658],[363,40967,2810],{"className":40968},[407,658],[11,40970,35029,40971,5992,41036,41284],{},[363,40972,40974,40997],{"className":40973,"translate":367},[366],[363,40975,40977],{"className":40976},[371],[373,40978,40979],{"xmlns":375},[377,40980,40981,40995],{},[380,40982,40983,40985,40987,40989,40991,40993],{},[383,40984,385],{},[458,40986,461],{"stretchy":460},[463,40988,465],{},[458,40990,468],{"stretchy":460},[458,40992,471],{},[463,40994,474],{},[387,40996,477],{"encoding":389},[363,40998,41000,41027],{"className":40999,"ariaHidden":394},[393],[363,41001,41003,41006,41009,41012,41015,41018,41021,41024],{"className":41002},[398],[363,41004],{"className":41005,"style":487},[402],[363,41007,385],{"className":41008,"style":409},[407,408],[363,41010,461],{"className":41011},[494],[363,41013,465],{"className":41014},[407],[363,41016,468],{"className":41017},[501],[363,41019],{"className":41020,"style":506},[505],[363,41022,471],{"className":41023},[510],[363,41025],{"className":41026,"style":506},[505],[363,41028,41030,41033],{"className":41029},[398],[363,41031],{"className":41032,"style":520},[402],[363,41034,474],{"className":41035},[407],[363,41037,41039,41094],{"className":41038,"translate":367},[366],[363,41040,41042],{"className":41041},[371],[373,41043,41044],{"xmlns":375},[377,41045,41046,41091],{},[380,41047,41048,41058,41060,41062,41064,41066,41087,41089],{},[7161,41049,41050,41052],{},[383,41051,385],{},[380,41053,41054,41056],{},[458,41055,7167],{"mathvariant":557},[458,41057,7167],{"mathvariant":557},[458,41059,461],{"stretchy":460},[383,41061,1116],{},[458,41063,468],{"stretchy":460},[458,41065,471],{},[586,41067,41068,41070],{},[463,41069,465],{},[380,41071,41072,41074],{},[463,41073,2810],{},[7161,41075,41076,41078],{},[383,41077,1116],{},[380,41079,41080,41083,41085],{},[463,41081,41082],{},"3",[383,41084,1288],{"mathvariant":557},[463,41086,2810],{},[458,41088,3250],{},[463,41090,474],{},[387,41092,41093],{"encoding":389},"f''(t)=\\frac{1}{2t^{3\u002F2}}>0",[363,41095,41097,41153,41275],{"className":41096,"ariaHidden":394},[393],[363,41098,41100,41103,41135,41138,41141,41144,41147,41150],{"className":41099},[398],[363,41101],{"className":41102,"style":7190},[402],[363,41104,41106,41109],{"className":41105},[407],[363,41107,385],{"className":41108,"style":409},[407,408],[363,41110,41112],{"className":41111},[629],[363,41113,41115],{"className":41114},[633],[363,41116,41118],{"className":41117},[638],[363,41119,41121],{"className":41120,"style":7209},[642],[363,41122,41123,41126],{"style":7212},[363,41124],{"className":41125,"style":651},[650],[363,41127,41129],{"className":41128},[655,656,657,658],[363,41130,41132],{"className":41131},[407,658],[363,41133,22095],{"className":41134},[407,658],[363,41136,461],{"className":41137},[494],[363,41139,1116],{"className":41140},[407,408],[363,41142,468],{"className":41143},[501],[363,41145],{"className":41146,"style":506},[505],[363,41148,471],{"className":41149},[510],[363,41151],{"className":41152,"style":506},[505],[363,41154,41156,41160,41266,41269,41272],{"className":41155},[398],[363,41157],{"className":41158,"style":41159},[402],"height:1.2305em;vertical-align:-0.3854em;",[363,41161,41163,41166,41263],{"className":41162},[407],[363,41164],{"className":41165},[494,789],[363,41167,41169],{"className":41168},[586],[363,41170,41172,41254],{"className":41171},[633,634],[363,41173,41175,41251],{"className":41174},[638],[363,41176,41178,41229,41237],{"className":41177,"style":2871},[642],[363,41179,41181,41184],{"style":41180},"top:-2.6146em;",[363,41182],{"className":41183,"style":809},[650],[363,41185,41187],{"className":41186},[655,656,657,658],[363,41188,41190,41193],{"className":41189},[407,658],[363,41191,2810],{"className":41192},[407,658],[363,41194,41196,41199],{"className":41195},[407,658],[363,41197,1116],{"className":41198},[407,408,658],[363,41200,41202],{"className":41201},[629],[363,41203,41205],{"className":41204},[633],[363,41206,41208],{"className":41207},[638],[363,41209,41212],{"className":41210,"style":41211},[642],"height:0.822em;",[363,41213,41215,41219],{"style":41214},"top:-2.822em;margin-right:0.0714em;",[363,41216],{"className":41217,"style":41218},[650],"height:2.5357em;",[363,41220,41222],{"className":41221},[655,30557,10021,658],[363,41223,41225],{"className":41224},[407,658],[363,41226,41228],{"className":41227},[407,658],"3\u002F2",[363,41230,41231,41234],{"style":821},[363,41232],{"className":41233,"style":809},[650],[363,41235],{"className":41236,"style":829},[828],[363,41238,41239,41242],{"style":2897},[363,41240],{"className":41241,"style":809},[650],[363,41243,41245],{"className":41244},[655,656,657,658],[363,41246,41248],{"className":41247},[407,658],[363,41249,465],{"className":41250},[407,658],[363,41252,666],{"className":41253},[665],[363,41255,41257],{"className":41256},[638],[363,41258,41261],{"className":41259,"style":41260},[642],"height:0.3854em;",[363,41262],{},[363,41264],{"className":41265},[501,789],[363,41267],{"className":41268,"style":506},[505],[363,41270,3250],{"className":41271},[510],[363,41273],{"className":41274,"style":506},[505],[363,41276,41278,41281],{"className":41277},[398],[363,41279],{"className":41280,"style":520},[402],[363,41282,474],{"className":41283},[407]," 凸，代入：",[363,41286,41288],{"className":41287,"translate":367},[528],[363,41289,41291,41381],{"className":41290,"translate":367},[366],[363,41292,41294],{"className":41293},[371],[373,41295,41296],{"xmlns":375,"display":537},[377,41297,41298,41378],{},[380,41299,41300,41306,41308,41310,41312,41314,41316,41318,41320,41322,41344,41346,41348,41350,41352,41354,41358,41360,41364,41370,41372,41374,41376],{},[543,41301,41302,41304],{},[383,41303,547],{},[383,41305,385],{},[458,41307,461],{"stretchy":460},[383,41309,554],{},[383,41311,558],{"mathvariant":557},[383,41313,561],{},[458,41315,468],{"stretchy":460},[458,41317,471],{},[458,41319,1634],{},[383,41321,1291],{},[7161,41323,41324,41342],{},[380,41325,41326,41328,41336,41338,41340],{},[458,41327,461],{"fence":394},[34686,41329,41330],{},[586,41331,41332,41334],{},[383,41333,11],{},[383,41335,1291],{},[458,41337,5160],{},[463,41339,465],{},[458,41341,468],{"fence":394},[463,41343,2810],{},[383,41345,592],{},[383,41347,1121],{},[458,41349,471],{},[458,41351,1634],{},[458,41353,461],{"stretchy":460},[34686,41355,41356],{},[383,41357,11],{},[458,41359,5160],{},[34686,41361,41362],{},[383,41363,1291],{},[7161,41365,41366,41368],{},[458,41367,468],{"stretchy":460},[463,41369,2810],{},[1644,41371,1646],{},[383,41373,592],{},[383,41375,1121],{},[383,41377,4722],{"mathvariant":557},[387,41379,41380],{"encoding":389},"D_f(P\\|Q)\n=\\int q\\left(\\sqrt{\\frac{p}{q}}-1\\right)^2dx\n=\\int (\\sqrt{p}-\\sqrt{q})^2\\,dx .",[363,41382,41384,41454,41659,41729],{"className":41383,"ariaHidden":394},[393],[363,41385,41387,41390,41430,41433,41436,41439,41442,41445,41448,41451],{"className":41386},[398],[363,41388],{"className":41389,"style":618},[402],[363,41391,41393,41396],{"className":41392},[407],[363,41394,547],{"className":41395,"style":625},[407,408],[363,41397,41399],{"className":41398},[629],[363,41400,41402,41422],{"className":41401},[633,634],[363,41403,41405,41419],{"className":41404},[638],[363,41406,41408],{"className":41407,"style":643},[642],[363,41409,41410,41413],{"style":646},[363,41411],{"className":41412,"style":651},[650],[363,41414,41416],{"className":41415},[655,656,657,658],[363,41417,385],{"className":41418,"style":409},[407,408,658],[363,41420,666],{"className":41421},[665],[363,41423,41425],{"className":41424},[638],[363,41426,41428],{"className":41427,"style":673},[642],[363,41429],{},[363,41431,461],{"className":41432},[494],[363,41434,554],{"className":41435,"style":682},[407,408],[363,41437,558],{"className":41438},[407],[363,41440,561],{"className":41441},[407,408],[363,41443,468],{"className":41444},[501],[363,41446],{"className":41447,"style":506},[505],[363,41449,471],{"className":41450},[510],[363,41452],{"className":41453,"style":506},[505],[363,41455,41457,41461,41464,41467,41470,41473,41641,41644,41647,41650,41653,41656],{"className":41456},[398],[363,41458],{"className":41459,"style":41460},[402],"height:2.6466em;vertical-align:-0.9926em;",[363,41462,1634],{"className":41463,"style":1834},[1831,1832,1833],[363,41465],{"className":41466,"style":754},[505],[363,41468,1291],{"className":41469,"style":1328},[407,408],[363,41471],{"className":41472,"style":754},[505],[363,41474,41476,41618],{"className":41475},[758],[363,41477,41479,41485,41600,41603,41606,41609,41612],{"className":41478},[758],[363,41480,41482],{"className":41481,"style":763},[494,762],[363,41483,461],{"className":41484},[767,657],[363,41486,41488],{"className":41487},[407,34714],[363,41489,41491,41591],{"className":41490},[633,634],[363,41492,41494,41588],{"className":41493},[638],[363,41495,41498,41571],{"className":41496,"style":41497},[642],"height:1.4474em;",[363,41499,41502,41505],{"className":41500,"style":41501},[6654],"top:-4.4em;",[363,41503],{"className":41504,"style":35392},[650],[363,41506,41509],{"className":41507,"style":41508},[407],"padding-left:1em;",[363,41510,41512,41515,41568],{"className":41511},[407],[363,41513],{"className":41514},[494,789],[363,41516,41518],{"className":41517},[586],[363,41519,41521,41560],{"className":41520},[633,634],[363,41522,41524,41557],{"className":41523},[638],[363,41525,41527,41538,41546],{"className":41526,"style":3901},[642],[363,41528,41529,41532],{"style":805},[363,41530],{"className":41531,"style":809},[650],[363,41533,41535],{"className":41534},[407],[363,41536,1291],{"className":41537,"style":1328},[407,408],[363,41539,41540,41543],{"style":821},[363,41541],{"className":41542,"style":809},[650],[363,41544],{"className":41545,"style":829},[828],[363,41547,41548,41551],{"style":832},[363,41549],{"className":41550,"style":809},[650],[363,41552,41554],{"className":41553},[407],[363,41555,11],{"className":41556},[407,408],[363,41558,666],{"className":41559},[665],[363,41561,41563],{"className":41562},[638],[363,41564,41566],{"className":41565,"style":854},[642],[363,41567],{},[363,41569],{"className":41570},[501,789],[363,41572,41574,41577],{"style":41573},"top:-3.4074em;",[363,41575],{"className":41576,"style":35392},[650],[363,41578,41581],{"className":41579,"style":41580},[34790],"min-width:1.02em;height:2.48em;",[6670,41582,41585],{"xmlns":6672,"width":6673,"height":41583,"viewBox":41584,"preserveAspectRatio":6676},"2.48em","0 0 400000 2592",[6678,41586],{"d":41587},"M424,2478\nc-1.3,-0.7,-38.5,-172,-111.5,-514c-73,-342,-109.8,-513.3,-110.5,-514\nc0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5,25c-5.7,9.3,-9.8,16,-12.5,20\ns-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13,-13s76,-122,76,-122s77,-121,77,-121\ns209,968,209,968c0,-2,84.7,-361.7,254,-1079c169.3,-717.3,254.7,-1077.7,256,-1081\nl0 -0c4,-6.7,10,-10,18,-10 H400000\nv40H1014.6\ns-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185\nc-2,6,-10,9,-24,9\nc-8,0,-12,-0.7,-12,-2z M1001 80\nh400000v40h-400000z",[363,41589,666],{"className":41590},[665],[363,41592,41594],{"className":41593},[638],[363,41595,41598],{"className":41596,"style":41597},[642],"height:0.9926em;",[363,41599],{},[363,41601],{"className":41602,"style":2934},[505],[363,41604,5160],{"className":41605},[2938],[363,41607],{"className":41608,"style":2934},[505],[363,41610,465],{"className":41611},[407],[363,41613,41615],{"className":41614,"style":763},[501,762],[363,41616,468],{"className":41617},[767,657],[363,41619,41621],{"className":41620},[629],[363,41622,41624],{"className":41623},[633],[363,41625,41627],{"className":41626},[638],[363,41628,41630],{"className":41629,"style":38008},[642],[363,41631,41632,41635],{"style":38011},[363,41633],{"className":41634,"style":651},[650],[363,41636,41638],{"className":41637},[655,656,657,658],[363,41639,2810],{"className":41640},[407,658],[363,41642],{"className":41643,"style":754},[505],[363,41645,592],{"className":41646},[407,408],[363,41648,1121],{"className":41649},[407,408],[363,41651],{"className":41652,"style":506},[505],[363,41654,471],{"className":41655},[510],[363,41657],{"className":41658,"style":506},[505],[363,41660,41662,41665,41668,41671,41720,41723,41726],{"className":41661},[398],[363,41663],{"className":41664,"style":6124},[402],[363,41666,1634],{"className":41667,"style":1834},[1831,1832,1833],[363,41669,461],{"className":41670},[494],[363,41672,41674],{"className":41673},[407,34714],[363,41675,41677,41711],{"className":41676},[633,634],[363,41678,41680,41708],{"className":41679},[638],[363,41681,41683,41695],{"className":41682,"style":7209},[642],[363,41684,41686,41689],{"className":41685,"style":12210},[6654],[363,41687],{"className":41688,"style":809},[650],[363,41690,41692],{"className":41691,"style":34734},[407],[363,41693,11],{"className":41694},[407,408],[363,41696,41698,41701],{"style":41697},"top:-2.7119em;",[363,41699],{"className":41700,"style":809},[650],[363,41702,41704],{"className":41703,"style":34791},[34790],[6670,41705,41706],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,41707],{"d":34798},[363,41709,666],{"className":41710},[665],[363,41712,41714],{"className":41713},[638],[363,41715,41718],{"className":41716,"style":41717},[642],"height:0.2881em;",[363,41719],{},[363,41721],{"className":41722,"style":2934},[505],[363,41724,5160],{"className":41725},[2938],[363,41727],{"className":41728,"style":2934},[505],[363,41730,41732,41736,41783,41812,41815,41818,41821],{"className":41731},[398],[363,41733],{"className":41734,"style":41735},[402],"height:1.1522em;vertical-align:-0.2881em;",[363,41737,41739],{"className":41738},[407,34714],[363,41740,41742,41775],{"className":41741},[633,634],[363,41743,41745,41772],{"className":41744},[638],[363,41746,41748,41760],{"className":41747,"style":7209},[642],[363,41749,41751,41754],{"className":41750,"style":12210},[6654],[363,41752],{"className":41753,"style":809},[650],[363,41755,41757],{"className":41756,"style":34734},[407],[363,41758,1291],{"className":41759,"style":1328},[407,408],[363,41761,41762,41765],{"style":41697},[363,41763],{"className":41764,"style":809},[650],[363,41766,41768],{"className":41767,"style":34791},[34790],[6670,41769,41770],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,41771],{"d":34798},[363,41773,666],{"className":41774},[665],[363,41776,41778],{"className":41777},[638],[363,41779,41781],{"className":41780,"style":41717},[642],[363,41782],{},[363,41784,41786,41789],{"className":41785},[501],[363,41787,468],{"className":41788},[501],[363,41790,41792],{"className":41791},[629],[363,41793,41795],{"className":41794},[633],[363,41796,41798],{"className":41797},[638],[363,41799,41801],{"className":41800,"style":20082},[642],[363,41802,41803,41806],{"style":8624},[363,41804],{"className":41805,"style":651},[650],[363,41807,41809],{"className":41808},[655,656,657,658],[363,41810,2810],{"className":41811},[407,658],[363,41813],{"className":41814,"style":754},[505],[363,41816,592],{"className":41817},[407,408],[363,41819,1121],{"className":41820},[407,408],[363,41822,4722],{"className":41823},[407],[11,41825,41826,41827,41985],{},"记 Bhattacharyya 系数 ",[363,41828,41830,41874],{"className":41829,"translate":367},[366],[363,41831,41833],{"className":41832},[371],[373,41834,41835],{"xmlns":375},[377,41836,41837,41871],{},[380,41838,41839,41841,41843,41845,41847,41849,41851,41853,41855,41857,41865,41867,41869],{},[383,41840,39638],{},[383,41842,39641],{},[458,41844,461],{"stretchy":460},[383,41846,554],{},[458,41848,898],{"separator":394},[383,41850,561],{},[458,41852,468],{"stretchy":460},[458,41854,471],{},[458,41856,1634],{},[34686,41858,41859],{},[380,41860,41861,41863],{},[383,41862,11],{},[383,41864,1291],{},[1644,41866,1646],{},[383,41868,592],{},[383,41870,1121],{},[387,41872,41873],{"encoding":389},"BC(P,Q)=\\int\\sqrt{pq}\\,dx",[363,41875,41877,41916],{"className":41876,"ariaHidden":394},[393],[363,41878,41880,41883,41886,41889,41892,41895,41898,41901,41904,41907,41910,41913],{"className":41879},[398],[363,41881],{"className":41882,"style":487},[402],[363,41884,39638],{"className":41885,"style":39734},[407,408],[363,41887,39641],{"className":41888,"style":11129},[407,408],[363,41890,461],{"className":41891},[494],[363,41893,554],{"className":41894,"style":682},[407,408],[363,41896,898],{"className":41897},[920],[363,41899],{"className":41900,"style":754},[505],[363,41902,561],{"className":41903},[407,408],[363,41905,468],{"className":41906},[501],[363,41908],{"className":41909,"style":506},[505],[363,41911,471],{"className":41912},[510],[363,41914],{"className":41915,"style":506},[505],[363,41917,41919,41922,41925,41928,41976,41979,41982],{"className":41918},[398],[363,41920],{"className":41921,"style":39355},[402],[363,41923,1634],{"className":41924,"style":5964},[1831,1832,5963],[363,41926],{"className":41927,"style":754},[505],[363,41929,41931],{"className":41930},[407,34714],[363,41932,41934,41968],{"className":41933},[633,634],[363,41935,41937,41965],{"className":41936},[638],[363,41938,41940,41953],{"className":41939,"style":39374},[642],[363,41941,41943,41946],{"className":41942,"style":12210},[6654],[363,41944],{"className":41945,"style":809},[650],[363,41947,41949],{"className":41948,"style":34734},[407],[363,41950,41952],{"className":41951,"style":1328},[407,408],"pq",[363,41954,41955,41958],{"style":39386},[363,41956],{"className":41957,"style":809},[650],[363,41959,41961],{"className":41960,"style":34791},[34790],[6670,41962,41963],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,41964],{"d":34798},[363,41966,666],{"className":41967},[665],[363,41969,41971],{"className":41970},[638],[363,41972,41974],{"className":41973,"style":39406},[642],[363,41975],{},[363,41977],{"className":41978,"style":754},[505],[363,41980,592],{"className":41981},[407,408],[363,41983,1121],{"className":41984},[407,408],"，则",[363,41987,41989],{"className":41988,"translate":367},[528],[363,41990,41992,42068],{"className":41991,"translate":367},[366],[363,41993,41995],{"className":41994},[371],[373,41996,41997],{"xmlns":375,"display":537},[377,41998,41999,42065],{},[380,42000,42001,42003,42005,42009,42011,42015,42021,42023,42025,42027,42029,42031,42033,42035,42037,42039,42047,42049,42051,42053,42055,42057,42059,42061,42063],{},[458,42002,1634],{},[458,42004,461],{"stretchy":460},[34686,42006,42007],{},[383,42008,11],{},[458,42010,5160],{},[34686,42012,42013],{},[383,42014,1291],{},[7161,42016,42017,42019],{},[458,42018,468],{"stretchy":460},[463,42020,2810],{},[458,42022,471],{},[458,42024,1634],{},[383,42026,11],{},[458,42028,2817],{},[458,42030,1634],{},[383,42032,1291],{},[458,42034,5160],{},[463,42036,2810],{},[458,42038,1634],{},[34686,42040,42041],{},[380,42042,42043,42045],{},[383,42044,11],{},[383,42046,1291],{},[458,42048,471],{},[463,42050,2810],{},[458,42052,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[463,42054,465],{},[458,42056,5160],{},[383,42058,39638],{},[383,42060,39641],{},[458,42062,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,42064,4722],{"mathvariant":557},[387,42066,42067],{"encoding":389},"\\int(\\sqrt p-\\sqrt q)^2\n=\\int p+\\int q-2\\int\\sqrt{pq}\n=2\\big(1-BC\\big).",[363,42069,42071,42136,42224,42248,42272,42346,42373],{"className":42070,"ariaHidden":394},[393],[363,42072,42074,42077,42080,42083,42127,42130,42133],{"className":42073},[398],[363,42075],{"className":42076,"style":6124},[402],[363,42078,1634],{"className":42079,"style":1834},[1831,1832,1833],[363,42081,461],{"className":42082},[494],[363,42084,42086],{"className":42085},[407,34714],[363,42087,42089,42119],{"className":42088},[633,634],[363,42090,42092,42116],{"className":42091},[638],[363,42093,42095,42104],{"className":42094,"style":7209},[642],[363,42096,42098,42101],{"className":42097,"style":12210},[6654],[363,42099],{"className":42100,"style":809},[650],[363,42102,11],{"className":42103,"style":34734},[407,408],[363,42105,42106,42109],{"style":41697},[363,42107],{"className":42108,"style":809},[650],[363,42110,42112],{"className":42111,"style":34791},[34790],[6670,42113,42114],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,42115],{"d":34798},[363,42117,666],{"className":42118},[665],[363,42120,42122],{"className":42121},[638],[363,42123,42125],{"className":42124,"style":41717},[642],[363,42126],{},[363,42128],{"className":42129,"style":2934},[505],[363,42131,5160],{"className":42132},[2938],[363,42134],{"className":42135,"style":2934},[505],[363,42137,42139,42142,42186,42215,42218,42221],{"className":42138},[398],[363,42140],{"className":42141,"style":41735},[402],[363,42143,42145],{"className":42144},[407,34714],[363,42146,42148,42178],{"className":42147},[633,634],[363,42149,42151,42175],{"className":42150},[638],[363,42152,42154,42163],{"className":42153,"style":7209},[642],[363,42155,42157,42160],{"className":42156,"style":12210},[6654],[363,42158],{"className":42159,"style":809},[650],[363,42161,1291],{"className":42162,"style":39446},[407,408],[363,42164,42165,42168],{"style":41697},[363,42166],{"className":42167,"style":809},[650],[363,42169,42171],{"className":42170,"style":34791},[34790],[6670,42172,42173],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,42174],{"d":34798},[363,42176,666],{"className":42177},[665],[363,42179,42181],{"className":42180},[638],[363,42182,42184],{"className":42183,"style":41717},[642],[363,42185],{},[363,42187,42189,42192],{"className":42188},[501],[363,42190,468],{"className":42191},[501],[363,42193,42195],{"className":42194},[629],[363,42196,42198],{"className":42197},[633],[363,42199,42201],{"className":42200},[638],[363,42202,42204],{"className":42203,"style":20082},[642],[363,42205,42206,42209],{"style":8624},[363,42207],{"className":42208,"style":651},[650],[363,42210,42212],{"className":42211},[655,656,657,658],[363,42213,2810],{"className":42214},[407,658],[363,42216],{"className":42217,"style":506},[505],[363,42219,471],{"className":42220},[510],[363,42222],{"className":42223,"style":506},[505],[363,42225,42227,42230,42233,42236,42239,42242,42245],{"className":42226},[398],[363,42228],{"className":42229,"style":6124},[402],[363,42231,1634],{"className":42232,"style":1834},[1831,1832,1833],[363,42234],{"className":42235,"style":754},[505],[363,42237,11],{"className":42238},[407,408],[363,42240],{"className":42241,"style":2934},[505],[363,42243,2817],{"className":42244},[2938],[363,42246],{"className":42247,"style":2934},[505],[363,42249,42251,42254,42257,42260,42263,42266,42269],{"className":42250},[398],[363,42252],{"className":42253,"style":6124},[402],[363,42255,1634],{"className":42256,"style":1834},[1831,1832,1833],[363,42258],{"className":42259,"style":754},[505],[363,42261,1291],{"className":42262,"style":1328},[407,408],[363,42264],{"className":42265,"style":2934},[505],[363,42267,5160],{"className":42268},[2938],[363,42270],{"className":42271,"style":2934},[505],[363,42273,42275,42278,42281,42284,42287,42290,42337,42340,42343],{"className":42274},[398],[363,42276],{"className":42277,"style":6124},[402],[363,42279,2810],{"className":42280},[407],[363,42282],{"className":42283,"style":754},[505],[363,42285,1634],{"className":42286,"style":1834},[1831,1832,1833],[363,42288],{"className":42289,"style":754},[505],[363,42291,42293],{"className":42292},[407,34714],[363,42294,42296,42329],{"className":42295},[633,634],[363,42297,42299,42326],{"className":42298},[638],[363,42300,42302,42314],{"className":42301,"style":7209},[642],[363,42303,42305,42308],{"className":42304,"style":12210},[6654],[363,42306],{"className":42307,"style":809},[650],[363,42309,42311],{"className":42310,"style":34734},[407],[363,42312,41952],{"className":42313,"style":1328},[407,408],[363,42315,42316,42319],{"style":41697},[363,42317],{"className":42318,"style":809},[650],[363,42320,42322],{"className":42321,"style":34791},[34790],[6670,42323,42324],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,42325],{"d":34798},[363,42327,666],{"className":42328},[665],[363,42330,42332],{"className":42331},[638],[363,42333,42335],{"className":42334,"style":41717},[642],[363,42336],{},[363,42338],{"className":42339,"style":506},[505],[363,42341,471],{"className":42342},[510],[363,42344],{"className":42345,"style":506},[505],[363,42347,42349,42352,42355,42361,42364,42367,42370],{"className":42348},[398],[363,42350],{"className":42351,"style":20910},[402],[363,42353,2810],{"className":42354},[407],[363,42356,42358],{"className":42357},[407],[363,42359,461],{"className":42360},[767,10021],[363,42362,465],{"className":42363},[407],[363,42365],{"className":42366,"style":2934},[505],[363,42368,5160],{"className":42369},[2938],[363,42371],{"className":42372,"style":2934},[505],[363,42374,42376,42379,42382,42385,42391],{"className":42375},[398],[363,42377],{"className":42378,"style":20910},[402],[363,42380,39638],{"className":42381,"style":39734},[407,408],[363,42383,39641],{"className":42384,"style":11129},[407,408],[363,42386,42388],{"className":42387},[407],[363,42389,468],{"className":42390},[767,10021],[363,42392,4722],{"className":42393},[407],[11,42395,42396,42397,42456],{},"文献里对 ",[363,42398,42400,42418],{"className":42399,"translate":367},[366],[363,42401,42403],{"className":42402},[371],[373,42404,42405],{"xmlns":375},[377,42406,42407,42415],{},[380,42408,42409],{},[7161,42410,42411,42413],{},[383,42412,34231],{},[463,42414,2810],{},[387,42416,42417],{"encoding":389},"H^2",[363,42419,42421],{"className":42420,"ariaHidden":394},[393],[363,42422,42424,42427],{"className":42423},[398],[363,42425],{"className":42426,"style":20375},[402],[363,42428,42430,42433],{"className":42429},[407],[363,42431,34231],{"className":42432,"style":34385},[407,408],[363,42434,42436],{"className":42435},[629],[363,42437,42439],{"className":42438},[633],[363,42440,42442],{"className":42441},[638],[363,42443,42445],{"className":42444,"style":20375},[642],[363,42446,42447,42450],{"style":7212},[363,42448],{"className":42449,"style":651},[650],[363,42451,42453],{"className":42452},[655,656,657,658],[363,42454,2810],{"className":42455},[407,658]," 有两种约定：",[363,42458,42460],{"className":42459,"translate":367},[528],[363,42461,42463,42569],{"className":42462,"translate":367},[366],[363,42464,42466],{"className":42465},[371],[373,42467,42468],{"xmlns":375,"display":537},[377,42469,42470,42566],{},[1590,42471,42472,42507],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,42473,42474,42487],{},[1599,42475,42476],{},[1602,42477,42478],{"scriptlevel":474,"displaystyle":394},[7900,42479,42480,42482,42485],{},[383,42481,34231],{},[1644,42483,42484],{},"Bhattacharyya",[463,42486,2810],{},[1599,42488,42489],{},[1602,42490,42491],{"scriptlevel":474,"displaystyle":394},[380,42492,42493,42495,42497,42499,42501,42503,42505],{},[380,42494],{},[458,42496,471],{},[463,42498,465],{},[458,42500,5160],{},[383,42502,39638],{},[383,42504,39641],{},[458,42506,898],{"separator":394},[1596,42508,42509,42528],{},[1599,42510,42511],{},[1602,42512,42513],{"scriptlevel":474,"displaystyle":394},[7900,42514,42515,42517,42526],{},[383,42516,34231],{},[380,42518,42519,42522,42524],{},[1644,42520,42521],{},"this",[1644,42523,1646],{},[383,42525,385],{},[463,42527,2810],{},[1599,42529,42530],{},[1602,42531,42532],{"scriptlevel":474,"displaystyle":394},[380,42533,42534,42536,42538,42540,42542,42544,42546,42548,42550,42552,42554,42556,42564],{},[380,42535],{},[458,42537,471],{},[463,42539,2810],{},[458,42541,461],{"stretchy":460},[463,42543,465],{},[458,42545,5160],{},[383,42547,39638],{},[383,42549,39641],{},[458,42551,468],{"stretchy":460},[458,42553,471],{},[463,42555,2810],{},[7900,42557,42558,42560,42562],{},[383,42559,34231],{},[1644,42561,42484],{},[463,42563,2810],{},[383,42565,4722],{"mathvariant":557},[387,42567,42568],{"encoding":389},"\\begin{aligned}\nH^2_{\\text{Bhattacharyya}}&=1-BC,\\\\[2pt]\nH^2_{\\text{this}\\,f}&=2(1-BC)\n=2H^2_{\\text{Bhattacharyya}} .\n\\end{aligned}",[363,42570,42572],{"className":42571,"ariaHidden":394},[393],[363,42573,42575,42579],{"className":42574},[398],[363,42576],{"className":42577,"style":42578},[402],"height:2.9713em;vertical-align:-1.2357em;",[363,42580,42582],{"className":42581},[407],[363,42583,42585,42751],{"className":42584},[1590],[363,42586,42588],{"className":42587},[1707],[363,42589,42591,42742],{"className":42590},[633,634],[363,42592,42594,42739],{"className":42593},[638],[363,42595,42598,42666],{"className":42596,"style":42597},[642],"height:1.7357em;",[363,42599,42601,42604],{"style":42600},"top:-3.8716em;",[363,42602],{"className":42603,"style":809},[650],[363,42605,42607],{"className":42606},[407],[363,42608,42610,42613],{"className":42609},[407],[363,42611,34231],{"className":42612,"style":34385},[407,408],[363,42614,42616],{"className":42615},[629],[363,42617,42619,42657],{"className":42618},[633,634],[363,42620,42622,42654],{"className":42621},[638],[363,42623,42625,42643],{"className":42624,"style":20082},[642],[363,42626,42628,42631],{"style":42627},"top:-2.453em;margin-left:-0.0813em;margin-right:0.05em;",[363,42629],{"className":42630,"style":651},[650],[363,42632,42634],{"className":42633},[655,656,657,658],[363,42635,42637],{"className":42636},[407,658],[363,42638,42640],{"className":42639},[407,4945,658],[363,42641,42484],{"className":42642},[407,658],[363,42644,42645,42648],{"style":8624},[363,42646],{"className":42647,"style":651},[650],[363,42649,42651],{"className":42650},[655,656,657,658],[363,42652,2810],{"className":42653},[407,658],[363,42655,666],{"className":42656},[665],[363,42658,42660],{"className":42659},[638],[363,42661,42664],{"className":42662,"style":42663},[642],"height:0.3831em;",[363,42665],{},[363,42667,42669,42672],{"style":42668},"top:-2.1474em;",[363,42670],{"className":42671,"style":809},[650],[363,42673,42675],{"className":42674},[407],[363,42676,42678,42681],{"className":42677},[407],[363,42679,34231],{"className":42680,"style":34385},[407,408],[363,42682,42684],{"className":42683},[629],[363,42685,42687,42731],{"className":42686},[633,634],[363,42688,42690,42728],{"className":42689},[638],[363,42691,42693,42717],{"className":42692,"style":20082},[642],[363,42694,42695,42698],{"style":42627},[363,42696],{"className":42697,"style":651},[650],[363,42699,42701],{"className":42700},[655,656,657,658],[363,42702,42704,42710,42714],{"className":42703},[407,658],[363,42705,42707],{"className":42706},[407,4945,658],[363,42708,42521],{"className":42709},[407,658],[363,42711],{"className":42712,"style":42713},[505,658],"margin-right:0.1952em;",[363,42715,385],{"className":42716,"style":409},[407,408,658],[363,42718,42719,42722],{"style":8624},[363,42720],{"className":42721,"style":651},[650],[363,42723,42725],{"className":42724},[655,656,657,658],[363,42726,2810],{"className":42727},[407,658],[363,42729,666],{"className":42730},[665],[363,42732,42734],{"className":42733},[638],[363,42735,42737],{"className":42736,"style":42663},[642],[363,42738],{},[363,42740,666],{"className":42741},[665],[363,42743,42745],{"className":42744},[638],[363,42746,42749],{"className":42747,"style":42748},[642],"height:1.2357em;",[363,42750],{},[363,42752,42754],{"className":42753},[1798],[363,42755,42757,42926],{"className":42756},[633,634],[363,42758,42760,42923],{"className":42759},[638],[363,42761,42763,42804],{"className":42762,"style":42597},[642],[363,42764,42765,42768],{"style":42600},[363,42766],{"className":42767,"style":809},[650],[363,42769,42771,42774,42777,42780,42783,42786,42789,42792,42795,42798,42801],{"className":42770},[407],[363,42772],{"className":42773},[407],[363,42775],{"className":42776,"style":506},[505],[363,42778,471],{"className":42779},[510],[363,42781],{"className":42782,"style":506},[505],[363,42784,465],{"className":42785},[407],[363,42787],{"className":42788,"style":2934},[505],[363,42790,5160],{"className":42791},[2938],[363,42793],{"className":42794,"style":2934},[505],[363,42796,39638],{"className":42797,"style":39734},[407,408],[363,42799,39641],{"className":42800,"style":11129},[407,408],[363,42802,898],{"className":42803},[920],[363,42805,42806,42809],{"style":42668},[363,42807],{"className":42808,"style":809},[650],[363,42810,42812,42815,42818,42821,42824,42827,42830,42833,42836,42839,42842,42845,42848,42851,42854,42857,42860,42863,42920],{"className":42811},[407],[363,42813],{"className":42814},[407],[363,42816],{"className":42817,"style":506},[505],[363,42819,471],{"className":42820},[510],[363,42822],{"className":42823,"style":506},[505],[363,42825,2810],{"className":42826},[407],[363,42828,461],{"className":42829},[494],[363,42831,465],{"className":42832},[407],[363,42834],{"className":42835,"style":2934},[505],[363,42837,5160],{"className":42838},[2938],[363,42840],{"className":42841,"style":2934},[505],[363,42843,39638],{"className":42844,"style":39734},[407,408],[363,42846,39641],{"className":42847,"style":11129},[407,408],[363,42849,468],{"className":42850},[501],[363,42852],{"className":42853,"style":506},[505],[363,42855,471],{"className":42856},[510],[363,42858],{"className":42859,"style":506},[505],[363,42861,2810],{"className":42862},[407],[363,42864,42866,42869],{"className":42865},[407],[363,42867,34231],{"className":42868,"style":34385},[407,408],[363,42870,42872],{"className":42871},[629],[363,42873,42875,42912],{"className":42874},[633,634],[363,42876,42878,42909],{"className":42877},[638],[363,42879,42881,42898],{"className":42880,"style":20082},[642],[363,42882,42883,42886],{"style":42627},[363,42884],{"className":42885,"style":651},[650],[363,42887,42889],{"className":42888},[655,656,657,658],[363,42890,42892],{"className":42891},[407,658],[363,42893,42895],{"className":42894},[407,4945,658],[363,42896,42484],{"className":42897},[407,658],[363,42899,42900,42903],{"style":8624},[363,42901],{"className":42902,"style":651},[650],[363,42904,42906],{"className":42905},[655,656,657,658],[363,42907,2810],{"className":42908},[407,658],[363,42910,666],{"className":42911},[665],[363,42913,42915],{"className":42914},[638],[363,42916,42918],{"className":42917,"style":42663},[642],[363,42919],{},[363,42921,4722],{"className":42922},[407],[363,42924,666],{"className":42925},[665],[363,42927,42929],{"className":42928},[638],[363,42930,42932],{"className":42931,"style":42748},[642],[363,42933],{},[11,42935,42936,42937,43112,43113,18488,43448,43506,43507,43551],{},"本文采用 ",[363,42938,42940,42978],{"className":42939,"translate":367},[366],[363,42941,42943],{"className":42942},[371],[373,42944,42945],{"xmlns":375},[377,42946,42947,42975],{},[380,42948,42949,42951,42953,42955,42957,42959,42961,42965,42967,42969],{},[383,42950,385],{},[458,42952,461],{"stretchy":460},[383,42954,1116],{},[458,42956,468],{"stretchy":460},[458,42958,471],{},[458,42960,461],{"stretchy":460},[34686,42962,42963],{},[383,42964,1116],{},[458,42966,5160],{},[463,42968,465],{},[7161,42970,42971,42973],{},[458,42972,468],{"stretchy":460},[463,42974,2810],{},[387,42976,42977],{"encoding":389},"f(t)=(\\sqrt t-1)^2",[363,42979,42981,43008,43074],{"className":42980,"ariaHidden":394},[393],[363,42982,42984,42987,42990,42993,42996,42999,43002,43005],{"className":42983},[398],[363,42985],{"className":42986,"style":487},[402],[363,42988,385],{"className":42989,"style":409},[407,408],[363,42991,461],{"className":42992},[494],[363,42994,1116],{"className":42995},[407,408],[363,42997,468],{"className":42998},[501],[363,43000],{"className":43001,"style":506},[505],[363,43003,471],{"className":43004},[510],[363,43006],{"className":43007,"style":506},[505],[363,43009,43011,43015,43018,43065,43068,43071],{"className":43010},[398],[363,43012],{"className":43013,"style":43014},[402],"height:1.1425em;vertical-align:-0.25em;",[363,43016,461],{"className":43017},[494],[363,43019,43021],{"className":43020},[407,34714],[363,43022,43024,43056],{"className":43023},[633,634],[363,43025,43027,43053],{"className":43026},[638],[363,43028,43031,43040],{"className":43029,"style":43030},[642],"height:0.8925em;",[363,43032,43034,43037],{"className":43033,"style":12210},[6654],[363,43035],{"className":43036,"style":809},[650],[363,43038,1116],{"className":43039,"style":34734},[407,408],[363,43041,43043,43046],{"style":43042},"top:-2.8525em;",[363,43044],{"className":43045,"style":809},[650],[363,43047,43049],{"className":43048,"style":34791},[34790],[6670,43050,43051],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,43052],{"d":34798},[363,43054,666],{"className":43055},[665],[363,43057,43059],{"className":43058},[638],[363,43060,43063],{"className":43061,"style":43062},[642],"height:0.1475em;",[363,43064],{},[363,43066],{"className":43067,"style":2934},[505],[363,43069,5160],{"className":43070},[2938],[363,43072],{"className":43073,"style":2934},[505],[363,43075,43077,43080,43083],{"className":43076},[398],[363,43078],{"className":43079,"style":20350},[402],[363,43081,465],{"className":43082},[407],[363,43084,43086,43089],{"className":43085},[501],[363,43087,468],{"className":43088},[501],[363,43090,43092],{"className":43091},[629],[363,43093,43095],{"className":43094},[633],[363,43096,43098],{"className":43097},[638],[363,43099,43101],{"className":43100,"style":20375},[642],[363,43102,43103,43106],{"style":7212},[363,43104],{"className":43105,"style":651},[650],[363,43107,43109],{"className":43108},[655,656,657,658],[363,43110,2810],{"className":43111},[407,658],"，故 ",[363,43114,43116,43168],{"className":43115,"translate":367},[366],[363,43117,43119],{"className":43118},[371],[373,43120,43121],{"xmlns":375},[377,43122,43123,43165],{},[380,43124,43125,43131,43133,43135,43143,43145,43147,43149,43153,43155,43159],{},[543,43126,43127,43129],{},[383,43128,547],{},[383,43130,385],{},[458,43132,471],{},[463,43134,2810],{},[7900,43136,43137,43139,43141],{},[383,43138,34231],{},[1644,43140,42484],{},[463,43142,2810],{},[458,43144,471],{},[458,43146,1634],{},[458,43148,461],{"stretchy":460},[34686,43150,43151],{},[383,43152,11],{},[458,43154,5160],{},[34686,43156,43157],{},[383,43158,1291],{},[7161,43160,43161,43163],{},[458,43162,468],{"stretchy":460},[463,43164,2810],{},[387,43166,43167],{"encoding":389},"D_f=2H^2_{\\text{Bhattacharyya}}=\\int(\\sqrt p-\\sqrt q)^2",[363,43169,43171,43226,43304,43369],{"className":43170,"ariaHidden":394},[393],[363,43172,43174,43177,43217,43220,43223],{"className":43173},[398],[363,43175],{"className":43176,"style":4379},[402],[363,43178,43180,43183],{"className":43179},[407],[363,43181,547],{"className":43182,"style":625},[407,408],[363,43184,43186],{"className":43185},[629],[363,43187,43189,43209],{"className":43188},[633,634],[363,43190,43192,43206],{"className":43191},[638],[363,43193,43195],{"className":43194,"style":643},[642],[363,43196,43197,43200],{"style":646},[363,43198],{"className":43199,"style":651},[650],[363,43201,43203],{"className":43202},[655,656,657,658],[363,43204,385],{"className":43205,"style":409},[407,408,658],[363,43207,666],{"className":43208},[665],[363,43210,43212],{"className":43211},[638],[363,43213,43215],{"className":43214,"style":673},[642],[363,43216],{},[363,43218],{"className":43219,"style":506},[505],[363,43221,471],{"className":43222},[510],[363,43224],{"className":43225,"style":506},[505],[363,43227,43229,43233,43236,43295,43298,43301],{"className":43228},[398],[363,43230],{"className":43231,"style":43232},[402],"height:1.2333em;vertical-align:-0.4192em;",[363,43234,2810],{"className":43235},[407],[363,43237,43239,43242],{"className":43238},[407],[363,43240,34231],{"className":43241,"style":34385},[407,408],[363,43243,43245],{"className":43244},[629],[363,43246,43248,43286],{"className":43247},[633,634],[363,43249,43251,43283],{"className":43250},[638],[363,43252,43254,43272],{"className":43253,"style":20375},[642],[363,43255,43257,43260],{"style":43256},"top:-2.4169em;margin-left:-0.0813em;margin-right:0.05em;",[363,43258],{"className":43259,"style":651},[650],[363,43261,43263],{"className":43262},[655,656,657,658],[363,43264,43266],{"className":43265},[407,658],[363,43267,43269],{"className":43268},[407,4945,658],[363,43270,42484],{"className":43271},[407,658],[363,43273,43274,43277],{"style":7212},[363,43275],{"className":43276,"style":651},[650],[363,43278,43280],{"className":43279},[655,656,657,658],[363,43281,2810],{"className":43282},[407,658],[363,43284,666],{"className":43285},[665],[363,43287,43289],{"className":43288},[638],[363,43290,43293],{"className":43291,"style":43292},[642],"height:0.4192em;",[363,43294],{},[363,43296],{"className":43297,"style":506},[505],[363,43299,471],{"className":43300},[510],[363,43302],{"className":43303,"style":506},[505],[363,43305,43307,43310,43313,43316,43360,43363,43366],{"className":43306},[398],[363,43308],{"className":43309,"style":39355},[402],[363,43311,1634],{"className":43312,"style":5964},[1831,1832,5963],[363,43314,461],{"className":43315},[494],[363,43317,43319],{"className":43318},[407,34714],[363,43320,43322,43352],{"className":43321},[633,634],[363,43323,43325,43349],{"className":43324},[638],[363,43326,43328,43337],{"className":43327,"style":39374},[642],[363,43329,43331,43334],{"className":43330,"style":12210},[6654],[363,43332],{"className":43333,"style":809},[650],[363,43335,11],{"className":43336,"style":34734},[407,408],[363,43338,43339,43342],{"style":39386},[363,43340],{"className":43341,"style":809},[650],[363,43343,43345],{"className":43344,"style":34791},[34790],[6670,43346,43347],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,43348],{"d":34798},[363,43350,666],{"className":43351},[665],[363,43353,43355],{"className":43354},[638],[363,43356,43358],{"className":43357,"style":39406},[642],[363,43359],{},[363,43361],{"className":43362,"style":2934},[505],[363,43364,5160],{"className":43365},[2938],[363,43367],{"className":43368,"style":2934},[505],[363,43370,43372,43375,43419],{"className":43371},[398],[363,43373],{"className":43374,"style":39424},[402],[363,43376,43378],{"className":43377},[407,34714],[363,43379,43381,43411],{"className":43380},[633,634],[363,43382,43384,43408],{"className":43383},[638],[363,43385,43387,43396],{"className":43386,"style":39374},[642],[363,43388,43390,43393],{"className":43389,"style":12210},[6654],[363,43391],{"className":43392,"style":809},[650],[363,43394,1291],{"className":43395,"style":39446},[407,408],[363,43397,43398,43401],{"style":39386},[363,43399],{"className":43400,"style":809},[650],[363,43402,43404],{"className":43403,"style":34791},[34790],[6670,43405,43406],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,43407],{"d":34798},[363,43409,666],{"className":43410},[665],[363,43412,43414],{"className":43413},[638],[363,43415,43417],{"className":43416,"style":39406},[642],[363,43418],{},[363,43420,43422,43425],{"className":43421},[501],[363,43423,468],{"className":43424},[501],[363,43426,43428],{"className":43427},[629],[363,43429,43431],{"className":43430},[633],[363,43432,43434],{"className":43433},[638],[363,43435,43437],{"className":43436,"style":20375},[642],[363,43438,43439,43442],{"style":7212},[363,43440],{"className":43441,"style":651},[650],[363,43443,43445],{"className":43444},[655,656,657,658],[363,43446,2810],{"className":43447},[407,658],[363,43449,43451,43468],{"className":43450,"translate":367},[366],[363,43452,43454],{"className":43453},[371],[373,43455,43456],{"xmlns":375},[377,43457,43458,43466],{},[380,43459,43460],{},[7161,43461,43462,43464],{},[383,43463,34231],{},[463,43465,2810],{},[387,43467,42417],{"encoding":389},[363,43469,43471],{"className":43470,"ariaHidden":394},[393],[363,43472,43474,43477],{"className":43473},[398],[363,43475],{"className":43476,"style":20375},[402],[363,43478,43480,43483],{"className":43479},[407],[363,43481,34231],{"className":43482,"style":34385},[407,408],[363,43484,43486],{"className":43485},[629],[363,43487,43489],{"className":43488},[633],[363,43490,43492],{"className":43491},[638],[363,43493,43495],{"className":43494,"style":20375},[642],[363,43496,43497,43500],{"style":7212},[363,43498],{"className":43499,"style":651},[650],[363,43501,43503],{"className":43502},[655,656,657,658],[363,43504,2810],{"className":43505},[407,658]," 有界（",[363,43508,43510,43526],{"className":43509,"translate":367},[366],[363,43511,43513],{"className":43512},[371],[373,43514,43515],{"xmlns":375},[377,43516,43517,43523],{},[380,43518,43519,43521],{},[458,43520,10299],{},[463,43522,2810],{},[387,43524,43525],{"encoding":389},"\\le 2",[363,43527,43529,43542],{"className":43528,"ariaHidden":394},[393],[363,43530,43532,43536,43539],{"className":43531},[398],[363,43533],{"className":43534,"style":43535},[402],"height:0.7719em;vertical-align:-0.136em;",[363,43537,10299],{"className":43538},[510],[363,43540],{"className":43541,"style":506},[505],[363,43543,43545,43548],{"className":43544},[398],[363,43546],{"className":43547,"style":520},[402],[363,43549,2810],{"className":43550},[407],"）。对称性可直接验算：",[363,43553,43555],{"className":43554,"translate":367},[528],[363,43556,43558,43734],{"className":43557,"translate":367},[366],[363,43559,43561],{"className":43560},[371],[373,43562,43563],{"xmlns":375,"display":537},[377,43564,43565,43731],{},[1590,43566,43567,43625,43669],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,43568,43569,43591],{},[1599,43570,43571],{},[1602,43572,43573],{"scriptlevel":474,"displaystyle":394},[380,43574,43575,43577,43579,43581,43583,43585,43587,43589],{},[383,43576,1116],{},[1644,43578,1646],{},[383,43580,385],{},[458,43582,461],{"stretchy":460},[463,43584,465],{},[383,43586,1288],{"mathvariant":557},[383,43588,1116],{},[458,43590,468],{"stretchy":460},[1599,43592,43593],{},[1602,43594,43595],{"scriptlevel":474,"displaystyle":394},[380,43596,43597,43599,43601,43603],{},[380,43598],{},[458,43600,471],{},[383,43602,1116],{},[7161,43604,43605,43623],{},[380,43606,43607,43609,43617,43619,43621],{},[458,43608,461],{"fence":394},[586,43610,43611,43613],{},[463,43612,465],{},[34686,43614,43615],{},[383,43616,1116],{},[458,43618,5160],{},[463,43620,465],{},[458,43622,468],{"fence":394},[463,43624,2810],{},[1596,43626,43627,43633],{},[1599,43628,43629],{},[1602,43630,43631],{"scriptlevel":474,"displaystyle":394},[380,43632],{},[1599,43634,43635],{},[1602,43636,43637],{"scriptlevel":474,"displaystyle":394},[380,43638,43639,43641,43643,43645,43647,43653,43655,43663,43665,43667],{},[380,43640],{},[458,43642,471],{},[383,43644,1116],{},[458,43646,461],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[586,43648,43649,43651],{},[463,43650,465],{},[383,43652,1116],{},[458,43654,5160],{},[586,43656,43657,43659],{},[463,43658,2810],{},[34686,43660,43661],{},[383,43662,1116],{},[458,43664,2817],{},[463,43666,465],{},[458,43668,468],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[1596,43670,43671,43677],{},[1599,43672,43673],{},[1602,43674,43675],{"scriptlevel":474,"displaystyle":394},[380,43676],{},[1599,43678,43679],{},[1602,43680,43681],{"scriptlevel":474,"displaystyle":394},[380,43682,43683,43685,43687,43689,43691,43693,43697,43699,43701,43703,43705,43709,43711,43713,43719,43721,43723,43725,43727,43729],{},[380,43684],{},[458,43686,471],{},[463,43688,465],{},[458,43690,5160],{},[463,43692,2810],{},[34686,43694,43695],{},[383,43696,1116],{},[458,43698,2817],{},[383,43700,1116],{},[458,43702,471],{},[458,43704,461],{"stretchy":460},[34686,43706,43707],{},[383,43708,1116],{},[458,43710,5160],{},[463,43712,465],{},[7161,43714,43715,43717],{},[458,43716,468],{"stretchy":460},[463,43718,2810],{},[458,43720,471],{},[383,43722,385],{},[458,43724,461],{"stretchy":460},[383,43726,1116],{},[458,43728,468],{"stretchy":460},[458,43730,898],{"separator":394},[387,43732,43733],{"encoding":389},"\\begin{aligned}\nt\\,f(1\u002Ft)\n&=t\\left(\\frac{1}{\\sqrt t}-1\\right)^2\\\\\n&=t\\Big(\\frac1t-\\frac{2}{\\sqrt t}+1\\Big)\\\\[2pt]\n&=1-2\\sqrt t+t=(\\sqrt t-1)^2=f(t),\n\\end{aligned}",[363,43735,43737],{"className":43736,"ariaHidden":394},[393],[363,43738,43740,43744],{"className":43739},[398],[363,43741],{"className":43742,"style":43743},[402],"height:6.7569em;vertical-align:-3.1284em;",[363,43745,43747],{"className":43746},[407],[363,43748,43750,43824],{"className":43749},[1590],[363,43751,43753],{"className":43752},[1707],[363,43754,43756,43815],{"className":43755},[633,634],[363,43757,43759,43812],{"className":43758},[638],[363,43760,43763,43794,43803],{"className":43761,"style":43762},[642],"height:3.6284em;",[363,43764,43766,43770],{"style":43765},"top:-5.6284em;",[363,43767],{"className":43768,"style":43769},[650],"height:3.654em;",[363,43771,43773,43776,43779,43782,43785,43788,43791],{"className":43772},[407],[363,43774,1116],{"className":43775},[407,408],[363,43777],{"className":43778,"style":754},[505],[363,43780,385],{"className":43781,"style":409},[407,408],[363,43783,461],{"className":43784},[494],[363,43786,8936],{"className":43787},[407],[363,43789,1116],{"className":43790},[407,408],[363,43792,468],{"className":43793},[501],[363,43795,43797,43800],{"style":43796},"top:-3.057em;",[363,43798],{"className":43799,"style":43769},[650],[363,43801],{"className":43802},[407],[363,43804,43806,43809],{"style":43805},"top:-0.8856em;",[363,43807],{"className":43808,"style":43769},[650],[363,43810],{"className":43811},[407],[363,43813,666],{"className":43814},[665],[363,43816,43818],{"className":43817},[638],[363,43819,43822],{"className":43820,"style":43821},[642],"height:3.1284em;",[363,43823],{},[363,43825,43827],{"className":43826},[1798],[363,43828,43830,44456],{"className":43829},[633,634],[363,43831,43833,44453],{"className":43832},[638],[363,43834,43836,44020,44241],{"className":43835,"style":43762},[642],[363,43837,43838,43841],{"style":43765},[363,43839],{"className":43840,"style":43769},[650],[363,43842,43844,43847,43850,43853,43856,43859,43862],{"className":43843},[407],[363,43845],{"className":43846},[407],[363,43848],{"className":43849,"style":506},[505],[363,43851,471],{"className":43852},[510],[363,43854],{"className":43855,"style":506},[505],[363,43857,1116],{"className":43858},[407,408],[363,43860],{"className":43861,"style":754},[505],[363,43863,43865,43997],{"className":43864},[758],[363,43866,43868,43874,43979,43982,43985,43988,43991],{"className":43867},[758],[363,43869,43871],{"className":43870,"style":763},[494,762],[363,43872,461],{"className":43873},[767,657],[363,43875,43877,43880,43976],{"className":43876},[407],[363,43878],{"className":43879},[494,789],[363,43881,43883],{"className":43882},[586],[363,43884,43886,43967],{"className":43885},[633,634],[363,43887,43889,43964],{"className":43888},[638],[363,43890,43892,43945,43953],{"className":43891,"style":23236},[642],[363,43893,43895,43898],{"style":43894},"top:-2.2175em;",[363,43896],{"className":43897,"style":809},[650],[363,43899,43901],{"className":43900},[407],[363,43902,43904],{"className":43903},[407,34714],[363,43905,43907,43937],{"className":43906},[633,634],[363,43908,43910,43934],{"className":43909},[638],[363,43911,43913,43922],{"className":43912,"style":43030},[642],[363,43914,43916,43919],{"className":43915,"style":12210},[6654],[363,43917],{"className":43918,"style":809},[650],[363,43920,1116],{"className":43921,"style":34734},[407,408],[363,43923,43924,43927],{"style":43042},[363,43925],{"className":43926,"style":809},[650],[363,43928,43930],{"className":43929,"style":34791},[34790],[6670,43931,43932],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,43933],{"d":34798},[363,43935,666],{"className":43936},[665],[363,43938,43940],{"className":43939},[638],[363,43941,43943],{"className":43942,"style":43062},[642],[363,43944],{},[363,43946,43947,43950],{"style":821},[363,43948],{"className":43949,"style":809},[650],[363,43951],{"className":43952,"style":829},[828],[363,43954,43955,43958],{"style":832},[363,43956],{"className":43957,"style":809},[650],[363,43959,43961],{"className":43960},[407],[363,43962,465],{"className":43963},[407],[363,43965,666],{"className":43966},[665],[363,43968,43970],{"className":43969},[638],[363,43971,43974],{"className":43972,"style":43973},[642],"height:0.93em;",[363,43975],{},[363,43977],{"className":43978},[501,789],[363,43980],{"className":43981,"style":2934},[505],[363,43983,5160],{"className":43984},[2938],[363,43986],{"className":43987,"style":2934},[505],[363,43989,465],{"className":43990},[407],[363,43992,43994],{"className":43993,"style":763},[501,762],[363,43995,468],{"className":43996},[767,657],[363,43998,44000],{"className":43999},[629],[363,44001,44003],{"className":44002},[633],[363,44004,44006],{"className":44005},[638],[363,44007,44009],{"className":44008,"style":38008},[642],[363,44010,44011,44014],{"style":38011},[363,44012],{"className":44013,"style":651},[650],[363,44015,44017],{"className":44016},[655,656,657,658],[363,44018,2810],{"className":44019},[407,658],[363,44021,44022,44025],{"style":43796},[363,44023],{"className":44024,"style":43769},[650],[363,44026,44028,44031,44034,44037,44040,44043,44049,44111,44114,44117,44120,44223,44226,44229,44232,44235],{"className":44027},[407],[363,44029],{"className":44030},[407],[363,44032],{"className":44033,"style":506},[505],[363,44035,471],{"className":44036},[510],[363,44038],{"className":44039,"style":506},[505],[363,44041,1116],{"className":44042},[407,408],[363,44044,44046],{"className":44045},[407],[363,44047,461],{"className":44048},[767,4067],[363,44050,44052,44055,44108],{"className":44051},[407],[363,44053],{"className":44054},[494,789],[363,44056,44058],{"className":44057},[586],[363,44059,44061,44100],{"className":44060},[633,634],[363,44062,44064,44097],{"className":44063},[638],[363,44065,44067,44078,44086],{"className":44066,"style":23236},[642],[363,44068,44069,44072],{"style":805},[363,44070],{"className":44071,"style":809},[650],[363,44073,44075],{"className":44074},[407],[363,44076,1116],{"className":44077},[407,408],[363,44079,44080,44083],{"style":821},[363,44081],{"className":44082,"style":809},[650],[363,44084],{"className":44085,"style":829},[828],[363,44087,44088,44091],{"style":832},[363,44089],{"className":44090,"style":809},[650],[363,44092,44094],{"className":44093},[407],[363,44095,465],{"className":44096},[407],[363,44098,666],{"className":44099},[665],[363,44101,44103],{"className":44102},[638],[363,44104,44106],{"className":44105,"style":4125},[642],[363,44107],{},[363,44109],{"className":44110},[501,789],[363,44112],{"className":44113,"style":2934},[505],[363,44115,5160],{"className":44116},[2938],[363,44118],{"className":44119,"style":2934},[505],[363,44121,44123,44126,44220],{"className":44122},[407],[363,44124],{"className":44125},[494,789],[363,44127,44129],{"className":44128},[586],[363,44130,44132,44212],{"className":44131},[633,634],[363,44133,44135,44209],{"className":44134},[638],[363,44136,44138,44190,44198],{"className":44137,"style":23236},[642],[363,44139,44140,44143],{"style":43894},[363,44141],{"className":44142,"style":809},[650],[363,44144,44146],{"className":44145},[407],[363,44147,44149],{"className":44148},[407,34714],[363,44150,44152,44182],{"className":44151},[633,634],[363,44153,44155,44179],{"className":44154},[638],[363,44156,44158,44167],{"className":44157,"style":43030},[642],[363,44159,44161,44164],{"className":44160,"style":12210},[6654],[363,44162],{"className":44163,"style":809},[650],[363,44165,1116],{"className":44166,"style":34734},[407,408],[363,44168,44169,44172],{"style":43042},[363,44170],{"className":44171,"style":809},[650],[363,44173,44175],{"className":44174,"style":34791},[34790],[6670,44176,44177],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,44178],{"d":34798},[363,44180,666],{"className":44181},[665],[363,44183,44185],{"className":44184},[638],[363,44186,44188],{"className":44187,"style":43062},[642],[363,44189],{},[363,44191,44192,44195],{"style":821},[363,44193],{"className":44194,"style":809},[650],[363,44196],{"className":44197,"style":829},[828],[363,44199,44200,44203],{"style":832},[363,44201],{"className":44202,"style":809},[650],[363,44204,44206],{"className":44205},[407],[363,44207,2810],{"className":44208},[407],[363,44210,666],{"className":44211},[665],[363,44213,44215],{"className":44214},[638],[363,44216,44218],{"className":44217,"style":43973},[642],[363,44219],{},[363,44221],{"className":44222},[501,789],[363,44224],{"className":44225,"style":2934},[505],[363,44227,2817],{"className":44228},[2938],[363,44230],{"className":44231,"style":2934},[505],[363,44233,465],{"className":44234},[407],[363,44236,44238],{"className":44237},[407],[363,44239,468],{"className":44240},[767,4067],[363,44242,44243,44246],{"style":43805},[363,44244],{"className":44245,"style":43769},[650],[363,44247,44249,44252,44255,44258,44261,44264,44267,44270,44273,44276,44320,44323,44326,44329,44332,44335,44338,44341,44344,44388,44391,44394,44397,44400,44429,44432,44435,44438,44441,44444,44447,44450],{"className":44248},[407],[363,44250],{"className":44251},[407],[363,44253],{"className":44254,"style":506},[505],[363,44256,471],{"className":44257},[510],[363,44259],{"className":44260,"style":506},[505],[363,44262,465],{"className":44263},[407],[363,44265],{"className":44266,"style":2934},[505],[363,44268,5160],{"className":44269},[2938],[363,44271],{"className":44272,"style":2934},[505],[363,44274,2810],{"className":44275},[407],[363,44277,44279],{"className":44278},[407,34714],[363,44280,44282,44312],{"className":44281},[633,634],[363,44283,44285,44309],{"className":44284},[638],[363,44286,44288,44297],{"className":44287,"style":40884},[642],[363,44289,44291,44294],{"className":44290,"style":12210},[6654],[363,44292],{"className":44293,"style":809},[650],[363,44295,1116],{"className":44296,"style":34734},[407,408],[363,44298,44299,44302],{"style":40899},[363,44300],{"className":44301,"style":809},[650],[363,44303,44305],{"className":44304,"style":34791},[34790],[6670,44306,44307],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,44308],{"d":34798},[363,44310,666],{"className":44311},[665],[363,44313,44315],{"className":44314},[638],[363,44316,44318],{"className":44317,"style":40919},[642],[363,44319],{},[363,44321],{"className":44322,"style":2934},[505],[363,44324,2817],{"className":44325},[2938],[363,44327],{"className":44328,"style":2934},[505],[363,44330,1116],{"className":44331},[407,408],[363,44333],{"className":44334,"style":506},[505],[363,44336,471],{"className":44337},[510],[363,44339],{"className":44340,"style":506},[505],[363,44342,461],{"className":44343},[494],[363,44345,44347],{"className":44346},[407,34714],[363,44348,44350,44380],{"className":44349},[633,634],[363,44351,44353,44377],{"className":44352},[638],[363,44354,44356,44365],{"className":44355,"style":40884},[642],[363,44357,44359,44362],{"className":44358,"style":12210},[6654],[363,44360],{"className":44361,"style":809},[650],[363,44363,1116],{"className":44364,"style":34734},[407,408],[363,44366,44367,44370],{"style":40899},[363,44368],{"className":44369,"style":809},[650],[363,44371,44373],{"className":44372,"style":34791},[34790],[6670,44374,44375],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,44376],{"d":34798},[363,44378,666],{"className":44379},[665],[363,44381,44383],{"className":44382},[638],[363,44384,44386],{"className":44385,"style":40919},[642],[363,44387],{},[363,44389],{"className":44390,"style":2934},[505],[363,44392,5160],{"className":44393},[2938],[363,44395],{"className":44396,"style":2934},[505],[363,44398,465],{"className":44399},[407],[363,44401,44403,44406],{"className":44402},[501],[363,44404,468],{"className":44405},[501],[363,44407,44409],{"className":44408},[629],[363,44410,44412],{"className":44411},[633],[363,44413,44415],{"className":44414},[638],[363,44416,44418],{"className":44417,"style":20082},[642],[363,44419,44420,44423],{"style":8624},[363,44421],{"className":44422,"style":651},[650],[363,44424,44426],{"className":44425},[655,656,657,658],[363,44427,2810],{"className":44428},[407,658],[363,44430],{"className":44431,"style":506},[505],[363,44433,471],{"className":44434},[510],[363,44436],{"className":44437,"style":506},[505],[363,44439,385],{"className":44440,"style":409},[407,408],[363,44442,461],{"className":44443},[494],[363,44445,1116],{"className":44446},[407,408],[363,44448,468],{"className":44449},[501],[363,44451,898],{"className":44452},[920],[363,44454,666],{"className":44455},[665],[363,44457,44459],{"className":44458},[638],[363,44460,44462],{"className":44461,"style":43821},[642],[363,44463],{},[11,44465,21627,44466,44595,44596,44654],{},[363,44467,44469,44501],{"className":44468,"translate":367},[366],[363,44470,44472],{"className":44471},[371],[373,44473,44474],{"xmlns":375},[377,44475,44476,44498],{},[380,44477,44478,44494,44496],{},[7900,44479,44480,44482,44492],{},[383,44481,385],{},[380,44483,44484,44486,44488,44490],{},[383,44485,7908],{},[383,44487,7911],{},[383,44489,7914],{},[383,44491,7917],{},[458,44493,7920],{"lspace":1594,"rspace":1594},[458,44495,471],{},[383,44497,385],{},[387,44499,44500],{"encoding":389},"f^{*}_{skew}=f",[363,44502,44504,44586],{"className":44503,"ariaHidden":394},[393],[363,44505,44507,44511,44577,44580,44583],{"className":44506},[398],[363,44508],{"className":44509,"style":44510},[402],"height:0.9775em;vertical-align:-0.2831em;",[363,44512,44514,44517],{"className":44513},[407],[363,44515,385],{"className":44516,"style":409},[407,408],[363,44518,44520],{"className":44519},[629],[363,44521,44523,44569],{"className":44522},[633,634],[363,44524,44526,44566],{"className":44525},[638],[363,44527,44529,44552],{"className":44528,"style":8846},[642],[363,44530,44531,44534],{"style":8849},[363,44532],{"className":44533,"style":651},[650],[363,44535,44537],{"className":44536},[655,656,657,658],[363,44538,44540,44543,44546,44549],{"className":44539},[407,658],[363,44541,7908],{"className":44542},[407,408,658],[363,44544,7911],{"className":44545,"style":8614},[407,408,658],[363,44547,7914],{"className":44548},[407,408,658],[363,44550,7917],{"className":44551,"style":8621},[407,408,658],[363,44553,44554,44557],{"style":7212},[363,44555],{"className":44556,"style":651},[650],[363,44558,44560],{"className":44559},[655,656,657,658],[363,44561,44563],{"className":44562},[407,658],[363,44564,7920],{"className":44565},[407,658],[363,44567,666],{"className":44568},[665],[363,44570,44572],{"className":44571},[638],[363,44573,44575],{"className":44574,"style":8894},[642],[363,44576],{},[363,44578],{"className":44579,"style":506},[505],[363,44581,471],{"className":44582},[510],[363,44584],{"className":44585,"style":506},[505],[363,44587,44589,44592],{"className":44588},[398],[363,44590],{"className":44591,"style":403},[402],[363,44593,385],{"className":44594,"style":409},[407,408],"，所以 Hellinger",[363,44597,44599,44617],{"className":44598,"translate":367},[366],[363,44600,44602],{"className":44601},[371],[373,44603,44604],{"xmlns":375},[377,44605,44606,44614],{},[380,44607,44608],{},[7161,44609,44610,44612],{},[380,44611],{},[463,44613,2810],{},[387,44615,44616],{"encoding":389},"^2",[363,44618,44620],{"className":44619,"ariaHidden":394},[393],[363,44621,44623,44626],{"className":44622},[398],[363,44624],{"className":44625,"style":20375},[402],[363,44627,44629,44631],{"className":44628},[407],[363,44630],{},[363,44632,44634],{"className":44633},[629],[363,44635,44637],{"className":44636},[633],[363,44638,44640],{"className":44639},[638],[363,44641,44643],{"className":44642,"style":20375},[642],[363,44644,44645,44648],{"style":7212},[363,44646],{"className":44647,"style":651},[650],[363,44649,44651],{"className":44650},[655,656,657,658],[363,44652,2810],{"className":44653},[407,658]," 也满足对称判别准则（4.3 节）。",[11,44656,44657,44659,44660,44774,44775,44778,44779,44835,44836,44892,44893,45051,45052,45080],{},[1572,44658,24540],{}," Hellinger 与 Bhattacharyya 系数 ",[363,44661,44663,44691],{"className":44662,"translate":367},[366],[363,44664,44666],{"className":44665},[371],[373,44667,44668],{"xmlns":375},[377,44669,44670,44688],{},[380,44671,44672,44674,44676,44678,44680],{},[383,44673,39638],{},[383,44675,39641],{},[458,44677,471],{},[458,44679,1634],{},[34686,44681,44682],{},[380,44683,44684,44686],{},[383,44685,11],{},[383,44687,1291],{},[387,44689,44690],{"encoding":389},"BC=\\int\\sqrt{pq}",[363,44692,44694,44715],{"className":44693,"ariaHidden":394},[393],[363,44695,44697,44700,44703,44706,44709,44712],{"className":44696},[398],[363,44698],{"className":44699,"style":1011},[402],[363,44701,39638],{"className":44702,"style":39734},[407,408],[363,44704,39641],{"className":44705,"style":11129},[407,408],[363,44707],{"className":44708,"style":506},[505],[363,44710,471],{"className":44711},[510],[363,44713],{"className":44714,"style":506},[505],[363,44716,44718,44721,44724,44727],{"className":44717},[398],[363,44719],{"className":44720,"style":39355},[402],[363,44722,1634],{"className":44723,"style":5964},[1831,1832,5963],[363,44725],{"className":44726,"style":754},[505],[363,44728,44730],{"className":44729},[407,34714],[363,44731,44733,44766],{"className":44732},[633,634],[363,44734,44736,44763],{"className":44735},[638],[363,44737,44739,44751],{"className":44738,"style":39374},[642],[363,44740,44742,44745],{"className":44741,"style":12210},[6654],[363,44743],{"className":44744,"style":809},[650],[363,44746,44748],{"className":44747,"style":34734},[407],[363,44749,41952],{"className":44750,"style":1328},[407,408],[363,44752,44753,44756],{"style":39386},[363,44754],{"className":44755,"style":809},[650],[363,44757,44759],{"className":44758,"style":34791},[34790],[6670,44760,44761],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,44762],{"d":34798},[363,44764,666],{"className":44765},[665],[363,44767,44769],{"className":44768},[638],[363,44770,44772],{"className":44771,"style":39406},[642],[363,44773],{}," 把「两个分布的",[1572,44776,44777],{},"重叠程度","」量化：",[363,44780,44782,44802],{"className":44781,"translate":367},[366],[363,44783,44785],{"className":44784},[371],[373,44786,44787],{"xmlns":375},[377,44788,44789,44799],{},[380,44790,44791,44793,44795,44797],{},[383,44792,39638],{},[383,44794,39641],{},[458,44796,471],{},[463,44798,465],{},[387,44800,44801],{"encoding":389},"BC=1",[363,44803,44805,44826],{"className":44804,"ariaHidden":394},[393],[363,44806,44808,44811,44814,44817,44820,44823],{"className":44807},[398],[363,44809],{"className":44810,"style":1011},[402],[363,44812,39638],{"className":44813,"style":39734},[407,408],[363,44815,39641],{"className":44816,"style":11129},[407,408],[363,44818],{"className":44819,"style":506},[505],[363,44821,471],{"className":44822},[510],[363,44824],{"className":44825,"style":506},[505],[363,44827,44829,44832],{"className":44828},[398],[363,44830],{"className":44831,"style":520},[402],[363,44833,465],{"className":44834},[407]," 表示完全重合，",[363,44837,44839,44859],{"className":44838,"translate":367},[366],[363,44840,44842],{"className":44841},[371],[373,44843,44844],{"xmlns":375},[377,44845,44846,44856],{},[380,44847,44848,44850,44852,44854],{},[383,44849,39638],{},[383,44851,39641],{},[458,44853,471],{},[463,44855,474],{},[387,44857,44858],{"encoding":389},"BC=0",[363,44860,44862,44883],{"className":44861,"ariaHidden":394},[393],[363,44863,44865,44868,44871,44874,44877,44880],{"className":44864},[398],[363,44866],{"className":44867,"style":1011},[402],[363,44869,39638],{"className":44870,"style":39734},[407,408],[363,44872,39641],{"className":44873,"style":11129},[407,408],[363,44875],{"className":44876,"style":506},[505],[363,44878,471],{"className":44879},[510],[363,44881],{"className":44882,"style":506},[505],[363,44884,44886,44889],{"className":44885},[398],[363,44887],{"className":44888,"style":520},[402],[363,44890,474],{"className":44891},[407]," 表示支撑分离。由它可造出真正的距离 ",[363,44894,44896,44937],{"className":44895,"translate":367},[366],[363,44897,44899],{"className":44898},[371],[373,44900,44901],{"xmlns":375},[377,44902,44903,44934],{},[380,44904,44905,44908,44910,44912,44914,44916,44918,44920],{},[383,44906,44907],{},"ρ",[458,44909,461],{"stretchy":460},[383,44911,554],{},[458,44913,898],{"separator":394},[383,44915,561],{},[458,44917,468],{"stretchy":460},[458,44919,471],{},[34686,44921,44922],{},[380,44923,44924,44926,44928,44930,44932],{},[463,44925,2810],{},[458,44927,5160],{},[463,44929,2810],{},[383,44931,39638],{},[383,44933,39641],{},[387,44935,44936],{"encoding":389},"\\rho(P,Q)=\\sqrt{2-2BC}",[363,44938,44940,44976],{"className":44939,"ariaHidden":394},[393],[363,44941,44943,44946,44949,44952,44955,44958,44961,44964,44967,44970,44973],{"className":44942},[398],[363,44944],{"className":44945,"style":487},[402],[363,44947,44907],{"className":44948},[407,408],[363,44950,461],{"className":44951},[494],[363,44953,554],{"className":44954,"style":682},[407,408],[363,44956,898],{"className":44957},[920],[363,44959],{"className":44960,"style":754},[505],[363,44962,561],{"className":44963},[407,408],[363,44965,468],{"className":44966},[501],[363,44968],{"className":44969,"style":506},[505],[363,44971,471],{"className":44972},[510],[363,44974],{"className":44975,"style":506},[505],[363,44977,44979,44983],{"className":44978},[398],[363,44980],{"className":44981,"style":44982},[402],"height:1.04em;vertical-align:-0.155em;",[363,44984,44986],{"className":44985},[407,34714],[363,44987,44989,45042],{"className":44988},[633,634],[363,44990,44992,45039],{"className":44991},[638],[363,44993,44996,45026],{"className":44994,"style":44995},[642],"height:0.885em;",[363,44997,44999,45002],{"className":44998,"style":12210},[6654],[363,45000],{"className":45001,"style":809},[650],[363,45003,45005,45008,45011,45014,45017,45020,45023],{"className":45004,"style":34734},[407],[363,45006,2810],{"className":45007},[407],[363,45009],{"className":45010,"style":2934},[505],[363,45012,5160],{"className":45013},[2938],[363,45015],{"className":45016,"style":2934},[505],[363,45018,2810],{"className":45019},[407],[363,45021,39638],{"className":45022,"style":39734},[407,408],[363,45024,39641],{"className":45025,"style":11129},[407,408],[363,45027,45029,45032],{"style":45028},"top:-2.845em;",[363,45030],{"className":45031,"style":809},[650],[363,45033,45035],{"className":45034,"style":34791},[34790],[6670,45036,45037],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,45038],{"d":34798},[363,45040,666],{"className":45041},[665],[363,45043,45045],{"className":45044},[638],[363,45046,45049],{"className":45047,"style":45048},[642],"height:0.155em;",[363,45050],{},"，而且它对绝对连续性不作要求，支撑分离时也只取到有限的最大值 ",[363,45053,45055,45068],{"className":45054,"translate":367},[366],[363,45056,45058],{"className":45057},[371],[373,45059,45060],{"xmlns":375},[377,45061,45062,45066],{},[380,45063,45064],{},[463,45065,2810],{},[387,45067,2810],{"encoding":389},[363,45069,45071],{"className":45070,"ariaHidden":394},[393],[363,45072,45074,45077],{"className":45073},[398],[363,45075],{"className":45076,"style":520},[402],[363,45078,2810],{"className":45079},[407],"，不会像 KL 那样发散——这让它在数值与统计上格外稳健。Hellinger 距离与 Fisher 信息度量在无穷小尺度上相容（4.6 节），并在非参数估计的 Le Cam 三点法、量子信息中的保真度（fidelity）、以及 Hellinger–Fisher–Rao 几何里扮演中心角色。",[2658,45082,45084],{"id":45083},"_36-α-散度","3.6 α-散度",[11,45086,14608,45087,45168],{},[363,45088,45090,45119],{"className":45089,"translate":367},[366],[363,45091,45093],{"className":45092},[371],[373,45094,45095],{"xmlns":375},[377,45096,45097,45116],{},[380,45098,45099,45102,45104,45106,45108,45110,45112,45114],{},[383,45100,45101],{},"α",[458,45103,6256],{},[458,45105,461],{"stretchy":460},[458,45107,5160],{},[463,45109,465],{},[458,45111,898],{"separator":394},[463,45113,465],{},[458,45115,468],{"stretchy":460},[387,45117,45118],{"encoding":389},"\\alpha\\in(-1,1)",[363,45120,45122,45141],{"className":45121,"ariaHidden":394},[393],[363,45123,45125,45128,45132,45135,45138],{"className":45124},[398],[363,45126],{"className":45127,"style":6271},[402],[363,45129,45101],{"className":45130,"style":45131},[407,408],"margin-right:0.0037em;",[363,45133],{"className":45134,"style":506},[505],[363,45136,6256],{"className":45137},[510],[363,45139],{"className":45140,"style":506},[505],[363,45142,45144,45147,45150,45153,45156,45159,45162,45165],{"className":45143},[398],[363,45145],{"className":45146,"style":487},[402],[363,45148,461],{"className":45149},[494],[363,45151,5160],{"className":45152},[407],[363,45154,465],{"className":45155},[407],[363,45157,898],{"className":45158},[920],[363,45160],{"className":45161,"style":754},[505],[363,45163,465],{"className":45164},[407],[363,45166,468],{"className":45167},[501],"，取",[363,45170,45172],{"className":45171,"translate":367},[528],[363,45173,45175,45249],{"className":45174,"translate":367},[366],[363,45176,45178],{"className":45177},[371],[373,45179,45180],{"xmlns":375,"display":537},[377,45181,45182,45246],{},[380,45183,45184,45190,45192,45194,45196,45198,45214,45244],{},[543,45185,45186,45188],{},[383,45187,385],{},[383,45189,45101],{},[458,45191,461],{"stretchy":460},[383,45193,1116],{},[458,45195,468],{"stretchy":460},[458,45197,471],{},[586,45199,45200,45202],{},[463,45201,39336],{},[380,45203,45204,45206,45208],{},[463,45205,465],{},[458,45207,5160],{},[7161,45209,45210,45212],{},[383,45211,45101],{},[463,45213,2810],{},[380,45215,45216,45218,45220,45222,45242],{},[458,45217,461],{"fence":394},[463,45219,465],{},[458,45221,5160],{},[7161,45223,45224,45226],{},[383,45225,1116],{},[380,45227,45228,45230,45232,45234,45236,45238,45240],{},[458,45229,461],{"stretchy":460},[463,45231,465],{},[458,45233,2817],{},[383,45235,45101],{},[458,45237,468],{"stretchy":460},[383,45239,1288],{"mathvariant":557},[463,45241,2810],{},[458,45243,468],{"fence":394},[383,45245,4722],{"mathvariant":557},[387,45247,45248],{"encoding":389},"f_\\alpha(t)=\\frac{4}{1-\\alpha^2}\n\\left(1-t^{(1+\\alpha)\u002F2}\\right).",[363,45250,45252,45317],{"className":45251,"ariaHidden":394},[393],[363,45253,45255,45258,45299,45302,45305,45308,45311,45314],{"className":45254},[398],[363,45256],{"className":45257,"style":487},[402],[363,45259,45261,45264],{"className":45260},[407],[363,45262,385],{"className":45263,"style":409},[407,408],[363,45265,45267],{"className":45266},[629],[363,45268,45270,45291],{"className":45269},[633,634],[363,45271,45273,45288],{"className":45272},[638],[363,45274,45277],{"className":45275,"style":45276},[642],"height:0.1514em;",[363,45278,45279,45282],{"style":27856},[363,45280],{"className":45281,"style":651},[650],[363,45283,45285],{"className":45284},[655,656,657,658],[363,45286,45101],{"className":45287,"style":45131},[407,408,658],[363,45289,666],{"className":45290},[665],[363,45292,45294],{"className":45293},[638],[363,45295,45297],{"className":45296,"style":8315},[642],[363,45298],{},[363,45300,461],{"className":45301},[494],[363,45303,1116],{"className":45304},[407,408],[363,45306,468],{"className":45307},[501],[363,45309],{"className":45310,"style":506},[505],[363,45312,471],{"className":45313},[510],[363,45315],{"className":45316,"style":506},[505],[363,45318,45320,45323,45425,45428,45504,45507],{"className":45319},[398],[363,45321],{"className":45322,"style":26963},[402],[363,45324,45326,45329,45422],{"className":45325},[407],[363,45327],{"className":45328},[494,789],[363,45330,45332],{"className":45331},[586],[363,45333,45335,45414],{"className":45334},[633,634],[363,45336,45338,45411],{"className":45337},[638],[363,45339,45341,45392,45400],{"className":45340,"style":23236},[642],[363,45342,45343,45346],{"style":805},[363,45344],{"className":45345,"style":809},[650],[363,45347,45349,45352,45355,45358,45361],{"className":45348},[407],[363,45350,465],{"className":45351},[407],[363,45353],{"className":45354,"style":2934},[505],[363,45356,5160],{"className":45357},[2938],[363,45359],{"className":45360,"style":2934},[505],[363,45362,45364,45367],{"className":45363},[407],[363,45365,45101],{"className":45366,"style":45131},[407,408],[363,45368,45370],{"className":45369},[629],[363,45371,45373],{"className":45372},[633],[363,45374,45376],{"className":45375},[638],[363,45377,45380],{"className":45378,"style":45379},[642],"height:0.7401em;",[363,45381,45383,45386],{"style":45382},"top:-2.989em;margin-right:0.05em;",[363,45384],{"className":45385,"style":651},[650],[363,45387,45389],{"className":45388},[655,656,657,658],[363,45390,2810],{"className":45391},[407,658],[363,45393,45394,45397],{"style":821},[363,45395],{"className":45396,"style":809},[650],[363,45398],{"className":45399,"style":829},[828],[363,45401,45402,45405],{"style":832},[363,45403],{"className":45404,"style":809},[650],[363,45406,45408],{"className":45407},[407],[363,45409,39336],{"className":45410},[407],[363,45412,666],{"className":45413},[665],[363,45415,45417],{"className":45416},[638],[363,45418,45420],{"className":45419,"style":17362},[642],[363,45421],{},[363,45423],{"className":45424},[501,789],[363,45426],{"className":45427,"style":754},[505],[363,45429,45431,45437,45440,45443,45446,45449,45498],{"className":45430},[758],[363,45432,45434],{"className":45433,"style":763},[494,762],[363,45435,461],{"className":45436},[767,4067],[363,45438,465],{"className":45439},[407],[363,45441],{"className":45442,"style":2934},[505],[363,45444,5160],{"className":45445},[2938],[363,45447],{"className":45448,"style":2934},[505],[363,45450,45452,45455],{"className":45451},[407],[363,45453,1116],{"className":45454},[407,408],[363,45456,45458],{"className":45457},[629],[363,45459,45461],{"className":45460},[633],[363,45462,45464],{"className":45463},[638],[363,45465,45468],{"className":45466,"style":45467},[642],"height:0.938em;",[363,45469,45470,45473],{"style":8624},[363,45471],{"className":45472,"style":651},[650],[363,45474,45476],{"className":45475},[655,656,657,658],[363,45477,45479,45482,45485,45488,45491,45494],{"className":45478},[407,658],[363,45480,461],{"className":45481},[494,658],[363,45483,465],{"className":45484},[407,658],[363,45486,2817],{"className":45487},[2938,658],[363,45489,45101],{"className":45490,"style":45131},[407,408,658],[363,45492,468],{"className":45493},[501,658],[363,45495,45497],{"className":45496},[407,658],"\u002F2",[363,45499,45501],{"className":45500,"style":763},[501,762],[363,45502,468],{"className":45503},[767,4067],[363,45505],{"className":45506,"style":754},[505],[363,45508,4722],{"className":45509},[407],[11,45511,45512,45513,45691,45692,45955],{},"代入模板，记 ",[363,45514,45516,45557],{"className":45515,"translate":367},[366],[363,45517,45519],{"className":45518},[371],[373,45520,45521],{"xmlns":375},[377,45522,45523,45554],{},[380,45524,45525,45528,45530,45542,45544,45546,45548,45550,45552],{},[383,45526,45527],{},"a",[458,45529,471],{},[586,45531,45532,45540],{},[380,45533,45534,45536,45538],{},[463,45535,465],{},[458,45537,2817],{},[383,45539,45101],{},[463,45541,2810],{},[458,45543,6256],{},[458,45545,461],{"stretchy":460},[463,45547,474],{},[458,45549,898],{"separator":394},[463,45551,465],{},[458,45553,468],{"stretchy":460},[387,45555,45556],{"encoding":389},"a=\\frac{1+\\alpha}{2}\\in(0,1)",[363,45558,45560,45578,45667],{"className":45559,"ariaHidden":394},[393],[363,45561,45563,45566,45569,45572,45575],{"className":45562},[398],[363,45564],{"className":45565,"style":2692},[402],[363,45567,45527],{"className":45568},[407,408],[363,45570],{"className":45571,"style":506},[505],[363,45573,471],{"className":45574},[510],[363,45576],{"className":45577,"style":506},[505],[363,45579,45581,45584,45658,45661,45664],{"className":45580},[398],[363,45582],{"className":45583,"style":2852},[402],[363,45585,45587,45590,45655],{"className":45586},[407],[363,45588],{"className":45589},[494,789],[363,45591,45593],{"className":45592},[586],[363,45594,45596,45647],{"className":45595},[633,634],[363,45597,45599,45644],{"className":45598},[638],[363,45600,45602,45616,45624],{"className":45601,"style":2871},[642],[363,45603,45604,45607],{"style":2874},[363,45605],{"className":45606,"style":809},[650],[363,45608,45610],{"className":45609},[655,656,657,658],[363,45611,45613],{"className":45612},[407,658],[363,45614,2810],{"className":45615},[407,658],[363,45617,45618,45621],{"style":821},[363,45619],{"className":45620,"style":809},[650],[363,45622],{"className":45623,"style":829},[828],[363,45625,45626,45629],{"style":2897},[363,45627],{"className":45628,"style":809},[650],[363,45630,45632],{"className":45631},[655,656,657,658],[363,45633,45635,45638,45641],{"className":45634},[407,658],[363,45636,465],{"className":45637},[407,658],[363,45639,2817],{"className":45640},[2938,658],[363,45642,45101],{"className":45643,"style":45131},[407,408,658],[363,45645,666],{"className":45646},[665],[363,45648,45650],{"className":45649},[638],[363,45651,45653],{"className":45652,"style":2919},[642],[363,45654],{},[363,45656],{"className":45657},[501,789],[363,45659],{"className":45660,"style":506},[505],[363,45662,6256],{"className":45663},[510],[363,45665],{"className":45666,"style":506},[505],[363,45668,45670,45673,45676,45679,45682,45685,45688],{"className":45669},[398],[363,45671],{"className":45672,"style":487},[402],[363,45674,461],{"className":45675},[494],[363,45677,474],{"className":45678},[407],[363,45680,898],{"className":45681},[920],[363,45683],{"className":45684,"style":754},[505],[363,45686,465],{"className":45687},[407],[363,45689,468],{"className":45690},[501],"（于是 ",[363,45693,45695,45743],{"className":45694,"translate":367},[366],[363,45696,45698],{"className":45697},[371],[373,45699,45700],{"xmlns":375},[377,45701,45702,45740],{},[380,45703,45704,45720,45722],{},[586,45705,45706,45708],{},[463,45707,39336],{},[380,45709,45710,45712,45714],{},[463,45711,465],{},[458,45713,5160],{},[7161,45715,45716,45718],{},[383,45717,45101],{},[463,45719,2810],{},[458,45721,471],{},[586,45723,45724,45726],{},[463,45725,465],{},[380,45727,45728,45730,45732,45734,45736,45738],{},[383,45729,45527],{},[458,45731,461],{"stretchy":460},[463,45733,465],{},[458,45735,5160],{},[383,45737,45527],{},[458,45739,468],{"stretchy":460},[387,45741,45742],{"encoding":389},"\\frac{4}{1-\\alpha^2}=\\frac{1}{a(1-a)}",[363,45744,45746,45864],{"className":45745,"ariaHidden":394},[393],[363,45747,45749,45753,45855,45858,45861],{"className":45748},[398],[363,45750],{"className":45751,"style":45752},[402],"height:1.2484em;vertical-align:-0.4033em;",[363,45754,45756,45759,45852],{"className":45755},[407],[363,45757],{"className":45758},[494,789],[363,45760,45762],{"className":45761},[586],[363,45763,45765,45844],{"className":45764},[633,634],[363,45766,45768,45841],{"className":45767},[638],[363,45769,45771,45819,45827],{"className":45770,"style":2871},[642],[363,45772,45773,45776],{"style":2874},[363,45774],{"className":45775,"style":809},[650],[363,45777,45779],{"className":45778},[655,656,657,658],[363,45780,45782,45785,45788],{"className":45781},[407,658],[363,45783,465],{"className":45784},[407,658],[363,45786,5160],{"className":45787},[2938,658],[363,45789,45791,45794],{"className":45790},[407,658],[363,45792,45101],{"className":45793,"style":45131},[407,408,658],[363,45795,45797],{"className":45796},[629],[363,45798,45800],{"className":45799},[633],[363,45801,45803],{"className":45802},[638],[363,45804,45807],{"className":45805,"style":45806},[642],"height:0.7463em;",[363,45808,45810,45813],{"style":45809},"top:-2.786em;margin-right:0.0714em;",[363,45811],{"className":45812,"style":30553},[650],[363,45814,45816],{"className":45815},[655,30557,10021,658],[363,45817,2810],{"className":45818},[407,658],[363,45820,45821,45824],{"style":821},[363,45822],{"className":45823,"style":809},[650],[363,45825],{"className":45826,"style":829},[828],[363,45828,45829,45832],{"style":2897},[363,45830],{"className":45831,"style":809},[650],[363,45833,45835],{"className":45834},[655,656,657,658],[363,45836,45838],{"className":45837},[407,658],[363,45839,39336],{"className":45840},[407,658],[363,45842,666],{"className":45843},[665],[363,45845,45847],{"className":45846},[638],[363,45848,45850],{"className":45849,"style":16776},[642],[363,45851],{},[363,45853],{"className":45854},[501,789],[363,45856],{"className":45857,"style":506},[505],[363,45859,471],{"className":45860},[510],[363,45862],{"className":45863,"style":506},[505],[363,45865,45867,45871],{"className":45866},[398],[363,45868],{"className":45869,"style":45870},[402],"height:1.3651em;vertical-align:-0.52em;",[363,45872,45874,45877,45952],{"className":45873},[407],[363,45875],{"className":45876},[494,789],[363,45878,45880],{"className":45879},[586],[363,45881,45883,45943],{"className":45882},[633,634],[363,45884,45886,45940],{"className":45885},[638],[363,45887,45889,45918,45926],{"className":45888,"style":2871},[642],[363,45890,45891,45894],{"style":2874},[363,45892],{"className":45893,"style":809},[650],[363,45895,45897],{"className":45896},[655,656,657,658],[363,45898,45900,45903,45906,45909,45912,45915],{"className":45899},[407,658],[363,45901,45527],{"className":45902},[407,408,658],[363,45904,461],{"className":45905},[494,658],[363,45907,465],{"className":45908},[407,658],[363,45910,5160],{"className":45911},[2938,658],[363,45913,45527],{"className":45914},[407,408,658],[363,45916,468],{"className":45917},[501,658],[363,45919,45920,45923],{"style":821},[363,45921],{"className":45922,"style":809},[650],[363,45924],{"className":45925,"style":829},[828],[363,45927,45928,45931],{"style":2897},[363,45929],{"className":45930,"style":809},[650],[363,45932,45934],{"className":45933},[655,656,657,658],[363,45935,45937],{"className":45936},[407,658],[363,45938,465],{"className":45939},[407,658],[363,45941,666],{"className":45942},[665],[363,45944,45946],{"className":45945},[638],[363,45947,45950],{"className":45948,"style":45949},[642],"height:0.52em;",[363,45951],{},[363,45953],{"className":45954},[501,789],"）：",[363,45957,45959],{"className":45958,"translate":367},[528],[363,45960,45962,46048],{"className":45961,"translate":367},[366],[363,45963,45965],{"className":45964},[371],[373,45966,45967],{"xmlns":375,"display":537},[377,45968,45969,46045],{},[380,45970,45971,45977,45979,45981,45983,45985,45987,45989,46007,46043],{},[543,45972,45973,45975],{},[383,45974,547],{},[383,45976,45101],{},[458,45978,461],{"stretchy":460},[383,45980,554],{},[383,45982,558],{"mathvariant":557},[383,45984,561],{},[458,45986,468],{"stretchy":460},[458,45988,471],{},[586,45990,45991,45993],{},[463,45992,465],{},[380,45994,45995,45997,45999,46001,46003,46005],{},[383,45996,45527],{},[458,45998,461],{"stretchy":460},[463,46000,465],{},[458,46002,5160],{},[383,46004,45527],{},[458,46006,468],{"stretchy":460},[380,46008,46009,46011,46013,46015,46017,46023,46035,46037,46039,46041],{},[458,46010,461],{"fence":394},[463,46012,465],{},[458,46014,5160],{},[458,46016,1634],{},[7161,46018,46019,46021],{},[383,46020,11],{},[383,46022,45527],{},[7161,46024,46025,46027],{},[383,46026,1291],{},[380,46028,46029,46031,46033],{},[463,46030,465],{},[458,46032,5160],{},[383,46034,45527],{},[1644,46036,1646],{},[383,46038,592],{},[383,46040,1121],{},[458,46042,468],{"fence":394},[383,46044,4722],{"mathvariant":557},[387,46046,46047],{"encoding":389},"D_\\alpha(P\\|Q)=\\frac{1}{a(1-a)}\n\\left(1-\\int p^{a}q^{1-a}\\,dx\\right).",[363,46049,46051,46121],{"className":46050,"ariaHidden":394},[393],[363,46052,46054,46057,46097,46100,46103,46106,46109,46112,46115,46118],{"className":46053},[398],[363,46055],{"className":46056,"style":487},[402],[363,46058,46060,46063],{"className":46059},[407],[363,46061,547],{"className":46062,"style":625},[407,408],[363,46064,46066],{"className":46065},[629],[363,46067,46069,46089],{"className":46068},[633,634],[363,46070,46072,46086],{"className":46071},[638],[363,46073,46075],{"className":46074,"style":45276},[642],[363,46076,46077,46080],{"style":646},[363,46078],{"className":46079,"style":651},[650],[363,46081,46083],{"className":46082},[655,656,657,658],[363,46084,45101],{"className":46085,"style":45131},[407,408,658],[363,46087,666],{"className":46088},[665],[363,46090,46092],{"className":46091},[638],[363,46093,46095],{"className":46094,"style":8315},[642],[363,46096],{},[363,46098,461],{"className":46099},[494],[363,46101,554],{"className":46102,"style":682},[407,408],[363,46104,558],{"className":46105},[407],[363,46107,561],{"className":46108},[407,408],[363,46110,468],{"className":46111},[501],[363,46113],{"className":46114,"style":506},[505],[363,46116,471],{"className":46117},[510],[363,46119],{"className":46120,"style":506},[505],[363,46122,46124,46127,46210,46213,46326,46329],{"className":46123},[398],[363,46125],{"className":46126,"style":707},[402],[363,46128,46130,46133,46207],{"className":46129},[407],[363,46131],{"className":46132},[494,789],[363,46134,46136],{"className":46135},[586],[363,46137,46139,46199],{"className":46138},[633,634],[363,46140,46142,46196],{"className":46141},[638],[363,46143,46145,46177,46185],{"className":46144,"style":23236},[642],[363,46146,46147,46150],{"style":805},[363,46148],{"className":46149,"style":809},[650],[363,46151,46153,46156,46159,46162,46165,46168,46171,46174],{"className":46152},[407],[363,46154,45527],{"className":46155},[407,408],[363,46157,461],{"className":46158},[494],[363,46160,465],{"className":46161},[407],[363,46163],{"className":46164,"style":2934},[505],[363,46166,5160],{"className":46167},[2938],[363,46169],{"className":46170,"style":2934},[505],[363,46172,45527],{"className":46173},[407,408],[363,46175,468],{"className":46176},[501],[363,46178,46179,46182],{"style":821},[363,46180],{"className":46181,"style":809},[650],[363,46183],{"className":46184,"style":829},[828],[363,46186,46187,46190],{"style":832},[363,46188],{"className":46189,"style":809},[650],[363,46191,46193],{"className":46192},[407],[363,46194,465],{"className":46195},[407],[363,46197,666],{"className":46198},[665],[363,46200,46202],{"className":46201},[638],[363,46203,46205],{"className":46204,"style":1948},[642],[363,46206],{},[363,46208],{"className":46209},[501,789],[363,46211],{"className":46212,"style":754},[505],[363,46214,46216,46222,46225,46228,46231,46234,46237,46240,46273,46311,46314,46317,46320],{"className":46215},[758],[363,46217,46219],{"className":46218,"style":763},[494,762],[363,46220,461],{"className":46221},[767,657],[363,46223,465],{"className":46224},[407],[363,46226],{"className":46227,"style":2934},[505],[363,46229,5160],{"className":46230},[2938],[363,46232],{"className":46233,"style":2934},[505],[363,46235,1634],{"className":46236,"style":1834},[1831,1832,1833],[363,46238],{"className":46239,"style":754},[505],[363,46241,46243,46246],{"className":46242},[407],[363,46244,11],{"className":46245},[407,408],[363,46247,46249],{"className":46248},[629],[363,46250,46252],{"className":46251},[633],[363,46253,46255],{"className":46254},[638],[363,46256,46259],{"className":46257,"style":46258},[642],"height:0.7144em;",[363,46260,46261,46264],{"style":8624},[363,46262],{"className":46263,"style":651},[650],[363,46265,46267],{"className":46266},[655,656,657,658],[363,46268,46270],{"className":46269},[407,658],[363,46271,45527],{"className":46272},[407,408,658],[363,46274,46276,46279],{"className":46275},[407],[363,46277,1291],{"className":46278,"style":1328},[407,408],[363,46280,46282],{"className":46281},[629],[363,46283,46285],{"className":46284},[633],[363,46286,46288],{"className":46287},[638],[363,46289,46291],{"className":46290,"style":20082},[642],[363,46292,46293,46296],{"style":8624},[363,46294],{"className":46295,"style":651},[650],[363,46297,46299],{"className":46298},[655,656,657,658],[363,46300,46302,46305,46308],{"className":46301},[407,658],[363,46303,465],{"className":46304},[407,658],[363,46306,5160],{"className":46307},[2938,658],[363,46309,45527],{"className":46310},[407,408,658],[363,46312],{"className":46313,"style":754},[505],[363,46315,592],{"className":46316},[407,408],[363,46318,1121],{"className":46319},[407,408],[363,46321,46323],{"className":46322,"style":763},[501,762],[363,46324,468],{"className":46325},[767,657],[363,46327],{"className":46328,"style":754},[505],[363,46330,4722],{"className":46331},[407],[11,46333,46334,46335,46338,46339,32571,46394,9747],{},"这正是 Csiszár \u002F Amari 的 ",[1572,46336,46337],{},"α-散度","（差一个参数重命名）。",[363,46340,46342,46364],{"className":46341,"translate":367},[366],[363,46343,46345],{"className":46344},[371],[373,46346,46347],{"xmlns":375},[377,46348,46349,46361],{},[380,46350,46351,46353,46355,46357,46359],{},[383,46352,45527],{},[458,46354,471],{},[463,46356,465],{},[383,46358,1288],{"mathvariant":557},[463,46360,2810],{},[387,46362,46363],{"encoding":389},"a=1\u002F2",[363,46365,46367,46385],{"className":46366,"ariaHidden":394},[393],[363,46368,46370,46373,46376,46379,46382],{"className":46369},[398],[363,46371],{"className":46372,"style":2692},[402],[363,46374,45527],{"className":46375},[407,408],[363,46377],{"className":46378,"style":506},[505],[363,46380,471],{"className":46381},[510],[363,46383],{"className":46384,"style":506},[505],[363,46386,46388,46391],{"className":46387},[398],[363,46389],{"className":46390,"style":487},[402],[363,46392,33986],{"className":46393},[407],[363,46395,46397,46431],{"className":46396,"translate":367},[366],[363,46398,46400],{"className":46399},[371],[373,46401,46402],{"xmlns":375},[377,46403,46404,46428],{},[380,46405,46406,46424,46426],{},[586,46407,46408,46410],{},[463,46409,465],{},[380,46411,46412,46414,46416,46418,46420,46422],{},[383,46413,45527],{},[458,46415,461],{"stretchy":460},[463,46417,465],{},[458,46419,5160],{},[383,46421,45527],{},[458,46423,468],{"stretchy":460},[458,46425,471],{},[463,46427,39336],{},[387,46429,46430],{"encoding":389},"\\frac{1}{a(1-a)}=4",[363,46432,46434,46532],{"className":46433,"ariaHidden":394},[393],[363,46435,46437,46440,46523,46526,46529],{"className":46436},[398],[363,46438],{"className":46439,"style":45870},[402],[363,46441,46443,46446,46520],{"className":46442},[407],[363,46444],{"className":46445},[494,789],[363,46447,46449],{"className":46448},[586],[363,46450,46452,46512],{"className":46451},[633,634],[363,46453,46455,46509],{"className":46454},[638],[363,46456,46458,46487,46495],{"className":46457,"style":2871},[642],[363,46459,46460,46463],{"style":2874},[363,46461],{"className":46462,"style":809},[650],[363,46464,46466],{"className":46465},[655,656,657,658],[363,46467,46469,46472,46475,46478,46481,46484],{"className":46468},[407,658],[363,46470,45527],{"className":46471},[407,408,658],[363,46473,461],{"className":46474},[494,658],[363,46476,465],{"className":46477},[407,658],[363,46479,5160],{"className":46480},[2938,658],[363,46482,45527],{"className":46483},[407,408,658],[363,46485,468],{"className":46486},[501,658],[363,46488,46489,46492],{"style":821},[363,46490],{"className":46491,"style":809},[650],[363,46493],{"className":46494,"style":829},[828],[363,46496,46497,46500],{"style":2897},[363,46498],{"className":46499,"style":809},[650],[363,46501,46503],{"className":46502},[655,656,657,658],[363,46504,46506],{"className":46505},[407,658],[363,46507,465],{"className":46508},[407,658],[363,46510,666],{"className":46511},[665],[363,46513,46515],{"className":46514},[638],[363,46516,46518],{"className":46517,"style":45949},[642],[363,46519],{},[363,46521],{"className":46522},[501,789],[363,46524],{"className":46525,"style":506},[505],[363,46527,471],{"className":46528},[510],[363,46530],{"className":46531,"style":506},[505],[363,46533,46535,46538],{"className":46534},[398],[363,46536],{"className":46537,"style":520},[402],[363,46539,39336],{"className":46540},[407],[363,46542,46544],{"className":46543,"translate":367},[528],[363,46545,46547,46613],{"className":46546,"translate":367},[366],[363,46548,46550],{"className":46549},[371],[373,46551,46552],{"xmlns":375,"display":537},[377,46553,46554,46610],{},[380,46555,46556,46568,46570,46572,46574,46576,46578,46580,46582,46596,46598,46600,46608],{},[543,46557,46558,46560],{},[383,46559,547],{},[380,46561,46562,46564,46566],{},[383,46563,45101],{},[458,46565,471],{},[463,46567,474],{},[458,46569,461],{"stretchy":460},[383,46571,554],{},[383,46573,558],{"mathvariant":557},[383,46575,561],{},[458,46577,468],{"stretchy":460},[458,46579,471],{},[463,46581,39336],{},[380,46583,46584,46586,46588,46590,46592,46594],{},[458,46585,461],{"fence":394},[463,46587,465],{},[458,46589,5160],{},[383,46591,39638],{},[383,46593,39641],{},[458,46595,468],{"fence":394},[458,46597,471],{},[463,46599,39336],{},[7900,46601,46602,46604,46606],{},[383,46603,34231],{},[1644,46605,42484],{},[463,46607,2810],{},[458,46609,898],{"separator":394},[387,46611,46612],{"encoding":389},"D_{\\alpha=0}(P\\|Q)=4\\left(1-BC\\right)\n=4H^2_{\\text{Bhattacharyya}},",[363,46614,46616,46695,46743],{"className":46615,"ariaHidden":394},[393],[363,46617,46619,46622,46671,46674,46677,46680,46683,46686,46689,46692],{"className":46618},[398],[363,46620],{"className":46621,"style":487},[402],[363,46623,46625,46628],{"className":46624},[407],[363,46626,547],{"className":46627,"style":625},[407,408],[363,46629,46631],{"className":46630},[629],[363,46632,46634,46663],{"className":46633},[633,634],[363,46635,46637,46660],{"className":46636},[638],[363,46638,46640],{"className":46639,"style":11480},[642],[363,46641,46642,46645],{"style":646},[363,46643],{"className":46644,"style":651},[650],[363,46646,46648],{"className":46647},[655,656,657,658],[363,46649,46651,46654,46657],{"className":46650},[407,658],[363,46652,45101],{"className":46653,"style":45131},[407,408,658],[363,46655,471],{"className":46656},[510,658],[363,46658,474],{"className":46659},[407,658],[363,46661,666],{"className":46662},[665],[363,46664,46666],{"className":46665},[638],[363,46667,46669],{"className":46668,"style":8315},[642],[363,46670],{},[363,46672,461],{"className":46673},[494],[363,46675,554],{"className":46676,"style":682},[407,408],[363,46678,558],{"className":46679},[407],[363,46681,561],{"className":46682},[407,408],[363,46684,468],{"className":46685},[501],[363,46687],{"className":46688,"style":506},[505],[363,46690,471],{"className":46691},[510],[363,46693],{"className":46694,"style":506},[505],[363,46696,46698,46701,46704,46707,46734,46737,46740],{"className":46697},[398],[363,46699],{"className":46700,"style":487},[402],[363,46702,39336],{"className":46703},[407],[363,46705],{"className":46706,"style":754},[505],[363,46708,46710,46713,46716,46719,46722,46725,46728,46731],{"className":46709},[758],[363,46711,461],{"className":46712,"style":763},[494,762],[363,46714,465],{"className":46715},[407],[363,46717],{"className":46718,"style":2934},[505],[363,46720,5160],{"className":46721},[2938],[363,46723],{"className":46724,"style":2934},[505],[363,46726,39638],{"className":46727,"style":39734},[407,408],[363,46729,39641],{"className":46730,"style":11129},[407,408],[363,46732,468],{"className":46733,"style":763},[501,762],[363,46735],{"className":46736,"style":506},[505],[363,46738,471],{"className":46739},[510],[363,46741],{"className":46742,"style":506},[505],[363,46744,46746,46750,46753,46810],{"className":46745},[398],[363,46747],{"className":46748,"style":46749},[402],"height:1.2472em;vertical-align:-0.3831em;",[363,46751,39336],{"className":46752},[407],[363,46754,46756,46759],{"className":46755},[407],[363,46757,34231],{"className":46758,"style":34385},[407,408],[363,46760,46762],{"className":46761},[629],[363,46763,46765,46802],{"className":46764},[633,634],[363,46766,46768,46799],{"className":46767},[638],[363,46769,46771,46788],{"className":46770,"style":20082},[642],[363,46772,46773,46776],{"style":42627},[363,46774],{"className":46775,"style":651},[650],[363,46777,46779],{"className":46778},[655,656,657,658],[363,46780,46782],{"className":46781},[407,658],[363,46783,46785],{"className":46784},[407,4945,658],[363,46786,42484],{"className":46787},[407,658],[363,46789,46790,46793],{"style":8624},[363,46791],{"className":46792,"style":651},[650],[363,46794,46796],{"className":46795},[655,656,657,658],[363,46797,2810],{"className":46798},[407,658],[363,46800,666],{"className":46801},[665],[363,46803,46805],{"className":46804},[638],[363,46806,46808],{"className":46807,"style":42663},[642],[363,46809],{},[363,46811,898],{"className":46812},[920],[11,46814,21627,46815,46866,46867,4200,46937,46994,46995,46998],{},[363,46816,46818,46836],{"className":46817,"translate":367},[366],[363,46819,46821],{"className":46820},[371],[373,46822,46823],{"xmlns":375},[377,46824,46825,46833],{},[380,46826,46827,46829,46831],{},[383,46828,45101],{},[458,46830,471],{},[463,46832,474],{},[387,46834,46835],{"encoding":389},"\\alpha=0",[363,46837,46839,46857],{"className":46838,"ariaHidden":394},[393],[363,46840,46842,46845,46848,46851,46854],{"className":46841},[398],[363,46843],{"className":46844,"style":2692},[402],[363,46846,45101],{"className":46847,"style":45131},[407,408],[363,46849],{"className":46850,"style":506},[505],[363,46852,471],{"className":46853},[510],[363,46855],{"className":46856,"style":506},[505],[363,46858,46860,46863],{"className":46859},[398],[363,46861],{"className":46862,"style":520},[402],[363,46864,474],{"className":46865},[407]," 是 Hellinger 型散度。两个端点极限要小心：",[363,46868,46870,46888],{"className":46869,"translate":367},[366],[363,46871,46873],{"className":46872},[371],[373,46874,46875],{"xmlns":375},[377,46876,46877,46885],{},[380,46878,46879],{},[543,46880,46881,46883],{},[383,46882,385],{},[383,46884,45101],{},[387,46886,46887],{"encoding":389},"f_\\alpha",[363,46889,46891],{"className":46890,"ariaHidden":394},[393],[363,46892,46894,46897],{"className":46893},[398],[363,46895],{"className":46896,"style":403},[402],[363,46898,46900,46903],{"className":46899},[407],[363,46901,385],{"className":46902,"style":409},[407,408],[363,46904,46906],{"className":46905},[629],[363,46907,46909,46929],{"className":46908},[633,634],[363,46910,46912,46926],{"className":46911},[638],[363,46913,46915],{"className":46914,"style":45276},[642],[363,46916,46917,46920],{"style":27856},[363,46918],{"className":46919,"style":651},[650],[363,46921,46923],{"className":46922},[655,656,657,658],[363,46924,45101],{"className":46925,"style":45131},[407,408,658],[363,46927,666],{"className":46928},[665],[363,46930,46932],{"className":46931},[638],[363,46933,46935],{"className":46934,"style":8315},[642],[363,46936],{},[363,46938,46940,46961],{"className":46939,"translate":367},[366],[363,46941,46943],{"className":46942},[371],[373,46944,46945],{"xmlns":375},[377,46946,46947,46958],{},[380,46948,46949,46951,46953,46956],{},[383,46950,45101],{},[458,46952,1376],{},[458,46954,46955],{},"±",[463,46957,465],{},[387,46959,46960],{"encoding":389},"\\alpha\\to\\pm1",[363,46962,46964,46982],{"className":46963,"ariaHidden":394},[393],[363,46965,46967,46970,46973,46976,46979],{"className":46966},[398],[363,46968],{"className":46969,"style":2692},[402],[363,46971,45101],{"className":46972,"style":45131},[407,408],[363,46974],{"className":46975,"style":506},[505],[363,46977,1376],{"className":46978},[510],[363,46980],{"className":46981,"style":506},[505],[363,46983,46985,46988,46991],{"className":46984},[398],[363,46986],{"className":46987,"style":12925},[402],[363,46989,46955],{"className":46990},[407],[363,46992,465],{"className":46993},[407]," 时逐点发散，但",[1572,46996,46997],{},"散度值","收敛到 KL：",[363,47000,47002],{"className":47001,"translate":367},[528],[363,47003,47005,47134],{"className":47004,"translate":367},[366],[363,47006,47008],{"className":47007},[371],[373,47009,47010],{"xmlns":375,"display":537},[377,47011,47012,47131],{},[380,47013,47014,47031,47037,47039,47041,47043,47045,47047,47049,47059,47061,47063,47065,47067,47069,47071,47073,47091,47097,47099,47101,47103,47105,47107,47109,47119,47121,47123,47125,47127,47129],{},[6363,47015,47016,47023],{},[380,47017,47018,47021],{},[383,47019,47020],{},"lim",[458,47022,4450],{},[380,47024,47025,47027,47029],{},[383,47026,45101],{},[458,47028,1376],{},[463,47030,465],{},[543,47032,47033,47035],{},[383,47034,547],{},[383,47036,45101],{},[458,47038,461],{"stretchy":460},[383,47040,554],{},[383,47042,558],{"mathvariant":557},[383,47044,561],{},[458,47046,468],{"stretchy":460},[458,47048,471],{},[543,47050,47051,47053],{},[383,47052,547],{},[380,47054,47055,47057],{},[383,47056,11041],{},[383,47058,22240],{},[458,47060,461],{"stretchy":460},[383,47062,554],{},[383,47064,558],{"mathvariant":557},[383,47066,561],{},[458,47068,468],{"stretchy":460},[458,47070,898],{"separator":394},[505,47072],{"width":3609},[6363,47074,47075,47081],{},[380,47076,47077,47079],{},[383,47078,47020],{},[458,47080,4450],{},[380,47082,47083,47085,47087,47089],{},[383,47084,45101],{},[458,47086,1376],{},[458,47088,5160],{},[463,47090,465],{},[543,47092,47093,47095],{},[383,47094,547],{},[383,47096,45101],{},[458,47098,461],{"stretchy":460},[383,47100,554],{},[383,47102,558],{"mathvariant":557},[383,47104,561],{},[458,47106,468],{"stretchy":460},[458,47108,471],{},[543,47110,47111,47113],{},[383,47112,547],{},[380,47114,47115,47117],{},[383,47116,11041],{},[383,47118,22240],{},[458,47120,461],{"stretchy":460},[383,47122,561],{},[383,47124,558],{"mathvariant":557},[383,47126,554],{},[458,47128,468],{"stretchy":460},[383,47130,4722],{"mathvariant":557},[387,47132,47133],{"encoding":389},"\\lim_{\\alpha\\to1}D_\\alpha(P\\|Q)=D_{KL}(P\\|Q),\n\\qquad\n\\lim_{\\alpha\\to-1}D_\\alpha(P\\|Q)=D_{KL}(Q\\|P).",[363,47135,47137,47266,47467],{"className":47136,"ariaHidden":394},[393],[363,47138,47140,47144,47199,47202,47242,47245,47248,47251,47254,47257,47260,47263],{"className":47139},[398],[363,47141],{"className":47142,"style":47143},[402],"height:1.4671em;vertical-align:-0.7171em;",[363,47145,47147],{"className":47146},[1831,14063],[363,47148,47150,47190],{"className":47149},[633,634],[363,47151,47153,47187],{"className":47152},[638],[363,47154,47156,47177],{"className":47155,"style":12944},[642],[363,47157,47159,47162],{"style":47158},"top:-2.3829em;margin-left:0em;",[363,47160],{"className":47161,"style":809},[650],[363,47163,47165],{"className":47164},[655,656,657,658],[363,47166,47168,47171,47174],{"className":47167},[407,658],[363,47169,45101],{"className":47170,"style":45131},[407,408,658],[363,47172,1376],{"className":47173},[510,658],[363,47175,465],{"className":47176},[407,658],[363,47178,47179,47182],{"style":12210},[363,47180],{"className":47181,"style":809},[650],[363,47183,47184],{},[363,47185,47020],{"className":47186},[1831],[363,47188,666],{"className":47189},[665],[363,47191,47193],{"className":47192},[638],[363,47194,47197],{"className":47195,"style":47196},[642],"height:0.7171em;",[363,47198],{},[363,47200],{"className":47201,"style":754},[505],[363,47203,47205,47208],{"className":47204},[407],[363,47206,547],{"className":47207,"style":625},[407,408],[363,47209,47211],{"className":47210},[629],[363,47212,47214,47234],{"className":47213},[633,634],[363,47215,47217,47231],{"className":47216},[638],[363,47218,47220],{"className":47219,"style":45276},[642],[363,47221,47222,47225],{"style":646},[363,47223],{"className":47224,"style":651},[650],[363,47226,47228],{"className":47227},[655,656,657,658],[363,47229,45101],{"className":47230,"style":45131},[407,408,658],[363,47232,666],{"className":47233},[665],[363,47235,47237],{"className":47236},[638],[363,47238,47240],{"className":47239,"style":8315},[642],[363,47241],{},[363,47243,461],{"className":47244},[494],[363,47246,554],{"className":47247,"style":682},[407,408],[363,47249,558],{"className":47250},[407],[363,47252,561],{"className":47253},[407,408],[363,47255,468],{"className":47256},[501],[363,47258],{"className":47259,"style":506},[505],[363,47261,471],{"className":47262},[510],[363,47264],{"className":47265,"style":506},[505],[363,47267,47269,47273,47319,47322,47325,47328,47331,47334,47337,47340,47343,47400,47403,47443,47446,47449,47452,47455,47458,47461,47464],{"className":47268},[398],[363,47270],{"className":47271,"style":47272},[402],"height:1.5254em;vertical-align:-0.7754em;",[363,47274,47276,47279],{"className":47275},[407],[363,47277,547],{"className":47278,"style":625},[407,408],[363,47280,47282],{"className":47281},[629],[363,47283,47285,47311],{"className":47284},[633,634],[363,47286,47288,47308],{"className":47287},[638],[363,47289,47291],{"className":47290,"style":727},[642],[363,47292,47293,47296],{"style":646},[363,47294],{"className":47295,"style":651},[650],[363,47297,47299],{"className":47298},[655,656,657,658],[363,47300,47302,47305],{"className":47301},[407,658],[363,47303,11041],{"className":47304,"style":11129},[407,408,658],[363,47306,22240],{"className":47307},[407,408,658],[363,47309,666],{"className":47310},[665],[363,47312,47314],{"className":47313},[638],[363,47315,47317],{"className":47316,"style":8315},[642],[363,47318],{},[363,47320,461],{"className":47321},[494],[363,47323,554],{"className":47324,"style":682},[407,408],[363,47326,558],{"className":47327},[407],[363,47329,561],{"className":47330},[407,408],[363,47332,468],{"className":47333},[501],[363,47335,898],{"className":47336},[920],[363,47338],{"className":47339,"style":3981},[505],[363,47341],{"className":47342,"style":754},[505],[363,47344,47346],{"className":47345},[1831,14063],[363,47347,47349,47391],{"className":47348},[633,634],[363,47350,47352,47388],{"className":47351},[638],[363,47353,47355,47378],{"className":47354,"style":12944},[642],[363,47356,47357,47360],{"style":47158},[363,47358],{"className":47359,"style":809},[650],[363,47361,47363],{"className":47362},[655,656,657,658],[363,47364,47366,47369,47372,47375],{"className":47365},[407,658],[363,47367,45101],{"className":47368,"style":45131},[407,408,658],[363,47370,1376],{"className":47371},[510,658],[363,47373,5160],{"className":47374},[407,658],[363,47376,465],{"className":47377},[407,658],[363,47379,47380,47383],{"style":12210},[363,47381],{"className":47382,"style":809},[650],[363,47384,47385],{},[363,47386,47020],{"className":47387},[1831],[363,47389,666],{"className":47390},[665],[363,47392,47394],{"className":47393},[638],[363,47395,47398],{"className":47396,"style":47397},[642],"height:0.7754em;",[363,47399],{},[363,47401],{"className":47402,"style":754},[505],[363,47404,47406,47409],{"className":47405},[407],[363,47407,547],{"className":47408,"style":625},[407,408],[363,47410,47412],{"className":47411},[629],[363,47413,47415,47435],{"className":47414},[633,634],[363,47416,47418,47432],{"className":47417},[638],[363,47419,47421],{"className":47420,"style":45276},[642],[363,47422,47423,47426],{"style":646},[363,47424],{"className":47425,"style":651},[650],[363,47427,47429],{"className":47428},[655,656,657,658],[363,47430,45101],{"className":47431,"style":45131},[407,408,658],[363,47433,666],{"className":47434},[665],[363,47436,47438],{"className":47437},[638],[363,47439,47441],{"className":47440,"style":8315},[642],[363,47442],{},[363,47444,461],{"className":47445},[494],[363,47447,554],{"className":47448,"style":682},[407,408],[363,47450,558],{"className":47451},[407],[363,47453,561],{"className":47454},[407,408],[363,47456,468],{"className":47457},[501],[363,47459],{"className":47460,"style":506},[505],[363,47462,471],{"className":47463},[510],[363,47465],{"className":47466,"style":506},[505],[363,47468,47470,47473,47519,47522,47525,47528,47531,47534],{"className":47469},[398],[363,47471],{"className":47472,"style":487},[402],[363,47474,47476,47479],{"className":47475},[407],[363,47477,547],{"className":47478,"style":625},[407,408],[363,47480,47482],{"className":47481},[629],[363,47483,47485,47511],{"className":47484},[633,634],[363,47486,47488,47508],{"className":47487},[638],[363,47489,47491],{"className":47490,"style":727},[642],[363,47492,47493,47496],{"style":646},[363,47494],{"className":47495,"style":651},[650],[363,47497,47499],{"className":47498},[655,656,657,658],[363,47500,47502,47505],{"className":47501},[407,658],[363,47503,11041],{"className":47504,"style":11129},[407,408,658],[363,47506,22240],{"className":47507},[407,408,658],[363,47509,666],{"className":47510},[665],[363,47512,47514],{"className":47513},[638],[363,47515,47517],{"className":47516,"style":8315},[642],[363,47518],{},[363,47520,461],{"className":47521},[494],[363,47523,561],{"className":47524},[407,408],[363,47526,558],{"className":47527},[407],[363,47529,554],{"className":47530,"style":682},[407,408],[363,47532,468],{"className":47533},[501],[363,47535,4722],{"className":47536},[407],[11,47538,47539,47594,47595,3092,47668,47822,47823,9747],{},[1572,47540,47541,47542,47593],{},"推导 ",[363,47543,47545,47563],{"className":47544,"translate":367},[366],[363,47546,47548],{"className":47547},[371],[373,47549,47550],{"xmlns":375},[377,47551,47552,47560],{},[380,47553,47554,47556,47558],{},[383,47555,45101],{},[458,47557,1376],{},[463,47559,465],{},[387,47561,47562],{"encoding":389},"\\alpha\\to1",[363,47564,47566,47584],{"className":47565,"ariaHidden":394},[393],[363,47567,47569,47572,47575,47578,47581],{"className":47568},[398],[363,47570],{"className":47571,"style":2692},[402],[363,47573,45101],{"className":47574,"style":45131},[407,408],[363,47576],{"className":47577,"style":506},[505],[363,47579,1376],{"className":47580},[510],[363,47582],{"className":47583,"style":506},[505],[363,47585,47587,47590],{"className":47586},[398],[363,47588],{"className":47589,"style":520},[402],[363,47591,465],{"className":47592},[407]," 的极限。"," 令 ",[363,47596,47598,47620],{"className":47597,"translate":367},[366],[363,47599,47601],{"className":47600},[371],[373,47602,47603],{"xmlns":375},[377,47604,47605,47617],{},[380,47606,47607,47609,47611,47613,47615],{},[383,47608,45527],{},[458,47610,471],{},[463,47612,465],{},[458,47614,5160],{},[383,47616,16059],{},[387,47618,47619],{"encoding":389},"a=1-\\delta",[363,47621,47623,47641,47659],{"className":47622,"ariaHidden":394},[393],[363,47624,47626,47629,47632,47635,47638],{"className":47625},[398],[363,47627],{"className":47628,"style":2692},[402],[363,47630,45527],{"className":47631},[407,408],[363,47633],{"className":47634,"style":506},[505],[363,47636,471],{"className":47637},[510],[363,47639],{"className":47640,"style":506},[505],[363,47642,47644,47647,47650,47653,47656],{"className":47643},[398],[363,47645],{"className":47646,"style":12925},[402],[363,47648,465],{"className":47649},[407],[363,47651],{"className":47652,"style":2934},[505],[363,47654,5160],{"className":47655},[2938],[363,47657],{"className":47658,"style":2934},[505],[363,47660,47662,47665],{"className":47661},[398],[363,47663],{"className":47664,"style":12944},[402],[363,47666,16059],{"className":47667,"style":16108},[407,408],[363,47669,47671,47703],{"className":47670,"translate":367},[366],[363,47672,47674],{"className":47673},[371],[373,47675,47676],{"xmlns":375},[377,47677,47678,47700],{},[380,47679,47680,47682,47684,47696,47698],{},[383,47681,16059],{},[458,47683,471],{},[586,47685,47686,47694],{},[380,47687,47688,47690,47692],{},[463,47689,465],{},[458,47691,5160],{},[383,47693,45101],{},[463,47695,2810],{},[458,47697,1376],{},[463,47699,474],{},[387,47701,47702],{"encoding":389},"\\delta=\\frac{1-\\alpha}{2}\\to0",[363,47704,47706,47724,47813],{"className":47705,"ariaHidden":394},[393],[363,47707,47709,47712,47715,47718,47721],{"className":47708},[398],[363,47710],{"className":47711,"style":12944},[402],[363,47713,16059],{"className":47714,"style":16108},[407,408],[363,47716],{"className":47717,"style":506},[505],[363,47719,471],{"className":47720},[510],[363,47722],{"className":47723,"style":506},[505],[363,47725,47727,47730,47804,47807,47810],{"className":47726},[398],[363,47728],{"className":47729,"style":2852},[402],[363,47731,47733,47736,47801],{"className":47732},[407],[363,47734],{"className":47735},[494,789],[363,47737,47739],{"className":47738},[586],[363,47740,47742,47793],{"className":47741},[633,634],[363,47743,47745,47790],{"className":47744},[638],[363,47746,47748,47762,47770],{"className":47747,"style":2871},[642],[363,47749,47750,47753],{"style":2874},[363,47751],{"className":47752,"style":809},[650],[363,47754,47756],{"className":47755},[655,656,657,658],[363,47757,47759],{"className":47758},[407,658],[363,47760,2810],{"className":47761},[407,658],[363,47763,47764,47767],{"style":821},[363,47765],{"className":47766,"style":809},[650],[363,47768],{"className":47769,"style":829},[828],[363,47771,47772,47775],{"style":2897},[363,47773],{"className":47774,"style":809},[650],[363,47776,47778],{"className":47777},[655,656,657,658],[363,47779,47781,47784,47787],{"className":47780},[407,658],[363,47782,465],{"className":47783},[407,658],[363,47785,5160],{"className":47786},[2938,658],[363,47788,45101],{"className":47789,"style":45131},[407,408,658],[363,47791,666],{"className":47792},[665],[363,47794,47796],{"className":47795},[638],[363,47797,47799],{"className":47798,"style":2919},[642],[363,47800],{},[363,47802],{"className":47803},[501,789],[363,47805],{"className":47806,"style":506},[505],[363,47808,1376],{"className":47809},[510],[363,47811],{"className":47812,"style":506},[505],[363,47814,47816,47819],{"className":47815},[398],[363,47817],{"className":47818,"style":520},[402],[363,47820,474],{"className":47821},[407],"。用 ",[363,47824,47826,47892],{"className":47825,"translate":367},[366],[363,47827,47829],{"className":47828},[371],[373,47830,47831],{"xmlns":375},[377,47832,47833,47889],{},[380,47834,47835,47847,47849,47851,47853,47869,47871,47873,47875,47877,47879,47881,47883,47885,47887],{},[7161,47836,47837,47839],{},[383,47838,1121],{},[380,47840,47841,47843,47845],{},[463,47842,465],{},[458,47844,5160],{},[383,47846,16059],{},[458,47848,471],{},[383,47850,1121],{},[1644,47852,1646],{},[7161,47854,47855,47857],{},[383,47856,7914],{},[380,47858,47859,47861,47863,47865,47867],{},[458,47860,5160],{},[383,47862,16059],{},[383,47864,4447],{},[458,47866,4450],{},[383,47868,1121],{},[458,47870,33306],{},[383,47872,1121],{},[458,47874,461],{"stretchy":460},[463,47876,465],{},[458,47878,5160],{},[383,47880,16059],{},[383,47882,4447],{},[458,47884,4450],{},[383,47886,1121],{},[458,47888,468],{"stretchy":460},[387,47890,47891],{"encoding":389},"x^{1-\\delta}=x\\,e^{-\\delta\\log x}\\approx x(1-\\delta\\log x)",[363,47893,47895,47949,48028,48052],{"className":47894,"ariaHidden":394},[393],[363,47896,47898,47902,47940,47943,47946],{"className":47897},[398],[363,47899],{"className":47900,"style":47901},[402],"height:0.8491em;",[363,47903,47905,47908],{"className":47904},[407],[363,47906,1121],{"className":47907},[407,408],[363,47909,47911],{"className":47910},[629],[363,47912,47914],{"className":47913},[633],[363,47915,47917],{"className":47916},[638],[363,47918,47920],{"className":47919,"style":47901},[642],[363,47921,47922,47925],{"style":7212},[363,47923],{"className":47924,"style":651},[650],[363,47926,47928],{"className":47927},[655,656,657,658],[363,47929,47931,47934,47937],{"className":47930},[407,658],[363,47932,465],{"className":47933},[407,658],[363,47935,5160],{"className":47936},[2938,658],[363,47938,16059],{"className":47939,"style":16108},[407,408,658],[363,47941],{"className":47942,"style":506},[505],[363,47944,471],{"className":47945},[510],[363,47947],{"className":47948,"style":506},[505],[363,47950,47952,47955,47958,47961,48019,48022,48025],{"className":47951},[398],[363,47953],{"className":47954,"style":47901},[402],[363,47956,1121],{"className":47957},[407,408],[363,47959],{"className":47960,"style":754},[505],[363,47962,47964,47967],{"className":47963},[407],[363,47965,7914],{"className":47966},[407,408],[363,47968,47970],{"className":47969},[629],[363,47971,47973],{"className":47972},[633],[363,47974,47976],{"className":47975},[638],[363,47977,47979],{"className":47978,"style":47901},[642],[363,47980,47981,47984],{"style":7212},[363,47982],{"className":47983,"style":651},[650],[363,47985,47987],{"className":47986},[655,656,657,658],[363,47988,47990,47993,47996,47999,48013,48016],{"className":47989},[407,658],[363,47991,5160],{"className":47992},[407,658],[363,47994,16059],{"className":47995,"style":16108},[407,408,658],[363,47997],{"className":47998,"style":42713},[505,658],[363,48000,48002,48006,48010],{"className":48001},[1831,658],[363,48003,48005],{"className":48004},[658],"l",[363,48007,48009],{"className":48008},[658],"o",[363,48011,4505],{"className":48012,"style":4504},[658],[363,48014],{"className":48015,"style":42713},[505,658],[363,48017,1121],{"className":48018},[407,408,658],[363,48020],{"className":48021,"style":506},[505],[363,48023,33306],{"className":48024},[510],[363,48026],{"className":48027,"style":506},[505],[363,48029,48031,48034,48037,48040,48043,48046,48049],{"className":48030},[398],[363,48032],{"className":48033,"style":487},[402],[363,48035,1121],{"className":48036},[407,408],[363,48038,461],{"className":48039},[494],[363,48041,465],{"className":48042},[407],[363,48044],{"className":48045,"style":2934},[505],[363,48047,5160],{"className":48048},[2938],[363,48050],{"className":48051,"style":2934},[505],[363,48053,48055,48058,48061,48064,48069,48072,48075],{"className":48054},[398],[363,48056],{"className":48057,"style":487},[402],[363,48059,16059],{"className":48060,"style":16108},[407,408],[363,48062],{"className":48063,"style":754},[505],[363,48065,4501,48067],{"className":48066},[1831],[363,48068,4505],{"style":4504},[363,48070],{"className":48071,"style":754},[505],[363,48073,1121],{"className":48074},[407,408],[363,48076,468],{"className":48077},[501],[363,48079,48081],{"className":48080,"translate":367},[528],[363,48082,48084,48178],{"className":48083,"translate":367},[366],[363,48085,48087],{"className":48086},[371],[373,48088,48089],{"xmlns":375,"display":537},[377,48090,48091,48175],{},[380,48092,48093,48095,48107,48113,48115,48117,48119,48121,48123,48125,48127,48129,48131,48137,48139,48141,48143,48145,48147,48149,48151,48153,48163,48165,48167,48169,48171,48173],{},[458,48094,1634],{},[7161,48096,48097,48099],{},[383,48098,11],{},[380,48100,48101,48103,48105],{},[463,48102,465],{},[458,48104,5160],{},[383,48106,16059],{},[7161,48108,48109,48111],{},[383,48110,1291],{},[383,48112,16059],{},[458,48114,33306],{},[458,48116,1634],{},[383,48118,11],{},[458,48120,461],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[463,48122,465],{},[458,48124,5160],{},[383,48126,16059],{},[383,48128,4447],{},[458,48130,4450],{},[586,48132,48133,48135],{},[383,48134,11],{},[383,48136,1291],{},[458,48138,468],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[383,48140,592],{},[383,48142,1121],{},[458,48144,471],{},[463,48146,465],{},[458,48148,5160],{},[383,48150,16059],{},[1644,48152,1646],{},[543,48154,48155,48157],{},[383,48156,547],{},[380,48158,48159,48161],{},[383,48160,11041],{},[383,48162,22240],{},[458,48164,461],{"stretchy":460},[383,48166,554],{},[383,48168,558],{"mathvariant":557},[383,48170,561],{},[458,48172,468],{"stretchy":460},[458,48174,898],{"separator":394},[387,48176,48177],{"encoding":389},"\\int p^{1-\\delta}q^{\\delta}\n\\approx\\int p\\Big(1-\\delta\\log\\frac{p}{q}\\Big)dx\n=1-\\delta\\,D_{KL}(P\\|Q),",[363,48179,48181,48273,48306,48410,48428],{"className":48180,"ariaHidden":394},[393],[363,48182,48184,48187,48190,48193,48232,48264,48267,48270],{"className":48183},[398],[363,48185],{"className":48186,"style":6124},[402],[363,48188,1634],{"className":48189,"style":1834},[1831,1832,1833],[363,48191],{"className":48192,"style":754},[505],[363,48194,48196,48199],{"className":48195},[407],[363,48197,11],{"className":48198},[407,408],[363,48200,48202],{"className":48201},[629],[363,48203,48205],{"className":48204},[633],[363,48206,48208],{"className":48207},[638],[363,48209,48212],{"className":48210,"style":48211},[642],"height:0.8991em;",[363,48213,48214,48217],{"style":8624},[363,48215],{"className":48216,"style":651},[650],[363,48218,48220],{"className":48219},[655,656,657,658],[363,48221,48223,48226,48229],{"className":48222},[407,658],[363,48224,465],{"className":48225},[407,658],[363,48227,5160],{"className":48228},[2938,658],[363,48230,16059],{"className":48231,"style":16108},[407,408,658],[363,48233,48235,48238],{"className":48234},[407],[363,48236,1291],{"className":48237,"style":1328},[407,408],[363,48239,48241],{"className":48240},[629],[363,48242,48244],{"className":48243},[633],[363,48245,48247],{"className":48246},[638],[363,48248,48250],{"className":48249,"style":48211},[642],[363,48251,48252,48255],{"style":8624},[363,48253],{"className":48254,"style":651},[650],[363,48256,48258],{"className":48257},[655,656,657,658],[363,48259,48261],{"className":48260},[407,658],[363,48262,16059],{"className":48263,"style":16108},[407,408,658],[363,48265],{"className":48266,"style":506},[505],[363,48268,33306],{"className":48269},[510],[363,48271],{"className":48272,"style":506},[505],[363,48274,48276,48279,48282,48285,48288,48294,48297,48300,48303],{"className":48275},[398],[363,48277],{"className":48278,"style":6124},[402],[363,48280,1634],{"className":48281,"style":1834},[1831,1832,1833],[363,48283],{"className":48284,"style":754},[505],[363,48286,11],{"className":48287},[407,408],[363,48289,48291],{"className":48290},[407],[363,48292,461],{"className":48293},[767,4067],[363,48295,465],{"className":48296},[407],[363,48298],{"className":48299,"style":2934},[505],[363,48301,5160],{"className":48302},[2938],[363,48304],{"className":48305,"style":2934},[505],[363,48307,48309,48313,48316,48319,48324,48327,48389,48395,48398,48401,48404,48407],{"className":48308},[398],[363,48310],{"className":48311,"style":48312},[402],"height:2.0304em;vertical-align:-0.8804em;",[363,48314,16059],{"className":48315,"style":16108},[407,408],[363,48317],{"className":48318,"style":754},[505],[363,48320,4501,48322],{"className":48321},[1831],[363,48323,4505],{"style":4504},[363,48325],{"className":48326,"style":754},[505],[363,48328,48330,48333,48386],{"className":48329},[407],[363,48331],{"className":48332},[494,789],[363,48334,48336],{"className":48335},[586],[363,48337,48339,48378],{"className":48338},[633,634],[363,48340,48342,48375],{"className":48341},[638],[363,48343,48345,48356,48364],{"className":48344,"style":3901},[642],[363,48346,48347,48350],{"style":805},[363,48348],{"className":48349,"style":809},[650],[363,48351,48353],{"className":48352},[407],[363,48354,1291],{"className":48355,"style":1328},[407,408],[363,48357,48358,48361],{"style":821},[363,48359],{"className":48360,"style":809},[650],[363,48362],{"className":48363,"style":829},[828],[363,48365,48366,48369],{"style":832},[363,48367],{"className":48368,"style":809},[650],[363,48370,48372],{"className":48371},[407],[363,48373,11],{"className":48374},[407,408],[363,48376,666],{"className":48377},[665],[363,48379,48381],{"className":48380},[638],[363,48382,48384],{"className":48383,"style":854},[642],[363,48385],{},[363,48387],{"className":48388},[501,789],[363,48390,48392],{"className":48391},[407],[363,48393,468],{"className":48394},[767,4067],[363,48396,592],{"className":48397},[407,408],[363,48399,1121],{"className":48400},[407,408],[363,48402],{"className":48403,"style":506},[505],[363,48405,471],{"className":48406},[510],[363,48408],{"className":48409,"style":506},[505],[363,48411,48413,48416,48419,48422,48425],{"className":48412},[398],[363,48414],{"className":48415,"style":12925},[402],[363,48417,465],{"className":48418},[407],[363,48420],{"className":48421,"style":2934},[505],[363,48423,5160],{"className":48424},[2938],[363,48426],{"className":48427,"style":2934},[505],[363,48429,48431,48434,48437,48440,48486,48489,48492,48495,48498,48501],{"className":48430},[398],[363,48432],{"className":48433,"style":487},[402],[363,48435,16059],{"className":48436,"style":16108},[407,408],[363,48438],{"className":48439,"style":754},[505],[363,48441,48443,48446],{"className":48442},[407],[363,48444,547],{"className":48445,"style":625},[407,408],[363,48447,48449],{"className":48448},[629],[363,48450,48452,48478],{"className":48451},[633,634],[363,48453,48455,48475],{"className":48454},[638],[363,48456,48458],{"className":48457,"style":727},[642],[363,48459,48460,48463],{"style":646},[363,48461],{"className":48462,"style":651},[650],[363,48464,48466],{"className":48465},[655,656,657,658],[363,48467,48469,48472],{"className":48468},[407,658],[363,48470,11041],{"className":48471,"style":11129},[407,408,658],[363,48473,22240],{"className":48474},[407,408,658],[363,48476,666],{"className":48477},[665],[363,48479,48481],{"className":48480},[638],[363,48482,48484],{"className":48483,"style":8315},[642],[363,48485],{},[363,48487,461],{"className":48488},[494],[363,48490,554],{"className":48491,"style":682},[407,408],[363,48493,558],{"className":48494},[407],[363,48496,561],{"className":48497},[407,408],[363,48499,468],{"className":48500},[501],[363,48502,898],{"className":48503},[920],[11,48505,48506],{},"于是",[363,48508,48510],{"className":48509,"translate":367},[528],[363,48511,48513,48714],{"className":48512,"translate":367},[366],[363,48514,48516],{"className":48515},[371],[373,48517,48518],{"xmlns":375,"display":537},[377,48519,48520,48711],{},[1590,48521,48522,48588,48648],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,48523,48524,48534],{},[1599,48525,48526],{},[1602,48527,48528],{"scriptlevel":474,"displaystyle":394},[543,48529,48530,48532],{},[383,48531,547],{},[383,48533,45101],{},[1599,48535,48536],{},[1602,48537,48538],{"scriptlevel":474,"displaystyle":394},[380,48539,48540,48542,48544,48562,48564,48566,48576,48578,48580,48582,48584,48586],{},[380,48541],{},[458,48543,471],{},[586,48545,48546,48548],{},[463,48547,465],{},[380,48549,48550,48552,48554,48556,48558,48560],{},[383,48551,45527],{},[458,48553,461],{"stretchy":460},[463,48555,465],{},[458,48557,5160],{},[383,48559,45527],{},[458,48561,468],{"stretchy":460},[458,48563,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,48565,16059],{},[543,48567,48568,48570],{},[383,48569,547],{},[380,48571,48572,48574],{},[383,48573,11041],{},[383,48575,22240],{},[458,48577,461],{"stretchy":460},[383,48579,554],{},[383,48581,558],{"mathvariant":557},[383,48583,561],{},[458,48585,468],{"stretchy":460},[458,48587,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[1596,48589,48590,48596],{},[1599,48591,48592],{},[1602,48593,48594],{"scriptlevel":474,"displaystyle":394},[380,48595],{},[1599,48597,48598],{},[1602,48599,48600],{"scriptlevel":474,"displaystyle":394},[380,48601,48602,48604,48606,48624,48626,48628,48638,48640,48642,48644,48646],{},[380,48603],{},[458,48605,471],{},[586,48607,48608,48610],{},[463,48609,465],{},[380,48611,48612,48614,48616,48618,48620,48622],{},[458,48613,461],{"stretchy":460},[463,48615,465],{},[458,48617,5160],{},[383,48619,16059],{},[458,48621,468],{"stretchy":460},[383,48623,16059],{},[458,48625,3646],{},[383,48627,16059],{},[543,48629,48630,48632],{},[383,48631,547],{},[380,48633,48634,48636],{},[383,48635,11041],{},[383,48637,22240],{},[458,48639,461],{"stretchy":460},[383,48641,554],{},[383,48643,558],{"mathvariant":557},[383,48645,561],{},[458,48647,468],{"stretchy":460},[1596,48649,48650,48656],{},[1599,48651,48652],{},[1602,48653,48654],{"scriptlevel":474,"displaystyle":394},[380,48655],{},[1599,48657,48658],{},[1602,48659,48660],{"scriptlevel":474,"displaystyle":394},[380,48661,48662,48664,48666,48689,48699,48701,48703,48705,48707,48709],{},[380,48663],{},[505,48665],{"width":3609},[48667,48668,48669,48672,48685],"munderover",{},[458,48670,1376],{"stretchy":394,"minsize":48671},"3.0em",[48673,48674,48677],"mpadded",{"width":48675,"lspace":48676},"+0.6em","0.3em",[380,48678,48679,48681,48683],{},[383,48680,16059],{},[458,48682,1376],{},[463,48684,474],{},[48673,48686,48687],{"width":48675,"lspace":48676},[380,48688],{},[543,48690,48691,48693],{},[383,48692,547],{},[380,48694,48695,48697],{},[383,48696,11041],{},[383,48698,22240],{},[458,48700,461],{"stretchy":460},[383,48702,554],{},[383,48704,558],{"mathvariant":557},[383,48706,561],{},[458,48708,468],{"stretchy":460},[383,48710,4722],{"mathvariant":557},[387,48712,48713],{"encoding":389},"\\begin{aligned}\nD_\\alpha\n&=\\frac{1}{a(1-a)}\n\\big(\\delta D_{KL}(P\\|Q)\\big)\\\\[2pt]\n&=\\frac{1}{(1-\\delta)\\delta}\n\\cdot\\delta D_{KL}(P\\|Q)\\\\\n&\\qquad\\xrightarrow[\\delta\\to0]{}D_{KL}(P\\|Q).\n\\end{aligned}",[363,48715,48717],{"className":48716,"ariaHidden":394},[393],[363,48718,48720,48724],{"className":48719},[398],[363,48721],{"className":48722,"style":48723},[402],"height:6.563em;vertical-align:-3.0315em;",[363,48725,48727],{"className":48726},[407],[363,48728,48730,48822],{"className":48729},[1590],[363,48731,48733],{"className":48732},[1707],[363,48734,48736,48813],{"className":48735},[633,634],[363,48737,48739,48810],{"className":48738},[638],[363,48740,48743,48792,48801],{"className":48741,"style":48742},[642],"height:3.5315em;",[363,48744,48746,48749],{"style":48745},"top:-5.5315em;",[363,48747],{"className":48748,"style":23013},[650],[363,48750,48752],{"className":48751},[407],[363,48753,48755,48758],{"className":48754},[407],[363,48756,547],{"className":48757,"style":625},[407,408],[363,48759,48761],{"className":48760},[629],[363,48762,48764,48784],{"className":48763},[633,634],[363,48765,48767,48781],{"className":48766},[638],[363,48768,48770],{"className":48769,"style":45276},[642],[363,48771,48772,48775],{"style":646},[363,48773],{"className":48774,"style":651},[650],[363,48776,48778],{"className":48777},[655,656,657,658],[363,48779,45101],{"className":48780,"style":45131},[407,408,658],[363,48782,666],{"className":48783},[665],[363,48785,48787],{"className":48786},[638],[363,48788,48790],{"className":48789,"style":8315},[642],[363,48791],{},[363,48793,48795,48798],{"style":48794},"top:-2.9741em;",[363,48796],{"className":48797,"style":23013},[650],[363,48799],{"className":48800},[407],[363,48802,48804,48807],{"style":48803},"top:-0.8981em;",[363,48805],{"className":48806,"style":23013},[650],[363,48808],{"className":48809},[407],[363,48811,666],{"className":48812},[665],[363,48814,48816],{"className":48815},[638],[363,48817,48820],{"className":48818,"style":48819},[642],"height:3.0315em;",[363,48821],{},[363,48823,48825],{"className":48824},[1798],[363,48826,48828,49354],{"className":48827},[633,634],[363,48829,48831,49351],{"className":48830},[638],[363,48832,48834,49013,49189],{"className":48833,"style":48742},[642],[363,48835,48836,48839],{"style":48745},[363,48837],{"className":48838,"style":23013},[650],[363,48840,48842,48845,48848,48851,48854,48937,48943,48946,48992,48995,48998,49001,49004,49007],{"className":48841},[407],[363,48843],{"className":48844},[407],[363,48846],{"className":48847,"style":506},[505],[363,48849,471],{"className":48850},[510],[363,48852],{"className":48853,"style":506},[505],[363,48855,48857,48860,48934],{"className":48856},[407],[363,48858],{"className":48859},[494,789],[363,48861,48863],{"className":48862},[586],[363,48864,48866,48926],{"className":48865},[633,634],[363,48867,48869,48923],{"className":48868},[638],[363,48870,48872,48904,48912],{"className":48871,"style":23236},[642],[363,48873,48874,48877],{"style":805},[363,48875],{"className":48876,"style":809},[650],[363,48878,48880,48883,48886,48889,48892,48895,48898,48901],{"className":48879},[407],[363,48881,45527],{"className":48882},[407,408],[363,48884,461],{"className":48885},[494],[363,48887,465],{"className":48888},[407],[363,48890],{"className":48891,"style":2934},[505],[363,48893,5160],{"className":48894},[2938],[363,48896],{"className":48897,"style":2934},[505],[363,48899,45527],{"className":48900},[407,408],[363,48902,468],{"className":48903},[501],[363,48905,48906,48909],{"style":821},[363,48907],{"className":48908,"style":809},[650],[363,48910],{"className":48911,"style":829},[828],[363,48913,48914,48917],{"style":832},[363,48915],{"className":48916,"style":809},[650],[363,48918,48920],{"className":48919},[407],[363,48921,465],{"className":48922},[407],[363,48924,666],{"className":48925},[665],[363,48927,48929],{"className":48928},[638],[363,48930,48932],{"className":48931,"style":1948},[642],[363,48933],{},[363,48935],{"className":48936},[501,789],[363,48938,48940],{"className":48939},[407],[363,48941,461],{"className":48942},[767,10021],[363,48944,16059],{"className":48945,"style":16108},[407,408],[363,48947,48949,48952],{"className":48948},[407],[363,48950,547],{"className":48951,"style":625},[407,408],[363,48953,48955],{"className":48954},[629],[363,48956,48958,48984],{"className":48957},[633,634],[363,48959,48961,48981],{"className":48960},[638],[363,48962,48964],{"className":48963,"style":727},[642],[363,48965,48966,48969],{"style":646},[363,48967],{"className":48968,"style":651},[650],[363,48970,48972],{"className":48971},[655,656,657,658],[363,48973,48975,48978],{"className":48974},[407,658],[363,48976,11041],{"className":48977,"style":11129},[407,408,658],[363,48979,22240],{"className":48980},[407,408,658],[363,48982,666],{"className":48983},[665],[363,48985,48987],{"className":48986},[638],[363,48988,48990],{"className":48989,"style":8315},[642],[363,48991],{},[363,48993,461],{"className":48994},[494],[363,48996,554],{"className":48997,"style":682},[407,408],[363,48999,558],{"className":49000},[407],[363,49002,561],{"className":49003},[407,408],[363,49005,468],{"className":49006},[501],[363,49008,49010],{"className":49009},[407],[363,49011,468],{"className":49012},[767,10021],[363,49014,49015,49018],{"style":48794},[363,49016],{"className":49017,"style":23013},[650],[363,49019,49021,49024,49027,49030,49033,49116,49119,49122,49125,49128,49174,49177,49180,49183,49186],{"className":49020},[407],[363,49022],{"className":49023},[407],[363,49025],{"className":49026,"style":506},[505],[363,49028,471],{"className":49029},[510],[363,49031],{"className":49032,"style":506},[505],[363,49034,49036,49039,49113],{"className":49035},[407],[363,49037],{"className":49038},[494,789],[363,49040,49042],{"className":49041},[586],[363,49043,49045,49105],{"className":49044},[633,634],[363,49046,49048,49102],{"className":49047},[638],[363,49049,49051,49083,49091],{"className":49050,"style":23236},[642],[363,49052,49053,49056],{"style":805},[363,49054],{"className":49055,"style":809},[650],[363,49057,49059,49062,49065,49068,49071,49074,49077,49080],{"className":49058},[407],[363,49060,461],{"className":49061},[494],[363,49063,465],{"className":49064},[407],[363,49066],{"className":49067,"style":2934},[505],[363,49069,5160],{"className":49070},[2938],[363,49072],{"className":49073,"style":2934},[505],[363,49075,16059],{"className":49076,"style":16108},[407,408],[363,49078,468],{"className":49079},[501],[363,49081,16059],{"className":49082,"style":16108},[407,408],[363,49084,49085,49088],{"style":821},[363,49086],{"className":49087,"style":809},[650],[363,49089],{"className":49090,"style":829},[828],[363,49092,49093,49096],{"style":832},[363,49094],{"className":49095,"style":809},[650],[363,49097,49099],{"className":49098},[407],[363,49100,465],{"className":49101},[407],[363,49103,666],{"className":49104},[665],[363,49106,49108],{"className":49107},[638],[363,49109,49111],{"className":49110,"style":1948},[642],[363,49112],{},[363,49114],{"className":49115},[501,789],[363,49117],{"className":49118,"style":2934},[505],[363,49120,3646],{"className":49121},[2938],[363,49123],{"className":49124,"style":2934},[505],[363,49126,16059],{"className":49127,"style":16108},[407,408],[363,49129,49131,49134],{"className":49130},[407],[363,49132,547],{"className":49133,"style":625},[407,408],[363,49135,49137],{"className":49136},[629],[363,49138,49140,49166],{"className":49139},[633,634],[363,49141,49143,49163],{"className":49142},[638],[363,49144,49146],{"className":49145,"style":727},[642],[363,49147,49148,49151],{"style":646},[363,49149],{"className":49150,"style":651},[650],[363,49152,49154],{"className":49153},[655,656,657,658],[363,49155,49157,49160],{"className":49156},[407,658],[363,49158,11041],{"className":49159,"style":11129},[407,408,658],[363,49161,22240],{"className":49162},[407,408,658],[363,49164,666],{"className":49165},[665],[363,49167,49169],{"className":49168},[638],[363,49170,49172],{"className":49171,"style":8315},[642],[363,49173],{},[363,49175,461],{"className":49176},[494],[363,49178,554],{"className":49179,"style":682},[407,408],[363,49181,558],{"className":49182},[407],[363,49184,561],{"className":49185},[407,408],[363,49187,468],{"className":49188},[501],[363,49190,49191,49194],{"style":48803},[363,49192],{"className":49193,"style":23013},[650],[363,49195,49197,49200,49203,49206,49284,49287,49333,49336,49339,49342,49345,49348],{"className":49196},[407],[363,49198],{"className":49199},[407],[363,49201],{"className":49202,"style":3981},[505],[363,49204],{"className":49205,"style":506},[505],[363,49207,49210],{"className":49208},[510,49209],"x-arrow",[363,49211,49213,49275],{"className":49212},[633,634],[363,49214,49216,49272],{"className":49215},[638],[363,49217,49220,49233,49251],{"className":49218,"style":49219},[642],"height:0.622em;",[363,49221,49223,49226],{"style":49222},"top:-3.322em;",[363,49224],{"className":49225,"style":651},[650],[363,49227,49230],{"className":49228},[655,656,657,658,49229],"x-arrow-pad",[363,49231],{"className":49232},[407,658],[363,49234,49237,49240],{"className":49235,"style":49236},[6654],"top:-2.689em;",[363,49238],{"className":49239,"style":651},[650],[363,49241,49244],{"className":49242,"style":49243},[34790],"height:0.522em;min-width:1.469em;",[6670,49245,49248],{"xmlns":6672,"width":6673,"height":49246,"viewBox":49247,"preserveAspectRatio":6697},"0.522em","0 0 400000 522",[6678,49249],{"d":49250},"M0 241v40h399891c-47.3 35.3-84 78-110 128\n-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20\n 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7\n 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85\n-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5\n-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67\n 151.7 139 205zm0 0v40h399900v-40z",[363,49252,49254,49257],{"style":49253},"top:-2.0919em;",[363,49255],{"className":49256,"style":651},[650],[363,49258,49260],{"className":49259},[655,656,657,658,49229],[363,49261,49263,49266,49269],{"className":49262},[407,658],[363,49264,16059],{"className":49265,"style":16108},[407,408,658],[363,49267,1376],{"className":49268},[510,658],[363,49270,474],{"className":49271},[407,658],[363,49273,666],{"className":49274},[665],[363,49276,49278],{"className":49277},[638],[363,49279,49282],{"className":49280,"style":49281},[642],"height:0.6081em;",[363,49283],{},[363,49285],{"className":49286,"style":506},[505],[363,49288,49290,49293],{"className":49289},[407],[363,49291,547],{"className":49292,"style":625},[407,408],[363,49294,49296],{"className":49295},[629],[363,49297,49299,49325],{"className":49298},[633,634],[363,49300,49302,49322],{"className":49301},[638],[363,49303,49305],{"className":49304,"style":727},[642],[363,49306,49307,49310],{"style":646},[363,49308],{"className":49309,"style":651},[650],[363,49311,49313],{"className":49312},[655,656,657,658],[363,49314,49316,49319],{"className":49315},[407,658],[363,49317,11041],{"className":49318,"style":11129},[407,408,658],[363,49320,22240],{"className":49321},[407,408,658],[363,49323,666],{"className":49324},[665],[363,49326,49328],{"className":49327},[638],[363,49329,49331],{"className":49330,"style":8315},[642],[363,49332],{},[363,49334,461],{"className":49335},[494],[363,49337,554],{"className":49338,"style":682},[407,408],[363,49340,558],{"className":49341},[407],[363,49343,561],{"className":49344},[407,408],[363,49346,468],{"className":49347},[501],[363,49349,4722],{"className":49350},[407],[363,49352,666],{"className":49353},[665],[363,49355,49357],{"className":49356},[638],[363,49358,49360],{"className":49359,"style":48819},[642],[363,49361],{},[11,49363,49364,49420,49421,49450],{},[363,49365,49367,49387],{"className":49366,"translate":367},[366],[363,49368,49370],{"className":49369},[371],[373,49371,49372],{"xmlns":375},[377,49373,49374,49384],{},[380,49375,49376,49378,49380,49382],{},[383,49377,45101],{},[458,49379,1376],{},[458,49381,5160],{},[463,49383,465],{},[387,49385,49386],{"encoding":389},"\\alpha\\to-1",[363,49388,49390,49408],{"className":49389,"ariaHidden":394},[393],[363,49391,49393,49396,49399,49402,49405],{"className":49392},[398],[363,49394],{"className":49395,"style":2692},[402],[363,49397,45101],{"className":49398,"style":45131},[407,408],[363,49400],{"className":49401,"style":506},[505],[363,49403,1376],{"className":49404},[510],[363,49406],{"className":49407,"style":506},[505],[363,49409,49411,49414,49417],{"className":49410},[398],[363,49412],{"className":49413,"style":12925},[402],[363,49415,5160],{"className":49416},[407],[363,49418,465],{"className":49419},[407]," 对称地给出反向 KL。所以 α-散度把 KL（两个方向）与 Hellinger 连成一条曲线，",[363,49422,49424,49438],{"className":49423,"translate":367},[366],[363,49425,49427],{"className":49426},[371],[373,49428,49429],{"xmlns":375},[377,49430,49431,49435],{},[380,49432,49433],{},[383,49434,45101],{},[387,49436,49437],{"encoding":389},"\\alpha",[363,49439,49441],{"className":49440,"ariaHidden":394},[393],[363,49442,49444,49447],{"className":49443},[398],[363,49445],{"className":49446,"style":2692},[402],[363,49448,45101],{"className":49449,"style":45131},[407,408]," 是「在对称与不对称之间连续插值」的旋钮。",[11,49452,49453,49455,49456,49484,49485,49519,49520,49548,49549,49599,49600,49603,49604,49632,49633,49661,49662,49690,49691,49719],{},[1572,49454,24540],{}," α-散度的价值在于它把「方向」与「强度」一并参数化：",[363,49457,49459,49472],{"className":49458,"translate":367},[366],[363,49460,49462],{"className":49461},[371],[373,49463,49464],{"xmlns":375},[377,49465,49466,49470],{},[380,49467,49468],{},[383,49469,45101],{},[387,49471,49437],{"encoding":389},[363,49473,49475],{"className":49474,"ariaHidden":394},[393],[363,49476,49478,49481],{"className":49477},[398],[363,49479],{"className":49480,"style":2692},[402],[363,49482,45101],{"className":49483,"style":45131},[407,408]," 从 ",[363,49486,49488,49504],{"className":49487,"translate":367},[366],[363,49489,49491],{"className":49490},[371],[373,49492,49493],{"xmlns":375},[377,49494,49495,49501],{},[380,49496,49497,49499],{},[458,49498,5160],{},[463,49500,465],{},[387,49502,49503],{"encoding":389},"-1",[363,49505,49507],{"className":49506,"ariaHidden":394},[393],[363,49508,49510,49513,49516],{"className":49509},[398],[363,49511],{"className":49512,"style":12925},[402],[363,49514,5160],{"className":49515},[407],[363,49517,465],{"className":49518},[407]," 扫到 ",[363,49521,49523,49536],{"className":49522,"translate":367},[366],[363,49524,49526],{"className":49525},[371],[373,49527,49528],{"xmlns":375},[377,49529,49530,49534],{},[380,49531,49532],{},[463,49533,465],{},[387,49535,465],{"encoding":389},[363,49537,49539],{"className":49538,"ariaHidden":394},[393],[363,49540,49542,49545],{"className":49541},[398],[363,49543],{"className":49544,"style":520},[402],[363,49546,465],{"className":49547},[407]," 时，散度由反向 KL（mode-seeking）连续过渡到正向 KL（mass-covering），中间在 ",[363,49550,49552,49569],{"className":49551,"translate":367},[366],[363,49553,49555],{"className":49554},[371],[373,49556,49557],{"xmlns":375},[377,49558,49559,49567],{},[380,49560,49561,49563,49565],{},[383,49562,45101],{},[458,49564,471],{},[463,49566,474],{},[387,49568,46835],{"encoding":389},[363,49570,49572,49590],{"className":49571,"ariaHidden":394},[393],[363,49573,49575,49578,49581,49584,49587],{"className":49574},[398],[363,49576],{"className":49577,"style":2692},[402],[363,49579,45101],{"className":49580,"style":45131},[407,408],[363,49582],{"className":49583,"style":506},[505],[363,49585,471],{"className":49586},[510],[363,49588],{"className":49589,"style":506},[505],[363,49591,49593,49596],{"className":49592},[398],[363,49594],{"className":49595,"style":520},[402],[363,49597,474],{"className":49598},[407]," 处恰好经过 Hellinger 这个对称点。在 Amari 的",[1572,49601,49602],{},"信息几何","里，α-族是唯一同时拥有 ",[363,49605,49607,49620],{"className":49606,"translate":367},[366],[363,49608,49610],{"className":49609},[371],[373,49611,49612],{"xmlns":375},[377,49613,49614,49618],{},[380,49615,49616],{},[383,49617,45101],{},[387,49619,49437],{"encoding":389},[363,49621,49623],{"className":49622,"ariaHidden":394},[393],[363,49624,49626,49629],{"className":49625},[398],[363,49627],{"className":49628,"style":2692},[402],[363,49630,45101],{"className":49631,"style":45131},[407,408],"-对偶平坦结构的单参数散度族：它诱导的度量是 Fisher 度量，诱导的仿射联络是 ",[363,49634,49636,49649],{"className":49635,"translate":367},[366],[363,49637,49639],{"className":49638},[371],[373,49640,49641],{"xmlns":375},[377,49642,49643,49647],{},[380,49644,49645],{},[383,49646,45101],{},[387,49648,49437],{"encoding":389},[363,49650,49652],{"className":49651,"ariaHidden":394},[393],[363,49653,49655,49658],{"className":49654},[398],[363,49656],{"className":49657,"style":2692},[402],[363,49659,45101],{"className":49660,"style":45131},[407,408],"-联络，这正是它被称为「散度范本」的原因。在机器学习中，",[363,49663,49665,49678],{"className":49664,"translate":367},[366],[363,49666,49668],{"className":49667},[371],[373,49669,49670],{"xmlns":375},[377,49671,49672,49676],{},[380,49673,49674],{},[383,49675,45101],{},[387,49677,49437],{"encoding":389},[363,49679,49681],{"className":49680,"ariaHidden":394},[393],[363,49682,49684,49687],{"className":49683},[398],[363,49685],{"className":49686,"style":2692},[402],[363,49688,45101],{"className":49689,"style":45131},[407,408],"-GAN 与 ",[363,49692,49694,49707],{"className":49693,"translate":367},[366],[363,49695,49697],{"className":49696},[371],[373,49698,49699],{"xmlns":375},[377,49700,49701,49705],{},[380,49702,49703],{},[383,49704,45101],{},[387,49706,49437],{"encoding":389},[363,49708,49710],{"className":49709,"ariaHidden":394},[393],[363,49711,49713,49716],{"className":49712},[398],[363,49714],{"className":49715,"style":2692},[402],[363,49717,45101],{"className":49718,"style":45131},[407,408],"-VI 用一个参数调节「对异常值的鲁棒性」与「模式覆盖」之间的取舍；在信号处理中它用于独立成分分析（ICA）与鲁棒估计。",[2658,49721,49723],{"id":49722},"_37-与-rényi-散度的关系","3.7 与 Rényi 散度的关系",[11,49725,49726],{},"Rényi 散度定义为",[363,49728,49730],{"className":49729,"translate":367},[528],[363,49731,49733,49861],{"className":49732,"translate":367},[366],[363,49734,49736],{"className":49735},[371],[373,49737,49738],{"xmlns":375,"display":537},[377,49739,49740,49858],{},[1590,49741,49742,49822],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,49743,49744,49768],{},[1599,49745,49746],{},[1602,49747,49748],{"scriptlevel":474,"displaystyle":394},[380,49749,49750,49758,49760,49762,49764,49766],{},[7900,49751,49752,49754,49756],{},[383,49753,547],{},[383,49755,45101],{},[383,49757,1379],{},[458,49759,461],{"stretchy":460},[383,49761,554],{},[383,49763,558],{"mathvariant":557},[383,49765,561],{},[458,49767,468],{"stretchy":460},[1599,49769,49770],{},[1602,49771,49772],{"scriptlevel":474,"displaystyle":394},[380,49773,49774,49776,49778,49790,49792,49794,49796,49802,49814,49816,49818,49820],{},[380,49775],{},[458,49777,471],{},[586,49779,49780,49782],{},[463,49781,465],{},[380,49783,49784,49786,49788],{},[383,49785,45101],{},[458,49787,5160],{},[463,49789,465],{},[383,49791,4447],{},[458,49793,4450],{},[458,49795,1634],{},[7161,49797,49798,49800],{},[383,49799,11],{},[383,49801,45101],{},[7161,49803,49804,49806],{},[383,49805,1291],{},[380,49807,49808,49810,49812],{},[463,49809,465],{},[458,49811,5160],{},[383,49813,45101],{},[1644,49815,1646],{},[383,49817,592],{},[383,49819,1121],{},[458,49821,898],{"separator":394},[1596,49823,49824,49830],{},[1599,49825,49826],{},[1602,49827,49828],{"scriptlevel":474,"displaystyle":394},[380,49829],{},[1599,49831,49832],{},[1602,49833,49834],{"scriptlevel":474,"displaystyle":394},[380,49835,49836,49838,49840,49842,49844,49846,49848,49850,49852,49855],{},[380,49837],{},[505,49839],{"width":3609},[383,49841,45101],{},[458,49843,3250],{},[463,49845,474],{},[458,49847,898],{"separator":394},[1644,49849,4630],{},[383,49851,45101],{},[458,49853,49854],{"mathvariant":557},"≠",[463,49856,49857],{},"1.",[387,49859,49860],{"encoding":389},"\\begin{aligned}\nD^{R}_{\\alpha}(P\\|Q)\n&=\\frac{1}{\\alpha-1}\n\\log\\int p^{\\alpha}q^{1-\\alpha}\\,dx,\\\\[2pt]\n&\\qquad \\alpha>0,\\ \\alpha\\ne1 .\n\\end{aligned}",[363,49862,49864],{"className":49863,"ariaHidden":394},[393],[363,49865,49867,49871],{"className":49866},[398],[363,49868],{"className":49869,"style":49870},[402],"height:3.7223em;vertical-align:-1.6111em;",[363,49872,49874],{"className":49873},[407],[363,49875,49877,49994],{"className":49876},[1590],[363,49878,49880],{"className":49879},[1707],[363,49881,49883,49985],{"className":49882},[633,634],[363,49884,49886,49982],{"className":49885},[638],[363,49887,49890,49973],{"className":49888,"style":49889},[642],"height:2.1111em;",[363,49891,49893,49896],{"style":49892},"top:-4.1111em;",[363,49894],{"className":49895,"style":6620},[650],[363,49897,49899,49958,49961,49964,49967,49970],{"className":49898},[407],[363,49900,49902,49905],{"className":49901},[407],[363,49903,547],{"className":49904,"style":625},[407,408],[363,49906,49908],{"className":49907},[629],[363,49909,49911,49950],{"className":49910},[633,634],[363,49912,49914,49947],{"className":49913},[638],[363,49915,49917,49932],{"className":49916,"style":38859},[642],[363,49918,49920,49923],{"style":49919},"top:-2.453em;margin-left:-0.0278em;margin-right:0.05em;",[363,49921],{"className":49922,"style":651},[650],[363,49924,49926],{"className":49925},[655,656,657,658],[363,49927,49929],{"className":49928},[407,658],[363,49930,45101],{"className":49931,"style":45131},[407,408,658],[363,49933,49934,49937],{"style":8624},[363,49935],{"className":49936,"style":651},[650],[363,49938,49940],{"className":49939},[655,656,657,658],[363,49941,49943],{"className":49942},[407,658],[363,49944,1379],{"className":49945,"style":49946},[407,408,658],"margin-right:0.0077em;",[363,49948,666],{"className":49949},[665],[363,49951,49953],{"className":49952},[638],[363,49954,49956],{"className":49955,"style":8646},[642],[363,49957],{},[363,49959,461],{"className":49960},[494],[363,49962,554],{"className":49963,"style":682},[407,408],[363,49965,558],{"className":49966},[407],[363,49968,561],{"className":49969},[407,408],[363,49971,468],{"className":49972},[501],[363,49974,49976,49979],{"style":49975},"top:-2.1089em;",[363,49977],{"className":49978,"style":6620},[650],[363,49980],{"className":49981},[407],[363,49983,666],{"className":49984},[665],[363,49986,49988],{"className":49987},[638],[363,49989,49992],{"className":49990,"style":49991},[642],"height:1.6111em;",[363,49993],{},[363,49995,49997],{"className":49996},[1798],[363,49998,50000,50288],{"className":49999},[633,634],[363,50001,50003,50285],{"className":50002},[638],[363,50004,50006,50199],{"className":50005,"style":49889},[642],[363,50007,50008,50011],{"style":49892},[363,50009],{"className":50010,"style":6620},[650],[363,50012,50014,50017,50020,50023,50026,50100,50103,50108,50111,50114,50117,50149,50187,50190,50193,50196],{"className":50013},[407],[363,50015],{"className":50016},[407],[363,50018],{"className":50019,"style":506},[505],[363,50021,471],{"className":50022},[510],[363,50024],{"className":50025,"style":506},[505],[363,50027,50029,50032,50097],{"className":50028},[407],[363,50030],{"className":50031},[494,789],[363,50033,50035],{"className":50034},[586],[363,50036,50038,50089],{"className":50037},[633,634],[363,50039,50041,50086],{"className":50040},[638],[363,50042,50044,50067,50075],{"className":50043,"style":23236},[642],[363,50045,50046,50049],{"style":805},[363,50047],{"className":50048,"style":809},[650],[363,50050,50052,50055,50058,50061,50064],{"className":50051},[407],[363,50053,45101],{"className":50054,"style":45131},[407,408],[363,50056],{"className":50057,"style":2934},[505],[363,50059,5160],{"className":50060},[2938],[363,50062],{"className":50063,"style":2934},[505],[363,50065,465],{"className":50066},[407],[363,50068,50069,50072],{"style":821},[363,50070],{"className":50071,"style":809},[650],[363,50073],{"className":50074,"style":829},[828],[363,50076,50077,50080],{"style":832},[363,50078],{"className":50079,"style":809},[650],[363,50081,50083],{"className":50082},[407],[363,50084,465],{"className":50085},[407],[363,50087,666],{"className":50088},[665],[363,50090,50092],{"className":50091},[638],[363,50093,50095],{"className":50094,"style":17362},[642],[363,50096],{},[363,50098],{"className":50099},[501,789],[363,50101],{"className":50102,"style":754},[505],[363,50104,4501,50106],{"className":50105},[1831],[363,50107,4505],{"style":4504},[363,50109],{"className":50110,"style":754},[505],[363,50112,1634],{"className":50113,"style":1834},[1831,1832,1833],[363,50115],{"className":50116,"style":754},[505],[363,50118,50120,50123],{"className":50119},[407],[363,50121,11],{"className":50122},[407,408],[363,50124,50126],{"className":50125},[629],[363,50127,50129],{"className":50128},[633],[363,50130,50132],{"className":50131},[638],[363,50133,50135],{"className":50134,"style":46258},[642],[363,50136,50137,50140],{"style":8624},[363,50138],{"className":50139,"style":651},[650],[363,50141,50143],{"className":50142},[655,656,657,658],[363,50144,50146],{"className":50145},[407,658],[363,50147,45101],{"className":50148,"style":45131},[407,408,658],[363,50150,50152,50155],{"className":50151},[407],[363,50153,1291],{"className":50154,"style":1328},[407,408],[363,50156,50158],{"className":50157},[629],[363,50159,50161],{"className":50160},[633],[363,50162,50164],{"className":50163},[638],[363,50165,50167],{"className":50166,"style":20082},[642],[363,50168,50169,50172],{"style":8624},[363,50170],{"className":50171,"style":651},[650],[363,50173,50175],{"className":50174},[655,656,657,658],[363,50176,50178,50181,50184],{"className":50177},[407,658],[363,50179,465],{"className":50180},[407,658],[363,50182,5160],{"className":50183},[2938,658],[363,50185,45101],{"className":50186,"style":45131},[407,408,658],[363,50188],{"className":50189,"style":754},[505],[363,50191,592],{"className":50192},[407,408],[363,50194,1121],{"className":50195},[407,408],[363,50197,898],{"className":50198},[920],[363,50200,50201,50204],{"style":49975},[363,50202],{"className":50203,"style":6620},[650],[363,50205,50207,50210,50213,50216,50219,50222,50225,50228,50231,50234,50237,50240,50243,50279,50282],{"className":50206},[407],[363,50208],{"className":50209},[407],[363,50211],{"className":50212,"style":3981},[505],[363,50214,45101],{"className":50215,"style":45131},[407,408],[363,50217],{"className":50218,"style":506},[505],[363,50220,3250],{"className":50221},[510],[363,50223],{"className":50224,"style":506},[505],[363,50226,474],{"className":50227},[407],[363,50229,898],{"className":50230},[920],[363,50232,4630],{"className":50233},[505],[363,50235],{"className":50236,"style":754},[505],[363,50238,45101],{"className":50239,"style":45131},[407,408],[363,50241],{"className":50242,"style":506},[505],[363,50244,50246,50273,50276],{"className":50245},[510],[363,50247,50249],{"className":50248},[510],[363,50250,50252],{"className":50251},[407,4747],[363,50253,50255],{"className":50254},[4751],[363,50256,50258,50261,50270],{"className":50257},[4755],[363,50259],{"className":50260,"style":403},[402],[363,50262,50264],{"className":50263},[4762],[363,50265,50267],{"className":50266},[407],[363,50268,4769],{"className":50269},[510],[363,50271],{"className":50272},[4773],[363,50274],{"className":50275},[505,4777],[363,50277,471],{"className":50278},[510],[363,50280],{"className":50281,"style":506},[505],[363,50283,49857],{"className":50284},[407],[363,50286,666],{"className":50287},[665],[363,50289,50291],{"className":50290},[638],[363,50292,50294],{"className":50293,"style":49991},[642],[363,50295],{},[11,50297,50298,50299,50331,50332,50383,50384,50560,50561,50762],{},"它不是（直接的）f-散度，因为 ",[363,50300,50302,50317],{"className":50301,"translate":367},[366],[363,50303,50305],{"className":50304},[371],[373,50306,50307],{"xmlns":375},[377,50308,50309,50315],{},[380,50310,50311,50313],{},[383,50312,4447],{},[458,50314,4450],{},[387,50316,21930],{"encoding":389},[363,50318,50320],{"className":50319,"ariaHidden":394},[393],[363,50321,50323,50326],{"className":50322},[398],[363,50324],{"className":50325,"style":403},[402],[363,50327,4501,50329],{"className":50328},[1831],[363,50330,4505],{"style":4504}," 包在积分外面（这正是它满足可乘可加性、但一般不满足数据处理不等式的根源：",[363,50333,50335,50353],{"className":50334,"translate":367},[366],[363,50336,50338],{"className":50337},[371],[373,50339,50340],{"xmlns":375},[377,50341,50342,50350],{},[380,50343,50344,50346,50348],{},[383,50345,45101],{},[458,50347,3250],{},[463,50349,465],{},[387,50351,50352],{"encoding":389},"\\alpha>1",[363,50354,50356,50374],{"className":50355,"ariaHidden":394},[393],[363,50357,50359,50362,50365,50368,50371],{"className":50358},[398],[363,50360],{"className":50361,"style":6271},[402],[363,50363,45101],{"className":50364,"style":45131},[407,408],[363,50366],{"className":50367,"style":506},[505],[363,50369,3250],{"className":50370},[510],[363,50372],{"className":50373,"style":506},[505],[363,50375,50377,50380],{"className":50376},[398],[363,50378],{"className":50379,"style":520},[402],[363,50381,465],{"className":50382},[407]," 的 Rényi 散度可以在随机变换下增大）。它与 α-散度是\"同一积分的两种包装\"：沿用 3.6 节的指数记号 ",[363,50385,50387,50426],{"className":50386,"translate":367},[366],[363,50388,50390],{"className":50389},[371],[373,50391,50392],{"xmlns":375},[377,50393,50394,50424],{},[380,50395,50396,50398,50400,50412,50414,50416,50418,50420,50422],{},[383,50397,45527],{},[458,50399,471],{},[586,50401,50402,50410],{},[380,50403,50404,50406,50408],{},[463,50405,465],{},[458,50407,2817],{},[383,50409,45101],{},[463,50411,2810],{},[458,50413,6256],{},[458,50415,461],{"stretchy":460},[463,50417,474],{},[458,50419,898],{"separator":394},[463,50421,465],{},[458,50423,468],{"stretchy":460},[387,50425,45556],{"encoding":389},[363,50427,50429,50447,50536],{"className":50428,"ariaHidden":394},[393],[363,50430,50432,50435,50438,50441,50444],{"className":50431},[398],[363,50433],{"className":50434,"style":2692},[402],[363,50436,45527],{"className":50437},[407,408],[363,50439],{"className":50440,"style":506},[505],[363,50442,471],{"className":50443},[510],[363,50445],{"className":50446,"style":506},[505],[363,50448,50450,50453,50527,50530,50533],{"className":50449},[398],[363,50451],{"className":50452,"style":2852},[402],[363,50454,50456,50459,50524],{"className":50455},[407],[363,50457],{"className":50458},[494,789],[363,50460,50462],{"className":50461},[586],[363,50463,50465,50516],{"className":50464},[633,634],[363,50466,50468,50513],{"className":50467},[638],[363,50469,50471,50485,50493],{"className":50470,"style":2871},[642],[363,50472,50473,50476],{"style":2874},[363,50474],{"className":50475,"style":809},[650],[363,50477,50479],{"className":50478},[655,656,657,658],[363,50480,50482],{"className":50481},[407,658],[363,50483,2810],{"className":50484},[407,658],[363,50486,50487,50490],{"style":821},[363,50488],{"className":50489,"style":809},[650],[363,50491],{"className":50492,"style":829},[828],[363,50494,50495,50498],{"style":2897},[363,50496],{"className":50497,"style":809},[650],[363,50499,50501],{"className":50500},[655,656,657,658],[363,50502,50504,50507,50510],{"className":50503},[407,658],[363,50505,465],{"className":50506},[407,658],[363,50508,2817],{"className":50509},[2938,658],[363,50511,45101],{"className":50512,"style":45131},[407,408,658],[363,50514,666],{"className":50515},[665],[363,50517,50519],{"className":50518},[638],[363,50520,50522],{"className":50521,"style":2919},[642],[363,50523],{},[363,50525],{"className":50526},[501,789],[363,50528],{"className":50529,"style":506},[505],[363,50531,6256],{"className":50532},[510],[363,50534],{"className":50535,"style":506},[505],[363,50537,50539,50542,50545,50548,50551,50554,50557],{"className":50538},[398],[363,50540],{"className":50541,"style":487},[402],[363,50543,461],{"className":50544},[494],[363,50546,474],{"className":50547},[407],[363,50549,898],{"className":50550},[920],[363,50552],{"className":50553,"style":754},[505],[363,50555,465],{"className":50556},[407],[363,50558,468],{"className":50559},[501],"， ",[363,50562,50564,50610],{"className":50563,"translate":367},[366],[363,50565,50567],{"className":50566},[371],[373,50568,50569],{"xmlns":375},[377,50570,50571,50607],{},[380,50572,50573,50579,50581,50583,50589,50601,50603,50605],{},[543,50574,50575,50577],{},[383,50576,33950],{},[383,50578,45527],{},[458,50580,471],{},[458,50582,1634],{},[7161,50584,50585,50587],{},[383,50586,11],{},[383,50588,45527],{},[7161,50590,50591,50593],{},[383,50592,1291],{},[380,50594,50595,50597,50599],{},[463,50596,465],{},[458,50598,5160],{},[383,50600,45527],{},[1644,50602,1646],{},[383,50604,592],{},[383,50606,1121],{},[387,50608,50609],{"encoding":389},"Z_a=\\int p^{a}q^{1-a}\\,dx",[363,50611,50613,50669],{"className":50612,"ariaHidden":394},[393],[363,50614,50616,50619,50660,50663,50666],{"className":50615},[398],[363,50617],{"className":50618,"style":16308},[402],[363,50620,50622,50625],{"className":50621},[407],[363,50623,33950],{"className":50624,"style":11129},[407,408],[363,50626,50628],{"className":50627},[629],[363,50629,50631,50652],{"className":50630},[633,634],[363,50632,50634,50649],{"className":50633},[638],[363,50635,50637],{"className":50636,"style":45276},[642],[363,50638,50640,50643],{"style":50639},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[363,50641],{"className":50642,"style":651},[650],[363,50644,50646],{"className":50645},[655,656,657,658],[363,50647,45527],{"className":50648},[407,408,658],[363,50650,666],{"className":50651},[665],[363,50653,50655],{"className":50654},[638],[363,50656,50658],{"className":50657,"style":8315},[642],[363,50659],{},[363,50661],{"className":50662,"style":506},[505],[363,50664,471],{"className":50665},[510],[363,50667],{"className":50668,"style":506},[505],[363,50670,50672,50676,50679,50682,50715,50753,50756,50759],{"className":50671},[398],[363,50673],{"className":50674,"style":50675},[402],"height:1.1202em;vertical-align:-0.3061em;",[363,50677,1634],{"className":50678,"style":5964},[1831,1832,5963],[363,50680],{"className":50681,"style":754},[505],[363,50683,50685,50688],{"className":50684},[407],[363,50686,11],{"className":50687},[407,408],[363,50689,50691],{"className":50690},[629],[363,50692,50694],{"className":50693},[633],[363,50695,50697],{"className":50696},[638],[363,50698,50701],{"className":50699,"style":50700},[642],"height:0.6644em;",[363,50702,50703,50706],{"style":7212},[363,50704],{"className":50705,"style":651},[650],[363,50707,50709],{"className":50708},[655,656,657,658],[363,50710,50712],{"className":50711},[407,658],[363,50713,45527],{"className":50714},[407,408,658],[363,50716,50718,50721],{"className":50717},[407],[363,50719,1291],{"className":50720,"style":1328},[407,408],[363,50722,50724],{"className":50723},[629],[363,50725,50727],{"className":50726},[633],[363,50728,50730],{"className":50729},[638],[363,50731,50733],{"className":50732,"style":20375},[642],[363,50734,50735,50738],{"style":7212},[363,50736],{"className":50737,"style":651},[650],[363,50739,50741],{"className":50740},[655,656,657,658],[363,50742,50744,50747,50750],{"className":50743},[407,658],[363,50745,465],{"className":50746},[407,658],[363,50748,5160],{"className":50749},[2938,658],[363,50751,45527],{"className":50752},[407,408,658],[363,50754],{"className":50755,"style":754},[505],[363,50757,592],{"className":50758},[407,408],[363,50760,1121],{"className":50761},[407,408],"，则 3.6 节给出",[363,50764,50766],{"className":50765,"translate":367},[528],[363,50767,50769,50815],{"className":50768,"translate":367},[366],[363,50770,50772],{"className":50771},[371],[373,50773,50774],{"xmlns":375,"display":537},[377,50775,50776,50812],{},[380,50777,50778,50784,50786,50788,50790,50792,50794,50796,50798,50800,50802,50804,50810],{},[543,50779,50780,50782],{},[383,50781,33950],{},[383,50783,45527],{},[458,50785,471],{},[463,50787,465],{},[458,50789,5160],{},[383,50791,45527],{},[458,50793,461],{"stretchy":460},[463,50795,465],{},[458,50797,5160],{},[383,50799,45527],{},[458,50801,468],{"stretchy":460},[1644,50803,1646],{},[543,50805,50806,50808],{},[383,50807,547],{},[383,50809,45101],{},[458,50811,898],{"separator":394},[387,50813,50814],{"encoding":389},"Z_a=1-a(1-a)\\,D_\\alpha ,",[363,50816,50818,50873,50891,50915],{"className":50817,"ariaHidden":394},[393],[363,50819,50821,50824,50864,50867,50870],{"className":50820},[398],[363,50822],{"className":50823,"style":16308},[402],[363,50825,50827,50830],{"className":50826},[407],[363,50828,33950],{"className":50829,"style":11129},[407,408],[363,50831,50833],{"className":50832},[629],[363,50834,50836,50856],{"className":50835},[633,634],[363,50837,50839,50853],{"className":50838},[638],[363,50840,50842],{"className":50841,"style":45276},[642],[363,50843,50844,50847],{"style":50639},[363,50845],{"className":50846,"style":651},[650],[363,50848,50850],{"className":50849},[655,656,657,658],[363,50851,45527],{"className":50852},[407,408,658],[363,50854,666],{"className":50855},[665],[363,50857,50859],{"className":50858},[638],[363,50860,50862],{"className":50861,"style":8315},[642],[363,50863],{},[363,50865],{"className":50866,"style":506},[505],[363,50868,471],{"className":50869},[510],[363,50871],{"className":50872,"style":506},[505],[363,50874,50876,50879,50882,50885,50888],{"className":50875},[398],[363,50877],{"className":50878,"style":12925},[402],[363,50880,465],{"className":50881},[407],[363,50883],{"className":50884,"style":2934},[505],[363,50886,5160],{"className":50887},[2938],[363,50889],{"className":50890,"style":2934},[505],[363,50892,50894,50897,50900,50903,50906,50909,50912],{"className":50893},[398],[363,50895],{"className":50896,"style":487},[402],[363,50898,45527],{"className":50899},[407,408],[363,50901,461],{"className":50902},[494],[363,50904,465],{"className":50905},[407],[363,50907],{"className":50908,"style":2934},[505],[363,50910,5160],{"className":50911},[2938],[363,50913],{"className":50914,"style":2934},[505],[363,50916,50918,50921,50924,50927,50930,50970],{"className":50917},[398],[363,50919],{"className":50920,"style":487},[402],[363,50922,45527],{"className":50923},[407,408],[363,50925,468],{"className":50926},[501],[363,50928],{"className":50929,"style":754},[505],[363,50931,50933,50936],{"className":50932},[407],[363,50934,547],{"className":50935,"style":625},[407,408],[363,50937,50939],{"className":50938},[629],[363,50940,50942,50962],{"className":50941},[633,634],[363,50943,50945,50959],{"className":50944},[638],[363,50946,50948],{"className":50947,"style":45276},[642],[363,50949,50950,50953],{"style":646},[363,50951],{"className":50952,"style":651},[650],[363,50954,50956],{"className":50955},[655,656,657,658],[363,50957,45101],{"className":50958,"style":45131},[407,408,658],[363,50960,666],{"className":50961},[665],[363,50963,50965],{"className":50964},[638],[363,50966,50968],{"className":50967,"style":8315},[642],[363,50969],{},[363,50971,898],{"className":50972},[920],[11,50974,50975,50976,50979,50980,51008,51009,51071,51072,51100],{},"而把 Rényi 的",[1572,50977,50978],{},"阶数","取为 ",[363,50981,50983,50996],{"className":50982,"translate":367},[366],[363,50984,50986],{"className":50985},[371],[373,50987,50988],{"xmlns":375},[377,50989,50990,50994],{},[380,50991,50992],{},[383,50993,45527],{},[387,50995,45527],{"encoding":389},[363,50997,50999],{"className":50998,"ariaHidden":394},[393],[363,51000,51002,51005],{"className":51001},[398],[363,51003],{"className":51004,"style":2692},[402],[363,51006,45527],{"className":51007},[407,408],"（注意 order ",[363,51010,51012,51026],{"className":51011,"translate":367},[366],[363,51013,51015],{"className":51014},[371],[373,51016,51017],{"xmlns":375},[377,51018,51019,51023],{},[380,51020,51021],{},[458,51022,49854],{"mathvariant":557},[387,51024,51025],{"encoding":389},"\\neq",[363,51027,51029],{"className":51028,"ariaHidden":394},[393],[363,51030,51032,51035],{"className":51031},[398],[363,51033],{"className":51034,"style":403},[402],[363,51036,51038,51065,51068],{"className":51037},[510],[363,51039,51041],{"className":51040},[510],[363,51042,51044],{"className":51043},[407,4747],[363,51045,51047],{"className":51046},[4751],[363,51048,51050,51053,51062],{"className":51049},[4755],[363,51051],{"className":51052,"style":403},[402],[363,51054,51056],{"className":51055},[4762],[363,51057,51059],{"className":51058},[407],[363,51060,4769],{"className":51061},[510],[363,51063],{"className":51064},[4773],[363,51066],{"className":51067},[505,4777],[363,51069,471],{"className":51070},[510]," 3.6 的参数 ",[363,51073,51075,51088],{"className":51074,"translate":367},[366],[363,51076,51078],{"className":51077},[371],[373,51079,51080],{"xmlns":375},[377,51081,51082,51086],{},[380,51083,51084],{},[383,51085,45101],{},[387,51087,49437],{"encoding":389},[363,51089,51091],{"className":51090,"ariaHidden":394},[393],[363,51092,51094,51097],{"className":51093},[398],[363,51095],{"className":51096,"style":2692},[402],[363,51098,45101],{"className":51099,"style":45131},[407,408],"，只是经过线性换算）：",[363,51102,51104],{"className":51103,"translate":367},[528],[363,51105,51107,51211],{"className":51106,"translate":367},[366],[363,51108,51110],{"className":51109},[371],[373,51111,51112],{"xmlns":375,"display":537},[377,51113,51114,51208],{},[380,51115,51116,51124,51126,51128,51130,51132,51134,51136,51148,51150,51152,51158,51160,51162,51174,51176,51178,51180,51182,51184,51186,51188,51190,51192,51194,51196,51198,51204,51206],{},[7900,51117,51118,51120,51122],{},[383,51119,547],{},[383,51121,45527],{},[383,51123,1379],{},[458,51125,461],{"stretchy":460},[383,51127,554],{},[383,51129,558],{"mathvariant":557},[383,51131,561],{},[458,51133,468],{"stretchy":460},[458,51135,471],{},[586,51137,51138,51140],{},[463,51139,465],{},[380,51141,51142,51144,51146],{},[383,51143,45527],{},[458,51145,5160],{},[463,51147,465],{},[383,51149,4447],{},[458,51151,4450],{},[543,51153,51154,51156],{},[383,51155,33950],{},[383,51157,45527],{},[458,51159,471],{},[458,51161,5160],{},[586,51163,51164,51166],{},[463,51165,465],{},[380,51167,51168,51170,51172],{},[463,51169,465],{},[458,51171,5160],{},[383,51173,45527],{},[1644,51175,1646],{},[383,51177,4447],{},[458,51179,4450],{},[458,51181,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[463,51183,465],{},[458,51185,5160],{},[383,51187,45527],{},[458,51189,461],{"stretchy":460},[463,51191,465],{},[458,51193,5160],{},[383,51195,45527],{},[458,51197,468],{"stretchy":460},[543,51199,51200,51202],{},[383,51201,547],{},[383,51203,45101],{},[458,51205,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,51207,4722],{"mathvariant":557},[387,51209,51210],{"encoding":389},"D^{R}_{a}(P\\|Q)=\\frac{1}{a-1}\\log Z_a\n=-\\frac{1}{1-a}\\,\\log\\big(1-a(1-a)D_\\alpha\\big).",[363,51212,51214,51302,51442,51557,51581],{"className":51213,"ariaHidden":394},[393],[363,51215,51217,51221,51278,51281,51284,51287,51290,51293,51296,51299],{"className":51216},[398],[363,51218],{"className":51219,"style":51220},[402],"height:1.1413em;vertical-align:-0.25em;",[363,51222,51224,51227],{"className":51223},[407],[363,51225,547],{"className":51226,"style":625},[407,408],[363,51228,51230],{"className":51229},[629],[363,51231,51233,51270],{"className":51232},[633,634],[363,51234,51236,51267],{"className":51235},[638],[363,51237,51239,51253],{"className":51238,"style":38859},[642],[363,51240,51241,51244],{"style":49919},[363,51242],{"className":51243,"style":651},[650],[363,51245,51247],{"className":51246},[655,656,657,658],[363,51248,51250],{"className":51249},[407,658],[363,51251,45527],{"className":51252},[407,408,658],[363,51254,51255,51258],{"style":8624},[363,51256],{"className":51257,"style":651},[650],[363,51259,51261],{"className":51260},[655,656,657,658],[363,51262,51264],{"className":51263},[407,658],[363,51265,1379],{"className":51266,"style":49946},[407,408,658],[363,51268,666],{"className":51269},[665],[363,51271,51273],{"className":51272},[638],[363,51274,51276],{"className":51275,"style":8646},[642],[363,51277],{},[363,51279,461],{"className":51280},[494],[363,51282,554],{"className":51283,"style":682},[407,408],[363,51285,558],{"className":51286},[407],[363,51288,561],{"className":51289},[407,408],[363,51291,468],{"className":51292},[501],[363,51294],{"className":51295,"style":506},[505],[363,51297,471],{"className":51298},[510],[363,51300],{"className":51301,"style":506},[505],[363,51303,51305,51308,51382,51385,51390,51393,51433,51436,51439],{"className":51304},[398],[363,51306],{"className":51307,"style":26963},[402],[363,51309,51311,51314,51379],{"className":51310},[407],[363,51312],{"className":51313},[494,789],[363,51315,51317],{"className":51316},[586],[363,51318,51320,51371],{"className":51319},[633,634],[363,51321,51323,51368],{"className":51322},[638],[363,51324,51326,51349,51357],{"className":51325,"style":23236},[642],[363,51327,51328,51331],{"style":805},[363,51329],{"className":51330,"style":809},[650],[363,51332,51334,51337,51340,51343,51346],{"className":51333},[407],[363,51335,45527],{"className":51336},[407,408],[363,51338],{"className":51339,"style":2934},[505],[363,51341,5160],{"className":51342},[2938],[363,51344],{"className":51345,"style":2934},[505],[363,51347,465],{"className":51348},[407],[363,51350,51351,51354],{"style":821},[363,51352],{"className":51353,"style":809},[650],[363,51355],{"className":51356,"style":829},[828],[363,51358,51359,51362],{"style":832},[363,51360],{"className":51361,"style":809},[650],[363,51363,51365],{"className":51364},[407],[363,51366,465],{"className":51367},[407],[363,51369,666],{"className":51370},[665],[363,51372,51374],{"className":51373},[638],[363,51375,51377],{"className":51376,"style":17362},[642],[363,51378],{},[363,51380],{"className":51381},[501,789],[363,51383],{"className":51384,"style":754},[505],[363,51386,4501,51388],{"className":51387},[1831],[363,51389,4505],{"style":4504},[363,51391],{"className":51392,"style":754},[505],[363,51394,51396,51399],{"className":51395},[407],[363,51397,33950],{"className":51398,"style":11129},[407,408],[363,51400,51402],{"className":51401},[629],[363,51403,51405,51425],{"className":51404},[633,634],[363,51406,51408,51422],{"className":51407},[638],[363,51409,51411],{"className":51410,"style":45276},[642],[363,51412,51413,51416],{"style":50639},[363,51414],{"className":51415,"style":651},[650],[363,51417,51419],{"className":51418},[655,656,657,658],[363,51420,45527],{"className":51421},[407,408,658],[363,51423,666],{"className":51424},[665],[363,51426,51428],{"className":51427},[638],[363,51429,51431],{"className":51430,"style":8315},[642],[363,51432],{},[363,51434],{"className":51435,"style":506},[505],[363,51437,471],{"className":51438},[510],[363,51440],{"className":51441,"style":506},[505],[363,51443,51445,51448,51451,51525,51528,51531,51536,51539,51545,51548,51551,51554],{"className":51444},[398],[363,51446],{"className":51447,"style":26963},[402],[363,51449,5160],{"className":51450},[407],[363,51452,51454,51457,51522],{"className":51453},[407],[363,51455],{"className":51456},[494,789],[363,51458,51460],{"className":51459},[586],[363,51461,51463,51514],{"className":51462},[633,634],[363,51464,51466,51511],{"className":51465},[638],[363,51467,51469,51492,51500],{"className":51468,"style":23236},[642],[363,51470,51471,51474],{"style":805},[363,51472],{"className":51473,"style":809},[650],[363,51475,51477,51480,51483,51486,51489],{"className":51476},[407],[363,51478,465],{"className":51479},[407],[363,51481],{"className":51482,"style":2934},[505],[363,51484,5160],{"className":51485},[2938],[363,51487],{"className":51488,"style":2934},[505],[363,51490,45527],{"className":51491},[407,408],[363,51493,51494,51497],{"style":821},[363,51495],{"className":51496,"style":809},[650],[363,51498],{"className":51499,"style":829},[828],[363,51501,51502,51505],{"style":832},[363,51503],{"className":51504,"style":809},[650],[363,51506,51508],{"className":51507},[407],[363,51509,465],{"className":51510},[407],[363,51512,666],{"className":51513},[665],[363,51515,51517],{"className":51516},[638],[363,51518,51520],{"className":51519,"style":17362},[642],[363,51521],{},[363,51523],{"className":51524},[501,789],[363,51526],{"className":51527,"style":754},[505],[363,51529],{"className":51530,"style":754},[505],[363,51532,4501,51534],{"className":51533},[1831],[363,51535,4505],{"style":4504},[363,51537],{"className":51538,"style":754},[505],[363,51540,51542],{"className":51541},[407],[363,51543,461],{"className":51544},[767,10021],[363,51546,465],{"className":51547},[407],[363,51549],{"className":51550,"style":2934},[505],[363,51552,5160],{"className":51553},[2938],[363,51555],{"className":51556,"style":2934},[505],[363,51558,51560,51563,51566,51569,51572,51575,51578],{"className":51559},[398],[363,51561],{"className":51562,"style":487},[402],[363,51564,45527],{"className":51565},[407,408],[363,51567,461],{"className":51568},[494],[363,51570,465],{"className":51571},[407],[363,51573],{"className":51574,"style":2934},[505],[363,51576,5160],{"className":51577},[2938],[363,51579],{"className":51580,"style":2934},[505],[363,51582,51584,51587,51590,51593,51633,51639],{"className":51583},[398],[363,51585],{"className":51586,"style":20910},[402],[363,51588,45527],{"className":51589},[407,408],[363,51591,468],{"className":51592},[501],[363,51594,51596,51599],{"className":51595},[407],[363,51597,547],{"className":51598,"style":625},[407,408],[363,51600,51602],{"className":51601},[629],[363,51603,51605,51625],{"className":51604},[633,634],[363,51606,51608,51622],{"className":51607},[638],[363,51609,51611],{"className":51610,"style":45276},[642],[363,51612,51613,51616],{"style":646},[363,51614],{"className":51615,"style":651},[650],[363,51617,51619],{"className":51618},[655,656,657,658],[363,51620,45101],{"className":51621,"style":45131},[407,408,658],[363,51623,666],{"className":51624},[665],[363,51626,51628],{"className":51627},[638],[363,51629,51631],{"className":51630,"style":8315},[642],[363,51632],{},[363,51634,51636],{"className":51635},[407],[363,51637,468],{"className":51638},[767,10021],[363,51640,4722],{"className":51641},[407],[11,51643,51644,51645,51792,51793,51821,51822,51854],{},"这说明两者是一条\"幂—对数\"的两级包装链：f-散度是对似然比幂 ",[363,51646,51648,51674],{"className":51647,"translate":367},[366],[363,51649,51651],{"className":51650},[371],[373,51652,51653],{"xmlns":375},[377,51654,51655,51671],{},[380,51656,51657,51659,51665],{},[458,51658,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[586,51660,51661,51663],{},[383,51662,11],{},[383,51664,1291],{},[7161,51666,51667,51669],{},[458,51668,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,51670,45527],{},[387,51672,51673],{"encoding":389},"\\big(\\frac pq\\big)^a",[363,51675,51677],{"className":51676,"ariaHidden":394},[393],[363,51678,51680,51684,51690,51758],{"className":51679},[398],[363,51681],{"className":51682,"style":51683},[402],"height:1.3854em;vertical-align:-0.4811em;",[363,51685,51687],{"className":51686},[407],[363,51688,461],{"className":51689},[767,10021],[363,51691,51693,51696,51755],{"className":51692},[407],[363,51694],{"className":51695},[494,789],[363,51697,51699],{"className":51698},[586],[363,51700,51702,51747],{"className":51701},[633,634],[363,51703,51705,51744],{"className":51704},[638],[363,51706,51708,51722,51730],{"className":51707,"style":3450},[642],[363,51709,51710,51713],{"style":2874},[363,51711],{"className":51712,"style":809},[650],[363,51714,51716],{"className":51715},[655,656,657,658],[363,51717,51719],{"className":51718},[407,658],[363,51720,1291],{"className":51721,"style":1328},[407,408,658],[363,51723,51724,51727],{"style":821},[363,51725],{"className":51726,"style":809},[650],[363,51728],{"className":51729,"style":829},[828],[363,51731,51732,51735],{"style":3200},[363,51733],{"className":51734,"style":809},[650],[363,51736,51738],{"className":51737},[655,656,657,658],[363,51739,51741],{"className":51740},[407,658],[363,51742,11],{"className":51743},[407,408,658],[363,51745,666],{"className":51746},[665],[363,51748,51750],{"className":51749},[638],[363,51751,51753],{"className":51752,"style":3086},[642],[363,51754],{},[363,51756],{"className":51757},[501,789],[363,51759,51761,51767],{"className":51760},[407],[363,51762,51764],{"className":51763},[407],[363,51765,468],{"className":51766},[767,10021],[363,51768,51770],{"className":51769},[629],[363,51771,51773],{"className":51772},[633],[363,51774,51776],{"className":51775},[638],[363,51777,51780],{"className":51778,"style":51779},[642],"height:0.9043em;",[363,51781,51783,51786],{"style":51782},"top:-3.3029em;margin-right:0.05em;",[363,51784],{"className":51785,"style":651},[650],[363,51787,51789],{"className":51788},[655,656,657,658],[363,51790,45527],{"className":51791},[407,408,658]," 做 ",[363,51794,51796,51809],{"className":51795,"translate":367},[366],[363,51797,51799],{"className":51798},[371],[373,51800,51801],{"xmlns":375},[377,51802,51803,51807],{},[380,51804,51805],{},[383,51806,561],{},[387,51808,561],{"encoding":389},[363,51810,51812],{"className":51811,"ariaHidden":394},[393],[363,51813,51815,51818],{"className":51814},[398],[363,51816],{"className":51817,"style":913},[402],[363,51819,561],{"className":51820},[407,408]," 下的线性平均，Rényi 在外面再套一层对数。所以 f-散度族与 Rényi 族\"同源\"：后者是前者经 ",[363,51823,51825,51840],{"className":51824,"translate":367},[366],[363,51826,51828],{"className":51827},[371],[373,51829,51830],{"xmlns":375},[377,51831,51832,51838],{},[380,51833,51834,51836],{},[383,51835,4447],{},[458,51837,4450],{},[387,51839,21930],{"encoding":389},[363,51841,51843],{"className":51842,"ariaHidden":394},[393],[363,51844,51846,51849],{"className":51845},[398],[363,51847],{"className":51848,"style":403},[402],[363,51850,4501,51852],{"className":51851},[1831],[363,51853,4505],{"style":4504}," 变换后的\"信息量\"版本。",[11,51856,51857,51859,51860,51863],{},[1572,51858,24540],{}," Rényi 散度在",[1572,51861,51862],{},"假设检验","中直接就是误差指数：Chernoff 信息",[363,51865,51867],{"className":51866,"translate":367},[528],[363,51868,51870,51993],{"className":51869,"translate":367},[366],[363,51871,51873],{"className":51872},[371],[373,51874,51875],{"xmlns":375,"display":537},[377,51876,51877,51990],{},[380,51878,51879,51881,51883,51885,51887,51889,51891,51893,51913,51915,51917,51919,51921,51923,51931,51933,51935,51937,51939,51941,51943,51945,51947,51949,51970,51972,51978],{},[383,51880,39641],{},[458,51882,461],{"stretchy":460},[383,51884,554],{},[458,51886,898],{"separator":394},[383,51888,561],{},[458,51890,468],{"stretchy":460},[458,51892,471],{},[6363,51894,51895,51901],{},[380,51896,51897,51899],{},[383,51898,35779],{},[458,51900,4450],{},[380,51902,51903,51905,51907,51909,51911],{},[463,51904,474],{},[458,51906,7598],{},[383,51908,11686],{},[458,51910,7598],{},[463,51912,465],{},[458,51914,461],{"stretchy":460},[463,51916,465],{},[458,51918,5160],{},[383,51920,11686],{},[458,51922,468],{"stretchy":460},[7900,51924,51925,51927,51929],{},[383,51926,547],{},[383,51928,11686],{},[383,51930,1379],{},[458,51932,461],{"stretchy":460},[383,51934,554],{},[383,51936,558],{"mathvariant":557},[383,51938,561],{},[458,51940,468],{"stretchy":460},[458,51942,471],{},[458,51944,5160],{},[383,51946,4447],{},[458,51948,4450],{},[6363,51950,51951,51958],{},[380,51952,51953,51956],{},[383,51954,51955],{},"min",[458,51957,4450],{},[380,51959,51960,51962,51964,51966,51968],{},[463,51961,474],{},[458,51963,10299],{},[383,51965,11686],{},[458,51967,10299],{},[463,51969,465],{},[458,51971,1634],{},[7161,51973,51974,51976],{},[383,51975,11],{},[383,51977,11686],{},[7161,51979,51980,51982],{},[383,51981,1291],{},[380,51983,51984,51986,51988],{},[463,51985,465],{},[458,51987,5160],{},[383,51989,11686],{},[387,51991,51992],{"encoding":389},"C(P,Q)=\\sup_{0\u003C\\lambda\u003C1}\n(1-\\lambda)D^{R}_{\\lambda}(P\\|Q)\n=-\\log\\min_{0\\le\\lambda\\le1}\n\\int p^\\lambda q^{1-\\lambda}",[363,51994,51996,52032,52115,52208],{"className":51995,"ariaHidden":394},[393],[363,51997,51999,52002,52005,52008,52011,52014,52017,52020,52023,52026,52029],{"className":51998},[398],[363,52000],{"className":52001,"style":487},[402],[363,52003,39641],{"className":52004,"style":11129},[407,408],[363,52006,461],{"className":52007},[494],[363,52009,554],{"className":52010,"style":682},[407,408],[363,52012,898],{"className":52013},[920],[363,52015],{"className":52016,"style":754},[505],[363,52018,561],{"className":52019},[407,408],[363,52021,468],{"className":52022},[501],[363,52024],{"className":52025,"style":506},[505],[363,52027,471],{"className":52028},[510],[363,52030],{"className":52031,"style":506},[505],[363,52033,52035,52039,52100,52103,52106,52109,52112],{"className":52034},[398],[363,52036],{"className":52037,"style":52038},[402],"height:1.7239em;vertical-align:-0.9739em;",[363,52040,52042],{"className":52041},[1831,14063],[363,52043,52045,52091],{"className":52044},[633,634],[363,52046,52048,52088],{"className":52047},[638],[363,52049,52051,52078],{"className":52050,"style":2692},[642],[363,52052,52054,52057],{"style":52053},"top:-2.1535em;margin-left:0em;",[363,52055],{"className":52056,"style":809},[650],[363,52058,52060],{"className":52059},[655,656,657,658],[363,52061,52063,52066,52069,52072,52075],{"className":52062},[407,658],[363,52064,474],{"className":52065},[407,658],[363,52067,7598],{"className":52068},[510,658],[363,52070,11686],{"className":52071},[407,408,658],[363,52073,7598],{"className":52074},[510,658],[363,52076,465],{"className":52077},[407,658],[363,52079,52080,52083],{"style":12210},[363,52081],{"className":52082,"style":809},[650],[363,52084,52085],{},[363,52086,35779],{"className":52087},[1831],[363,52089,666],{"className":52090},[665],[363,52092,52094],{"className":52093},[638],[363,52095,52098],{"className":52096,"style":52097},[642],"height:0.9739em;",[363,52099],{},[363,52101,461],{"className":52102},[494],[363,52104,465],{"className":52105},[407],[363,52107],{"className":52108,"style":2934},[505],[363,52110,5160],{"className":52111},[2938],[363,52113],{"className":52114,"style":2934},[505],[363,52116,52118,52121,52124,52127,52184,52187,52190,52193,52196,52199,52202,52205],{"className":52117},[398],[363,52119],{"className":52120,"style":51220},[402],[363,52122,11686],{"className":52123},[407,408],[363,52125,468],{"className":52126},[501],[363,52128,52130,52133],{"className":52129},[407],[363,52131,547],{"className":52132,"style":625},[407,408],[363,52134,52136],{"className":52135},[629],[363,52137,52139,52176],{"className":52138},[633,634],[363,52140,52142,52173],{"className":52141},[638],[363,52143,52145,52159],{"className":52144,"style":38859},[642],[363,52146,52147,52150],{"style":49919},[363,52148],{"className":52149,"style":651},[650],[363,52151,52153],{"className":52152},[655,656,657,658],[363,52154,52156],{"className":52155},[407,658],[363,52157,11686],{"className":52158},[407,408,658],[363,52160,52161,52164],{"style":8624},[363,52162],{"className":52163,"style":651},[650],[363,52165,52167],{"className":52166},[655,656,657,658],[363,52168,52170],{"className":52169},[407,658],[363,52171,1379],{"className":52172,"style":49946},[407,408,658],[363,52174,666],{"className":52175},[665],[363,52177,52179],{"className":52178},[638],[363,52180,52182],{"className":52181,"style":8646},[642],[363,52183],{},[363,52185,461],{"className":52186},[494],[363,52188,554],{"className":52189,"style":682},[407,408],[363,52191,558],{"className":52192},[407],[363,52194,561],{"className":52195},[407,408],[363,52197,468],{"className":52198},[501],[363,52200],{"className":52201,"style":506},[505],[363,52203,471],{"className":52204},[510],[363,52206],{"className":52207,"style":506},[505],[363,52209,52211,52214,52217,52220,52225,52228,52290,52293,52296,52299,52328],{"className":52210},[398],[363,52212],{"className":52213,"style":6124},[402],[363,52215,5160],{"className":52216},[407],[363,52218],{"className":52219,"style":754},[505],[363,52221,4501,52223],{"className":52222},[1831],[363,52224,4505],{"style":4504},[363,52226],{"className":52227,"style":754},[505],[363,52229,52231],{"className":52230},[1831,14063],[363,52232,52234,52281],{"className":52233},[633,634],[363,52235,52237,52278],{"className":52236},[638],[363,52238,52241,52268],{"className":52239,"style":52240},[642],"height:0.6679em;",[363,52242,52244,52247],{"style":52243},"top:-2.3479em;margin-left:0em;",[363,52245],{"className":52246,"style":809},[650],[363,52248,52250],{"className":52249},[655,656,657,658],[363,52251,52253,52256,52259,52262,52265],{"className":52252},[407,658],[363,52254,474],{"className":52255},[407,658],[363,52257,10299],{"className":52258},[510,658],[363,52260,11686],{"className":52261},[407,408,658],[363,52263,10299],{"className":52264},[510,658],[363,52266,465],{"className":52267},[407,658],[363,52269,52270,52273],{"style":12210},[363,52271],{"className":52272,"style":809},[650],[363,52274,52275],{},[363,52276,51955],{"className":52277},[1831],[363,52279,666],{"className":52280},[665],[363,52282,52284],{"className":52283},[638],[363,52285,52288],{"className":52286,"style":52287},[642],"height:0.8473em;",[363,52289],{},[363,52291],{"className":52292,"style":754},[505],[363,52294,1634],{"className":52295,"style":1834},[1831,1832,1833],[363,52297],{"className":52298,"style":754},[505],[363,52300,52302,52305],{"className":52301},[407],[363,52303,11],{"className":52304},[407,408],[363,52306,52308],{"className":52307},[629],[363,52309,52311],{"className":52310},[633],[363,52312,52314],{"className":52313},[638],[363,52315,52317],{"className":52316,"style":48211},[642],[363,52318,52319,52322],{"style":8624},[363,52320],{"className":52321,"style":651},[650],[363,52323,52325],{"className":52324},[655,656,657,658],[363,52326,11686],{"className":52327},[407,408,658],[363,52329,52331,52334],{"className":52330},[407],[363,52332,1291],{"className":52333,"style":1328},[407,408],[363,52335,52337],{"className":52336},[629],[363,52338,52340],{"className":52339},[633],[363,52341,52343],{"className":52342},[638],[363,52344,52346],{"className":52345,"style":48211},[642],[363,52347,52348,52351],{"style":8624},[363,52349],{"className":52350,"style":651},[650],[363,52352,52354],{"className":52353},[655,656,657,658],[363,52355,52357,52360,52363],{"className":52356},[407,658],[363,52358,465],{"className":52359},[407,658],[363,52361,5160],{"className":52362},[2938,658],[363,52364,11686],{"className":52365},[407,408,658],[11,52367,52368,52369,52535,52536,4200,52607,52657,52658,52709,52710,52829,52830,52833],{},"决定对称检验错误概率的衰减速率，Stein 引理给出的单侧指数则是 ",[363,52370,52372,52404],{"className":52371,"translate":367},[366],[363,52373,52375],{"className":52374},[371],[373,52376,52377],{"xmlns":375},[377,52378,52379,52401],{},[380,52380,52381,52389,52391],{},[7900,52382,52383,52385,52387],{},[383,52384,547],{},[463,52386,465],{},[383,52388,1379],{},[458,52390,471],{},[543,52392,52393,52395],{},[383,52394,547],{},[380,52396,52397,52399],{},[383,52398,11041],{},[383,52400,22240],{},[387,52402,52403],{"encoding":389},"D^{R}_{1}=D_{KL}",[363,52405,52407,52483],{"className":52406,"ariaHidden":394},[393],[363,52408,52410,52414,52474,52477,52480],{"className":52409},[398],[363,52411],{"className":52412,"style":52413},[402],"height:1.0894em;vertical-align:-0.2481em;",[363,52415,52417,52420],{"className":52416},[407],[363,52418,547],{"className":52419,"style":625},[407,408],[363,52421,52423],{"className":52422},[629],[363,52424,52426,52465],{"className":52425},[633,634],[363,52427,52429,52462],{"className":52428},[638],[363,52430,52433,52448],{"className":52431,"style":52432},[642],"height:0.8413em;",[363,52434,52436,52439],{"style":52435},"top:-2.4519em;margin-left:-0.0278em;margin-right:0.05em;",[363,52437],{"className":52438,"style":651},[650],[363,52440,52442],{"className":52441},[655,656,657,658],[363,52443,52445],{"className":52444},[407,658],[363,52446,465],{"className":52447},[407,658],[363,52449,52450,52453],{"style":7212},[363,52451],{"className":52452,"style":651},[650],[363,52454,52456],{"className":52455},[655,656,657,658],[363,52457,52459],{"className":52458},[407,658],[363,52460,1379],{"className":52461,"style":49946},[407,408,658],[363,52463,666],{"className":52464},[665],[363,52466,52468],{"className":52467},[638],[363,52469,52472],{"className":52470,"style":52471},[642],"height:0.2481em;",[363,52473],{},[363,52475],{"className":52476,"style":506},[505],[363,52478,471],{"className":52479},[510],[363,52481],{"className":52482,"style":506},[505],[363,52484,52486,52489],{"className":52485},[398],[363,52487],{"className":52488,"style":16308},[402],[363,52490,52492,52495],{"className":52491},[407],[363,52493,547],{"className":52494,"style":625},[407,408],[363,52496,52498],{"className":52497},[629],[363,52499,52501,52527],{"className":52500},[633,634],[363,52502,52504,52524],{"className":52503},[638],[363,52505,52507],{"className":52506,"style":727},[642],[363,52508,52509,52512],{"style":646},[363,52510],{"className":52511,"style":651},[650],[363,52513,52515],{"className":52514},[655,656,657,658],[363,52516,52518,52521],{"className":52517},[407,658],[363,52519,11041],{"className":52520,"style":11129},[407,408,658],[363,52522,22240],{"className":52523},[407,408,658],[363,52525,666],{"className":52526},[665],[363,52528,52530],{"className":52529},[638],[363,52531,52533],{"className":52532,"style":8315},[642],[363,52534],{},"。对应的 Rényi 熵 ",[363,52537,52539,52557],{"className":52538,"translate":367},[366],[363,52540,52542],{"className":52541},[371],[373,52543,52544],{"xmlns":375},[377,52545,52546,52554],{},[380,52547,52548],{},[543,52549,52550,52552],{},[383,52551,34231],{},[383,52553,45101],{},[387,52555,52556],{"encoding":389},"H_\\alpha",[363,52558,52560],{"className":52559,"ariaHidden":394},[393],[363,52561,52563,52566],{"className":52562},[398],[363,52564],{"className":52565,"style":16308},[402],[363,52567,52569,52572],{"className":52568},[407],[363,52570,34231],{"className":52571,"style":34385},[407,408],[363,52573,52575],{"className":52574},[629],[363,52576,52578,52599],{"className":52577},[633,634],[363,52579,52581,52596],{"className":52580},[638],[363,52582,52584],{"className":52583,"style":45276},[642],[363,52585,52587,52590],{"style":52586},"top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;",[363,52588],{"className":52589,"style":651},[650],[363,52591,52593],{"className":52592},[655,656,657,658],[363,52594,45101],{"className":52595,"style":45131},[407,408,658],[363,52597,666],{"className":52598},[665],[363,52600,52602],{"className":52601},[638],[363,52603,52605],{"className":52604,"style":8315},[642],[363,52606],{},[363,52608,52610,52627],{"className":52609,"translate":367},[366],[363,52611,52613],{"className":52612},[371],[373,52614,52615],{"xmlns":375},[377,52616,52617,52625],{},[380,52618,52619,52621,52623],{},[383,52620,45101],{},[458,52622,1376],{},[463,52624,465],{},[387,52626,47562],{"encoding":389},[363,52628,52630,52648],{"className":52629,"ariaHidden":394},[393],[363,52631,52633,52636,52639,52642,52645],{"className":52632},[398],[363,52634],{"className":52635,"style":2692},[402],[363,52637,45101],{"className":52638,"style":45131},[407,408],[363,52640],{"className":52641,"style":506},[505],[363,52643,1376],{"className":52644},[510],[363,52646],{"className":52647,"style":506},[505],[363,52649,52651,52654],{"className":52650},[398],[363,52652],{"className":52653,"style":520},[402],[363,52655,465],{"className":52656},[407]," 时退化为 Shannon 熵、在 ",[363,52659,52661,52679],{"className":52660,"translate":367},[366],[363,52662,52664],{"className":52663},[371],[373,52665,52666],{"xmlns":375},[377,52667,52668,52676],{},[380,52669,52670,52672,52674],{},[383,52671,45101],{},[458,52673,1376],{},[383,52675,1371],{"mathvariant":557},[387,52677,52678],{"encoding":389},"\\alpha\\to\\infty",[363,52680,52682,52700],{"className":52681,"ariaHidden":394},[393],[363,52683,52685,52688,52691,52694,52697],{"className":52684},[398],[363,52686],{"className":52687,"style":2692},[402],[363,52689,45101],{"className":52690,"style":45131},[407,408],[363,52692],{"className":52693,"style":506},[505],[363,52695,1376],{"className":52696},[510],[363,52698],{"className":52699,"style":506},[505],[363,52701,52703,52706],{"className":52702},[398],[363,52704],{"className":52705,"style":2692},[402],[363,52707,1371],{"className":52708},[407]," 时退化为 min-entropy ",[363,52711,52713,52750],{"className":52712,"translate":367},[366],[363,52714,52716],{"className":52715},[371],[373,52717,52718],{"xmlns":375},[377,52719,52720,52747],{},[380,52721,52722,52724,52726,52728,52739,52741,52743,52745],{},[458,52723,5160],{},[383,52725,4447],{},[458,52727,4450],{},[543,52729,52730,52737],{},[380,52731,52732,52735],{},[383,52733,52734],{},"max",[458,52736,4450],{},[383,52738,1121],{},[383,52740,11],{},[458,52742,461],{"stretchy":460},[383,52744,1121],{},[458,52746,468],{"stretchy":460},[387,52748,52749],{"encoding":389},"-\\log\\max_x p(x)",[363,52751,52753],{"className":52752,"ariaHidden":394},[393],[363,52754,52756,52759,52762,52765,52770,52773,52814,52817,52820,52823,52826],{"className":52755},[398],[363,52757],{"className":52758,"style":487},[402],[363,52760,5160],{"className":52761},[407],[363,52763],{"className":52764,"style":754},[505],[363,52766,4501,52768],{"className":52767},[1831],[363,52769,4505],{"style":4504},[363,52771],{"className":52772,"style":754},[505],[363,52774,52776,52779],{"className":52775},[1831],[363,52777,52734],{"className":52778},[1831],[363,52780,52782],{"className":52781},[629],[363,52783,52785,52806],{"className":52784},[633,634],[363,52786,52788,52803],{"className":52787},[638],[363,52789,52791],{"className":52790,"style":45276},[642],[363,52792,52794,52797],{"style":52793},"top:-2.55em;margin-right:0.05em;",[363,52795],{"className":52796,"style":651},[650],[363,52798,52800],{"className":52799},[655,656,657,658],[363,52801,1121],{"className":52802},[407,408,658],[363,52804,666],{"className":52805},[665],[363,52807,52809],{"className":52808},[638],[363,52810,52812],{"className":52811,"style":8315},[642],[363,52813],{},[363,52815],{"className":52816,"style":754},[505],[363,52818,11],{"className":52819},[407,408],[363,52821,461],{"className":52822},[494],[363,52824,1121],{"className":52825},[407,408],[363,52827,468],{"className":52828},[501],"，因此在密码学、随机性提取与 ",[1572,52831,52832],{},"Rényi 差分隐私（RDP）"," 中被用来对隐私预算做更紧致的记账。它与 f-散度族的\"同源\"关系也给出一条实用经验：讨论可加性、信息几何与变分表示时用 f-散度更顺手，讨论误差指数与熵时用它的对数版本更自然。",[2658,52835,52837],{"id":52836},"_38-汇总表","3.8 汇总表",[52839,52840,52841,52936],"table",{},[52842,52843,52844],"thead",{},[52845,52846,52847,52851,52897,52899,52902],"tr",{},[52848,52849,52850],"th",{},"散度",[52848,52852,52853],{},[363,52854,52856,52876],{"className":52855,"translate":367},[366],[363,52857,52859],{"className":52858},[371],[373,52860,52861],{"xmlns":375},[377,52862,52863,52873],{},[380,52864,52865,52867,52869,52871],{},[383,52866,385],{},[458,52868,461],{"stretchy":460},[383,52870,1116],{},[458,52872,468],{"stretchy":460},[387,52874,52875],{"encoding":389},"f(t)",[363,52877,52879],{"className":52878,"ariaHidden":394},[393],[363,52880,52882,52885,52888,52891,52894],{"className":52881},[398],[363,52883],{"className":52884,"style":487},[402],[363,52886,385],{"className":52887,"style":409},[407,408],[363,52889,461],{"className":52890},[494],[363,52892,1116],{"className":52893},[407,408],[363,52895,468],{"className":52896},[501],[52848,52898,30033],{},[52848,52900,52901],{},"有界",[52848,52903,52904,52935],{},[363,52905,52907,52923],{"className":52906,"translate":367},[366],[363,52908,52910],{"className":52909},[371],[373,52911,52912],{"xmlns":375},[377,52913,52914,52920],{},[380,52915,52916,52918],{},[383,52917,47020],{},[458,52919,4450],{},[387,52921,52922],{"encoding":389},"\\lim",[363,52924,52926],{"className":52925,"ariaHidden":394},[393],[363,52927,52929,52932],{"className":52928},[398],[363,52930],{"className":52931,"style":12944},[402],[363,52933,47020],{"className":52934},[1831]," 行为（不重叠支撑）",[52937,52938,52939,53140,53339,53467,53865,54084,54279,54559,54835],"tbody",{},[52845,52940,52941,53049,53100,53103,53105],{},[52942,52943,52944,52945],"td",{},"KL ",[363,52946,52948,52979],{"className":52947,"translate":367},[366],[363,52949,52951],{"className":52950},[371],[373,52952,52953],{"xmlns":375},[377,52954,52955,52977],{},[380,52956,52957,52967,52969,52971,52973,52975],{},[543,52958,52959,52961],{},[383,52960,547],{},[380,52962,52963,52965],{},[383,52964,11041],{},[383,52966,22240],{},[458,52968,461],{"stretchy":460},[383,52970,554],{},[383,52972,558],{"mathvariant":557},[383,52974,561],{},[458,52976,468],{"stretchy":460},[387,52978,24700],{"encoding":389},[363,52980,52982],{"className":52981,"ariaHidden":394},[393],[363,52983,52985,52988,53034,53037,53040,53043,53046],{"className":52984},[398],[363,52986],{"className":52987,"style":487},[402],[363,52989,52991,52994],{"className":52990},[407],[363,52992,547],{"className":52993,"style":625},[407,408],[363,52995,52997],{"className":52996},[629],[363,52998,53000,53026],{"className":52999},[633,634],[363,53001,53003,53023],{"className":53002},[638],[363,53004,53006],{"className":53005,"style":727},[642],[363,53007,53008,53011],{"style":646},[363,53009],{"className":53010,"style":651},[650],[363,53012,53014],{"className":53013},[655,656,657,658],[363,53015,53017,53020],{"className":53016},[407,658],[363,53018,11041],{"className":53019,"style":11129},[407,408,658],[363,53021,22240],{"className":53022},[407,408,658],[363,53024,666],{"className":53025},[665],[363,53027,53029],{"className":53028},[638],[363,53030,53032],{"className":53031,"style":8315},[642],[363,53033],{},[363,53035,461],{"className":53036},[494],[363,53038,554],{"className":53039,"style":682},[407,408],[363,53041,558],{"className":53042},[407],[363,53044,561],{"className":53045},[407,408],[363,53047,468],{"className":53048},[501],[52942,53050,53051],{},[363,53052,53054,53074],{"className":53053,"translate":367},[366],[363,53055,53057],{"className":53056},[371],[373,53058,53059],{"xmlns":375},[377,53060,53061,53071],{},[380,53062,53063,53065,53067,53069],{},[383,53064,1116],{},[383,53066,4447],{},[458,53068,4450],{},[383,53070,1116],{},[387,53072,53073],{"encoding":389},"t\\log t",[363,53075,53077],{"className":53076,"ariaHidden":394},[393],[363,53078,53080,53083,53086,53089,53094,53097],{"className":53079},[398],[363,53081],{"className":53082,"style":403},[402],[363,53084,1116],{"className":53085},[407,408],[363,53087],{"className":53088,"style":754},[505],[363,53090,4501,53092],{"className":53091},[1831],[363,53093,4505],{"style":4504},[363,53095],{"className":53096,"style":754},[505],[363,53098,1116],{"className":53099},[407,408],[52942,53101,53102],{},"否",[52942,53104,53102],{},[52942,53106,53107],{},[363,53108,53110,53125],{"className":53109,"translate":367},[366],[363,53111,53113],{"className":53112},[371],[373,53114,53115],{"xmlns":375},[377,53116,53117,53123],{},[380,53118,53119,53121],{},[458,53120,2817],{},[383,53122,1371],{"mathvariant":557},[387,53124,4588],{"encoding":389},[363,53126,53128],{"className":53127,"ariaHidden":394},[393],[363,53129,53131,53134,53137],{"className":53130},[398],[363,53132],{"className":53133,"style":4598},[402],[363,53135,2817],{"className":53136},[407],[363,53138,1371],{"className":53139},[407],[52845,53141,53142,53249,53300,53302,53304],{},[52942,53143,53144,53145],{},"反向 KL ",[363,53146,53148,53179],{"className":53147,"translate":367},[366],[363,53149,53151],{"className":53150},[371],[373,53152,53153],{"xmlns":375},[377,53154,53155,53177],{},[380,53156,53157,53167,53169,53171,53173,53175],{},[543,53158,53159,53161],{},[383,53160,547],{},[380,53162,53163,53165],{},[383,53164,11041],{},[383,53166,22240],{},[458,53168,461],{"stretchy":460},[383,53170,561],{},[383,53172,558],{"mathvariant":557},[383,53174,554],{},[458,53176,468],{"stretchy":460},[387,53178,22722],{"encoding":389},[363,53180,53182],{"className":53181,"ariaHidden":394},[393],[363,53183,53185,53188,53234,53237,53240,53243,53246],{"className":53184},[398],[363,53186],{"className":53187,"style":487},[402],[363,53189,53191,53194],{"className":53190},[407],[363,53192,547],{"className":53193,"style":625},[407,408],[363,53195,53197],{"className":53196},[629],[363,53198,53200,53226],{"className":53199},[633,634],[363,53201,53203,53223],{"className":53202},[638],[363,53204,53206],{"className":53205,"style":727},[642],[363,53207,53208,53211],{"style":646},[363,53209],{"className":53210,"style":651},[650],[363,53212,53214],{"className":53213},[655,656,657,658],[363,53215,53217,53220],{"className":53216},[407,658],[363,53218,11041],{"className":53219,"style":11129},[407,408,658],[363,53221,22240],{"className":53222},[407,408,658],[363,53224,666],{"className":53225},[665],[363,53227,53229],{"className":53228},[638],[363,53230,53232],{"className":53231,"style":8315},[642],[363,53233],{},[363,53235,461],{"className":53236},[494],[363,53238,561],{"className":53239},[407,408],[363,53241,558],{"className":53242},[407],[363,53244,554],{"className":53245,"style":682},[407,408],[363,53247,468],{"className":53248},[501],[52942,53250,53251],{},[363,53252,53254,53274],{"className":53253,"translate":367},[366],[363,53255,53257],{"className":53256},[371],[373,53258,53259],{"xmlns":375},[377,53260,53261,53271],{},[380,53262,53263,53265,53267,53269],{},[458,53264,5160],{},[383,53266,4447],{},[458,53268,4450],{},[383,53270,1116],{},[387,53272,53273],{"encoding":389},"-\\log t",[363,53275,53277],{"className":53276,"ariaHidden":394},[393],[363,53278,53280,53283,53286,53289,53294,53297],{"className":53279},[398],[363,53281],{"className":53282,"style":403},[402],[363,53284,5160],{"className":53285},[407],[363,53287],{"className":53288,"style":754},[505],[363,53290,4501,53292],{"className":53291},[1831],[363,53293,4505],{"style":4504},[363,53295],{"className":53296,"style":754},[505],[363,53298,1116],{"className":53299},[407,408],[52942,53301,53102],{},[52942,53303,53102],{},[52942,53305,53306],{},[363,53307,53309,53324],{"className":53308,"translate":367},[366],[363,53310,53312],{"className":53311},[371],[373,53313,53314],{"xmlns":375},[377,53315,53316,53322],{},[380,53317,53318,53320],{},[458,53319,2817],{},[383,53321,1371],{"mathvariant":557},[387,53323,4588],{"encoding":389},[363,53325,53327],{"className":53326,"ariaHidden":394},[393],[363,53328,53330,53333,53336],{"className":53329},[398],[363,53331],{"className":53332,"style":4598},[402],[363,53334,2817],{"className":53335},[407],[363,53337,1371],{"className":53338},[407],[52845,53340,53341,53344,53427,53430,53432],{},[52942,53342,53343],{},"Jeffreys（对称 KL）",[52942,53345,53346],{},[363,53347,53349,53377],{"className":53348,"translate":367},[366],[363,53350,53352],{"className":53351},[371],[373,53353,53354],{"xmlns":375},[377,53355,53356,53374],{},[380,53357,53358,53360,53362,53364,53366,53368,53370,53372],{},[458,53359,461],{"stretchy":460},[383,53361,1116],{},[458,53363,5160],{},[463,53365,465],{},[458,53367,468],{"stretchy":460},[383,53369,4447],{},[458,53371,4450],{},[383,53373,1116],{},[387,53375,53376],{"encoding":389},"(t-1)\\log t",[363,53378,53380,53401],{"className":53379,"ariaHidden":394},[393],[363,53381,53383,53386,53389,53392,53395,53398],{"className":53382},[398],[363,53384],{"className":53385,"style":487},[402],[363,53387,461],{"className":53388},[494],[363,53390,1116],{"className":53391},[407,408],[363,53393],{"className":53394,"style":2934},[505],[363,53396,5160],{"className":53397},[2938],[363,53399],{"className":53400,"style":2934},[505],[363,53402,53404,53407,53410,53413,53416,53421,53424],{"className":53403},[398],[363,53405],{"className":53406,"style":487},[402],[363,53408,465],{"className":53409},[407],[363,53411,468],{"className":53412},[501],[363,53414],{"className":53415,"style":754},[505],[363,53417,4501,53419],{"className":53418},[1831],[363,53420,4505],{"style":4504},[363,53422],{"className":53423,"style":754},[505],[363,53425,1116],{"className":53426},[407,408],[52942,53428,53429],{},"是",[52942,53431,53102],{},[52942,53433,53434],{},[363,53435,53437,53452],{"className":53436,"translate":367},[366],[363,53438,53440],{"className":53439},[371],[373,53441,53442],{"xmlns":375},[377,53443,53444,53450],{},[380,53445,53446,53448],{},[458,53447,2817],{},[383,53449,1371],{"mathvariant":557},[387,53451,4588],{"encoding":389},[363,53453,53455],{"className":53454,"ariaHidden":394},[393],[363,53456,53458,53461,53464],{"className":53457},[398],[363,53459],{"className":53460,"style":4598},[402],[363,53462,2817],{"className":53463},[407],[363,53465,1371],{"className":53466},[407],[52845,53468,53469,53472,53762,53764,53823],{},[52942,53470,53471],{},"JS",[52942,53473,53474],{},[363,53475,53477,53535],{"className":53476,"translate":367},[366],[363,53478,53480],{"className":53479},[371],[373,53481,53482],{"xmlns":375},[377,53483,53484,53532],{},[380,53485,53486,53492,53494,53496,53498,53500,53502,53504,53506,53508,53510,53512,53514,53516,53518,53530],{},[586,53487,53488,53490],{},[463,53489,465],{},[463,53491,2810],{},[458,53493,578],{"stretchy":460},[383,53495,1116],{},[383,53497,4447],{},[458,53499,4450],{},[383,53501,1116],{},[458,53503,5160],{},[458,53505,461],{"stretchy":460},[383,53507,1116],{},[458,53509,2817],{},[463,53511,465],{},[458,53513,468],{"stretchy":460},[383,53515,4447],{},[458,53517,4450],{},[586,53519,53520,53528],{},[380,53521,53522,53524,53526],{},[383,53523,1116],{},[458,53525,2817],{},[463,53527,465],{},[463,53529,2810],{},[458,53531,605],{"stretchy":460},[387,53533,53534],{"encoding":389},"\\frac12[t\\log t-(t+1)\\log\\frac{t+1}{2}]",[363,53536,53538,53641,53662],{"className":53537,"ariaHidden":394},[393],[363,53539,53541,53544,53612,53615,53618,53621,53626,53629,53632,53635,53638],{"className":53540},[398],[363,53542],{"className":53543,"style":2852},[402],[363,53545,53547,53550,53609],{"className":53546},[407],[363,53548],{"className":53549},[494,789],[363,53551,53553],{"className":53552},[586],[363,53554,53556,53601],{"className":53555},[633,634],[363,53557,53559,53598],{"className":53558},[638],[363,53560,53562,53576,53584],{"className":53561,"style":2871},[642],[363,53563,53564,53567],{"style":2874},[363,53565],{"className":53566,"style":809},[650],[363,53568,53570],{"className":53569},[655,656,657,658],[363,53571,53573],{"className":53572},[407,658],[363,53574,2810],{"className":53575},[407,658],[363,53577,53578,53581],{"style":821},[363,53579],{"className":53580,"style":809},[650],[363,53582],{"className":53583,"style":829},[828],[363,53585,53586,53589],{"style":2897},[363,53587],{"className":53588,"style":809},[650],[363,53590,53592],{"className":53591},[655,656,657,658],[363,53593,53595],{"className":53594},[407,658],[363,53596,465],{"className":53597},[407,658],[363,53599,666],{"className":53600},[665],[363,53602,53604],{"className":53603},[638],[363,53605,53607],{"className":53606,"style":2919},[642],[363,53608],{},[363,53610],{"className":53611},[501,789],[363,53613,578],{"className":53614},[494],[363,53616,1116],{"className":53617},[407,408],[363,53619],{"className":53620,"style":754},[505],[363,53622,4501,53624],{"className":53623},[1831],[363,53625,4505],{"style":4504},[363,53627],{"className":53628,"style":754},[505],[363,53630,1116],{"className":53631},[407,408],[363,53633],{"className":53634,"style":2934},[505],[363,53636,5160],{"className":53637},[2938],[363,53639],{"className":53640,"style":2934},[505],[363,53642,53644,53647,53650,53653,53656,53659],{"className":53643},[398],[363,53645],{"className":53646,"style":487},[402],[363,53648,461],{"className":53649},[494],[363,53651,1116],{"className":53652},[407,408],[363,53654],{"className":53655,"style":2934},[505],[363,53657,2817],{"className":53658},[2938],[363,53660],{"className":53661,"style":2934},[505],[363,53663,53665,53668,53671,53674,53677,53682,53685,53759],{"className":53664},[398],[363,53666],{"className":53667,"style":2852},[402],[363,53669,465],{"className":53670},[407],[363,53672,468],{"className":53673},[501],[363,53675],{"className":53676,"style":754},[505],[363,53678,4501,53680],{"className":53679},[1831],[363,53681,4505],{"style":4504},[363,53683],{"className":53684,"style":754},[505],[363,53686,53688,53691,53756],{"className":53687},[407],[363,53689],{"className":53690},[494,789],[363,53692,53694],{"className":53693},[586],[363,53695,53697,53748],{"className":53696},[633,634],[363,53698,53700,53745],{"className":53699},[638],[363,53701,53703,53717,53725],{"className":53702,"style":2871},[642],[363,53704,53705,53708],{"style":2874},[363,53706],{"className":53707,"style":809},[650],[363,53709,53711],{"className":53710},[655,656,657,658],[363,53712,53714],{"className":53713},[407,658],[363,53715,2810],{"className":53716},[407,658],[363,53718,53719,53722],{"style":821},[363,53720],{"className":53721,"style":809},[650],[363,53723],{"className":53724,"style":829},[828],[363,53726,53727,53730],{"style":2897},[363,53728],{"className":53729,"style":809},[650],[363,53731,53733],{"className":53732},[655,656,657,658],[363,53734,53736,53739,53742],{"className":53735},[407,658],[363,53737,1116],{"className":53738},[407,408,658],[363,53740,2817],{"className":53741},[2938,658],[363,53743,465],{"className":53744},[407,658],[363,53746,666],{"className":53747},[665],[363,53749,53751],{"className":53750},[638],[363,53752,53754],{"className":53753,"style":2919},[642],[363,53755],{},[363,53757],{"className":53758},[501,789],[363,53760,605],{"className":53761},[501],[52942,53763,53429],{},[52942,53765,53766,53767,53822],{},"是（",[363,53768,53770,53790],{"className":53769,"translate":367},[366],[363,53771,53773],{"className":53772},[371],[373,53774,53775],{"xmlns":375},[377,53776,53777,53787],{},[380,53778,53779,53781,53783,53785],{},[458,53780,10299],{},[383,53782,4447],{},[458,53784,4450],{},[463,53786,2810],{},[387,53788,53789],{"encoding":389},"\\le\\log2",[363,53791,53793,53805],{"className":53792,"ariaHidden":394},[393],[363,53794,53796,53799,53802],{"className":53795},[398],[363,53797],{"className":53798,"style":43535},[402],[363,53800,10299],{"className":53801},[510],[363,53803],{"className":53804,"style":506},[505],[363,53806,53808,53811,53816,53819],{"className":53807},[398],[363,53809],{"className":53810,"style":403},[402],[363,53812,4501,53814],{"className":53813},[1831],[363,53815,4505],{"style":4504},[363,53817],{"className":53818,"style":754},[505],[363,53820,2810],{"className":53821},[407],"）",[52942,53824,53825],{},[363,53826,53828,53845],{"className":53827,"translate":367},[366],[363,53829,53831],{"className":53830},[371],[373,53832,53833],{"xmlns":375},[377,53834,53835,53843],{},[380,53836,53837,53839,53841],{},[383,53838,4447],{},[458,53840,4450],{},[463,53842,2810],{},[387,53844,34651],{"encoding":389},[363,53846,53848],{"className":53847,"ariaHidden":394},[393],[363,53849,53851,53854,53859,53862],{"className":53850},[398],[363,53852],{"className":53853,"style":403},[402],[363,53855,4501,53857],{"className":53856},[1831],[363,53858,4505],{"style":4504},[363,53860],{"className":53861,"style":754},[505],[363,53863,2810],{"className":53864},[407],[52845,53866,53867,53870,54007,54009,54054],{},[52942,53868,53869],{},"全变差 TV",[52942,53871,53872],{},[363,53873,53875,53903],{"className":53874,"translate":367},[366],[363,53876,53878],{"className":53877},[371],[373,53879,53880],{"xmlns":375},[377,53881,53882,53900],{},[380,53883,53884,53890,53892,53894,53896,53898],{},[586,53885,53886,53888],{},[463,53887,465],{},[463,53889,2810],{},[458,53891,5155],{"stretchy":460},[383,53893,1116],{},[458,53895,5160],{},[463,53897,465],{},[458,53899,5155],{"stretchy":460},[387,53901,53902],{"encoding":389},"\\frac12\\lvert t-1\\rvert",[363,53904,53906,53995],{"className":53905,"ariaHidden":394},[393],[363,53907,53909,53912,53980,53983,53986,53989,53992],{"className":53908},[398],[363,53910],{"className":53911,"style":2852},[402],[363,53913,53915,53918,53977],{"className":53914},[407],[363,53916],{"className":53917},[494,789],[363,53919,53921],{"className":53920},[586],[363,53922,53924,53969],{"className":53923},[633,634],[363,53925,53927,53966],{"className":53926},[638],[363,53928,53930,53944,53952],{"className":53929,"style":2871},[642],[363,53931,53932,53935],{"style":2874},[363,53933],{"className":53934,"style":809},[650],[363,53936,53938],{"className":53937},[655,656,657,658],[363,53939,53941],{"className":53940},[407,658],[363,53942,2810],{"className":53943},[407,658],[363,53945,53946,53949],{"style":821},[363,53947],{"className":53948,"style":809},[650],[363,53950],{"className":53951,"style":829},[828],[363,53953,53954,53957],{"style":2897},[363,53955],{"className":53956,"style":809},[650],[363,53958,53960],{"className":53959},[655,656,657,658],[363,53961,53963],{"className":53962},[407,658],[363,53964,465],{"className":53965},[407,658],[363,53967,666],{"className":53968},[665],[363,53970,53972],{"className":53971},[638],[363,53973,53975],{"className":53974,"style":2919},[642],[363,53976],{},[363,53978],{"className":53979},[501,789],[363,53981,5155],{"className":53982},[494],[363,53984,1116],{"className":53985},[407,408],[363,53987],{"className":53988,"style":2934},[505],[363,53990,5160],{"className":53991},[2938],[363,53993],{"className":53994,"style":2934},[505],[363,53996,53998,54001,54004],{"className":53997},[398],[363,53999],{"className":54000,"style":487},[402],[363,54002,465],{"className":54003},[407],[363,54005,5155],{"className":54006},[501],[52942,54008,53429],{},[52942,54010,53766,54011,53822],{},[363,54012,54014,54030],{"className":54013,"translate":367},[366],[363,54015,54017],{"className":54016},[371],[373,54018,54019],{"xmlns":375},[377,54020,54021,54027],{},[380,54022,54023,54025],{},[458,54024,10299],{},[463,54026,465],{},[387,54028,54029],{"encoding":389},"\\le1",[363,54031,54033,54045],{"className":54032,"ariaHidden":394},[393],[363,54034,54036,54039,54042],{"className":54035},[398],[363,54037],{"className":54038,"style":43535},[402],[363,54040,10299],{"className":54041},[510],[363,54043],{"className":54044,"style":506},[505],[363,54046,54048,54051],{"className":54047},[398],[363,54049],{"className":54050,"style":520},[402],[363,54052,465],{"className":54053},[407],[52942,54055,54056],{},[363,54057,54059,54072],{"className":54058,"translate":367},[366],[363,54060,54062],{"className":54061},[371],[373,54063,54064],{"xmlns":375},[377,54065,54066,54070],{},[380,54067,54068],{},[463,54069,465],{},[387,54071,465],{"encoding":389},[363,54073,54075],{"className":54074,"ariaHidden":394},[393],[363,54076,54078,54081],{"className":54077},[398],[363,54079],{"className":54080,"style":520},[402],[363,54082,465],{"className":54083},[407],[52845,54085,54086,54147,54240,54242,54244],{},[52942,54087,54088,54089],{},"Pearson ",[363,54090,54092,54109],{"className":54091,"translate":367},[366],[363,54093,54095],{"className":54094},[371],[373,54096,54097],{"xmlns":375},[377,54098,54099,54107],{},[380,54100,54101],{},[7161,54102,54103,54105],{},[383,54104,37796],{},[463,54106,2810],{},[387,54108,40741],{"encoding":389},[363,54110,54112],{"className":54111,"ariaHidden":394},[393],[363,54113,54115,54118],{"className":54114},[398],[363,54116],{"className":54117,"style":40751},[402],[363,54119,54121,54124],{"className":54120},[407],[363,54122,37796],{"className":54123},[407,408],[363,54125,54127],{"className":54126},[629],[363,54128,54130],{"className":54129},[633],[363,54131,54133],{"className":54132},[638],[363,54134,54136],{"className":54135,"style":20375},[642],[363,54137,54138,54141],{"style":7212},[363,54139],{"className":54140,"style":651},[650],[363,54142,54144],{"className":54143},[655,656,657,658],[363,54145,2810],{"className":54146},[407,658],[52942,54148,54149],{},[363,54150,54152,54178],{"className":54151,"translate":367},[366],[363,54153,54155],{"className":54154},[371],[373,54156,54157],{"xmlns":375},[377,54158,54159,54175],{},[380,54160,54161,54163,54165,54167,54169],{},[458,54162,461],{"stretchy":460},[383,54164,1116],{},[458,54166,5160],{},[463,54168,465],{},[7161,54170,54171,54173],{},[458,54172,468],{"stretchy":460},[463,54174,2810],{},[387,54176,54177],{"encoding":389},"(t-1)^2",[363,54179,54181,54202],{"className":54180,"ariaHidden":394},[393],[363,54182,54184,54187,54190,54193,54196,54199],{"className":54183},[398],[363,54185],{"className":54186,"style":487},[402],[363,54188,461],{"className":54189},[494],[363,54191,1116],{"className":54192},[407,408],[363,54194],{"className":54195,"style":2934},[505],[363,54197,5160],{"className":54198},[2938],[363,54200],{"className":54201,"style":2934},[505],[363,54203,54205,54208,54211],{"className":54204},[398],[363,54206],{"className":54207,"style":20350},[402],[363,54209,465],{"className":54210},[407],[363,54212,54214,54217],{"className":54213},[501],[363,54215,468],{"className":54216},[501],[363,54218,54220],{"className":54219},[629],[363,54221,54223],{"className":54222},[633],[363,54224,54226],{"className":54225},[638],[363,54227,54229],{"className":54228,"style":20375},[642],[363,54230,54231,54234],{"style":7212},[363,54232],{"className":54233,"style":651},[650],[363,54235,54237],{"className":54236},[655,656,657,658],[363,54238,2810],{"className":54239},[407,658],[52942,54241,53102],{},[52942,54243,53102],{},[52942,54245,54246],{},[363,54247,54249,54264],{"className":54248,"translate":367},[366],[363,54250,54252],{"className":54251},[371],[373,54253,54254],{"xmlns":375},[377,54255,54256,54262],{},[380,54257,54258,54260],{},[458,54259,2817],{},[383,54261,1371],{"mathvariant":557},[387,54263,4588],{"encoding":389},[363,54265,54267],{"className":54266,"ariaHidden":394},[393],[363,54268,54270,54273,54276],{"className":54269},[398],[363,54271],{"className":54272,"style":4598},[402],[363,54274,2817],{"className":54275},[407],[363,54277,1371],{"className":54278},[407],[52845,54280,54281,54367,54520,54522,54524],{},[52942,54282,54283,54284],{},"Neyman ",[363,54285,54287,54307],{"className":54286,"translate":367},[366],[363,54288,54290],{"className":54289},[371],[373,54291,54292],{"xmlns":375},[377,54293,54294,54304],{},[380,54295,54296],{},[7900,54297,54298,54300,54302],{},[383,54299,37796],{},[383,54301,38631],{},[463,54303,2810],{},[387,54305,54306],{"encoding":389},"\\chi^2_N",[363,54308,54310],{"className":54309,"ariaHidden":394},[393],[363,54311,54313,54316],{"className":54312},[398],[363,54314],{"className":54315,"style":38686},[402],[363,54317,54319,54322],{"className":54318},[407],[363,54320,37796],{"className":54321},[407,408],[363,54323,54325],{"className":54324},[629],[363,54326,54328,54359],{"className":54327},[633,634],[363,54329,54331,54356],{"className":54330},[638],[363,54332,54334,54345],{"className":54333,"style":20375},[642],[363,54335,54336,54339],{"style":38707},[363,54337],{"className":54338,"style":651},[650],[363,54340,54342],{"className":54341},[655,656,657,658],[363,54343,38631],{"className":54344,"style":25948},[407,408,658],[363,54346,54347,54350],{"style":7212},[363,54348],{"className":54349,"style":651},[650],[363,54351,54353],{"className":54352},[655,656,657,658],[363,54354,2810],{"className":54355},[407,658],[363,54357,666],{"className":54358},[665],[363,54360,54362],{"className":54361},[638],[363,54363,54365],{"className":54364,"style":38737},[642],[363,54366],{},[52942,54368,54369],{},[363,54370,54372,54404],{"className":54371,"translate":367},[366],[363,54373,54375],{"className":54374},[371],[373,54376,54377],{"xmlns":375},[377,54378,54379,54401],{},[380,54380,54381],{},[586,54382,54383,54399],{},[380,54384,54385,54387,54389,54391,54393],{},[458,54386,461],{"stretchy":460},[383,54388,1116],{},[458,54390,5160],{},[463,54392,465],{},[7161,54394,54395,54397],{},[458,54396,468],{"stretchy":460},[463,54398,2810],{},[383,54400,1116],{},[387,54402,54403],{"encoding":389},"\\frac{(t-1)^2}{t}",[363,54405,54407],{"className":54406,"ariaHidden":394},[393],[363,54408,54410,54414],{"className":54409},[398],[363,54411],{"className":54412,"style":54413},[402],"height:1.4539em;vertical-align:-0.345em;",[363,54415,54417,54420,54517],{"className":54416},[407],[363,54418],{"className":54419},[494,789],[363,54421,54423],{"className":54422},[586],[363,54424,54426,54509],{"className":54425},[633,634],[363,54427,54429,54506],{"className":54428},[638],[363,54430,54432,54446,54454],{"className":54431,"style":38795},[642],[363,54433,54434,54437],{"style":2874},[363,54435],{"className":54436,"style":809},[650],[363,54438,54440],{"className":54439},[655,656,657,658],[363,54441,54443],{"className":54442},[407,658],[363,54444,1116],{"className":54445},[407,408,658],[363,54447,54448,54451],{"style":821},[363,54449],{"className":54450,"style":809},[650],[363,54452],{"className":54453,"style":829},[828],[363,54455,54456,54459],{"style":26765},[363,54457],{"className":54458,"style":809},[650],[363,54460,54462],{"className":54461},[655,656,657,658],[363,54463,54465,54468,54471,54474,54477],{"className":54464},[407,658],[363,54466,461],{"className":54467},[494,658],[363,54469,1116],{"className":54470},[407,408,658],[363,54472,5160],{"className":54473},[2938,658],[363,54475,465],{"className":54476},[407,658],[363,54478,54480,54483],{"className":54479},[501,658],[363,54481,468],{"className":54482},[501,658],[363,54484,54486],{"className":54485},[629],[363,54487,54489],{"className":54488},[633],[363,54490,54492],{"className":54491},[638],[363,54493,54495],{"className":54494,"style":38859},[642],[363,54496,54497,54500],{"style":38862},[363,54498],{"className":54499,"style":30553},[650],[363,54501,54503],{"className":54502},[655,30557,10021,658],[363,54504,2810],{"className":54505},[407,658],[363,54507,666],{"className":54508},[665],[363,54510,54512],{"className":54511},[638],[363,54513,54515],{"className":54514,"style":2919},[642],[363,54516],{},[363,54518],{"className":54519},[501,789],[52942,54521,53102],{},[52942,54523,53102],{},[52942,54525,54526],{},[363,54527,54529,54544],{"className":54528,"translate":367},[366],[363,54530,54532],{"className":54531},[371],[373,54533,54534],{"xmlns":375},[377,54535,54536,54542],{},[380,54537,54538,54540],{},[458,54539,2817],{},[383,54541,1371],{"mathvariant":557},[387,54543,4588],{"encoding":389},[363,54545,54547],{"className":54546,"ariaHidden":394},[393],[363,54548,54550,54553,54556],{"className":54549},[398],[363,54551],{"className":54552,"style":4598},[402],[363,54554,2817],{"className":54555},[407],[363,54557,1371],{"className":54558},[407],[52845,54560,54561,54622,54758,54760,54805],{},[52942,54562,54563,54564,54621],{},"Hellinger",[363,54565,54567,54584],{"className":54566,"translate":367},[366],[363,54568,54570],{"className":54569},[371],[373,54571,54572],{"xmlns":375},[377,54573,54574,54582],{},[380,54575,54576],{},[7161,54577,54578,54580],{},[380,54579],{},[463,54581,2810],{},[387,54583,44616],{"encoding":389},[363,54585,54587],{"className":54586,"ariaHidden":394},[393],[363,54588,54590,54593],{"className":54589},[398],[363,54591],{"className":54592,"style":20375},[402],[363,54594,54596,54598],{"className":54595},[407],[363,54597],{},[363,54599,54601],{"className":54600},[629],[363,54602,54604],{"className":54603},[633],[363,54605,54607],{"className":54606},[638],[363,54608,54610],{"className":54609,"style":20375},[642],[363,54611,54612,54615],{"style":7212},[363,54613],{"className":54614,"style":651},[650],[363,54616,54618],{"className":54617},[655,656,657,658],[363,54619,2810],{"className":54620},[407,658],"（本文约定）",[52942,54623,54624],{},[363,54625,54627,54655],{"className":54626,"translate":367},[366],[363,54628,54630],{"className":54629},[371],[373,54631,54632],{"xmlns":375},[377,54633,54634,54652],{},[380,54635,54636,54638,54642,54644,54646],{},[458,54637,461],{"stretchy":460},[34686,54639,54640],{},[383,54641,1116],{},[458,54643,5160],{},[463,54645,465],{},[7161,54647,54648,54650],{},[458,54649,468],{"stretchy":460},[463,54651,2810],{},[387,54653,54654],{"encoding":389},"(\\sqrt t-1)^2",[363,54656,54658,54720],{"className":54657,"ariaHidden":394},[393],[363,54659,54661,54664,54667,54711,54714,54717],{"className":54660},[398],[363,54662],{"className":54663,"style":43014},[402],[363,54665,461],{"className":54666},[494],[363,54668,54670],{"className":54669},[407,34714],[363,54671,54673,54703],{"className":54672},[633,634],[363,54674,54676,54700],{"className":54675},[638],[363,54677,54679,54688],{"className":54678,"style":43030},[642],[363,54680,54682,54685],{"className":54681,"style":12210},[6654],[363,54683],{"className":54684,"style":809},[650],[363,54686,1116],{"className":54687,"style":34734},[407,408],[363,54689,54690,54693],{"style":43042},[363,54691],{"className":54692,"style":809},[650],[363,54694,54696],{"className":54695,"style":34791},[34790],[6670,54697,54698],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,54699],{"d":34798},[363,54701,666],{"className":54702},[665],[363,54704,54706],{"className":54705},[638],[363,54707,54709],{"className":54708,"style":43062},[642],[363,54710],{},[363,54712],{"className":54713,"style":2934},[505],[363,54715,5160],{"className":54716},[2938],[363,54718],{"className":54719,"style":2934},[505],[363,54721,54723,54726,54729],{"className":54722},[398],[363,54724],{"className":54725,"style":20350},[402],[363,54727,465],{"className":54728},[407],[363,54730,54732,54735],{"className":54731},[501],[363,54733,468],{"className":54734},[501],[363,54736,54738],{"className":54737},[629],[363,54739,54741],{"className":54740},[633],[363,54742,54744],{"className":54743},[638],[363,54745,54747],{"className":54746,"style":20375},[642],[363,54748,54749,54752],{"style":7212},[363,54750],{"className":54751,"style":651},[650],[363,54753,54755],{"className":54754},[655,656,657,658],[363,54756,2810],{"className":54757},[407,658],[52942,54759,53429],{},[52942,54761,53766,54762,53822],{},[363,54763,54765,54781],{"className":54764,"translate":367},[366],[363,54766,54768],{"className":54767},[371],[373,54769,54770],{"xmlns":375},[377,54771,54772,54778],{},[380,54773,54774,54776],{},[458,54775,10299],{},[463,54777,2810],{},[387,54779,54780],{"encoding":389},"\\le2",[363,54782,54784,54796],{"className":54783,"ariaHidden":394},[393],[363,54785,54787,54790,54793],{"className":54786},[398],[363,54788],{"className":54789,"style":43535},[402],[363,54791,10299],{"className":54792},[510],[363,54794],{"className":54795,"style":506},[505],[363,54797,54799,54802],{"className":54798},[398],[363,54800],{"className":54801,"style":520},[402],[363,54803,2810],{"className":54804},[407],[52942,54806,54807],{},[363,54808,54810,54823],{"className":54809,"translate":367},[366],[363,54811,54813],{"className":54812},[371],[373,54814,54815],{"xmlns":375},[377,54816,54817,54821],{},[380,54818,54819],{},[463,54820,2810],{},[387,54822,2810],{"encoding":389},[363,54824,54826],{"className":54825,"ariaHidden":394},[393],[363,54827,54829,54832],{"className":54828},[398],[363,54830],{"className":54831,"style":520},[402],[363,54833,2810],{"className":54834},[407],[52845,54836,54837,54918,55161,55163,55165],{},[52942,54838,54839,54840],{},"α-散度 ",[363,54841,54843,54870],{"className":54842,"translate":367},[366],[363,54844,54846],{"className":54845},[371],[373,54847,54848],{"xmlns":375},[377,54849,54850,54868],{},[380,54851,54852,54854,54856,54858,54860,54862,54864,54866],{},[383,54853,45101],{},[458,54855,6256],{},[458,54857,461],{"stretchy":460},[458,54859,5160],{},[463,54861,465],{},[458,54863,898],{"separator":394},[463,54865,465],{},[458,54867,468],{"stretchy":460},[387,54869,45118],{"encoding":389},[363,54871,54873,54891],{"className":54872,"ariaHidden":394},[393],[363,54874,54876,54879,54882,54885,54888],{"className":54875},[398],[363,54877],{"className":54878,"style":6271},[402],[363,54880,45101],{"className":54881,"style":45131},[407,408],[363,54883],{"className":54884,"style":506},[505],[363,54886,6256],{"className":54887},[510],[363,54889],{"className":54890,"style":506},[505],[363,54892,54894,54897,54900,54903,54906,54909,54912,54915],{"className":54893},[398],[363,54895],{"className":54896,"style":487},[402],[363,54898,461],{"className":54899},[494],[363,54901,5160],{"className":54902},[407],[363,54904,465],{"className":54905},[407],[363,54907,898],{"className":54908},[920],[363,54910],{"className":54911,"style":754},[505],[363,54913,465],{"className":54914},[407],[363,54916,468],{"className":54917},[501],[52942,54919,54920],{},[363,54921,54923,54979],{"className":54922,"translate":367},[366],[363,54924,54926],{"className":54925},[371],[373,54927,54928],{"xmlns":375},[377,54929,54930,54976],{},[380,54931,54932,54948,54950,54952,54954,54974],{},[586,54933,54934,54936],{},[463,54935,39336],{},[380,54937,54938,54940,54942],{},[463,54939,465],{},[458,54941,5160],{},[7161,54943,54944,54946],{},[383,54945,45101],{},[463,54947,2810],{},[458,54949,461],{"stretchy":460},[463,54951,465],{},[458,54953,5160],{},[7161,54955,54956,54958],{},[383,54957,1116],{},[380,54959,54960,54962,54964,54966,54968,54970,54972],{},[458,54961,461],{"stretchy":460},[463,54963,465],{},[458,54965,2817],{},[383,54967,45101],{},[458,54969,468],{"stretchy":460},[383,54971,1288],{"mathvariant":557},[463,54973,2810],{},[458,54975,468],{"stretchy":460},[387,54977,54978],{"encoding":389},"\\frac{4}{1-\\alpha^2}(1-t^{(1+\\alpha)\u002F2})",[363,54980,54982,55103],{"className":54981,"ariaHidden":394},[393],[363,54983,54985,54988,55088,55091,55094,55097,55100],{"className":54984},[398],[363,54986],{"className":54987,"style":45752},[402],[363,54989,54991,54994,55085],{"className":54990},[407],[363,54992],{"className":54993},[494,789],[363,54995,54997],{"className":54996},[586],[363,54998,55000,55077],{"className":54999},[633,634],[363,55001,55003,55074],{"className":55002},[638],[363,55004,55006,55052,55060],{"className":55005,"style":2871},[642],[363,55007,55008,55011],{"style":2874},[363,55009],{"className":55010,"style":809},[650],[363,55012,55014],{"className":55013},[655,656,657,658],[363,55015,55017,55020,55023],{"className":55016},[407,658],[363,55018,465],{"className":55019},[407,658],[363,55021,5160],{"className":55022},[2938,658],[363,55024,55026,55029],{"className":55025},[407,658],[363,55027,45101],{"className":55028,"style":45131},[407,408,658],[363,55030,55032],{"className":55031},[629],[363,55033,55035],{"className":55034},[633],[363,55036,55038],{"className":55037},[638],[363,55039,55041],{"className":55040,"style":45806},[642],[363,55042,55043,55046],{"style":45809},[363,55044],{"className":55045,"style":30553},[650],[363,55047,55049],{"className":55048},[655,30557,10021,658],[363,55050,2810],{"className":55051},[407,658],[363,55053,55054,55057],{"style":821},[363,55055],{"className":55056,"style":809},[650],[363,55058],{"className":55059,"style":829},[828],[363,55061,55062,55065],{"style":2897},[363,55063],{"className":55064,"style":809},[650],[363,55066,55068],{"className":55067},[655,656,657,658],[363,55069,55071],{"className":55070},[407,658],[363,55072,39336],{"className":55073},[407,658],[363,55075,666],{"className":55076},[665],[363,55078,55080],{"className":55079},[638],[363,55081,55083],{"className":55082,"style":16776},[642],[363,55084],{},[363,55086],{"className":55087},[501,789],[363,55089,461],{"className":55090},[494],[363,55092,465],{"className":55093},[407],[363,55095],{"className":55096,"style":2934},[505],[363,55098,5160],{"className":55099},[2938],[363,55101],{"className":55102,"style":2934},[505],[363,55104,55106,55110,55158],{"className":55105},[398],[363,55107],{"className":55108,"style":55109},[402],"height:1.138em;vertical-align:-0.25em;",[363,55111,55113,55116],{"className":55112},[407],[363,55114,1116],{"className":55115},[407,408],[363,55117,55119],{"className":55118},[629],[363,55120,55122],{"className":55121},[633],[363,55123,55125],{"className":55124},[638],[363,55126,55129],{"className":55127,"style":55128},[642],"height:0.888em;",[363,55130,55131,55134],{"style":7212},[363,55132],{"className":55133,"style":651},[650],[363,55135,55137],{"className":55136},[655,656,657,658],[363,55138,55140,55143,55146,55149,55152,55155],{"className":55139},[407,658],[363,55141,461],{"className":55142},[494,658],[363,55144,465],{"className":55145},[407,658],[363,55147,2817],{"className":55148},[2938,658],[363,55150,45101],{"className":55151,"style":45131},[407,408,658],[363,55153,468],{"className":55154},[501,658],[363,55156,45497],{"className":55157},[407,658],[363,55159,468],{"className":55160},[501],[52942,55162,53102],{},[52942,55164,53102],{},[52942,55166,55167,55168,53822],{},"有限（",[363,55169,55171,55191],{"className":55170,"translate":367},[366],[363,55172,55174],{"className":55173},[371],[373,55175,55176],{"xmlns":375},[377,55177,55178,55188],{},[380,55179,55180,55182,55184,55186],{},[383,55181,45101],{},[458,55183,49854],{"mathvariant":557},[458,55185,46955],{},[463,55187,465],{},[387,55189,55190],{"encoding":389},"\\alpha\\ne\\pm1",[363,55192,55194,55245],{"className":55193,"ariaHidden":394},[393],[363,55195,55197,55200,55203,55206,55242],{"className":55196},[398],[363,55198],{"className":55199,"style":403},[402],[363,55201,45101],{"className":55202,"style":45131},[407,408],[363,55204],{"className":55205,"style":506},[505],[363,55207,55209,55236,55239],{"className":55208},[510],[363,55210,55212],{"className":55211},[510],[363,55213,55215],{"className":55214},[407,4747],[363,55216,55218],{"className":55217},[4751],[363,55219,55221,55224,55233],{"className":55220},[4755],[363,55222],{"className":55223,"style":403},[402],[363,55225,55227],{"className":55226},[4762],[363,55228,55230],{"className":55229},[407],[363,55231,4769],{"className":55232},[510],[363,55234],{"className":55235},[4773],[363,55237],{"className":55238},[505,4777],[363,55240,471],{"className":55241},[510],[363,55243],{"className":55244,"style":506},[505],[363,55246,55248,55251,55254],{"className":55247},[398],[363,55249],{"className":55250,"style":12925},[402],[363,55252,46955],{"className":55253},[407],[363,55255,465],{"className":55256},[407],[18,55258,55260],{"id":55259},"_4-基本性质","4. 基本性质",[11,55262,55263,55264,16142,55328,55485,55486,10527],{},"下列性质逐个给出推导。约定 ",[363,55265,55267,55289],{"className":55266,"translate":367},[366],[363,55268,55270],{"className":55269},[371],[373,55271,55272],{"xmlns":375},[377,55273,55274,55286],{},[380,55275,55276,55278,55280,55282,55284],{},[383,55277,554],{},[458,55279,898],{"separator":394},[383,55281,561],{},[458,55283,1061],{},[383,55285,2711],{},[387,55287,55288],{"encoding":389},"P,Q\\ll\\mu",[363,55290,55292,55319],{"className":55291,"ariaHidden":394},[393],[363,55293,55295,55298,55301,55304,55307,55310,55313,55316],{"className":55294},[398],[363,55296],{"className":55297,"style":913},[402],[363,55299,554],{"className":55300,"style":682},[407,408],[363,55302,898],{"className":55303},[920],[363,55305],{"className":55306,"style":754},[505],[363,55308,561],{"className":55309},[407,408],[363,55311],{"className":55312,"style":506},[505],[363,55314,1061],{"className":55315},[510],[363,55317],{"className":55318,"style":506},[505],[363,55320,55322,55325],{"className":55321},[398],[363,55323],{"className":55324,"style":2623},[402],[363,55326,2711],{"className":55327},[407,408],[363,55329,55331,55363],{"className":55330,"translate":367},[366],[363,55332,55334],{"className":55333},[371],[373,55335,55336],{"xmlns":375},[377,55337,55338,55360],{},[380,55339,55340,55342,55344,55350,55352,55354,55356,55358],{},[383,55341,2711],{},[458,55343,471],{},[586,55345,55346,55348],{},[463,55347,465],{},[463,55349,2810],{},[458,55351,461],{"stretchy":460},[383,55353,554],{},[458,55355,2817],{},[383,55357,561],{},[458,55359,468],{"stretchy":460},[387,55361,55362],{"encoding":389},"\\mu=\\frac12(P+Q)",[363,55364,55366,55384,55473],{"className":55365,"ariaHidden":394},[393],[363,55367,55369,55372,55375,55378,55381],{"className":55368},[398],[363,55370],{"className":55371,"style":2623},[402],[363,55373,2711],{"className":55374},[407,408],[363,55376],{"className":55377,"style":506},[505],[363,55379,471],{"className":55380},[510],[363,55382],{"className":55383,"style":506},[505],[363,55385,55387,55390,55458,55461,55464,55467,55470],{"className":55386},[398],[363,55388],{"className":55389,"style":2852},[402],[363,55391,55393,55396,55455],{"className":55392},[407],[363,55394],{"className":55395},[494,789],[363,55397,55399],{"className":55398},[586],[363,55400,55402,55447],{"className":55401},[633,634],[363,55403,55405,55444],{"className":55404},[638],[363,55406,55408,55422,55430],{"className":55407,"style":2871},[642],[363,55409,55410,55413],{"style":2874},[363,55411],{"className":55412,"style":809},[650],[363,55414,55416],{"className":55415},[655,656,657,658],[363,55417,55419],{"className":55418},[407,658],[363,55420,2810],{"className":55421},[407,658],[363,55423,55424,55427],{"style":821},[363,55425],{"className":55426,"style":809},[650],[363,55428],{"className":55429,"style":829},[828],[363,55431,55432,55435],{"style":2897},[363,55433],{"className":55434,"style":809},[650],[363,55436,55438],{"className":55437},[655,656,657,658],[363,55439,55441],{"className":55440},[407,658],[363,55442,465],{"className":55443},[407,658],[363,55445,666],{"className":55446},[665],[363,55448,55450],{"className":55449},[638],[363,55451,55453],{"className":55452,"style":2919},[642],[363,55454],{},[363,55456],{"className":55457},[501,789],[363,55459,461],{"className":55460},[494],[363,55462,554],{"className":55463,"style":682},[407,408],[363,55465],{"className":55466,"style":2934},[505],[363,55468,2817],{"className":55469},[2938],[363,55471],{"className":55472,"style":2934},[505],[363,55474,55476,55479,55482],{"className":55475},[398],[363,55477],{"className":55478,"style":487},[402],[363,55480,561],{"className":55481},[407,408],[363,55483,468],{"className":55484},[501]," 或任一控制测度），",[363,55487,55489,55514],{"className":55488,"translate":367},[366],[363,55490,55492],{"className":55491},[371],[373,55493,55494],{"xmlns":375},[377,55495,55496,55512],{},[380,55497,55498,55500,55502,55504,55506,55508,55510],{},[383,55499,1116],{},[458,55501,471],{},[383,55503,592],{},[383,55505,554],{},[383,55507,1288],{"mathvariant":557},[383,55509,592],{},[383,55511,561],{},[387,55513,5680],{"encoding":389},[363,55515,55517,55535],{"className":55516,"ariaHidden":394},[393],[363,55518,55520,55523,55526,55529,55532],{"className":55519},[398],[363,55521],{"className":55522,"style":5690},[402],[363,55524,1116],{"className":55525},[407,408],[363,55527],{"className":55528,"style":506},[505],[363,55530,471],{"className":55531},[510],[363,55533],{"className":55534,"style":506},[505],[363,55536,55538,55541,55544,55547,55550,55553],{"className":55537},[398],[363,55539],{"className":55540,"style":487},[402],[363,55542,592],{"className":55543},[407,408],[363,55545,554],{"className":55546,"style":682},[407,408],[363,55548,1288],{"className":55549},[407],[363,55551,592],{"className":55552},[407,408],[363,55554,561],{"className":55555},[407,408],[2658,55557,55559],{"id":55558},"_41-非负性","4.1 非负性",[1340,55561,55563,55607,55732],{"title":55562},"命题 4.1（非负性）",[11,55564,55565,55566,3092],{},"对一切概率分布 ",[363,55567,55569,55586],{"className":55568,"translate":367},[366],[363,55570,55572],{"className":55571},[371],[373,55573,55574],{"xmlns":375},[377,55575,55576,55584],{},[380,55577,55578,55580,55582],{},[383,55579,554],{},[458,55581,898],{"separator":394},[383,55583,561],{},[387,55585,903],{"encoding":389},[363,55587,55589],{"className":55588,"ariaHidden":394},[393],[363,55590,55592,55595,55598,55601,55604],{"className":55591},[398],[363,55593],{"className":55594,"style":913},[402],[363,55596,554],{"className":55597,"style":682},[407,408],[363,55599,898],{"className":55600},[920],[363,55602],{"className":55603,"style":754},[505],[363,55605,561],{"className":55606},[407,408],[363,55608,55610],{"className":55609,"translate":367},[528],[363,55611,55613,55647],{"className":55612,"translate":367},[366],[363,55614,55616],{"className":55615},[371],[373,55617,55618],{"xmlns":375,"display":537},[377,55619,55620,55644],{},[380,55621,55622,55628,55630,55632,55634,55636,55638,55640,55642],{},[543,55623,55624,55626],{},[383,55625,547],{},[383,55627,385],{},[458,55629,461],{"stretchy":460},[383,55631,554],{},[383,55633,558],{"mathvariant":557},[383,55635,561],{},[458,55637,468],{"stretchy":460},[458,55639,7275],{},[463,55641,474],{},[458,55643,898],{"separator":394},[387,55645,55646],{"encoding":389},"D_f(P\\|Q)\\ge 0,",[363,55648,55650,55720],{"className":55649,"ariaHidden":394},[393],[363,55651,55653,55656,55696,55699,55702,55705,55708,55711,55714,55717],{"className":55652},[398],[363,55654],{"className":55655,"style":618},[402],[363,55657,55659,55662],{"className":55658},[407],[363,55660,547],{"className":55661,"style":625},[407,408],[363,55663,55665],{"className":55664},[629],[363,55666,55668,55688],{"className":55667},[633,634],[363,55669,55671,55685],{"className":55670},[638],[363,55672,55674],{"className":55673,"style":643},[642],[363,55675,55676,55679],{"style":646},[363,55677],{"className":55678,"style":651},[650],[363,55680,55682],{"className":55681},[655,656,657,658],[363,55683,385],{"className":55684,"style":409},[407,408,658],[363,55686,666],{"className":55687},[665],[363,55689,55691],{"className":55690},[638],[363,55692,55694],{"className":55693,"style":673},[642],[363,55695],{},[363,55697,461],{"className":55698},[494],[363,55700,554],{"className":55701,"style":682},[407,408],[363,55703,558],{"className":55704},[407],[363,55706,561],{"className":55707},[407,408],[363,55709,468],{"className":55710},[501],[363,55712],{"className":55713,"style":506},[505],[363,55715,7275],{"className":55716},[510],[363,55718],{"className":55719,"style":506},[505],[363,55721,55723,55726,55729],{"className":55722},[398],[363,55724],{"className":55725,"style":9705},[402],[363,55727,474],{"className":55728},[407],[363,55730,898],{"className":55731},[920],[11,55733,55734,55735,55763,55764,10527],{},"且当 ",[363,55736,55738,55751],{"className":55737,"translate":367},[366],[363,55739,55741],{"className":55740},[371],[373,55742,55743],{"xmlns":375},[377,55744,55745,55749],{},[380,55746,55747],{},[383,55748,385],{},[387,55750,385],{"encoding":389},[363,55752,55754],{"className":55753,"ariaHidden":394},[393],[363,55755,55757,55760],{"className":55756},[398],[363,55758],{"className":55759,"style":403},[402],[363,55761,385],{"className":55762,"style":409},[407,408]," 严格凸时，等号成立当且仅当 ",[363,55765,55767,55784],{"className":55766,"translate":367},[366],[363,55768,55770],{"className":55769},[371],[373,55771,55772],{"xmlns":375},[377,55773,55774,55782],{},[380,55775,55776,55778,55780],{},[383,55777,554],{},[458,55779,471],{},[383,55781,561],{},[387,55783,10618],{"encoding":389},[363,55785,55787,55805],{"className":55786,"ariaHidden":394},[393],[363,55788,55790,55793,55796,55799,55802],{"className":55789},[398],[363,55791],{"className":55792,"style":1011},[402],[363,55794,554],{"className":55795,"style":682},[407,408],[363,55797],{"className":55798,"style":506},[505],[363,55800,471],{"className":55801},[510],[363,55803],{"className":55804,"style":506},[505],[363,55806,55808,55811],{"className":55807},[398],[363,55809],{"className":55810,"style":913},[402],[363,55812,561],{"className":55813},[407,408],[11,55815,55816,55819,55820,55849,55850,55878,55879,4200,56008,56036,56037,56087,56088,56116,56117,56285,56286,56378,56379,56429,56430,56480],{},[1572,55817,55818],{},"证明。"," Jensen 已给出 ",[363,55821,55823,55837],{"className":55822,"translate":367},[366],[363,55824,55826],{"className":55825},[371],[373,55827,55828],{"xmlns":375},[377,55829,55830,55834],{},[380,55831,55832],{},[458,55833,7275],{},[387,55835,55836],{"encoding":389},"\\ge",[363,55838,55840],{"className":55839,"ariaHidden":394},[393],[363,55841,55843,55846],{"className":55842},[398],[363,55844],{"className":55845,"style":43535},[402],[363,55847,7275],{"className":55848},[510],"（见 2.1）。等号条件：若 ",[363,55851,55853,55866],{"className":55852,"translate":367},[366],[363,55854,55856],{"className":55855},[371],[373,55857,55858],{"xmlns":375},[377,55859,55860,55864],{},[380,55861,55862],{},[383,55863,385],{},[387,55865,385],{"encoding":389},[363,55867,55869],{"className":55868,"ariaHidden":394},[393],[363,55870,55872,55875],{"className":55871},[398],[363,55873],{"className":55874,"style":403},[402],[363,55876,385],{"className":55877,"style":409},[407,408]," 严格凸，Jensen 取等号当且仅当 ",[363,55880,55882,55914],{"className":55881,"translate":367},[366],[363,55883,55885],{"className":55884},[371],[373,55886,55887],{"xmlns":375},[377,55888,55889,55911],{},[380,55890,55891,55893,55895,55901,55903,55905,55907,55909],{},[383,55892,1116],{},[458,55894,471],{},[543,55896,55897,55899],{},[383,55898,571],{"mathvariant":570},[383,55900,561],{},[458,55902,578],{"stretchy":460},[383,55904,1116],{},[458,55906,605],{"stretchy":460},[458,55908,471],{},[463,55910,465],{},[387,55912,55913],{"encoding":389},"t=\\mathbb E_Q[t]=1",[363,55915,55917,55935,55999],{"className":55916,"ariaHidden":394},[393],[363,55918,55920,55923,55926,55929,55932],{"className":55919},[398],[363,55921],{"className":55922,"style":5690},[402],[363,55924,1116],{"className":55925},[407,408],[363,55927],{"className":55928,"style":506},[505],[363,55930,471],{"className":55931},[510],[363,55933],{"className":55934,"style":506},[505],[363,55936,55938,55941,55981,55984,55987,55990,55993,55996],{"className":55937},[398],[363,55939],{"className":55940,"style":618},[402],[363,55942,55944,55947],{"className":55943},[407],[363,55945,571],{"className":55946},[407,714],[363,55948,55950],{"className":55949},[629],[363,55951,55953,55973],{"className":55952},[633,634],[363,55954,55956,55970],{"className":55955},[638],[363,55957,55959],{"className":55958,"style":727},[642],[363,55960,55961,55964],{"style":730},[363,55962],{"className":55963,"style":651},[650],[363,55965,55967],{"className":55966},[655,656,657,658],[363,55968,561],{"className":55969},[407,408,658],[363,55971,666],{"className":55972},[665],[363,55974,55976],{"className":55975},[638],[363,55977,55979],{"className":55978,"style":673},[642],[363,55980],{},[363,55982,578],{"className":55983},[494],[363,55985,1116],{"className":55986},[407,408],[363,55988,605],{"className":55989},[501],[363,55991],{"className":55992,"style":506},[505],[363,55994,471],{"className":55995},[510],[363,55997],{"className":55998,"style":506},[505],[363,56000,56002,56005],{"className":56001},[398],[363,56003],{"className":56004,"style":520},[402],[363,56006,465],{"className":56007},[407],[363,56009,56011,56024],{"className":56010,"translate":367},[366],[363,56012,56014],{"className":56013},[371],[373,56015,56016],{"xmlns":375},[377,56017,56018,56022],{},[380,56019,56020],{},[383,56021,561],{},[387,56023,561],{"encoding":389},[363,56025,56027],{"className":56026,"ariaHidden":394},[393],[363,56028,56030,56033],{"className":56029},[398],[363,56031],{"className":56032,"style":913},[402],[363,56034,561],{"className":56035},[407,408]," 下几乎必然成立，即 ",[363,56038,56040,56057],{"className":56039,"translate":367},[366],[363,56041,56043],{"className":56042},[371],[373,56044,56045],{"xmlns":375},[377,56046,56047,56055],{},[380,56048,56049,56051,56053],{},[383,56050,554],{},[458,56052,471],{},[383,56054,561],{},[387,56056,10618],{"encoding":389},[363,56058,56060,56078],{"className":56059,"ariaHidden":394},[393],[363,56061,56063,56066,56069,56072,56075],{"className":56062},[398],[363,56064],{"className":56065,"style":1011},[402],[363,56067,554],{"className":56068,"style":682},[407,408],[363,56070],{"className":56071,"style":506},[505],[363,56073,471],{"className":56074},[510],[363,56076],{"className":56077,"style":506},[505],[363,56079,56081,56084],{"className":56080},[398],[363,56082],{"className":56083,"style":913},[402],[363,56085,561],{"className":56086},[407,408],"。若 ",[363,56089,56091,56104],{"className":56090,"translate":367},[366],[363,56092,56094],{"className":56093},[371],[373,56095,56096],{"xmlns":375},[377,56097,56098,56102],{},[380,56099,56100],{},[383,56101,385],{},[387,56103,385],{"encoding":389},[363,56105,56107],{"className":56106,"ariaHidden":394},[393],[363,56108,56110,56113],{"className":56109},[398],[363,56111],{"className":56112,"style":403},[402],[363,56114,385],{"className":56115,"style":409},[407,408]," 只是凸而非严格凸（如 ",[363,56118,56120,56157],{"className":56119,"translate":367},[366],[363,56121,56123],{"className":56122},[371],[373,56124,56125],{"xmlns":375},[377,56126,56127,56155],{},[380,56128,56129,56131,56133,56135,56137,56139,56145,56147,56149,56151,56153],{},[383,56130,385],{},[458,56132,461],{"stretchy":460},[383,56134,1116],{},[458,56136,468],{"stretchy":460},[458,56138,471],{},[586,56140,56141,56143],{},[463,56142,465],{},[463,56144,2810],{},[383,56146,5155],{"mathvariant":557},[383,56148,1116],{},[458,56150,5160],{},[463,56152,465],{},[383,56154,5155],{"mathvariant":557},[387,56156,34903],{"encoding":389},[363,56158,56160,56187,56276],{"className":56159,"ariaHidden":394},[393],[363,56161,56163,56166,56169,56172,56175,56178,56181,56184],{"className":56162},[398],[363,56164],{"className":56165,"style":487},[402],[363,56167,385],{"className":56168,"style":409},[407,408],[363,56170,461],{"className":56171},[494],[363,56173,1116],{"className":56174},[407,408],[363,56176,468],{"className":56177},[501],[363,56179],{"className":56180,"style":506},[505],[363,56182,471],{"className":56183},[510],[363,56185],{"className":56186,"style":506},[505],[363,56188,56190,56193,56261,56264,56267,56270,56273],{"className":56189},[398],[363,56191],{"className":56192,"style":2852},[402],[363,56194,56196,56199,56258],{"className":56195},[407],[363,56197],{"className":56198},[494,789],[363,56200,56202],{"className":56201},[586],[363,56203,56205,56250],{"className":56204},[633,634],[363,56206,56208,56247],{"className":56207},[638],[363,56209,56211,56225,56233],{"className":56210,"style":2871},[642],[363,56212,56213,56216],{"style":2874},[363,56214],{"className":56215,"style":809},[650],[363,56217,56219],{"className":56218},[655,656,657,658],[363,56220,56222],{"className":56221},[407,658],[363,56223,2810],{"className":56224},[407,658],[363,56226,56227,56230],{"style":821},[363,56228],{"className":56229,"style":809},[650],[363,56231],{"className":56232,"style":829},[828],[363,56234,56235,56238],{"style":2897},[363,56236],{"className":56237,"style":809},[650],[363,56239,56241],{"className":56240},[655,656,657,658],[363,56242,56244],{"className":56243},[407,658],[363,56245,465],{"className":56246},[407,658],[363,56248,666],{"className":56249},[665],[363,56251,56253],{"className":56252},[638],[363,56254,56256],{"className":56255,"style":2919},[642],[363,56257],{},[363,56259],{"className":56260},[501,789],[363,56262,5155],{"className":56263},[407],[363,56265,1116],{"className":56266},[407,408],[363,56268],{"className":56269,"style":2934},[505],[363,56271,5160],{"className":56272},[2938],[363,56274],{"className":56275,"style":2934},[505],[363,56277,56279,56282],{"className":56278},[398],[363,56280],{"className":56281,"style":487},[402],[363,56283,35026],{"className":56284},[407],"），则只能保证 ",[363,56287,56289,56311],{"className":56288,"translate":367},[366],[363,56290,56292],{"className":56291},[371],[373,56293,56294],{"xmlns":375},[377,56295,56296,56308],{},[380,56297,56298,56304,56306],{},[543,56299,56300,56302],{},[383,56301,547],{},[383,56303,385],{},[458,56305,471],{},[463,56307,474],{},[387,56309,56310],{"encoding":389},"D_f=0",[363,56312,56314,56369],{"className":56313,"ariaHidden":394},[393],[363,56315,56317,56320,56360,56363,56366],{"className":56316},[398],[363,56318],{"className":56319,"style":4379},[402],[363,56321,56323,56326],{"className":56322},[407],[363,56324,547],{"className":56325,"style":625},[407,408],[363,56327,56329],{"className":56328},[629],[363,56330,56332,56352],{"className":56331},[633,634],[363,56333,56335,56349],{"className":56334},[638],[363,56336,56338],{"className":56337,"style":643},[642],[363,56339,56340,56343],{"style":646},[363,56341],{"className":56342,"style":651},[650],[363,56344,56346],{"className":56345},[655,656,657,658],[363,56347,385],{"className":56348,"style":409},[407,408,658],[363,56350,666],{"className":56351},[665],[363,56353,56355],{"className":56354},[638],[363,56356,56358],{"className":56357,"style":673},[642],[363,56359],{},[363,56361],{"className":56362,"style":506},[505],[363,56364,471],{"className":56365},[510],[363,56367],{"className":56368,"style":506},[505],[363,56370,56372,56375],{"className":56371},[398],[363,56373],{"className":56374,"style":520},[402],[363,56376,474],{"className":56377},[407]," 时不必然 ",[363,56380,56382,56399],{"className":56381,"translate":367},[366],[363,56383,56385],{"className":56384},[371],[373,56386,56387],{"xmlns":375},[377,56388,56389,56397],{},[380,56390,56391,56393,56395],{},[383,56392,554],{},[458,56394,471],{},[383,56396,561],{},[387,56398,10618],{"encoding":389},[363,56400,56402,56420],{"className":56401,"ariaHidden":394},[393],[363,56403,56405,56408,56411,56414,56417],{"className":56404},[398],[363,56406],{"className":56407,"style":1011},[402],[363,56409,554],{"className":56410,"style":682},[407,408],[363,56412],{"className":56413,"style":506},[505],[363,56415,471],{"className":56416},[510],[363,56418],{"className":56419,"style":506},[505],[363,56421,56423,56426],{"className":56422},[398],[363,56424],{"className":56425,"style":913},[402],[363,56427,561],{"className":56428},[407,408],"：TV 是反例，",[363,56431,56433,56450],{"className":56432,"translate":367},[366],[363,56434,56436],{"className":56435},[371],[373,56437,56438],{"xmlns":375},[377,56439,56440,56448],{},[380,56441,56442,56444,56446],{},[383,56443,554],{},[458,56445,471],{},[383,56447,561],{},[387,56449,10618],{"encoding":389},[363,56451,56453,56471],{"className":56452,"ariaHidden":394},[393],[363,56454,56456,56459,56462,56465,56468],{"className":56455},[398],[363,56457],{"className":56458,"style":1011},[402],[363,56460,554],{"className":56461,"style":682},[407,408],[363,56463],{"className":56464,"style":506},[505],[363,56466,471],{"className":56467},[510],[363,56469],{"className":56470,"style":506},[505],[363,56472,56474,56477],{"className":56473},[398],[363,56475],{"className":56476,"style":913},[402],[363,56478,561],{"className":56479},[407,408]," 时才是唯一使 TV 为 0 的一对（TV 也对）。",[2658,56482,56484],{"id":56483},"_42-联合凸性","4.2 联合凸性",[1340,56486,56488,56957],{"title":56487},"命题 4.2（联合凸性）",[11,56489,56490,56491,3092,56687,3092,56883,41985],{},"若 ",[363,56492,56494,56535],{"className":56493,"translate":367},[366],[363,56495,56497],{"className":56496},[371],[373,56498,56499],{"xmlns":375},[377,56500,56501,56533],{},[380,56502,56503,56505,56507,56509,56515,56517,56519,56521,56523,56525,56527],{},[383,56504,554],{},[458,56506,471],{},[383,56508,11686],{},[543,56510,56511,56513],{},[383,56512,554],{},[463,56514,465],{},[458,56516,2817],{},[458,56518,461],{"stretchy":460},[463,56520,465],{},[458,56522,5160],{},[383,56524,11686],{},[458,56526,468],{"stretchy":460},[543,56528,56529,56531],{},[383,56530,554],{},[463,56532,2810],{},[387,56534,11793],{"encoding":389},[363,56536,56538,56556,56614,56635],{"className":56537,"ariaHidden":394},[393],[363,56539,56541,56544,56547,56550,56553],{"className":56540},[398],[363,56542],{"className":56543,"style":1011},[402],[363,56545,554],{"className":56546,"style":682},[407,408],[363,56548],{"className":56549,"style":506},[505],[363,56551,471],{"className":56552},[510],[363,56554],{"className":56555,"style":506},[505],[363,56557,56559,56562,56565,56605,56608,56611],{"className":56558},[398],[363,56560],{"className":56561,"style":11821},[402],[363,56563,11686],{"className":56564},[407,408],[363,56566,56568,56571],{"className":56567},[407],[363,56569,554],{"className":56570,"style":682},[407,408],[363,56572,56574],{"className":56573},[629],[363,56575,56577,56597],{"className":56576},[633,634],[363,56578,56580,56594],{"className":56579},[638],[363,56581,56583],{"className":56582,"style":11480},[642],[363,56584,56585,56588],{"style":11483},[363,56586],{"className":56587,"style":651},[650],[363,56589,56591],{"className":56590},[655,656,657,658],[363,56592,465],{"className":56593},[407,658],[363,56595,666],{"className":56596},[665],[363,56598,56600],{"className":56599},[638],[363,56601,56603],{"className":56602,"style":8315},[642],[363,56604],{},[363,56606],{"className":56607,"style":2934},[505],[363,56609,2817],{"className":56610},[2938],[363,56612],{"className":56613,"style":2934},[505],[363,56615,56617,56620,56623,56626,56629,56632],{"className":56616},[398],[363,56618],{"className":56619,"style":487},[402],[363,56621,461],{"className":56622},[494],[363,56624,465],{"className":56625},[407],[363,56627],{"className":56628,"style":2934},[505],[363,56630,5160],{"className":56631},[2938],[363,56633],{"className":56634,"style":2934},[505],[363,56636,56638,56641,56644,56647],{"className":56637},[398],[363,56639],{"className":56640,"style":487},[402],[363,56642,11686],{"className":56643},[407,408],[363,56645,468],{"className":56646},[501],[363,56648,56650,56653],{"className":56649},[407],[363,56651,554],{"className":56652,"style":682},[407,408],[363,56654,56656],{"className":56655},[629],[363,56657,56659,56679],{"className":56658},[633,634],[363,56660,56662,56676],{"className":56661},[638],[363,56663,56665],{"className":56664,"style":11480},[642],[363,56666,56667,56670],{"style":11483},[363,56668],{"className":56669,"style":651},[650],[363,56671,56673],{"className":56672},[655,656,657,658],[363,56674,2810],{"className":56675},[407,658],[363,56677,666],{"className":56678},[665],[363,56680,56682],{"className":56681},[638],[363,56683,56685],{"className":56684,"style":8315},[642],[363,56686],{},[363,56688,56690,56731],{"className":56689,"translate":367},[366],[363,56691,56693],{"className":56692},[371],[373,56694,56695],{"xmlns":375},[377,56696,56697,56729],{},[380,56698,56699,56701,56703,56705,56711,56713,56715,56717,56719,56721,56723],{},[383,56700,561],{},[458,56702,471],{},[383,56704,11686],{},[543,56706,56707,56709],{},[383,56708,561],{},[463,56710,465],{},[458,56712,2817],{},[458,56714,461],{"stretchy":460},[463,56716,465],{},[458,56718,5160],{},[383,56720,11686],{},[458,56722,468],{"stretchy":460},[543,56724,56725,56727],{},[383,56726,561],{},[463,56728,2810],{},[387,56730,11991],{"encoding":389},[363,56732,56734,56752,56810,56831],{"className":56733,"ariaHidden":394},[393],[363,56735,56737,56740,56743,56746,56749],{"className":56736},[398],[363,56738],{"className":56739,"style":913},[402],[363,56741,561],{"className":56742},[407,408],[363,56744],{"className":56745,"style":506},[505],[363,56747,471],{"className":56748},[510],[363,56750],{"className":56751,"style":506},[505],[363,56753,56755,56758,56761,56801,56804,56807],{"className":56754},[398],[363,56756],{"className":56757,"style":403},[402],[363,56759,11686],{"className":56760},[407,408],[363,56762,56764,56767],{"className":56763},[407],[363,56765,561],{"className":56766},[407,408],[363,56768,56770],{"className":56769},[629],[363,56771,56773,56793],{"className":56772},[633,634],[363,56774,56776,56790],{"className":56775},[638],[363,56777,56779],{"className":56778,"style":11480},[642],[363,56780,56781,56784],{"style":730},[363,56782],{"className":56783,"style":651},[650],[363,56785,56787],{"className":56786},[655,656,657,658],[363,56788,465],{"className":56789},[407,658],[363,56791,666],{"className":56792},[665],[363,56794,56796],{"className":56795},[638],[363,56797,56799],{"className":56798,"style":8315},[642],[363,56800],{},[363,56802],{"className":56803,"style":2934},[505],[363,56805,2817],{"className":56806},[2938],[363,56808],{"className":56809,"style":2934},[505],[363,56811,56813,56816,56819,56822,56825,56828],{"className":56812},[398],[363,56814],{"className":56815,"style":487},[402],[363,56817,461],{"className":56818},[494],[363,56820,465],{"className":56821},[407],[363,56823],{"className":56824,"style":2934},[505],[363,56826,5160],{"className":56827},[2938],[363,56829],{"className":56830,"style":2934},[505],[363,56832,56834,56837,56840,56843],{"className":56833},[398],[363,56835],{"className":56836,"style":487},[402],[363,56838,11686],{"className":56839},[407,408],[363,56841,468],{"className":56842},[501],[363,56844,56846,56849],{"className":56845},[407],[363,56847,561],{"className":56848},[407,408],[363,56850,56852],{"className":56851},[629],[363,56853,56855,56875],{"className":56854},[633,634],[363,56856,56858,56872],{"className":56857},[638],[363,56859,56861],{"className":56860,"style":11480},[642],[363,56862,56863,56866],{"style":730},[363,56864],{"className":56865,"style":651},[650],[363,56867,56869],{"className":56868},[655,656,657,658],[363,56870,2810],{"className":56871},[407,658],[363,56873,666],{"className":56874},[665],[363,56876,56878],{"className":56877},[638],[363,56879,56881],{"className":56880,"style":8315},[642],[363,56882],{},[363,56884,56886,56912],{"className":56885,"translate":367},[366],[363,56887,56889],{"className":56888},[371],[373,56890,56891],{"xmlns":375},[377,56892,56893,56909],{},[380,56894,56895,56897,56899,56901,56903,56905,56907],{},[383,56896,11686],{},[458,56898,6256],{},[458,56900,578],{"stretchy":460},[463,56902,474],{},[458,56904,898],{"separator":394},[463,56906,465],{},[458,56908,605],{"stretchy":460},[387,56910,56911],{"encoding":389},"\\lambda\\in[0,1]",[363,56913,56915,56933],{"className":56914,"ariaHidden":394},[393],[363,56916,56918,56921,56924,56927,56930],{"className":56917},[398],[363,56919],{"className":56920,"style":11711},[402],[363,56922,11686],{"className":56923},[407,408],[363,56925],{"className":56926,"style":506},[505],[363,56928,6256],{"className":56929},[510],[363,56931],{"className":56932,"style":506},[505],[363,56934,56936,56939,56942,56945,56948,56951,56954],{"className":56935},[398],[363,56937],{"className":56938,"style":487},[402],[363,56940,578],{"className":56941},[494],[363,56943,474],{"className":56944},[407],[363,56946,898],{"className":56947},[920],[363,56949],{"className":56950,"style":754},[505],[363,56952,465],{"className":56953},[407],[363,56955,605],{"className":56956},[501],[363,56958,56960],{"className":56959,"translate":367},[528],[363,56961,56963,57057],{"className":56962,"translate":367},[366],[363,56964,56966],{"className":56965},[371],[373,56967,56968],{"xmlns":375,"display":537},[377,56969,56970,57054],{},[380,56971,56972,56978,56980,56982,56984,56986,56988,56990,56992,56998,57000,57006,57008,57014,57016,57018,57020,57022,57024,57026,57028,57034,57036,57042,57044,57050,57052],{},[543,56973,56974,56976],{},[383,56975,547],{},[383,56977,385],{},[458,56979,461],{"stretchy":460},[383,56981,554],{},[383,56983,558],{"mathvariant":557},[383,56985,561],{},[458,56987,468],{"stretchy":460},[458,56989,10299],{},[383,56991,11686],{},[543,56993,56994,56996],{},[383,56995,547],{},[383,56997,385],{},[458,56999,461],{"stretchy":460},[543,57001,57002,57004],{},[383,57003,554],{},[463,57005,465],{},[383,57007,558],{"mathvariant":557},[543,57009,57010,57012],{},[383,57011,561],{},[463,57013,465],{},[458,57015,468],{"stretchy":460},[458,57017,2817],{},[458,57019,461],{"stretchy":460},[463,57021,465],{},[458,57023,5160],{},[383,57025,11686],{},[458,57027,468],{"stretchy":460},[543,57029,57030,57032],{},[383,57031,547],{},[383,57033,385],{},[458,57035,461],{"stretchy":460},[543,57037,57038,57040],{},[383,57039,554],{},[463,57041,2810],{},[383,57043,558],{"mathvariant":557},[543,57045,57046,57048],{},[383,57047,561],{},[463,57049,2810],{},[458,57051,468],{"stretchy":460},[383,57053,4722],{"mathvariant":557},[387,57055,57056],{"encoding":389},"D_f(P\\|Q)\n\\le \\lambda D_f(P_1\\|Q_1)\n+(1-\\lambda)D_f(P_2\\|Q_2).",[363,57058,57060,57130,57277,57298],{"className":57059,"ariaHidden":394},[393],[363,57061,57063,57066,57106,57109,57112,57115,57118,57121,57124,57127],{"className":57062},[398],[363,57064],{"className":57065,"style":618},[402],[363,57067,57069,57072],{"className":57068},[407],[363,57070,547],{"className":57071,"style":625},[407,408],[363,57073,57075],{"className":57074},[629],[363,57076,57078,57098],{"className":57077},[633,634],[363,57079,57081,57095],{"className":57080},[638],[363,57082,57084],{"className":57083,"style":643},[642],[363,57085,57086,57089],{"style":646},[363,57087],{"className":57088,"style":651},[650],[363,57090,57092],{"className":57091},[655,656,657,658],[363,57093,385],{"className":57094,"style":409},[407,408,658],[363,57096,666],{"className":57097},[665],[363,57099,57101],{"className":57100},[638],[363,57102,57104],{"className":57103,"style":673},[642],[363,57105],{},[363,57107,461],{"className":57108},[494],[363,57110,554],{"className":57111,"style":682},[407,408],[363,57113,558],{"className":57114},[407],[363,57116,561],{"className":57117},[407,408],[363,57119,468],{"className":57120},[501],[363,57122],{"className":57123,"style":506},[505],[363,57125,10299],{"className":57126},[510],[363,57128],{"className":57129,"style":506},[505],[363,57131,57133,57136,57139,57179,57182,57222,57225,57265,57268,57271,57274],{"className":57132},[398],[363,57134],{"className":57135,"style":618},[402],[363,57137,11686],{"className":57138},[407,408],[363,57140,57142,57145],{"className":57141},[407],[363,57143,547],{"className":57144,"style":625},[407,408],[363,57146,57148],{"className":57147},[629],[363,57149,57151,57171],{"className":57150},[633,634],[363,57152,57154,57168],{"className":57153},[638],[363,57155,57157],{"className":57156,"style":643},[642],[363,57158,57159,57162],{"style":646},[363,57160],{"className":57161,"style":651},[650],[363,57163,57165],{"className":57164},[655,656,657,658],[363,57166,385],{"className":57167,"style":409},[407,408,658],[363,57169,666],{"className":57170},[665],[363,57172,57174],{"className":57173},[638],[363,57175,57177],{"className":57176,"style":673},[642],[363,57178],{},[363,57180,461],{"className":57181},[494],[363,57183,57185,57188],{"className":57184},[407],[363,57186,554],{"className":57187,"style":682},[407,408],[363,57189,57191],{"className":57190},[629],[363,57192,57194,57214],{"className":57193},[633,634],[363,57195,57197,57211],{"className":57196},[638],[363,57198,57200],{"className":57199,"style":11480},[642],[363,57201,57202,57205],{"style":11483},[363,57203],{"className":57204,"style":651},[650],[363,57206,57208],{"className":57207},[655,656,657,658],[363,57209,465],{"className":57210},[407,658],[363,57212,666],{"className":57213},[665],[363,57215,57217],{"className":57216},[638],[363,57218,57220],{"className":57219,"style":8315},[642],[363,57221],{},[363,57223,558],{"className":57224},[407],[363,57226,57228,57231],{"className":57227},[407],[363,57229,561],{"className":57230},[407,408],[363,57232,57234],{"className":57233},[629],[363,57235,57237,57257],{"className":57236},[633,634],[363,57238,57240,57254],{"className":57239},[638],[363,57241,57243],{"className":57242,"style":11480},[642],[363,57244,57245,57248],{"style":730},[363,57246],{"className":57247,"style":651},[650],[363,57249,57251],{"className":57250},[655,656,657,658],[363,57252,465],{"className":57253},[407,658],[363,57255,666],{"className":57256},[665],[363,57258,57260],{"className":57259},[638],[363,57261,57263],{"className":57262,"style":8315},[642],[363,57264],{},[363,57266,468],{"className":57267},[501],[363,57269],{"className":57270,"style":2934},[505],[363,57272,2817],{"className":57273},[2938],[363,57275],{"className":57276,"style":2934},[505],[363,57278,57280,57283,57286,57289,57292,57295],{"className":57279},[398],[363,57281],{"className":57282,"style":487},[402],[363,57284,461],{"className":57285},[494],[363,57287,465],{"className":57288},[407],[363,57290],{"className":57291,"style":2934},[505],[363,57293,5160],{"className":57294},[2938],[363,57296],{"className":57297,"style":2934},[505],[363,57299,57301,57304,57307,57310,57350,57353,57393,57396,57436,57439],{"className":57300},[398],[363,57302],{"className":57303,"style":618},[402],[363,57305,11686],{"className":57306},[407,408],[363,57308,468],{"className":57309},[501],[363,57311,57313,57316],{"className":57312},[407],[363,57314,547],{"className":57315,"style":625},[407,408],[363,57317,57319],{"className":57318},[629],[363,57320,57322,57342],{"className":57321},[633,634],[363,57323,57325,57339],{"className":57324},[638],[363,57326,57328],{"className":57327,"style":643},[642],[363,57329,57330,57333],{"style":646},[363,57331],{"className":57332,"style":651},[650],[363,57334,57336],{"className":57335},[655,656,657,658],[363,57337,385],{"className":57338,"style":409},[407,408,658],[363,57340,666],{"className":57341},[665],[363,57343,57345],{"className":57344},[638],[363,57346,57348],{"className":57347,"style":673},[642],[363,57349],{},[363,57351,461],{"className":57352},[494],[363,57354,57356,57359],{"className":57355},[407],[363,57357,554],{"className":57358,"style":682},[407,408],[363,57360,57362],{"className":57361},[629],[363,57363,57365,57385],{"className":57364},[633,634],[363,57366,57368,57382],{"className":57367},[638],[363,57369,57371],{"className":57370,"style":11480},[642],[363,57372,57373,57376],{"style":11483},[363,57374],{"className":57375,"style":651},[650],[363,57377,57379],{"className":57378},[655,656,657,658],[363,57380,2810],{"className":57381},[407,658],[363,57383,666],{"className":57384},[665],[363,57386,57388],{"className":57387},[638],[363,57389,57391],{"className":57390,"style":8315},[642],[363,57392],{},[363,57394,558],{"className":57395},[407],[363,57397,57399,57402],{"className":57398},[407],[363,57400,561],{"className":57401},[407,408],[363,57403,57405],{"className":57404},[629],[363,57406,57408,57428],{"className":57407},[633,634],[363,57409,57411,57425],{"className":57410},[638],[363,57412,57414],{"className":57413,"style":11480},[642],[363,57415,57416,57419],{"style":730},[363,57417],{"className":57418,"style":651},[650],[363,57420,57422],{"className":57421},[655,656,657,658],[363,57423,2810],{"className":57424},[407,658],[363,57426,666],{"className":57427},[665],[363,57429,57431],{"className":57430},[638],[363,57432,57434],{"className":57433,"style":8315},[642],[363,57435],{},[363,57437,468],{"className":57438},[501],[363,57440,4722],{"className":57441},[407],[11,57443,57444,57446,57447,57475,57476,57507,57508,57861,57862,57913,57914,57999,58000,58132],{},[1572,57445,55818],{}," 这是 ",[363,57448,57450,57463],{"className":57449,"translate":367},[366],[363,57451,57453],{"className":57452},[371],[373,57454,57455],{"xmlns":375},[377,57456,57457,57461],{},[380,57458,57459],{},[383,57460,385],{},[387,57462,385],{"encoding":389},[363,57464,57466],{"className":57465,"ariaHidden":394},[393],[363,57467,57469,57472],{"className":57468},[398],[363,57470],{"className":57471,"style":403},[402],[363,57473,385],{"className":57474,"style":409},[407,408]," 凸性加上「",[363,57477,57479,57495],{"className":57478,"translate":367},[366],[363,57480,57482],{"className":57481},[371],[373,57483,57484],{"xmlns":375},[377,57485,57486,57492],{},[380,57487,57488,57490],{},[383,57489,35779],{},[458,57491,4450],{},[387,57493,57494],{"encoding":389},"\\sup",[363,57496,57498],{"className":57497,"ariaHidden":394},[393],[363,57499,57501,57504],{"className":57500},[398],[363,57502],{"className":57503,"style":2623},[402],[363,57505,35779],{"className":57506},[1831]," 与线性运算」的标准结果，也可用 f-散度的变分表示（4.4 节）直接看：",[363,57509,57511,57591],{"className":57510,"translate":367},[366],[363,57512,57514],{"className":57513},[371],[373,57515,57516],{"xmlns":375},[377,57517,57518,57588],{},[380,57519,57520,57526,57528,57530,57532,57534,57536,57538,57548,57550,57556,57558,57560,57562,57564,57570,57572,57578,57580,57582,57584,57586],{},[543,57521,57522,57524],{},[383,57523,547],{},[383,57525,385],{},[458,57527,461],{"stretchy":460},[383,57529,554],{},[383,57531,558],{"mathvariant":557},[383,57533,561],{},[458,57535,468],{"stretchy":460},[458,57537,471],{},[543,57539,57540,57546],{},[380,57541,57542,57544],{},[383,57543,35779],{},[458,57545,4450],{},[383,57547,4505],{},[458,57549,3245],{"stretchy":460},[543,57551,57552,57554],{},[383,57553,571],{"mathvariant":570},[383,57555,554],{},[458,57557,578],{"stretchy":460},[383,57559,4505],{},[458,57561,605],{"stretchy":460},[458,57563,5160],{},[543,57565,57566,57568],{},[383,57567,571],{"mathvariant":570},[383,57569,561],{},[458,57571,578],{"stretchy":460},[7161,57573,57574,57576],{},[383,57575,385],{},[458,57577,7920],{},[458,57579,461],{"stretchy":460},[383,57581,4505],{},[458,57583,468],{"stretchy":460},[458,57585,605],{"stretchy":460},[458,57587,3255],{"stretchy":460},[387,57589,57590],{"encoding":389},"D_f(P\\|Q)=\\sup_g\\{\\mathbb E_P[g]-\\mathbb E_Q[f^*(g)]\\}",[363,57592,57594,57664,57773],{"className":57593,"ariaHidden":394},[393],[363,57595,57597,57600,57640,57643,57646,57649,57652,57655,57658,57661],{"className":57596},[398],[363,57598],{"className":57599,"style":618},[402],[363,57601,57603,57606],{"className":57602},[407],[363,57604,547],{"className":57605,"style":625},[407,408],[363,57607,57609],{"className":57608},[629],[363,57610,57612,57632],{"className":57611},[633,634],[363,57613,57615,57629],{"className":57614},[638],[363,57616,57618],{"className":57617,"style":643},[642],[363,57619,57620,57623],{"style":646},[363,57621],{"className":57622,"style":651},[650],[363,57624,57626],{"className":57625},[655,656,657,658],[363,57627,385],{"className":57628,"style":409},[407,408,658],[363,57630,666],{"className":57631},[665],[363,57633,57635],{"className":57634},[638],[363,57636,57638],{"className":57637,"style":673},[642],[363,57639],{},[363,57641,461],{"className":57642},[494],[363,57644,554],{"className":57645,"style":682},[407,408],[363,57647,558],{"className":57648},[407],[363,57650,561],{"className":57651},[407,408],[363,57653,468],{"className":57654},[501],[363,57656],{"className":57657,"style":506},[505],[363,57659,471],{"className":57660},[510],[363,57662],{"className":57663,"style":506},[505],[363,57665,57667,57671,57712,57715,57755,57758,57761,57764,57767,57770],{"className":57666},[398],[363,57668],{"className":57669,"style":57670},[402],"height:1.1302em;vertical-align:-0.3802em;",[363,57672,57674,57677],{"className":57673},[1831],[363,57675,35779],{"className":57676},[1831],[363,57678,57680],{"className":57679},[629],[363,57681,57683,57703],{"className":57682},[633,634],[363,57684,57686,57700],{"className":57685},[638],[363,57687,57689],{"className":57688,"style":37346},[642],[363,57690,57691,57694],{"style":35925},[363,57692],{"className":57693,"style":651},[650],[363,57695,57697],{"className":57696},[655,656,657,658],[363,57698,4505],{"className":57699,"style":1328},[407,408,658],[363,57701,666],{"className":57702},[665],[363,57704,57706],{"className":57705},[638],[363,57707,57710],{"className":57708,"style":57709},[642],"height:0.3802em;",[363,57711],{},[363,57713,3245],{"className":57714},[494],[363,57716,57718,57721],{"className":57717},[407],[363,57719,571],{"className":57720},[407,714],[363,57722,57724],{"className":57723},[629],[363,57725,57727,57747],{"className":57726},[633,634],[363,57728,57730,57744],{"className":57729},[638],[363,57731,57733],{"className":57732,"style":727},[642],[363,57734,57735,57738],{"style":730},[363,57736],{"className":57737,"style":651},[650],[363,57739,57741],{"className":57740},[655,656,657,658],[363,57742,554],{"className":57743,"style":682},[407,408,658],[363,57745,666],{"className":57746},[665],[363,57748,57750],{"className":57749},[638],[363,57751,57753],{"className":57752,"style":8315},[642],[363,57754],{},[363,57756,578],{"className":57757},[494],[363,57759,4505],{"className":57760,"style":1328},[407,408],[363,57762,605],{"className":57763},[501],[363,57765],{"className":57766,"style":2934},[505],[363,57768,5160],{"className":57769},[2938],[363,57771],{"className":57772,"style":2934},[505],[363,57774,57776,57779,57819,57822,57851,57854,57857],{"className":57775},[398],[363,57777],{"className":57778,"style":618},[402],[363,57780,57782,57785],{"className":57781},[407],[363,57783,571],{"className":57784},[407,714],[363,57786,57788],{"className":57787},[629],[363,57789,57791,57811],{"className":57790},[633,634],[363,57792,57794,57808],{"className":57793},[638],[363,57795,57797],{"className":57796,"style":727},[642],[363,57798,57799,57802],{"style":730},[363,57800],{"className":57801,"style":651},[650],[363,57803,57805],{"className":57804},[655,656,657,658],[363,57806,561],{"className":57807},[407,408,658],[363,57809,666],{"className":57810},[665],[363,57812,57814],{"className":57813},[638],[363,57815,57817],{"className":57816,"style":673},[642],[363,57818],{},[363,57820,578],{"className":57821},[494],[363,57823,57825,57828],{"className":57824},[407],[363,57826,385],{"className":57827,"style":409},[407,408],[363,57829,57831],{"className":57830},[629],[363,57832,57834],{"className":57833},[633],[363,57835,57837],{"className":57836},[638],[363,57838,57840],{"className":57839,"style":8846},[642],[363,57841,57842,57845],{"style":7212},[363,57843],{"className":57844,"style":651},[650],[363,57846,57848],{"className":57847},[655,656,657,658],[363,57849,7920],{"className":57850},[2938,658],[363,57852,461],{"className":57853},[494],[363,57855,4505],{"className":57856,"style":1328},[407,408],[363,57858,57860],{"className":57859},[501],")]}","，右端关于 ",[363,57863,57865,57886],{"className":57864,"translate":367},[366],[363,57866,57868],{"className":57867},[371],[373,57869,57870],{"xmlns":375},[377,57871,57872,57884],{},[380,57873,57874,57876,57878,57880,57882],{},[458,57875,461],{"stretchy":460},[383,57877,554],{},[458,57879,898],{"separator":394},[383,57881,561],{},[458,57883,468],{"stretchy":460},[387,57885,11378],{"encoding":389},[363,57887,57889],{"className":57888,"ariaHidden":394},[393],[363,57890,57892,57895,57898,57901,57904,57907,57910],{"className":57891},[398],[363,57893],{"className":57894,"style":487},[402],[363,57896,461],{"className":57897},[494],[363,57899,554],{"className":57900,"style":682},[407,408],[363,57902,898],{"className":57903},[920],[363,57905],{"className":57906,"style":754},[505],[363,57908,561],{"className":57909},[407,408],[363,57911,468],{"className":57912},[501]," 是凸的（",[363,57915,57917,57941],{"className":57916,"translate":367},[366],[363,57918,57920],{"className":57919},[371],[373,57921,57922],{"xmlns":375},[377,57923,57924,57938],{},[380,57925,57926,57932,57934,57936],{},[543,57927,57928,57930],{},[383,57929,571],{"mathvariant":570},[383,57931,554],{},[458,57933,578],{"stretchy":460},[383,57935,4505],{},[458,57937,605],{"stretchy":460},[387,57939,57940],{"encoding":389},"\\mathbb E_P[g]",[363,57942,57944],{"className":57943,"ariaHidden":394},[393],[363,57945,57947,57950,57990,57993,57996],{"className":57946},[398],[363,57948],{"className":57949,"style":487},[402],[363,57951,57953,57956],{"className":57952},[407],[363,57954,571],{"className":57955},[407,714],[363,57957,57959],{"className":57958},[629],[363,57960,57962,57982],{"className":57961},[633,634],[363,57963,57965,57979],{"className":57964},[638],[363,57966,57968],{"className":57967,"style":727},[642],[363,57969,57970,57973],{"style":730},[363,57971],{"className":57972,"style":651},[650],[363,57974,57976],{"className":57975},[655,656,657,658],[363,57977,554],{"className":57978,"style":682},[407,408,658],[363,57980,666],{"className":57981},[665],[363,57983,57985],{"className":57984},[638],[363,57986,57988],{"className":57987,"style":8315},[642],[363,57989],{},[363,57991,578],{"className":57992},[494],[363,57994,4505],{"className":57995,"style":1328},[407,408],[363,57997,605],{"className":57998},[501]," 线性、",[363,58001,58003,58039],{"className":58002,"translate":367},[366],[363,58004,58006],{"className":58005},[371],[373,58007,58008],{"xmlns":375},[377,58009,58010,58036],{},[380,58011,58012,58014,58020,58022,58028,58030,58032,58034],{},[458,58013,5160],{},[543,58015,58016,58018],{},[383,58017,571],{"mathvariant":570},[383,58019,561],{},[458,58021,578],{"stretchy":460},[7161,58023,58024,58026],{},[383,58025,385],{},[458,58027,7920],{},[458,58029,461],{"stretchy":460},[383,58031,4505],{},[458,58033,468],{"stretchy":460},[458,58035,605],{"stretchy":460},[387,58037,58038],{"encoding":389},"-\\mathbb E_Q[f^*(g)]",[363,58040,58042],{"className":58041,"ariaHidden":394},[393],[363,58043,58045,58048,58051,58091,58094,58123,58126,58129],{"className":58044},[398],[363,58046],{"className":58047,"style":618},[402],[363,58049,5160],{"className":58050},[407],[363,58052,58054,58057],{"className":58053},[407],[363,58055,571],{"className":58056},[407,714],[363,58058,58060],{"className":58059},[629],[363,58061,58063,58083],{"className":58062},[633,634],[363,58064,58066,58080],{"className":58065},[638],[363,58067,58069],{"className":58068,"style":727},[642],[363,58070,58071,58074],{"style":730},[363,58072],{"className":58073,"style":651},[650],[363,58075,58077],{"className":58076},[655,656,657,658],[363,58078,561],{"className":58079},[407,408,658],[363,58081,666],{"className":58082},[665],[363,58084,58086],{"className":58085},[638],[363,58087,58089],{"className":58088,"style":673},[642],[363,58090],{},[363,58092,578],{"className":58093},[494],[363,58095,58097,58100],{"className":58096},[407],[363,58098,385],{"className":58099,"style":409},[407,408],[363,58101,58103],{"className":58102},[629],[363,58104,58106],{"className":58105},[633],[363,58107,58109],{"className":58108},[638],[363,58110,58112],{"className":58111,"style":8846},[642],[363,58113,58114,58117],{"style":7212},[363,58115],{"className":58116,"style":651},[650],[363,58118,58120],{"className":58119},[655,656,657,658],[363,58121,7920],{"className":58122},[2938,658],[363,58124,461],{"className":58125},[494],[363,58127,4505],{"className":58128,"style":1328},[407,408],[363,58130,20737],{"className":58131},[501]," 线性），取上确界后仍凸。",[11,58134,58135,58136,3092,58164,58282,58283,3092,58311,11312,58428,9747,58431,58547,58548,58576,58577,58605,58606,58634],{},"等价地，固定 ",[363,58137,58139,58152],{"className":58138,"translate":367},[366],[363,58140,58142],{"className":58141},[371],[373,58143,58144],{"xmlns":375},[377,58145,58146,58150],{},[380,58147,58148],{},[383,58149,561],{},[387,58151,561],{"encoding":389},[363,58153,58155],{"className":58154,"ariaHidden":394},[393],[363,58156,58158,58161],{"className":58157},[398],[363,58159],{"className":58160,"style":913},[402],[363,58162,561],{"className":58163},[407,408],[363,58165,58167,58199],{"className":58166,"translate":367},[366],[363,58168,58170],{"className":58169},[371],[373,58171,58172],{"xmlns":375},[377,58173,58174,58196],{},[380,58175,58176,58178,58180,58186,58188,58190,58192,58194],{},[383,58177,554],{},[458,58179,9031],{},[543,58181,58182,58184],{},[383,58183,547],{},[383,58185,385],{},[458,58187,461],{"stretchy":460},[383,58189,554],{},[383,58191,558],{"mathvariant":557},[383,58193,561],{},[458,58195,468],{"stretchy":460},[387,58197,58198],{"encoding":389},"P\\mapsto D_f(P\\|Q)",[363,58200,58202,58221],{"className":58201,"ariaHidden":394},[393],[363,58203,58205,58209,58212,58215,58218],{"className":58204},[398],[363,58206],{"className":58207,"style":58208},[402],"height:0.6943em;vertical-align:-0.011em;",[363,58210,554],{"className":58211,"style":682},[407,408],[363,58213],{"className":58214,"style":506},[505],[363,58216,9031],{"className":58217},[510],[363,58219],{"className":58220,"style":506},[505],[363,58222,58224,58227,58267,58270,58273,58276,58279],{"className":58223},[398],[363,58225],{"className":58226,"style":618},[402],[363,58228,58230,58233],{"className":58229},[407],[363,58231,547],{"className":58232,"style":625},[407,408],[363,58234,58236],{"className":58235},[629],[363,58237,58239,58259],{"className":58238},[633,634],[363,58240,58242,58256],{"className":58241},[638],[363,58243,58245],{"className":58244,"style":643},[642],[363,58246,58247,58250],{"style":646},[363,58248],{"className":58249,"style":651},[650],[363,58251,58253],{"className":58252},[655,656,657,658],[363,58254,385],{"className":58255,"style":409},[407,408,658],[363,58257,666],{"className":58258},[665],[363,58260,58262],{"className":58261},[638],[363,58263,58265],{"className":58264,"style":673},[642],[363,58266],{},[363,58268,461],{"className":58269},[494],[363,58271,554],{"className":58272,"style":682},[407,408],[363,58274,558],{"className":58275},[407],[363,58277,561],{"className":58278},[407,408],[363,58280,468],{"className":58281},[501]," 凸；固定 ",[363,58284,58286,58299],{"className":58285,"translate":367},[366],[363,58287,58289],{"className":58288},[371],[373,58290,58291],{"xmlns":375},[377,58292,58293,58297],{},[380,58294,58295],{},[383,58296,554],{},[387,58298,554],{"encoding":389},[363,58300,58302],{"className":58301,"ariaHidden":394},[393],[363,58303,58305,58308],{"className":58304},[398],[363,58306],{"className":58307,"style":1011},[402],[363,58309,554],{"className":58310,"style":682},[407,408],[363,58312,58314,58346],{"className":58313,"translate":367},[366],[363,58315,58317],{"className":58316},[371],[373,58318,58319],{"xmlns":375},[377,58320,58321,58343],{},[380,58322,58323,58325,58327,58333,58335,58337,58339,58341],{},[383,58324,561],{},[458,58326,9031],{},[543,58328,58329,58331],{},[383,58330,547],{},[383,58332,385],{},[458,58334,461],{"stretchy":460},[383,58336,554],{},[383,58338,558],{"mathvariant":557},[383,58340,561],{},[458,58342,468],{"stretchy":460},[387,58344,58345],{"encoding":389},"Q\\mapsto D_f(P\\|Q)",[363,58347,58349,58367],{"className":58348,"ariaHidden":394},[393],[363,58350,58352,58355,58358,58361,58364],{"className":58351},[398],[363,58353],{"className":58354,"style":913},[402],[363,58356,561],{"className":58357},[407,408],[363,58359],{"className":58360,"style":506},[505],[363,58362,9031],{"className":58363},[510],[363,58365],{"className":58366,"style":506},[505],[363,58368,58370,58373,58413,58416,58419,58422,58425],{"className":58369},[398],[363,58371],{"className":58372,"style":618},[402],[363,58374,58376,58379],{"className":58375},[407],[363,58377,547],{"className":58378,"style":625},[407,408],[363,58380,58382],{"className":58381},[629],[363,58383,58385,58405],{"className":58384},[633,634],[363,58386,58388,58402],{"className":58387},[638],[363,58389,58391],{"className":58390,"style":643},[642],[363,58392,58393,58396],{"style":646},[363,58394],{"className":58395,"style":651},[650],[363,58397,58399],{"className":58398},[655,656,657,658],[363,58400,385],{"className":58401,"style":409},[407,408,658],[363,58403,666],{"className":58404},[665],[363,58406,58408],{"className":58407},[638],[363,58409,58411],{"className":58410,"style":673},[642],[363,58412],{},[363,58414,461],{"className":58415},[494],[363,58417,554],{"className":58418,"style":682},[407,408],[363,58420,558],{"className":58421},[407],[363,58423,561],{"className":58424},[407,408],[363,58426,468],{"className":58427},[501],[1572,58429,58430],{},"注意",[363,58432,58434,58465],{"className":58433,"translate":367},[366],[363,58435,58437],{"className":58436},[371],[373,58438,58439],{"xmlns":375},[377,58440,58441,58463],{},[380,58442,58443,58445,58447,58453,58455,58457,58459,58461],{},[383,58444,561],{},[458,58446,9031],{},[543,58448,58449,58451],{},[383,58450,547],{},[383,58452,385],{},[458,58454,461],{"stretchy":460},[383,58456,554],{},[383,58458,558],{"mathvariant":557},[383,58460,561],{},[458,58462,468],{"stretchy":460},[387,58464,58345],{"encoding":389},[363,58466,58468,58486],{"className":58467,"ariaHidden":394},[393],[363,58469,58471,58474,58477,58480,58483],{"className":58470},[398],[363,58472],{"className":58473,"style":913},[402],[363,58475,561],{"className":58476},[407,408],[363,58478],{"className":58479,"style":506},[505],[363,58481,9031],{"className":58482},[510],[363,58484],{"className":58485,"style":506},[505],[363,58487,58489,58492,58532,58535,58538,58541,58544],{"className":58488},[398],[363,58490],{"className":58491,"style":618},[402],[363,58493,58495,58498],{"className":58494},[407],[363,58496,547],{"className":58497,"style":625},[407,408],[363,58499,58501],{"className":58500},[629],[363,58502,58504,58524],{"className":58503},[633,634],[363,58505,58507,58521],{"className":58506},[638],[363,58508,58510],{"className":58509,"style":643},[642],[363,58511,58512,58515],{"style":646},[363,58513],{"className":58514,"style":651},[650],[363,58516,58518],{"className":58517},[655,656,657,658],[363,58519,385],{"className":58520,"style":409},[407,408,658],[363,58522,666],{"className":58523},[665],[363,58525,58527],{"className":58526},[638],[363,58528,58530],{"className":58529,"style":673},[642],[363,58531],{},[363,58533,461],{"className":58534},[494],[363,58536,554],{"className":58537,"style":682},[407,408],[363,58539,558],{"className":58540},[407],[363,58542,561],{"className":58543},[407,408],[363,58545,468],{"className":58546},[501]," 凸是「以 ",[363,58549,58551,58564],{"className":58550,"translate":367},[366],[363,58552,58554],{"className":58553},[371],[373,58555,58556],{"xmlns":375},[377,58557,58558,58562],{},[380,58559,58560],{},[383,58561,561],{},[387,58563,561],{"encoding":389},[363,58565,58567],{"className":58566,"ariaHidden":394},[393],[363,58568,58570,58573],{"className":58569},[398],[363,58571],{"className":58572,"style":913},[402],[363,58574,561],{"className":58575},[407,408]," 为参照」的凸性，它与「",[363,58578,58580,58593],{"className":58579,"translate":367},[366],[363,58581,58583],{"className":58582},[371],[373,58584,58585],{"xmlns":375},[377,58586,58587,58591],{},[380,58588,58589],{},[383,58590,561],{},[387,58592,561],{"encoding":389},[363,58594,58596],{"className":58595,"ariaHidden":394},[393],[363,58597,58599,58602],{"className":58598},[398],[363,58600],{"className":58601,"style":913},[402],[363,58603,561],{"className":58604},[407,408]," 出现在分母上」的直觉相反，这个凸性正是变分推断里「对 ",[363,58607,58609,58622],{"className":58608,"translate":367},[366],[363,58610,58612],{"className":58611},[371],[373,58613,58614],{"xmlns":375},[377,58615,58616,58620],{},[380,58617,58618],{},[383,58619,1291],{},[387,58621,1291],{"encoding":389},[363,58623,58625],{"className":58624,"ariaHidden":394},[393],[363,58626,58628,58631],{"className":58627},[398],[363,58629],{"className":58630,"style":2623},[402],[363,58632,1291],{"className":58633,"style":1328},[407,408]," 做平均场优化收敛到全局最优」的根据之一。",[2658,58636,58638],{"id":58637},"_43-斜对称关系","4.3 斜对称关系",[1340,58640,58642,58740,58958],{"title":58641},"定义 4.1（斜共轭）",[11,58643,14608,58644,58739],{},[363,58645,58647,58676],{"className":58646,"translate":367},[366],[363,58648,58650],{"className":58649},[371],[373,58651,58652],{"xmlns":375},[377,58653,58654,58674],{},[380,58655,58656,58658,58660,58662,58664,58666,58668,58670,58672],{},[383,58657,385],{},[458,58659,1362],{},[458,58661,578],{"stretchy":460},[463,58663,474],{},[458,58665,898],{"separator":394},[383,58667,1371],{"mathvariant":557},[458,58669,468],{"stretchy":460},[458,58671,1376],{},[383,58673,1379],{"mathvariant":570},[387,58675,1382],{"encoding":389},[363,58677,58679,58697,58730],{"className":58678,"ariaHidden":394},[393],[363,58680,58682,58685,58688,58691,58694],{"className":58681},[398],[363,58683],{"className":58684,"style":403},[402],[363,58686,385],{"className":58687,"style":409},[407,408],[363,58689],{"className":58690,"style":506},[505],[363,58692,1362],{"className":58693},[510],[363,58695],{"className":58696,"style":506},[505],[363,58698,58700,58703,58706,58709,58712,58715,58718,58721,58724,58727],{"className":58699},[398],[363,58701],{"className":58702,"style":487},[402],[363,58704,578],{"className":58705},[494],[363,58707,474],{"className":58708},[407],[363,58710,898],{"className":58711},[920],[363,58713],{"className":58714,"style":754},[505],[363,58716,1371],{"className":58717},[407],[363,58719,468],{"className":58720},[501],[363,58722],{"className":58723,"style":506},[505],[363,58725,1376],{"className":58726},[510],[363,58728],{"className":58729,"style":506},[505],[363,58731,58733,58736],{"className":58732},[398],[363,58734],{"className":58735,"style":1443},[402],[363,58737,1379],{"className":58738},[407,714],"，称",[363,58741,58743],{"className":58742,"translate":367},[528],[363,58744,58746,58808],{"className":58745,"translate":367},[366],[363,58747,58749],{"className":58748},[371],[373,58750,58751],{"xmlns":375,"display":537},[377,58752,58753,58805],{},[380,58754,58755,58771,58773,58775,58777,58779,58781,58783,58785,58787,58789,58791,58793,58795,58797,58799,58801,58803],{},[7900,58756,58757,58759,58769],{},[383,58758,385],{},[380,58760,58761,58763,58765,58767],{},[383,58762,7908],{},[383,58764,7911],{},[383,58766,7914],{},[383,58768,7917],{},[458,58770,7920],{"lspace":1594,"rspace":1594},[458,58772,461],{"stretchy":460},[383,58774,1116],{},[458,58776,468],{"stretchy":460},[458,58778,471],{},[383,58780,1116],{},[1644,58782,1646],{},[383,58784,385],{},[458,58786,461],{"stretchy":460},[463,58788,465],{},[383,58790,1288],{"mathvariant":557},[383,58792,1116],{},[458,58794,468],{"stretchy":460},[458,58796,898],{"separator":394},[505,58798],{"width":3609},[383,58800,1116],{},[458,58802,3250],{},[463,58804,474],{},[387,58806,58807],{"encoding":389},"f^{*}_{skew}(t)=t\\,f(1\u002Ft),\\qquad t>0",[363,58809,58811,58901,58949],{"className":58810,"ariaHidden":394},[393],[363,58812,58814,58817,58883,58886,58889,58892,58895,58898],{"className":58813},[398],[363,58815],{"className":58816,"style":487},[402],[363,58818,58820,58823],{"className":58819},[407],[363,58821,385],{"className":58822,"style":409},[407,408],[363,58824,58826],{"className":58825},[629],[363,58827,58829,58875],{"className":58828},[633,634],[363,58830,58832,58872],{"className":58831},[638],[363,58833,58835,58858],{"className":58834,"style":8595},[642],[363,58836,58837,58840],{"style":8598},[363,58838],{"className":58839,"style":651},[650],[363,58841,58843],{"className":58842},[655,656,657,658],[363,58844,58846,58849,58852,58855],{"className":58845},[407,658],[363,58847,7908],{"className":58848},[407,408,658],[363,58850,7911],{"className":58851,"style":8614},[407,408,658],[363,58853,7914],{"className":58854},[407,408,658],[363,58856,7917],{"className":58857,"style":8621},[407,408,658],[363,58859,58860,58863],{"style":8624},[363,58861],{"className":58862,"style":651},[650],[363,58864,58866],{"className":58865},[655,656,657,658],[363,58867,58869],{"className":58868},[407,658],[363,58870,7920],{"className":58871},[407,658],[363,58873,666],{"className":58874},[665],[363,58876,58878],{"className":58877},[638],[363,58879,58881],{"className":58880,"style":8646},[642],[363,58882],{},[363,58884,461],{"className":58885},[494],[363,58887,1116],{"className":58888},[407,408],[363,58890,468],{"className":58891},[501],[363,58893],{"className":58894,"style":506},[505],[363,58896,471],{"className":58897},[510],[363,58899],{"className":58900,"style":506},[505],[363,58902,58904,58907,58910,58913,58916,58919,58922,58925,58928,58931,58934,58937,58940,58943,58946],{"className":58903},[398],[363,58905],{"className":58906,"style":487},[402],[363,58908,1116],{"className":58909},[407,408],[363,58911],{"className":58912,"style":754},[505],[363,58914,385],{"className":58915,"style":409},[407,408],[363,58917,461],{"className":58918},[494],[363,58920,8936],{"className":58921},[407],[363,58923,1116],{"className":58924},[407,408],[363,58926,468],{"className":58927},[501],[363,58929,898],{"className":58930},[920],[363,58932],{"className":58933,"style":3981},[505],[363,58935],{"className":58936,"style":754},[505],[363,58938,1116],{"className":58939},[407,408],[363,58941],{"className":58942,"style":506},[505],[363,58944,3250],{"className":58945},[510],[363,58947],{"className":58948,"style":506},[505],[363,58950,58952,58955],{"className":58951},[398],[363,58953],{"className":58954,"style":520},[402],[363,58956,474],{"className":58957},[407],[11,58959,58960,58961,34172,58989,10527],{},"为 ",[363,58962,58964,58977],{"className":58963,"translate":367},[366],[363,58965,58967],{"className":58966},[371],[373,58968,58969],{"xmlns":375},[377,58970,58971,58975],{},[380,58972,58973],{},[383,58974,385],{},[387,58976,385],{"encoding":389},[363,58978,58980],{"className":58979,"ariaHidden":394},[393],[363,58981,58983,58986],{"className":58982},[398],[363,58984],{"className":58985,"style":403},[402],[363,58987,385],{"className":58988,"style":409},[407,408],[1572,58990,36135],{},[1340,58992,58994,59038],{"title":58993},"命题 4.3（斜对称）",[11,58995,58996,58997,3092],{},"对任意概率分布 ",[363,58998,59000,59017],{"className":58999,"translate":367},[366],[363,59001,59003],{"className":59002},[371],[373,59004,59005],{"xmlns":375},[377,59006,59007,59015],{},[380,59008,59009,59011,59013],{},[383,59010,554],{},[458,59012,898],{"separator":394},[383,59014,561],{},[387,59016,903],{"encoding":389},[363,59018,59020],{"className":59019,"ariaHidden":394},[393],[363,59021,59023,59026,59029,59032,59035],{"className":59022},[398],[363,59024],{"className":59025,"style":913},[402],[363,59027,554],{"className":59028,"style":682},[407,408],[363,59030,898],{"className":59031},[920],[363,59033],{"className":59034,"style":754},[505],[363,59036,561],{"className":59037},[407,408],[363,59039,59041],{"className":59040,"translate":367},[528],[363,59042,59044,59106],{"className":59043,"translate":367},[366],[363,59045,59047],{"className":59046},[371],[373,59048,59049],{"xmlns":375,"display":537},[377,59050,59051,59103],{},[380,59052,59053,59059,59061,59063,59065,59067,59069,59071,59091,59093,59095,59097,59099,59101],{},[543,59054,59055,59057],{},[383,59056,547],{},[383,59058,385],{},[458,59060,461],{"stretchy":460},[383,59062,554],{},[383,59064,558],{"mathvariant":557},[383,59066,561],{},[458,59068,468],{"stretchy":460},[458,59070,471],{},[543,59072,59073,59075],{},[383,59074,547],{},[7900,59076,59077,59079,59089],{},[383,59078,385],{},[380,59080,59081,59083,59085,59087],{},[383,59082,7908],{},[383,59084,7911],{},[383,59086,7914],{},[383,59088,7917],{},[458,59090,7920],{"lspace":1594,"rspace":1594},[458,59092,461],{"stretchy":460},[383,59094,561],{},[383,59096,558],{"mathvariant":557},[383,59098,554],{},[458,59100,468],{"stretchy":460},[383,59102,4722],{"mathvariant":557},[387,59104,59105],{"encoding":389},"D_f(P\\|Q)=D_{f^{*}_{skew}}(Q\\|P).",[363,59107,59109,59179],{"className":59108,"ariaHidden":394},[393],[363,59110,59112,59115,59155,59158,59161,59164,59167,59170,59173,59176],{"className":59111},[398],[363,59113],{"className":59114,"style":618},[402],[363,59116,59118,59121],{"className":59117},[407],[363,59119,547],{"className":59120,"style":625},[407,408],[363,59122,59124],{"className":59123},[629],[363,59125,59127,59147],{"className":59126},[633,634],[363,59128,59130,59144],{"className":59129},[638],[363,59131,59133],{"className":59132,"style":643},[642],[363,59134,59135,59138],{"style":646},[363,59136],{"className":59137,"style":651},[650],[363,59139,59141],{"className":59140},[655,656,657,658],[363,59142,385],{"className":59143,"style":409},[407,408,658],[363,59145,666],{"className":59146},[665],[363,59148,59150],{"className":59149},[638],[363,59151,59153],{"className":59152,"style":673},[642],[363,59154],{},[363,59156,461],{"className":59157},[494],[363,59159,554],{"className":59160,"style":682},[407,408],[363,59162,558],{"className":59163},[407],[363,59165,561],{"className":59166},[407,408],[363,59168,468],{"className":59169},[501],[363,59171],{"className":59172,"style":506},[505],[363,59174,471],{"className":59175},[510],[363,59177],{"className":59178,"style":506},[505],[363,59180,59182,59186,59297,59300,59303,59306,59309,59312],{"className":59181},[398],[363,59183],{"className":59184,"style":59185},[402],"height:1.1431em;vertical-align:-0.3931em;",[363,59187,59189,59192],{"className":59188},[407],[363,59190,547],{"className":59191,"style":625},[407,408],[363,59193,59195],{"className":59194},[629],[363,59196,59198,59288],{"className":59197},[633,634],[363,59199,59201,59285],{"className":59200},[638],[363,59202,59204],{"className":59203,"style":643},[642],[363,59205,59206,59209],{"style":646},[363,59207],{"className":59208,"style":651},[650],[363,59210,59212],{"className":59211},[655,656,657,658],[363,59213,59215],{"className":59214},[407,658],[363,59216,59218,59221],{"className":59217},[407,658],[363,59219,385],{"className":59220,"style":409},[407,408,658],[363,59222,59224],{"className":59223},[629],[363,59225,59227,59276],{"className":59226},[633,634],[363,59228,59230,59273],{"className":59229},[638],[363,59231,59234,59258],{"className":59232,"style":59233},[642],"height:0.6771em;",[363,59235,59237,59240],{"style":59236},"top:-2.1528em;margin-left:-0.1076em;margin-right:0.0714em;",[363,59238],{"className":59239,"style":30553},[650],[363,59241,59243],{"className":59242},[655,30557,10021,658],[363,59244,59246,59249,59252,59255],{"className":59245},[407,658],[363,59247,7908],{"className":59248},[407,408,658],[363,59250,7911],{"className":59251,"style":8614},[407,408,658],[363,59253,7914],{"className":59254},[407,408,658],[363,59256,7917],{"className":59257,"style":8621},[407,408,658],[363,59259,59261,59264],{"style":59260},"top:-2.8448em;margin-right:0.0714em;",[363,59262],{"className":59263,"style":30553},[650],[363,59265,59267],{"className":59266},[655,30557,10021,658],[363,59268,59270],{"className":59269},[407,658],[363,59271,7920],{"className":59272},[407,658],[363,59274,666],{"className":59275},[665],[363,59277,59279],{"className":59278},[638],[363,59280,59283],{"className":59281,"style":59282},[642],"height:0.3472em;",[363,59284],{},[363,59286,666],{"className":59287},[665],[363,59289,59291],{"className":59290},[638],[363,59292,59295],{"className":59293,"style":59294},[642],"height:0.3931em;",[363,59296],{},[363,59298,461],{"className":59299},[494],[363,59301,561],{"className":59302},[407,408],[363,59304,558],{"className":59305},[407],[363,59307,554],{"className":59308,"style":682},[407,408],[363,59310,468],{"className":59311},[501],[363,59313,4722],{"className":59314},[407],[11,59316,59317,11407,59319,59419],{},[1572,59318,55818],{},[363,59320,59322,59356],{"className":59321,"translate":367},[366],[363,59323,59325],{"className":59324},[371],[373,59326,59327],{"xmlns":375},[377,59328,59329,59353],{},[380,59330,59331,59333,59335,59337,59339,59341,59343,59345,59347,59349,59351],{},[383,59332,7908],{},[458,59334,471],{},[383,59336,592],{},[383,59338,561],{},[383,59340,1288],{"mathvariant":557},[383,59342,592],{},[383,59344,554],{},[458,59346,471],{},[463,59348,465],{},[383,59350,1288],{"mathvariant":557},[383,59352,1116],{},[387,59354,59355],{"encoding":389},"s=dQ\u002FdP=1\u002Ft",[363,59357,59359,59377,59407],{"className":59358,"ariaHidden":394},[393],[363,59360,59362,59365,59368,59371,59374],{"className":59361},[398],[363,59363],{"className":59364,"style":2692},[402],[363,59366,7908],{"className":59367},[407,408],[363,59369],{"className":59370,"style":506},[505],[363,59372,471],{"className":59373},[510],[363,59375],{"className":59376,"style":506},[505],[363,59378,59380,59383,59386,59389,59392,59395,59398,59401,59404],{"className":59379},[398],[363,59381],{"className":59382,"style":487},[402],[363,59384,592],{"className":59385},[407,408],[363,59387,561],{"className":59388},[407,408],[363,59390,1288],{"className":59391},[407],[363,59393,592],{"className":59394},[407,408],[363,59396,554],{"className":59397,"style":682},[407,408],[363,59399],{"className":59400,"style":506},[505],[363,59402,471],{"className":59403},[510],[363,59405],{"className":59406,"style":506},[505],[363,59408,59410,59413,59416],{"className":59409},[398],[363,59411],{"className":59412,"style":487},[402],[363,59414,8936],{"className":59415},[407],[363,59417,1116],{"className":59418},[407,408],"。则",[363,59421,59423],{"className":59422,"translate":367},[528],[363,59424,59426,59603],{"className":59425,"translate":367},[366],[363,59427,59429],{"className":59428},[371],[373,59430,59431],{"xmlns":375,"display":537},[377,59432,59433,59600],{},[1590,59434,59435,59513],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,59436,59437,59459],{},[1599,59438,59439],{},[1602,59440,59441],{"scriptlevel":474,"displaystyle":394},[380,59442,59443,59449,59451,59453,59455,59457],{},[543,59444,59445,59447],{},[383,59446,547],{},[383,59448,385],{},[458,59450,461],{"stretchy":460},[383,59452,554],{},[383,59454,558],{"mathvariant":557},[383,59456,561],{},[458,59458,468],{"stretchy":460},[1599,59460,59461],{},[1602,59462,59463],{"scriptlevel":474,"displaystyle":394},[380,59464,59465,59467,59469,59471,59473,59475,59477,59479,59481,59483,59485,59487,59489,59491,59493,59505,59507,59509,59511],{},[380,59466],{},[458,59468,471],{},[458,59470,1634],{},[383,59472,385],{},[458,59474,461],{"stretchy":460},[383,59476,1116],{},[458,59478,468],{"stretchy":460},[1644,59480,1646],{},[383,59482,592],{},[383,59484,561],{},[458,59486,471],{},[458,59488,1634],{},[383,59490,385],{},[1644,59492,1651],{},[380,59494,59495,59497,59503],{},[458,59496,461],{"fence":394},[586,59498,59499,59501],{},[463,59500,465],{},[383,59502,7908],{},[458,59504,468],{"fence":394},[383,59506,7908],{},[1644,59508,1646],{},[383,59510,592],{},[383,59512,554],{},[1596,59514,59515,59521],{},[1599,59516,59517],{},[1602,59518,59519],{"scriptlevel":474,"displaystyle":394},[380,59520],{},[1599,59522,59523],{},[1602,59524,59525],{"scriptlevel":474,"displaystyle":394},[380,59526,59527,59529,59531,59533,59549,59551,59553,59555,59557,59559,59561,59563,59583,59585,59587,59589,59591,59593,59595,59597],{},[380,59528],{},[458,59530,471],{},[458,59532,1634],{},[7900,59534,59535,59537,59547],{},[383,59536,385],{},[380,59538,59539,59541,59543,59545],{},[383,59540,7908],{},[383,59542,7911],{},[383,59544,7914],{},[383,59546,7917],{},[458,59548,7920],{"lspace":1594,"rspace":1594},[458,59550,461],{"stretchy":460},[383,59552,7908],{},[458,59554,468],{"stretchy":460},[1644,59556,1646],{},[383,59558,592],{},[383,59560,554],{},[458,59562,471],{},[543,59564,59565,59567],{},[383,59566,547],{},[7900,59568,59569,59571,59581],{},[383,59570,385],{},[380,59572,59573,59575,59577,59579],{},[383,59574,7908],{},[383,59576,7911],{},[383,59578,7914],{},[383,59580,7917],{},[458,59582,7920],{"lspace":1594,"rspace":1594},[458,59584,461],{"stretchy":460},[383,59586,561],{},[383,59588,558],{"mathvariant":557},[383,59590,554],{},[458,59592,468],{"stretchy":460},[383,59594,4722],{"mathvariant":557},[505,59596],{"width":3609},[383,59598,59599],{"mathvariant":557},"□",[387,59601,59602],{"encoding":389},"\\begin{aligned}\nD_f(P\\|Q)&=\\int f(t)\\,dQ\n=\\int f\\!\\left(\\frac1s\\right) s\\,dP\\\\\n&=\\int f^{*}_{skew}(s)\\,dP\n=D_{f^{*}_{skew}}(Q\\|P).\\qquad\\square\n\\end{aligned}",[363,59604,59606],{"className":59605,"ariaHidden":394},[393],[363,59607,59609,59613],{"className":59608},[398],[363,59610],{"className":59611,"style":59612},[402],"height:4.9223em;vertical-align:-2.2111em;",[363,59614,59616],{"className":59615},[407],[363,59617,59619,59717],{"className":59618},[1590],[363,59620,59622],{"className":59621},[1707],[363,59623,59625,59708],{"className":59624},[633,634],[363,59626,59628,59705],{"className":59627},[638],[363,59629,59632,59696],{"className":59630,"style":59631},[642],"height:2.7111em;",[363,59633,59635,59638],{"style":59634},"top:-4.7111em;",[363,59636],{"className":59637,"style":1724},[650],[363,59639,59641,59681,59684,59687,59690,59693],{"className":59640},[407],[363,59642,59644,59647],{"className":59643},[407],[363,59645,547],{"className":59646,"style":625},[407,408],[363,59648,59650],{"className":59649},[629],[363,59651,59653,59673],{"className":59652},[633,634],[363,59654,59656,59670],{"className":59655},[638],[363,59657,59659],{"className":59658,"style":643},[642],[363,59660,59661,59664],{"style":646},[363,59662],{"className":59663,"style":651},[650],[363,59665,59667],{"className":59666},[655,656,657,658],[363,59668,385],{"className":59669,"style":409},[407,408,658],[363,59671,666],{"className":59672},[665],[363,59674,59676],{"className":59675},[638],[363,59677,59679],{"className":59678,"style":673},[642],[363,59680],{},[363,59682,461],{"className":59683},[494],[363,59685,554],{"className":59686,"style":682},[407,408],[363,59688,558],{"className":59689},[407],[363,59691,561],{"className":59692},[407,408],[363,59694,468],{"className":59695},[501],[363,59697,59699,59702],{"style":59698},"top:-2.1011em;",[363,59700],{"className":59701,"style":1724},[650],[363,59703],{"className":59704},[407],[363,59706,666],{"className":59707},[665],[363,59709,59711],{"className":59710},[638],[363,59712,59715],{"className":59713,"style":59714},[642],"height:2.2111em;",[363,59716],{},[363,59718,59720],{"className":59719},[1798],[363,59721,59723,60145],{"className":59722},[633,634],[363,59724,59726,60142],{"className":59725},[638],[363,59727,59729,59892],{"className":59728,"style":59631},[642],[363,59730,59731,59734],{"style":59634},[363,59732],{"className":59733,"style":1724},[650],[363,59735,59737,59740,59743,59746,59749,59752,59755,59758,59761,59764,59767,59770,59773,59776,59779,59782,59785,59788,59791,59794,59797,59800,59877,59880,59883,59886,59889],{"className":59736},[407],[363,59738],{"className":59739},[407],[363,59741],{"className":59742,"style":506},[505],[363,59744,471],{"className":59745},[510],[363,59747],{"className":59748,"style":506},[505],[363,59750,1634],{"className":59751,"style":1834},[1831,1832,1833],[363,59753],{"className":59754,"style":754},[505],[363,59756,385],{"className":59757,"style":409},[407,408],[363,59759,461],{"className":59760},[494],[363,59762,1116],{"className":59763},[407,408],[363,59765,468],{"className":59766},[501],[363,59768],{"className":59769,"style":754},[505],[363,59771,592],{"className":59772},[407,408],[363,59774,561],{"className":59775},[407,408],[363,59777],{"className":59778,"style":506},[505],[363,59780,471],{"className":59781},[510],[363,59783],{"className":59784,"style":506},[505],[363,59786,1634],{"className":59787,"style":1834},[1831,1832,1833],[363,59789],{"className":59790,"style":754},[505],[363,59792,385],{"className":59793,"style":409},[407,408],[363,59795],{"className":59796,"style":1859},[505],[363,59798],{"className":59799,"style":754},[505],[363,59801,59803,59809,59871],{"className":59802},[758],[363,59804,59806],{"className":59805,"style":763},[494,762],[363,59807,461],{"className":59808},[767,657],[363,59810,59812,59815,59868],{"className":59811},[407],[363,59813],{"className":59814},[494,789],[363,59816,59818],{"className":59817},[586],[363,59819,59821,59860],{"className":59820},[633,634],[363,59822,59824,59857],{"className":59823},[638],[363,59825,59827,59838,59846],{"className":59826,"style":23236},[642],[363,59828,59829,59832],{"style":805},[363,59830],{"className":59831,"style":809},[650],[363,59833,59835],{"className":59834},[407],[363,59836,7908],{"className":59837},[407,408],[363,59839,59840,59843],{"style":821},[363,59841],{"className":59842,"style":809},[650],[363,59844],{"className":59845,"style":829},[828],[363,59847,59848,59851],{"style":832},[363,59849],{"className":59850,"style":809},[650],[363,59852,59854],{"className":59853},[407],[363,59855,465],{"className":59856},[407],[363,59858,666],{"className":59859},[665],[363,59861,59863],{"className":59862},[638],[363,59864,59866],{"className":59865,"style":4125},[642],[363,59867],{},[363,59869],{"className":59870},[501,789],[363,59872,59874],{"className":59873,"style":763},[501,762],[363,59875,468],{"className":59876},[767,657],[363,59878],{"className":59879,"style":754},[505],[363,59881,7908],{"className":59882},[407,408],[363,59884],{"className":59885,"style":754},[505],[363,59887,592],{"className":59888},[407,408],[363,59890,554],{"className":59891,"style":682},[407,408],[363,59893,59894,59897],{"style":59698},[363,59895],{"className":59896,"style":1724},[650],[363,59898,59900,59903,59906,59909,59912,59915,59918,59984,59987,59990,59993,59996,59999,60002,60005,60008,60011,60117,60120,60123,60126,60129,60132,60135,60138],{"className":59899},[407],[363,59901],{"className":59902},[407],[363,59904],{"className":59905,"style":506},[505],[363,59907,471],{"className":59908},[510],[363,59910],{"className":59911,"style":506},[505],[363,59913,1634],{"className":59914,"style":1834},[1831,1832,1833],[363,59916],{"className":59917,"style":754},[505],[363,59919,59921,59924],{"className":59920},[407],[363,59922,385],{"className":59923,"style":409},[407,408],[363,59925,59927],{"className":59926},[629],[363,59928,59930,59976],{"className":59929},[633,634],[363,59931,59933,59973],{"className":59932},[638],[363,59934,59936,59959],{"className":59935,"style":8595},[642],[363,59937,59938,59941],{"style":8598},[363,59939],{"className":59940,"style":651},[650],[363,59942,59944],{"className":59943},[655,656,657,658],[363,59945,59947,59950,59953,59956],{"className":59946},[407,658],[363,59948,7908],{"className":59949},[407,408,658],[363,59951,7911],{"className":59952,"style":8614},[407,408,658],[363,59954,7914],{"className":59955},[407,408,658],[363,59957,7917],{"className":59958,"style":8621},[407,408,658],[363,59960,59961,59964],{"style":8624},[363,59962],{"className":59963,"style":651},[650],[363,59965,59967],{"className":59966},[655,656,657,658],[363,59968,59970],{"className":59969},[407,658],[363,59971,7920],{"className":59972},[407,658],[363,59974,666],{"className":59975},[665],[363,59977,59979],{"className":59978},[638],[363,59980,59982],{"className":59981,"style":8646},[642],[363,59983],{},[363,59985,461],{"className":59986},[494],[363,59988,7908],{"className":59989},[407,408],[363,59991,468],{"className":59992},[501],[363,59994],{"className":59995,"style":754},[505],[363,59997,592],{"className":59998},[407,408],[363,60000,554],{"className":60001,"style":682},[407,408],[363,60003],{"className":60004,"style":506},[505],[363,60006,471],{"className":60007},[510],[363,60009],{"className":60010,"style":506},[505],[363,60012,60014,60017],{"className":60013},[407],[363,60015,547],{"className":60016,"style":625},[407,408],[363,60018,60020],{"className":60019},[629],[363,60021,60023,60109],{"className":60022},[633,634],[363,60024,60026,60106],{"className":60025},[638],[363,60027,60029],{"className":60028,"style":643},[642],[363,60030,60031,60034],{"style":646},[363,60032],{"className":60033,"style":651},[650],[363,60035,60037],{"className":60036},[655,656,657,658],[363,60038,60040],{"className":60039},[407,658],[363,60041,60043,60046],{"className":60042},[407,658],[363,60044,385],{"className":60045,"style":409},[407,408,658],[363,60047,60049],{"className":60048},[629],[363,60050,60052,60098],{"className":60051},[633,634],[363,60053,60055,60095],{"className":60054},[638],[363,60056,60058,60081],{"className":60057,"style":59233},[642],[363,60059,60060,60063],{"style":59236},[363,60061],{"className":60062,"style":30553},[650],[363,60064,60066],{"className":60065},[655,30557,10021,658],[363,60067,60069,60072,60075,60078],{"className":60068},[407,658],[363,60070,7908],{"className":60071},[407,408,658],[363,60073,7911],{"className":60074,"style":8614},[407,408,658],[363,60076,7914],{"className":60077},[407,408,658],[363,60079,7917],{"className":60080,"style":8621},[407,408,658],[363,60082,60083,60086],{"style":59260},[363,60084],{"className":60085,"style":30553},[650],[363,60087,60089],{"className":60088},[655,30557,10021,658],[363,60090,60092],{"className":60091},[407,658],[363,60093,7920],{"className":60094},[407,658],[363,60096,666],{"className":60097},[665],[363,60099,60101],{"className":60100},[638],[363,60102,60104],{"className":60103,"style":59282},[642],[363,60105],{},[363,60107,666],{"className":60108},[665],[363,60110,60112],{"className":60111},[638],[363,60113,60115],{"className":60114,"style":59294},[642],[363,60116],{},[363,60118,461],{"className":60119},[494],[363,60121,561],{"className":60122},[407,408],[363,60124,558],{"className":60125},[407],[363,60127,554],{"className":60128,"style":682},[407,408],[363,60130,468],{"className":60131},[501],[363,60133,4722],{"className":60134},[407],[363,60136],{"className":60137,"style":3981},[505],[363,60139,59599],{"className":60140},[407,60141],"amsrm",[363,60143,666],{"className":60144},[665],[363,60146,60148],{"className":60147},[638],[363,60149,60151],{"className":60150,"style":59714},[642],[363,60152],{},[11,60154,60155,6841,60158,60227,60228,60411,60412,60453,60454,60581,60582,60647,60648,60932,60933,61025],{},[1572,60156,60157],{},"推论（对称判别准则）。",[363,60159,60161,60178],{"className":60160,"translate":367},[366],[363,60162,60164],{"className":60163},[371],[373,60165,60166],{"xmlns":375},[377,60167,60168,60176],{},[380,60169,60170],{},[543,60171,60172,60174],{},[383,60173,547],{},[383,60175,385],{},[387,60177,4369],{"encoding":389},[363,60179,60181],{"className":60180,"ariaHidden":394},[393],[363,60182,60184,60187],{"className":60183},[398],[363,60185],{"className":60186,"style":4379},[402],[363,60188,60190,60193],{"className":60189},[407],[363,60191,547],{"className":60192,"style":625},[407,408],[363,60194,60196],{"className":60195},[629],[363,60197,60199,60219],{"className":60198},[633,634],[363,60200,60202,60216],{"className":60201},[638],[363,60203,60205],{"className":60204,"style":643},[642],[363,60206,60207,60210],{"style":646},[363,60208],{"className":60209,"style":651},[650],[363,60211,60213],{"className":60212},[655,656,657,658],[363,60214,385],{"className":60215,"style":409},[407,408,658],[363,60217,666],{"className":60218},[665],[363,60220,60222],{"className":60221},[638],[363,60223,60225],{"className":60224,"style":673},[642],[363,60226],{}," 对称（",[363,60229,60231,60277],{"className":60230,"translate":367},[366],[363,60232,60234],{"className":60233},[371],[373,60235,60236],{"xmlns":375},[377,60237,60238,60274],{},[380,60239,60240,60246,60248,60250,60252,60254,60256,60258,60264,60266,60268,60270,60272],{},[543,60241,60242,60244],{},[383,60243,547],{},[383,60245,385],{},[458,60247,461],{"stretchy":460},[383,60249,554],{},[383,60251,558],{"mathvariant":557},[383,60253,561],{},[458,60255,468],{"stretchy":460},[458,60257,471],{},[543,60259,60260,60262],{},[383,60261,547],{},[383,60263,385],{},[458,60265,461],{"stretchy":460},[383,60267,561],{},[383,60269,558],{"mathvariant":557},[383,60271,554],{},[458,60273,468],{"stretchy":460},[387,60275,60276],{"encoding":389},"D_f(P\\|Q)=D_f(Q\\|P)",[363,60278,60280,60350],{"className":60279,"ariaHidden":394},[393],[363,60281,60283,60286,60326,60329,60332,60335,60338,60341,60344,60347],{"className":60282},[398],[363,60284],{"className":60285,"style":618},[402],[363,60287,60289,60292],{"className":60288},[407],[363,60290,547],{"className":60291,"style":625},[407,408],[363,60293,60295],{"className":60294},[629],[363,60296,60298,60318],{"className":60297},[633,634],[363,60299,60301,60315],{"className":60300},[638],[363,60302,60304],{"className":60303,"style":643},[642],[363,60305,60306,60309],{"style":646},[363,60307],{"className":60308,"style":651},[650],[363,60310,60312],{"className":60311},[655,656,657,658],[363,60313,385],{"className":60314,"style":409},[407,408,658],[363,60316,666],{"className":60317},[665],[363,60319,60321],{"className":60320},[638],[363,60322,60324],{"className":60323,"style":673},[642],[363,60325],{},[363,60327,461],{"className":60328},[494],[363,60330,554],{"className":60331,"style":682},[407,408],[363,60333,558],{"className":60334},[407],[363,60336,561],{"className":60337},[407,408],[363,60339,468],{"className":60340},[501],[363,60342],{"className":60343,"style":506},[505],[363,60345,471],{"className":60346},[510],[363,60348],{"className":60349,"style":506},[505],[363,60351,60353,60356,60396,60399,60402,60405,60408],{"className":60352},[398],[363,60354],{"className":60355,"style":618},[402],[363,60357,60359,60362],{"className":60358},[407],[363,60360,547],{"className":60361,"style":625},[407,408],[363,60363,60365],{"className":60364},[629],[363,60366,60368,60388],{"className":60367},[633,634],[363,60369,60371,60385],{"className":60370},[638],[363,60372,60374],{"className":60373,"style":643},[642],[363,60375,60376,60379],{"style":646},[363,60377],{"className":60378,"style":651},[650],[363,60380,60382],{"className":60381},[655,656,657,658],[363,60383,385],{"className":60384,"style":409},[407,408,658],[363,60386,666],{"className":60387},[665],[363,60389,60391],{"className":60390},[638],[363,60392,60394],{"className":60393,"style":673},[642],[363,60395],{},[363,60397,461],{"className":60398},[494],[363,60400,561],{"className":60401},[407,408],[363,60403,558],{"className":60404},[407],[363,60406,554],{"className":60407,"style":682},[407,408],[363,60409,468],{"className":60410},[501]," 对所有 ",[363,60413,60415,60432],{"className":60414,"translate":367},[366],[363,60416,60418],{"className":60417},[371],[373,60419,60420],{"xmlns":375},[377,60421,60422,60430],{},[380,60423,60424,60426,60428],{},[383,60425,554],{},[458,60427,898],{"separator":394},[383,60429,561],{},[387,60431,903],{"encoding":389},[363,60433,60435],{"className":60434,"ariaHidden":394},[393],[363,60436,60438,60441,60444,60447,60450],{"className":60437},[398],[363,60439],{"className":60440,"style":913},[402],[363,60442,554],{"className":60443,"style":682},[407,408],[363,60445,898],{"className":60446},[920],[363,60448],{"className":60449,"style":754},[505],[363,60451,561],{"className":60452},[407,408],"）当且仅当 ",[363,60455,60457,60488],{"className":60456,"translate":367},[366],[363,60458,60460],{"className":60459},[371],[373,60461,60462],{"xmlns":375},[377,60463,60464,60486],{},[380,60465,60466,60482,60484],{},[7900,60467,60468,60470,60480],{},[383,60469,385],{},[380,60471,60472,60474,60476,60478],{},[383,60473,7908],{},[383,60475,7911],{},[383,60477,7914],{},[383,60479,7917],{},[458,60481,7920],{"lspace":1594,"rspace":1594},[458,60483,471],{},[383,60485,385],{},[387,60487,44500],{"encoding":389},[363,60489,60491,60572],{"className":60490,"ariaHidden":394},[393],[363,60492,60494,60497,60563,60566,60569],{"className":60493},[398],[363,60495],{"className":60496,"style":44510},[402],[363,60498,60500,60503],{"className":60499},[407],[363,60501,385],{"className":60502,"style":409},[407,408],[363,60504,60506],{"className":60505},[629],[363,60507,60509,60555],{"className":60508},[633,634],[363,60510,60512,60552],{"className":60511},[638],[363,60513,60515,60538],{"className":60514,"style":8846},[642],[363,60516,60517,60520],{"style":8849},[363,60518],{"className":60519,"style":651},[650],[363,60521,60523],{"className":60522},[655,656,657,658],[363,60524,60526,60529,60532,60535],{"className":60525},[407,658],[363,60527,7908],{"className":60528},[407,408,658],[363,60530,7911],{"className":60531,"style":8614},[407,408,658],[363,60533,7914],{"className":60534},[407,408,658],[363,60536,7917],{"className":60537,"style":8621},[407,408,658],[363,60539,60540,60543],{"style":7212},[363,60541],{"className":60542,"style":651},[650],[363,60544,60546],{"className":60545},[655,656,657,658],[363,60547,60549],{"className":60548},[407,658],[363,60550,7920],{"className":60551},[407,658],[363,60553,666],{"className":60554},[665],[363,60556,60558],{"className":60557},[638],[363,60559,60561],{"className":60560,"style":8894},[642],[363,60562],{},[363,60564],{"className":60565,"style":506},[505],[363,60567,471],{"className":60568},[510],[363,60570],{"className":60571,"style":506},[505],[363,60573,60575,60578],{"className":60574},[398],[363,60576],{"className":60577,"style":403},[402],[363,60579,385],{"className":60580,"style":409},[407,408],"（模去 ",[363,60583,60585,60608],{"className":60584,"translate":367},[366],[363,60586,60588],{"className":60587},[371],[373,60589,60590],{"xmlns":375},[377,60591,60592,60606],{},[380,60593,60594,60596,60598,60600,60602,60604],{},[383,60595,6253],{},[458,60597,461],{"stretchy":460},[383,60599,1116],{},[458,60601,5160],{},[463,60603,465],{},[458,60605,468],{"stretchy":460},[387,60607,6967],{"encoding":389},[363,60609,60611,60635],{"className":60610,"ariaHidden":394},[393],[363,60612,60614,60617,60620,60623,60626,60629,60632],{"className":60613},[398],[363,60615],{"className":60616,"style":487},[402],[363,60618,6253],{"className":60619},[407,408],[363,60621,461],{"className":60622},[494],[363,60624,1116],{"className":60625},[407,408],[363,60627],{"className":60628,"style":2934},[505],[363,60630,5160],{"className":60631},[2938],[363,60633],{"className":60634,"style":2934},[505],[363,60636,60638,60641,60644],{"className":60637},[398],[363,60639],{"className":60640,"style":487},[402],[363,60642,465],{"className":60643},[407],[363,60645,468],{"className":60646},[501],"）。验证 TV：",[363,60649,60651,60705],{"className":60650,"translate":367},[366],[363,60652,60654],{"className":60653},[371],[373,60655,60656],{"xmlns":375},[377,60657,60658,60702],{},[380,60659,60660,60662,60664,60670,60672,60674,60676,60678,60680,60682,60684,60686,60692,60694,60696,60698,60700],{},[383,60661,1116],{},[458,60663,3646],{},[586,60665,60666,60668],{},[463,60667,465],{},[463,60669,2810],{},[383,60671,5155],{"mathvariant":557},[463,60673,465],{},[383,60675,1288],{"mathvariant":557},[383,60677,1116],{},[458,60679,5160],{},[463,60681,465],{},[383,60683,5155],{"mathvariant":557},[458,60685,471],{},[586,60687,60688,60690],{},[463,60689,465],{},[463,60691,2810],{},[383,60693,5155],{"mathvariant":557},[383,60695,1116],{},[458,60697,5160],{},[463,60699,465],{},[383,60701,5155],{"mathvariant":557},[387,60703,60704],{"encoding":389},"t\\cdot\\frac12|1\u002Ft-1|=\\frac12|t-1|",[363,60706,60708,60726,60816,60834,60923],{"className":60707,"ariaHidden":394},[393],[363,60709,60711,60714,60717,60720,60723],{"className":60710},[398],[363,60712],{"className":60713,"style":5690},[402],[363,60715,1116],{"className":60716},[407,408],[363,60718],{"className":60719,"style":2934},[505],[363,60721,3646],{"className":60722},[2938],[363,60724],{"className":60725,"style":2934},[505],[363,60727,60729,60732,60800,60804,60807,60810,60813],{"className":60728},[398],[363,60730],{"className":60731,"style":2852},[402],[363,60733,60735,60738,60797],{"className":60734},[407],[363,60736],{"className":60737},[494,789],[363,60739,60741],{"className":60740},[586],[363,60742,60744,60789],{"className":60743},[633,634],[363,60745,60747,60786],{"className":60746},[638],[363,60748,60750,60764,60772],{"className":60749,"style":2871},[642],[363,60751,60752,60755],{"style":2874},[363,60753],{"className":60754,"style":809},[650],[363,60756,60758],{"className":60757},[655,656,657,658],[363,60759,60761],{"className":60760},[407,658],[363,60762,2810],{"className":60763},[407,658],[363,60765,60766,60769],{"style":821},[363,60767],{"className":60768,"style":809},[650],[363,60770],{"className":60771,"style":829},[828],[363,60773,60774,60777],{"style":2897},[363,60775],{"className":60776,"style":809},[650],[363,60778,60780],{"className":60779},[655,656,657,658],[363,60781,60783],{"className":60782},[407,658],[363,60784,465],{"className":60785},[407,658],[363,60787,666],{"className":60788},[665],[363,60790,60792],{"className":60791},[638],[363,60793,60795],{"className":60794,"style":2919},[642],[363,60796],{},[363,60798],{"className":60799},[501,789],[363,60801,60803],{"className":60802},[407],"∣1\u002F",[363,60805,1116],{"className":60806},[407,408],[363,60808],{"className":60809,"style":2934},[505],[363,60811,5160],{"className":60812},[2938],[363,60814],{"className":60815,"style":2934},[505],[363,60817,60819,60822,60825,60828,60831],{"className":60818},[398],[363,60820],{"className":60821,"style":487},[402],[363,60823,35026],{"className":60824},[407],[363,60826],{"className":60827,"style":506},[505],[363,60829,471],{"className":60830},[510],[363,60832],{"className":60833,"style":506},[505],[363,60835,60837,60840,60908,60911,60914,60917,60920],{"className":60836},[398],[363,60838],{"className":60839,"style":2852},[402],[363,60841,60843,60846,60905],{"className":60842},[407],[363,60844],{"className":60845},[494,789],[363,60847,60849],{"className":60848},[586],[363,60850,60852,60897],{"className":60851},[633,634],[363,60853,60855,60894],{"className":60854},[638],[363,60856,60858,60872,60880],{"className":60857,"style":2871},[642],[363,60859,60860,60863],{"style":2874},[363,60861],{"className":60862,"style":809},[650],[363,60864,60866],{"className":60865},[655,656,657,658],[363,60867,60869],{"className":60868},[407,658],[363,60870,2810],{"className":60871},[407,658],[363,60873,60874,60877],{"style":821},[363,60875],{"className":60876,"style":809},[650],[363,60878],{"className":60879,"style":829},[828],[363,60881,60882,60885],{"style":2897},[363,60883],{"className":60884,"style":809},[650],[363,60886,60888],{"className":60887},[655,656,657,658],[363,60889,60891],{"className":60890},[407,658],[363,60892,465],{"className":60893},[407,658],[363,60895,666],{"className":60896},[665],[363,60898,60900],{"className":60899},[638],[363,60901,60903],{"className":60902,"style":2919},[642],[363,60904],{},[363,60906],{"className":60907},[501,789],[363,60909,5155],{"className":60910},[407],[363,60912,1116],{"className":60913},[407,408],[363,60915],{"className":60916,"style":2934},[505],[363,60918,5160],{"className":60919},[2938],[363,60921],{"className":60922,"style":2934},[505],[363,60924,60926,60929],{"className":60925},[398],[363,60927],{"className":60928,"style":487},[402],[363,60930,35026],{"className":60931},[407],"；JS 的 ",[363,60934,60936,60971],{"className":60935,"translate":367},[366],[363,60937,60939],{"className":60938},[371],[373,60940,60941],{"xmlns":375},[377,60942,60943,60969],{},[380,60944,60945,60947,60949,60951,60953,60955,60957,60959,60961,60963,60965,60967],{},[383,60946,1116],{},[383,60948,385],{},[458,60950,461],{"stretchy":460},[463,60952,465],{},[383,60954,1288],{"mathvariant":557},[383,60956,1116],{},[458,60958,468],{"stretchy":460},[458,60960,471],{},[383,60962,385],{},[458,60964,461],{"stretchy":460},[383,60966,1116],{},[458,60968,468],{"stretchy":460},[387,60970,23916],{"encoding":389},[363,60972,60974,61007],{"className":60973,"ariaHidden":394},[393],[363,60975,60977,60980,60983,60986,60989,60992,60995,60998,61001,61004],{"className":60976},[398],[363,60978],{"className":60979,"style":487},[402],[363,60981,1116],{"className":60982},[407,408],[363,60984,385],{"className":60985,"style":409},[407,408],[363,60987,461],{"className":60988},[494],[363,60990,8936],{"className":60991},[407],[363,60993,1116],{"className":60994},[407,408],[363,60996,468],{"className":60997},[501],[363,60999],{"className":61000,"style":506},[505],[363,61002,471],{"className":61003},[510],[363,61005],{"className":61006,"style":506},[505],[363,61008,61010,61013,61016,61019,61022],{"className":61009},[398],[363,61011],{"className":61012,"style":487},[402],[363,61014,385],{"className":61015,"style":409},[407,408],[363,61017,461],{"className":61018},[494],[363,61020,1116],{"className":61021},[407,408],[363,61023,468],{"className":61024},[501]," 也已验算；KL 显然不满足，故不对称。",[2658,61027,61029],{"id":61028},"_44-变分表示","4.4 变分表示",[1340,61031,61033,61124,61350,61353,61729],{"title":61032},"定理 4.1（变分表示 \u002F Fenchel 对偶）",[11,61034,881,61035,61094,61095,61123],{},[363,61036,61038,61056],{"className":61037,"translate":367},[366],[363,61039,61041],{"className":61040},[371],[373,61042,61043],{"xmlns":375},[377,61044,61045,61053],{},[380,61046,61047],{},[7161,61048,61049,61051],{},[383,61050,385],{},[458,61052,7920],{},[387,61054,61055],{"encoding":389},"f^*",[363,61057,61059],{"className":61058,"ariaHidden":394},[393],[363,61060,61062,61065],{"className":61061},[398],[363,61063],{"className":61064,"style":403},[402],[363,61066,61068,61071],{"className":61067},[407],[363,61069,385],{"className":61070,"style":409},[407,408],[363,61072,61074],{"className":61073},[629],[363,61075,61077],{"className":61076},[633],[363,61078,61080],{"className":61079},[638],[363,61081,61083],{"className":61082,"style":8846},[642],[363,61084,61085,61088],{"style":7212},[363,61086],{"className":61087,"style":651},[650],[363,61089,61091],{"className":61090},[655,656,657,658],[363,61092,7920],{"className":61093},[2938,658]," 为 ",[363,61096,61098,61111],{"className":61097,"translate":367},[366],[363,61099,61101],{"className":61100},[371],[373,61102,61103],{"xmlns":375},[377,61104,61105,61109],{},[380,61106,61107],{},[383,61108,385],{},[387,61110,385],{"encoding":389},[363,61112,61114],{"className":61113,"ariaHidden":394},[393],[363,61115,61117,61120],{"className":61116},[398],[363,61118],{"className":61119,"style":403},[402],[363,61121,385],{"className":61122,"style":409},[407,408]," 的凸共轭（Fenchel 共轭）",[363,61125,61127],{"className":61126,"translate":367},[528],[363,61128,61130,61192],{"className":61129,"translate":367},[366],[363,61131,61133],{"className":61132},[371],[373,61134,61135],{"xmlns":375,"display":537},[377,61136,61137,61189],{},[380,61138,61139,61145,61147,61149,61151,61153,61169,61171,61173,61175,61177,61179,61181,61183,61185,61187],{},[7161,61140,61141,61143],{},[383,61142,385],{},[458,61144,7920],{},[458,61146,461],{"stretchy":460},[383,61148,40584],{},[458,61150,468],{"stretchy":460},[458,61152,471],{},[6363,61154,61155,61161],{},[380,61156,61157,61159],{},[383,61158,35779],{},[458,61160,4450],{},[380,61162,61163,61165,61167],{},[383,61164,1116],{},[458,61166,7275],{},[463,61168,474],{},[458,61170,3245],{"stretchy":460},[383,61172,40584],{},[383,61174,1116],{},[458,61176,5160],{},[383,61178,385],{},[458,61180,461],{"stretchy":460},[383,61182,1116],{},[458,61184,468],{"stretchy":460},[458,61186,3255],{"stretchy":460},[458,61188,898],{"separator":394},[387,61190,61191],{"encoding":389},"f^*(y)=\\sup_{t\\ge0}\\{yt-f(t)\\},",[363,61193,61195,61248,61328],{"className":61194,"ariaHidden":394},[393],[363,61196,61198,61201,61230,61233,61236,61239,61242,61245],{"className":61197},[398],[363,61199],{"className":61200,"style":487},[402],[363,61202,61204,61207],{"className":61203},[407],[363,61205,385],{"className":61206,"style":409},[407,408],[363,61208,61210],{"className":61209},[629],[363,61211,61213],{"className":61212},[633],[363,61214,61216],{"className":61215},[638],[363,61217,61219],{"className":61218,"style":8595},[642],[363,61220,61221,61224],{"style":8624},[363,61222],{"className":61223,"style":651},[650],[363,61225,61227],{"className":61226},[655,656,657,658],[363,61228,7920],{"className":61229},[2938,658],[363,61231,461],{"className":61232},[494],[363,61234,40584],{"className":61235,"style":1328},[407,408],[363,61237,468],{"className":61238},[501],[363,61240],{"className":61241,"style":506},[505],[363,61243,471],{"className":61244},[510],[363,61246],{"className":61247,"style":506},[505],[363,61249,61251,61255,61310,61313,61316,61319,61322,61325],{"className":61250},[398],[363,61252],{"className":61253,"style":61254},[402],"height:1.7567em;vertical-align:-1.0067em;",[363,61256,61258],{"className":61257},[1831,14063],[363,61259,61261,61301],{"className":61260},[633,634],[363,61262,61264,61298],{"className":61263},[638],[363,61265,61267,61288],{"className":61266,"style":2692},[642],[363,61268,61270,61273],{"style":61269},"top:-2.1885em;margin-left:0em;",[363,61271],{"className":61272,"style":809},[650],[363,61274,61276],{"className":61275},[655,656,657,658],[363,61277,61279,61282,61285],{"className":61278},[407,658],[363,61280,1116],{"className":61281},[407,408,658],[363,61283,7275],{"className":61284},[510,658],[363,61286,474],{"className":61287},[407,658],[363,61289,61290,61293],{"style":12210},[363,61291],{"className":61292,"style":809},[650],[363,61294,61295],{},[363,61296,35779],{"className":61297},[1831],[363,61299,666],{"className":61300},[665],[363,61302,61304],{"className":61303},[638],[363,61305,61308],{"className":61306,"style":61307},[642],"height:1.0067em;",[363,61309],{},[363,61311,3245],{"className":61312},[494],[363,61314,40584],{"className":61315,"style":1328},[407,408],[363,61317,1116],{"className":61318},[407,408],[363,61320],{"className":61321,"style":2934},[505],[363,61323,5160],{"className":61324},[2938],[363,61326],{"className":61327,"style":2934},[505],[363,61329,61331,61334,61337,61340,61343,61347],{"className":61330},[398],[363,61332],{"className":61333,"style":487},[402],[363,61335,385],{"className":61336,"style":409},[407,408],[363,61338,461],{"className":61339},[494],[363,61341,1116],{"className":61342},[407,408],[363,61344,61346],{"className":61345},[501],")}",[363,61348,898],{"className":61349},[920],[11,61351,61352],{},"则",[363,61354,61356],{"className":61355,"translate":367},[528],[363,61357,61359,61443],{"className":61358,"translate":367},[366],[363,61360,61362],{"className":61361},[371],[373,61363,61364],{"xmlns":375,"display":537},[377,61365,61366,61440],{},[380,61367,61368,61374,61376,61378,61380,61382,61384,61386,61396,61438],{},[543,61369,61370,61372],{},[383,61371,547],{},[383,61373,385],{},[458,61375,461],{"stretchy":460},[383,61377,554],{},[383,61379,558],{"mathvariant":557},[383,61381,561],{},[458,61383,468],{"stretchy":460},[458,61385,471],{},[6363,61387,61388,61394],{},[380,61389,61390,61392],{},[383,61391,35779],{},[458,61393,4450],{},[383,61395,4505],{},[380,61397,61398,61400,61406,61408,61410,61412,61414,61420,61422,61428,61430,61432,61434,61436],{},[458,61399,3245],{"fence":394},[543,61401,61402,61404],{},[383,61403,571],{"mathvariant":570},[383,61405,554],{},[458,61407,578],{"stretchy":460},[383,61409,4505],{},[458,61411,605],{"stretchy":460},[458,61413,5160],{},[543,61415,61416,61418],{},[383,61417,571],{"mathvariant":570},[383,61419,561],{},[458,61421,578],{"stretchy":460},[7161,61423,61424,61426],{},[383,61425,385],{},[458,61427,7920],{},[458,61429,461],{"stretchy":460},[383,61431,4505],{},[458,61433,468],{"stretchy":460},[458,61435,605],{"stretchy":460},[458,61437,3255],{"fence":394},[458,61439,898],{"separator":394},[387,61441,61442],{"encoding":389},"D_f(P\\|Q)=\\sup_{g}\n\\left\\{\\mathbb E_P[g]\n-\\mathbb E_Q[f^*(g)]\\right\\},",[363,61444,61446,61516],{"className":61445,"ariaHidden":394},[393],[363,61447,61449,61452,61492,61495,61498,61501,61504,61507,61510,61513],{"className":61448},[398],[363,61450],{"className":61451,"style":618},[402],[363,61453,61455,61458],{"className":61454},[407],[363,61456,547],{"className":61457,"style":625},[407,408],[363,61459,61461],{"className":61460},[629],[363,61462,61464,61484],{"className":61463},[633,634],[363,61465,61467,61481],{"className":61466},[638],[363,61468,61470],{"className":61469,"style":643},[642],[363,61471,61472,61475],{"style":646},[363,61473],{"className":61474,"style":651},[650],[363,61476,61478],{"className":61477},[655,656,657,658],[363,61479,385],{"className":61480,"style":409},[407,408,658],[363,61482,666],{"className":61483},[665],[363,61485,61487],{"className":61486},[638],[363,61488,61490],{"className":61489,"style":673},[642],[363,61491],{},[363,61493,461],{"className":61494},[494],[363,61496,554],{"className":61497,"style":682},[407,408],[363,61499,558],{"className":61500},[407],[363,61502,561],{"className":61503},[407,408],[363,61505,468],{"className":61506},[501],[363,61508],{"className":61509,"style":506},[505],[363,61511,471],{"className":61512},[510],[363,61514],{"className":61515,"style":506},[505],[363,61517,61519,61523,61572,61575,61723,61726],{"className":61518},[398],[363,61520],{"className":61521,"style":61522},[402],"height:1.7805em;vertical-align:-1.0305em;",[363,61524,61526],{"className":61525},[1831,14063],[363,61527,61529,61563],{"className":61528},[633,634],[363,61530,61532,61560],{"className":61531},[638],[363,61533,61535,61550],{"className":61534,"style":2692},[642],[363,61536,61538,61541],{"style":61537},"top:-2.2056em;margin-left:0em;",[363,61539],{"className":61540,"style":809},[650],[363,61542,61544],{"className":61543},[655,656,657,658],[363,61545,61547],{"className":61546},[407,658],[363,61548,4505],{"className":61549,"style":1328},[407,408,658],[363,61551,61552,61555],{"style":12210},[363,61553],{"className":61554,"style":809},[650],[363,61556,61557],{},[363,61558,35779],{"className":61559},[1831],[363,61561,666],{"className":61562},[665],[363,61564,61566],{"className":61565},[638],[363,61567,61570],{"className":61568,"style":61569},[642],"height:1.0305em;",[363,61571],{},[363,61573],{"className":61574,"style":754},[505],[363,61576,61578,61581,61621,61624,61627,61630,61633,61636,61639,61679,61682,61711,61714,61717,61720],{"className":61577},[758],[363,61579,3245],{"className":61580,"style":763},[494,762],[363,61582,61584,61587],{"className":61583},[407],[363,61585,571],{"className":61586},[407,714],[363,61588,61590],{"className":61589},[629],[363,61591,61593,61613],{"className":61592},[633,634],[363,61594,61596,61610],{"className":61595},[638],[363,61597,61599],{"className":61598,"style":727},[642],[363,61600,61601,61604],{"style":730},[363,61602],{"className":61603,"style":651},[650],[363,61605,61607],{"className":61606},[655,656,657,658],[363,61608,554],{"className":61609,"style":682},[407,408,658],[363,61611,666],{"className":61612},[665],[363,61614,61616],{"className":61615},[638],[363,61617,61619],{"className":61618,"style":8315},[642],[363,61620],{},[363,61622,578],{"className":61623},[494],[363,61625,4505],{"className":61626,"style":1328},[407,408],[363,61628,605],{"className":61629},[501],[363,61631],{"className":61632,"style":2934},[505],[363,61634,5160],{"className":61635},[2938],[363,61637],{"className":61638,"style":2934},[505],[363,61640,61642,61645],{"className":61641},[407],[363,61643,571],{"className":61644},[407,714],[363,61646,61648],{"className":61647},[629],[363,61649,61651,61671],{"className":61650},[633,634],[363,61652,61654,61668],{"className":61653},[638],[363,61655,61657],{"className":61656,"style":727},[642],[363,61658,61659,61662],{"style":730},[363,61660],{"className":61661,"style":651},[650],[363,61663,61665],{"className":61664},[655,656,657,658],[363,61666,561],{"className":61667},[407,408,658],[363,61669,666],{"className":61670},[665],[363,61672,61674],{"className":61673},[638],[363,61675,61677],{"className":61676,"style":673},[642],[363,61678],{},[363,61680,578],{"className":61681},[494],[363,61683,61685,61688],{"className":61684},[407],[363,61686,385],{"className":61687,"style":409},[407,408],[363,61689,61691],{"className":61690},[629],[363,61692,61694],{"className":61693},[633],[363,61695,61697],{"className":61696},[638],[363,61698,61700],{"className":61699,"style":8595},[642],[363,61701,61702,61705],{"style":8624},[363,61703],{"className":61704,"style":651},[650],[363,61706,61708],{"className":61707},[655,656,657,658],[363,61709,7920],{"className":61710},[2938,658],[363,61712,461],{"className":61713},[494],[363,61715,4505],{"className":61716,"style":1328},[407,408],[363,61718,20737],{"className":61719},[501],[363,61721,3255],{"className":61722,"style":763},[501,762],[363,61724],{"className":61725,"style":754},[505],[363,61727,898],{"className":61728},[920],[11,61730,61731,61732,10527],{},"其中上确界取遍所有使两个期望都有定义的可测函数 ",[363,61733,61735,61766],{"className":61734,"translate":367},[366],[363,61736,61738],{"className":61737},[371],[373,61739,61740],{"xmlns":375},[377,61741,61742,61763],{},[380,61743,61744,61746,61748,61750,61752,61755,61757],{},[383,61745,4505],{},[458,61747,1362],{},[383,61749,945],{"mathvariant":944},[458,61751,1376],{},[383,61753,61754],{"mathvariant":557},"dom",[458,61756,4450],{},[7161,61758,61759,61761],{},[383,61760,385],{},[458,61762,7920],{},[387,61764,61765],{"encoding":389},"g:\\mathcal X\\to\\operatorname{dom} f^*",[363,61767,61769,61787,61805],{"className":61768,"ariaHidden":394},[393],[363,61770,61772,61775,61778,61781,61784],{"className":61771},[398],[363,61773],{"className":61774,"style":2623},[402],[363,61776,4505],{"className":61777,"style":1328},[407,408],[363,61779],{"className":61780,"style":506},[505],[363,61782,1362],{"className":61783},[510],[363,61785],{"className":61786,"style":506},[505],[363,61788,61790,61793,61796,61799,61802],{"className":61789},[398],[363,61791],{"className":61792,"style":1011},[402],[363,61794,945],{"className":61795,"style":972},[407,971],[363,61797],{"className":61798,"style":506},[505],[363,61800,1376],{"className":61801},[510],[363,61803],{"className":61804,"style":506},[505],[363,61806,61808,61811,61817,61820],{"className":61807},[398],[363,61809],{"className":61810,"style":403},[402],[363,61812,61814],{"className":61813},[1831],[363,61815,61754],{"className":61816},[407,33009],[363,61818],{"className":61819,"style":754},[505],[363,61821,61823,61826],{"className":61822},[407],[363,61824,385],{"className":61825,"style":409},[407,408],[363,61827,61829],{"className":61828},[629],[363,61830,61832],{"className":61831},[633],[363,61833,61835],{"className":61834},[638],[363,61836,61838],{"className":61837,"style":8846},[642],[363,61839,61840,61843],{"style":7212},[363,61841],{"className":61842,"style":651},[650],[363,61844,61846],{"className":61845},[655,656,657,658],[363,61847,7920],{"className":61848},[2938,658],[11,61850,61851,61854,61855,61883],{},[1572,61852,61853],{},"证明（Fenchel 对偶）。"," 由共轭函数的性质（Fenchel–Moreau，",[363,61856,61858,61871],{"className":61857,"translate":367},[366],[363,61859,61861],{"className":61860},[371],[373,61862,61863],{"xmlns":375},[377,61864,61865,61869],{},[380,61866,61867],{},[383,61868,385],{},[387,61870,385],{"encoding":389},[363,61872,61874],{"className":61873,"ariaHidden":394},[393],[363,61875,61877,61880],{"className":61876},[398],[363,61878],{"className":61879,"style":403},[402],[363,61881,385],{"className":61882,"style":409},[407,408]," 凸闭），",[363,61885,61887],{"className":61886,"translate":367},[528],[363,61888,61890,61957],{"className":61889,"translate":367},[366],[363,61891,61893],{"className":61892},[371],[373,61894,61895],{"xmlns":375,"display":537},[377,61896,61897,61954],{},[380,61898,61899,61901,61903,61905,61907,61909,61919,61921,61923,61925,61927,61933,61935,61937,61939,61941,61943,61945,61948,61950,61952],{},[383,61900,385],{},[458,61902,461],{"stretchy":460},[383,61904,1116],{},[458,61906,468],{"stretchy":460},[458,61908,471],{},[6363,61910,61911,61917],{},[380,61912,61913,61915],{},[383,61914,35779],{},[458,61916,4450],{},[383,61918,40584],{},[458,61920,3245],{"stretchy":460},[383,61922,40584],{},[383,61924,1116],{},[458,61926,5160],{},[7161,61928,61929,61931],{},[383,61930,385],{},[458,61932,7920],{},[458,61934,461],{"stretchy":460},[383,61936,40584],{},[458,61938,468],{"stretchy":460},[458,61940,3255],{"stretchy":460},[458,61942,898],{"separator":394},[505,61944],{"width":3609},[383,61946,61947],{"mathvariant":557},"∀",[383,61949,1116],{},[458,61951,7275],{},[463,61953,6111],{},[387,61955,61956],{"encoding":389},"f(t)=\\sup_{y}\\{yt-f^*(y)\\},\n\\qquad \\forall t\\ge0 .",[363,61958,61960,61987,62058,62126],{"className":61959,"ariaHidden":394},[393],[363,61961,61963,61966,61969,61972,61975,61978,61981,61984],{"className":61962},[398],[363,61964],{"className":61965,"style":487},[402],[363,61967,385],{"className":61968,"style":409},[407,408],[363,61970,461],{"className":61971},[494],[363,61973,1116],{"className":61974},[407,408],[363,61976,468],{"className":61977},[501],[363,61979],{"className":61980,"style":506},[505],[363,61982,471],{"className":61983},[510],[363,61985],{"className":61986,"style":506},[505],[363,61988,61990,61993,62040,62043,62046,62049,62052,62055],{"className":61989},[398],[363,61991],{"className":61992,"style":61522},[402],[363,61994,61996],{"className":61995},[1831,14063],[363,61997,61999,62032],{"className":61998},[633,634],[363,62000,62002,62029],{"className":62001},[638],[363,62003,62005,62019],{"className":62004,"style":2692},[642],[363,62006,62007,62010],{"style":61537},[363,62008],{"className":62009,"style":809},[650],[363,62011,62013],{"className":62012},[655,656,657,658],[363,62014,62016],{"className":62015},[407,658],[363,62017,40584],{"className":62018,"style":1328},[407,408,658],[363,62020,62021,62024],{"style":12210},[363,62022],{"className":62023,"style":809},[650],[363,62025,62026],{},[363,62027,35779],{"className":62028},[1831],[363,62030,666],{"className":62031},[665],[363,62033,62035],{"className":62034},[638],[363,62036,62038],{"className":62037,"style":61569},[642],[363,62039],{},[363,62041,3245],{"className":62042},[494],[363,62044,40584],{"className":62045,"style":1328},[407,408],[363,62047,1116],{"className":62048},[407,408],[363,62050],{"className":62051,"style":2934},[505],[363,62053,5160],{"className":62054},[2938],[363,62056],{"className":62057,"style":2934},[505],[363,62059,62061,62064,62093,62096,62099,62102,62105,62108,62111,62114,62117,62120,62123],{"className":62060},[398],[363,62062],{"className":62063,"style":487},[402],[363,62065,62067,62070],{"className":62066},[407],[363,62068,385],{"className":62069,"style":409},[407,408],[363,62071,62073],{"className":62072},[629],[363,62074,62076],{"className":62075},[633],[363,62077,62079],{"className":62078},[638],[363,62080,62082],{"className":62081,"style":8595},[642],[363,62083,62084,62087],{"style":8624},[363,62085],{"className":62086,"style":651},[650],[363,62088,62090],{"className":62089},[655,656,657,658],[363,62091,7920],{"className":62092},[2938,658],[363,62094,461],{"className":62095},[494],[363,62097,40584],{"className":62098,"style":1328},[407,408],[363,62100,61346],{"className":62101},[501],[363,62103,898],{"className":62104},[920],[363,62106],{"className":62107,"style":3981},[505],[363,62109],{"className":62110,"style":754},[505],[363,62112,61947],{"className":62113},[407],[363,62115,1116],{"className":62116},[407,408],[363,62118],{"className":62119,"style":506},[505],[363,62121,7275],{"className":62122},[510],[363,62124],{"className":62125,"style":506},[505],[363,62127,62129,62132],{"className":62128},[398],[363,62130],{"className":62131,"style":520},[402],[363,62133,6111],{"className":62134},[407],[11,62136,17393,62137,62271,62272,62300],{},[363,62138,62140,62170],{"className":62139,"translate":367},[366],[363,62141,62143],{"className":62142},[371],[373,62144,62145],{"xmlns":375},[377,62146,62147,62167],{},[380,62148,62149,62151,62153],{},[383,62150,1116],{},[458,62152,471],{},[586,62154,62155,62161],{},[380,62156,62157,62159],{},[383,62158,592],{},[383,62160,554],{},[380,62162,62163,62165],{},[383,62164,592],{},[383,62166,561],{},[387,62168,62169],{"encoding":389},"t=\\frac{dP}{dQ}",[363,62171,62173,62191],{"className":62172,"ariaHidden":394},[393],[363,62174,62176,62179,62182,62185,62188],{"className":62175},[398],[363,62177],{"className":62178,"style":5690},[402],[363,62180,1116],{"className":62181},[407,408],[363,62183],{"className":62184,"style":506},[505],[363,62186,471],{"className":62187},[510],[363,62189],{"className":62190,"style":506},[505],[363,62192,62194,62197],{"className":62193},[398],[363,62195],{"className":62196,"style":3015},[402],[363,62198,62200,62203,62268],{"className":62199},[407],[363,62201],{"className":62202},[494,789],[363,62204,62206],{"className":62205},[586],[363,62207,62209,62260],{"className":62208},[633,634],[363,62210,62212,62257],{"className":62211},[638],[363,62213,62215,62232,62240],{"className":62214,"style":3034},[642],[363,62216,62217,62220],{"style":2874},[363,62218],{"className":62219,"style":809},[650],[363,62221,62223],{"className":62222},[655,656,657,658],[363,62224,62226,62229],{"className":62225},[407,658],[363,62227,592],{"className":62228},[407,408,658],[363,62230,561],{"className":62231},[407,408,658],[363,62233,62234,62237],{"style":821},[363,62235],{"className":62236,"style":809},[650],[363,62238],{"className":62239,"style":829},[828],[363,62241,62242,62245],{"style":2897},[363,62243],{"className":62244,"style":809},[650],[363,62246,62248],{"className":62247},[655,656,657,658],[363,62249,62251,62254],{"className":62250},[407,658],[363,62252,592],{"className":62253},[407,408,658],[363,62255,554],{"className":62256,"style":682},[407,408,658],[363,62258,666],{"className":62259},[665],[363,62261,62263],{"className":62262},[638],[363,62264,62266],{"className":62265,"style":3086},[642],[363,62267],{},[363,62269],{"className":62270},[501,789]," 代入并对 ",[363,62273,62275,62288],{"className":62274,"translate":367},[366],[363,62276,62278],{"className":62277},[371],[373,62279,62280],{"xmlns":375},[377,62281,62282,62286],{},[380,62283,62284],{},[383,62285,561],{},[387,62287,561],{"encoding":389},[363,62289,62291],{"className":62290,"ariaHidden":394},[393],[363,62292,62294,62297],{"className":62293},[398],[363,62295],{"className":62296,"style":913},[402],[363,62298,561],{"className":62299},[407,408]," 积分：",[363,62302,62304],{"className":62303,"translate":367},[528],[363,62305,62307,62549],{"className":62306,"translate":367},[366],[363,62308,62310],{"className":62309},[371],[373,62311,62312],{"xmlns":375,"display":537},[377,62313,62314,62546],{},[1590,62315,62316,62402,62476],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,62317,62318,62340],{},[1599,62319,62320],{},[1602,62321,62322],{"scriptlevel":474,"displaystyle":394},[380,62323,62324,62330,62332,62334,62336,62338],{},[543,62325,62326,62328],{},[383,62327,547],{},[383,62329,385],{},[458,62331,461],{"stretchy":460},[383,62333,554],{},[383,62335,558],{"mathvariant":557},[383,62337,561],{},[458,62339,468],{"stretchy":460},[1599,62341,62342],{},[1602,62343,62344],{"scriptlevel":474,"displaystyle":394},[380,62345,62346,62348,62350,62352,62362,62364,62366,62368,62382,62384,62390,62392,62394,62396,62398,62400],{},[380,62347],{},[458,62349,471],{},[458,62351,1634],{},[6363,62353,62354,62360],{},[380,62355,62356,62358],{},[383,62357,35779],{},[458,62359,4450],{},[383,62361,40584],{},[458,62363,3245],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[383,62365,40584],{},[1644,62367,1646],{},[586,62369,62370,62376],{},[380,62371,62372,62374],{},[383,62373,592],{},[383,62375,554],{},[380,62377,62378,62380],{},[383,62379,592],{},[383,62381,561],{},[458,62383,5160],{},[7161,62385,62386,62388],{},[383,62387,385],{},[458,62389,7920],{},[458,62391,461],{"stretchy":460},[383,62393,40584],{},[458,62395,468],{"stretchy":460},[458,62397,3255],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[383,62399,592],{},[383,62401,561],{},[1596,62403,62404,62410],{},[1599,62405,62406],{},[1602,62407,62408],{"scriptlevel":474,"displaystyle":394},[380,62409],{},[1599,62411,62412],{},[1602,62413,62414],{"scriptlevel":474,"displaystyle":394},[380,62415,62416,62418,62420,62422,62424,62434,62436,62438,62440,62442,62456,62458,62464,62466,62468,62470,62472,62474],{},[380,62417],{},[1644,62419,4630],{},[458,62421,7275],{},[1644,62423,4630],{},[6363,62425,62426,62432],{},[380,62427,62428,62430],{},[383,62429,35779],{},[458,62431,4450],{},[383,62433,40584],{},[458,62435,1634],{},[458,62437,3245],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[383,62439,40584],{},[1644,62441,1646],{},[586,62443,62444,62450],{},[380,62445,62446,62448],{},[383,62447,592],{},[383,62449,554],{},[380,62451,62452,62454],{},[383,62453,592],{},[383,62455,561],{},[458,62457,5160],{},[7161,62459,62460,62462],{},[383,62461,385],{},[458,62463,7920],{},[458,62465,461],{"stretchy":460},[383,62467,40584],{},[458,62469,468],{"stretchy":460},[458,62471,3255],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[383,62473,592],{},[383,62475,561],{},[1596,62477,62478,62484],{},[1599,62479,62480],{},[1602,62481,62482],{"scriptlevel":474,"displaystyle":394},[380,62483],{},[1599,62485,62486],{},[1602,62487,62488],{"scriptlevel":474,"displaystyle":394},[380,62489,62490,62492,62494,62504,62506,62512,62514,62516,62518,62520,62526,62528,62534,62536,62538,62540,62542,62544],{},[380,62491],{},[458,62493,471],{},[6363,62495,62496,62502],{},[380,62497,62498,62500],{},[383,62499,35779],{},[458,62501,4450],{},[383,62503,40584],{},[458,62505,3245],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[543,62507,62508,62510],{},[383,62509,571],{"mathvariant":570},[383,62511,554],{},[458,62513,578],{"stretchy":460},[383,62515,40584],{},[458,62517,605],{"stretchy":460},[458,62519,5160],{},[543,62521,62522,62524],{},[383,62523,571],{"mathvariant":570},[383,62525,561],{},[458,62527,578],{"stretchy":460},[7161,62529,62530,62532],{},[383,62531,385],{},[458,62533,7920],{},[458,62535,461],{"stretchy":460},[383,62537,40584],{},[458,62539,468],{"stretchy":460},[458,62541,605],{"stretchy":460},[458,62543,3255],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,62545,4722],{"mathvariant":557},[387,62547,62548],{"encoding":389},"\\begin{aligned}\nD_f(P\\|Q)\n&=\\int \\sup_y\\Big\\{y\\,\\frac{dP}{dQ}\n-f^*(y)\\Big\\}dQ\\\\\n&\\ \\ge\\ \\sup_y\\int\\Big\\{y\\,\\frac{dP}{dQ}\n-f^*(y)\\Big\\}dQ\\\\\n&=\\sup_y\\big\\{\\mathbb E_P[y]\n-\\mathbb E_Q[f^*(y)]\\big\\}.\n\\end{aligned}",[363,62550,62552],{"className":62551,"ariaHidden":394},[393],[363,62553,62555,62559],{"className":62554},[398],[363,62556],{"className":62557,"style":62558},[402],"height:7.2845em;vertical-align:-3.3923em;",[363,62560,62562],{"className":62561},[407],[363,62563,62565,62673],{"className":62564},[1590],[363,62566,62568],{"className":62567},[1707],[363,62569,62571,62664],{"className":62570},[633,634],[363,62572,62574,62661],{"className":62573},[638],[363,62575,62578,62643,62652],{"className":62576,"style":62577},[642],"height:3.8923em;",[363,62579,62581,62585],{"style":62580},"top:-5.8923em;",[363,62582],{"className":62583,"style":62584},[650],"height:3.3714em;",[363,62586,62588,62628,62631,62634,62637,62640],{"className":62587},[407],[363,62589,62591,62594],{"className":62590},[407],[363,62592,547],{"className":62593,"style":625},[407,408],[363,62595,62597],{"className":62596},[629],[363,62598,62600,62620],{"className":62599},[633,634],[363,62601,62603,62617],{"className":62602},[638],[363,62604,62606],{"className":62605,"style":643},[642],[363,62607,62608,62611],{"style":646},[363,62609],{"className":62610,"style":651},[650],[363,62612,62614],{"className":62613},[655,656,657,658],[363,62615,385],{"className":62616,"style":409},[407,408,658],[363,62618,666],{"className":62619},[665],[363,62621,62623],{"className":62622},[638],[363,62624,62626],{"className":62625,"style":673},[642],[363,62627],{},[363,62629,461],{"className":62630},[494],[363,62632,554],{"className":62633,"style":682},[407,408],[363,62635,558],{"className":62636},[407],[363,62638,561],{"className":62639},[407,408],[363,62641,468],{"className":62642},[501],[363,62644,62646,62649],{"style":62645},"top:-3.1903em;",[363,62647],{"className":62648,"style":62584},[650],[363,62650],{"className":62651},[407],[363,62653,62655,62658],{"style":62654},"top:-1.0097em;",[363,62656],{"className":62657,"style":62584},[650],[363,62659],{"className":62660},[407],[363,62662,666],{"className":62663},[665],[363,62665,62667],{"className":62666},[638],[363,62668,62671],{"className":62669,"style":62670},[642],"height:3.3923em;",[363,62672],{},[363,62674,62676],{"className":62675},[1798],[363,62677,62679,63339],{"className":62678},[633,634],[363,62680,62682,63336],{"className":62681},[638],[363,62683,62685,62897,63115],{"className":62684,"style":62577},[642],[363,62686,62687,62690],{"style":62580},[363,62688],{"className":62689,"style":62584},[650],[363,62691,62693,62696,62699,62702,62705,62708,62711,62755,62758,62764,62767,62770,62838,62841,62844,62847,62876,62879,62882,62885,62891,62894],{"className":62692},[407],[363,62694],{"className":62695},[407],[363,62697],{"className":62698,"style":506},[505],[363,62700,471],{"className":62701},[510],[363,62703],{"className":62704,"style":506},[505],[363,62706,1634],{"className":62707,"style":1834},[1831,1832,1833],[363,62709],{"className":62710,"style":754},[505],[363,62712,62714],{"className":62713},[1831,14063],[363,62715,62717,62747],{"className":62716},[633,634],[363,62718,62720,62744],{"className":62719},[638],[363,62721,62723,62734],{"className":62722,"style":2692},[642],[363,62724,62725,62728],{"style":61537},[363,62726],{"className":62727,"style":809},[650],[363,62729,62731],{"className":62730},[655,656,657,658],[363,62732,40584],{"className":62733,"style":1328},[407,408,658],[363,62735,62736,62739],{"style":12210},[363,62737],{"className":62738,"style":809},[650],[363,62740,62741],{},[363,62742,35779],{"className":62743},[1831],[363,62745,666],{"className":62746},[665],[363,62748,62750],{"className":62749},[638],[363,62751,62753],{"className":62752,"style":61569},[642],[363,62754],{},[363,62756],{"className":62757,"style":754},[505],[363,62759,62761],{"className":62760},[407],[363,62762,3245],{"className":62763},[767,4067],[363,62765,40584],{"className":62766,"style":1328},[407,408],[363,62768],{"className":62769,"style":754},[505],[363,62771,62773,62776,62835],{"className":62772},[407],[363,62774],{"className":62775},[494,789],[363,62777,62779],{"className":62778},[586],[363,62780,62782,62827],{"className":62781},[633,634],[363,62783,62785,62824],{"className":62784},[638],[363,62786,62788,62802,62810],{"className":62787,"style":802},[642],[363,62789,62790,62793],{"style":805},[363,62791],{"className":62792,"style":809},[650],[363,62794,62796,62799],{"className":62795},[407],[363,62797,592],{"className":62798},[407,408],[363,62800,561],{"className":62801},[407,408],[363,62803,62804,62807],{"style":821},[363,62805],{"className":62806,"style":809},[650],[363,62808],{"className":62809,"style":829},[828],[363,62811,62812,62815],{"style":832},[363,62813],{"className":62814,"style":809},[650],[363,62816,62818,62821],{"className":62817},[407],[363,62819,592],{"className":62820},[407,408],[363,62822,554],{"className":62823,"style":682},[407,408],[363,62825,666],{"className":62826},[665],[363,62828,62830],{"className":62829},[638],[363,62831,62833],{"className":62832,"style":854},[642],[363,62834],{},[363,62836],{"className":62837},[501,789],[363,62839],{"className":62840,"style":2934},[505],[363,62842,5160],{"className":62843},[2938],[363,62845],{"className":62846,"style":2934},[505],[363,62848,62850,62853],{"className":62849},[407],[363,62851,385],{"className":62852,"style":409},[407,408],[363,62854,62856],{"className":62855},[629],[363,62857,62859],{"className":62858},[633],[363,62860,62862],{"className":62861},[638],[363,62863,62865],{"className":62864,"style":8595},[642],[363,62866,62867,62870],{"style":8624},[363,62868],{"className":62869,"style":651},[650],[363,62871,62873],{"className":62872},[655,656,657,658],[363,62874,7920],{"className":62875},[2938,658],[363,62877,461],{"className":62878},[494],[363,62880,40584],{"className":62881,"style":1328},[407,408],[363,62883,468],{"className":62884},[501],[363,62886,62888],{"className":62887},[407],[363,62889,3255],{"className":62890},[767,4067],[363,62892,592],{"className":62893},[407,408],[363,62895,561],{"className":62896},[407,408],[363,62898,62899,62902],{"style":62645},[363,62900],{"className":62901,"style":62584},[650],[363,62903,62905,62908,62911,62914,62917,62920,62923,62967,62970,62973,62976,62982,62985,62988,63056,63059,63062,63065,63094,63097,63100,63103,63109,63112],{"className":62904},[407],[363,62906],{"className":62907},[407],[363,62909,4630],{"className":62910},[505],[363,62912],{"className":62913,"style":506},[505],[363,62915,7275],{"className":62916},[510],[363,62918,4630],{"className":62919},[505],[363,62921],{"className":62922,"style":506},[505],[363,62924,62926],{"className":62925},[1831,14063],[363,62927,62929,62959],{"className":62928},[633,634],[363,62930,62932,62956],{"className":62931},[638],[363,62933,62935,62946],{"className":62934,"style":2692},[642],[363,62936,62937,62940],{"style":61537},[363,62938],{"className":62939,"style":809},[650],[363,62941,62943],{"className":62942},[655,656,657,658],[363,62944,40584],{"className":62945,"style":1328},[407,408,658],[363,62947,62948,62951],{"style":12210},[363,62949],{"className":62950,"style":809},[650],[363,62952,62953],{},[363,62954,35779],{"className":62955},[1831],[363,62957,666],{"className":62958},[665],[363,62960,62962],{"className":62961},[638],[363,62963,62965],{"className":62964,"style":61569},[642],[363,62966],{},[363,62968],{"className":62969,"style":754},[505],[363,62971,1634],{"className":62972,"style":1834},[1831,1832,1833],[363,62974],{"className":62975,"style":754},[505],[363,62977,62979],{"className":62978},[407],[363,62980,3245],{"className":62981},[767,4067],[363,62983,40584],{"className":62984,"style":1328},[407,408],[363,62986],{"className":62987,"style":754},[505],[363,62989,62991,62994,63053],{"className":62990},[407],[363,62992],{"className":62993},[494,789],[363,62995,62997],{"className":62996},[586],[363,62998,63000,63045],{"className":62999},[633,634],[363,63001,63003,63042],{"className":63002},[638],[363,63004,63006,63020,63028],{"className":63005,"style":802},[642],[363,63007,63008,63011],{"style":805},[363,63009],{"className":63010,"style":809},[650],[363,63012,63014,63017],{"className":63013},[407],[363,63015,592],{"className":63016},[407,408],[363,63018,561],{"className":63019},[407,408],[363,63021,63022,63025],{"style":821},[363,63023],{"className":63024,"style":809},[650],[363,63026],{"className":63027,"style":829},[828],[363,63029,63030,63033],{"style":832},[363,63031],{"className":63032,"style":809},[650],[363,63034,63036,63039],{"className":63035},[407],[363,63037,592],{"className":63038},[407,408],[363,63040,554],{"className":63041,"style":682},[407,408],[363,63043,666],{"className":63044},[665],[363,63046,63048],{"className":63047},[638],[363,63049,63051],{"className":63050,"style":854},[642],[363,63052],{},[363,63054],{"className":63055},[501,789],[363,63057],{"className":63058,"style":2934},[505],[363,63060,5160],{"className":63061},[2938],[363,63063],{"className":63064,"style":2934},[505],[363,63066,63068,63071],{"className":63067},[407],[363,63069,385],{"className":63070,"style":409},[407,408],[363,63072,63074],{"className":63073},[629],[363,63075,63077],{"className":63076},[633],[363,63078,63080],{"className":63079},[638],[363,63081,63083],{"className":63082,"style":8595},[642],[363,63084,63085,63088],{"style":8624},[363,63086],{"className":63087,"style":651},[650],[363,63089,63091],{"className":63090},[655,656,657,658],[363,63092,7920],{"className":63093},[2938,658],[363,63095,461],{"className":63096},[494],[363,63098,40584],{"className":63099,"style":1328},[407,408],[363,63101,468],{"className":63102},[501],[363,63104,63106],{"className":63105},[407],[363,63107,3255],{"className":63108},[767,4067],[363,63110,592],{"className":63111},[407,408],[363,63113,561],{"className":63114},[407,408],[363,63116,63117,63120],{"style":62654},[363,63118],{"className":63119,"style":62584},[650],[363,63121,63123,63126,63129,63132,63135,63179,63182,63188,63228,63231,63234,63237,63240,63243,63246,63286,63289,63318,63321,63324,63327,63333],{"className":63122},[407],[363,63124],{"className":63125},[407],[363,63127],{"className":63128,"style":506},[505],[363,63130,471],{"className":63131},[510],[363,63133],{"className":63134,"style":506},[505],[363,63136,63138],{"className":63137},[1831,14063],[363,63139,63141,63171],{"className":63140},[633,634],[363,63142,63144,63168],{"className":63143},[638],[363,63145,63147,63158],{"className":63146,"style":2692},[642],[363,63148,63149,63152],{"style":61537},[363,63150],{"className":63151,"style":809},[650],[363,63153,63155],{"className":63154},[655,656,657,658],[363,63156,40584],{"className":63157,"style":1328},[407,408,658],[363,63159,63160,63163],{"style":12210},[363,63161],{"className":63162,"style":809},[650],[363,63164,63165],{},[363,63166,35779],{"className":63167},[1831],[363,63169,666],{"className":63170},[665],[363,63172,63174],{"className":63173},[638],[363,63175,63177],{"className":63176,"style":61569},[642],[363,63178],{},[363,63180],{"className":63181,"style":754},[505],[363,63183,63185],{"className":63184},[407],[363,63186,3245],{"className":63187},[767,10021],[363,63189,63191,63194],{"className":63190},[407],[363,63192,571],{"className":63193},[407,714],[363,63195,63197],{"className":63196},[629],[363,63198,63200,63220],{"className":63199},[633,634],[363,63201,63203,63217],{"className":63202},[638],[363,63204,63206],{"className":63205,"style":727},[642],[363,63207,63208,63211],{"style":730},[363,63209],{"className":63210,"style":651},[650],[363,63212,63214],{"className":63213},[655,656,657,658],[363,63215,554],{"className":63216,"style":682},[407,408,658],[363,63218,666],{"className":63219},[665],[363,63221,63223],{"className":63222},[638],[363,63224,63226],{"className":63225,"style":8315},[642],[363,63227],{},[363,63229,578],{"className":63230},[494],[363,63232,40584],{"className":63233,"style":1328},[407,408],[363,63235,605],{"className":63236},[501],[363,63238],{"className":63239,"style":2934},[505],[363,63241,5160],{"className":63242},[2938],[363,63244],{"className":63245,"style":2934},[505],[363,63247,63249,63252],{"className":63248},[407],[363,63250,571],{"className":63251},[407,714],[363,63253,63255],{"className":63254},[629],[363,63256,63258,63278],{"className":63257},[633,634],[363,63259,63261,63275],{"className":63260},[638],[363,63262,63264],{"className":63263,"style":727},[642],[363,63265,63266,63269],{"style":730},[363,63267],{"className":63268,"style":651},[650],[363,63270,63272],{"className":63271},[655,656,657,658],[363,63273,561],{"className":63274},[407,408,658],[363,63276,666],{"className":63277},[665],[363,63279,63281],{"className":63280},[638],[363,63282,63284],{"className":63283,"style":673},[642],[363,63285],{},[363,63287,578],{"className":63288},[494],[363,63290,63292,63295],{"className":63291},[407],[363,63293,385],{"className":63294,"style":409},[407,408],[363,63296,63298],{"className":63297},[629],[363,63299,63301],{"className":63300},[633],[363,63302,63304],{"className":63303},[638],[363,63305,63307],{"className":63306,"style":8595},[642],[363,63308,63309,63312],{"style":8624},[363,63310],{"className":63311,"style":651},[650],[363,63313,63315],{"className":63314},[655,656,657,658],[363,63316,7920],{"className":63317},[2938,658],[363,63319,461],{"className":63320},[494],[363,63322,40584],{"className":63323,"style":1328},[407,408],[363,63325,20737],{"className":63326},[501],[363,63328,63330],{"className":63329},[407],[363,63331,3255],{"className":63332},[767,10021],[363,63334,4722],{"className":63335},[407],[363,63337,666],{"className":63338},[665],[363,63340,63342],{"className":63341},[638],[363,63343,63345],{"className":63344,"style":62670},[642],[363,63346],{},[11,63348,63349,63350,63378,63379,63407,63408,63603,63604,63632,63633,63710,63711,63810,63811,63970,63971,63999],{},"这里只能得到 ",[363,63351,63353,63366],{"className":63352,"translate":367},[366],[363,63354,63356],{"className":63355},[371],[373,63357,63358],{"xmlns":375},[377,63359,63360,63364],{},[380,63361,63362],{},[458,63363,7275],{},[387,63365,55836],{"encoding":389},[363,63367,63369],{"className":63368,"ariaHidden":394},[393],[363,63370,63372,63375],{"className":63371},[398],[363,63373],{"className":63374,"style":43535},[402],[363,63376,7275],{"className":63377},[510],"，因为「积分的上确界 ≥ 上确界的积分」。反向不等式需要一个可测选择\u002F极大值论证：由于 ",[363,63380,63382,63395],{"className":63381,"translate":367},[366],[363,63383,63385],{"className":63384},[371],[373,63386,63387],{"xmlns":375},[377,63388,63389,63393],{},[380,63390,63391],{},[383,63392,385],{},[387,63394,385],{"encoding":389},[363,63396,63398],{"className":63397,"ariaHidden":394},[393],[363,63399,63401,63404],{"className":63400},[398],[363,63402],{"className":63403,"style":403},[402],[363,63405,385],{"className":63406,"style":409},[407,408]," 凸，",[363,63409,63411,63465],{"className":63410,"translate":367},[366],[363,63412,63414],{"className":63413},[371],[373,63415,63416],{"xmlns":375},[377,63417,63418,63462],{},[380,63419,63420,63422,63424,63426,63428,63430,63440,63442,63444,63446,63448,63454,63456,63458,63460],{},[383,63421,385],{},[458,63423,461],{"stretchy":460},[383,63425,1116],{},[458,63427,468],{"stretchy":460},[458,63429,471],{},[543,63431,63432,63438],{},[380,63433,63434,63436],{},[383,63435,35779],{},[458,63437,4450],{},[383,63439,40584],{},[458,63441,3245],{"stretchy":460},[383,63443,40584],{},[383,63445,1116],{},[458,63447,5160],{},[7161,63449,63450,63452],{},[383,63451,385],{},[458,63453,7920],{},[458,63455,461],{"stretchy":460},[383,63457,40584],{},[458,63459,468],{"stretchy":460},[458,63461,3255],{"stretchy":460},[387,63463,63464],{"encoding":389},"f(t)=\\sup_y\\{yt-f^*(y)\\}",[363,63466,63468,63495,63559],{"className":63467,"ariaHidden":394},[393],[363,63469,63471,63474,63477,63480,63483,63486,63489,63492],{"className":63470},[398],[363,63472],{"className":63473,"style":487},[402],[363,63475,385],{"className":63476,"style":409},[407,408],[363,63478,461],{"className":63479},[494],[363,63481,1116],{"className":63482},[407,408],[363,63484,468],{"className":63485},[501],[363,63487],{"className":63488,"style":506},[505],[363,63490,471],{"className":63491},[510],[363,63493],{"className":63494,"style":506},[505],[363,63496,63498,63501,63541,63544,63547,63550,63553,63556],{"className":63497},[398],[363,63499],{"className":63500,"style":57670},[402],[363,63502,63504,63507],{"className":63503},[1831],[363,63505,35779],{"className":63506},[1831],[363,63508,63510],{"className":63509},[629],[363,63511,63513,63533],{"className":63512},[633,634],[363,63514,63516,63530],{"className":63515},[638],[363,63517,63519],{"className":63518,"style":37346},[642],[363,63520,63521,63524],{"style":35925},[363,63522],{"className":63523,"style":651},[650],[363,63525,63527],{"className":63526},[655,656,657,658],[363,63528,40584],{"className":63529,"style":1328},[407,408,658],[363,63531,666],{"className":63532},[665],[363,63534,63536],{"className":63535},[638],[363,63537,63539],{"className":63538,"style":57709},[642],[363,63540],{},[363,63542,3245],{"className":63543},[494],[363,63545,40584],{"className":63546,"style":1328},[407,408],[363,63548,1116],{"className":63549},[407,408],[363,63551],{"className":63552,"style":2934},[505],[363,63554,5160],{"className":63555},[2938],[363,63557],{"className":63558,"style":2934},[505],[363,63560,63562,63565,63594,63597,63600],{"className":63561},[398],[363,63563],{"className":63564,"style":487},[402],[363,63566,63568,63571],{"className":63567},[407],[363,63569,385],{"className":63570,"style":409},[407,408],[363,63572,63574],{"className":63573},[629],[363,63575,63577],{"className":63576},[633],[363,63578,63580],{"className":63579},[638],[363,63581,63583],{"className":63582,"style":8846},[642],[363,63584,63585,63588],{"style":7212},[363,63586],{"className":63587,"style":651},[650],[363,63589,63591],{"className":63590},[655,656,657,658],[363,63592,7920],{"className":63593},[2938,658],[363,63595,461],{"className":63596},[494],[363,63598,40584],{"className":63599,"style":1328},[407,408],[363,63601,61346],{"className":63602},[501]," 中的 ",[363,63605,63607,63620],{"className":63606,"translate":367},[366],[363,63608,63610],{"className":63609},[371],[373,63611,63612],{"xmlns":375},[377,63613,63614,63618],{},[380,63615,63616],{},[383,63617,40584],{},[387,63619,40584],{"encoding":389},[363,63621,63623],{"className":63622,"ariaHidden":394},[393],[363,63624,63626,63629],{"className":63625},[398],[363,63627],{"className":63628,"style":2623},[402],[363,63630,40584],{"className":63631,"style":1328},[407,408]," 可取为 ",[363,63634,63636,63660],{"className":63635,"translate":367},[366],[363,63637,63639],{"className":63638},[371],[373,63640,63641],{"xmlns":375},[377,63642,63643,63657],{},[380,63644,63645,63651,63653,63655],{},[7161,63646,63647,63649],{},[383,63648,385],{},[458,63650,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,63652,461],{"stretchy":460},[383,63654,1116],{},[458,63656,468],{"stretchy":460},[387,63658,63659],{"encoding":389},"f'(t)",[363,63661,63663],{"className":63662,"ariaHidden":394},[393],[363,63664,63666,63669,63701,63704,63707],{"className":63665},[398],[363,63667],{"className":63668,"style":7190},[402],[363,63670,63672,63675],{"className":63671},[407],[363,63673,385],{"className":63674,"style":409},[407,408],[363,63676,63678],{"className":63677},[629],[363,63679,63681],{"className":63680},[633],[363,63682,63684],{"className":63683},[638],[363,63685,63687],{"className":63686,"style":7209},[642],[363,63688,63689,63692],{"style":7212},[363,63690],{"className":63691,"style":651},[650],[363,63693,63695],{"className":63694},[655,656,657,658],[363,63696,63698],{"className":63697},[407,658],[363,63699,7167],{"className":63700},[407,658],[363,63702,461],{"className":63703},[494],[363,63705,1116],{"className":63706},[407,408],[363,63708,468],{"className":63709},[501],"（在可微点），而 ",[363,63712,63714,63742],{"className":63713,"translate":367},[366],[363,63715,63717],{"className":63716},[371],[373,63718,63719],{"xmlns":375},[377,63720,63721,63739],{},[380,63722,63723,63725,63727,63733,63735,63737],{},[383,63724,1116],{},[458,63726,9031],{},[7161,63728,63729,63731],{},[383,63730,385],{},[458,63732,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,63734,461],{"stretchy":460},[383,63736,1116],{},[458,63738,468],{"stretchy":460},[387,63740,63741],{"encoding":389},"t\\mapsto f'(t)",[363,63743,63745,63763],{"className":63744,"ariaHidden":394},[393],[363,63746,63748,63751,63754,63757,63760],{"className":63747},[398],[363,63749],{"className":63750,"style":9058},[402],[363,63752,1116],{"className":63753},[407,408],[363,63755],{"className":63756,"style":506},[505],[363,63758,9031],{"className":63759},[510],[363,63761],{"className":63762,"style":506},[505],[363,63764,63766,63769,63801,63804,63807],{"className":63765},[398],[363,63767],{"className":63768,"style":7190},[402],[363,63770,63772,63775],{"className":63771},[407],[363,63773,385],{"className":63774,"style":409},[407,408],[363,63776,63778],{"className":63777},[629],[363,63779,63781],{"className":63780},[633],[363,63782,63784],{"className":63783},[638],[363,63785,63787],{"className":63786,"style":7209},[642],[363,63788,63789,63792],{"style":7212},[363,63790],{"className":63791,"style":651},[650],[363,63793,63795],{"className":63794},[655,656,657,658],[363,63796,63798],{"className":63797},[407,658],[363,63799,7167],{"className":63800},[407,658],[363,63802,461],{"className":63803},[494],[363,63805,1116],{"className":63806},[407,408],[363,63808,468],{"className":63809},[501]," 单调，于是 ",[363,63812,63814,63860],{"className":63813,"translate":367},[366],[363,63815,63817],{"className":63816},[371],[373,63818,63819],{"xmlns":375},[377,63820,63821,63857],{},[380,63822,63823,63829,63831,63833,63835,63837,63839,63845,63847,63849,63851,63853,63855],{},[7161,63824,63825,63827],{},[383,63826,4505],{},[458,63828,7920],{},[458,63830,461],{"stretchy":460},[383,63832,1121],{},[458,63834,468],{"stretchy":460},[458,63836,1362],{},[458,63838,471],{},[7161,63840,63841,63843],{},[383,63842,385],{},[458,63844,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,63846,461],{"stretchy":460},[383,63848,1116],{},[458,63850,461],{"stretchy":460},[383,63852,1121],{},[458,63854,468],{"stretchy":460},[458,63856,468],{"stretchy":460},[387,63858,63859],{"encoding":389},"g^*(x):=f'(t(x))",[363,63861,63863,63917],{"className":63862,"ariaHidden":394},[393],[363,63864,63866,63869,63898,63901,63904,63907,63910,63914],{"className":63865},[398],[363,63867],{"className":63868,"style":487},[402],[363,63870,63872,63875],{"className":63871},[407],[363,63873,4505],{"className":63874,"style":1328},[407,408],[363,63876,63878],{"className":63877},[629],[363,63879,63881],{"className":63880},[633],[363,63882,63884],{"className":63883},[638],[363,63885,63887],{"className":63886,"style":8846},[642],[363,63888,63889,63892],{"style":7212},[363,63890],{"className":63891,"style":651},[650],[363,63893,63895],{"className":63894},[655,656,657,658],[363,63896,7920],{"className":63897},[2938,658],[363,63899,461],{"className":63900},[494],[363,63902,1121],{"className":63903},[407,408],[363,63905,468],{"className":63906},[501],[363,63908],{"className":63909,"style":506},[505],[363,63911,63913],{"className":63912},[510],":=",[363,63915],{"className":63916,"style":506},[505],[363,63918,63920,63923,63955,63958,63961,63964,63967],{"className":63919},[398],[363,63921],{"className":63922,"style":7190},[402],[363,63924,63926,63929],{"className":63925},[407],[363,63927,385],{"className":63928,"style":409},[407,408],[363,63930,63932],{"className":63931},[629],[363,63933,63935],{"className":63934},[633],[363,63936,63938],{"className":63937},[638],[363,63939,63941],{"className":63940,"style":7209},[642],[363,63942,63943,63946],{"style":7212},[363,63944],{"className":63945,"style":651},[650],[363,63947,63949],{"className":63948},[655,656,657,658],[363,63950,63952],{"className":63951},[407,658],[363,63953,7167],{"className":63954},[407,658],[363,63956,461],{"className":63957},[494],[363,63959,1116],{"className":63960},[407,408],[363,63962,461],{"className":63963},[494],[363,63965,1121],{"className":63966},[407,408],[363,63968,19394],{"className":63969},[501]," 是可测的，并且对每个 ",[363,63972,63974,63987],{"className":63973,"translate":367},[366],[363,63975,63977],{"className":63976},[371],[373,63978,63979],{"xmlns":375},[377,63980,63981,63985],{},[380,63982,63983],{},[383,63984,1121],{},[387,63986,1121],{"encoding":389},[363,63988,63990],{"className":63989,"ariaHidden":394},[393],[363,63991,63993,63996],{"className":63992},[398],[363,63994],{"className":63995,"style":2692},[402],[363,63997,1121],{"className":63998},[407,408]," 达到上确界。于是不等式取等号。",[11,64001,64002,64005],{},[1572,64003,64004],{},"最优解。"," 达到上确界的函数为",[363,64007,64009],{"className":64008,"translate":367},[528],[363,64010,64012,64074],{"className":64011,"translate":367},[366],[363,64013,64015],{"className":64014},[371],[373,64016,64017],{"xmlns":375,"display":537},[377,64018,64019,64071],{},[380,64020,64021,64027,64029,64031,64033,64035,64041,64043,64069],{},[7161,64022,64023,64025],{},[383,64024,4505],{},[458,64026,7920],{},[458,64028,461],{"stretchy":460},[383,64030,1121],{},[458,64032,468],{"stretchy":460},[458,64034,471],{},[7161,64036,64037,64039],{},[383,64038,385],{},[458,64040,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[1644,64042,1651],{},[380,64044,64045,64047,64061,64063,64065,64067],{},[458,64046,461],{"fence":394},[586,64048,64049,64055],{},[380,64050,64051,64053],{},[383,64052,592],{},[383,64054,554],{},[380,64056,64057,64059],{},[383,64058,592],{},[383,64060,561],{},[458,64062,461],{"stretchy":460},[383,64064,1121],{},[458,64066,468],{"stretchy":460},[458,64068,468],{"fence":394},[458,64070,898],{"separator":394},[387,64072,64073],{"encoding":389},"g^*(x)=f'\\!\\left(\\frac{dP}{dQ}(x)\\right),",[363,64075,64077,64130],{"className":64076,"ariaHidden":394},[393],[363,64078,64080,64083,64112,64115,64118,64121,64124,64127],{"className":64079},[398],[363,64081],{"className":64082,"style":487},[402],[363,64084,64086,64089],{"className":64085},[407],[363,64087,4505],{"className":64088,"style":1328},[407,408],[363,64090,64092],{"className":64091},[629],[363,64093,64095],{"className":64094},[633],[363,64096,64098],{"className":64097},[638],[363,64099,64101],{"className":64100,"style":8595},[642],[363,64102,64103,64106],{"style":8624},[363,64104],{"className":64105,"style":651},[650],[363,64107,64109],{"className":64108},[655,656,657,658],[363,64110,7920],{"className":64111},[2938,658],[363,64113,461],{"className":64114},[494],[363,64116,1121],{"className":64117},[407,408],[363,64119,468],{"className":64120},[501],[363,64122],{"className":64123,"style":506},[505],[363,64125,471],{"className":64126},[510],[363,64128],{"className":64129,"style":506},[505],[363,64131,64133,64136,64168,64171,64174,64266,64269],{"className":64132},[398],[363,64134],{"className":64135,"style":707},[402],[363,64137,64139,64142],{"className":64138},[407],[363,64140,385],{"className":64141,"style":409},[407,408],[363,64143,64145],{"className":64144},[629],[363,64146,64148],{"className":64147},[633],[363,64149,64151],{"className":64150},[638],[363,64152,64154],{"className":64153,"style":29318},[642],[363,64155,64156,64159],{"style":8624},[363,64157],{"className":64158,"style":651},[650],[363,64160,64162],{"className":64161},[655,656,657,658],[363,64163,64165],{"className":64164},[407,658],[363,64166,7167],{"className":64167},[407,658],[363,64169],{"className":64170,"style":1859},[505],[363,64172],{"className":64173,"style":754},[505],[363,64175,64177,64183,64251,64254,64257,64260],{"className":64176},[758],[363,64178,64180],{"className":64179,"style":763},[494,762],[363,64181,461],{"className":64182},[767,657],[363,64184,64186,64189,64248],{"className":64185},[407],[363,64187],{"className":64188},[494,789],[363,64190,64192],{"className":64191},[586],[363,64193,64195,64240],{"className":64194},[633,634],[363,64196,64198,64237],{"className":64197},[638],[363,64199,64201,64215,64223],{"className":64200,"style":802},[642],[363,64202,64203,64206],{"style":805},[363,64204],{"className":64205,"style":809},[650],[363,64207,64209,64212],{"className":64208},[407],[363,64210,592],{"className":64211},[407,408],[363,64213,561],{"className":64214},[407,408],[363,64216,64217,64220],{"style":821},[363,64218],{"className":64219,"style":809},[650],[363,64221],{"className":64222,"style":829},[828],[363,64224,64225,64228],{"style":832},[363,64226],{"className":64227,"style":809},[650],[363,64229,64231,64234],{"className":64230},[407],[363,64232,592],{"className":64233},[407,408],[363,64235,554],{"className":64236,"style":682},[407,408],[363,64238,666],{"className":64239},[665],[363,64241,64243],{"className":64242},[638],[363,64244,64246],{"className":64245,"style":854},[642],[363,64247],{},[363,64249],{"className":64250},[501,789],[363,64252,461],{"className":64253},[494],[363,64255,1121],{"className":64256},[407,408],[363,64258,468],{"className":64259},[501],[363,64261,64263],{"className":64262,"style":763},[501,762],[363,64264,468],{"className":64265},[767,657],[363,64267],{"className":64268,"style":754},[505],[363,64270,898],{"className":64271},[920],[11,64273,64274,64275,4200,64303,64331,64332,64392,64393,64465,64466,45955,64585,64769],{},"条件是 ",[363,64276,64278,64291],{"className":64277,"translate":367},[366],[363,64279,64281],{"className":64280},[371],[373,64282,64283],{"xmlns":375},[377,64284,64285,64289],{},[380,64286,64287],{},[383,64288,385],{},[387,64290,385],{"encoding":389},[363,64292,64294],{"className":64293,"ariaHidden":394},[393],[363,64295,64297,64300],{"className":64296},[398],[363,64298],{"className":64299,"style":403},[402],[363,64301,385],{"className":64302,"style":409},[407,408],[363,64304,64306,64319],{"className":64305,"translate":367},[366],[363,64307,64309],{"className":64308},[371],[373,64310,64311],{"xmlns":375},[377,64312,64313,64317],{},[380,64314,64315],{},[383,64316,1116],{},[387,64318,1116],{"encoding":389},[363,64320,64322],{"className":64321,"ariaHidden":394},[393],[363,64323,64325,64328],{"className":64324},[398],[363,64326],{"className":64327,"style":5690},[402],[363,64329,1116],{"className":64330},[407,408]," 处可微、且 ",[363,64333,64335,64353],{"className":64334,"translate":367},[366],[363,64336,64338],{"className":64337},[371],[373,64339,64340],{"xmlns":375},[377,64341,64342,64350],{},[380,64343,64344],{},[7161,64345,64346,64348],{},[383,64347,4505],{},[458,64349,7920],{},[387,64351,64352],{"encoding":389},"g^*",[363,64354,64356],{"className":64355,"ariaHidden":394},[393],[363,64357,64359,64363],{"className":64358},[398],[363,64360],{"className":64361,"style":64362},[402],"height:0.8831em;vertical-align:-0.1944em;",[363,64364,64366,64369],{"className":64365},[407],[363,64367,4505],{"className":64368,"style":1328},[407,408],[363,64370,64372],{"className":64371},[629],[363,64373,64375],{"className":64374},[633],[363,64376,64378],{"className":64377},[638],[363,64379,64381],{"className":64380,"style":8846},[642],[363,64382,64383,64386],{"style":7212},[363,64384],{"className":64385,"style":651},[650],[363,64387,64389],{"className":64388},[655,656,657,658],[363,64390,7920],{"className":64391},[2938,658]," 落在 ",[363,64394,64396,64418],{"className":64395,"translate":367},[366],[363,64397,64399],{"className":64398},[371],[373,64400,64401],{"xmlns":375},[377,64402,64403,64415],{},[380,64404,64405,64407,64409],{},[383,64406,61754],{"mathvariant":557},[458,64408,4450],{},[7161,64410,64411,64413],{},[383,64412,385],{},[458,64414,7920],{},[387,64416,64417],{"encoding":389},"\\operatorname{dom} f^*",[363,64419,64421],{"className":64420,"ariaHidden":394},[393],[363,64422,64424,64427,64433,64436],{"className":64423},[398],[363,64425],{"className":64426,"style":403},[402],[363,64428,64430],{"className":64429},[1831],[363,64431,61754],{"className":64432},[407,33009],[363,64434],{"className":64435,"style":754},[505],[363,64437,64439,64442],{"className":64438},[407],[363,64440,385],{"className":64441,"style":409},[407,408],[363,64443,64445],{"className":64444},[629],[363,64446,64448],{"className":64447},[633],[363,64449,64451],{"className":64450},[638],[363,64452,64454],{"className":64453,"style":8846},[642],[363,64455,64456,64459],{"style":7212},[363,64457],{"className":64458,"style":651},[650],[363,64460,64462],{"className":64461},[655,656,657,658],[363,64463,7920],{"className":64464},[2938,658]," 内。例如 KL（",[363,64467,64469,64499],{"className":64468,"translate":367},[366],[363,64470,64472],{"className":64471},[371],[373,64473,64474],{"xmlns":375},[377,64475,64476,64496],{},[380,64477,64478,64484,64486,64488,64490,64492,64494],{},[7161,64479,64480,64482],{},[383,64481,385],{},[458,64483,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,64485,471],{},[383,64487,4447],{},[458,64489,4450],{},[383,64491,1116],{},[458,64493,2817],{},[463,64495,465],{},[387,64497,64498],{"encoding":389},"f'=\\log t+1",[363,64500,64502,64550,64576],{"className":64501,"ariaHidden":394},[393],[363,64503,64505,64509,64541,64544,64547],{"className":64504},[398],[363,64506],{"className":64507,"style":64508},[402],"height:0.9463em;vertical-align:-0.1944em;",[363,64510,64512,64515],{"className":64511},[407],[363,64513,385],{"className":64514,"style":409},[407,408],[363,64516,64518],{"className":64517},[629],[363,64519,64521],{"className":64520},[633],[363,64522,64524],{"className":64523},[638],[363,64525,64527],{"className":64526,"style":7209},[642],[363,64528,64529,64532],{"style":7212},[363,64530],{"className":64531,"style":651},[650],[363,64533,64535],{"className":64534},[655,656,657,658],[363,64536,64538],{"className":64537},[407,658],[363,64539,7167],{"className":64540},[407,658],[363,64542],{"className":64543,"style":506},[505],[363,64545,471],{"className":64546},[510],[363,64548],{"className":64549,"style":506},[505],[363,64551,64553,64556,64561,64564,64567,64570,64573],{"className":64552},[398],[363,64554],{"className":64555,"style":403},[402],[363,64557,4501,64559],{"className":64558},[1831],[363,64560,4505],{"style":4504},[363,64562],{"className":64563,"style":754},[505],[363,64565,1116],{"className":64566},[407,408],[363,64568],{"className":64569,"style":2934},[505],[363,64571,2817],{"className":64572},[2938],[363,64574],{"className":64575,"style":2934},[505],[363,64577,64579,64582],{"className":64578},[398],[363,64580],{"className":64581,"style":520},[402],[363,64583,465],{"className":64584},[407],[363,64586,64588,64622],{"className":64587,"translate":367},[366],[363,64589,64591],{"className":64590},[371],[373,64592,64593],{"xmlns":375},[377,64594,64595,64619],{},[380,64596,64597,64603,64605,64607,64609,64615,64617],{},[7161,64598,64599,64601],{},[383,64600,4505],{},[458,64602,7920],{},[458,64604,471],{},[383,64606,4447],{},[458,64608,4450],{},[586,64610,64611,64613],{},[383,64612,11],{},[383,64614,1291],{},[458,64616,2817],{},[463,64618,465],{},[387,64620,64621],{"encoding":389},"g^*=\\log\\frac{p}{q}+1",[363,64623,64625,64669,64760],{"className":64624,"ariaHidden":394},[393],[363,64626,64628,64631,64660,64663,64666],{"className":64627},[398],[363,64629],{"className":64630,"style":64362},[402],[363,64632,64634,64637],{"className":64633},[407],[363,64635,4505],{"className":64636,"style":1328},[407,408],[363,64638,64640],{"className":64639},[629],[363,64641,64643],{"className":64642},[633],[363,64644,64646],{"className":64645},[638],[363,64647,64649],{"className":64648,"style":8846},[642],[363,64650,64651,64654],{"style":7212},[363,64652],{"className":64653,"style":651},[650],[363,64655,64657],{"className":64656},[655,656,657,658],[363,64658,7920],{"className":64659},[2938,658],[363,64661],{"className":64662,"style":506},[505],[363,64664,471],{"className":64665},[510],[363,64667],{"className":64668,"style":506},[505],[363,64670,64672,64675,64680,64683,64751,64754,64757],{"className":64671},[398],[363,64673],{"className":64674,"style":3431},[402],[363,64676,4501,64678],{"className":64677},[1831],[363,64679,4505],{"style":4504},[363,64681],{"className":64682,"style":754},[505],[363,64684,64686,64689,64748],{"className":64685},[407],[363,64687],{"className":64688},[494,789],[363,64690,64692],{"className":64691},[586],[363,64693,64695,64740],{"className":64694},[633,634],[363,64696,64698,64737],{"className":64697},[638],[363,64699,64701,64715,64723],{"className":64700,"style":3450},[642],[363,64702,64703,64706],{"style":2874},[363,64704],{"className":64705,"style":809},[650],[363,64707,64709],{"className":64708},[655,656,657,658],[363,64710,64712],{"className":64711},[407,658],[363,64713,1291],{"className":64714,"style":1328},[407,408,658],[363,64716,64717,64720],{"style":821},[363,64718],{"className":64719,"style":809},[650],[363,64721],{"className":64722,"style":829},[828],[363,64724,64725,64728],{"style":3200},[363,64726],{"className":64727,"style":809},[650],[363,64729,64731],{"className":64730},[655,656,657,658],[363,64732,64734],{"className":64733},[407,658],[363,64735,11],{"className":64736},[407,408,658],[363,64738,666],{"className":64739},[665],[363,64741,64743],{"className":64742},[638],[363,64744,64746],{"className":64745,"style":3086},[642],[363,64747],{},[363,64749],{"className":64750},[501,789],[363,64752],{"className":64753,"style":2934},[505],[363,64755,2817],{"className":64756},[2938],[363,64758],{"className":64759,"style":2934},[505],[363,64761,64763,64766],{"className":64762},[398],[363,64764],{"className":64765,"style":520},[402],[363,64767,465],{"className":64768},[407],"；这解释了为什么「对判别器做 log 密度比」是 f-GAN 的最佳策略。",[11,64771,64772,64834,64835,64934,64935,45955],{},[1572,64773,64774,64775,64833],{},"常用 ",[363,64776,64778,64795],{"className":64777,"translate":367},[366],[363,64779,64781],{"className":64780},[371],[373,64782,64783],{"xmlns":375},[377,64784,64785,64793],{},[380,64786,64787],{},[7161,64788,64789,64791],{},[383,64790,385],{},[458,64792,7920],{},[387,64794,61055],{"encoding":389},[363,64796,64798],{"className":64797,"ariaHidden":394},[393],[363,64799,64801,64804],{"className":64800},[398],[363,64802],{"className":64803,"style":403},[402],[363,64805,64807,64810],{"className":64806},[407],[363,64808,385],{"className":64809,"style":409},[407,408],[363,64811,64813],{"className":64812},[629],[363,64814,64816],{"className":64815},[633],[363,64817,64819],{"className":64818},[638],[363,64820,64822],{"className":64821,"style":8846},[642],[363,64823,64824,64827],{"style":7212},[363,64825],{"className":64826,"style":651},[650],[363,64828,64830],{"className":64829},[655,656,657,658],[363,64831,7920],{"className":64832},[2938,658]," 表","（结合 ",[363,64836,64838,64868],{"className":64837,"translate":367},[366],[363,64839,64841],{"className":64840},[371],[373,64842,64843],{"xmlns":375},[377,64844,64845,64865],{},[380,64846,64847,64849,64851,64853,64855,64857,64859,64861,64863],{},[458,64848,1634],{},[383,64850,592],{},[383,64852,554],{},[458,64854,471],{},[458,64856,1634],{},[383,64858,592],{},[383,64860,561],{},[458,64862,471],{},[463,64864,465],{},[387,64866,64867],{"encoding":389},"\\int dP=\\int dQ=1",[363,64869,64871,64898,64925],{"className":64870,"ariaHidden":394},[393],[363,64872,64874,64877,64880,64883,64886,64889,64892,64895],{"className":64873},[398],[363,64875],{"className":64876,"style":5959},[402],[363,64878,1634],{"className":64879,"style":5964},[1831,1832,5963],[363,64881],{"className":64882,"style":754},[505],[363,64884,592],{"className":64885},[407,408],[363,64887,554],{"className":64888,"style":682},[407,408],[363,64890],{"className":64891,"style":506},[505],[363,64893,471],{"className":64894},[510],[363,64896],{"className":64897,"style":506},[505],[363,64899,64901,64904,64907,64910,64913,64916,64919,64922],{"className":64900},[398],[363,64902],{"className":64903,"style":5959},[402],[363,64905,1634],{"className":64906,"style":5964},[1831,1832,5963],[363,64908],{"className":64909,"style":754},[505],[363,64911,592],{"className":64912},[407,408],[363,64914,561],{"className":64915},[407,408],[363,64917],{"className":64918,"style":506},[505],[363,64920,471],{"className":64921},[510],[363,64923],{"className":64924,"style":506},[505],[363,64926,64928,64931],{"className":64927},[398],[363,64929],{"className":64930,"style":520},[402],[363,64932,465],{"className":64933},[407]," 可加任意常数 ",[363,64936,64938,64951],{"className":64937,"translate":367},[366],[363,64939,64941],{"className":64940},[371],[373,64942,64943],{"xmlns":375},[377,64944,64945,64949],{},[380,64946,64947],{},[383,64948,6253],{},[387,64950,6253],{"encoding":389},[363,64952,64954],{"className":64953,"ariaHidden":394},[393],[363,64955,64957,64960],{"className":64956},[398],[363,64958],{"className":64959,"style":2692},[402],[363,64961,6253],{"className":64962},[407,408],[52839,64964,64965,65166],{},[52842,64966,64967],{},[52845,64968,64969,65014,65090,65163],{},[52848,64970,64971],{},[363,64972,64974,64993],{"className":64973,"translate":367},[366],[363,64975,64977],{"className":64976},[371],[373,64978,64979],{"xmlns":375},[377,64980,64981,64991],{},[380,64982,64983,64985,64987,64989],{},[383,64984,385],{},[458,64986,461],{"stretchy":460},[383,64988,1116],{},[458,64990,468],{"stretchy":460},[387,64992,52875],{"encoding":389},[363,64994,64996],{"className":64995,"ariaHidden":394},[393],[363,64997,64999,65002,65005,65008,65011],{"className":64998},[398],[363,65000],{"className":65001,"style":487},[402],[363,65003,385],{"className":65004,"style":409},[407,408],[363,65006,461],{"className":65007},[494],[363,65009,1116],{"className":65010},[407,408],[363,65012,468],{"className":65013},[501],[52848,65015,65016],{},[363,65017,65019,65043],{"className":65018,"translate":367},[366],[363,65020,65022],{"className":65021},[371],[373,65023,65024],{"xmlns":375},[377,65025,65026,65040],{},[380,65027,65028,65034,65036,65038],{},[7161,65029,65030,65032],{},[383,65031,385],{},[458,65033,7920],{},[458,65035,461],{"stretchy":460},[383,65037,40584],{},[458,65039,468],{"stretchy":460},[387,65041,65042],{"encoding":389},"f^*(y)",[363,65044,65046],{"className":65045,"ariaHidden":394},[393],[363,65047,65049,65052,65081,65084,65087],{"className":65048},[398],[363,65050],{"className":65051,"style":487},[402],[363,65053,65055,65058],{"className":65054},[407],[363,65056,385],{"className":65057,"style":409},[407,408],[363,65059,65061],{"className":65060},[629],[363,65062,65064],{"className":65063},[633],[363,65065,65067],{"className":65066},[638],[363,65068,65070],{"className":65069,"style":8846},[642],[363,65071,65072,65075],{"style":7212},[363,65073],{"className":65074,"style":651},[650],[363,65076,65078],{"className":65077},[655,656,657,658],[363,65079,7920],{"className":65080},[2938,658],[363,65082,461],{"className":65083},[494],[363,65085,40584],{"className":65086,"style":1328},[407,408],[363,65088,468],{"className":65089},[501],[52848,65091,65092],{},[363,65093,65095,65116],{"className":65094,"translate":367},[366],[363,65096,65098],{"className":65097},[371],[373,65099,65100],{"xmlns":375},[377,65101,65102,65114],{},[380,65103,65104,65106,65108],{},[383,65105,61754],{"mathvariant":557},[458,65107,4450],{},[7161,65109,65110,65112],{},[383,65111,385],{},[458,65113,7920],{},[387,65115,64417],{"encoding":389},[363,65117,65119],{"className":65118,"ariaHidden":394},[393],[363,65120,65122,65125,65131,65134],{"className":65121},[398],[363,65123],{"className":65124,"style":403},[402],[363,65126,65128],{"className":65127},[1831],[363,65129,61754],{"className":65130},[407,33009],[363,65132],{"className":65133,"style":754},[505],[363,65135,65137,65140],{"className":65136},[407],[363,65138,385],{"className":65139,"style":409},[407,408],[363,65141,65143],{"className":65142},[629],[363,65144,65146],{"className":65145},[633],[363,65147,65149],{"className":65148},[638],[363,65150,65152],{"className":65151,"style":8846},[642],[363,65153,65154,65157],{"style":7212},[363,65155],{"className":65156,"style":651},[650],[363,65158,65160],{"className":65159},[655,656,657,658],[363,65161,7920],{"className":65162},[2938,658],[52848,65164,65165],{},"对应 GAN 损失",[52937,65167,65168,65331,65572,66205,66509,66848],{},[52845,65169,65170,65221,65297,65328],{},[52942,65171,65172,65220],{},[363,65173,65175,65194],{"className":65174,"translate":367},[366],[363,65176,65178],{"className":65177},[371],[373,65179,65180],{"xmlns":375},[377,65181,65182,65192],{},[380,65183,65184,65186,65188,65190],{},[383,65185,1116],{},[383,65187,4447],{},[458,65189,4450],{},[383,65191,1116],{},[387,65193,53073],{"encoding":389},[363,65195,65197],{"className":65196,"ariaHidden":394},[393],[363,65198,65200,65203,65206,65209,65214,65217],{"className":65199},[398],[363,65201],{"className":65202,"style":403},[402],[363,65204,1116],{"className":65205},[407,408],[363,65207],{"className":65208,"style":754},[505],[363,65210,4501,65212],{"className":65211},[1831],[363,65213,4505],{"style":4504},[363,65215],{"className":65216,"style":754},[505],[363,65218,1116],{"className":65219},[407,408],"（KL）",[52942,65222,65223],{},[363,65224,65226,65250],{"className":65225,"translate":367},[366],[363,65227,65229],{"className":65228},[371],[373,65230,65231],{"xmlns":375},[377,65232,65233,65247],{},[380,65234,65235],{},[7161,65236,65237,65239],{},[383,65238,7914],{},[380,65240,65241,65243,65245],{},[383,65242,40584],{},[458,65244,5160],{},[463,65246,465],{},[387,65248,65249],{"encoding":389},"e^{y-1}",[363,65251,65253],{"className":65252,"ariaHidden":394},[393],[363,65254,65256,65259],{"className":65255},[398],[363,65257],{"className":65258,"style":20375},[402],[363,65260,65262,65265],{"className":65261},[407],[363,65263,7914],{"className":65264},[407,408],[363,65266,65268],{"className":65267},[629],[363,65269,65271],{"className":65270},[633],[363,65272,65274],{"className":65273},[638],[363,65275,65277],{"className":65276,"style":20375},[642],[363,65278,65279,65282],{"style":7212},[363,65280],{"className":65281,"style":651},[650],[363,65283,65285],{"className":65284},[655,656,657,658],[363,65286,65288,65291,65294],{"className":65287},[407,658],[363,65289,40584],{"className":65290,"style":1328},[407,408,658],[363,65292,5160],{"className":65293},[2938,658],[363,65295,465],{"className":65296},[407,658],[52942,65298,65299],{},[363,65300,65302,65316],{"className":65301,"translate":367},[366],[363,65303,65305],{"className":65304},[371],[373,65306,65307],{"xmlns":375},[377,65308,65309,65313],{},[380,65310,65311],{},[383,65312,1379],{"mathvariant":570},[387,65314,65315],{"encoding":389},"\\mathbb R",[363,65317,65319],{"className":65318,"ariaHidden":394},[393],[363,65320,65322,65325],{"className":65321},[398],[363,65323],{"className":65324,"style":1443},[402],[363,65326,1379],{"className":65327},[407,714],[52942,65329,65330],{},"MINE-f \u002F f-GAN",[52845,65332,65333,65384,65466,65519],{},[52942,65334,65335,65383],{},[363,65336,65338,65357],{"className":65337,"translate":367},[366],[363,65339,65341],{"className":65340},[371],[373,65342,65343],{"xmlns":375},[377,65344,65345,65355],{},[380,65346,65347,65349,65351,65353],{},[458,65348,5160],{},[383,65350,4447],{},[458,65352,4450],{},[383,65354,1116],{},[387,65356,53273],{"encoding":389},[363,65358,65360],{"className":65359,"ariaHidden":394},[393],[363,65361,65363,65366,65369,65372,65377,65380],{"className":65362},[398],[363,65364],{"className":65365,"style":403},[402],[363,65367,5160],{"className":65368},[407],[363,65370],{"className":65371,"style":754},[505],[363,65373,4501,65375],{"className":65374},[1831],[363,65376,4505],{"style":4504},[363,65378],{"className":65379,"style":754},[505],[363,65381,1116],{"className":65382},[407,408],"（反向 KL）",[52942,65385,65386],{},[363,65387,65389,65419],{"className":65388,"translate":367},[366],[363,65390,65392],{"className":65391},[371],[373,65393,65394],{"xmlns":375},[377,65395,65396,65416],{},[380,65397,65398,65400,65402,65404,65406,65408,65410,65412,65414],{},[458,65399,5160],{},[463,65401,465],{},[458,65403,5160],{},[383,65405,4447],{},[458,65407,4450],{},[458,65409,461],{"stretchy":460},[458,65411,5160],{},[383,65413,40584],{},[458,65415,468],{"stretchy":460},[387,65417,65418],{"encoding":389},"-1-\\log(-y)",[363,65420,65422,65443],{"className":65421,"ariaHidden":394},[393],[363,65423,65425,65428,65431,65434,65437,65440],{"className":65424},[398],[363,65426],{"className":65427,"style":12925},[402],[363,65429,5160],{"className":65430},[407],[363,65432,465],{"className":65433},[407],[363,65435],{"className":65436,"style":2934},[505],[363,65438,5160],{"className":65439},[2938],[363,65441],{"className":65442,"style":2934},[505],[363,65444,65446,65449,65454,65457,65460,65463],{"className":65445},[398],[363,65447],{"className":65448,"style":487},[402],[363,65450,4501,65452],{"className":65451},[1831],[363,65453,4505],{"style":4504},[363,65455,461],{"className":65456},[494],[363,65458,5160],{"className":65459},[407],[363,65461,40584],{"className":65462,"style":1328},[407,408],[363,65464,468],{"className":65465},[501],[52942,65467,65468],{},[363,65469,65471,65489],{"className":65470,"translate":367},[366],[363,65472,65474],{"className":65473},[371],[373,65475,65476],{"xmlns":375},[377,65477,65478,65486],{},[380,65479,65480,65482,65484],{},[383,65481,40584],{},[458,65483,7598],{},[463,65485,474],{},[387,65487,65488],{"encoding":389},"y\u003C0",[363,65490,65492,65510],{"className":65491,"ariaHidden":394},[393],[363,65493,65495,65498,65501,65504,65507],{"className":65494},[398],[363,65496],{"className":65497,"style":32039},[402],[363,65499,40584],{"className":65500,"style":1328},[407,408],[363,65502],{"className":65503,"style":506},[505],[363,65505,7598],{"className":65506},[510],[363,65508],{"className":65509,"style":506},[505],[363,65511,65513,65516],{"className":65512},[398],[363,65514],{"className":65515,"style":520},[402],[363,65517,474],{"className":65518},[407],[52942,65520,65521,65571],{},[363,65522,65524,65541],{"className":65523,"translate":367},[366],[363,65525,65527],{"className":65526},[371],[373,65528,65529],{"xmlns":375},[377,65530,65531,65539],{},[380,65532,65533,65535,65537],{},[383,65534,45101],{},[458,65536,471],{},[463,65538,474],{},[387,65540,46835],{"encoding":389},[363,65542,65544,65562],{"className":65543,"ariaHidden":394},[393],[363,65545,65547,65550,65553,65556,65559],{"className":65546},[398],[363,65548],{"className":65549,"style":2692},[402],[363,65551,45101],{"className":65552,"style":45131},[407,408],[363,65554],{"className":65555,"style":506},[505],[363,65557,471],{"className":65558},[510],[363,65560],{"className":65561,"style":506},[505],[363,65563,65565,65568],{"className":65564},[398],[363,65566],{"className":65567,"style":520},[402],[363,65569,474],{"className":65570},[407]," 端",[52845,65573,65574,65864,66058,66202],{},[52942,65575,65576,65863],{},[363,65577,65579,65636],{"className":65578,"translate":367},[366],[363,65580,65582],{"className":65581},[371],[373,65583,65584],{"xmlns":375},[377,65585,65586,65634],{},[380,65587,65588,65594,65596,65598,65600,65602,65604,65606,65608,65610,65612,65614,65616,65618,65620,65632],{},[586,65589,65590,65592],{},[463,65591,465],{},[463,65593,2810],{},[458,65595,578],{"stretchy":460},[383,65597,1116],{},[383,65599,4447],{},[458,65601,4450],{},[383,65603,1116],{},[458,65605,5160],{},[458,65607,461],{"stretchy":460},[383,65609,1116],{},[458,65611,2817],{},[463,65613,465],{},[458,65615,468],{"stretchy":460},[383,65617,4447],{},[458,65619,4450],{},[586,65621,65622,65630],{},[380,65623,65624,65626,65628],{},[383,65625,1116],{},[458,65627,2817],{},[463,65629,465],{},[463,65631,2810],{},[458,65633,605],{"stretchy":460},[387,65635,53534],{"encoding":389},[363,65637,65639,65742,65763],{"className":65638,"ariaHidden":394},[393],[363,65640,65642,65645,65713,65716,65719,65722,65727,65730,65733,65736,65739],{"className":65641},[398],[363,65643],{"className":65644,"style":2852},[402],[363,65646,65648,65651,65710],{"className":65647},[407],[363,65649],{"className":65650},[494,789],[363,65652,65654],{"className":65653},[586],[363,65655,65657,65702],{"className":65656},[633,634],[363,65658,65660,65699],{"className":65659},[638],[363,65661,65663,65677,65685],{"className":65662,"style":2871},[642],[363,65664,65665,65668],{"style":2874},[363,65666],{"className":65667,"style":809},[650],[363,65669,65671],{"className":65670},[655,656,657,658],[363,65672,65674],{"className":65673},[407,658],[363,65675,2810],{"className":65676},[407,658],[363,65678,65679,65682],{"style":821},[363,65680],{"className":65681,"style":809},[650],[363,65683],{"className":65684,"style":829},[828],[363,65686,65687,65690],{"style":2897},[363,65688],{"className":65689,"style":809},[650],[363,65691,65693],{"className":65692},[655,656,657,658],[363,65694,65696],{"className":65695},[407,658],[363,65697,465],{"className":65698},[407,658],[363,65700,666],{"className":65701},[665],[363,65703,65705],{"className":65704},[638],[363,65706,65708],{"className":65707,"style":2919},[642],[363,65709],{},[363,65711],{"className":65712},[501,789],[363,65714,578],{"className":65715},[494],[363,65717,1116],{"className":65718},[407,408],[363,65720],{"className":65721,"style":754},[505],[363,65723,4501,65725],{"className":65724},[1831],[363,65726,4505],{"style":4504},[363,65728],{"className":65729,"style":754},[505],[363,65731,1116],{"className":65732},[407,408],[363,65734],{"className":65735,"style":2934},[505],[363,65737,5160],{"className":65738},[2938],[363,65740],{"className":65741,"style":2934},[505],[363,65743,65745,65748,65751,65754,65757,65760],{"className":65744},[398],[363,65746],{"className":65747,"style":487},[402],[363,65749,461],{"className":65750},[494],[363,65752,1116],{"className":65753},[407,408],[363,65755],{"className":65756,"style":2934},[505],[363,65758,2817],{"className":65759},[2938],[363,65761],{"className":65762,"style":2934},[505],[363,65764,65766,65769,65772,65775,65778,65783,65786,65860],{"className":65765},[398],[363,65767],{"className":65768,"style":2852},[402],[363,65770,465],{"className":65771},[407],[363,65773,468],{"className":65774},[501],[363,65776],{"className":65777,"style":754},[505],[363,65779,4501,65781],{"className":65780},[1831],[363,65782,4505],{"style":4504},[363,65784],{"className":65785,"style":754},[505],[363,65787,65789,65792,65857],{"className":65788},[407],[363,65790],{"className":65791},[494,789],[363,65793,65795],{"className":65794},[586],[363,65796,65798,65849],{"className":65797},[633,634],[363,65799,65801,65846],{"className":65800},[638],[363,65802,65804,65818,65826],{"className":65803,"style":2871},[642],[363,65805,65806,65809],{"style":2874},[363,65807],{"className":65808,"style":809},[650],[363,65810,65812],{"className":65811},[655,656,657,658],[363,65813,65815],{"className":65814},[407,658],[363,65816,2810],{"className":65817},[407,658],[363,65819,65820,65823],{"style":821},[363,65821],{"className":65822,"style":809},[650],[363,65824],{"className":65825,"style":829},[828],[363,65827,65828,65831],{"style":2897},[363,65829],{"className":65830,"style":809},[650],[363,65832,65834],{"className":65833},[655,656,657,658],[363,65835,65837,65840,65843],{"className":65836},[407,658],[363,65838,1116],{"className":65839},[407,408,658],[363,65841,2817],{"className":65842},[2938,658],[363,65844,465],{"className":65845},[407,658],[363,65847,666],{"className":65848},[665],[363,65850,65852],{"className":65851},[638],[363,65853,65855],{"className":65854,"style":2919},[642],[363,65856],{},[363,65858],{"className":65859},[501,789],[363,65861,605],{"className":65862},[501],"（JS）",[52942,65865,65866],{},[363,65867,65869,65911],{"className":65868,"translate":367},[366],[363,65870,65872],{"className":65871},[371],[373,65873,65874],{"xmlns":375},[377,65875,65876,65908],{},[380,65877,65878,65880,65886,65888,65890,65892,65894,65896,65906],{},[458,65879,5160],{},[586,65881,65882,65884],{},[463,65883,465],{},[463,65885,2810],{},[383,65887,4447],{},[458,65889,4450],{},[458,65891,461],{"stretchy":460},[463,65893,2810],{},[458,65895,5160],{},[7161,65897,65898,65900],{},[383,65899,7914],{},[380,65901,65902,65904],{},[463,65903,2810],{},[383,65905,40584],{},[458,65907,468],{"stretchy":460},[387,65909,65910],{"encoding":389},"-\\frac12\\log(2-e^{2y})",[363,65912,65914,66014],{"className":65913,"ariaHidden":394},[393],[363,65915,65917,65920,65923,65991,65994,65999,66002,66005,66008,66011],{"className":65916},[398],[363,65918],{"className":65919,"style":2852},[402],[363,65921,5160],{"className":65922},[407],[363,65924,65926,65929,65988],{"className":65925},[407],[363,65927],{"className":65928},[494,789],[363,65930,65932],{"className":65931},[586],[363,65933,65935,65980],{"className":65934},[633,634],[363,65936,65938,65977],{"className":65937},[638],[363,65939,65941,65955,65963],{"className":65940,"style":2871},[642],[363,65942,65943,65946],{"style":2874},[363,65944],{"className":65945,"style":809},[650],[363,65947,65949],{"className":65948},[655,656,657,658],[363,65950,65952],{"className":65951},[407,658],[363,65953,2810],{"className":65954},[407,658],[363,65956,65957,65960],{"style":821},[363,65958],{"className":65959,"style":809},[650],[363,65961],{"className":65962,"style":829},[828],[363,65964,65965,65968],{"style":2897},[363,65966],{"className":65967,"style":809},[650],[363,65969,65971],{"className":65970},[655,656,657,658],[363,65972,65974],{"className":65973},[407,658],[363,65975,465],{"className":65976},[407,658],[363,65978,666],{"className":65979},[665],[363,65981,65983],{"className":65982},[638],[363,65984,65986],{"className":65985,"style":2919},[642],[363,65987],{},[363,65989],{"className":65990},[501,789],[363,65992],{"className":65993,"style":754},[505],[363,65995,4501,65997],{"className":65996},[1831],[363,65998,4505],{"style":4504},[363,66000,461],{"className":66001},[494],[363,66003,2810],{"className":66004},[407],[363,66006],{"className":66007,"style":2934},[505],[363,66009,5160],{"className":66010},[2938],[363,66012],{"className":66013,"style":2934},[505],[363,66015,66017,66020,66055],{"className":66016},[398],[363,66018],{"className":66019,"style":20350},[402],[363,66021,66023,66026],{"className":66022},[407],[363,66024,7914],{"className":66025},[407,408],[363,66027,66029],{"className":66028},[629],[363,66030,66032],{"className":66031},[633],[363,66033,66035],{"className":66034},[638],[363,66036,66038],{"className":66037,"style":20375},[642],[363,66039,66040,66043],{"style":7212},[363,66041],{"className":66042,"style":651},[650],[363,66044,66046],{"className":66045},[655,656,657,658],[363,66047,66049,66052],{"className":66048},[407,658],[363,66050,2810],{"className":66051},[407,658],[363,66053,40584],{"className":66054,"style":1328},[407,408,658],[363,66056,468],{"className":66057},[501],[52942,66059,66060],{},[363,66061,66063,66091],{"className":66062,"translate":367},[366],[363,66064,66066],{"className":66065},[371],[373,66067,66068],{"xmlns":375},[377,66069,66070,66088],{},[380,66071,66072,66074,66076],{},[383,66073,40584],{},[458,66075,7598],{},[586,66077,66078,66086],{},[380,66079,66080,66082,66084],{},[383,66081,4447],{},[458,66083,4450],{},[463,66085,2810],{},[463,66087,2810],{},[387,66089,66090],{"encoding":389},"y\u003C\\frac{\\log2}{2}",[363,66092,66094,66112],{"className":66093,"ariaHidden":394},[393],[363,66095,66097,66100,66103,66106,66109],{"className":66096},[398],[363,66098],{"className":66099,"style":32039},[402],[363,66101,40584],{"className":66102,"style":1328},[407,408],[363,66104],{"className":66105,"style":506},[505],[363,66107,7598],{"className":66108},[510],[363,66110],{"className":66111,"style":506},[505],[363,66113,66115,66119],{"className":66114},[398],[363,66116],{"className":66117,"style":66118},[402],"height:1.2772em;vertical-align:-0.345em;",[363,66120,66122,66125,66199],{"className":66121},[407],[363,66123],{"className":66124},[494,789],[363,66126,66128],{"className":66127},[586],[363,66129,66131,66191],{"className":66130},[633,634],[363,66132,66134,66188],{"className":66133},[638],[363,66135,66137,66151,66159],{"className":66136,"style":3172},[642],[363,66138,66139,66142],{"style":2874},[363,66140],{"className":66141,"style":809},[650],[363,66143,66145],{"className":66144},[655,656,657,658],[363,66146,66148],{"className":66147},[407,658],[363,66149,2810],{"className":66150},[407,658],[363,66152,66153,66156],{"style":821},[363,66154],{"className":66155,"style":809},[650],[363,66157],{"className":66158,"style":829},[828],[363,66160,66161,66164],{"style":3200},[363,66162],{"className":66163,"style":809},[650],[363,66165,66167],{"className":66166},[655,656,657,658],[363,66168,66170,66182,66185],{"className":66169},[407,658],[363,66171,66173,66176,66179],{"className":66172},[1831,658],[363,66174,48005],{"className":66175},[658],[363,66177,48009],{"className":66178},[658],[363,66180,4505],{"className":66181,"style":4504},[658],[363,66183],{"className":66184,"style":42713},[505,658],[363,66186,2810],{"className":66187},[407,658],[363,66189,666],{"className":66190},[665],[363,66192,66194],{"className":66193},[638],[363,66195,66197],{"className":66196,"style":2919},[642],[363,66198],{},[363,66200],{"className":66201},[501,789],[52942,66203,66204],{},"原始 GAN",[52845,66206,66207,66344,66374,66506],{},[52942,66208,66209,66343],{},[363,66210,66212,66239],{"className":66211,"translate":367},[366],[363,66213,66215],{"className":66214},[371],[373,66216,66217],{"xmlns":375},[377,66218,66219,66237],{},[380,66220,66221,66227,66229,66231,66233,66235],{},[586,66222,66223,66225],{},[463,66224,465],{},[463,66226,2810],{},[458,66228,5155],{"stretchy":460},[383,66230,1116],{},[458,66232,5160],{},[463,66234,465],{},[458,66236,5155],{"stretchy":460},[387,66238,53902],{"encoding":389},[363,66240,66242,66331],{"className":66241,"ariaHidden":394},[393],[363,66243,66245,66248,66316,66319,66322,66325,66328],{"className":66244},[398],[363,66246],{"className":66247,"style":2852},[402],[363,66249,66251,66254,66313],{"className":66250},[407],[363,66252],{"className":66253},[494,789],[363,66255,66257],{"className":66256},[586],[363,66258,66260,66305],{"className":66259},[633,634],[363,66261,66263,66302],{"className":66262},[638],[363,66264,66266,66280,66288],{"className":66265,"style":2871},[642],[363,66267,66268,66271],{"style":2874},[363,66269],{"className":66270,"style":809},[650],[363,66272,66274],{"className":66273},[655,656,657,658],[363,66275,66277],{"className":66276},[407,658],[363,66278,2810],{"className":66279},[407,658],[363,66281,66282,66285],{"style":821},[363,66283],{"className":66284,"style":809},[650],[363,66286],{"className":66287,"style":829},[828],[363,66289,66290,66293],{"style":2897},[363,66291],{"className":66292,"style":809},[650],[363,66294,66296],{"className":66295},[655,656,657,658],[363,66297,66299],{"className":66298},[407,658],[363,66300,465],{"className":66301},[407,658],[363,66303,666],{"className":66304},[665],[363,66306,66308],{"className":66307},[638],[363,66309,66311],{"className":66310,"style":2919},[642],[363,66312],{},[363,66314],{"className":66315},[501,789],[363,66317,5155],{"className":66318},[494],[363,66320,1116],{"className":66321},[407,408],[363,66323],{"className":66324,"style":2934},[505],[363,66326,5160],{"className":66327},[2938],[363,66329],{"className":66330,"style":2934},[505],[363,66332,66334,66337,66340],{"className":66333},[398],[363,66335],{"className":66336,"style":487},[402],[363,66338,465],{"className":66339},[407],[363,66341,5155],{"className":66342},[501],"（TV）",[52942,66345,66346],{},[363,66347,66349,66362],{"className":66348,"translate":367},[366],[363,66350,66352],{"className":66351},[371],[373,66353,66354],{"xmlns":375},[377,66355,66356,66360],{},[380,66357,66358],{},[383,66359,40584],{},[387,66361,40584],{"encoding":389},[363,66363,66365],{"className":66364,"ariaHidden":394},[393],[363,66366,66368,66371],{"className":66367},[398],[363,66369],{"className":66370,"style":2623},[402],[363,66372,40584],{"className":66373,"style":1328},[407,408],[52942,66375,66376],{},[363,66377,66379,66405],{"className":66378,"translate":367},[366],[363,66380,66382],{"className":66381},[371],[373,66383,66384],{"xmlns":375},[377,66385,66386,66402],{},[380,66387,66388,66390,66392,66394,66396],{},[458,66389,5155],{"stretchy":460},[383,66391,40584],{},[458,66393,5155],{"stretchy":460},[458,66395,10299],{},[586,66397,66398,66400],{},[463,66399,465],{},[463,66401,2810],{},[387,66403,66404],{"encoding":389},"\\lvert y\\rvert\\le\\frac12",[363,66406,66408,66432],{"className":66407,"ariaHidden":394},[393],[363,66409,66411,66414,66417,66420,66423,66426,66429],{"className":66410},[398],[363,66412],{"className":66413,"style":487},[402],[363,66415,5155],{"className":66416},[494],[363,66418,40584],{"className":66419,"style":1328},[407,408],[363,66421,5155],{"className":66422},[501],[363,66424],{"className":66425,"style":506},[505],[363,66427,10299],{"className":66428},[510],[363,66430],{"className":66431,"style":506},[505],[363,66433,66435,66438],{"className":66434},[398],[363,66436],{"className":66437,"style":2852},[402],[363,66439,66441,66444,66503],{"className":66440},[407],[363,66442],{"className":66443},[494,789],[363,66445,66447],{"className":66446},[586],[363,66448,66450,66495],{"className":66449},[633,634],[363,66451,66453,66492],{"className":66452},[638],[363,66454,66456,66470,66478],{"className":66455,"style":2871},[642],[363,66457,66458,66461],{"style":2874},[363,66459],{"className":66460,"style":809},[650],[363,66462,66464],{"className":66463},[655,656,657,658],[363,66465,66467],{"className":66466},[407,658],[363,66468,2810],{"className":66469},[407,658],[363,66471,66472,66475],{"style":821},[363,66473],{"className":66474,"style":809},[650],[363,66476],{"className":66477,"style":829},[828],[363,66479,66480,66483],{"style":2897},[363,66481],{"className":66482,"style":809},[650],[363,66484,66486],{"className":66485},[655,656,657,658],[363,66487,66489],{"className":66488},[407,658],[363,66490,465],{"className":66491},[407,658],[363,66493,666],{"className":66494},[665],[363,66496,66498],{"className":66497},[638],[363,66499,66501],{"className":66500,"style":2919},[642],[363,66502],{},[363,66504],{"className":66505},[501,789],[52942,66507,66508],{},"—",[52845,66510,66511,66661,66815,66845],{},[52942,66512,66513,16142,66603,53822],{},[363,66514,66516,66541],{"className":66515,"translate":367},[366],[363,66517,66519],{"className":66518},[371],[373,66520,66521],{"xmlns":375},[377,66522,66523,66539],{},[380,66524,66525,66527,66529,66531,66533],{},[458,66526,461],{"stretchy":460},[383,66528,1116],{},[458,66530,5160],{},[463,66532,465],{},[7161,66534,66535,66537],{},[458,66536,468],{"stretchy":460},[463,66538,2810],{},[387,66540,54177],{"encoding":389},[363,66542,66544,66565],{"className":66543,"ariaHidden":394},[393],[363,66545,66547,66550,66553,66556,66559,66562],{"className":66546},[398],[363,66548],{"className":66549,"style":487},[402],[363,66551,461],{"className":66552},[494],[363,66554,1116],{"className":66555},[407,408],[363,66557],{"className":66558,"style":2934},[505],[363,66560,5160],{"className":66561},[2938],[363,66563],{"className":66564,"style":2934},[505],[363,66566,66568,66571,66574],{"className":66567},[398],[363,66569],{"className":66570,"style":20350},[402],[363,66572,465],{"className":66573},[407],[363,66575,66577,66580],{"className":66576},[501],[363,66578,468],{"className":66579},[501],[363,66581,66583],{"className":66582},[629],[363,66584,66586],{"className":66585},[633],[363,66587,66589],{"className":66588},[638],[363,66590,66592],{"className":66591,"style":20375},[642],[363,66593,66594,66597],{"style":7212},[363,66595],{"className":66596,"style":651},[650],[363,66598,66600],{"className":66599},[655,656,657,658],[363,66601,2810],{"className":66602},[407,658],[363,66604,66606,66623],{"className":66605,"translate":367},[366],[363,66607,66609],{"className":66608},[371],[373,66610,66611],{"xmlns":375},[377,66612,66613,66621],{},[380,66614,66615],{},[7161,66616,66617,66619],{},[383,66618,37796],{},[463,66620,2810],{},[387,66622,40741],{"encoding":389},[363,66624,66626],{"className":66625,"ariaHidden":394},[393],[363,66627,66629,66632],{"className":66628},[398],[363,66630],{"className":66631,"style":40751},[402],[363,66633,66635,66638],{"className":66634},[407],[363,66636,37796],{"className":66637},[407,408],[363,66639,66641],{"className":66640},[629],[363,66642,66644],{"className":66643},[633],[363,66645,66647],{"className":66646},[638],[363,66648,66650],{"className":66649,"style":20375},[642],[363,66651,66652,66655],{"style":7212},[363,66653],{"className":66654,"style":651},[650],[363,66656,66658],{"className":66657},[655,656,657,658],[363,66659,2810],{"className":66660},[407,658],[52942,66662,66663],{},[363,66664,66666,66692],{"className":66665,"translate":367},[366],[363,66667,66669],{"className":66668},[371],[373,66670,66671],{"xmlns":375},[377,66672,66673,66689],{},[380,66674,66675,66677,66679],{},[383,66676,40584],{},[458,66678,2817],{},[586,66680,66681,66687],{},[7161,66682,66683,66685],{},[383,66684,40584],{},[463,66686,2810],{},[463,66688,39336],{},[387,66690,66691],{"encoding":389},"y+\\frac{y^2}{4}",[363,66693,66695,66713],{"className":66694,"ariaHidden":394},[393],[363,66696,66698,66701,66704,66707,66710],{"className":66697},[398],[363,66699],{"className":66700,"style":40668},[402],[363,66702,40584],{"className":66703,"style":1328},[407,408],[363,66705],{"className":66706,"style":2934},[505],[363,66708,2817],{"className":66709},[2938],[363,66711],{"className":66712,"style":2934},[505],[363,66714,66716,66720],{"className":66715},[398],[363,66717],{"className":66718,"style":66719},[402],"height:1.415em;vertical-align:-0.345em;",[363,66721,66723,66726,66812],{"className":66722},[407],[363,66724],{"className":66725},[494,789],[363,66727,66729],{"className":66728},[586],[363,66730,66732,66804],{"className":66731},[633,634],[363,66733,66735,66801],{"className":66734},[638],[363,66736,66739,66753,66761],{"className":66737,"style":66738},[642],"height:1.07em;",[363,66740,66741,66744],{"style":2874},[363,66742],{"className":66743,"style":809},[650],[363,66745,66747],{"className":66746},[655,656,657,658],[363,66748,66750],{"className":66749},[407,658],[363,66751,39336],{"className":66752},[407,658],[363,66754,66755,66758],{"style":821},[363,66756],{"className":66757,"style":809},[650],[363,66759],{"className":66760,"style":829},[828],[363,66762,66763,66766],{"style":3200},[363,66764],{"className":66765,"style":809},[650],[363,66767,66769],{"className":66768},[655,656,657,658],[363,66770,66772],{"className":66771},[407,658],[363,66773,66775,66778],{"className":66774},[407,658],[363,66776,40584],{"className":66777,"style":1328},[407,408,658],[363,66779,66781],{"className":66780},[629],[363,66782,66784],{"className":66783},[633],[363,66785,66787],{"className":66786},[638],[363,66788,66790],{"className":66789,"style":38859},[642],[363,66791,66792,66795],{"style":38862},[363,66793],{"className":66794,"style":30553},[650],[363,66796,66798],{"className":66797},[655,30557,10021,658],[363,66799,2810],{"className":66800},[407,658],[363,66802,666],{"className":66803},[665],[363,66805,66807],{"className":66806},[638],[363,66808,66810],{"className":66809,"style":2919},[642],[363,66811],{},[363,66813],{"className":66814},[501,789],[52942,66816,66817],{},[363,66818,66820,66833],{"className":66819,"translate":367},[366],[363,66821,66823],{"className":66822},[371],[373,66824,66825],{"xmlns":375},[377,66826,66827,66831],{},[380,66828,66829],{},[383,66830,1379],{"mathvariant":570},[387,66832,65315],{"encoding":389},[363,66834,66836],{"className":66835,"ariaHidden":394},[393],[363,66837,66839,66842],{"className":66838},[398],[363,66840],{"className":66841,"style":1443},[402],[363,66843,1379],{"className":66844},[407,714],[52942,66846,66847],{},"LSGAN",[52845,66849,66850,66986,67098,67151],{},[52942,66851,66852,66985],{},[363,66853,66855,66882],{"className":66854,"translate":367},[366],[363,66856,66858],{"className":66857},[371],[373,66859,66860],{"xmlns":375},[377,66861,66862,66880],{},[380,66863,66864,66866,66870,66872,66874],{},[458,66865,461],{"stretchy":460},[34686,66867,66868],{},[383,66869,1116],{},[458,66871,5160],{},[463,66873,465],{},[7161,66875,66876,66878],{},[458,66877,468],{"stretchy":460},[463,66879,2810],{},[387,66881,54654],{"encoding":389},[363,66883,66885,66947],{"className":66884,"ariaHidden":394},[393],[363,66886,66888,66891,66894,66938,66941,66944],{"className":66887},[398],[363,66889],{"className":66890,"style":43014},[402],[363,66892,461],{"className":66893},[494],[363,66895,66897],{"className":66896},[407,34714],[363,66898,66900,66930],{"className":66899},[633,634],[363,66901,66903,66927],{"className":66902},[638],[363,66904,66906,66915],{"className":66905,"style":43030},[642],[363,66907,66909,66912],{"className":66908,"style":12210},[6654],[363,66910],{"className":66911,"style":809},[650],[363,66913,1116],{"className":66914,"style":34734},[407,408],[363,66916,66917,66920],{"style":43042},[363,66918],{"className":66919,"style":809},[650],[363,66921,66923],{"className":66922,"style":34791},[34790],[6670,66924,66925],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,66926],{"d":34798},[363,66928,666],{"className":66929},[665],[363,66931,66933],{"className":66932},[638],[363,66934,66936],{"className":66935,"style":43062},[642],[363,66937],{},[363,66939],{"className":66940,"style":2934},[505],[363,66942,5160],{"className":66943},[2938],[363,66945],{"className":66946,"style":2934},[505],[363,66948,66950,66953,66956],{"className":66949},[398],[363,66951],{"className":66952,"style":20350},[402],[363,66954,465],{"className":66955},[407],[363,66957,66959,66962],{"className":66958},[501],[363,66960,468],{"className":66961},[501],[363,66963,66965],{"className":66964},[629],[363,66966,66968],{"className":66967},[633],[363,66969,66971],{"className":66970},[638],[363,66972,66974],{"className":66973,"style":20375},[642],[363,66975,66976,66979],{"style":7212},[363,66977],{"className":66978,"style":651},[650],[363,66980,66982],{"className":66981},[655,656,657,658],[363,66983,2810],{"className":66984},[407,658],"（Hellinger²）",[52942,66987,66988],{},[363,66989,66991,67015],{"className":66990,"translate":367},[366],[363,66992,66994],{"className":66993},[371],[373,66995,66996],{"xmlns":375},[377,66997,66998,67012],{},[380,66999,67000],{},[586,67001,67002,67004],{},[383,67003,40584],{},[380,67005,67006,67008,67010],{},[463,67007,465],{},[458,67009,5160],{},[383,67011,40584],{},[387,67013,67014],{"encoding":389},"\\frac{y}{1-y}",[363,67016,67018],{"className":67017,"ariaHidden":394},[393],[363,67019,67021,67024],{"className":67020},[398],[363,67022],{"className":67023,"style":3431},[402],[363,67025,67027,67030,67095],{"className":67026},[407],[363,67028],{"className":67029},[494,789],[363,67031,67033],{"className":67032},[586],[363,67034,67036,67087],{"className":67035},[633,634],[363,67037,67039,67084],{"className":67038},[638],[363,67040,67042,67062,67070],{"className":67041,"style":3450},[642],[363,67043,67044,67047],{"style":2874},[363,67045],{"className":67046,"style":809},[650],[363,67048,67050],{"className":67049},[655,656,657,658],[363,67051,67053,67056,67059],{"className":67052},[407,658],[363,67054,465],{"className":67055},[407,658],[363,67057,5160],{"className":67058},[2938,658],[363,67060,40584],{"className":67061,"style":1328},[407,408,658],[363,67063,67064,67067],{"style":821},[363,67065],{"className":67066,"style":809},[650],[363,67068],{"className":67069,"style":829},[828],[363,67071,67072,67075],{"style":3200},[363,67073],{"className":67074,"style":809},[650],[363,67076,67078],{"className":67077},[655,656,657,658],[363,67079,67081],{"className":67080},[407,658],[363,67082,40584],{"className":67083,"style":1328},[407,408,658],[363,67085,666],{"className":67086},[665],[363,67088,67090],{"className":67089},[638],[363,67091,67093],{"className":67092,"style":3086},[642],[363,67094],{},[363,67096],{"className":67097},[501,789],[52942,67099,67100],{},[363,67101,67103,67121],{"className":67102,"translate":367},[366],[363,67104,67106],{"className":67105},[371],[373,67107,67108],{"xmlns":375},[377,67109,67110,67118],{},[380,67111,67112,67114,67116],{},[383,67113,40584],{},[458,67115,7598],{},[463,67117,465],{},[387,67119,67120],{"encoding":389},"y\u003C1",[363,67122,67124,67142],{"className":67123,"ariaHidden":394},[393],[363,67125,67127,67130,67133,67136,67139],{"className":67126},[398],[363,67128],{"className":67129,"style":32039},[402],[363,67131,40584],{"className":67132,"style":1328},[407,408],[363,67134],{"className":67135,"style":506},[505],[363,67137,7598],{"className":67138},[510],[363,67140],{"className":67141,"style":506},[505],[363,67143,67145,67148],{"className":67144},[398],[363,67146],{"className":67147,"style":520},[402],[363,67149,465],{"className":67150},[407],[52942,67152,66508],{},[11,67154,67155,67156,67214,67215,67461,67462,67623,67624,67889,67890,21303,68050,68166],{},"以 ",[363,67157,67159,67176],{"className":67158,"translate":367},[366],[363,67160,67162],{"className":67161},[371],[373,67163,67164],{"xmlns":375},[377,67165,67166,67174],{},[380,67167,67168],{},[7161,67169,67170,67172],{},[383,67171,37796],{},[463,67173,2810],{},[387,67175,40741],{"encoding":389},[363,67177,67179],{"className":67178,"ariaHidden":394},[393],[363,67180,67182,67185],{"className":67181},[398],[363,67183],{"className":67184,"style":40751},[402],[363,67186,67188,67191],{"className":67187},[407],[363,67189,37796],{"className":67190},[407,408],[363,67192,67194],{"className":67193},[629],[363,67195,67197],{"className":67196},[633],[363,67198,67200],{"className":67199},[638],[363,67201,67203],{"className":67202,"style":20375},[642],[363,67204,67205,67208],{"style":7212},[363,67206],{"className":67207,"style":651},[650],[363,67209,67211],{"className":67210},[655,656,657,658],[363,67212,2810],{"className":67213},[407,658]," 为例验证：",[363,67216,67218,67278],{"className":67217,"translate":367},[366],[363,67219,67221],{"className":67220},[371],[373,67222,67223],{"xmlns":375},[377,67224,67225,67275],{},[380,67226,67227,67233,67235,67237,67239,67241,67251,67253,67255,67257,67259,67261,67263,67265,67267,67273],{},[7161,67228,67229,67231],{},[383,67230,385],{},[458,67232,7920],{},[458,67234,461],{"stretchy":460},[383,67236,40584],{},[458,67238,468],{"stretchy":460},[458,67240,471],{},[543,67242,67243,67249],{},[380,67244,67245,67247],{},[383,67246,35779],{},[458,67248,4450],{},[383,67250,1116],{},[458,67252,3245],{"stretchy":460},[383,67254,1116],{},[383,67256,40584],{},[458,67258,5160],{},[458,67260,461],{"stretchy":460},[383,67262,1116],{},[458,67264,5160],{},[463,67266,465],{},[7161,67268,67269,67271],{},[458,67270,468],{"stretchy":460},[463,67272,2810],{},[458,67274,3255],{"stretchy":460},[387,67276,67277],{"encoding":389},"f^*(y)=\\sup_t\\{ty-(t-1)^2\\}",[363,67279,67281,67334,67399,67420],{"className":67280,"ariaHidden":394},[393],[363,67282,67284,67287,67316,67319,67322,67325,67328,67331],{"className":67283},[398],[363,67285],{"className":67286,"style":487},[402],[363,67288,67290,67293],{"className":67289},[407],[363,67291,385],{"className":67292,"style":409},[407,408],[363,67294,67296],{"className":67295},[629],[363,67297,67299],{"className":67298},[633],[363,67300,67302],{"className":67301},[638],[363,67303,67305],{"className":67304,"style":8846},[642],[363,67306,67307,67310],{"style":7212},[363,67308],{"className":67309,"style":651},[650],[363,67311,67313],{"className":67312},[655,656,657,658],[363,67314,7920],{"className":67315},[2938,658],[363,67317,461],{"className":67318},[494],[363,67320,40584],{"className":67321,"style":1328},[407,408],[363,67323,468],{"className":67324},[501],[363,67326],{"className":67327,"style":506},[505],[363,67329,471],{"className":67330},[510],[363,67332],{"className":67333,"style":506},[505],[363,67335,67337,67340,67381,67384,67387,67390,67393,67396],{"className":67336},[398],[363,67338],{"className":67339,"style":487},[402],[363,67341,67343,67346],{"className":67342},[1831],[363,67344,35779],{"className":67345},[1831],[363,67347,67349],{"className":67348},[629],[363,67350,67352,67373],{"className":67351},[633,634],[363,67353,67355,67370],{"className":67354},[638],[363,67356,67359],{"className":67357,"style":67358},[642],"height:0.1864em;",[363,67360,67361,67364],{"style":35925},[363,67362],{"className":67363,"style":651},[650],[363,67365,67367],{"className":67366},[655,656,657,658],[363,67368,1116],{"className":67369},[407,408,658],[363,67371,666],{"className":67372},[665],[363,67374,67376],{"className":67375},[638],[363,67377,67379],{"className":67378,"style":37367},[642],[363,67380],{},[363,67382,3245],{"className":67383},[494],[363,67385,1116],{"className":67386},[407,408],[363,67388,40584],{"className":67389,"style":1328},[407,408],[363,67391],{"className":67392,"style":2934},[505],[363,67394,5160],{"className":67395},[2938],[363,67397],{"className":67398,"style":2934},[505],[363,67400,67402,67405,67408,67411,67414,67417],{"className":67401},[398],[363,67403],{"className":67404,"style":487},[402],[363,67406,461],{"className":67407},[494],[363,67409,1116],{"className":67410},[407,408],[363,67412],{"className":67413,"style":2934},[505],[363,67415,5160],{"className":67416},[2938],[363,67418],{"className":67419,"style":2934},[505],[363,67421,67423,67426,67429,67458],{"className":67422},[398],[363,67424],{"className":67425,"style":20350},[402],[363,67427,465],{"className":67428},[407],[363,67430,67432,67435],{"className":67431},[501],[363,67433,468],{"className":67434},[501],[363,67436,67438],{"className":67437},[629],[363,67439,67441],{"className":67440},[633],[363,67442,67444],{"className":67443},[638],[363,67445,67447],{"className":67446,"style":20375},[642],[363,67448,67449,67452],{"style":7212},[363,67450],{"className":67451,"style":651},[650],[363,67453,67455],{"className":67454},[655,656,657,658],[363,67456,2810],{"className":67457},[407,658],[363,67459,3255],{"className":67460},[501],"，驻点 ",[363,67463,67465,67509],{"className":67464,"translate":367},[366],[363,67466,67468],{"className":67467},[371],[373,67469,67470],{"xmlns":375},[377,67471,67472,67506],{},[380,67473,67474,67476,67478,67480,67482,67484,67486,67488,67490,67492,67494,67496,67498,67500,67502,67504],{},[383,67475,40584],{},[458,67477,471],{},[463,67479,2810],{},[458,67481,461],{"stretchy":460},[383,67483,1116],{},[458,67485,5160],{},[463,67487,465],{},[458,67489,468],{"stretchy":460},[458,67491,11337],{},[383,67493,1116],{},[458,67495,471],{},[463,67497,465],{},[458,67499,2817],{},[383,67501,40584],{},[383,67503,1288],{"mathvariant":557},[463,67505,2810],{},[387,67507,67508],{"encoding":389},"y=2(t-1)\\Rightarrow t=1+y\u002F2",[363,67510,67512,67530,67554,67575,67593,67611],{"className":67511,"ariaHidden":394},[393],[363,67513,67515,67518,67521,67524,67527],{"className":67514},[398],[363,67516],{"className":67517,"style":2623},[402],[363,67519,40584],{"className":67520,"style":1328},[407,408],[363,67522],{"className":67523,"style":506},[505],[363,67525,471],{"className":67526},[510],[363,67528],{"className":67529,"style":506},[505],[363,67531,67533,67536,67539,67542,67545,67548,67551],{"className":67532},[398],[363,67534],{"className":67535,"style":487},[402],[363,67537,2810],{"className":67538},[407],[363,67540,461],{"className":67541},[494],[363,67543,1116],{"className":67544},[407,408],[363,67546],{"className":67547,"style":2934},[505],[363,67549,5160],{"className":67550},[2938],[363,67552],{"className":67553,"style":2934},[505],[363,67555,67557,67560,67563,67566,67569,67572],{"className":67556},[398],[363,67558],{"className":67559,"style":487},[402],[363,67561,465],{"className":67562},[407],[363,67564,468],{"className":67565},[501],[363,67567],{"className":67568,"style":506},[505],[363,67570,11337],{"className":67571},[510],[363,67573],{"className":67574,"style":506},[505],[363,67576,67578,67581,67584,67587,67590],{"className":67577},[398],[363,67579],{"className":67580,"style":5690},[402],[363,67582,1116],{"className":67583},[407,408],[363,67585],{"className":67586,"style":506},[505],[363,67588,471],{"className":67589},[510],[363,67591],{"className":67592,"style":506},[505],[363,67594,67596,67599,67602,67605,67608],{"className":67595},[398],[363,67597],{"className":67598,"style":12925},[402],[363,67600,465],{"className":67601},[407],[363,67603],{"className":67604,"style":2934},[505],[363,67606,2817],{"className":67607},[2938],[363,67609],{"className":67610,"style":2934},[505],[363,67612,67614,67617,67620],{"className":67613},[398],[363,67615],{"className":67616,"style":487},[402],[363,67618,40584],{"className":67619,"style":1328},[407,408],[363,67621,45497],{"className":67622},[407],"，得 ",[363,67625,67627,67691],{"className":67626,"translate":367},[366],[363,67628,67630],{"className":67629},[371],[373,67631,67632],{"xmlns":375},[377,67633,67634,67688],{},[380,67635,67636,67642,67644,67646,67648,67650,67652,67654,67656,67658,67660,67662,67668,67670,67672,67674,67676,67678,67684,67686],{},[7161,67637,67638,67640],{},[383,67639,385],{},[458,67641,7920],{},[458,67643,471],{},[383,67645,40584],{},[458,67647,461],{"stretchy":460},[463,67649,465],{},[458,67651,2817],{},[383,67653,40584],{},[383,67655,1288],{"mathvariant":557},[463,67657,2810],{},[458,67659,468],{"stretchy":460},[458,67661,5160],{},[7161,67663,67664,67666],{},[383,67665,40584],{},[463,67667,2810],{},[383,67669,1288],{"mathvariant":557},[463,67671,39336],{},[458,67673,471],{},[383,67675,40584],{},[458,67677,2817],{},[7161,67679,67680,67682],{},[383,67681,40584],{},[463,67683,2810],{},[383,67685,1288],{"mathvariant":557},[463,67687,39336],{},[387,67689,67690],{"encoding":389},"f^*=y(1+y\u002F2)-y^2\u002F4=y+y^2\u002F4",[363,67692,67694,67738,67762,67786,67833,67851],{"className":67693,"ariaHidden":394},[393],[363,67695,67697,67700,67729,67732,67735],{"className":67696},[398],[363,67698],{"className":67699,"style":403},[402],[363,67701,67703,67706],{"className":67702},[407],[363,67704,385],{"className":67705,"style":409},[407,408],[363,67707,67709],{"className":67708},[629],[363,67710,67712],{"className":67711},[633],[363,67713,67715],{"className":67714},[638],[363,67716,67718],{"className":67717,"style":8846},[642],[363,67719,67720,67723],{"style":7212},[363,67721],{"className":67722,"style":651},[650],[363,67724,67726],{"className":67725},[655,656,657,658],[363,67727,7920],{"className":67728},[2938,658],[363,67730],{"className":67731,"style":506},[505],[363,67733,471],{"className":67734},[510],[363,67736],{"className":67737,"style":506},[505],[363,67739,67741,67744,67747,67750,67753,67756,67759],{"className":67740},[398],[363,67742],{"className":67743,"style":487},[402],[363,67745,40584],{"className":67746,"style":1328},[407,408],[363,67748,461],{"className":67749},[494],[363,67751,465],{"className":67752},[407],[363,67754],{"className":67755,"style":2934},[505],[363,67757,2817],{"className":67758},[2938],[363,67760],{"className":67761,"style":2934},[505],[363,67763,67765,67768,67771,67774,67777,67780,67783],{"className":67764},[398],[363,67766],{"className":67767,"style":487},[402],[363,67769,40584],{"className":67770,"style":1328},[407,408],[363,67772,45497],{"className":67773},[407],[363,67775,468],{"className":67776},[501],[363,67778],{"className":67779,"style":2934},[505],[363,67781,5160],{"className":67782},[2938],[363,67784],{"className":67785,"style":2934},[505],[363,67787,67789,67792,67821,67824,67827,67830],{"className":67788},[398],[363,67790],{"className":67791,"style":20350},[402],[363,67793,67795,67798],{"className":67794},[407],[363,67796,40584],{"className":67797,"style":1328},[407,408],[363,67799,67801],{"className":67800},[629],[363,67802,67804],{"className":67803},[633],[363,67805,67807],{"className":67806},[638],[363,67808,67810],{"className":67809,"style":20375},[642],[363,67811,67812,67815],{"style":7212},[363,67813],{"className":67814,"style":651},[650],[363,67816,67818],{"className":67817},[655,656,657,658],[363,67819,2810],{"className":67820},[407,658],[363,67822,40719],{"className":67823},[407],[363,67825],{"className":67826,"style":506},[505],[363,67828,471],{"className":67829},[510],[363,67831],{"className":67832,"style":506},[505],[363,67834,67836,67839,67842,67845,67848],{"className":67835},[398],[363,67837],{"className":67838,"style":40668},[402],[363,67840,40584],{"className":67841,"style":1328},[407,408],[363,67843],{"className":67844,"style":2934},[505],[363,67846,2817],{"className":67847},[2938],[363,67849],{"className":67850,"style":2934},[505],[363,67852,67854,67857,67886],{"className":67853},[398],[363,67855],{"className":67856,"style":20350},[402],[363,67858,67860,67863],{"className":67859},[407],[363,67861,40584],{"className":67862,"style":1328},[407,408],[363,67864,67866],{"className":67865},[629],[363,67867,67869],{"className":67868},[633],[363,67870,67872],{"className":67871},[638],[363,67873,67875],{"className":67874,"style":20375},[642],[363,67876,67877,67880],{"style":7212},[363,67878],{"className":67879,"style":651},[650],[363,67881,67883],{"className":67882},[655,656,657,658],[363,67884,2810],{"className":67885},[407,658],[363,67887,40719],{"className":67888},[407],"。以 Hellinger² 为例：",[363,67891,67893,67929],{"className":67892,"translate":367},[366],[363,67894,67896],{"className":67895},[371],[373,67897,67898],{"xmlns":375},[377,67899,67900,67926],{},[380,67901,67902,67904,67906,67908,67910,67912,67914,67916,67918,67922,67924],{},[383,67903,385],{},[458,67905,461],{"stretchy":460},[383,67907,1116],{},[458,67909,468],{"stretchy":460},[458,67911,471],{},[383,67913,1116],{},[458,67915,5160],{},[463,67917,2810],{},[34686,67919,67920],{},[383,67921,1116],{},[458,67923,2817],{},[463,67925,465],{},[387,67927,67928],{"encoding":389},"f(t)=t-2\\sqrt t+1",[363,67930,67932,67959,67978,68041],{"className":67931,"ariaHidden":394},[393],[363,67933,67935,67938,67941,67944,67947,67950,67953,67956],{"className":67934},[398],[363,67936],{"className":67937,"style":487},[402],[363,67939,385],{"className":67940,"style":409},[407,408],[363,67942,461],{"className":67943},[494],[363,67945,1116],{"className":67946},[407,408],[363,67948,468],{"className":67949},[501],[363,67951],{"className":67952,"style":506},[505],[363,67954,471],{"className":67955},[510],[363,67957],{"className":67958,"style":506},[505],[363,67960,67962,67966,67969,67972,67975],{"className":67961},[398],[363,67963],{"className":67964,"style":67965},[402],"height:0.6984em;vertical-align:-0.0833em;",[363,67967,1116],{"className":67968},[407,408],[363,67970],{"className":67971,"style":2934},[505],[363,67973,5160],{"className":67974},[2938],[363,67976],{"className":67977,"style":2934},[505],[363,67979,67981,67985,67988,68032,68035,68038],{"className":67980},[398],[363,67982],{"className":67983,"style":67984},[402],"height:1.04em;vertical-align:-0.1475em;",[363,67986,2810],{"className":67987},[407],[363,67989,67991],{"className":67990},[407,34714],[363,67992,67994,68024],{"className":67993},[633,634],[363,67995,67997,68021],{"className":67996},[638],[363,67998,68000,68009],{"className":67999,"style":43030},[642],[363,68001,68003,68006],{"className":68002,"style":12210},[6654],[363,68004],{"className":68005,"style":809},[650],[363,68007,1116],{"className":68008,"style":34734},[407,408],[363,68010,68011,68014],{"style":43042},[363,68012],{"className":68013,"style":809},[650],[363,68015,68017],{"className":68016,"style":34791},[34790],[6670,68018,68019],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,68020],{"d":34798},[363,68022,666],{"className":68023},[665],[363,68025,68027],{"className":68026},[638],[363,68028,68030],{"className":68029,"style":43062},[642],[363,68031],{},[363,68033],{"className":68034,"style":2934},[505],[363,68036,2817],{"className":68037},[2938],[363,68039],{"className":68040,"style":2934},[505],[363,68042,68044,68047],{"className":68043},[398],[363,68045],{"className":68046,"style":520},[402],[363,68048,465],{"className":68049},[407],[363,68051,68053,68077],{"className":68052,"translate":367},[366],[363,68054,68056],{"className":68055},[371],[373,68057,68058],{"xmlns":375},[377,68059,68060,68074],{},[380,68061,68062,68064,68066,68070,68072],{},[383,68063,15747],{},[458,68065,471],{},[34686,68067,68068],{},[383,68069,1116],{},[458,68071,7275],{},[463,68073,474],{},[387,68075,68076],{"encoding":389},"u=\\sqrt t\\ge0",[363,68078,68080,68098,68157],{"className":68079,"ariaHidden":394},[393],[363,68081,68083,68086,68089,68092,68095],{"className":68082},[398],[363,68084],{"className":68085,"style":2692},[402],[363,68087,15747],{"className":68088},[407,408],[363,68090],{"className":68091,"style":506},[505],[363,68093,471],{"className":68094},[510],[363,68096],{"className":68097,"style":506},[505],[363,68099,68101,68104,68148,68151,68154],{"className":68100},[398],[363,68102],{"className":68103,"style":67984},[402],[363,68105,68107],{"className":68106},[407,34714],[363,68108,68110,68140],{"className":68109},[633,634],[363,68111,68113,68137],{"className":68112},[638],[363,68114,68116,68125],{"className":68115,"style":43030},[642],[363,68117,68119,68122],{"className":68118,"style":12210},[6654],[363,68120],{"className":68121,"style":809},[650],[363,68123,1116],{"className":68124,"style":34734},[407,408],[363,68126,68127,68130],{"style":43042},[363,68128],{"className":68129,"style":809},[650],[363,68131,68133],{"className":68132,"style":34791},[34790],[6670,68134,68135],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,68136],{"d":34798},[363,68138,666],{"className":68139},[665],[363,68141,68143],{"className":68142},[638],[363,68144,68146],{"className":68145,"style":43062},[642],[363,68147],{},[363,68149],{"className":68150,"style":506},[505],[363,68152,7275],{"className":68153},[510],[363,68155],{"className":68156,"style":506},[505],[363,68158,68160,68163],{"className":68159},[398],[363,68161],{"className":68162,"style":520},[402],[363,68164,474],{"className":68165},[407],"，把共轭写成有限上确界",[363,68168,68170],{"className":68169,"translate":367},[528],[363,68171,68173,68247],{"className":68172,"translate":367},[366],[363,68174,68176],{"className":68175},[371],[373,68177,68178],{"xmlns":375,"display":537},[377,68179,68180,68244],{},[380,68181,68182,68188,68190,68192,68194,68196,68212,68214,68216,68218,68220,68222,68224,68230,68232,68234,68236,68238,68240,68242],{},[7161,68183,68184,68186],{},[383,68185,385],{},[458,68187,7920],{},[458,68189,461],{"stretchy":460},[383,68191,40584],{},[458,68193,468],{"stretchy":460},[458,68195,471],{},[6363,68197,68198,68204],{},[380,68199,68200,68202],{},[383,68201,35779],{},[458,68203,4450],{},[380,68205,68206,68208,68210],{},[383,68207,15747],{},[458,68209,7275],{},[463,68211,474],{},[458,68213,3245],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[458,68215,461],{"stretchy":460},[383,68217,40584],{},[458,68219,5160],{},[463,68221,465],{},[458,68223,468],{"stretchy":460},[7161,68225,68226,68228],{},[383,68227,15747],{},[463,68229,2810],{},[458,68231,2817],{},[463,68233,2810],{},[383,68235,15747],{},[458,68237,5160],{},[463,68239,465],{},[458,68241,3255],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[458,68243,898],{"separator":394},[387,68245,68246],{"encoding":389},"f^*(y)=\\sup_{u\\ge0}\\Big\\{(y-1)u^2+2u-1\\Big\\},",[363,68248,68250,68303,68387,68437,68458],{"className":68249,"ariaHidden":394},[393],[363,68251,68253,68256,68285,68288,68291,68294,68297,68300],{"className":68252},[398],[363,68254],{"className":68255,"style":487},[402],[363,68257,68259,68262],{"className":68258},[407],[363,68260,385],{"className":68261,"style":409},[407,408],[363,68263,68265],{"className":68264},[629],[363,68266,68268],{"className":68267},[633],[363,68269,68271],{"className":68270},[638],[363,68272,68274],{"className":68273,"style":8595},[642],[363,68275,68276,68279],{"style":8624},[363,68277],{"className":68278,"style":651},[650],[363,68280,68282],{"className":68281},[655,656,657,658],[363,68283,7920],{"className":68284},[2938,658],[363,68286,461],{"className":68287},[494],[363,68289,40584],{"className":68290,"style":1328},[407,408],[363,68292,468],{"className":68293},[501],[363,68295],{"className":68296,"style":506},[505],[363,68298,471],{"className":68299},[510],[363,68301],{"className":68302,"style":506},[505],[363,68304,68306,68310,68363,68366,68372,68375,68378,68381,68384],{"className":68305},[398],[363,68307],{"className":68308,"style":68309},[402],"height:2.1567em;vertical-align:-1.0067em;",[363,68311,68313],{"className":68312},[1831,14063],[363,68314,68316,68355],{"className":68315},[633,634],[363,68317,68319,68352],{"className":68318},[638],[363,68320,68322,68342],{"className":68321,"style":2692},[642],[363,68323,68324,68327],{"style":61269},[363,68325],{"className":68326,"style":809},[650],[363,68328,68330],{"className":68329},[655,656,657,658],[363,68331,68333,68336,68339],{"className":68332},[407,658],[363,68334,15747],{"className":68335},[407,408,658],[363,68337,7275],{"className":68338},[510,658],[363,68340,474],{"className":68341},[407,658],[363,68343,68344,68347],{"style":12210},[363,68345],{"className":68346,"style":809},[650],[363,68348,68349],{},[363,68350,35779],{"className":68351},[1831],[363,68353,666],{"className":68354},[665],[363,68356,68358],{"className":68357},[638],[363,68359,68361],{"className":68360,"style":61307},[642],[363,68362],{},[363,68364],{"className":68365,"style":754},[505],[363,68367,68369],{"className":68368},[407],[363,68370,3245],{"className":68371},[767,4067],[363,68373,461],{"className":68374},[494],[363,68376,40584],{"className":68377,"style":1328},[407,408],[363,68379],{"className":68380,"style":2934},[505],[363,68382,5160],{"className":68383},[2938],[363,68385],{"className":68386,"style":2934},[505],[363,68388,68390,68393,68396,68399,68428,68431,68434],{"className":68389},[398],[363,68391],{"className":68392,"style":37598},[402],[363,68394,465],{"className":68395},[407],[363,68397,468],{"className":68398},[501],[363,68400,68402,68405],{"className":68401},[407],[363,68403,15747],{"className":68404},[407,408],[363,68406,68408],{"className":68407},[629],[363,68409,68411],{"className":68410},[633],[363,68412,68414],{"className":68413},[638],[363,68415,68417],{"className":68416,"style":20082},[642],[363,68418,68419,68422],{"style":8624},[363,68420],{"className":68421,"style":651},[650],[363,68423,68425],{"className":68424},[655,656,657,658],[363,68426,2810],{"className":68427},[407,658],[363,68429],{"className":68430,"style":2934},[505],[363,68432,2817],{"className":68433},[2938],[363,68435],{"className":68436,"style":2934},[505],[363,68438,68440,68443,68446,68449,68452,68455],{"className":68439},[398],[363,68441],{"className":68442,"style":12925},[402],[363,68444,2810],{"className":68445},[407],[363,68447,15747],{"className":68448},[407,408],[363,68450],{"className":68451,"style":2934},[505],[363,68453,5160],{"className":68454},[2938],[363,68456],{"className":68457,"style":2934},[505],[363,68459,68461,68465,68468,68474],{"className":68460},[398],[363,68462],{"className":68463,"style":68464},[402],"height:1.8em;vertical-align:-0.65em;",[363,68466,465],{"className":68467},[407],[363,68469,68471],{"className":68470},[407],[363,68472,3255],{"className":68473},[767,4067],[363,68475,898],{"className":68476},[920],[11,68478,68479,68480,68531,68532,68565,68566,68616,68617,68751],{},"当 ",[363,68481,68483,68501],{"className":68482,"translate":367},[366],[363,68484,68486],{"className":68485},[371],[373,68487,68488],{"xmlns":375},[377,68489,68490,68498],{},[380,68491,68492,68494,68496],{},[383,68493,40584],{},[458,68495,7275],{},[463,68497,465],{},[387,68499,68500],{"encoding":389},"y\\ge1",[363,68502,68504,68522],{"className":68503,"ariaHidden":394},[393],[363,68505,68507,68510,68513,68516,68519],{"className":68506},[398],[363,68508],{"className":68509,"style":15764},[402],[363,68511,40584],{"className":68512,"style":1328},[407,408],[363,68514],{"className":68515,"style":506},[505],[363,68517,7275],{"className":68518},[510],[363,68520],{"className":68521,"style":506},[505],[363,68523,68525,68528],{"className":68524},[398],[363,68526],{"className":68527,"style":520},[402],[363,68529,465],{"className":68530},[407]," 时上确界为 ",[363,68533,68535,68550],{"className":68534,"translate":367},[366],[363,68536,68538],{"className":68537},[371],[373,68539,68540],{"xmlns":375},[377,68541,68542,68548],{},[380,68543,68544,68546],{},[458,68545,2817],{},[383,68547,1371],{"mathvariant":557},[387,68549,4588],{"encoding":389},[363,68551,68553],{"className":68552,"ariaHidden":394},[393],[363,68554,68556,68559,68562],{"className":68555},[398],[363,68557],{"className":68558,"style":4598},[402],[363,68560,2817],{"className":68561},[407],[363,68563,1371],{"className":68564},[407],"；当 ",[363,68567,68569,68586],{"className":68568,"translate":367},[366],[363,68570,68572],{"className":68571},[371],[373,68573,68574],{"xmlns":375},[377,68575,68576,68584],{},[380,68577,68578,68580,68582],{},[383,68579,40584],{},[458,68581,7598],{},[463,68583,465],{},[387,68585,67120],{"encoding":389},[363,68587,68589,68607],{"className":68588,"ariaHidden":394},[393],[363,68590,68592,68595,68598,68601,68604],{"className":68591},[398],[363,68593],{"className":68594,"style":32039},[402],[363,68596,40584],{"className":68597,"style":1328},[407,408],[363,68599],{"className":68600,"style":506},[505],[363,68602,7598],{"className":68603},[510],[363,68605],{"className":68606,"style":506},[505],[363,68608,68610,68613],{"className":68609},[398],[363,68611],{"className":68612,"style":520},[402],[363,68614,465],{"className":68615},[407]," 时上式是开口向下的二次函数，最大点 ",[363,68618,68620,68650],{"className":68619,"translate":367},[366],[363,68621,68623],{"className":68622},[371],[373,68624,68625],{"xmlns":375},[377,68626,68627,68647],{},[380,68628,68629,68631,68633],{},[383,68630,15747],{},[458,68632,471],{},[1602,68634,68635],{"scriptlevel":474,"displaystyle":394},[586,68636,68637,68639],{},[463,68638,465],{},[380,68640,68641,68643,68645],{},[463,68642,465],{},[458,68644,5160],{},[383,68646,40584],{},[387,68648,68649],{"encoding":389},"u=\\dfrac{1}{1-y}",[363,68651,68653,68671],{"className":68652,"ariaHidden":394},[393],[363,68654,68656,68659,68662,68665,68668],{"className":68655},[398],[363,68657],{"className":68658,"style":2692},[402],[363,68660,15747],{"className":68661},[407,408],[363,68663],{"className":68664,"style":506},[505],[363,68666,471],{"className":68667},[510],[363,68669],{"className":68670,"style":506},[505],[363,68672,68674,68677],{"className":68673},[398],[363,68675],{"className":68676,"style":31650},[402],[363,68678,68680,68683,68748],{"className":68679},[407],[363,68681],{"className":68682},[494,789],[363,68684,68686],{"className":68685},[586],[363,68687,68689,68740],{"className":68688},[633,634],[363,68690,68692,68737],{"className":68691},[638],[363,68693,68695,68718,68726],{"className":68694,"style":23236},[642],[363,68696,68697,68700],{"style":805},[363,68698],{"className":68699,"style":809},[650],[363,68701,68703,68706,68709,68712,68715],{"className":68702},[407],[363,68704,465],{"className":68705},[407],[363,68707],{"className":68708,"style":2934},[505],[363,68710,5160],{"className":68711},[2938],[363,68713],{"className":68714,"style":2934},[505],[363,68716,40584],{"className":68717,"style":1328},[407,408],[363,68719,68720,68723],{"style":821},[363,68721],{"className":68722,"style":809},[650],[363,68724],{"className":68725,"style":829},[828],[363,68727,68728,68731],{"style":832},[363,68729],{"className":68730,"style":809},[650],[363,68732,68734],{"className":68733},[407],[363,68735,465],{"className":68736},[407],[363,68738,666],{"className":68739},[665],[363,68741,68743],{"className":68742},[638],[363,68744,68746],{"className":68745,"style":854},[642],[363,68747],{},[363,68749],{"className":68750},[501,789],"，代回得",[363,68753,68755],{"className":68754,"translate":367},[528],[363,68756,68758,68854],{"className":68757,"translate":367},[366],[363,68759,68761],{"className":68760},[371],[373,68762,68763],{"xmlns":375,"display":537},[377,68764,68765,68851],{},[380,68766,68767,68773,68775,68777,68779,68781,68807,68809,68811,68823,68825,68827,68829,68841,68843,68845,68847,68849],{},[7161,68768,68769,68771],{},[383,68770,385],{},[458,68772,7920],{},[458,68774,461],{"stretchy":460},[383,68776,40584],{},[458,68778,468],{"stretchy":460},[458,68780,471],{},[586,68782,68783,68791],{},[380,68784,68785,68787,68789],{},[383,68786,40584],{},[458,68788,5160],{},[463,68790,465],{},[380,68792,68793,68795,68797,68799,68801],{},[458,68794,461],{"stretchy":460},[463,68796,465],{},[458,68798,5160],{},[383,68800,40584],{},[7161,68802,68803,68805],{},[458,68804,468],{"stretchy":460},[463,68806,2810],{},[458,68808,2817],{},[463,68810,2810],{},[586,68812,68813,68815],{},[463,68814,465],{},[380,68816,68817,68819,68821],{},[463,68818,465],{},[458,68820,5160],{},[383,68822,40584],{},[458,68824,5160],{},[463,68826,465],{},[458,68828,471],{},[586,68830,68831,68833],{},[383,68832,40584],{},[380,68834,68835,68837,68839],{},[463,68836,465],{},[458,68838,5160],{},[383,68840,40584],{},[458,68842,898],{"separator":394},[505,68844],{"width":3609},[383,68846,40584],{},[458,68848,7598],{},[463,68850,49857],{},[387,68852,68853],{"encoding":389},"f^*(y)=\\frac{y-1}{(1-y)^2}+2\\frac{1}{1-y}-1\n=\\frac{y}{1-y},\\qquad y\u003C1 .",[363,68855,68857,68910,69044,69136,69154,69255],{"className":68856,"ariaHidden":394},[393],[363,68858,68860,68863,68892,68895,68898,68901,68904,68907],{"className":68859},[398],[363,68861],{"className":68862,"style":487},[402],[363,68864,68866,68869],{"className":68865},[407],[363,68867,385],{"className":68868,"style":409},[407,408],[363,68870,68872],{"className":68871},[629],[363,68873,68875],{"className":68874},[633],[363,68876,68878],{"className":68877},[638],[363,68879,68881],{"className":68880,"style":8595},[642],[363,68882,68883,68886],{"style":8624},[363,68884],{"className":68885,"style":651},[650],[363,68887,68889],{"className":68888},[655,656,657,658],[363,68890,7920],{"className":68891},[2938,658],[363,68893,461],{"className":68894},[494],[363,68896,40584],{"className":68897,"style":1328},[407,408],[363,68899,468],{"className":68900},[501],[363,68902],{"className":68903,"style":506},[505],[363,68905,471],{"className":68906},[510],[363,68908],{"className":68909,"style":506},[505],[363,68911,68913,68917,69035,69038,69041],{"className":68912},[398],[363,68914],{"className":68915,"style":68916},[402],"height:2.2574em;vertical-align:-0.936em;",[363,68918,68920,68923,69032],{"className":68919},[407],[363,68921],{"className":68922},[494,789],[363,68924,68926],{"className":68925},[586],[363,68927,68929,69024],{"className":68928},[633,634],[363,68930,68932,69021],{"className":68931},[638],[363,68933,68935,68990,68998],{"className":68934,"style":23236},[642],[363,68936,68937,68940],{"style":805},[363,68938],{"className":68939,"style":809},[650],[363,68941,68943,68946,68949,68952,68955,68958,68961],{"className":68942},[407],[363,68944,461],{"className":68945},[494],[363,68947,465],{"className":68948},[407],[363,68950],{"className":68951,"style":2934},[505],[363,68953,5160],{"className":68954},[2938],[363,68956],{"className":68957,"style":2934},[505],[363,68959,40584],{"className":68960,"style":1328},[407,408],[363,68962,68964,68967],{"className":68963},[501],[363,68965,468],{"className":68966},[501],[363,68968,68970],{"className":68969},[629],[363,68971,68973],{"className":68972},[633],[363,68974,68976],{"className":68975},[638],[363,68977,68979],{"className":68978,"style":45379},[642],[363,68980,68981,68984],{"style":45382},[363,68982],{"className":68983,"style":651},[650],[363,68985,68987],{"className":68986},[655,656,657,658],[363,68988,2810],{"className":68989},[407,658],[363,68991,68992,68995],{"style":821},[363,68993],{"className":68994,"style":809},[650],[363,68996],{"className":68997,"style":829},[828],[363,68999,69000,69003],{"style":832},[363,69001],{"className":69002,"style":809},[650],[363,69004,69006,69009,69012,69015,69018],{"className":69005},[407],[363,69007,40584],{"className":69008,"style":1328},[407,408],[363,69010],{"className":69011,"style":2934},[505],[363,69013,5160],{"className":69014},[2938],[363,69016],{"className":69017,"style":2934},[505],[363,69019,465],{"className":69020},[407],[363,69022,666],{"className":69023},[665],[363,69025,69027],{"className":69026},[638],[363,69028,69030],{"className":69029,"style":1948},[642],[363,69031],{},[363,69033],{"className":69034},[501,789],[363,69036],{"className":69037,"style":2934},[505],[363,69039,2817],{"className":69040},[2938],[363,69042],{"className":69043,"style":2934},[505],[363,69045,69047,69050,69053,69127,69130,69133],{"className":69046},[398],[363,69048],{"className":69049,"style":31650},[402],[363,69051,2810],{"className":69052},[407],[363,69054,69056,69059,69124],{"className":69055},[407],[363,69057],{"className":69058},[494,789],[363,69060,69062],{"className":69061},[586],[363,69063,69065,69116],{"className":69064},[633,634],[363,69066,69068,69113],{"className":69067},[638],[363,69069,69071,69094,69102],{"className":69070,"style":23236},[642],[363,69072,69073,69076],{"style":805},[363,69074],{"className":69075,"style":809},[650],[363,69077,69079,69082,69085,69088,69091],{"className":69078},[407],[363,69080,465],{"className":69081},[407],[363,69083],{"className":69084,"style":2934},[505],[363,69086,5160],{"className":69087},[2938],[363,69089],{"className":69090,"style":2934},[505],[363,69092,40584],{"className":69093,"style":1328},[407,408],[363,69095,69096,69099],{"style":821},[363,69097],{"className":69098,"style":809},[650],[363,69100],{"className":69101,"style":829},[828],[363,69103,69104,69107],{"style":832},[363,69105],{"className":69106,"style":809},[650],[363,69108,69110],{"className":69109},[407],[363,69111,465],{"className":69112},[407],[363,69114,666],{"className":69115},[665],[363,69117,69119],{"className":69118},[638],[363,69120,69122],{"className":69121,"style":854},[642],[363,69123],{},[363,69125],{"className":69126},[501,789],[363,69128],{"className":69129,"style":2934},[505],[363,69131,5160],{"className":69132},[2938],[363,69134],{"className":69135,"style":2934},[505],[363,69137,69139,69142,69145,69148,69151],{"className":69138},[398],[363,69140],{"className":69141,"style":520},[402],[363,69143,465],{"className":69144},[407],[363,69146],{"className":69147,"style":506},[505],[363,69149,471],{"className":69150},[510],[363,69152],{"className":69153,"style":506},[505],[363,69155,69157,69160,69234,69237,69240,69243,69246,69249,69252],{"className":69156},[398],[363,69158],{"className":69159,"style":22357},[402],[363,69161,69163,69166,69231],{"className":69162},[407],[363,69164],{"className":69165},[494,789],[363,69167,69169],{"className":69168},[586],[363,69170,69172,69223],{"className":69171},[633,634],[363,69173,69175,69220],{"className":69174},[638],[363,69176,69178,69201,69209],{"className":69177,"style":3901},[642],[363,69179,69180,69183],{"style":805},[363,69181],{"className":69182,"style":809},[650],[363,69184,69186,69189,69192,69195,69198],{"className":69185},[407],[363,69187,465],{"className":69188},[407],[363,69190],{"className":69191,"style":2934},[505],[363,69193,5160],{"className":69194},[2938],[363,69196],{"className":69197,"style":2934},[505],[363,69199,40584],{"className":69200,"style":1328},[407,408],[363,69202,69203,69206],{"style":821},[363,69204],{"className":69205,"style":809},[650],[363,69207],{"className":69208,"style":829},[828],[363,69210,69211,69214],{"style":832},[363,69212],{"className":69213,"style":809},[650],[363,69215,69217],{"className":69216},[407],[363,69218,40584],{"className":69219,"style":1328},[407,408],[363,69221,666],{"className":69222},[665],[363,69224,69226],{"className":69225},[638],[363,69227,69229],{"className":69228,"style":854},[642],[363,69230],{},[363,69232],{"className":69233},[501,789],[363,69235,898],{"className":69236},[920],[363,69238],{"className":69239,"style":3981},[505],[363,69241],{"className":69242,"style":754},[505],[363,69244,40584],{"className":69245,"style":1328},[407,408],[363,69247],{"className":69248,"style":506},[505],[363,69250,7598],{"className":69251},[510],[363,69253],{"className":69254,"style":506},[505],[363,69256,69258,69261],{"className":69257},[398],[363,69259],{"className":69260,"style":520},[402],[363,69262,49857],{"className":69263},[407],[11,69265,69266,69267,3092,69643,69955,69956,19055,70089,70268,70269,70484,70485,19055,70577,70717,70718,70951],{},"顺带把 JS 的共轭也完整算出（它是表中最容易出错的一个）：",[363,69268,69270,69346],{"className":69269,"translate":367},[366],[363,69271,69273],{"className":69272},[371],[373,69274,69275],{"xmlns":375},[377,69276,69277,69343],{},[380,69278,69279,69289,69291,69293,69295,69297,69303,69305,69307,69309,69311,69313,69315,69317,69319,69321,69323,69325,69327,69329,69341],{},[543,69280,69281,69283],{},[383,69282,385],{},[380,69284,69285,69287],{},[383,69286,24090],{},[383,69288,26084],{},[458,69290,461],{"stretchy":460},[383,69292,1116],{},[458,69294,468],{"stretchy":460},[458,69296,471],{},[586,69298,69299,69301],{},[463,69300,465],{},[463,69302,2810],{},[458,69304,578],{"stretchy":460},[383,69306,1116],{},[383,69308,4447],{},[458,69310,4450],{},[383,69312,1116],{},[458,69314,5160],{},[458,69316,461],{"stretchy":460},[383,69318,1116],{},[458,69320,2817],{},[463,69322,465],{},[458,69324,468],{"stretchy":460},[383,69326,4447],{},[458,69328,4450],{},[586,69330,69331,69339],{},[380,69332,69333,69335,69337],{},[383,69334,1116],{},[458,69336,2817],{},[463,69338,465],{},[463,69340,2810],{},[458,69342,605],{"stretchy":460},[387,69344,69345],{"encoding":389},"f_{JS}(t)=\\frac12[t\\log t-(t+1)\\log\\frac{t+1}{2}]",[363,69347,69349,69419,69522,69543],{"className":69348,"ariaHidden":394},[393],[363,69350,69352,69355,69401,69404,69407,69410,69413,69416],{"className":69351},[398],[363,69353],{"className":69354,"style":487},[402],[363,69356,69358,69361],{"className":69357},[407],[363,69359,385],{"className":69360,"style":409},[407,408],[363,69362,69364],{"className":69363},[629],[363,69365,69367,69393],{"className":69366},[633,634],[363,69368,69370,69390],{"className":69369},[638],[363,69371,69373],{"className":69372,"style":727},[642],[363,69374,69375,69378],{"style":27856},[363,69376],{"className":69377,"style":651},[650],[363,69379,69381],{"className":69380},[655,656,657,658],[363,69382,69384,69387],{"className":69383},[407,658],[363,69385,24090],{"className":69386,"style":24500},[407,408,658],[363,69388,26084],{"className":69389,"style":26208},[407,408,658],[363,69391,666],{"className":69392},[665],[363,69394,69396],{"className":69395},[638],[363,69397,69399],{"className":69398,"style":8315},[642],[363,69400],{},[363,69402,461],{"className":69403},[494],[363,69405,1116],{"className":69406},[407,408],[363,69408,468],{"className":69409},[501],[363,69411],{"className":69412,"style":506},[505],[363,69414,471],{"className":69415},[510],[363,69417],{"className":69418,"style":506},[505],[363,69420,69422,69425,69493,69496,69499,69502,69507,69510,69513,69516,69519],{"className":69421},[398],[363,69423],{"className":69424,"style":2852},[402],[363,69426,69428,69431,69490],{"className":69427},[407],[363,69429],{"className":69430},[494,789],[363,69432,69434],{"className":69433},[586],[363,69435,69437,69482],{"className":69436},[633,634],[363,69438,69440,69479],{"className":69439},[638],[363,69441,69443,69457,69465],{"className":69442,"style":2871},[642],[363,69444,69445,69448],{"style":2874},[363,69446],{"className":69447,"style":809},[650],[363,69449,69451],{"className":69450},[655,656,657,658],[363,69452,69454],{"className":69453},[407,658],[363,69455,2810],{"className":69456},[407,658],[363,69458,69459,69462],{"style":821},[363,69460],{"className":69461,"style":809},[650],[363,69463],{"className":69464,"style":829},[828],[363,69466,69467,69470],{"style":2897},[363,69468],{"className":69469,"style":809},[650],[363,69471,69473],{"className":69472},[655,656,657,658],[363,69474,69476],{"className":69475},[407,658],[363,69477,465],{"className":69478},[407,658],[363,69480,666],{"className":69481},[665],[363,69483,69485],{"className":69484},[638],[363,69486,69488],{"className":69487,"style":2919},[642],[363,69489],{},[363,69491],{"className":69492},[501,789],[363,69494,578],{"className":69495},[494],[363,69497,1116],{"className":69498},[407,408],[363,69500],{"className":69501,"style":754},[505],[363,69503,4501,69505],{"className":69504},[1831],[363,69506,4505],{"style":4504},[363,69508],{"className":69509,"style":754},[505],[363,69511,1116],{"className":69512},[407,408],[363,69514],{"className":69515,"style":2934},[505],[363,69517,5160],{"className":69518},[2938],[363,69520],{"className":69521,"style":2934},[505],[363,69523,69525,69528,69531,69534,69537,69540],{"className":69524},[398],[363,69526],{"className":69527,"style":487},[402],[363,69529,461],{"className":69530},[494],[363,69532,1116],{"className":69533},[407,408],[363,69535],{"className":69536,"style":2934},[505],[363,69538,2817],{"className":69539},[2938],[363,69541],{"className":69542,"style":2934},[505],[363,69544,69546,69549,69552,69555,69558,69563,69566,69640],{"className":69545},[398],[363,69547],{"className":69548,"style":2852},[402],[363,69550,465],{"className":69551},[407],[363,69553,468],{"className":69554},[501],[363,69556],{"className":69557,"style":754},[505],[363,69559,4501,69561],{"className":69560},[1831],[363,69562,4505],{"style":4504},[363,69564],{"className":69565,"style":754},[505],[363,69567,69569,69572,69637],{"className":69568},[407],[363,69570],{"className":69571},[494,789],[363,69573,69575],{"className":69574},[586],[363,69576,69578,69629],{"className":69577},[633,634],[363,69579,69581,69626],{"className":69580},[638],[363,69582,69584,69598,69606],{"className":69583,"style":2871},[642],[363,69585,69586,69589],{"style":2874},[363,69587],{"className":69588,"style":809},[650],[363,69590,69592],{"className":69591},[655,656,657,658],[363,69593,69595],{"className":69594},[407,658],[363,69596,2810],{"className":69597},[407,658],[363,69599,69600,69603],{"style":821},[363,69601],{"className":69602,"style":809},[650],[363,69604],{"className":69605,"style":829},[828],[363,69607,69608,69611],{"style":2897},[363,69609],{"className":69610,"style":809},[650],[363,69612,69614],{"className":69613},[655,656,657,658],[363,69615,69617,69620,69623],{"className":69616},[407,658],[363,69618,1116],{"className":69619},[407,408,658],[363,69621,2817],{"className":69622},[2938,658],[363,69624,465],{"className":69625},[407,658],[363,69627,666],{"className":69628},[665],[363,69630,69632],{"className":69631},[638],[363,69633,69635],{"className":69634,"style":2919},[642],[363,69636],{},[363,69638],{"className":69639},[501,789],[363,69641,605],{"className":69642},[501],[363,69644,69646,69704],{"className":69645,"translate":367},[366],[363,69647,69649],{"className":69648},[371],[373,69650,69651],{"xmlns":375},[377,69652,69653,69701],{},[380,69654,69655,69667,69669,69671,69673,69675,69681,69683,69685],{},[7900,69656,69657,69659,69665],{},[383,69658,385],{},[380,69660,69661,69663],{},[383,69662,24090],{},[383,69664,26084],{},[458,69666,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,69668,461],{"stretchy":460},[383,69670,1116],{},[458,69672,468],{"stretchy":460},[458,69674,471],{},[586,69676,69677,69679],{},[463,69678,465],{},[463,69680,2810],{},[383,69682,4447],{},[458,69684,4450],{},[586,69686,69687,69693],{},[380,69688,69689,69691],{},[463,69690,2810],{},[383,69692,1116],{},[380,69694,69695,69697,69699],{},[383,69696,1116],{},[458,69698,2817],{},[463,69700,465],{},[387,69702,69703],{"encoding":389},"f_{JS}'(t)=\\frac12\\log\\frac{2t}{t+1}",[363,69705,69707,69793],{"className":69706,"ariaHidden":394},[393],[363,69708,69710,69714,69775,69778,69781,69784,69787,69790],{"className":69709},[398],[363,69711],{"className":69712,"style":69713},[402],"height:1.0272em;vertical-align:-0.2753em;",[363,69715,69717,69720],{"className":69716},[407],[363,69718,385],{"className":69719,"style":409},[407,408],[363,69721,69723],{"className":69722},[629],[363,69724,69726,69767],{"className":69725},[633,634],[363,69727,69729,69764],{"className":69728},[638],[363,69730,69732,69750],{"className":69731,"style":7209},[642],[363,69733,69735,69738],{"style":69734},"top:-2.4247em;margin-left:-0.1076em;margin-right:0.05em;",[363,69736],{"className":69737,"style":651},[650],[363,69739,69741],{"className":69740},[655,656,657,658],[363,69742,69744,69747],{"className":69743},[407,658],[363,69745,24090],{"className":69746,"style":24500},[407,408,658],[363,69748,26084],{"className":69749,"style":26208},[407,408,658],[363,69751,69752,69755],{"style":7212},[363,69753],{"className":69754,"style":651},[650],[363,69756,69758],{"className":69757},[655,656,657,658],[363,69759,69761],{"className":69760},[407,658],[363,69762,7167],{"className":69763},[407,658],[363,69765,666],{"className":69766},[665],[363,69768,69770],{"className":69769},[638],[363,69771,69773],{"className":69772,"style":38737},[642],[363,69774],{},[363,69776,461],{"className":69777},[494],[363,69779,1116],{"className":69780},[407,408],[363,69782,468],{"className":69783},[501],[363,69785],{"className":69786,"style":506},[505],[363,69788,471],{"className":69789},[510],[363,69791],{"className":69792,"style":506},[505],[363,69794,69796,69799,69867,69870,69875,69878],{"className":69795},[398],[363,69797],{"className":69798,"style":45752},[402],[363,69800,69802,69805,69864],{"className":69801},[407],[363,69803],{"className":69804},[494,789],[363,69806,69808],{"className":69807},[586],[363,69809,69811,69856],{"className":69810},[633,634],[363,69812,69814,69853],{"className":69813},[638],[363,69815,69817,69831,69839],{"className":69816,"style":2871},[642],[363,69818,69819,69822],{"style":2874},[363,69820],{"className":69821,"style":809},[650],[363,69823,69825],{"className":69824},[655,656,657,658],[363,69826,69828],{"className":69827},[407,658],[363,69829,2810],{"className":69830},[407,658],[363,69832,69833,69836],{"style":821},[363,69834],{"className":69835,"style":809},[650],[363,69837],{"className":69838,"style":829},[828],[363,69840,69841,69844],{"style":2897},[363,69842],{"className":69843,"style":809},[650],[363,69845,69847],{"className":69846},[655,656,657,658],[363,69848,69850],{"className":69849},[407,658],[363,69851,465],{"className":69852},[407,658],[363,69854,666],{"className":69855},[665],[363,69857,69859],{"className":69858},[638],[363,69860,69862],{"className":69861,"style":2919},[642],[363,69863],{},[363,69865],{"className":69866},[501,789],[363,69868],{"className":69869,"style":754},[505],[363,69871,4501,69873],{"className":69872},[1831],[363,69874,4505],{"style":4504},[363,69876],{"className":69877,"style":754},[505],[363,69879,69881,69884,69952],{"className":69880},[407],[363,69882],{"className":69883},[494,789],[363,69885,69887],{"className":69886},[586],[363,69888,69890,69944],{"className":69889},[633,634],[363,69891,69893,69941],{"className":69892},[638],[363,69894,69896,69916,69924],{"className":69895,"style":2871},[642],[363,69897,69898,69901],{"style":2874},[363,69899],{"className":69900,"style":809},[650],[363,69902,69904],{"className":69903},[655,656,657,658],[363,69905,69907,69910,69913],{"className":69906},[407,658],[363,69908,1116],{"className":69909},[407,408,658],[363,69911,2817],{"className":69912},[2938,658],[363,69914,465],{"className":69915},[407,658],[363,69917,69918,69921],{"style":821},[363,69919],{"className":69920,"style":809},[650],[363,69922],{"className":69923,"style":829},[828],[363,69925,69926,69929],{"style":2897},[363,69927],{"className":69928,"style":809},[650],[363,69930,69932],{"className":69931},[655,656,657,658],[363,69933,69935,69938],{"className":69934},[407,658],[363,69936,2810],{"className":69937},[407,658],[363,69939,1116],{"className":69940},[407,408,658],[363,69942,666],{"className":69943},[665],[363,69945,69947],{"className":69946},[638],[363,69948,69950],{"className":69949,"style":16776},[642],[363,69951],{},[363,69953],{"className":69954},[501,789],"。令 ",[363,69957,69959,69993],{"className":69958,"translate":367},[366],[363,69960,69962],{"className":69961},[371],[373,69963,69964],{"xmlns":375},[377,69965,69966,69990],{},[380,69967,69968,69970,69972,69984,69986,69988],{},[383,69969,40584],{},[458,69971,471],{},[7900,69973,69974,69976,69982],{},[383,69975,385],{},[380,69977,69978,69980],{},[383,69979,24090],{},[383,69981,26084],{},[458,69983,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,69985,461],{"stretchy":460},[383,69987,1116],{},[458,69989,468],{"stretchy":460},[387,69991,69992],{"encoding":389},"y=f_{JS}'(t)",[363,69994,69996,70014],{"className":69995,"ariaHidden":394},[393],[363,69997,69999,70002,70005,70008,70011],{"className":69998},[398],[363,70000],{"className":70001,"style":2623},[402],[363,70003,40584],{"className":70004,"style":1328},[407,408],[363,70006],{"className":70007,"style":506},[505],[363,70009,471],{"className":70010},[510],[363,70012],{"className":70013,"style":506},[505],[363,70015,70017,70020,70080,70083,70086],{"className":70016},[398],[363,70018],{"className":70019,"style":69713},[402],[363,70021,70023,70026],{"className":70022},[407],[363,70024,385],{"className":70025,"style":409},[407,408],[363,70027,70029],{"className":70028},[629],[363,70030,70032,70072],{"className":70031},[633,634],[363,70033,70035,70069],{"className":70034},[638],[363,70036,70038,70055],{"className":70037,"style":7209},[642],[363,70039,70040,70043],{"style":69734},[363,70041],{"className":70042,"style":651},[650],[363,70044,70046],{"className":70045},[655,656,657,658],[363,70047,70049,70052],{"className":70048},[407,658],[363,70050,24090],{"className":70051,"style":24500},[407,408,658],[363,70053,26084],{"className":70054,"style":26208},[407,408,658],[363,70056,70057,70060],{"style":7212},[363,70058],{"className":70059,"style":651},[650],[363,70061,70063],{"className":70062},[655,656,657,658],[363,70064,70066],{"className":70065},[407,658],[363,70067,7167],{"className":70068},[407,658],[363,70070,666],{"className":70071},[665],[363,70073,70075],{"className":70074},[638],[363,70076,70078],{"className":70077,"style":38737},[642],[363,70079],{},[363,70081,461],{"className":70082},[494],[363,70084,1116],{"className":70085},[407,408],[363,70087,468],{"className":70088},[501],[363,70090,70092,70132],{"className":70091,"translate":367},[366],[363,70093,70095],{"className":70094},[371],[373,70096,70097],{"xmlns":375},[377,70098,70099,70129],{},[380,70100,70101,70111,70113],{},[7161,70102,70103,70105],{},[383,70104,7914],{},[380,70106,70107,70109],{},[463,70108,2810],{},[383,70110,40584],{},[458,70112,471],{},[586,70114,70115,70121],{},[380,70116,70117,70119],{},[463,70118,2810],{},[383,70120,1116],{},[380,70122,70123,70125,70127],{},[383,70124,1116],{},[458,70126,2817],{},[463,70128,465],{},[387,70130,70131],{"encoding":389},"e^{2y}=\\frac{2t}{t+1}",[363,70133,70135,70185],{"className":70134,"ariaHidden":394},[393],[363,70136,70138,70141,70176,70179,70182],{"className":70137},[398],[363,70139],{"className":70140,"style":20375},[402],[363,70142,70144,70147],{"className":70143},[407],[363,70145,7914],{"className":70146},[407,408],[363,70148,70150],{"className":70149},[629],[363,70151,70153],{"className":70152},[633],[363,70154,70156],{"className":70155},[638],[363,70157,70159],{"className":70158,"style":20375},[642],[363,70160,70161,70164],{"style":7212},[363,70162],{"className":70163,"style":651},[650],[363,70165,70167],{"className":70166},[655,656,657,658],[363,70168,70170,70173],{"className":70169},[407,658],[363,70171,2810],{"className":70172},[407,658],[363,70174,40584],{"className":70175,"style":1328},[407,408,658],[363,70177],{"className":70178,"style":506},[505],[363,70180,471],{"className":70181},[510],[363,70183],{"className":70184,"style":506},[505],[363,70186,70188,70191],{"className":70187},[398],[363,70189],{"className":70190,"style":45752},[402],[363,70192,70194,70197,70265],{"className":70193},[407],[363,70195],{"className":70196},[494,789],[363,70198,70200],{"className":70199},[586],[363,70201,70203,70257],{"className":70202},[633,634],[363,70204,70206,70254],{"className":70205},[638],[363,70207,70209,70229,70237],{"className":70208,"style":2871},[642],[363,70210,70211,70214],{"style":2874},[363,70212],{"className":70213,"style":809},[650],[363,70215,70217],{"className":70216},[655,656,657,658],[363,70218,70220,70223,70226],{"className":70219},[407,658],[363,70221,1116],{"className":70222},[407,408,658],[363,70224,2817],{"className":70225},[2938,658],[363,70227,465],{"className":70228},[407,658],[363,70230,70231,70234],{"style":821},[363,70232],{"className":70233,"style":809},[650],[363,70235],{"className":70236,"style":829},[828],[363,70238,70239,70242],{"style":2897},[363,70240],{"className":70241,"style":809},[650],[363,70243,70245],{"className":70244},[655,656,657,658],[363,70246,70248,70251],{"className":70247},[407,658],[363,70249,2810],{"className":70250},[407,658],[363,70252,1116],{"className":70253},[407,408,658],[363,70255,666],{"className":70256},[665],[363,70258,70260],{"className":70259},[638],[363,70261,70263],{"className":70262,"style":16776},[642],[363,70264],{},[363,70266],{"className":70267},[501,789],"，解得 ",[363,70270,70272,70318],{"className":70271,"translate":367},[366],[363,70273,70275],{"className":70274},[371],[373,70276,70277],{"xmlns":375},[377,70278,70279,70315],{},[380,70280,70281,70283,70285],{},[383,70282,1116],{},[458,70284,471],{},[1602,70286,70287],{"scriptlevel":474,"displaystyle":394},[586,70288,70289,70299],{},[7161,70290,70291,70293],{},[383,70292,7914],{},[380,70294,70295,70297],{},[463,70296,2810],{},[383,70298,40584],{},[380,70300,70301,70303,70305],{},[463,70302,2810],{},[458,70304,5160],{},[7161,70306,70307,70309],{},[383,70308,7914],{},[380,70310,70311,70313],{},[463,70312,2810],{},[383,70314,40584],{},[387,70316,70317],{"encoding":389},"t=\\dfrac{e^{2y}}{2-e^{2y}}",[363,70319,70321,70339],{"className":70320,"ariaHidden":394},[393],[363,70322,70324,70327,70330,70333,70336],{"className":70323},[398],[363,70325],{"className":70326,"style":5690},[402],[363,70328,1116],{"className":70329},[407,408],[363,70331],{"className":70332,"style":506},[505],[363,70334,471],{"className":70335},[510],[363,70337],{"className":70338,"style":506},[505],[363,70340,70342,70346],{"className":70341},[398],[363,70343],{"className":70344,"style":70345},[402],"height:2.2604em;vertical-align:-0.7693em;",[363,70347,70349,70352,70481],{"className":70348},[407],[363,70350],{"className":70351},[494,789],[363,70353,70355],{"className":70354},[586],[363,70356,70358,70473],{"className":70357},[633,634],[363,70359,70361,70470],{"className":70360},[638],[363,70362,70364,70419,70427],{"className":70363,"style":38070},[642],[363,70365,70366,70369],{"style":805},[363,70367],{"className":70368,"style":809},[650],[363,70370,70372,70375,70378,70381,70384],{"className":70371},[407],[363,70373,2810],{"className":70374},[407],[363,70376],{"className":70377,"style":2934},[505],[363,70379,5160],{"className":70380},[2938],[363,70382],{"className":70383,"style":2934},[505],[363,70385,70387,70390],{"className":70386},[407],[363,70388,7914],{"className":70389},[407,408],[363,70391,70393],{"className":70392},[629],[363,70394,70396],{"className":70395},[633],[363,70397,70399],{"className":70398},[638],[363,70400,70402],{"className":70401,"style":45379},[642],[363,70403,70404,70407],{"style":45382},[363,70405],{"className":70406,"style":651},[650],[363,70408,70410],{"className":70409},[655,656,657,658],[363,70411,70413,70416],{"className":70412},[407,658],[363,70414,2810],{"className":70415},[407,658],[363,70417,40584],{"className":70418,"style":1328},[407,408,658],[363,70420,70421,70424],{"style":821},[363,70422],{"className":70423,"style":809},[650],[363,70425],{"className":70426,"style":829},[828],[363,70428,70429,70432],{"style":832},[363,70430],{"className":70431,"style":809},[650],[363,70433,70435],{"className":70434},[407],[363,70436,70438,70441],{"className":70437},[407],[363,70439,7914],{"className":70440},[407,408],[363,70442,70444],{"className":70443},[629],[363,70445,70447],{"className":70446},[633],[363,70448,70450],{"className":70449},[638],[363,70451,70453],{"className":70452,"style":20375},[642],[363,70454,70455,70458],{"style":7212},[363,70456],{"className":70457,"style":651},[650],[363,70459,70461],{"className":70460},[655,656,657,658],[363,70462,70464,70467],{"className":70463},[407,658],[363,70465,2810],{"className":70466},[407,658],[363,70468,40584],{"className":70469,"style":1328},[407,408,658],[363,70471,666],{"className":70472},[665],[363,70474,70476],{"className":70475},[638],[363,70477,70479],{"className":70478,"style":17362},[642],[363,70480],{},[363,70482],{"className":70483},[501,789],"（这要求 ",[363,70486,70488,70514],{"className":70487,"translate":367},[366],[363,70489,70491],{"className":70490},[371],[373,70492,70493],{"xmlns":375},[377,70494,70495,70511],{},[380,70496,70497,70507,70509],{},[7161,70498,70499,70501],{},[383,70500,7914],{},[380,70502,70503,70505],{},[463,70504,2810],{},[383,70506,40584],{},[458,70508,7598],{},[463,70510,2810],{},[387,70512,70513],{"encoding":389},"e^{2y}\u003C2",[363,70515,70517,70568],{"className":70516,"ariaHidden":394},[393],[363,70518,70520,70524,70559,70562,70565],{"className":70519},[398],[363,70521],{"className":70522,"style":70523},[402],"height:0.8532em;vertical-align:-0.0391em;",[363,70525,70527,70530],{"className":70526},[407],[363,70528,7914],{"className":70529},[407,408],[363,70531,70533],{"className":70532},[629],[363,70534,70536],{"className":70535},[633],[363,70537,70539],{"className":70538},[638],[363,70540,70542],{"className":70541,"style":20375},[642],[363,70543,70544,70547],{"style":7212},[363,70545],{"className":70546,"style":651},[650],[363,70548,70550],{"className":70549},[655,656,657,658],[363,70551,70553,70556],{"className":70552},[407,658],[363,70554,2810],{"className":70555},[407,658],[363,70557,40584],{"className":70558,"style":1328},[407,408,658],[363,70560],{"className":70561,"style":506},[505],[363,70563,7598],{"className":70564},[510],[363,70566],{"className":70567,"style":506},[505],[363,70569,70571,70574],{"className":70570},[398],[363,70572],{"className":70573,"style":520},[402],[363,70575,2810],{"className":70576},[407],[363,70578,70580,70607],{"className":70579,"translate":367},[366],[363,70581,70583],{"className":70582},[371],[373,70584,70585],{"xmlns":375},[377,70586,70587,70605],{},[380,70588,70589,70591,70593],{},[383,70590,40584],{},[458,70592,7598],{},[586,70594,70595,70603],{},[380,70596,70597,70599,70601],{},[383,70598,4447],{},[458,70600,4450],{},[463,70602,2810],{},[463,70604,2810],{},[387,70606,66090],{"encoding":389},[363,70608,70610,70628],{"className":70609,"ariaHidden":394},[393],[363,70611,70613,70616,70619,70622,70625],{"className":70612},[398],[363,70614],{"className":70615,"style":32039},[402],[363,70617,40584],{"className":70618,"style":1328},[407,408],[363,70620],{"className":70621,"style":506},[505],[363,70623,7598],{"className":70624},[510],[363,70626],{"className":70627,"style":506},[505],[363,70629,70631,70634],{"className":70630},[398],[363,70632],{"className":70633,"style":66118},[402],[363,70635,70637,70640,70714],{"className":70636},[407],[363,70638],{"className":70639},[494,789],[363,70641,70643],{"className":70642},[586],[363,70644,70646,70706],{"className":70645},[633,634],[363,70647,70649,70703],{"className":70648},[638],[363,70650,70652,70666,70674],{"className":70651,"style":3172},[642],[363,70653,70654,70657],{"style":2874},[363,70655],{"className":70656,"style":809},[650],[363,70658,70660],{"className":70659},[655,656,657,658],[363,70661,70663],{"className":70662},[407,658],[363,70664,2810],{"className":70665},[407,658],[363,70667,70668,70671],{"style":821},[363,70669],{"className":70670,"style":809},[650],[363,70672],{"className":70673,"style":829},[828],[363,70675,70676,70679],{"style":3200},[363,70677],{"className":70678,"style":809},[650],[363,70680,70682],{"className":70681},[655,656,657,658],[363,70683,70685,70697,70700],{"className":70684},[407,658],[363,70686,70688,70691,70694],{"className":70687},[1831,658],[363,70689,48005],{"className":70690},[658],[363,70692,48009],{"className":70693},[658],[363,70695,4505],{"className":70696,"style":4504},[658],[363,70698],{"className":70699,"style":42713},[505,658],[363,70701,2810],{"className":70702},[407,658],[363,70704,666],{"className":70705},[665],[363,70707,70709],{"className":70708},[638],[363,70710,70712],{"className":70711,"style":2919},[642],[363,70713],{},[363,70715],{"className":70716},[501,789],"）。于是 ",[363,70719,70721,70775],{"className":70720,"translate":367},[366],[363,70722,70724],{"className":70723},[371],[373,70725,70726],{"xmlns":375},[377,70727,70728,70772],{},[380,70729,70730,70732,70734,70746,70748,70750,70752,70754,70756,70758,70760,70770],{},[383,70731,4447],{},[458,70733,4450],{},[586,70735,70736,70744],{},[380,70737,70738,70740,70742],{},[383,70739,1116],{},[458,70741,2817],{},[463,70743,465],{},[463,70745,2810],{},[458,70747,471],{},[458,70749,5160],{},[383,70751,4447],{},[458,70753,4450],{},[458,70755,461],{"stretchy":460},[463,70757,2810],{},[458,70759,5160],{},[7161,70761,70762,70764],{},[383,70763,7914],{},[380,70765,70766,70768],{},[463,70767,2810],{},[383,70769,40584],{},[458,70771,468],{"stretchy":460},[387,70773,70774],{"encoding":389},"\\log\\frac{t+1}{2}=-\\log(2-e^{2y})",[363,70776,70778,70875,70907],{"className":70777,"ariaHidden":394},[393],[363,70779,70781,70784,70789,70792,70866,70869,70872],{"className":70780},[398],[363,70782],{"className":70783,"style":2852},[402],[363,70785,4501,70787],{"className":70786},[1831],[363,70788,4505],{"style":4504},[363,70790],{"className":70791,"style":754},[505],[363,70793,70795,70798,70863],{"className":70794},[407],[363,70796],{"className":70797},[494,789],[363,70799,70801],{"className":70800},[586],[363,70802,70804,70855],{"className":70803},[633,634],[363,70805,70807,70852],{"className":70806},[638],[363,70808,70810,70824,70832],{"className":70809,"style":2871},[642],[363,70811,70812,70815],{"style":2874},[363,70813],{"className":70814,"style":809},[650],[363,70816,70818],{"className":70817},[655,656,657,658],[363,70819,70821],{"className":70820},[407,658],[363,70822,2810],{"className":70823},[407,658],[363,70825,70826,70829],{"style":821},[363,70827],{"className":70828,"style":809},[650],[363,70830],{"className":70831,"style":829},[828],[363,70833,70834,70837],{"style":2897},[363,70835],{"className":70836,"style":809},[650],[363,70838,70840],{"className":70839},[655,656,657,658],[363,70841,70843,70846,70849],{"className":70842},[407,658],[363,70844,1116],{"className":70845},[407,408,658],[363,70847,2817],{"className":70848},[2938,658],[363,70850,465],{"className":70851},[407,658],[363,70853,666],{"className":70854},[665],[363,70856,70858],{"className":70857},[638],[363,70859,70861],{"className":70860,"style":2919},[642],[363,70862],{},[363,70864],{"className":70865},[501,789],[363,70867],{"className":70868,"style":506},[505],[363,70870,471],{"className":70871},[510],[363,70873],{"className":70874,"style":506},[505],[363,70876,70878,70881,70884,70887,70892,70895,70898,70901,70904],{"className":70877},[398],[363,70879],{"className":70880,"style":487},[402],[363,70882,5160],{"className":70883},[407],[363,70885],{"className":70886,"style":754},[505],[363,70888,4501,70890],{"className":70889},[1831],[363,70891,4505],{"style":4504},[363,70893,461],{"className":70894},[494],[363,70896,2810],{"className":70897},[407],[363,70899],{"className":70900,"style":2934},[505],[363,70902,5160],{"className":70903},[2938],[363,70905],{"className":70906,"style":2934},[505],[363,70908,70910,70913,70948],{"className":70909},[398],[363,70911],{"className":70912,"style":20350},[402],[363,70914,70916,70919],{"className":70915},[407],[363,70917,7914],{"className":70918},[407,408],[363,70920,70922],{"className":70921},[629],[363,70923,70925],{"className":70924},[633],[363,70926,70928],{"className":70927},[638],[363,70929,70931],{"className":70930,"style":20375},[642],[363,70932,70933,70936],{"style":7212},[363,70934],{"className":70935,"style":651},[650],[363,70937,70939],{"className":70938},[655,656,657,658],[363,70940,70942,70945],{"className":70941},[407,658],[363,70943,2810],{"className":70944},[407,658],[363,70946,40584],{"className":70947,"style":1328},[407,408,658],[363,70949,468],{"className":70950},[501],"，代入",[363,70953,70955],{"className":70954,"translate":367},[528],[363,70956,70958,71156],{"className":70957,"translate":367},[366],[363,70959,70961],{"className":70960},[371],[373,70962,70963],{"xmlns":375,"display":537},[377,70964,70965,71153],{},[1590,70966,70967,71019,71101],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,70968,70969,70987],{},[1599,70970,70971],{},[1602,70972,70973],{"scriptlevel":474,"displaystyle":394},[380,70974,70975,70981,70983,70985],{},[7161,70976,70977,70979],{},[383,70978,385],{},[458,70980,7920],{},[458,70982,461],{"stretchy":460},[383,70984,40584],{},[458,70986,468],{"stretchy":460},[1599,70988,70989],{},[1602,70990,70991],{"scriptlevel":474,"displaystyle":394},[380,70992,70993,70995,70997,70999,71001,71003,71013,71015,71017],{},[380,70994],{},[458,70996,471],{},[383,70998,40584],{},[383,71000,1116],{},[458,71002,5160],{},[543,71004,71005,71007],{},[383,71006,385],{},[380,71008,71009,71011],{},[383,71010,24090],{},[383,71012,26084],{},[458,71014,461],{"stretchy":460},[383,71016,1116],{},[458,71018,468],{"stretchy":460},[1596,71020,71021,71027],{},[1599,71022,71023],{},[1602,71024,71025],{"scriptlevel":474,"displaystyle":394},[380,71026],{},[1599,71028,71029],{},[1602,71030,71031],{"scriptlevel":474,"displaystyle":394},[380,71032,71033,71035,71037,71043,71045,71047,71049,71051,71053,71063,71065,71067,71079,71081,71083,71085,71087,71089,71099],{},[380,71034],{},[458,71036,471],{},[586,71038,71039,71041],{},[383,71040,1116],{},[463,71042,2810],{},[383,71044,4447],{},[458,71046,4450],{},[458,71048,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[463,71050,2810],{},[458,71052,5160],{},[7161,71054,71055,71057],{},[383,71056,7914],{},[380,71058,71059,71061],{},[463,71060,2810],{},[383,71062,40584],{},[458,71064,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,71066,5160],{},[586,71068,71069,71077],{},[380,71070,71071,71073,71075],{},[383,71072,1116],{},[458,71074,2817],{},[463,71076,465],{},[463,71078,2810],{},[383,71080,4447],{},[458,71082,4450],{},[458,71084,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[463,71086,2810],{},[458,71088,5160],{},[7161,71090,71091,71093],{},[383,71092,7914],{},[380,71094,71095,71097],{},[463,71096,2810],{},[383,71098,40584],{},[458,71100,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[1596,71102,71103,71109],{},[1599,71104,71105],{},[1602,71106,71107],{"scriptlevel":474,"displaystyle":394},[380,71108],{},[1599,71110,71111],{},[1602,71112,71113],{"scriptlevel":474,"displaystyle":394},[380,71114,71115,71117,71119,71121,71127,71129,71131,71133,71135,71137,71139,71149,71151],{},[380,71116],{},[458,71118,471],{},[458,71120,5160],{},[586,71122,71123,71125],{},[463,71124,465],{},[463,71126,2810],{},[383,71128,4447],{},[458,71130,4450],{},[1644,71132,1651],{},[458,71134,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[463,71136,2810],{},[458,71138,5160],{},[7161,71140,71141,71143],{},[383,71142,7914],{},[380,71144,71145,71147],{},[463,71146,2810],{},[383,71148,40584],{},[458,71150,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,71152,4722],{"mathvariant":557},[387,71154,71155],{"encoding":389},"\\begin{aligned}\nf^*(y)&=yt-f_{JS}(t)\\\\\n&=\\frac{t}{2}\\log\\big(2-e^{2y}\\big)\n-\\frac{t+1}{2}\\log\\big(2-e^{2y}\\big)\\\\\n&=-\\frac12\\log\\!\\big(2-e^{2y}\\big).\n\\end{aligned}",[363,71157,71159],{"className":71158,"ariaHidden":394},[393],[363,71160,71162,71166],{"className":71161},[398],[363,71163],{"className":71164,"style":71165},[402],"height:5.8149em;vertical-align:-2.6574em;",[363,71167,71169],{"className":71168},[407],[363,71170,71172,71262],{"className":71171},[1590],[363,71173,71175],{"className":71174},[1707],[363,71176,71178,71253],{"className":71177},[633,634],[363,71179,71181,71250],{"className":71180},[638],[363,71182,71185,71232,71241],{"className":71183,"style":71184},[642],"height:3.1574em;",[363,71186,71188,71191],{"style":71187},"top:-5.6389em;",[363,71189],{"className":71190,"style":23013},[650],[363,71192,71194,71223,71226,71229],{"className":71193},[407],[363,71195,71197,71200],{"className":71196},[407],[363,71198,385],{"className":71199,"style":409},[407,408],[363,71201,71203],{"className":71202},[629],[363,71204,71206],{"className":71205},[633],[363,71207,71209],{"className":71208},[638],[363,71210,71212],{"className":71211,"style":8595},[642],[363,71213,71214,71217],{"style":8624},[363,71215],{"className":71216,"style":651},[650],[363,71218,71220],{"className":71219},[655,656,657,658],[363,71221,7920],{"className":71222},[2938,658],[363,71224,461],{"className":71225},[494],[363,71227,40584],{"className":71228,"style":1328},[407,408],[363,71230,468],{"className":71231},[501],[363,71233,71235,71238],{"style":71234},"top:-3.6574em;",[363,71236],{"className":71237,"style":23013},[650],[363,71239],{"className":71240},[407],[363,71242,71244,71247],{"style":71243},"top:-1.35em;",[363,71245],{"className":71246,"style":23013},[650],[363,71248],{"className":71249},[407],[363,71251,666],{"className":71252},[665],[363,71254,71256],{"className":71255},[638],[363,71257,71260],{"className":71258,"style":71259},[642],"height:2.6574em;",[363,71261],{},[363,71263,71265],{"className":71264},[1798],[363,71266,71268,71834],{"className":71267},[633,634],[363,71269,71271,71831],{"className":71270},[638],[363,71272,71274,71364,71670],{"className":71273,"style":71184},[642],[363,71275,71276,71279],{"style":71187},[363,71277],{"className":71278,"style":23013},[650],[363,71280,71282,71285,71288,71291,71294,71297,71300,71303,71306,71309,71355,71358,71361],{"className":71281},[407],[363,71283],{"className":71284},[407],[363,71286],{"className":71287,"style":506},[505],[363,71289,471],{"className":71290},[510],[363,71292],{"className":71293,"style":506},[505],[363,71295,40584],{"className":71296,"style":1328},[407,408],[363,71298,1116],{"className":71299},[407,408],[363,71301],{"className":71302,"style":2934},[505],[363,71304,5160],{"className":71305},[2938],[363,71307],{"className":71308,"style":2934},[505],[363,71310,71312,71315],{"className":71311},[407],[363,71313,385],{"className":71314,"style":409},[407,408],[363,71316,71318],{"className":71317},[629],[363,71319,71321,71347],{"className":71320},[633,634],[363,71322,71324,71344],{"className":71323},[638],[363,71325,71327],{"className":71326,"style":727},[642],[363,71328,71329,71332],{"style":27856},[363,71330],{"className":71331,"style":651},[650],[363,71333,71335],{"className":71334},[655,656,657,658],[363,71336,71338,71341],{"className":71337},[407,658],[363,71339,24090],{"className":71340,"style":24500},[407,408,658],[363,71342,26084],{"className":71343,"style":26208},[407,408,658],[363,71345,666],{"className":71346},[665],[363,71348,71350],{"className":71349},[638],[363,71351,71353],{"className":71352,"style":8315},[642],[363,71354],{},[363,71356,461],{"className":71357},[494],[363,71359,1116],{"className":71360},[407,408],[363,71362,468],{"className":71363},[501],[363,71365,71366,71369],{"style":71234},[363,71367],{"className":71368,"style":23013},[650],[363,71370,71372,71375,71378,71381,71384,71447,71450,71455,71458,71464,71467,71470,71473,71476,71511,71517,71520,71523,71526,71600,71603,71608,71611,71617,71620,71623,71626,71629,71664],{"className":71371},[407],[363,71373],{"className":71374},[407],[363,71376],{"className":71377,"style":506},[505],[363,71379,471],{"className":71380},[510],[363,71382],{"className":71383,"style":506},[505],[363,71385,71387,71390,71444],{"className":71386},[407],[363,71388],{"className":71389},[494,789],[363,71391,71393],{"className":71392},[586],[363,71394,71396,71436],{"className":71395},[633,634],[363,71397,71399,71433],{"className":71398},[638],[363,71400,71403,71414,71422],{"className":71401,"style":71402},[642],"height:1.2921em;",[363,71404,71405,71408],{"style":805},[363,71406],{"className":71407,"style":809},[650],[363,71409,71411],{"className":71410},[407],[363,71412,2810],{"className":71413},[407],[363,71415,71416,71419],{"style":821},[363,71417],{"className":71418,"style":809},[650],[363,71420],{"className":71421,"style":829},[828],[363,71423,71424,71427],{"style":832},[363,71425],{"className":71426,"style":809},[650],[363,71428,71430],{"className":71429},[407],[363,71431,1116],{"className":71432},[407,408],[363,71434,666],{"className":71435},[665],[363,71437,71439],{"className":71438},[638],[363,71440,71442],{"className":71441,"style":4125},[642],[363,71443],{},[363,71445],{"className":71446},[501,789],[363,71448],{"className":71449,"style":754},[505],[363,71451,4501,71453],{"className":71452},[1831],[363,71454,4505],{"style":4504},[363,71456],{"className":71457,"style":754},[505],[363,71459,71461],{"className":71460},[407],[363,71462,461],{"className":71463},[767,10021],[363,71465,2810],{"className":71466},[407],[363,71468],{"className":71469,"style":2934},[505],[363,71471,5160],{"className":71472},[2938],[363,71474],{"className":71475,"style":2934},[505],[363,71477,71479,71482],{"className":71478},[407],[363,71480,7914],{"className":71481},[407,408],[363,71483,71485],{"className":71484},[629],[363,71486,71488],{"className":71487},[633],[363,71489,71491],{"className":71490},[638],[363,71492,71494],{"className":71493,"style":20082},[642],[363,71495,71496,71499],{"style":8624},[363,71497],{"className":71498,"style":651},[650],[363,71500,71502],{"className":71501},[655,656,657,658],[363,71503,71505,71508],{"className":71504},[407,658],[363,71506,2810],{"className":71507},[407,658],[363,71509,40584],{"className":71510,"style":1328},[407,408,658],[363,71512,71514],{"className":71513},[407],[363,71515,468],{"className":71516},[767,10021],[363,71518],{"className":71519,"style":2934},[505],[363,71521,5160],{"className":71522},[2938],[363,71524],{"className":71525,"style":2934},[505],[363,71527,71529,71532,71597],{"className":71528},[407],[363,71530],{"className":71531},[494,789],[363,71533,71535],{"className":71534},[586],[363,71536,71538,71589],{"className":71537},[633,634],[363,71539,71541,71586],{"className":71540},[638],[363,71542,71544,71555,71563],{"className":71543,"style":23236},[642],[363,71545,71546,71549],{"style":805},[363,71547],{"className":71548,"style":809},[650],[363,71550,71552],{"className":71551},[407],[363,71553,2810],{"className":71554},[407],[363,71556,71557,71560],{"style":821},[363,71558],{"className":71559,"style":809},[650],[363,71561],{"className":71562,"style":829},[828],[363,71564,71565,71568],{"style":832},[363,71566],{"className":71567,"style":809},[650],[363,71569,71571,71574,71577,71580,71583],{"className":71570},[407],[363,71572,1116],{"className":71573},[407,408],[363,71575],{"className":71576,"style":2934},[505],[363,71578,2817],{"className":71579},[2938],[363,71581],{"className":71582,"style":2934},[505],[363,71584,465],{"className":71585},[407],[363,71587,666],{"className":71588},[665],[363,71590,71592],{"className":71591},[638],[363,71593,71595],{"className":71594,"style":4125},[642],[363,71596],{},[363,71598],{"className":71599},[501,789],[363,71601],{"className":71602,"style":754},[505],[363,71604,4501,71606],{"className":71605},[1831],[363,71607,4505],{"style":4504},[363,71609],{"className":71610,"style":754},[505],[363,71612,71614],{"className":71613},[407],[363,71615,461],{"className":71616},[767,10021],[363,71618,2810],{"className":71619},[407],[363,71621],{"className":71622,"style":2934},[505],[363,71624,5160],{"className":71625},[2938],[363,71627],{"className":71628,"style":2934},[505],[363,71630,71632,71635],{"className":71631},[407],[363,71633,7914],{"className":71634},[407,408],[363,71636,71638],{"className":71637},[629],[363,71639,71641],{"className":71640},[633],[363,71642,71644],{"className":71643},[638],[363,71645,71647],{"className":71646,"style":20082},[642],[363,71648,71649,71652],{"style":8624},[363,71650],{"className":71651,"style":651},[650],[363,71653,71655],{"className":71654},[655,656,657,658],[363,71656,71658,71661],{"className":71657},[407,658],[363,71659,2810],{"className":71660},[407,658],[363,71662,40584],{"className":71663,"style":1328},[407,408,658],[363,71665,71667],{"className":71666},[407],[363,71668,468],{"className":71669},[767,10021],[363,71671,71672,71675],{"style":71243},[363,71673],{"className":71674,"style":23013},[650],[363,71676,71678,71681,71684,71687,71690,71693,71755,71758,71763,71766,71769,71775,71778,71781,71784,71787,71822,71828],{"className":71677},[407],[363,71679],{"className":71680},[407],[363,71682],{"className":71683,"style":506},[505],[363,71685,471],{"className":71686},[510],[363,71688],{"className":71689,"style":506},[505],[363,71691,5160],{"className":71692},[407],[363,71694,71696,71699,71752],{"className":71695},[407],[363,71697],{"className":71698},[494,789],[363,71700,71702],{"className":71701},[586],[363,71703,71705,71744],{"className":71704},[633,634],[363,71706,71708,71741],{"className":71707},[638],[363,71709,71711,71722,71730],{"className":71710,"style":23236},[642],[363,71712,71713,71716],{"style":805},[363,71714],{"className":71715,"style":809},[650],[363,71717,71719],{"className":71718},[407],[363,71720,2810],{"className":71721},[407],[363,71723,71724,71727],{"style":821},[363,71725],{"className":71726,"style":809},[650],[363,71728],{"className":71729,"style":829},[828],[363,71731,71732,71735],{"style":832},[363,71733],{"className":71734,"style":809},[650],[363,71736,71738],{"className":71737},[407],[363,71739,465],{"className":71740},[407],[363,71742,666],{"className":71743},[665],[363,71745,71747],{"className":71746},[638],[363,71748,71750],{"className":71749,"style":4125},[642],[363,71751],{},[363,71753],{"className":71754},[501,789],[363,71756],{"className":71757,"style":754},[505],[363,71759,4501,71761],{"className":71760},[1831],[363,71762,4505],{"style":4504},[363,71764],{"className":71765,"style":1859},[505],[363,71767],{"className":71768,"style":754},[505],[363,71770,71772],{"className":71771},[407],[363,71773,461],{"className":71774},[767,10021],[363,71776,2810],{"className":71777},[407],[363,71779],{"className":71780,"style":2934},[505],[363,71782,5160],{"className":71783},[2938],[363,71785],{"className":71786,"style":2934},[505],[363,71788,71790,71793],{"className":71789},[407],[363,71791,7914],{"className":71792},[407,408],[363,71794,71796],{"className":71795},[629],[363,71797,71799],{"className":71798},[633],[363,71800,71802],{"className":71801},[638],[363,71803,71805],{"className":71804,"style":20082},[642],[363,71806,71807,71810],{"style":8624},[363,71808],{"className":71809,"style":651},[650],[363,71811,71813],{"className":71812},[655,656,657,658],[363,71814,71816,71819],{"className":71815},[407,658],[363,71817,2810],{"className":71818},[407,658],[363,71820,40584],{"className":71821,"style":1328},[407,408,658],[363,71823,71825],{"className":71824},[407],[363,71826,468],{"className":71827},[767,10021],[363,71829,4722],{"className":71830},[407],[363,71832,666],{"className":71833},[665],[363,71835,71837],{"className":71836},[638],[363,71838,71840],{"className":71839,"style":71259},[642],[363,71841],{},[11,71843,71844,71845,72149,72150,72201,72202,72558,72559,72201,72610,72966,72967,73096,73097,73148,73149,68565,73177,73297,73298,68565,73331,73456,73457,73148,73508,73611],{},"TV 的共轭也很干净：",[363,71846,71848,71916],{"className":71847,"translate":367},[366],[363,71849,71851],{"className":71850},[371],[373,71852,71853],{"xmlns":375},[377,71854,71855,71913],{},[380,71856,71857,71863,71865,71867,71869,71871,71887,71889,71891,71893,71895,71901,71903,71905,71907,71909,71911],{},[7161,71858,71859,71861],{},[383,71860,385],{},[458,71862,7920],{},[458,71864,461],{"stretchy":460},[383,71866,40584],{},[458,71868,468],{"stretchy":460},[458,71870,471],{},[543,71872,71873,71879],{},[380,71874,71875,71877],{},[383,71876,35779],{},[458,71878,4450],{},[380,71880,71881,71883,71885],{},[383,71882,1116],{},[458,71884,7275],{},[463,71886,474],{},[458,71888,3245],{"stretchy":460},[383,71890,40584],{},[383,71892,1116],{},[458,71894,5160],{},[586,71896,71897,71899],{},[463,71898,465],{},[463,71900,2810],{},[383,71902,5155],{"mathvariant":557},[383,71904,1116],{},[458,71906,5160],{},[463,71908,465],{},[383,71910,5155],{"mathvariant":557},[458,71912,3255],{"stretchy":460},[387,71914,71915],{"encoding":389},"f^*(y)=\\sup_{t\\ge0}\\{yt-\\frac12|t-1|\\}",[363,71917,71919,71972,72048,72137],{"className":71918,"ariaHidden":394},[393],[363,71920,71922,71925,71954,71957,71960,71963,71966,71969],{"className":71921},[398],[363,71923],{"className":71924,"style":487},[402],[363,71926,71928,71931],{"className":71927},[407],[363,71929,385],{"className":71930,"style":409},[407,408],[363,71932,71934],{"className":71933},[629],[363,71935,71937],{"className":71936},[633],[363,71938,71940],{"className":71939},[638],[363,71941,71943],{"className":71942,"style":8846},[642],[363,71944,71945,71948],{"style":7212},[363,71946],{"className":71947,"style":651},[650],[363,71949,71951],{"className":71950},[655,656,657,658],[363,71952,7920],{"className":71953},[2938,658],[363,71955,461],{"className":71956},[494],[363,71958,40584],{"className":71959,"style":1328},[407,408],[363,71961,468],{"className":71962},[501],[363,71964],{"className":71965,"style":506},[505],[363,71967,471],{"className":71968},[510],[363,71970],{"className":71971,"style":506},[505],[363,71973,71975,71979,72030,72033,72036,72039,72042,72045],{"className":71974},[398],[363,71976],{"className":71977,"style":71978},[402],"height:1.0893em;vertical-align:-0.3393em;",[363,71980,71982,71985],{"className":71981},[1831],[363,71983,35779],{"className":71984},[1831],[363,71986,71988],{"className":71987},[629],[363,71989,71991,72021],{"className":71990},[633,634],[363,71992,71994,72018],{"className":71993},[638],[363,71995,71998],{"className":71996,"style":71997},[642],"height:0.207em;",[363,71999,72000,72003],{"style":35925},[363,72001],{"className":72002,"style":651},[650],[363,72004,72006],{"className":72005},[655,656,657,658],[363,72007,72009,72012,72015],{"className":72008},[407,658],[363,72010,1116],{"className":72011},[407,408,658],[363,72013,7275],{"className":72014},[510,658],[363,72016,474],{"className":72017},[407,658],[363,72019,666],{"className":72020},[665],[363,72022,72024],{"className":72023},[638],[363,72025,72028],{"className":72026,"style":72027},[642],"height:0.3393em;",[363,72029],{},[363,72031,3245],{"className":72032},[494],[363,72034,40584],{"className":72035,"style":1328},[407,408],[363,72037,1116],{"className":72038},[407,408],[363,72040],{"className":72041,"style":2934},[505],[363,72043,5160],{"className":72044},[2938],[363,72046],{"className":72047,"style":2934},[505],[363,72049,72051,72054,72122,72125,72128,72131,72134],{"className":72050},[398],[363,72052],{"className":72053,"style":2852},[402],[363,72055,72057,72060,72119],{"className":72056},[407],[363,72058],{"className":72059},[494,789],[363,72061,72063],{"className":72062},[586],[363,72064,72066,72111],{"className":72065},[633,634],[363,72067,72069,72108],{"className":72068},[638],[363,72070,72072,72086,72094],{"className":72071,"style":2871},[642],[363,72073,72074,72077],{"style":2874},[363,72075],{"className":72076,"style":809},[650],[363,72078,72080],{"className":72079},[655,656,657,658],[363,72081,72083],{"className":72082},[407,658],[363,72084,2810],{"className":72085},[407,658],[363,72087,72088,72091],{"style":821},[363,72089],{"className":72090,"style":809},[650],[363,72092],{"className":72093,"style":829},[828],[363,72095,72096,72099],{"style":2897},[363,72097],{"className":72098,"style":809},[650],[363,72100,72102],{"className":72101},[655,656,657,658],[363,72103,72105],{"className":72104},[407,658],[363,72106,465],{"className":72107},[407,658],[363,72109,666],{"className":72110},[665],[363,72112,72114],{"className":72113},[638],[363,72115,72117],{"className":72116,"style":2919},[642],[363,72118],{},[363,72120],{"className":72121},[501,789],[363,72123,5155],{"className":72124},[407],[363,72126,1116],{"className":72127},[407,408],[363,72129],{"className":72130,"style":2934},[505],[363,72132,5160],{"className":72133},[2938],[363,72135],{"className":72136,"style":2934},[505],[363,72138,72140,72143,72146],{"className":72139},[398],[363,72141],{"className":72142,"style":487},[402],[363,72144,35026],{"className":72145},[407],[363,72147,3255],{"className":72148},[501],"。在 ",[363,72151,72153,72171],{"className":72152,"translate":367},[366],[363,72154,72156],{"className":72155},[371],[373,72157,72158],{"xmlns":375},[377,72159,72160,72168],{},[380,72161,72162,72164,72166],{},[383,72163,1116],{},[458,72165,10299],{},[463,72167,465],{},[387,72169,72170],{"encoding":389},"t\\le1",[363,72172,72174,72192],{"className":72173,"ariaHidden":394},[393],[363,72175,72177,72180,72183,72186,72189],{"className":72176},[398],[363,72178],{"className":72179,"style":43535},[402],[363,72181,1116],{"className":72182},[407,408],[363,72184],{"className":72185,"style":506},[505],[363,72187,10299],{"className":72188},[510],[363,72190],{"className":72191,"style":506},[505],[363,72193,72195,72198],{"className":72194},[398],[363,72196],{"className":72197,"style":520},[402],[363,72199,465],{"className":72200},[407]," 一侧，",[363,72203,72205,72261],{"className":72204,"translate":367},[366],[363,72206,72208],{"className":72207},[371],[373,72209,72210],{"xmlns":375},[377,72211,72212,72258],{},[380,72213,72214,72216,72218,72220,72232,72234,72236,72238,72240,72242,72248,72250,72252],{},[383,72215,40584],{},[383,72217,1116],{},[458,72219,5160],{},[586,72221,72222,72230],{},[380,72223,72224,72226,72228],{},[463,72225,465],{},[458,72227,5160],{},[383,72229,1116],{},[463,72231,2810],{},[458,72233,471],{},[383,72235,1116],{},[458,72237,461],{"stretchy":460},[383,72239,40584],{},[458,72241,2817],{},[586,72243,72244,72246],{},[463,72245,465],{},[463,72247,2810],{},[458,72249,468],{"stretchy":460},[458,72251,5160],{},[586,72253,72254,72256],{},[463,72255,465],{},[463,72257,2810],{},[387,72259,72260],{"encoding":389},"yt-\\frac{1-t}{2}=t(y+\\frac12)-\\frac12",[363,72262,72264,72285,72374,72398,72484],{"className":72263,"ariaHidden":394},[393],[363,72265,72267,72270,72273,72276,72279,72282],{"className":72266},[398],[363,72268],{"className":72269,"style":26621},[402],[363,72271,40584],{"className":72272,"style":1328},[407,408],[363,72274,1116],{"className":72275},[407,408],[363,72277],{"className":72278,"style":2934},[505],[363,72280,5160],{"className":72281},[2938],[363,72283],{"className":72284,"style":2934},[505],[363,72286,72288,72291,72365,72368,72371],{"className":72287},[398],[363,72289],{"className":72290,"style":2852},[402],[363,72292,72294,72297,72362],{"className":72293},[407],[363,72295],{"className":72296},[494,789],[363,72298,72300],{"className":72299},[586],[363,72301,72303,72354],{"className":72302},[633,634],[363,72304,72306,72351],{"className":72305},[638],[363,72307,72309,72323,72331],{"className":72308,"style":2871},[642],[363,72310,72311,72314],{"style":2874},[363,72312],{"className":72313,"style":809},[650],[363,72315,72317],{"className":72316},[655,656,657,658],[363,72318,72320],{"className":72319},[407,658],[363,72321,2810],{"className":72322},[407,658],[363,72324,72325,72328],{"style":821},[363,72326],{"className":72327,"style":809},[650],[363,72329],{"className":72330,"style":829},[828],[363,72332,72333,72336],{"style":2897},[363,72334],{"className":72335,"style":809},[650],[363,72337,72339],{"className":72338},[655,656,657,658],[363,72340,72342,72345,72348],{"className":72341},[407,658],[363,72343,465],{"className":72344},[407,658],[363,72346,5160],{"className":72347},[2938,658],[363,72349,1116],{"className":72350},[407,408,658],[363,72352,666],{"className":72353},[665],[363,72355,72357],{"className":72356},[638],[363,72358,72360],{"className":72359,"style":2919},[642],[363,72361],{},[363,72363],{"className":72364},[501,789],[363,72366],{"className":72367,"style":506},[505],[363,72369,471],{"className":72370},[510],[363,72372],{"className":72373,"style":506},[505],[363,72375,72377,72380,72383,72386,72389,72392,72395],{"className":72376},[398],[363,72378],{"className":72379,"style":487},[402],[363,72381,1116],{"className":72382},[407,408],[363,72384,461],{"className":72385},[494],[363,72387,40584],{"className":72388,"style":1328},[407,408],[363,72390],{"className":72391,"style":2934},[505],[363,72393,2817],{"className":72394},[2938],[363,72396],{"className":72397,"style":2934},[505],[363,72399,72401,72404,72472,72475,72478,72481],{"className":72400},[398],[363,72402],{"className":72403,"style":2852},[402],[363,72405,72407,72410,72469],{"className":72406},[407],[363,72408],{"className":72409},[494,789],[363,72411,72413],{"className":72412},[586],[363,72414,72416,72461],{"className":72415},[633,634],[363,72417,72419,72458],{"className":72418},[638],[363,72420,72422,72436,72444],{"className":72421,"style":2871},[642],[363,72423,72424,72427],{"style":2874},[363,72425],{"className":72426,"style":809},[650],[363,72428,72430],{"className":72429},[655,656,657,658],[363,72431,72433],{"className":72432},[407,658],[363,72434,2810],{"className":72435},[407,658],[363,72437,72438,72441],{"style":821},[363,72439],{"className":72440,"style":809},[650],[363,72442],{"className":72443,"style":829},[828],[363,72445,72446,72449],{"style":2897},[363,72447],{"className":72448,"style":809},[650],[363,72450,72452],{"className":72451},[655,656,657,658],[363,72453,72455],{"className":72454},[407,658],[363,72456,465],{"className":72457},[407,658],[363,72459,666],{"className":72460},[665],[363,72462,72464],{"className":72463},[638],[363,72465,72467],{"className":72466,"style":2919},[642],[363,72468],{},[363,72470],{"className":72471},[501,789],[363,72473,468],{"className":72474},[501],[363,72476],{"className":72477,"style":2934},[505],[363,72479,5160],{"className":72480},[2938],[363,72482],{"className":72483,"style":2934},[505],[363,72485,72487,72490],{"className":72486},[398],[363,72488],{"className":72489,"style":2852},[402],[363,72491,72493,72496,72555],{"className":72492},[407],[363,72494],{"className":72495},[494,789],[363,72497,72499],{"className":72498},[586],[363,72500,72502,72547],{"className":72501},[633,634],[363,72503,72505,72544],{"className":72504},[638],[363,72506,72508,72522,72530],{"className":72507,"style":2871},[642],[363,72509,72510,72513],{"style":2874},[363,72511],{"className":72512,"style":809},[650],[363,72514,72516],{"className":72515},[655,656,657,658],[363,72517,72519],{"className":72518},[407,658],[363,72520,2810],{"className":72521},[407,658],[363,72523,72524,72527],{"style":821},[363,72525],{"className":72526,"style":809},[650],[363,72528],{"className":72529,"style":829},[828],[363,72531,72532,72535],{"style":2897},[363,72533],{"className":72534,"style":809},[650],[363,72536,72538],{"className":72537},[655,656,657,658],[363,72539,72541],{"className":72540},[407,658],[363,72542,465],{"className":72543},[407,658],[363,72545,666],{"className":72546},[665],[363,72548,72550],{"className":72549},[638],[363,72551,72553],{"className":72552,"style":2919},[642],[363,72554],{},[363,72556],{"className":72557},[501,789],"；在 ",[363,72560,72562,72580],{"className":72561,"translate":367},[366],[363,72563,72565],{"className":72564},[371],[373,72566,72567],{"xmlns":375},[377,72568,72569,72577],{},[380,72570,72571,72573,72575],{},[383,72572,1116],{},[458,72574,7275],{},[463,72576,465],{},[387,72578,72579],{"encoding":389},"t\\ge1",[363,72581,72583,72601],{"className":72582,"ariaHidden":394},[393],[363,72584,72586,72589,72592,72595,72598],{"className":72585},[398],[363,72587],{"className":72588,"style":43535},[402],[363,72590,1116],{"className":72591},[407,408],[363,72593],{"className":72594,"style":506},[505],[363,72596,7275],{"className":72597},[510],[363,72599],{"className":72600,"style":506},[505],[363,72602,72604,72607],{"className":72603},[398],[363,72605],{"className":72606,"style":520},[402],[363,72608,465],{"className":72609},[407],[363,72611,72613,72669],{"className":72612,"translate":367},[366],[363,72614,72616],{"className":72615},[371],[373,72617,72618],{"xmlns":375},[377,72619,72620,72666],{},[380,72621,72622,72624,72626,72628,72640,72642,72644,72646,72648,72650,72656,72658,72660],{},[383,72623,40584],{},[383,72625,1116],{},[458,72627,5160],{},[586,72629,72630,72638],{},[380,72631,72632,72634,72636],{},[383,72633,1116],{},[458,72635,5160],{},[463,72637,465],{},[463,72639,2810],{},[458,72641,471],{},[383,72643,1116],{},[458,72645,461],{"stretchy":460},[383,72647,40584],{},[458,72649,5160],{},[586,72651,72652,72654],{},[463,72653,465],{},[463,72655,2810],{},[458,72657,468],{"stretchy":460},[458,72659,2817],{},[586,72661,72662,72664],{},[463,72663,465],{},[463,72665,2810],{},[387,72667,72668],{"encoding":389},"yt-\\frac{t-1}{2}=t(y-\\frac12)+\\frac12",[363,72670,72672,72693,72782,72806,72892],{"className":72671,"ariaHidden":394},[393],[363,72673,72675,72678,72681,72684,72687,72690],{"className":72674},[398],[363,72676],{"className":72677,"style":26621},[402],[363,72679,40584],{"className":72680,"style":1328},[407,408],[363,72682,1116],{"className":72683},[407,408],[363,72685],{"className":72686,"style":2934},[505],[363,72688,5160],{"className":72689},[2938],[363,72691],{"className":72692,"style":2934},[505],[363,72694,72696,72699,72773,72776,72779],{"className":72695},[398],[363,72697],{"className":72698,"style":2852},[402],[363,72700,72702,72705,72770],{"className":72701},[407],[363,72703],{"className":72704},[494,789],[363,72706,72708],{"className":72707},[586],[363,72709,72711,72762],{"className":72710},[633,634],[363,72712,72714,72759],{"className":72713},[638],[363,72715,72717,72731,72739],{"className":72716,"style":2871},[642],[363,72718,72719,72722],{"style":2874},[363,72720],{"className":72721,"style":809},[650],[363,72723,72725],{"className":72724},[655,656,657,658],[363,72726,72728],{"className":72727},[407,658],[363,72729,2810],{"className":72730},[407,658],[363,72732,72733,72736],{"style":821},[363,72734],{"className":72735,"style":809},[650],[363,72737],{"className":72738,"style":829},[828],[363,72740,72741,72744],{"style":2897},[363,72742],{"className":72743,"style":809},[650],[363,72745,72747],{"className":72746},[655,656,657,658],[363,72748,72750,72753,72756],{"className":72749},[407,658],[363,72751,1116],{"className":72752},[407,408,658],[363,72754,5160],{"className":72755},[2938,658],[363,72757,465],{"className":72758},[407,658],[363,72760,666],{"className":72761},[665],[363,72763,72765],{"className":72764},[638],[363,72766,72768],{"className":72767,"style":2919},[642],[363,72769],{},[363,72771],{"className":72772},[501,789],[363,72774],{"className":72775,"style":506},[505],[363,72777,471],{"className":72778},[510],[363,72780],{"className":72781,"style":506},[505],[363,72783,72785,72788,72791,72794,72797,72800,72803],{"className":72784},[398],[363,72786],{"className":72787,"style":487},[402],[363,72789,1116],{"className":72790},[407,408],[363,72792,461],{"className":72793},[494],[363,72795,40584],{"className":72796,"style":1328},[407,408],[363,72798],{"className":72799,"style":2934},[505],[363,72801,5160],{"className":72802},[2938],[363,72804],{"className":72805,"style":2934},[505],[363,72807,72809,72812,72880,72883,72886,72889],{"className":72808},[398],[363,72810],{"className":72811,"style":2852},[402],[363,72813,72815,72818,72877],{"className":72814},[407],[363,72816],{"className":72817},[494,789],[363,72819,72821],{"className":72820},[586],[363,72822,72824,72869],{"className":72823},[633,634],[363,72825,72827,72866],{"className":72826},[638],[363,72828,72830,72844,72852],{"className":72829,"style":2871},[642],[363,72831,72832,72835],{"style":2874},[363,72833],{"className":72834,"style":809},[650],[363,72836,72838],{"className":72837},[655,656,657,658],[363,72839,72841],{"className":72840},[407,658],[363,72842,2810],{"className":72843},[407,658],[363,72845,72846,72849],{"style":821},[363,72847],{"className":72848,"style":809},[650],[363,72850],{"className":72851,"style":829},[828],[363,72853,72854,72857],{"style":2897},[363,72855],{"className":72856,"style":809},[650],[363,72858,72860],{"className":72859},[655,656,657,658],[363,72861,72863],{"className":72862},[407,658],[363,72864,465],{"className":72865},[407,658],[363,72867,666],{"className":72868},[665],[363,72870,72872],{"className":72871},[638],[363,72873,72875],{"className":72874,"style":2919},[642],[363,72876],{},[363,72878],{"className":72879},[501,789],[363,72881,468],{"className":72882},[501],[363,72884],{"className":72885,"style":2934},[505],[363,72887,2817],{"className":72888},[2938],[363,72890],{"className":72891,"style":2934},[505],[363,72893,72895,72898],{"className":72894},[398],[363,72896],{"className":72897,"style":2852},[402],[363,72899,72901,72904,72963],{"className":72900},[407],[363,72902],{"className":72903},[494,789],[363,72905,72907],{"className":72906},[586],[363,72908,72910,72955],{"className":72909},[633,634],[363,72911,72913,72952],{"className":72912},[638],[363,72914,72916,72930,72938],{"className":72915,"style":2871},[642],[363,72917,72918,72921],{"style":2874},[363,72919],{"className":72920,"style":809},[650],[363,72922,72924],{"className":72923},[655,656,657,658],[363,72925,72927],{"className":72926},[407,658],[363,72928,2810],{"className":72929},[407,658],[363,72931,72932,72935],{"style":821},[363,72933],{"className":72934,"style":809},[650],[363,72936],{"className":72937,"style":829},[828],[363,72939,72940,72943],{"style":2897},[363,72941],{"className":72942,"style":809},[650],[363,72944,72946],{"className":72945},[655,656,657,658],[363,72947,72949],{"className":72948},[407,658],[363,72950,465],{"className":72951},[407,658],[363,72953,666],{"className":72954},[665],[363,72956,72958],{"className":72957},[638],[363,72959,72961],{"className":72960,"style":2919},[642],[363,72962],{},[363,72964],{"className":72965},[501,789],"。两段都是线性的：当 ",[363,72968,72970,72995],{"className":72969,"translate":367},[366],[363,72971,72973],{"className":72972},[371],[373,72974,72975],{"xmlns":375},[377,72976,72977,72993],{},[380,72978,72979,72981,72983,72985,72987],{},[458,72980,5155],{"stretchy":460},[383,72982,40584],{},[458,72984,5155],{"stretchy":460},[458,72986,10299],{},[586,72988,72989,72991],{},[463,72990,465],{},[463,72992,2810],{},[387,72994,66404],{"encoding":389},[363,72996,72998,73022],{"className":72997,"ariaHidden":394},[393],[363,72999,73001,73004,73007,73010,73013,73016,73019],{"className":73000},[398],[363,73002],{"className":73003,"style":487},[402],[363,73005,5155],{"className":73006},[494],[363,73008,40584],{"className":73009,"style":1328},[407,408],[363,73011,5155],{"className":73012},[501],[363,73014],{"className":73015,"style":506},[505],[363,73017,10299],{"className":73018},[510],[363,73020],{"className":73021,"style":506},[505],[363,73023,73025,73028],{"className":73024},[398],[363,73026],{"className":73027,"style":2852},[402],[363,73029,73031,73034,73093],{"className":73030},[407],[363,73032],{"className":73033},[494,789],[363,73035,73037],{"className":73036},[586],[363,73038,73040,73085],{"className":73039},[633,634],[363,73041,73043,73082],{"className":73042},[638],[363,73044,73046,73060,73068],{"className":73045,"style":2871},[642],[363,73047,73048,73051],{"style":2874},[363,73049],{"className":73050,"style":809},[650],[363,73052,73054],{"className":73053},[655,656,657,658],[363,73055,73057],{"className":73056},[407,658],[363,73058,2810],{"className":73059},[407,658],[363,73061,73062,73065],{"style":821},[363,73063],{"className":73064,"style":809},[650],[363,73066],{"className":73067,"style":829},[828],[363,73069,73070,73073],{"style":2897},[363,73071],{"className":73072,"style":809},[650],[363,73074,73076],{"className":73075},[655,656,657,658],[363,73077,73079],{"className":73078},[407,658],[363,73080,465],{"className":73081},[407,658],[363,73083,666],{"className":73084},[665],[363,73086,73088],{"className":73087},[638],[363,73089,73091],{"className":73090,"style":2919},[642],[363,73092],{},[363,73094],{"className":73095},[501,789]," 时两段的最大值都在 ",[363,73098,73100,73118],{"className":73099,"translate":367},[366],[363,73101,73103],{"className":73102},[371],[373,73104,73105],{"xmlns":375},[377,73106,73107,73115],{},[380,73108,73109,73111,73113],{},[383,73110,1116],{},[458,73112,471],{},[463,73114,465],{},[387,73116,73117],{"encoding":389},"t=1",[363,73119,73121,73139],{"className":73120,"ariaHidden":394},[393],[363,73122,73124,73127,73130,73133,73136],{"className":73123},[398],[363,73125],{"className":73126,"style":5690},[402],[363,73128,1116],{"className":73129},[407,408],[363,73131],{"className":73132,"style":506},[505],[363,73134,471],{"className":73135},[510],[363,73137],{"className":73138,"style":506},[505],[363,73140,73142,73145],{"className":73141},[398],[363,73143],{"className":73144,"style":520},[402],[363,73146,465],{"className":73147},[407]," 取到，为 ",[363,73150,73152,73165],{"className":73151,"translate":367},[366],[363,73153,73155],{"className":73154},[371],[373,73156,73157],{"xmlns":375},[377,73158,73159,73163],{},[380,73160,73161],{},[383,73162,40584],{},[387,73164,40584],{"encoding":389},[363,73166,73168],{"className":73167,"ariaHidden":394},[393],[363,73169,73171,73174],{"className":73170},[398],[363,73172],{"className":73173,"style":2623},[402],[363,73175,40584],{"className":73176,"style":1328},[407,408],[363,73178,73180,73202],{"className":73179,"translate":367},[366],[363,73181,73183],{"className":73182},[371],[373,73184,73185],{"xmlns":375},[377,73186,73187,73199],{},[380,73188,73189,73191,73193],{},[383,73190,40584],{},[458,73192,3250],{},[586,73194,73195,73197],{},[463,73196,465],{},[463,73198,2810],{},[387,73200,73201],{"encoding":389},"y>\\frac12",[363,73203,73205,73223],{"className":73204,"ariaHidden":394},[393],[363,73206,73208,73211,73214,73217,73220],{"className":73207},[398],[363,73209],{"className":73210,"style":32039},[402],[363,73212,40584],{"className":73213,"style":1328},[407,408],[363,73215],{"className":73216,"style":506},[505],[363,73218,3250],{"className":73219},[510],[363,73221],{"className":73222,"style":506},[505],[363,73224,73226,73229],{"className":73225},[398],[363,73227],{"className":73228,"style":2852},[402],[363,73230,73232,73235,73294],{"className":73231},[407],[363,73233],{"className":73234},[494,789],[363,73236,73238],{"className":73237},[586],[363,73239,73241,73286],{"className":73240},[633,634],[363,73242,73244,73283],{"className":73243},[638],[363,73245,73247,73261,73269],{"className":73246,"style":2871},[642],[363,73248,73249,73252],{"style":2874},[363,73250],{"className":73251,"style":809},[650],[363,73253,73255],{"className":73254},[655,656,657,658],[363,73256,73258],{"className":73257},[407,658],[363,73259,2810],{"className":73260},[407,658],[363,73262,73263,73266],{"style":821},[363,73264],{"className":73265,"style":809},[650],[363,73267],{"className":73268,"style":829},[828],[363,73270,73271,73274],{"style":2897},[363,73272],{"className":73273,"style":809},[650],[363,73275,73277],{"className":73276},[655,656,657,658],[363,73278,73280],{"className":73279},[407,658],[363,73281,465],{"className":73282},[407,658],[363,73284,666],{"className":73285},[665],[363,73287,73289],{"className":73288},[638],[363,73290,73292],{"className":73291,"style":2919},[642],[363,73293],{},[363,73295],{"className":73296},[501,789]," 时第二段严格递增，上确界为 ",[363,73299,73301,73316],{"className":73300,"translate":367},[366],[363,73302,73304],{"className":73303},[371],[373,73305,73306],{"xmlns":375},[377,73307,73308,73314],{},[380,73309,73310,73312],{},[458,73311,2817],{},[383,73313,1371],{"mathvariant":557},[387,73315,4588],{"encoding":389},[363,73317,73319],{"className":73318,"ariaHidden":394},[393],[363,73320,73322,73325,73328],{"className":73321},[398],[363,73323],{"className":73324,"style":4598},[402],[363,73326,2817],{"className":73327},[407],[363,73329,1371],{"className":73330},[407],[363,73332,73334,73358],{"className":73333,"translate":367},[366],[363,73335,73337],{"className":73336},[371],[373,73338,73339],{"xmlns":375},[377,73340,73341,73355],{},[380,73342,73343,73345,73347,73349],{},[383,73344,40584],{},[458,73346,7598],{},[458,73348,5160],{},[586,73350,73351,73353],{},[463,73352,465],{},[463,73354,2810],{},[387,73356,73357],{"encoding":389},"y\u003C-\\frac12",[363,73359,73361,73379],{"className":73360,"ariaHidden":394},[393],[363,73362,73364,73367,73370,73373,73376],{"className":73363},[398],[363,73365],{"className":73366,"style":32039},[402],[363,73368,40584],{"className":73369,"style":1328},[407,408],[363,73371],{"className":73372,"style":506},[505],[363,73374,7598],{"className":73375},[510],[363,73377],{"className":73378,"style":506},[505],[363,73380,73382,73385,73388],{"className":73381},[398],[363,73383],{"className":73384,"style":2852},[402],[363,73386,5160],{"className":73387},[407],[363,73389,73391,73394,73453],{"className":73390},[407],[363,73392],{"className":73393},[494,789],[363,73395,73397],{"className":73396},[586],[363,73398,73400,73445],{"className":73399},[633,634],[363,73401,73403,73442],{"className":73402},[638],[363,73404,73406,73420,73428],{"className":73405,"style":2871},[642],[363,73407,73408,73411],{"style":2874},[363,73409],{"className":73410,"style":809},[650],[363,73412,73414],{"className":73413},[655,656,657,658],[363,73415,73417],{"className":73416},[407,658],[363,73418,2810],{"className":73419},[407,658],[363,73421,73422,73425],{"style":821},[363,73423],{"className":73424,"style":809},[650],[363,73426],{"className":73427,"style":829},[828],[363,73429,73430,73433],{"style":2897},[363,73431],{"className":73432,"style":809},[650],[363,73434,73436],{"className":73435},[655,656,657,658],[363,73437,73439],{"className":73438},[407,658],[363,73440,465],{"className":73441},[407,658],[363,73443,666],{"className":73444},[665],[363,73446,73448],{"className":73447},[638],[363,73449,73451],{"className":73450,"style":2919},[642],[363,73452],{},[363,73454],{"className":73455},[501,789]," 时第一段严格递减，上确界在 ",[363,73458,73460,73478],{"className":73459,"translate":367},[366],[363,73461,73463],{"className":73462},[371],[373,73464,73465],{"xmlns":375},[377,73466,73467,73475],{},[380,73468,73469,73471,73473],{},[383,73470,1116],{},[458,73472,471],{},[463,73474,474],{},[387,73476,73477],{"encoding":389},"t=0",[363,73479,73481,73499],{"className":73480,"ariaHidden":394},[393],[363,73482,73484,73487,73490,73493,73496],{"className":73483},[398],[363,73485],{"className":73486,"style":5690},[402],[363,73488,1116],{"className":73489},[407,408],[363,73491],{"className":73492,"style":506},[505],[363,73494,471],{"className":73495},[510],[363,73497],{"className":73498,"style":506},[505],[363,73500,73502,73505],{"className":73501},[398],[363,73503],{"className":73504,"style":520},[402],[363,73506,474],{"className":73507},[407],[363,73509,73511,73531],{"className":73510,"translate":367},[366],[363,73512,73514],{"className":73513},[371],[373,73515,73516],{"xmlns":375},[377,73517,73518,73528],{},[380,73519,73520,73522],{},[458,73521,5160],{},[586,73523,73524,73526],{},[463,73525,465],{},[463,73527,2810],{},[387,73529,73530],{"encoding":389},"-\\frac12",[363,73532,73534],{"className":73533,"ariaHidden":394},[393],[363,73535,73537,73540,73543],{"className":73536},[398],[363,73538],{"className":73539,"style":2852},[402],[363,73541,5160],{"className":73542},[407],[363,73544,73546,73549,73608],{"className":73545},[407],[363,73547],{"className":73548},[494,789],[363,73550,73552],{"className":73551},[586],[363,73553,73555,73600],{"className":73554},[633,634],[363,73556,73558,73597],{"className":73557},[638],[363,73559,73561,73575,73583],{"className":73560,"style":2871},[642],[363,73562,73563,73566],{"style":2874},[363,73564],{"className":73565,"style":809},[650],[363,73567,73569],{"className":73568},[655,656,657,658],[363,73570,73572],{"className":73571},[407,658],[363,73573,2810],{"className":73574},[407,658],[363,73576,73577,73580],{"style":821},[363,73578],{"className":73579,"style":809},[650],[363,73581],{"className":73582,"style":829},[828],[363,73584,73585,73588],{"style":2897},[363,73586],{"className":73587,"style":809},[650],[363,73589,73591],{"className":73590},[655,656,657,658],[363,73592,73594],{"className":73593},[407,658],[363,73595,465],{"className":73596},[407,658],[363,73598,666],{"className":73599},[665],[363,73601,73603],{"className":73602},[638],[363,73604,73606],{"className":73605,"style":2919},[642],[363,73607],{},[363,73609],{"className":73610},[501,789],"。于是",[363,73613,73615],{"className":73614,"translate":367},[528],[363,73616,73618,73754],{"className":73617,"translate":367},[366],[363,73619,73621],{"className":73620},[371],[373,73622,73623],{"xmlns":375,"display":537},[377,73624,73625,73751],{},[380,73626,73627,73633,73635,73637,73639,73641],{},[7161,73628,73629,73631],{},[383,73630,385],{},[458,73632,7920],{},[458,73634,461],{"stretchy":460},[383,73636,40584],{},[458,73638,468],{"stretchy":460},[458,73640,471],{},[380,73642,73643,73645],{},[458,73644,3245],{"fence":394},[1590,73646,73647,73681,73719],{"rowspacing":4660,"columnalign":4661,"columnspacing":4662},[1596,73648,73649,73659],{},[1599,73650,73651],{},[1602,73652,73653],{"scriptlevel":474,"displaystyle":460},[380,73654,73655,73657],{},[383,73656,40584],{},[458,73658,898],{"separator":394},[1599,73660,73661],{},[1602,73662,73663],{"scriptlevel":474,"displaystyle":460},[380,73664,73665,73667,73669,73671,73673,73679],{},[458,73666,5155],{"stretchy":460},[383,73668,40584],{},[458,73670,5155],{"stretchy":460},[458,73672,10299],{},[586,73674,73675,73677],{},[463,73676,465],{},[463,73678,2810],{},[458,73680,898],{"separator":394},[1596,73682,73683,73699],{},[1599,73684,73685],{},[1602,73686,73687],{"scriptlevel":474,"displaystyle":460},[380,73688,73689,73691,73697],{},[458,73690,5160],{},[586,73692,73693,73695],{},[463,73694,465],{},[463,73696,2810],{},[458,73698,898],{"separator":394},[1599,73700,73701],{},[1602,73702,73703],{"scriptlevel":474,"displaystyle":460},[380,73704,73705,73707,73709,73711,73717],{},[383,73706,40584],{},[458,73708,10299],{},[458,73710,5160],{},[586,73712,73713,73715],{},[463,73714,465],{},[463,73716,2810],{},[458,73718,898],{"separator":394},[1596,73720,73721,73733],{},[1599,73722,73723],{},[1602,73724,73725],{"scriptlevel":474,"displaystyle":460},[380,73726,73727,73729,73731],{},[458,73728,2817],{},[383,73730,1371],{"mathvariant":557},[458,73732,898],{"separator":394},[1599,73734,73735],{},[1602,73736,73737],{"scriptlevel":474,"displaystyle":460},[380,73738,73739,73741,73743,73749],{},[383,73740,40584],{},[458,73742,3250],{},[586,73744,73745,73747],{},[463,73746,465],{},[463,73748,2810],{},[383,73750,4722],{"mathvariant":557},[387,73752,73753],{"encoding":389},"f^*(y)=\n\\begin{cases}\ny, & \\lvert y\\rvert\\le\\frac12,\\\\[2pt]\n-\\frac12, & y\\le-\\frac12,\\\\[2pt]\n+\\infty, & y>\\frac12.\n\\end{cases}",[363,73755,73757,73810],{"className":73756,"ariaHidden":394},[393],[363,73758,73760,73763,73792,73795,73798,73801,73804,73807],{"className":73759},[398],[363,73761],{"className":73762,"style":487},[402],[363,73764,73766,73769],{"className":73765},[407],[363,73767,385],{"className":73768,"style":409},[407,408],[363,73770,73772],{"className":73771},[629],[363,73773,73775],{"className":73774},[633],[363,73776,73778],{"className":73777},[638],[363,73779,73781],{"className":73780,"style":8595},[642],[363,73782,73783,73786],{"style":8624},[363,73784],{"className":73785,"style":651},[650],[363,73787,73789],{"className":73788},[655,656,657,658],[363,73790,7920],{"className":73791},[2938,658],[363,73793,461],{"className":73794},[494],[363,73796,40584],{"className":73797,"style":1328},[407,408],[363,73799,468],{"className":73800},[501],[363,73802],{"className":73803,"style":506},[505],[363,73805,471],{"className":73806},[510],[363,73808],{"className":73809,"style":506},[505],[363,73811,73813,73817],{"className":73812},[398],[363,73814],{"className":73815,"style":73816},[402],"height:4.8em;vertical-align:-2.15em;",[363,73818,73820,73917,74372],{"className":73819},[758],[363,73821,73823],{"className":73822},[494],[363,73824,73826],{"className":73825},[767,15176],[363,73827,73829,73908],{"className":73828},[633,634],[363,73830,73832,73905],{"className":73831},[638],[363,73833,73836,73850,73869,73881,73893],{"className":73834,"style":73835},[642],"height:2.65em;",[363,73837,73839,73842],{"style":73838},"top:-1.9em;",[363,73840],{"className":73841,"style":17935},[650],[363,73843,73847],{"className":73844},[73845,73846],"delimsizinginner","delim-size4",[363,73848,73849],{},"⎩",[363,73851,73853,73856],{"style":73852},"top:-1.892em;",[363,73854],{"className":73855,"style":17935},[650],[363,73857,73859],{"style":73858},"height:0.616em;width:0.8889em;",[6670,73860,73866],{"xmlns":6672,"width":73861,"height":73862,"style":73863,"viewBox":73864,"preserveAspectRatio":73865},"0.8889em","0.616em","width:0.8889em","0 0 888.89 616","xMinYMin",[6678,73867],{"d":73868},"M384 0 H504 V616 H384z M384 0 H504 V616 H384z",[363,73870,73872,73875],{"style":73871},"top:-3.15em;",[363,73873],{"className":73874,"style":17935},[650],[363,73876,73878],{"className":73877},[73845,73846],[363,73879,73880],{},"⎨",[363,73882,73884,73887],{"style":73883},"top:-4.292em;",[363,73885],{"className":73886,"style":17935},[650],[363,73888,73889],{"style":73858},[6670,73890,73891],{"xmlns":6672,"width":73861,"height":73862,"style":73863,"viewBox":73864,"preserveAspectRatio":73865},[6678,73892],{"d":73868},[363,73894,73896,73899],{"style":73895},"top:-4.9em;",[363,73897],{"className":73898,"style":17935},[650],[363,73900,73902],{"className":73901},[73845,73846],[363,73903,73904],{},"⎧",[363,73906,666],{"className":73907},[665],[363,73909,73911],{"className":73910},[638],[363,73912,73915],{"className":73913,"style":73914},[642],"height:2.15em;",[363,73916],{},[363,73918,73920],{"className":73919},[407],[363,73921,73923,74064,74067],{"className":73922},[1590],[363,73924,73926],{"className":73925},[1798],[363,73927,73929,74055],{"className":73928},[633,634],[363,73930,73932,74052],{"className":73931},[638],[363,73933,73936,73951,74034],{"className":73934,"style":73935},[642],"height:2.61em;",[363,73937,73939,73942],{"style":73938},"top:-4.61em;",[363,73940],{"className":73941,"style":4920},[650],[363,73943,73945,73948],{"className":73944},[407],[363,73946,40584],{"className":73947,"style":1328},[407,408],[363,73949,898],{"className":73950},[920],[363,73952,73954,73957],{"style":73953},"top:-2.97em;",[363,73955],{"className":73956,"style":4920},[650],[363,73958,73960,73963,74031],{"className":73959},[407],[363,73961,5160],{"className":73962},[407],[363,73964,73966,73969,74028],{"className":73965},[407],[363,73967],{"className":73968},[494,789],[363,73970,73972],{"className":73971},[586],[363,73973,73975,74020],{"className":73974},[633,634],[363,73976,73978,74017],{"className":73977},[638],[363,73979,73981,73995,74003],{"className":73980,"style":2871},[642],[363,73982,73983,73986],{"style":2874},[363,73984],{"className":73985,"style":809},[650],[363,73987,73989],{"className":73988},[655,656,657,658],[363,73990,73992],{"className":73991},[407,658],[363,73993,2810],{"className":73994},[407,658],[363,73996,73997,74000],{"style":821},[363,73998],{"className":73999,"style":809},[650],[363,74001],{"className":74002,"style":829},[828],[363,74004,74005,74008],{"style":2897},[363,74006],{"className":74007,"style":809},[650],[363,74009,74011],{"className":74010},[655,656,657,658],[363,74012,74014],{"className":74013},[407,658],[363,74015,465],{"className":74016},[407,658],[363,74018,666],{"className":74019},[665],[363,74021,74023],{"className":74022},[638],[363,74024,74026],{"className":74025,"style":2919},[642],[363,74027],{},[363,74029],{"className":74030},[501,789],[363,74032,898],{"className":74033},[920],[363,74035,74037,74040],{"style":74036},"top:-1.33em;",[363,74038],{"className":74039,"style":4920},[650],[363,74041,74043,74046,74049],{"className":74042},[407],[363,74044,2817],{"className":74045},[407],[363,74047,1371],{"className":74048},[407],[363,74050,898],{"className":74051},[920],[363,74053,666],{"className":74054},[665],[363,74056,74058],{"className":74057},[638],[363,74059,74062],{"className":74060,"style":74061},[642],"height:2.11em;",[363,74063],{},[363,74065],{"className":74066,"style":4969},[4968],[363,74068,74070],{"className":74069},[1798],[363,74071,74073,74364],{"className":74072},[633,634],[363,74074,74076,74361],{"className":74075},[638],[363,74077,74079,74176,74270],{"className":74078,"style":73935},[642],[363,74080,74081,74084],{"style":73938},[363,74082],{"className":74083,"style":4920},[650],[363,74085,74087,74090,74093,74096,74099,74102,74105,74173],{"className":74086},[407],[363,74088,5155],{"className":74089},[494],[363,74091,40584],{"className":74092,"style":1328},[407,408],[363,74094,5155],{"className":74095},[501],[363,74097],{"className":74098,"style":506},[505],[363,74100,10299],{"className":74101},[510],[363,74103],{"className":74104,"style":506},[505],[363,74106,74108,74111,74170],{"className":74107},[407],[363,74109],{"className":74110},[494,789],[363,74112,74114],{"className":74113},[586],[363,74115,74117,74162],{"className":74116},[633,634],[363,74118,74120,74159],{"className":74119},[638],[363,74121,74123,74137,74145],{"className":74122,"style":2871},[642],[363,74124,74125,74128],{"style":2874},[363,74126],{"className":74127,"style":809},[650],[363,74129,74131],{"className":74130},[655,656,657,658],[363,74132,74134],{"className":74133},[407,658],[363,74135,2810],{"className":74136},[407,658],[363,74138,74139,74142],{"style":821},[363,74140],{"className":74141,"style":809},[650],[363,74143],{"className":74144,"style":829},[828],[363,74146,74147,74150],{"style":2897},[363,74148],{"className":74149,"style":809},[650],[363,74151,74153],{"className":74152},[655,656,657,658],[363,74154,74156],{"className":74155},[407,658],[363,74157,465],{"className":74158},[407,658],[363,74160,666],{"className":74161},[665],[363,74163,74165],{"className":74164},[638],[363,74166,74168],{"className":74167,"style":2919},[642],[363,74169],{},[363,74171],{"className":74172},[501,789],[363,74174,898],{"className":74175},[920],[363,74177,74178,74181],{"style":73953},[363,74179],{"className":74180,"style":4920},[650],[363,74182,74184,74187,74190,74193,74196,74199,74267],{"className":74183},[407],[363,74185,40584],{"className":74186,"style":1328},[407,408],[363,74188],{"className":74189,"style":506},[505],[363,74191,10299],{"className":74192},[510],[363,74194],{"className":74195,"style":506},[505],[363,74197,5160],{"className":74198},[407],[363,74200,74202,74205,74264],{"className":74201},[407],[363,74203],{"className":74204},[494,789],[363,74206,74208],{"className":74207},[586],[363,74209,74211,74256],{"className":74210},[633,634],[363,74212,74214,74253],{"className":74213},[638],[363,74215,74217,74231,74239],{"className":74216,"style":2871},[642],[363,74218,74219,74222],{"style":2874},[363,74220],{"className":74221,"style":809},[650],[363,74223,74225],{"className":74224},[655,656,657,658],[363,74226,74228],{"className":74227},[407,658],[363,74229,2810],{"className":74230},[407,658],[363,74232,74233,74236],{"style":821},[363,74234],{"className":74235,"style":809},[650],[363,74237],{"className":74238,"style":829},[828],[363,74240,74241,74244],{"style":2897},[363,74242],{"className":74243,"style":809},[650],[363,74245,74247],{"className":74246},[655,656,657,658],[363,74248,74250],{"className":74249},[407,658],[363,74251,465],{"className":74252},[407,658],[363,74254,666],{"className":74255},[665],[363,74257,74259],{"className":74258},[638],[363,74260,74262],{"className":74261,"style":2919},[642],[363,74263],{},[363,74265],{"className":74266},[501,789],[363,74268,898],{"className":74269},[920],[363,74271,74272,74275],{"style":74036},[363,74273],{"className":74274,"style":4920},[650],[363,74276,74278,74281,74284,74287,74290,74358],{"className":74277},[407],[363,74279,40584],{"className":74280,"style":1328},[407,408],[363,74282],{"className":74283,"style":506},[505],[363,74285,3250],{"className":74286},[510],[363,74288],{"className":74289,"style":506},[505],[363,74291,74293,74296,74355],{"className":74292},[407],[363,74294],{"className":74295},[494,789],[363,74297,74299],{"className":74298},[586],[363,74300,74302,74347],{"className":74301},[633,634],[363,74303,74305,74344],{"className":74304},[638],[363,74306,74308,74322,74330],{"className":74307,"style":2871},[642],[363,74309,74310,74313],{"style":2874},[363,74311],{"className":74312,"style":809},[650],[363,74314,74316],{"className":74315},[655,656,657,658],[363,74317,74319],{"className":74318},[407,658],[363,74320,2810],{"className":74321},[407,658],[363,74323,74324,74327],{"style":821},[363,74325],{"className":74326,"style":809},[650],[363,74328],{"className":74329,"style":829},[828],[363,74331,74332,74335],{"style":2897},[363,74333],{"className":74334,"style":809},[650],[363,74336,74338],{"className":74337},[655,656,657,658],[363,74339,74341],{"className":74340},[407,658],[363,74342,465],{"className":74343},[407,658],[363,74345,666],{"className":74346},[665],[363,74348,74350],{"className":74349},[638],[363,74351,74353],{"className":74352,"style":2919},[642],[363,74354],{},[363,74356],{"className":74357},[501,789],[363,74359,4722],{"className":74360},[407],[363,74362,666],{"className":74363},[665],[363,74365,74367],{"className":74366},[638],[363,74368,74370],{"className":74369,"style":74061},[642],[363,74371],{},[363,74373],{"className":74374},[501,789],[11,74376,74377],{},"这正对应经典表示",[363,74379,74381],{"className":74380,"translate":367},[528],[363,74382,74384,74472],{"className":74383,"translate":367},[366],[363,74385,74387],{"className":74386},[371],[373,74388,74389],{"xmlns":375,"display":537},[377,74390,74391,74469],{},[380,74392,74393,74403,74405,74407,74409,74411,74413,74415,74439,74441,74447,74449,74451,74453,74455,74461,74463,74465,74467],{},[543,74394,74395,74397],{},[383,74396,547],{},[380,74398,74399,74401],{},[383,74400,5739],{},[383,74402,35197],{},[458,74404,461],{"stretchy":460},[383,74406,554],{},[458,74408,898],{"separator":394},[383,74410,561],{},[458,74412,468],{"stretchy":460},[458,74414,471],{},[6363,74416,74417,74423],{},[380,74418,74419,74421],{},[383,74420,35779],{},[458,74422,4450],{},[380,74424,74425,74427,74429,74435,74437],{},[458,74426,558],{"stretchy":460},[383,74428,4505],{},[543,74430,74431,74433],{},[458,74432,558],{"stretchy":460},[383,74434,1371],{"mathvariant":557},[458,74436,10299],{},[463,74438,465],{},[458,74440,3245],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[543,74442,74443,74445],{},[383,74444,571],{"mathvariant":570},[383,74446,554],{},[458,74448,578],{"stretchy":460},[383,74450,4505],{},[458,74452,605],{"stretchy":460},[458,74454,5160],{},[543,74456,74457,74459],{},[383,74458,571],{"mathvariant":570},[383,74460,561],{},[458,74462,578],{"stretchy":460},[383,74464,4505],{},[458,74466,605],{"stretchy":460},[458,74468,3255],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[387,74470,74471],{"encoding":389},"D_{TV}(P,Q)=\\sup_{\\lVert g\\rVert_\\infty\\le1}\n\\big\\{\\mathbb E_P[g]-\\mathbb E_Q[g]\\big\\}",[363,74473,74475,74554,74728],{"className":74474,"ariaHidden":394},[393],[363,74476,74478,74481,74527,74530,74533,74536,74539,74542,74545,74548,74551],{"className":74477},[398],[363,74479],{"className":74480,"style":487},[402],[363,74482,74484,74487],{"className":74483},[407],[363,74485,547],{"className":74486,"style":625},[407,408],[363,74488,74490],{"className":74489},[629],[363,74491,74493,74519],{"className":74492},[633,634],[363,74494,74496,74516],{"className":74495},[638],[363,74497,74499],{"className":74498,"style":727},[642],[363,74500,74501,74504],{"style":646},[363,74502],{"className":74503,"style":651},[650],[363,74505,74507],{"className":74506},[655,656,657,658],[363,74508,74510,74513],{"className":74509},[407,658],[363,74511,5739],{"className":74512,"style":682},[407,408,658],[363,74514,35197],{"className":74515,"style":2934},[407,408,658],[363,74517,666],{"className":74518},[665],[363,74520,74522],{"className":74521},[638],[363,74523,74525],{"className":74524,"style":8315},[642],[363,74526],{},[363,74528,461],{"className":74529},[494],[363,74531,554],{"className":74532,"style":682},[407,408],[363,74534,898],{"className":74535},[920],[363,74537],{"className":74538,"style":754},[505],[363,74540,561],{"className":74541},[407,408],[363,74543,468],{"className":74544},[501],[363,74546],{"className":74547,"style":506},[505],[363,74549,471],{"className":74550},[510],[363,74552],{"className":74553,"style":506},[505],[363,74555,74557,74561,74661,74664,74670,74710,74713,74716,74719,74722,74725],{"className":74556},[398],[363,74558],{"className":74559,"style":74560},[402],"height:2.0104em;vertical-align:-1.1604em;",[363,74562,74564],{"className":74563},[1831,14063],[363,74565,74567,74652],{"className":74566},[633,634],[363,74568,74570,74649],{"className":74569},[638],[363,74571,74573,74639],{"className":74572,"style":2692},[642],[363,74574,74576,74579],{"style":74575},"top:-2.1146em;margin-left:0em;",[363,74577],{"className":74578,"style":809},[650],[363,74580,74582],{"className":74581},[655,656,657,658],[363,74583,74585,74588,74591,74633,74636],{"className":74584},[407,658],[363,74586,558],{"className":74587},[494,658],[363,74589,4505],{"className":74590,"style":1328},[407,408,658],[363,74592,74594,74597],{"className":74593},[501,658],[363,74595,558],{"className":74596},[501,658],[363,74598,74600],{"className":74599},[629],[363,74601,74603,74625],{"className":74602},[633,634],[363,74604,74606,74622],{"className":74605},[638],[363,74607,74610],{"className":74608,"style":74609},[642],"height:0.1645em;",[363,74611,74613,74616],{"style":74612},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[363,74614],{"className":74615,"style":30553},[650],[363,74617,74619],{"className":74618},[655,30557,10021,658],[363,74620,1371],{"className":74621},[407,658],[363,74623,666],{"className":74624},[665],[363,74626,74628],{"className":74627},[638],[363,74629,74631],{"className":74630,"style":40117},[642],[363,74632],{},[363,74634,10299],{"className":74635},[510,658],[363,74637,465],{"className":74638},[407,658],[363,74640,74641,74644],{"style":12210},[363,74642],{"className":74643,"style":809},[650],[363,74645,74646],{},[363,74647,35779],{"className":74648},[1831],[363,74650,666],{"className":74651},[665],[363,74653,74655],{"className":74654},[638],[363,74656,74659],{"className":74657,"style":74658},[642],"height:1.1604em;",[363,74660],{},[363,74662],{"className":74663,"style":754},[505],[363,74665,74667],{"className":74666},[407],[363,74668,3245],{"className":74669},[767,10021],[363,74671,74673,74676],{"className":74672},[407],[363,74674,571],{"className":74675},[407,714],[363,74677,74679],{"className":74678},[629],[363,74680,74682,74702],{"className":74681},[633,634],[363,74683,74685,74699],{"className":74684},[638],[363,74686,74688],{"className":74687,"style":727},[642],[363,74689,74690,74693],{"style":730},[363,74691],{"className":74692,"style":651},[650],[363,74694,74696],{"className":74695},[655,656,657,658],[363,74697,554],{"className":74698,"style":682},[407,408,658],[363,74700,666],{"className":74701},[665],[363,74703,74705],{"className":74704},[638],[363,74706,74708],{"className":74707,"style":8315},[642],[363,74709],{},[363,74711,578],{"className":74712},[494],[363,74714,4505],{"className":74715,"style":1328},[407,408],[363,74717,605],{"className":74718},[501],[363,74720],{"className":74721,"style":2934},[505],[363,74723,5160],{"className":74724},[2938],[363,74726],{"className":74727,"style":2934},[505],[363,74729,74731,74734,74774,74777,74780,74783],{"className":74730},[398],[363,74732],{"className":74733,"style":20910},[402],[363,74735,74737,74740],{"className":74736},[407],[363,74738,571],{"className":74739},[407,714],[363,74741,74743],{"className":74742},[629],[363,74744,74746,74766],{"className":74745},[633,634],[363,74747,74749,74763],{"className":74748},[638],[363,74750,74752],{"className":74751,"style":727},[642],[363,74753,74754,74757],{"style":730},[363,74755],{"className":74756,"style":651},[650],[363,74758,74760],{"className":74759},[655,656,657,658],[363,74761,561],{"className":74762},[407,408,658],[363,74764,666],{"className":74765},[665],[363,74767,74769],{"className":74768},[638],[363,74770,74772],{"className":74771,"style":673},[642],[363,74773],{},[363,74775,578],{"className":74776},[494],[363,74778,4505],{"className":74779,"style":1328},[407,408],[363,74781,605],{"className":74782},[501],[363,74784,74786],{"className":74785},[407],[363,74787,3255],{"className":74788},[767,10021],[11,74790,74791],{},"的 Kantorovich 型对偶。",[11,74793,74794],{},"这个对偶表示在机器学习中非常有用，例如 f-GAN 就是基于此构造的（第 5 节详述）。",[2658,74796,74798],{"id":74797},"_45-数据处理不等式","4.5 数据处理不等式",[1340,74800,74802,74902],{"title":74801},"命题 4.4（数据处理不等式）",[11,74803,881,74804,74832,74833,5992,74867,74901],{},[363,74805,74807,74820],{"className":74806,"translate":367},[366],[363,74808,74810],{"className":74809},[371],[373,74811,74812],{"xmlns":375},[377,74813,74814,74818],{},[380,74815,74816],{},[383,74817,11041],{},[387,74819,11041],{"encoding":389},[363,74821,74823],{"className":74822,"ariaHidden":394},[393],[363,74824,74826,74829],{"className":74825},[398],[363,74827],{"className":74828,"style":1011},[402],[363,74830,11041],{"className":74831,"style":11129},[407,408]," 是一个马尔可夫核（随机变换），记 ",[363,74834,74836,74852],{"className":74835,"translate":367},[366],[363,74837,74839],{"className":74838},[371],[373,74840,74841],{"xmlns":375},[377,74842,74843,74849],{},[380,74844,74845,74847],{},[383,74846,554],{},[383,74848,11041],{},[387,74850,74851],{"encoding":389},"PK",[363,74853,74855],{"className":74854,"ariaHidden":394},[393],[363,74856,74858,74861,74864],{"className":74857},[398],[363,74859],{"className":74860,"style":1011},[402],[363,74862,554],{"className":74863,"style":682},[407,408],[363,74865,11041],{"className":74866,"style":11129},[407,408],[363,74868,74870,74886],{"className":74869,"translate":367},[366],[363,74871,74873],{"className":74872},[371],[373,74874,74875],{"xmlns":375},[377,74876,74877,74883],{},[380,74878,74879,74881],{},[383,74880,561],{},[383,74882,11041],{},[387,74884,74885],{"encoding":389},"QK",[363,74887,74889],{"className":74888,"ariaHidden":394},[393],[363,74890,74892,74895,74898],{"className":74891},[398],[363,74893],{"className":74894,"style":913},[402],[363,74896,561],{"className":74897},[407,408],[363,74899,11041],{"className":74900,"style":11129},[407,408]," 为输出分布，则",[363,74903,74905],{"className":74904,"translate":367},[528],[363,74906,74908,74960],{"className":74907,"translate":367},[366],[363,74909,74911],{"className":74910},[371],[373,74912,74913],{"xmlns":375,"display":537},[377,74914,74915,74957],{},[380,74916,74917,74923,74925,74927,74929,74931,74933,74935,74937,74939,74945,74947,74949,74951,74953,74955],{},[543,74918,74919,74921],{},[383,74920,547],{},[383,74922,385],{},[458,74924,461],{"stretchy":460},[383,74926,554],{},[383,74928,11041],{},[383,74930,558],{"mathvariant":557},[383,74932,561],{},[383,74934,11041],{},[458,74936,468],{"stretchy":460},[458,74938,10299],{},[543,74940,74941,74943],{},[383,74942,547],{},[383,74944,385],{},[458,74946,461],{"stretchy":460},[383,74948,554],{},[383,74950,558],{"mathvariant":557},[383,74952,561],{},[458,74954,468],{"stretchy":460},[383,74956,4722],{"mathvariant":557},[387,74958,74959],{"encoding":389},"D_f(PK\\|QK)\\le D_f(P\\|Q).",[363,74961,74963,75039],{"className":74962,"ariaHidden":394},[393],[363,74964,74966,74969,75009,75012,75015,75018,75021,75024,75027,75030,75033,75036],{"className":74965},[398],[363,74967],{"className":74968,"style":618},[402],[363,74970,74972,74975],{"className":74971},[407],[363,74973,547],{"className":74974,"style":625},[407,408],[363,74976,74978],{"className":74977},[629],[363,74979,74981,75001],{"className":74980},[633,634],[363,74982,74984,74998],{"className":74983},[638],[363,74985,74987],{"className":74986,"style":643},[642],[363,74988,74989,74992],{"style":646},[363,74990],{"className":74991,"style":651},[650],[363,74993,74995],{"className":74994},[655,656,657,658],[363,74996,385],{"className":74997,"style":409},[407,408,658],[363,74999,666],{"className":75000},[665],[363,75002,75004],{"className":75003},[638],[363,75005,75007],{"className":75006,"style":673},[642],[363,75008],{},[363,75010,461],{"className":75011},[494],[363,75013,554],{"className":75014,"style":682},[407,408],[363,75016,11041],{"className":75017,"style":11129},[407,408],[363,75019,558],{"className":75020},[407],[363,75022,561],{"className":75023},[407,408],[363,75025,11041],{"className":75026,"style":11129},[407,408],[363,75028,468],{"className":75029},[501],[363,75031],{"className":75032,"style":506},[505],[363,75034,10299],{"className":75035},[510],[363,75037],{"className":75038,"style":506},[505],[363,75040,75042,75045,75085,75088,75091,75094,75097,75100],{"className":75041},[398],[363,75043],{"className":75044,"style":618},[402],[363,75046,75048,75051],{"className":75047},[407],[363,75049,547],{"className":75050,"style":625},[407,408],[363,75052,75054],{"className":75053},[629],[363,75055,75057,75077],{"className":75056},[633,634],[363,75058,75060,75074],{"className":75059},[638],[363,75061,75063],{"className":75062,"style":643},[642],[363,75064,75065,75068],{"style":646},[363,75066],{"className":75067,"style":651},[650],[363,75069,75071],{"className":75070},[655,656,657,658],[363,75072,385],{"className":75073,"style":409},[407,408,658],[363,75075,666],{"className":75076},[665],[363,75078,75080],{"className":75079},[638],[363,75081,75083],{"className":75082,"style":673},[642],[363,75084],{},[363,75086,461],{"className":75087},[494],[363,75089,554],{"className":75090,"style":682},[407,408],[363,75092,558],{"className":75093},[407],[363,75095,561],{"className":75096},[407,408],[363,75098,468],{"className":75099},[501],[363,75101,4722],{"className":75102},[407],[11,75104,75105,11407,75108,3092,75164,3092,75214,56087,75300,75350,75351,75412,75413,9747],{},[1572,75106,75107],{},"证明（条件 Jensen）。",[363,75109,75111,75131],{"className":75110,"translate":367},[366],[363,75112,75114],{"className":75113},[371],[373,75115,75116],{"xmlns":375},[377,75117,75118,75128],{},[380,75119,75120,75122,75124,75126],{},[383,75121,5748],{},[458,75123,9216],{},[383,75125,561],{},[383,75127,11041],{},[387,75129,75130],{"encoding":389},"Y\\sim QK",[363,75132,75134,75152],{"className":75133,"ariaHidden":394},[393],[363,75135,75137,75140,75143,75146,75149],{"className":75136},[398],[363,75138],{"className":75139,"style":1011},[402],[363,75141,5748],{"className":75142,"style":2934},[407,408],[363,75144],{"className":75145,"style":506},[505],[363,75147,9216],{"className":75148},[510],[363,75150],{"className":75151,"style":506},[505],[363,75153,75155,75158,75161],{"className":75154},[398],[363,75156],{"className":75157,"style":913},[402],[363,75159,561],{"className":75160},[407,408],[363,75162,11041],{"className":75163,"style":11129},[407,408],[363,75165,75167,75184],{"className":75166,"translate":367},[366],[363,75168,75170],{"className":75169},[371],[373,75171,75172],{"xmlns":375},[377,75173,75174,75182],{},[380,75175,75176,75178,75180],{},[383,75177,945],{},[458,75179,9216],{},[383,75181,561],{},[387,75183,9221],{"encoding":389},[363,75185,75187,75205],{"className":75186,"ariaHidden":394},[393],[363,75188,75190,75193,75196,75199,75202],{"className":75189},[398],[363,75191],{"className":75192,"style":1011},[402],[363,75194,945],{"className":75195,"style":9234},[407,408],[363,75197],{"className":75198,"style":506},[505],[363,75200,9216],{"className":75201},[510],[363,75203],{"className":75204,"style":506},[505],[363,75206,75208,75211],{"className":75207},[398],[363,75209],{"className":75210,"style":913},[402],[363,75212,561],{"className":75213},[407,408],[363,75215,75217,75249],{"className":75216,"translate":367},[366],[363,75218,75220],{"className":75219},[371],[373,75221,75222],{"xmlns":375},[377,75223,75224,75246],{},[380,75225,75226,75228,75230,75232,75234,75236,75238,75240,75242,75244],{},[383,75227,5748],{},[383,75229,5155],{"mathvariant":557},[383,75231,945],{},[458,75233,9216],{},[383,75235,11041],{},[458,75237,461],{"stretchy":460},[458,75239,3646],{},[383,75241,5155],{"mathvariant":557},[383,75243,945],{},[458,75245,468],{"stretchy":460},[387,75247,75248],{"encoding":389},"Y|X\\sim K(\\cdot|X)",[363,75250,75252,75276],{"className":75251,"ariaHidden":394},[393],[363,75253,75255,75258,75261,75264,75267,75270,75273],{"className":75254},[398],[363,75256],{"className":75257,"style":487},[402],[363,75259,5748],{"className":75260,"style":2934},[407,408],[363,75262,5155],{"className":75263},[407],[363,75265,945],{"className":75266,"style":9234},[407,408],[363,75268],{"className":75269,"style":506},[505],[363,75271,9216],{"className":75272},[510],[363,75274],{"className":75275,"style":506},[505],[363,75277,75279,75282,75285,75288,75291,75294,75297],{"className":75278},[398],[363,75280],{"className":75281,"style":487},[402],[363,75283,11041],{"className":75284,"style":11129},[407,408],[363,75286,461],{"className":75287},[494],[363,75289,3646],{"className":75290},[407],[363,75292,5155],{"className":75293},[407],[363,75295,945],{"className":75296,"style":9234},[407,408],[363,75298,468],{"className":75299},[501],[363,75301,75303,75320],{"className":75302,"translate":367},[366],[363,75304,75306],{"className":75305},[371],[373,75307,75308],{"xmlns":375},[377,75309,75310,75318],{},[380,75311,75312,75314,75316],{},[383,75313,554],{},[458,75315,1061],{},[383,75317,561],{},[387,75319,1066],{"encoding":389},[363,75321,75323,75341],{"className":75322,"ariaHidden":394},[393],[363,75324,75326,75329,75332,75335,75338],{"className":75325},[398],[363,75327],{"className":75328,"style":1076},[402],[363,75330,554],{"className":75331,"style":682},[407,408],[363,75333],{"className":75334,"style":506},[505],[363,75336,1061],{"className":75337},[510],[363,75339],{"className":75340,"style":506},[505],[363,75342,75344,75347],{"className":75343},[398],[363,75345],{"className":75346,"style":913},[402],[363,75348,561],{"className":75349},[407,408]," 则 ",[363,75352,75354,75376],{"className":75353,"translate":367},[366],[363,75355,75357],{"className":75356},[371],[373,75358,75359],{"xmlns":375},[377,75360,75361,75373],{},[380,75362,75363,75365,75367,75369,75371],{},[383,75364,554],{},[383,75366,11041],{},[458,75368,1061],{},[383,75370,561],{},[383,75372,11041],{},[387,75374,75375],{"encoding":389},"PK\\ll QK",[363,75377,75379,75400],{"className":75378,"ariaHidden":394},[393],[363,75380,75382,75385,75388,75391,75394,75397],{"className":75381},[398],[363,75383],{"className":75384,"style":1076},[402],[363,75386,554],{"className":75387,"style":682},[407,408],[363,75389,11041],{"className":75390,"style":11129},[407,408],[363,75392],{"className":75393,"style":506},[505],[363,75395,1061],{"className":75396},[510],[363,75398],{"className":75399,"style":506},[505],[363,75401,75403,75406,75409],{"className":75402},[398],[363,75404],{"className":75405,"style":913},[402],[363,75407,561],{"className":75408},[407,408],[363,75410,11041],{"className":75411,"style":11129},[407,408],"，且对任意可测集 ",[363,75414,75416,75429],{"className":75415,"translate":367},[366],[363,75417,75419],{"className":75418},[371],[373,75420,75421],{"xmlns":375},[377,75422,75423,75427],{},[380,75424,75425],{},[383,75426,950],{},[387,75428,950],{"encoding":389},[363,75430,75432],{"className":75431,"ariaHidden":394},[393],[363,75433,75435,75438],{"className":75434},[398],[363,75436],{"className":75437,"style":1011},[402],[363,75439,950],{"className":75440},[407,408],[363,75442,75444],{"className":75443,"translate":367},[528],[363,75445,75447,75646],{"className":75446,"translate":367},[366],[363,75448,75450],{"className":75449},[371],[373,75451,75452],{"xmlns":375,"display":537},[377,75453,75454,75643],{},[1590,75455,75456,75520,75575],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,75457,75458,75474],{},[1599,75459,75460],{},[1602,75461,75462],{"scriptlevel":474,"displaystyle":394},[380,75463,75464,75466,75468,75470,75472],{},[383,75465,554],{},[383,75467,11041],{},[458,75469,461],{"stretchy":460},[383,75471,950],{},[458,75473,468],{"stretchy":460},[1599,75475,75476],{},[1602,75477,75478],{"scriptlevel":474,"displaystyle":394},[380,75479,75480,75482,75484,75486,75488,75490,75492,75494,75496,75498,75500,75502,75504,75506,75508,75510,75512,75514,75516,75518],{},[380,75481],{},[458,75483,471],{},[458,75485,1634],{},[383,75487,11041],{},[458,75489,461],{"stretchy":460},[383,75491,950],{},[383,75493,5155],{"mathvariant":557},[383,75495,1121],{},[458,75497,468],{"stretchy":460},[1644,75499,1646],{},[383,75501,1116],{},[458,75503,461],{"stretchy":460},[383,75505,1121],{},[458,75507,468],{"stretchy":460},[1644,75509,1646],{},[383,75511,592],{},[383,75513,561],{},[458,75515,461],{"stretchy":460},[383,75517,1121],{},[458,75519,468],{"stretchy":460},[1596,75521,75522,75528],{},[1599,75523,75524],{},[1602,75525,75526],{"scriptlevel":474,"displaystyle":394},[380,75527],{},[1599,75529,75530],{},[1602,75531,75532],{"scriptlevel":474,"displaystyle":394},[380,75533,75534,75536,75538,75544,75546,75548,75550,75552,75554,75556,75573],{},[380,75535],{},[458,75537,471],{},[543,75539,75540,75542],{},[383,75541,571],{"mathvariant":570},[383,75543,561],{},[458,75545,578],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,75547,1116],{},[458,75549,461],{"stretchy":460},[383,75551,945],{},[458,75553,468],{"stretchy":460},[1644,75555,1646],{},[543,75557,75558,75561],{},[463,75559,465],{"mathvariant":75560},"bold",[380,75562,75563,75565,75567,75569,75571],{},[458,75564,3245],{"stretchy":460},[383,75566,5748],{},[458,75568,6256],{},[383,75570,950],{},[458,75572,3255],{"stretchy":460},[458,75574,605],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[1596,75576,75577,75583],{},[1599,75578,75579],{},[1602,75580,75581],{"scriptlevel":474,"displaystyle":394},[380,75582],{},[1599,75584,75585],{},[1602,75586,75587],{"scriptlevel":474,"displaystyle":394},[380,75588,75589,75591,75593,75603,75605,75611,75613,75615,75617,75619,75621,75623,75625,75627,75629,75631,75633,75639,75641],{},[380,75590],{},[458,75592,471],{},[543,75594,75595,75597],{},[383,75596,571],{"mathvariant":570},[380,75598,75599,75601],{},[383,75600,561],{},[383,75602,11041],{},[458,75604,578],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[543,75606,75607,75609],{},[383,75608,571],{"mathvariant":570},[383,75610,561],{},[458,75612,578],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,75614,1116],{},[458,75616,461],{"stretchy":460},[383,75618,945],{},[458,75620,468],{"stretchy":460},[1644,75622,1646],{},[458,75624,5155],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[1644,75626,1646],{},[383,75628,5748],{},[458,75630,605],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[1644,75632,1646],{},[543,75634,75635,75637],{},[463,75636,465],{"mathvariant":75560},[383,75638,950],{},[458,75640,605],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[458,75642,898],{"separator":394},[387,75644,75645],{"encoding":389},"\\begin{aligned}\nPK(A)\n&=\\int K(A|x)\\,t(x)\\,dQ(x)\\\\[2pt]\n&=\\mathbb E_Q\\big[t(X)\\,\n\\mathbf 1_{\\{Y\\in A\\}}\\big]\\\\\n&=\\mathbb E_{QK}\\Big[\n\\mathbb E_Q\\big[t(X)\\,\\big|\\,Y\\big]\\,\n\\mathbf 1_A\\Big],\n\\end{aligned}",[363,75647,75649],{"className":75648,"ariaHidden":394},[393],[363,75650,75652,75656],{"className":75651},[398],[363,75653],{"className":75654,"style":75655},[402],"height:5.8323em;vertical-align:-2.6661em;",[363,75657,75659],{"className":75658},[407],[363,75660,75662,75729],{"className":75661},[1590],[363,75663,75665],{"className":75664},[1707],[363,75666,75668,75720],{"className":75667},[633,634],[363,75669,75671,75717],{"className":75670},[638],[363,75672,75675,75699,75708],{"className":75673,"style":75674},[642],"height:3.1661em;",[363,75676,75678,75681],{"style":75677},"top:-5.1661em;",[363,75679],{"className":75680,"style":6620},[650],[363,75682,75684,75687,75690,75693,75696],{"className":75683},[407],[363,75685,554],{"className":75686,"style":682},[407,408],[363,75688,11041],{"className":75689,"style":11129},[407,408],[363,75691,461],{"className":75692},[494],[363,75694,950],{"className":75695},[407,408],[363,75697,468],{"className":75698},[501],[363,75700,75702,75705],{"style":75701},"top:-3.1539em;",[363,75703],{"className":75704,"style":6620},[650],[363,75706],{"className":75707},[407],[363,75709,75711,75714],{"style":75710},"top:-1.3439em;",[363,75712],{"className":75713,"style":6620},[650],[363,75715],{"className":75716},[407],[363,75718,666],{"className":75719},[665],[363,75721,75723],{"className":75722},[638],[363,75724,75727],{"className":75725,"style":75726},[642],"height:2.6661em;",[363,75728],{},[363,75730,75732],{"className":75731},[1798],[363,75733,75735,76199],{"className":75734},[633,634],[363,75736,75738,76196],{"className":75737},[638],[363,75739,75741,75818,75962],{"className":75740,"style":75674},[642],[363,75742,75743,75746],{"style":75677},[363,75744],{"className":75745,"style":6620},[650],[363,75747,75749,75752,75755,75758,75761,75764,75767,75770,75773,75776,75779,75782,75785,75788,75791,75794,75797,75800,75803,75806,75809,75812,75815],{"className":75748},[407],[363,75750],{"className":75751},[407],[363,75753],{"className":75754,"style":506},[505],[363,75756,471],{"className":75757},[510],[363,75759],{"className":75760,"style":506},[505],[363,75762,1634],{"className":75763,"style":1834},[1831,1832,1833],[363,75765],{"className":75766,"style":754},[505],[363,75768,11041],{"className":75769,"style":11129},[407,408],[363,75771,461],{"className":75772},[494],[363,75774,950],{"className":75775},[407,408],[363,75777,5155],{"className":75778},[407],[363,75780,1121],{"className":75781},[407,408],[363,75783,468],{"className":75784},[501],[363,75786],{"className":75787,"style":754},[505],[363,75789,1116],{"className":75790},[407,408],[363,75792,461],{"className":75793},[494],[363,75795,1121],{"className":75796},[407,408],[363,75798,468],{"className":75799},[501],[363,75801],{"className":75802,"style":754},[505],[363,75804,592],{"className":75805},[407,408],[363,75807,561],{"className":75808},[407,408],[363,75810,461],{"className":75811},[494],[363,75813,1121],{"className":75814},[407,408],[363,75816,468],{"className":75817},[501],[363,75819,75820,75823],{"style":75701},[363,75821],{"className":75822,"style":6620},[650],[363,75824,75826,75829,75832,75835,75838,75878,75884,75887,75890,75893,75896,75899,75956],{"className":75825},[407],[363,75827],{"className":75828},[407],[363,75830],{"className":75831,"style":506},[505],[363,75833,471],{"className":75834},[510],[363,75836],{"className":75837,"style":506},[505],[363,75839,75841,75844],{"className":75840},[407],[363,75842,571],{"className":75843},[407,714],[363,75845,75847],{"className":75846},[629],[363,75848,75850,75870],{"className":75849},[633,634],[363,75851,75853,75867],{"className":75852},[638],[363,75854,75856],{"className":75855,"style":727},[642],[363,75857,75858,75861],{"style":730},[363,75859],{"className":75860,"style":651},[650],[363,75862,75864],{"className":75863},[655,656,657,658],[363,75865,561],{"className":75866},[407,408,658],[363,75868,666],{"className":75869},[665],[363,75871,75873],{"className":75872},[638],[363,75874,75876],{"className":75875,"style":673},[642],[363,75877],{},[363,75879,75881],{"className":75880},[407],[363,75882,578],{"className":75883},[767,10021],[363,75885,1116],{"className":75886},[407,408],[363,75888,461],{"className":75889},[494],[363,75891,945],{"className":75892,"style":9234},[407,408],[363,75894,468],{"className":75895},[501],[363,75897],{"className":75898,"style":754},[505],[363,75900,75902,75906],{"className":75901},[407],[363,75903,465],{"className":75904},[407,75905],"mathbf",[363,75907,75909],{"className":75908},[629],[363,75910,75912,75948],{"className":75911},[633,634],[363,75913,75915,75945],{"className":75914},[638],[363,75916,75918],{"className":75917,"style":6445},[642],[363,75919,75921,75924],{"style":75920},"top:-2.5198em;margin-left:0em;margin-right:0.05em;",[363,75922],{"className":75923,"style":651},[650],[363,75925,75927],{"className":75926},[655,656,657,658],[363,75928,75930,75933,75936,75939,75942],{"className":75929},[407,658],[363,75931,3245],{"className":75932},[494,658],[363,75934,5748],{"className":75935,"style":2934},[407,408,658],[363,75937,6256],{"className":75938},[510,658],[363,75940,950],{"className":75941},[407,408,658],[363,75943,3255],{"className":75944},[501,658],[363,75946,666],{"className":75947},[665],[363,75949,75951],{"className":75950},[638],[363,75952,75954],{"className":75953,"style":6491},[642],[363,75955],{},[363,75957,75959],{"className":75958},[407],[363,75960,605],{"className":75961},[767,10021],[363,75963,75964,75967],{"style":75710},[363,75965],{"className":75966,"style":6620},[650],[363,75968,75970,75973,75976,75979,75982,76028,76034,76074,76080,76083,76086,76089,76092,76095,76132,76135,76138,76144,76147,76187,76193],{"className":75969},[407],[363,75971],{"className":75972},[407],[363,75974],{"className":75975,"style":506},[505],[363,75977,471],{"className":75978},[510],[363,75980],{"className":75981,"style":506},[505],[363,75983,75985,75988],{"className":75984},[407],[363,75986,571],{"className":75987},[407,714],[363,75989,75991],{"className":75990},[629],[363,75992,75994,76020],{"className":75993},[633,634],[363,75995,75997,76017],{"className":75996},[638],[363,75998,76000],{"className":75999,"style":727},[642],[363,76001,76002,76005],{"style":730},[363,76003],{"className":76004,"style":651},[650],[363,76006,76008],{"className":76007},[655,656,657,658],[363,76009,76011,76014],{"className":76010},[407,658],[363,76012,561],{"className":76013},[407,408,658],[363,76015,11041],{"className":76016,"style":11129},[407,408,658],[363,76018,666],{"className":76019},[665],[363,76021,76023],{"className":76022},[638],[363,76024,76026],{"className":76025,"style":673},[642],[363,76027],{},[363,76029,76031],{"className":76030},[407],[363,76032,578],{"className":76033},[767,4067],[363,76035,76037,76040],{"className":76036},[407],[363,76038,571],{"className":76039},[407,714],[363,76041,76043],{"className":76042},[629],[363,76044,76046,76066],{"className":76045},[633,634],[363,76047,76049,76063],{"className":76048},[638],[363,76050,76052],{"className":76051,"style":727},[642],[363,76053,76054,76057],{"style":730},[363,76055],{"className":76056,"style":651},[650],[363,76058,76060],{"className":76059},[655,656,657,658],[363,76061,561],{"className":76062},[407,408,658],[363,76064,666],{"className":76065},[665],[363,76067,76069],{"className":76068},[638],[363,76070,76072],{"className":76071,"style":673},[642],[363,76073],{},[363,76075,76077],{"className":76076},[407],[363,76078,578],{"className":76079},[767,10021],[363,76081,1116],{"className":76082},[407,408],[363,76084,461],{"className":76085},[494],[363,76087,945],{"className":76088,"style":9234},[407,408],[363,76090,468],{"className":76091},[501],[363,76093],{"className":76094,"style":754},[505],[363,76096,76098],{"className":76097},[407],[363,76099,76101],{"className":76100},[767,15176],[363,76102,76104,76124],{"className":76103},[633,634],[363,76105,76107,76121],{"className":76106},[638],[363,76108,76110],{"className":76109,"style":15186},[642],[363,76111,76112,76115],{"style":15189},[363,76113],{"className":76114,"style":15193},[650],[363,76116,76117],{"style":36781},[6670,76118,76119],{"xmlns":6672,"width":35398,"height":9797,"viewBox":36784},[6678,76120],{"d":36787},[363,76122,666],{"className":76123},[665],[363,76125,76127],{"className":76126},[638],[363,76128,76130],{"className":76129,"style":15213},[642],[363,76131],{},[363,76133],{"className":76134,"style":754},[505],[363,76136,5748],{"className":76137,"style":2934},[407,408],[363,76139,76141],{"className":76140},[407],[363,76142,605],{"className":76143},[767,10021],[363,76145],{"className":76146,"style":754},[505],[363,76148,76150,76153],{"className":76149},[407],[363,76151,465],{"className":76152},[407,75905],[363,76154,76156],{"className":76155},[629],[363,76157,76159,76179],{"className":76158},[633,634],[363,76160,76162,76176],{"className":76161},[638],[363,76163,76165],{"className":76164,"style":727},[642],[363,76166,76167,76170],{"style":730},[363,76168],{"className":76169,"style":651},[650],[363,76171,76173],{"className":76172},[655,656,657,658],[363,76174,950],{"className":76175},[407,408,658],[363,76177,666],{"className":76178},[665],[363,76180,76182],{"className":76181},[638],[363,76183,76185],{"className":76184,"style":8315},[642],[363,76186],{},[363,76188,76190],{"className":76189},[407],[363,76191,605],{"className":76192},[767,4067],[363,76194,898],{"className":76195},[920],[363,76197,666],{"className":76198},[665],[363,76200,76202],{"className":76201},[638],[363,76203,76205],{"className":76204,"style":75726},[642],[363,76206],{},[11,76208,76209],{},"故",[363,76211,76213],{"className":76212,"translate":367},[528],[363,76214,76216,76311],{"className":76215,"translate":367},[366],[363,76217,76219],{"className":76218},[371],[373,76220,76221],{"xmlns":375,"display":537},[377,76222,76223,76308],{},[1590,76224,76226],{"width":76225},"100%",[1596,76227,76228,76231,76293,76295],{},[1599,76229],{"width":76230},"50%",[1599,76232,76233],{},[380,76234,76235,76253,76255,76257,76259,76261,76267,76269,76271,76273,76275,76277,76279,76281,76283,76285,76287,76289,76291],{},[586,76236,76237,76245],{},[380,76238,76239,76241,76243],{},[383,76240,592],{},[383,76242,554],{},[383,76244,11041],{},[380,76246,76247,76249,76251],{},[383,76248,592],{},[383,76250,561],{},[383,76252,11041],{},[458,76254,461],{"stretchy":460},[383,76256,40584],{},[458,76258,468],{"stretchy":460},[458,76260,471],{},[543,76262,76263,76265],{},[383,76264,571],{"mathvariant":570},[383,76266,561],{},[458,76268,578],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,76270,1116],{},[458,76272,461],{"stretchy":460},[383,76274,945],{},[458,76276,468],{"stretchy":460},[1644,76278,1646],{},[458,76280,5155],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[1644,76282,1646],{},[383,76284,5748],{},[458,76286,471],{},[383,76288,40584],{},[458,76290,605],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,76292,4722],{"mathvariant":557},[1599,76294],{"width":76230},[1599,76296,76297],{},[380,76298,76299,76301,76306],{},[1644,76300,461],{},[1602,76302,76303],{"scriptlevel":474,"displaystyle":460},[458,76304,76305],{},"⋆",[1644,76307,468],{},[387,76309,76310],{"encoding":389},"\\frac{dPK}{dQK}(y)\n=\\mathbb E_Q\\big[t(X)\\,\\big|\\,Y=y\\big].\n\\tag{$\\star$}",[363,76312,76314,76412,76531,76549],{"className":76313,"ariaHidden":394},[393],[363,76315,76317,76320,76394,76397,76400,76403,76406,76409],{"className":76316},[398],[363,76318],{"className":76319,"style":1185},[402],[363,76321,76323,76326,76391],{"className":76322},[407],[363,76324],{"className":76325},[494,789],[363,76327,76329],{"className":76328},[586],[363,76330,76332,76383],{"className":76331},[633,634],[363,76333,76335,76380],{"className":76334},[638],[363,76336,76338,76355,76363],{"className":76337,"style":802},[642],[363,76339,76340,76343],{"style":805},[363,76341],{"className":76342,"style":809},[650],[363,76344,76346,76349,76352],{"className":76345},[407],[363,76347,592],{"className":76348},[407,408],[363,76350,561],{"className":76351},[407,408],[363,76353,11041],{"className":76354,"style":11129},[407,408],[363,76356,76357,76360],{"style":821},[363,76358],{"className":76359,"style":809},[650],[363,76361],{"className":76362,"style":829},[828],[363,76364,76365,76368],{"style":832},[363,76366],{"className":76367,"style":809},[650],[363,76369,76371,76374,76377],{"className":76370},[407],[363,76372,592],{"className":76373},[407,408],[363,76375,554],{"className":76376,"style":682},[407,408],[363,76378,11041],{"className":76379,"style":11129},[407,408],[363,76381,666],{"className":76382},[665],[363,76384,76386],{"className":76385},[638],[363,76387,76389],{"className":76388,"style":854},[642],[363,76390],{},[363,76392],{"className":76393},[501,789],[363,76395,461],{"className":76396},[494],[363,76398,40584],{"className":76399,"style":1328},[407,408],[363,76401,468],{"className":76402},[501],[363,76404],{"className":76405,"style":506},[505],[363,76407,471],{"className":76408},[510],[363,76410],{"className":76411,"style":506},[505],[363,76413,76415,76418,76458,76464,76467,76470,76473,76476,76479,76516,76519,76522,76525,76528],{"className":76414},[398],[363,76416],{"className":76417,"style":20910},[402],[363,76419,76421,76424],{"className":76420},[407],[363,76422,571],{"className":76423},[407,714],[363,76425,76427],{"className":76426},[629],[363,76428,76430,76450],{"className":76429},[633,634],[363,76431,76433,76447],{"className":76432},[638],[363,76434,76436],{"className":76435,"style":727},[642],[363,76437,76438,76441],{"style":730},[363,76439],{"className":76440,"style":651},[650],[363,76442,76444],{"className":76443},[655,656,657,658],[363,76445,561],{"className":76446},[407,408,658],[363,76448,666],{"className":76449},[665],[363,76451,76453],{"className":76452},[638],[363,76454,76456],{"className":76455,"style":673},[642],[363,76457],{},[363,76459,76461],{"className":76460},[407],[363,76462,578],{"className":76463},[767,10021],[363,76465,1116],{"className":76466},[407,408],[363,76468,461],{"className":76469},[494],[363,76471,945],{"className":76472,"style":9234},[407,408],[363,76474,468],{"className":76475},[501],[363,76477],{"className":76478,"style":754},[505],[363,76480,76482],{"className":76481},[407],[363,76483,76485],{"className":76484},[767,15176],[363,76486,76488,76508],{"className":76487},[633,634],[363,76489,76491,76505],{"className":76490},[638],[363,76492,76494],{"className":76493,"style":15186},[642],[363,76495,76496,76499],{"style":15189},[363,76497],{"className":76498,"style":15193},[650],[363,76500,76501],{"style":36781},[6670,76502,76503],{"xmlns":6672,"width":35398,"height":9797,"viewBox":36784},[6678,76504],{"d":36787},[363,76506,666],{"className":76507},[665],[363,76509,76511],{"className":76510},[638],[363,76512,76514],{"className":76513,"style":15213},[642],[363,76515],{},[363,76517],{"className":76518,"style":754},[505],[363,76520,5748],{"className":76521,"style":2934},[407,408],[363,76523],{"className":76524,"style":506},[505],[363,76526,471],{"className":76527},[510],[363,76529],{"className":76530,"style":506},[505],[363,76532,76534,76537,76540,76546],{"className":76533},[398],[363,76535],{"className":76536,"style":20910},[402],[363,76538,40584],{"className":76539,"style":1328},[407,408],[363,76541,76543],{"className":76542},[407],[363,76544,605],{"className":76545},[767,10021],[363,76547,4722],{"className":76548},[407],[363,76550,76553,76556],{"className":76551},[76552],"tag",[363,76554],{"className":76555,"style":1185},[402],[363,76557,76559,76562,76568],{"className":76558},[407,4945],[363,76560,461],{"className":76561},[407],[363,76563,76565],{"className":76564},[407],[363,76566,76305],{"className":76567},[407],[363,76569,468],{"className":76570},[407],[11,76572,76573,76574,76602],{},"由 ",[363,76575,76577,76590],{"className":76576,"translate":367},[366],[363,76578,76580],{"className":76579},[371],[373,76581,76582],{"xmlns":375},[377,76583,76584,76588],{},[380,76585,76586],{},[383,76587,385],{},[387,76589,385],{"encoding":389},[363,76591,76593],{"className":76592,"ariaHidden":394},[393],[363,76594,76596,76599],{"className":76595},[398],[363,76597],{"className":76598,"style":403},[402],[363,76600,385],{"className":76601,"style":409},[407,408]," 凸及条件 Jensen：",[363,76604,76606],{"className":76605,"translate":367},[528],[363,76607,76609,76721],{"className":76608,"translate":367},[366],[363,76610,76612],{"className":76611},[371],[373,76613,76614],{"xmlns":375,"display":537},[377,76615,76616,76718],{},[380,76617,76618,76620,76622,76652,76654,76656,76658,76664,76666,76668,76670,76672,76674,76676,76678,76680,76682,76684,76686,76692,76694,76696,76698,76700,76702,76704,76706,76708,76710,76712,76714,76716],{},[383,76619,385],{},[1644,76621,1651],{},[380,76623,76624,76626,76644,76646,76648,76650],{},[458,76625,461],{"fence":394},[586,76627,76628,76636],{},[380,76629,76630,76632,76634],{},[383,76631,592],{},[383,76633,554],{},[383,76635,11041],{},[380,76637,76638,76640,76642],{},[383,76639,592],{},[383,76641,561],{},[383,76643,11041],{},[458,76645,461],{"stretchy":460},[383,76647,40584],{},[458,76649,468],{"stretchy":460},[458,76651,468],{"fence":394},[458,76653,471],{},[383,76655,385],{},[458,76657,461],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[543,76659,76660,76662],{},[383,76661,571],{"mathvariant":570},[383,76663,561],{},[458,76665,578],{"stretchy":460},[383,76667,1116],{},[1644,76669,1646],{},[383,76671,5155],{"mathvariant":557},[1644,76673,1646],{},[383,76675,5748],{},[458,76677,471],{},[383,76679,40584],{},[458,76681,605],{"stretchy":460},[458,76683,468],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[458,76685,10299],{},[543,76687,76688,76690],{},[383,76689,571],{"mathvariant":570},[383,76691,561],{},[458,76693,578],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,76695,385],{},[458,76697,461],{"stretchy":460},[383,76699,1116],{},[458,76701,468],{"stretchy":460},[1644,76703,1646],{},[458,76705,5155],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[1644,76707,1646],{},[383,76709,5748],{},[458,76711,471],{},[383,76713,40584],{},[458,76715,605],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,76717,4722],{"mathvariant":557},[387,76719,76720],{"encoding":389},"f\\!\\left(\\frac{dPK}{dQK}(y)\\right)\n=f\\Big(\\mathbb E_Q[t\\,|\\,Y=y]\\Big)\n\\le \\mathbb E_Q\\big[f(t)\\,\\big|\\,Y=y\\big].",[363,76722,76724,76846,76928,76955,77074],{"className":76723,"ariaHidden":394},[393],[363,76725,76727,76730,76733,76736,76739,76837,76840,76843],{"className":76726},[398],[363,76728],{"className":76729,"style":707},[402],[363,76731,385],{"className":76732,"style":409},[407,408],[363,76734],{"className":76735,"style":1859},[505],[363,76737],{"className":76738,"style":754},[505],[363,76740,76742,76748,76822,76825,76828,76831],{"className":76741},[758],[363,76743,76745],{"className":76744,"style":763},[494,762],[363,76746,461],{"className":76747},[767,657],[363,76749,76751,76754,76819],{"className":76750},[407],[363,76752],{"className":76753},[494,789],[363,76755,76757],{"className":76756},[586],[363,76758,76760,76811],{"className":76759},[633,634],[363,76761,76763,76808],{"className":76762},[638],[363,76764,76766,76783,76791],{"className":76765,"style":802},[642],[363,76767,76768,76771],{"style":805},[363,76769],{"className":76770,"style":809},[650],[363,76772,76774,76777,76780],{"className":76773},[407],[363,76775,592],{"className":76776},[407,408],[363,76778,561],{"className":76779},[407,408],[363,76781,11041],{"className":76782,"style":11129},[407,408],[363,76784,76785,76788],{"style":821},[363,76786],{"className":76787,"style":809},[650],[363,76789],{"className":76790,"style":829},[828],[363,76792,76793,76796],{"style":832},[363,76794],{"className":76795,"style":809},[650],[363,76797,76799,76802,76805],{"className":76798},[407],[363,76800,592],{"className":76801},[407,408],[363,76803,554],{"className":76804,"style":682},[407,408],[363,76806,11041],{"className":76807,"style":11129},[407,408],[363,76809,666],{"className":76810},[665],[363,76812,76814],{"className":76813},[638],[363,76815,76817],{"className":76816,"style":854},[642],[363,76818],{},[363,76820],{"className":76821},[501,789],[363,76823,461],{"className":76824},[494],[363,76826,40584],{"className":76827,"style":1328},[407,408],[363,76829,468],{"className":76830},[501],[363,76832,76834],{"className":76833,"style":763},[501,762],[363,76835,468],{"className":76836},[767,657],[363,76838],{"className":76839,"style":506},[505],[363,76841,471],{"className":76842},[510],[363,76844],{"className":76845,"style":506},[505],[363,76847,76849,76852,76855,76861,76901,76904,76907,76910,76913,76916,76919,76922,76925],{"className":76848},[398],[363,76850],{"className":76851,"style":68464},[402],[363,76853,385],{"className":76854,"style":409},[407,408],[363,76856,76858],{"className":76857},[407],[363,76859,461],{"className":76860},[767,4067],[363,76862,76864,76867],{"className":76863},[407],[363,76865,571],{"className":76866},[407,714],[363,76868,76870],{"className":76869},[629],[363,76871,76873,76893],{"className":76872},[633,634],[363,76874,76876,76890],{"className":76875},[638],[363,76877,76879],{"className":76878,"style":727},[642],[363,76880,76881,76884],{"style":730},[363,76882],{"className":76883,"style":651},[650],[363,76885,76887],{"className":76886},[655,656,657,658],[363,76888,561],{"className":76889},[407,408,658],[363,76891,666],{"className":76892},[665],[363,76894,76896],{"className":76895},[638],[363,76897,76899],{"className":76898,"style":673},[642],[363,76900],{},[363,76902,578],{"className":76903},[494],[363,76905,1116],{"className":76906},[407,408],[363,76908],{"className":76909,"style":754},[505],[363,76911,5155],{"className":76912},[407],[363,76914],{"className":76915,"style":754},[505],[363,76917,5748],{"className":76918,"style":2934},[407,408],[363,76920],{"className":76921,"style":506},[505],[363,76923,471],{"className":76924},[510],[363,76926],{"className":76927,"style":506},[505],[363,76929,76931,76934,76937,76940,76946,76949,76952],{"className":76930},[398],[363,76932],{"className":76933,"style":68464},[402],[363,76935,40584],{"className":76936,"style":1328},[407,408],[363,76938,605],{"className":76939},[501],[363,76941,76943],{"className":76942},[407],[363,76944,468],{"className":76945},[767,4067],[363,76947],{"className":76948,"style":506},[505],[363,76950,10299],{"className":76951},[510],[363,76953],{"className":76954,"style":506},[505],[363,76956,76958,76961,77001,77007,77010,77013,77016,77019,77022,77059,77062,77065,77068,77071],{"className":76957},[398],[363,76959],{"className":76960,"style":20910},[402],[363,76962,76964,76967],{"className":76963},[407],[363,76965,571],{"className":76966},[407,714],[363,76968,76970],{"className":76969},[629],[363,76971,76973,76993],{"className":76972},[633,634],[363,76974,76976,76990],{"className":76975},[638],[363,76977,76979],{"className":76978,"style":727},[642],[363,76980,76981,76984],{"style":730},[363,76982],{"className":76983,"style":651},[650],[363,76985,76987],{"className":76986},[655,656,657,658],[363,76988,561],{"className":76989},[407,408,658],[363,76991,666],{"className":76992},[665],[363,76994,76996],{"className":76995},[638],[363,76997,76999],{"className":76998,"style":673},[642],[363,77000],{},[363,77002,77004],{"className":77003},[407],[363,77005,578],{"className":77006},[767,10021],[363,77008,385],{"className":77009,"style":409},[407,408],[363,77011,461],{"className":77012},[494],[363,77014,1116],{"className":77015},[407,408],[363,77017,468],{"className":77018},[501],[363,77020],{"className":77021,"style":754},[505],[363,77023,77025],{"className":77024},[407],[363,77026,77028],{"className":77027},[767,15176],[363,77029,77031,77051],{"className":77030},[633,634],[363,77032,77034,77048],{"className":77033},[638],[363,77035,77037],{"className":77036,"style":15186},[642],[363,77038,77039,77042],{"style":15189},[363,77040],{"className":77041,"style":15193},[650],[363,77043,77044],{"style":36781},[6670,77045,77046],{"xmlns":6672,"width":35398,"height":9797,"viewBox":36784},[6678,77047],{"d":36787},[363,77049,666],{"className":77050},[665],[363,77052,77054],{"className":77053},[638],[363,77055,77057],{"className":77056,"style":15213},[642],[363,77058],{},[363,77060],{"className":77061,"style":754},[505],[363,77063,5748],{"className":77064,"style":2934},[407,408],[363,77066],{"className":77067,"style":506},[505],[363,77069,471],{"className":77070},[510],[363,77072],{"className":77073,"style":506},[505],[363,77075,77077,77080,77083,77089],{"className":77076},[398],[363,77078],{"className":77079,"style":20910},[402],[363,77081,40584],{"className":77082,"style":1328},[407,408],[363,77084,77086],{"className":77085},[407],[363,77087,605],{"className":77088},[767,10021],[363,77090,4722],{"className":77091},[407],[11,77093,14608,77094,1015,77122,62300],{},[363,77095,77097,77110],{"className":77096,"translate":367},[366],[363,77098,77100],{"className":77099},[371],[373,77101,77102],{"xmlns":375},[377,77103,77104,77108],{},[380,77105,77106],{},[383,77107,40584],{},[387,77109,40584],{"encoding":389},[363,77111,77113],{"className":77112,"ariaHidden":394},[393],[363,77114,77116,77119],{"className":77115},[398],[363,77117],{"className":77118,"style":2623},[402],[363,77120,40584],{"className":77121,"style":1328},[407,408],[363,77123,77125,77140],{"className":77124,"translate":367},[366],[363,77126,77128],{"className":77127},[371],[373,77129,77130],{"xmlns":375},[377,77131,77132,77138],{},[380,77133,77134,77136],{},[383,77135,561],{},[383,77137,11041],{},[387,77139,74885],{"encoding":389},[363,77141,77143],{"className":77142,"ariaHidden":394},[393],[363,77144,77146,77149,77152],{"className":77145},[398],[363,77147],{"className":77148,"style":913},[402],[363,77150,561],{"className":77151},[407,408],[363,77153,11041],{"className":77154,"style":11129},[407,408],[363,77156,77158],{"className":77157,"translate":367},[528],[363,77159,77161,77361],{"className":77160,"translate":367},[366],[363,77162,77164],{"className":77163},[371],[373,77165,77166],{"xmlns":375,"display":537},[377,77167,77168,77358],{},[1590,77169,77170,77244,77298],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,77171,77172,77198],{},[1599,77173,77174],{},[1602,77175,77176],{"scriptlevel":474,"displaystyle":394},[380,77177,77178,77184,77186,77188,77190,77192,77194,77196],{},[543,77179,77180,77182],{},[383,77181,547],{},[383,77183,385],{},[458,77185,461],{"stretchy":460},[383,77187,554],{},[383,77189,11041],{},[383,77191,558],{"mathvariant":557},[383,77193,561],{},[383,77195,11041],{},[458,77197,468],{"stretchy":460},[1599,77199,77200],{},[1602,77201,77202],{"scriptlevel":474,"displaystyle":394},[380,77203,77204,77206,77208,77218,77220,77222,77224,77230,77232,77234,77236,77238,77240,77242],{},[380,77205],{},[458,77207,471],{},[543,77209,77210,77212],{},[383,77211,571],{"mathvariant":570},[380,77213,77214,77216],{},[383,77215,561],{},[383,77217,11041],{},[458,77219,578],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[383,77221,385],{},[458,77223,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[543,77225,77226,77228],{},[383,77227,571],{"mathvariant":570},[383,77229,561],{},[458,77231,578],{"stretchy":460},[383,77233,1116],{},[383,77235,5155],{"mathvariant":557},[383,77237,5748],{},[458,77239,605],{"stretchy":460},[458,77241,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,77243,605],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[1596,77245,77246,77252],{},[1599,77247,77248],{},[1602,77249,77250],{"scriptlevel":474,"displaystyle":394},[380,77251],{},[1599,77253,77254],{},[1602,77255,77256],{"scriptlevel":474,"displaystyle":394},[380,77257,77258,77260,77262,77272,77274,77280,77282,77284,77286,77288,77290,77292,77294,77296],{},[380,77259],{},[458,77261,10299],{},[543,77263,77264,77266],{},[383,77265,571],{"mathvariant":570},[380,77267,77268,77270],{},[383,77269,561],{},[383,77271,11041],{},[458,77273,578],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[543,77275,77276,77278],{},[383,77277,571],{"mathvariant":570},[383,77279,561],{},[458,77281,578],{"stretchy":460},[383,77283,385],{},[458,77285,461],{"stretchy":460},[383,77287,1116],{},[458,77289,468],{"stretchy":460},[383,77291,5155],{"mathvariant":557},[383,77293,5748],{},[458,77295,605],{"stretchy":460},[458,77297,605],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[1596,77299,77300,77306],{},[1599,77301,77302],{},[1602,77303,77304],{"scriptlevel":474,"displaystyle":394},[380,77305],{},[1599,77307,77308],{},[1602,77309,77310],{"scriptlevel":474,"displaystyle":394},[380,77311,77312,77314,77316,77322,77324,77326,77328,77330,77332,77334,77336,77342,77344,77346,77348,77350,77352,77354,77356],{},[380,77313],{},[458,77315,471],{},[543,77317,77318,77320],{},[383,77319,571],{"mathvariant":570},[383,77321,561],{},[458,77323,578],{"stretchy":460},[383,77325,385],{},[458,77327,461],{"stretchy":460},[383,77329,1116],{},[458,77331,468],{"stretchy":460},[458,77333,605],{"stretchy":460},[458,77335,471],{},[543,77337,77338,77340],{},[383,77339,547],{},[383,77341,385],{},[458,77343,461],{"stretchy":460},[383,77345,554],{},[383,77347,558],{"mathvariant":557},[383,77349,561],{},[458,77351,468],{"stretchy":460},[383,77353,4722],{"mathvariant":557},[505,77355],{"width":3609},[383,77357,59599],{"mathvariant":557},[387,77359,77360],{"encoding":389},"\\begin{aligned}\nD_f(PK\\|QK)\n&=\\mathbb E_{QK}\\Big[\nf\\big(\\mathbb E_Q[t|Y]\\big)\\Big]\\\\\n&\\le \\mathbb E_{QK}\\Big[\n\\mathbb E_Q[f(t)|Y]\\Big]\\\\\n&=\\mathbb E_Q[f(t)]=D_f(P\\|Q).\\qquad\\square\n\\end{aligned}",[363,77362,77364],{"className":77363,"ariaHidden":394},[393],[363,77365,77367,77371],{"className":77366},[398],[363,77368],{"className":77369,"style":77370},[402],"height:5.4em;vertical-align:-2.45em;",[363,77372,77374],{"className":77373},[407],[363,77375,77377,77489],{"className":77376},[1590],[363,77378,77380],{"className":77379},[1707],[363,77381,77383,77480],{"className":77382},[633,634],[363,77384,77386,77477],{"className":77385},[638],[363,77387,77390,77460,77468],{"className":77388,"style":77389},[642],"height:2.95em;",[363,77391,77393,77396],{"style":77392},"top:-4.95em;",[363,77394],{"className":77395,"style":17935},[650],[363,77397,77399,77439,77442,77445,77448,77451,77454,77457],{"className":77398},[407],[363,77400,77402,77405],{"className":77401},[407],[363,77403,547],{"className":77404,"style":625},[407,408],[363,77406,77408],{"className":77407},[629],[363,77409,77411,77431],{"className":77410},[633,634],[363,77412,77414,77428],{"className":77413},[638],[363,77415,77417],{"className":77416,"style":643},[642],[363,77418,77419,77422],{"style":646},[363,77420],{"className":77421,"style":651},[650],[363,77423,77425],{"className":77424},[655,656,657,658],[363,77426,385],{"className":77427,"style":409},[407,408,658],[363,77429,666],{"className":77430},[665],[363,77432,77434],{"className":77433},[638],[363,77435,77437],{"className":77436,"style":673},[642],[363,77438],{},[363,77440,461],{"className":77441},[494],[363,77443,554],{"className":77444,"style":682},[407,408],[363,77446,11041],{"className":77447,"style":11129},[407,408],[363,77449,558],{"className":77450},[407],[363,77452,561],{"className":77453},[407,408],[363,77455,11041],{"className":77456,"style":11129},[407,408],[363,77458,468],{"className":77459},[501],[363,77461,77462,77465],{"style":15189},[363,77463],{"className":77464,"style":17935},[650],[363,77466],{"className":77467},[407],[363,77469,77471,77474],{"style":77470},"top:-1.06em;",[363,77472],{"className":77473,"style":17935},[650],[363,77475],{"className":77476},[407],[363,77478,666],{"className":77479},[665],[363,77481,77483],{"className":77482},[638],[363,77484,77487],{"className":77485,"style":77486},[642],"height:2.45em;",[363,77488],{},[363,77490,77492],{"className":77491},[1798],[363,77493,77495,77942],{"className":77494},[633,634],[363,77496,77498,77939],{"className":77497},[638],[363,77499,77501,77649,77791],{"className":77500,"style":77389},[642],[363,77502,77503,77506],{"style":77392},[363,77504],{"className":77505,"style":17935},[650],[363,77507,77509,77512,77515,77518,77521,77567,77573,77576,77582,77622,77625,77628,77631,77634,77637,77643],{"className":77508},[407],[363,77510],{"className":77511},[407],[363,77513],{"className":77514,"style":506},[505],[363,77516,471],{"className":77517},[510],[363,77519],{"className":77520,"style":506},[505],[363,77522,77524,77527],{"className":77523},[407],[363,77525,571],{"className":77526},[407,714],[363,77528,77530],{"className":77529},[629],[363,77531,77533,77559],{"className":77532},[633,634],[363,77534,77536,77556],{"className":77535},[638],[363,77537,77539],{"className":77538,"style":727},[642],[363,77540,77541,77544],{"style":730},[363,77542],{"className":77543,"style":651},[650],[363,77545,77547],{"className":77546},[655,656,657,658],[363,77548,77550,77553],{"className":77549},[407,658],[363,77551,561],{"className":77552},[407,408,658],[363,77554,11041],{"className":77555,"style":11129},[407,408,658],[363,77557,666],{"className":77558},[665],[363,77560,77562],{"className":77561},[638],[363,77563,77565],{"className":77564,"style":673},[642],[363,77566],{},[363,77568,77570],{"className":77569},[407],[363,77571,578],{"className":77572},[767,4067],[363,77574,385],{"className":77575,"style":409},[407,408],[363,77577,77579],{"className":77578},[407],[363,77580,461],{"className":77581},[767,10021],[363,77583,77585,77588],{"className":77584},[407],[363,77586,571],{"className":77587},[407,714],[363,77589,77591],{"className":77590},[629],[363,77592,77594,77614],{"className":77593},[633,634],[363,77595,77597,77611],{"className":77596},[638],[363,77598,77600],{"className":77599,"style":727},[642],[363,77601,77602,77605],{"style":730},[363,77603],{"className":77604,"style":651},[650],[363,77606,77608],{"className":77607},[655,656,657,658],[363,77609,561],{"className":77610},[407,408,658],[363,77612,666],{"className":77613},[665],[363,77615,77617],{"className":77616},[638],[363,77618,77620],{"className":77619,"style":673},[642],[363,77621],{},[363,77623,578],{"className":77624},[494],[363,77626,1116],{"className":77627},[407,408],[363,77629,5155],{"className":77630},[407],[363,77632,5748],{"className":77633,"style":2934},[407,408],[363,77635,605],{"className":77636},[501],[363,77638,77640],{"className":77639},[407],[363,77641,468],{"className":77642},[767,10021],[363,77644,77646],{"className":77645},[407],[363,77647,605],{"className":77648},[767,4067],[363,77650,77651,77654],{"style":15189},[363,77652],{"className":77653,"style":17935},[650],[363,77655,77657,77660,77663,77666,77669,77715,77721,77761,77764,77767,77770,77773,77776,77779,77782,77785],{"className":77656},[407],[363,77658],{"className":77659},[407],[363,77661],{"className":77662,"style":506},[505],[363,77664,10299],{"className":77665},[510],[363,77667],{"className":77668,"style":506},[505],[363,77670,77672,77675],{"className":77671},[407],[363,77673,571],{"className":77674},[407,714],[363,77676,77678],{"className":77677},[629],[363,77679,77681,77707],{"className":77680},[633,634],[363,77682,77684,77704],{"className":77683},[638],[363,77685,77687],{"className":77686,"style":727},[642],[363,77688,77689,77692],{"style":730},[363,77690],{"className":77691,"style":651},[650],[363,77693,77695],{"className":77694},[655,656,657,658],[363,77696,77698,77701],{"className":77697},[407,658],[363,77699,561],{"className":77700},[407,408,658],[363,77702,11041],{"className":77703,"style":11129},[407,408,658],[363,77705,666],{"className":77706},[665],[363,77708,77710],{"className":77709},[638],[363,77711,77713],{"className":77712,"style":673},[642],[363,77714],{},[363,77716,77718],{"className":77717},[407],[363,77719,578],{"className":77720},[767,4067],[363,77722,77724,77727],{"className":77723},[407],[363,77725,571],{"className":77726},[407,714],[363,77728,77730],{"className":77729},[629],[363,77731,77733,77753],{"className":77732},[633,634],[363,77734,77736,77750],{"className":77735},[638],[363,77737,77739],{"className":77738,"style":727},[642],[363,77740,77741,77744],{"style":730},[363,77742],{"className":77743,"style":651},[650],[363,77745,77747],{"className":77746},[655,656,657,658],[363,77748,561],{"className":77749},[407,408,658],[363,77751,666],{"className":77752},[665],[363,77754,77756],{"className":77755},[638],[363,77757,77759],{"className":77758,"style":673},[642],[363,77760],{},[363,77762,578],{"className":77763},[494],[363,77765,385],{"className":77766,"style":409},[407,408],[363,77768,461],{"className":77769},[494],[363,77771,1116],{"className":77772},[407,408],[363,77774,468],{"className":77775},[501],[363,77777,5155],{"className":77778},[407],[363,77780,5748],{"className":77781,"style":2934},[407,408],[363,77783,605],{"className":77784},[501],[363,77786,77788],{"className":77787},[407],[363,77789,605],{"className":77790},[767,4067],[363,77792,77793,77796],{"style":77470},[363,77794],{"className":77795,"style":17935},[650],[363,77797,77799,77802,77805,77808,77811,77851,77854,77857,77860,77863,77866,77869,77872,77875,77915,77918,77921,77924,77927,77930,77933,77936],{"className":77798},[407],[363,77800],{"className":77801},[407],[363,77803],{"className":77804,"style":506},[505],[363,77806,471],{"className":77807},[510],[363,77809],{"className":77810,"style":506},[505],[363,77812,77814,77817],{"className":77813},[407],[363,77815,571],{"className":77816},[407,714],[363,77818,77820],{"className":77819},[629],[363,77821,77823,77843],{"className":77822},[633,634],[363,77824,77826,77840],{"className":77825},[638],[363,77827,77829],{"className":77828,"style":727},[642],[363,77830,77831,77834],{"style":730},[363,77832],{"className":77833,"style":651},[650],[363,77835,77837],{"className":77836},[655,656,657,658],[363,77838,561],{"className":77839},[407,408,658],[363,77841,666],{"className":77842},[665],[363,77844,77846],{"className":77845},[638],[363,77847,77849],{"className":77848,"style":673},[642],[363,77850],{},[363,77852,578],{"className":77853},[494],[363,77855,385],{"className":77856,"style":409},[407,408],[363,77858,461],{"className":77859},[494],[363,77861,1116],{"className":77862},[407,408],[363,77864,20737],{"className":77865},[501],[363,77867],{"className":77868,"style":506},[505],[363,77870,471],{"className":77871},[510],[363,77873],{"className":77874,"style":506},[505],[363,77876,77878,77881],{"className":77877},[407],[363,77879,547],{"className":77880,"style":625},[407,408],[363,77882,77884],{"className":77883},[629],[363,77885,77887,77907],{"className":77886},[633,634],[363,77888,77890,77904],{"className":77889},[638],[363,77891,77893],{"className":77892,"style":643},[642],[363,77894,77895,77898],{"style":646},[363,77896],{"className":77897,"style":651},[650],[363,77899,77901],{"className":77900},[655,656,657,658],[363,77902,385],{"className":77903,"style":409},[407,408,658],[363,77905,666],{"className":77906},[665],[363,77908,77910],{"className":77909},[638],[363,77911,77913],{"className":77912,"style":673},[642],[363,77914],{},[363,77916,461],{"className":77917},[494],[363,77919,554],{"className":77920,"style":682},[407,408],[363,77922,558],{"className":77923},[407],[363,77925,561],{"className":77926},[407,408],[363,77928,468],{"className":77929},[501],[363,77931,4722],{"className":77932},[407],[363,77934],{"className":77935,"style":3981},[505],[363,77937,59599],{"className":77938},[407,60141],[363,77940,666],{"className":77941},[665],[363,77943,77945],{"className":77944},[638],[363,77946,77948],{"className":77947,"style":77486},[642],[363,77949],{},[11,77951,77952,77955,77956,77984,77985,78080,78081,78125,78126,78154,78155,78225,78226,78254,78255,78283,78284,34172,78325,78328],{},[1572,77953,77954],{},"等号条件。"," 若 ",[363,77957,77959,77972],{"className":77958,"translate":367},[366],[363,77960,77962],{"className":77961},[371],[373,77963,77964],{"xmlns":375},[377,77965,77966,77970],{},[380,77967,77968],{},[383,77969,385],{},[387,77971,385],{"encoding":389},[363,77973,77975],{"className":77974,"ariaHidden":394},[393],[363,77976,77978,77981],{"className":77977},[398],[363,77979],{"className":77980,"style":403},[402],[363,77982,385],{"className":77983,"style":409},[407,408]," 严格凸，等号成立当且仅当 ",[363,77986,77988,78016],{"className":77987,"translate":367},[366],[363,77989,77991],{"className":77990},[371],[373,77992,77993],{"xmlns":375},[377,77994,77995,78013],{},[380,77996,77997,78003,78005,78007,78009,78011],{},[543,77998,77999,78001],{},[383,78000,571],{"mathvariant":570},[383,78002,561],{},[458,78004,578],{"stretchy":460},[383,78006,1116],{},[383,78008,5155],{"mathvariant":557},[383,78010,5748],{},[458,78012,605],{"stretchy":460},[387,78014,78015],{"encoding":389},"\\mathbb E_Q[t|Y]",[363,78017,78019],{"className":78018,"ariaHidden":394},[393],[363,78020,78022,78025,78065,78068,78071,78074,78077],{"className":78021},[398],[363,78023],{"className":78024,"style":618},[402],[363,78026,78028,78031],{"className":78027},[407],[363,78029,571],{"className":78030},[407,714],[363,78032,78034],{"className":78033},[629],[363,78035,78037,78057],{"className":78036},[633,634],[363,78038,78040,78054],{"className":78039},[638],[363,78041,78043],{"className":78042,"style":727},[642],[363,78044,78045,78048],{"style":730},[363,78046],{"className":78047,"style":651},[650],[363,78049,78051],{"className":78050},[655,656,657,658],[363,78052,561],{"className":78053},[407,408,658],[363,78055,666],{"className":78056},[665],[363,78058,78060],{"className":78059},[638],[363,78061,78063],{"className":78062,"style":673},[642],[363,78064],{},[363,78066,578],{"className":78067},[494],[363,78069,1116],{"className":78070},[407,408],[363,78072,5155],{"className":78073},[407],[363,78075,5748],{"className":78076,"style":2934},[407,408],[363,78078,605],{"className":78079},[501]," 本身是 ",[363,78082,78084,78104],{"className":78083,"translate":367},[366],[363,78085,78087],{"className":78086},[371],[373,78088,78089],{"xmlns":375},[377,78090,78091,78101],{},[380,78092,78093,78095,78097,78099],{},[383,78094,2679],{},[458,78096,461],{"stretchy":460},[383,78098,5748],{},[458,78100,468],{"stretchy":460},[387,78102,78103],{"encoding":389},"\\sigma(Y)",[363,78105,78107],{"className":78106,"ariaHidden":394},[393],[363,78108,78110,78113,78116,78119,78122],{"className":78109},[398],[363,78111],{"className":78112,"style":487},[402],[363,78114,2679],{"className":78115,"style":1328},[407,408],[363,78117,461],{"className":78118},[494],[363,78120,5748],{"className":78121,"style":2934},[407,408],[363,78123,468],{"className":78124},[501],"-可测的（对每个 ",[363,78127,78129,78142],{"className":78128,"translate":367},[366],[363,78130,78132],{"className":78131},[371],[373,78133,78134],{"xmlns":375},[377,78135,78136,78140],{},[380,78137,78138],{},[383,78139,40584],{},[387,78141,40584],{"encoding":389},[363,78143,78145],{"className":78144,"ariaHidden":394},[393],[363,78146,78148,78151],{"className":78147},[398],[363,78149],{"className":78150,"style":2623},[402],[363,78152,40584],{"className":78153,"style":1328},[407,408]," 是常数），即 ",[363,78156,78158,78183],{"className":78157,"translate":367},[366],[363,78159,78161],{"className":78160},[371],[373,78162,78163],{"xmlns":375},[377,78164,78165,78181],{},[380,78166,78167,78169,78171,78173,78175,78177,78179],{},[383,78168,1116],{},[458,78170,471],{},[383,78172,592],{},[383,78174,554],{},[383,78176,1288],{"mathvariant":557},[383,78178,592],{},[383,78180,561],{},[387,78182,5680],{"encoding":389},[363,78184,78186,78204],{"className":78185,"ariaHidden":394},[393],[363,78187,78189,78192,78195,78198,78201],{"className":78188},[398],[363,78190],{"className":78191,"style":5690},[402],[363,78193,1116],{"className":78194},[407,408],[363,78196],{"className":78197,"style":506},[505],[363,78199,471],{"className":78200},[510],[363,78202],{"className":78203,"style":506},[505],[363,78205,78207,78210,78213,78216,78219,78222],{"className":78206},[398],[363,78208],{"className":78209,"style":487},[402],[363,78211,592],{"className":78212},[407,408],[363,78214,554],{"className":78215,"style":682},[407,408],[363,78217,1288],{"className":78218},[407],[363,78220,592],{"className":78221},[407,408],[363,78223,561],{"className":78224},[407,408]," 可表为 ",[363,78227,78229,78242],{"className":78228,"translate":367},[366],[363,78230,78232],{"className":78231},[371],[373,78233,78234],{"xmlns":375},[377,78235,78236,78240],{},[380,78237,78238],{},[383,78239,5748],{},[387,78241,5748],{"encoding":389},[363,78243,78245],{"className":78244,"ariaHidden":394},[393],[363,78246,78248,78251],{"className":78247},[398],[363,78249],{"className":78250,"style":1011},[402],[363,78252,5748],{"className":78253,"style":2934},[407,408]," 的函数。此时 ",[363,78256,78258,78271],{"className":78257,"translate":367},[366],[363,78259,78261],{"className":78260},[371],[373,78262,78263],{"xmlns":375},[377,78264,78265,78269],{},[380,78266,78267],{},[383,78268,5748],{},[387,78270,5748],{"encoding":389},[363,78272,78274],{"className":78273,"ariaHidden":394},[393],[363,78275,78277,78280],{"className":78276},[398],[363,78278],{"className":78279,"style":1011},[402],[363,78281,5748],{"className":78282,"style":2934},[407,408]," 是关于 ",[363,78285,78287,78304],{"className":78286,"translate":367},[366],[363,78288,78290],{"className":78289},[371],[373,78291,78292],{"xmlns":375},[377,78293,78294,78302],{},[380,78295,78296,78298,78300],{},[383,78297,554],{},[458,78299,898],{"separator":394},[383,78301,561],{},[387,78303,903],{"encoding":389},[363,78305,78307],{"className":78306,"ariaHidden":394},[393],[363,78308,78310,78313,78316,78319,78322],{"className":78309},[398],[363,78311],{"className":78312,"style":913},[402],[363,78314,554],{"className":78315,"style":682},[407,408],[363,78317,898],{"className":78318},[920],[363,78320],{"className":78321,"style":754},[505],[363,78323,561],{"className":78324},[407,408],[1572,78326,78327],{},"充分统计量","：随机变换没有丢信息。这正是 f-散度能担当「信息量」的原因。",[11,78330,78331,78334,78335,78376],{},[1572,78332,78333],{},"信息单调性（Csiszár 的更进一步结果）。"," 对 α-散度族，还有更强的「信息单调性」：把 ",[363,78336,78338,78355],{"className":78337,"translate":367},[366],[363,78339,78341],{"className":78340},[371],[373,78342,78343],{"xmlns":375},[377,78344,78345,78353],{},[380,78346,78347,78349,78351],{},[383,78348,554],{},[458,78350,898],{"separator":394},[383,78352,561],{},[387,78354,903],{"encoding":389},[363,78356,78358],{"className":78357,"ariaHidden":394},[393],[363,78359,78361,78364,78367,78370,78373],{"className":78360},[398],[363,78362],{"className":78363,"style":913},[402],[363,78365,554],{"className":78366,"style":682},[407,408],[363,78368,898],{"className":78369},[920],[363,78371],{"className":78372,"style":754},[505],[363,78374,561],{"className":78375},[407,408]," 粗粒化（把样本空间划分得更粗）时散度不增，且存在严格单调的「信息序」。这构成了 Chentsov–Morozova 定理与信息几何中单调度量的基础。",[2658,78378,78380],{"id":78379},"_46-局部二次展开","4.6 局部二次展开",[1340,78382,78384,78794],{"title":78383},"命题 4.5（局部二次展开）",[11,78385,881,78386,78414,78415,5992,78489,21303,78593,78742,78743,30280],{},[363,78387,78389,78402],{"className":78388,"translate":367},[366],[363,78390,78392],{"className":78391},[371],[373,78393,78394],{"xmlns":375},[377,78395,78396,78400],{},[380,78397,78398],{},[383,78399,39012],{},[387,78401,39012],{"encoding":389},[363,78403,78405],{"className":78404,"ariaHidden":394},[393],[363,78406,78408,78411],{"className":78407},[398],[363,78409],{"className":78410,"style":12944},[402],[363,78412,39012],{"className":78413},[407,408]," 满足 ",[363,78416,78418,78444],{"className":78417,"translate":367},[366],[363,78419,78421],{"className":78420},[371],[373,78422,78423],{"xmlns":375},[377,78424,78425,78441],{},[380,78426,78427,78429,78431,78433,78435,78437,78439],{},[458,78428,1634],{},[383,78430,39012],{},[1644,78432,1646],{},[383,78434,592],{},[383,78436,554],{},[458,78438,471],{},[463,78440,474],{},[387,78442,78443],{"encoding":389},"\\int h\\,dP=0",[363,78445,78447,78480],{"className":78446,"ariaHidden":394},[393],[363,78448,78450,78453,78456,78459,78462,78465,78468,78471,78474,78477],{"className":78449},[398],[363,78451],{"className":78452,"style":5959},[402],[363,78454,1634],{"className":78455,"style":5964},[1831,1832,5963],[363,78457],{"className":78458,"style":754},[505],[363,78460,39012],{"className":78461},[407,408],[363,78463],{"className":78464,"style":754},[505],[363,78466,592],{"className":78467},[407,408],[363,78469,554],{"className":78470,"style":682},[407,408],[363,78472],{"className":78473,"style":506},[505],[363,78475,471],{"className":78476},[510],[363,78478],{"className":78479,"style":506},[505],[363,78481,78483,78486],{"className":78482},[398],[363,78484],{"className":78485,"style":520},[402],[363,78487,474],{"className":78488},[407],[363,78490,78492,78522],{"className":78491,"translate":367},[366],[363,78493,78495],{"className":78494},[371],[373,78496,78497],{"xmlns":375},[377,78498,78499,78519],{},[380,78500,78501,78503,78509,78511,78513,78515,78517],{},[458,78502,1634],{},[7161,78504,78505,78507],{},[383,78506,39012],{},[463,78508,2810],{},[1644,78510,1646],{},[383,78512,592],{},[383,78514,554],{},[458,78516,7598],{},[383,78518,1371],{"mathvariant":557},[387,78520,78521],{"encoding":389},"\\int h^2\\,dP\u003C\\infty",[363,78523,78525,78584],{"className":78524,"ariaHidden":394},[393],[363,78526,78528,78531,78534,78537,78566,78569,78572,78575,78578,78581],{"className":78527},[398],[363,78529],{"className":78530,"style":50675},[402],[363,78532,1634],{"className":78533,"style":5964},[1831,1832,5963],[363,78535],{"className":78536,"style":754},[505],[363,78538,78540,78543],{"className":78539},[407],[363,78541,39012],{"className":78542},[407,408],[363,78544,78546],{"className":78545},[629],[363,78547,78549],{"className":78548},[633],[363,78550,78552],{"className":78551},[638],[363,78553,78555],{"className":78554,"style":20375},[642],[363,78556,78557,78560],{"style":7212},[363,78558],{"className":78559,"style":651},[650],[363,78561,78563],{"className":78562},[655,656,657,658],[363,78564,2810],{"className":78565},[407,658],[363,78567],{"className":78568,"style":754},[505],[363,78570,592],{"className":78571},[407,408],[363,78573,554],{"className":78574,"style":682},[407,408],[363,78576],{"className":78577,"style":506},[505],[363,78579,7598],{"className":78580},[510],[363,78582],{"className":78583,"style":506},[505],[363,78585,78587,78590],{"className":78586},[398],[363,78588],{"className":78589,"style":2692},[402],[363,78591,1371],{"className":78592},[407],[363,78594,78596,78636],{"className":78595,"translate":367},[366],[363,78597,78599],{"className":78598},[371],[373,78600,78601],{"xmlns":375},[377,78602,78603,78633],{},[380,78604,78605,78607,78613,78615,78617,78619,78621,78623,78625,78627,78629,78631],{},[383,78606,592],{},[543,78608,78609,78611],{},[383,78610,561],{},[383,78612,39009],{},[458,78614,471],{},[458,78616,461],{"stretchy":460},[463,78618,465],{},[458,78620,2817],{},[383,78622,39009],{},[383,78624,39012],{},[458,78626,468],{"stretchy":460},[1644,78628,1646],{},[383,78630,592],{},[383,78632,554],{},[387,78634,78635],{"encoding":389},"dQ_\\varepsilon=(1+\\varepsilon h)\\,dP",[363,78637,78639,78697,78718],{"className":78638,"ariaHidden":394},[393],[363,78640,78642,78645,78648,78688,78691,78694],{"className":78641},[398],[363,78643],{"className":78644,"style":403},[402],[363,78646,592],{"className":78647},[407,408],[363,78649,78651,78654],{"className":78650},[407],[363,78652,561],{"className":78653},[407,408],[363,78655,78657],{"className":78656},[629],[363,78658,78660,78680],{"className":78659},[633,634],[363,78661,78663,78677],{"className":78662},[638],[363,78664,78666],{"className":78665,"style":45276},[642],[363,78667,78668,78671],{"style":730},[363,78669],{"className":78670,"style":651},[650],[363,78672,78674],{"className":78673},[655,656,657,658],[363,78675,39009],{"className":78676},[407,408,658],[363,78678,666],{"className":78679},[665],[363,78681,78683],{"className":78682},[638],[363,78684,78686],{"className":78685,"style":8315},[642],[363,78687],{},[363,78689],{"className":78690,"style":506},[505],[363,78692,471],{"className":78693},[510],[363,78695],{"className":78696,"style":506},[505],[363,78698,78700,78703,78706,78709,78712,78715],{"className":78699},[398],[363,78701],{"className":78702,"style":487},[402],[363,78704,461],{"className":78705},[494],[363,78707,465],{"className":78708},[407],[363,78710],{"className":78711,"style":2934},[505],[363,78713,2817],{"className":78714},[2938],[363,78716],{"className":78717,"style":2934},[505],[363,78719,78721,78724,78727,78730,78733,78736,78739],{"className":78720},[398],[363,78722],{"className":78723,"style":487},[402],[363,78725,39009],{"className":78726},[407,408],[363,78728,39012],{"className":78729},[407,408],[363,78731,468],{"className":78732},[501],[363,78734],{"className":78735,"style":754},[505],[363,78737,592],{"className":78738},[407,408],[363,78740,554],{"className":78741,"style":682},[407,408],"，则当 ",[363,78744,78746,78764],{"className":78745,"translate":367},[366],[363,78747,78749],{"className":78748},[371],[373,78750,78751],{"xmlns":375},[377,78752,78753,78761],{},[380,78754,78755,78757,78759],{},[383,78756,39009],{},[458,78758,1376],{},[463,78760,474],{},[387,78762,78763],{"encoding":389},"\\varepsilon\\to0",[363,78765,78767,78785],{"className":78766,"ariaHidden":394},[393],[363,78768,78770,78773,78776,78779,78782],{"className":78769},[398],[363,78771],{"className":78772,"style":2692},[402],[363,78774,39009],{"className":78775},[407,408],[363,78777],{"className":78778,"style":506},[505],[363,78780,1376],{"className":78781},[510],[363,78783],{"className":78784,"style":506},[505],[363,78786,78788,78791],{"className":78787},[398],[363,78789],{"className":78790,"style":520},[402],[363,78792,474],{"className":78793},[407],[363,78795,78797],{"className":78796,"translate":367},[528],[363,78798,78800,78896],{"className":78799,"translate":367},[366],[363,78801,78803],{"className":78802},[371],[373,78804,78805],{"xmlns":375,"display":537},[377,78806,78807,78893],{},[380,78808,78809,78815,78817,78823,78825,78827,78829,78831,78853,78855,78861,78863,78865,78871,78873,78875,78877,78879,78881,78883,78889,78891],{},[543,78810,78811,78813],{},[383,78812,547],{},[383,78814,385],{},[458,78816,461],{"stretchy":460},[543,78818,78819,78821],{},[383,78820,561],{},[383,78822,39009],{},[383,78824,558],{"mathvariant":557},[383,78826,554],{},[458,78828,468],{"stretchy":460},[458,78830,471],{},[586,78832,78833,78851],{},[380,78834,78835,78845,78847,78849],{},[7161,78836,78837,78839],{},[383,78838,385],{},[380,78840,78841,78843],{},[458,78842,7167],{"mathvariant":557},[458,78844,7167],{"mathvariant":557},[458,78846,461],{"stretchy":460},[463,78848,465],{},[458,78850,468],{"stretchy":460},[463,78852,2810],{},[1644,78854,1646],{},[7161,78856,78857,78859],{},[383,78858,39009],{},[463,78860,2810],{},[1644,78862,1651],{},[458,78864,1634],{},[7161,78866,78867,78869],{},[383,78868,39012],{},[463,78870,2810],{},[1644,78872,1646],{},[383,78874,592],{},[383,78876,554],{},[458,78878,2817],{},[383,78880,19568],{},[458,78882,461],{"stretchy":460},[7161,78884,78885,78887],{},[383,78886,39009],{},[463,78888,41082],{},[458,78890,468],{"stretchy":460},[383,78892,4722],{"mathvariant":557},[387,78894,78895],{"encoding":389},"D_f(Q_\\varepsilon\\|P)\n=\\frac{f''(1)}{2}\\,\\varepsilon^{2}\\!\n\\int h^{2}\\,dP\n+O(\\varepsilon^{3}).",[363,78897,78899,79006,79211],{"className":78898,"ariaHidden":394},[393],[363,78900,78902,78905,78945,78948,78988,78991,78994,78997,79000,79003],{"className":78901},[398],[363,78903],{"className":78904,"style":618},[402],[363,78906,78908,78911],{"className":78907},[407],[363,78909,547],{"className":78910,"style":625},[407,408],[363,78912,78914],{"className":78913},[629],[363,78915,78917,78937],{"className":78916},[633,634],[363,78918,78920,78934],{"className":78919},[638],[363,78921,78923],{"className":78922,"style":643},[642],[363,78924,78925,78928],{"style":646},[363,78926],{"className":78927,"style":651},[650],[363,78929,78931],{"className":78930},[655,656,657,658],[363,78932,385],{"className":78933,"style":409},[407,408,658],[363,78935,666],{"className":78936},[665],[363,78938,78940],{"className":78939},[638],[363,78941,78943],{"className":78942,"style":673},[642],[363,78944],{},[363,78946,461],{"className":78947},[494],[363,78949,78951,78954],{"className":78950},[407],[363,78952,561],{"className":78953},[407,408],[363,78955,78957],{"className":78956},[629],[363,78958,78960,78980],{"className":78959},[633,634],[363,78961,78963,78977],{"className":78962},[638],[363,78964,78966],{"className":78965,"style":45276},[642],[363,78967,78968,78971],{"style":730},[363,78969],{"className":78970,"style":651},[650],[363,78972,78974],{"className":78973},[655,656,657,658],[363,78975,39009],{"className":78976},[407,408,658],[363,78978,666],{"className":78979},[665],[363,78981,78983],{"className":78982},[638],[363,78984,78986],{"className":78985,"style":8315},[642],[363,78987],{},[363,78989,558],{"className":78990},[407],[363,78992,554],{"className":78993,"style":682},[407,408],[363,78995,468],{"className":78996},[501],[363,78998],{"className":78999,"style":506},[505],[363,79001,471],{"className":79002},[510],[363,79004],{"className":79005,"style":506},[505],[363,79007,79009,79013,79114,79117,79149,79152,79155,79158,79161,79193,79196,79199,79202,79205,79208],{"className":79008},[398],[363,79010],{"className":79011,"style":79012},[402],"height:2.2911em;vertical-align:-0.8622em;",[363,79014,79016,79019,79111],{"className":79015},[407],[363,79017],{"className":79018},[494,789],[363,79020,79022],{"className":79021},[586],[363,79023,79025,79103],{"className":79024},[633,634],[363,79026,79028,79100],{"className":79027},[638],[363,79029,79032,79043,79051],{"className":79030,"style":79031},[642],"height:1.4289em;",[363,79033,79034,79037],{"style":805},[363,79035],{"className":79036,"style":809},[650],[363,79038,79040],{"className":79039},[407],[363,79041,2810],{"className":79042},[407],[363,79044,79045,79048],{"style":821},[363,79046],{"className":79047,"style":809},[650],[363,79049],{"className":79050,"style":829},[828],[363,79052,79053,79056],{"style":832},[363,79054],{"className":79055,"style":809},[650],[363,79057,79059,79091,79094,79097],{"className":79058},[407],[363,79060,79062,79065],{"className":79061},[407],[363,79063,385],{"className":79064,"style":409},[407,408],[363,79066,79068],{"className":79067},[629],[363,79069,79071],{"className":79070},[633],[363,79072,79074],{"className":79073},[638],[363,79075,79077],{"className":79076,"style":7209},[642],[363,79078,79079,79082],{"style":7212},[363,79080],{"className":79081,"style":651},[650],[363,79083,79085],{"className":79084},[655,656,657,658],[363,79086,79088],{"className":79087},[407,658],[363,79089,22095],{"className":79090},[407,658],[363,79092,461],{"className":79093},[494],[363,79095,465],{"className":79096},[407],[363,79098,468],{"className":79099},[501],[363,79101,666],{"className":79102},[665],[363,79104,79106],{"className":79105},[638],[363,79107,79109],{"className":79108,"style":4125},[642],[363,79110],{},[363,79112],{"className":79113},[501,789],[363,79115],{"className":79116,"style":754},[505],[363,79118,79120,79123],{"className":79119},[407],[363,79121,39009],{"className":79122},[407,408],[363,79124,79126],{"className":79125},[629],[363,79127,79129],{"className":79128},[633],[363,79130,79132],{"className":79131},[638],[363,79133,79135],{"className":79134,"style":20082},[642],[363,79136,79137,79140],{"style":8624},[363,79138],{"className":79139,"style":651},[650],[363,79141,79143],{"className":79142},[655,656,657,658],[363,79144,79146],{"className":79145},[407,658],[363,79147,2810],{"className":79148},[407,658],[363,79150],{"className":79151,"style":1859},[505],[363,79153],{"className":79154,"style":754},[505],[363,79156,1634],{"className":79157,"style":1834},[1831,1832,1833],[363,79159],{"className":79160,"style":754},[505],[363,79162,79164,79167],{"className":79163},[407],[363,79165,39012],{"className":79166},[407,408],[363,79168,79170],{"className":79169},[629],[363,79171,79173],{"className":79172},[633],[363,79174,79176],{"className":79175},[638],[363,79177,79179],{"className":79178,"style":20082},[642],[363,79180,79181,79184],{"style":8624},[363,79182],{"className":79183,"style":651},[650],[363,79185,79187],{"className":79186},[655,656,657,658],[363,79188,79190],{"className":79189},[407,658],[363,79191,2810],{"className":79192},[407,658],[363,79194],{"className":79195,"style":754},[505],[363,79197,592],{"className":79198},[407,408],[363,79200,554],{"className":79201,"style":682},[407,408],[363,79203],{"className":79204,"style":2934},[505],[363,79206,2817],{"className":79207},[2938],[363,79209],{"className":79210,"style":2934},[505],[363,79212,79214,79217,79220,79223,79255,79258],{"className":79213},[398],[363,79215],{"className":79216,"style":37598},[402],[363,79218,19568],{"className":79219,"style":625},[407,408],[363,79221,461],{"className":79222},[494],[363,79224,79226,79229],{"className":79225},[407],[363,79227,39009],{"className":79228},[407,408],[363,79230,79232],{"className":79231},[629],[363,79233,79235],{"className":79234},[633],[363,79236,79238],{"className":79237},[638],[363,79239,79241],{"className":79240,"style":20082},[642],[363,79242,79243,79246],{"style":8624},[363,79244],{"className":79245,"style":651},[650],[363,79247,79249],{"className":79248},[655,656,657,658],[363,79250,79252],{"className":79251},[407,658],[363,79253,41082],{"className":79254},[407,658],[363,79256,468],{"className":79257},[501],[363,79259,4722],{"className":79260},[407],[11,79262,79263,79265,79266,79427,79428,5992,79493,79566],{},[1572,79264,55818],{}," 记 ",[363,79267,79269,79309],{"className":79268,"translate":367},[366],[363,79270,79272],{"className":79271},[371],[373,79273,79274],{"xmlns":375},[377,79275,79276,79306],{},[380,79277,79278,79280,79282,79284,79290,79292,79294,79296,79298,79300,79302,79304],{},[383,79279,1116],{},[458,79281,471],{},[383,79283,592],{},[543,79285,79286,79288],{},[383,79287,561],{},[383,79289,39009],{},[383,79291,1288],{"mathvariant":557},[383,79293,592],{},[383,79295,554],{},[458,79297,471],{},[463,79299,465],{},[458,79301,2817],{},[383,79303,39009],{},[383,79305,39012],{},[387,79307,79308],{"encoding":389},"t=dQ_\\varepsilon\u002FdP=1+\\varepsilon h",[363,79310,79312,79330,79397,79415],{"className":79311,"ariaHidden":394},[393],[363,79313,79315,79318,79321,79324,79327],{"className":79314},[398],[363,79316],{"className":79317,"style":5690},[402],[363,79319,1116],{"className":79320},[407,408],[363,79322],{"className":79323,"style":506},[505],[363,79325,471],{"className":79326},[510],[363,79328],{"className":79329,"style":506},[505],[363,79331,79333,79336,79339,79379,79382,79385,79388,79391,79394],{"className":79332},[398],[363,79334],{"className":79335,"style":487},[402],[363,79337,592],{"className":79338},[407,408],[363,79340,79342,79345],{"className":79341},[407],[363,79343,561],{"className":79344},[407,408],[363,79346,79348],{"className":79347},[629],[363,79349,79351,79371],{"className":79350},[633,634],[363,79352,79354,79368],{"className":79353},[638],[363,79355,79357],{"className":79356,"style":45276},[642],[363,79358,79359,79362],{"style":730},[363,79360],{"className":79361,"style":651},[650],[363,79363,79365],{"className":79364},[655,656,657,658],[363,79366,39009],{"className":79367},[407,408,658],[363,79369,666],{"className":79370},[665],[363,79372,79374],{"className":79373},[638],[363,79375,79377],{"className":79376,"style":8315},[642],[363,79378],{},[363,79380,1288],{"className":79381},[407],[363,79383,592],{"className":79384},[407,408],[363,79386,554],{"className":79387,"style":682},[407,408],[363,79389],{"className":79390,"style":506},[505],[363,79392,471],{"className":79393},[510],[363,79395],{"className":79396,"style":506},[505],[363,79398,79400,79403,79406,79409,79412],{"className":79399},[398],[363,79401],{"className":79402,"style":12925},[402],[363,79404,465],{"className":79405},[407],[363,79407],{"className":79408,"style":2934},[505],[363,79410,2817],{"className":79411},[2938],[363,79413],{"className":79414,"style":2934},[505],[363,79416,79418,79421,79424],{"className":79417},[398],[363,79419],{"className":79420,"style":12944},[402],[363,79422,39009],{"className":79423},[407,408],[363,79425,39012],{"className":79426},[407,408],"，由 ",[363,79429,79431,79454],{"className":79430,"translate":367},[366],[363,79432,79434],{"className":79433},[371],[373,79435,79436],{"xmlns":375},[377,79437,79438,79452],{},[380,79439,79440,79442,79444,79446,79448,79450],{},[383,79441,385],{},[458,79443,461],{"stretchy":460},[463,79445,465],{},[458,79447,468],{"stretchy":460},[458,79449,471],{},[463,79451,474],{},[387,79453,477],{"encoding":389},[363,79455,79457,79484],{"className":79456,"ariaHidden":394},[393],[363,79458,79460,79463,79466,79469,79472,79475,79478,79481],{"className":79459},[398],[363,79461],{"className":79462,"style":487},[402],[363,79464,385],{"className":79465,"style":409},[407,408],[363,79467,461],{"className":79468},[494],[363,79470,465],{"className":79471},[407],[363,79473,468],{"className":79474},[501],[363,79476],{"className":79477,"style":506},[505],[363,79479,471],{"className":79480},[510],[363,79482],{"className":79483,"style":506},[505],[363,79485,79487,79490],{"className":79486},[398],[363,79488],{"className":79489,"style":520},[402],[363,79491,474],{"className":79492},[407],[363,79494,79496,79521],{"className":79495,"translate":367},[366],[363,79497,79499],{"className":79498},[371],[373,79500,79501],{"xmlns":375},[377,79502,79503,79519],{},[380,79504,79505,79507,79509,79511,79513,79515,79517],{},[458,79506,1634],{},[383,79508,39012],{},[1644,79510,1646],{},[383,79512,592],{},[383,79514,554],{},[458,79516,471],{},[463,79518,474],{},[387,79520,78443],{"encoding":389},[363,79522,79524,79557],{"className":79523,"ariaHidden":394},[393],[363,79525,79527,79530,79533,79536,79539,79542,79545,79548,79551,79554],{"className":79526},[398],[363,79528],{"className":79529,"style":5959},[402],[363,79531,1634],{"className":79532,"style":5964},[1831,1832,5963],[363,79534],{"className":79535,"style":754},[505],[363,79537,39012],{"className":79538},[407,408],[363,79540],{"className":79541,"style":754},[505],[363,79543,592],{"className":79544},[407,408],[363,79546,554],{"className":79547,"style":682},[407,408],[363,79549],{"className":79550,"style":506},[505],[363,79552,471],{"className":79553},[510],[363,79555],{"className":79556,"style":506},[505],[363,79558,79560,79563],{"className":79559},[398],[363,79561],{"className":79562,"style":520},[402],[363,79564,474],{"className":79565},[407]," 做 Taylor 展开：",[363,79568,79570],{"className":79569,"translate":367},[528],[363,79571,79573,79801],{"className":79572,"translate":367},[366],[363,79574,79576],{"className":79575},[371],[373,79577,79578],{"xmlns":375,"display":537},[377,79579,79580,79798],{},[1590,79581,79582,79644,79718],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,79583,79584,79610],{},[1599,79585,79586],{},[1602,79587,79588],{"scriptlevel":474,"displaystyle":394},[380,79589,79590,79596,79598,79604,79606,79608],{},[543,79591,79592,79594],{},[383,79593,547],{},[383,79595,385],{},[458,79597,461],{"stretchy":460},[543,79599,79600,79602],{},[383,79601,561],{},[383,79603,39009],{},[383,79605,558],{"mathvariant":557},[383,79607,554],{},[458,79609,468],{"stretchy":460},[1599,79611,79612],{},[1602,79613,79614],{"scriptlevel":474,"displaystyle":394},[380,79615,79616,79618,79620,79626,79628,79630,79632,79634,79636,79638,79640,79642],{},[380,79617],{},[458,79619,471],{},[543,79621,79622,79624],{},[383,79623,571],{"mathvariant":570},[383,79625,554],{},[458,79627,578],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,79629,385],{},[458,79631,461],{"stretchy":460},[463,79633,465],{},[458,79635,2817],{},[383,79637,39009],{},[383,79639,39012],{},[458,79641,468],{"stretchy":460},[458,79643,605],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[1596,79645,79646,79652],{},[1599,79647,79648],{},[1602,79649,79650],{"scriptlevel":474,"displaystyle":394},[380,79651],{},[1599,79653,79654],{},[1602,79655,79656],{"scriptlevel":474,"displaystyle":394},[380,79657,79658,79660,79662,79680,79682,79684,79690,79692,79694,79696],{},[380,79659],{},[458,79661,471],{},[6363,79663,79664,79678],{},[6363,79665,79666,79676],{},[380,79667,79668,79670,79672,79674],{},[383,79669,385],{},[458,79671,461],{"stretchy":460},[463,79673,465],{},[458,79675,468],{"stretchy":460},[458,79677,6387],{"stretchy":394},[463,79679,474],{},[458,79681,2817],{},[383,79683,39009],{},[7161,79685,79686,79688],{},[383,79687,385],{},[458,79689,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,79691,461],{"stretchy":460},[463,79693,465],{},[458,79695,468],{"stretchy":460},[6363,79697,79698,79716],{},[6363,79699,79700,79714],{},[380,79701,79702,79708,79710,79712],{},[543,79703,79704,79706],{},[383,79705,571],{"mathvariant":570},[383,79707,554],{},[458,79709,578],{"stretchy":460},[383,79711,39012],{},[458,79713,605],{"stretchy":460},[458,79715,6387],{"stretchy":394},[463,79717,474],{},[1596,79719,79720,79726],{},[1599,79721,79722],{},[1602,79723,79724],{"scriptlevel":474,"displaystyle":394},[380,79725],{},[1599,79727,79728],{},[1602,79729,79730],{"scriptlevel":474,"displaystyle":394},[380,79731,79732,79734,79736,79738,79748,79758,79760,79762,79764,79766,79772,79774,79780,79782,79784,79786,79788,79794,79796],{},[380,79733],{},[505,79735],{"width":3609},[458,79737,2817],{},[586,79739,79740,79746],{},[7161,79741,79742,79744],{},[383,79743,39009],{},[463,79745,2810],{},[463,79747,2810],{},[7161,79749,79750,79752],{},[383,79751,385],{},[380,79753,79754,79756],{},[458,79755,7167],{"mathvariant":557},[458,79757,7167],{"mathvariant":557},[458,79759,461],{"stretchy":460},[463,79761,465],{},[458,79763,468],{"stretchy":460},[1644,79765,1646],{},[543,79767,79768,79770],{},[383,79769,571],{"mathvariant":570},[383,79771,554],{},[458,79773,578],{"stretchy":460},[7161,79775,79776,79778],{},[383,79777,39012],{},[463,79779,2810],{},[458,79781,605],{"stretchy":460},[458,79783,2817],{},[383,79785,19568],{},[458,79787,461],{"stretchy":460},[7161,79789,79790,79792],{},[383,79791,39009],{},[463,79793,41082],{},[458,79795,468],{"stretchy":460},[383,79797,4722],{"mathvariant":557},[387,79799,79800],{"encoding":389},"\\begin{aligned}\nD_f(Q_\\varepsilon\\|P)\n&=\\mathbb E_P\\big[f(1+\\varepsilon h)\\big]\\\\[2pt]\n&=\\underbrace{f(1)}_{0}\n+\\varepsilon f'(1)\n\\underbrace{\\mathbb E_P[h]}_{0}\\\\\n&\\qquad+\\frac{\\varepsilon^2}{2}f''(1)\\,\n\\mathbb E_P[h^2]\n+O(\\varepsilon^3).\n\\end{aligned}",[363,79802,79804],{"className":79803,"ariaHidden":394},[393],[363,79805,79807,79811],{"className":79806},[398],[363,79808],{"className":79809,"style":79810},[402],"height:6.5762em;vertical-align:-3.0381em;",[363,79812,79814],{"className":79813},[407],[363,79815,79817,79962],{"className":79816},[1590],[363,79818,79820],{"className":79819},[1707],[363,79821,79823,79953],{"className":79822},[633,634],[363,79824,79826,79950],{"className":79825},[638],[363,79827,79830,79932,79941],{"className":79828,"style":79829},[642],"height:3.5381em;",[363,79831,79833,79837],{"style":79832},"top:-6.1792em;",[363,79834],{"className":79835,"style":79836},[650],"height:3.4911em;",[363,79838,79840,79880,79883,79923,79926,79929],{"className":79839},[407],[363,79841,79843,79846],{"className":79842},[407],[363,79844,547],{"className":79845,"style":625},[407,408],[363,79847,79849],{"className":79848},[629],[363,79850,79852,79872],{"className":79851},[633,634],[363,79853,79855,79869],{"className":79854},[638],[363,79856,79858],{"className":79857,"style":643},[642],[363,79859,79860,79863],{"style":646},[363,79861],{"className":79862,"style":651},[650],[363,79864,79866],{"className":79865},[655,656,657,658],[363,79867,385],{"className":79868,"style":409},[407,408,658],[363,79870,666],{"className":79871},[665],[363,79873,79875],{"className":79874},[638],[363,79876,79878],{"className":79877,"style":673},[642],[363,79879],{},[363,79881,461],{"className":79882},[494],[363,79884,79886,79889],{"className":79885},[407],[363,79887,561],{"className":79888},[407,408],[363,79890,79892],{"className":79891},[629],[363,79893,79895,79915],{"className":79894},[633,634],[363,79896,79898,79912],{"className":79897},[638],[363,79899,79901],{"className":79900,"style":45276},[642],[363,79902,79903,79906],{"style":730},[363,79904],{"className":79905,"style":651},[650],[363,79907,79909],{"className":79908},[655,656,657,658],[363,79910,39009],{"className":79911},[407,408,658],[363,79913,666],{"className":79914},[665],[363,79916,79918],{"className":79917},[638],[363,79919,79921],{"className":79920,"style":8315},[642],[363,79922],{},[363,79924,558],{"className":79925},[407],[363,79927,554],{"className":79928,"style":682},[407,408],[363,79930,468],{"className":79931},[501],[363,79933,79935,79938],{"style":79934},"top:-4.4792em;",[363,79936],{"className":79937,"style":79836},[650],[363,79939],{"className":79940},[407],[363,79942,79944,79947],{"style":79943},"top:-1.139em;",[363,79945],{"className":79946,"style":79836},[650],[363,79948],{"className":79949},[407],[363,79951,666],{"className":79952},[665],[363,79954,79956],{"className":79955},[638],[363,79957,79960],{"className":79958,"style":79959},[642],"height:3.0381em;",[363,79961],{},[363,79963,79965],{"className":79964},[1798],[363,79966,79968,80701],{"className":79967},[633,634],[363,79969,79971,80698],{"className":79970},[638],[363,79972,79974,80073,80418],{"className":79973,"style":79829},[642],[363,79975,79976,79979],{"style":79832},[363,79977],{"className":79978,"style":79836},[650],[363,79980,79982,79985,79988,79991,79994,80034,80040,80043,80046,80049,80052,80055,80058,80061,80064,80067],{"className":79981},[407],[363,79983],{"className":79984},[407],[363,79986],{"className":79987,"style":506},[505],[363,79989,471],{"className":79990},[510],[363,79992],{"className":79993,"style":506},[505],[363,79995,79997,80000],{"className":79996},[407],[363,79998,571],{"className":79999},[407,714],[363,80001,80003],{"className":80002},[629],[363,80004,80006,80026],{"className":80005},[633,634],[363,80007,80009,80023],{"className":80008},[638],[363,80010,80012],{"className":80011,"style":727},[642],[363,80013,80014,80017],{"style":730},[363,80015],{"className":80016,"style":651},[650],[363,80018,80020],{"className":80019},[655,656,657,658],[363,80021,554],{"className":80022,"style":682},[407,408,658],[363,80024,666],{"className":80025},[665],[363,80027,80029],{"className":80028},[638],[363,80030,80032],{"className":80031,"style":8315},[642],[363,80033],{},[363,80035,80037],{"className":80036},[407],[363,80038,578],{"className":80039},[767,10021],[363,80041,385],{"className":80042,"style":409},[407,408],[363,80044,461],{"className":80045},[494],[363,80047,465],{"className":80048},[407],[363,80050],{"className":80051,"style":2934},[505],[363,80053,2817],{"className":80054},[2938],[363,80056],{"className":80057,"style":2934},[505],[363,80059,39009],{"className":80060},[407,408],[363,80062,39012],{"className":80063},[407,408],[363,80065,468],{"className":80066},[501],[363,80068,80070],{"className":80069},[407],[363,80071,605],{"className":80072},[767,10021],[363,80074,80075,80078],{"style":79934},[363,80076],{"className":80077,"style":79836},[650],[363,80079,80081,80084,80087,80090,80093,80210,80213,80216,80219,80222,80254,80257,80260,80263,80266],{"className":80080},[407],[363,80082],{"className":80083},[407],[363,80085],{"className":80086,"style":506},[505],[363,80088,471],{"className":80089},[510],[363,80091],{"className":80092,"style":506},[505],[363,80094,80096],{"className":80095},[758,6363],[363,80097,80099,80201],{"className":80098},[633,634],[363,80100,80102,80198],{"className":80101},[638],[363,80103,80105,80120],{"className":80104,"style":25146},[642],[363,80106,80108,80111],{"style":80107},"top:-1.4509em;",[363,80109],{"className":80110,"style":809},[650],[363,80112,80114],{"className":80113},[655,656,657,658],[363,80115,80117],{"className":80116},[407,658],[363,80118,474],{"className":80119},[407,658],[363,80121,80122,80125],{"style":12210},[363,80123],{"className":80124,"style":809},[650],[363,80126,80128],{"className":80127},[758,6363],[363,80129,80131,80190],{"className":80130},[633,634],[363,80132,80134,80187],{"className":80133},[638],[363,80135,80137,80167],{"className":80136,"style":25146},[642],[363,80138,80140,80143],{"className":80139,"style":25185},[6654],[363,80141],{"className":80142,"style":809},[650],[363,80144,80146,80153,80160],{"className":80145,"style":6663},[6662],[363,80147,80149],{"className":80148,"style":6668},[6667],[6670,80150,80151],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6676},[6678,80152],{"d":6680},[363,80154,80156],{"className":80155,"style":6668},[6684],[6670,80157,80158],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6687},[6678,80159],{"d":6690},[363,80161,80163],{"className":80162,"style":6668},[6694],[6670,80164,80165],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6697},[6678,80166],{"d":6700},[363,80168,80169,80172],{"style":12210},[363,80170],{"className":80171,"style":809},[650],[363,80173,80175,80178,80181,80184],{"className":80174},[407],[363,80176,385],{"className":80177,"style":409},[407,408],[363,80179,461],{"className":80180},[494],[363,80182,465],{"className":80183},[407],[363,80185,468],{"className":80186},[501],[363,80188,666],{"className":80189},[665],[363,80191,80193],{"className":80192},[638],[363,80194,80196],{"className":80195,"style":25299},[642],[363,80197],{},[363,80199,666],{"className":80200},[665],[363,80202,80204],{"className":80203},[638],[363,80205,80208],{"className":80206,"style":80207},[642],"height:1.5491em;",[363,80209],{},[363,80211],{"className":80212,"style":2934},[505],[363,80214,2817],{"className":80215},[2938],[363,80217],{"className":80218,"style":2934},[505],[363,80220,39009],{"className":80221},[407,408],[363,80223,80225,80228],{"className":80224},[407],[363,80226,385],{"className":80227,"style":409},[407,408],[363,80229,80231],{"className":80230},[629],[363,80232,80234],{"className":80233},[633],[363,80235,80237],{"className":80236},[638],[363,80238,80240],{"className":80239,"style":29318},[642],[363,80241,80242,80245],{"style":8624},[363,80243],{"className":80244,"style":651},[650],[363,80246,80248],{"className":80247},[655,656,657,658],[363,80249,80251],{"className":80250},[407,658],[363,80252,7167],{"className":80253},[407,658],[363,80255,461],{"className":80256},[494],[363,80258,465],{"className":80259},[407],[363,80261,468],{"className":80262},[501],[363,80264],{"className":80265,"style":754},[505],[363,80267,80269],{"className":80268},[758,6363],[363,80270,80272,80410],{"className":80271},[633,634],[363,80273,80275,80407],{"className":80274},[638],[363,80276,80278,80292],{"className":80277,"style":25146},[642],[363,80279,80280,80283],{"style":80107},[363,80281],{"className":80282,"style":809},[650],[363,80284,80286],{"className":80285},[655,656,657,658],[363,80287,80289],{"className":80288},[407,658],[363,80290,474],{"className":80291},[407,658],[363,80293,80294,80297],{"style":12210},[363,80295],{"className":80296,"style":809},[650],[363,80298,80300],{"className":80299},[758,6363],[363,80301,80303,80399],{"className":80302},[633,634],[363,80304,80306,80396],{"className":80305},[638],[363,80307,80309,80339],{"className":80308,"style":25146},[642],[363,80310,80312,80315],{"className":80311,"style":25185},[6654],[363,80313],{"className":80314,"style":809},[650],[363,80316,80318,80325,80332],{"className":80317,"style":6663},[6662],[363,80319,80321],{"className":80320,"style":6668},[6667],[6670,80322,80323],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6676},[6678,80324],{"d":6680},[363,80326,80328],{"className":80327,"style":6668},[6684],[6670,80329,80330],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6687},[6678,80331],{"d":6690},[363,80333,80335],{"className":80334,"style":6668},[6694],[6670,80336,80337],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6697},[6678,80338],{"d":6700},[363,80340,80341,80344],{"style":12210},[363,80342],{"className":80343,"style":809},[650],[363,80345,80347,80387,80390,80393],{"className":80346},[407],[363,80348,80350,80353],{"className":80349},[407],[363,80351,571],{"className":80352},[407,714],[363,80354,80356],{"className":80355},[629],[363,80357,80359,80379],{"className":80358},[633,634],[363,80360,80362,80376],{"className":80361},[638],[363,80363,80365],{"className":80364,"style":727},[642],[363,80366,80367,80370],{"style":730},[363,80368],{"className":80369,"style":651},[650],[363,80371,80373],{"className":80372},[655,656,657,658],[363,80374,554],{"className":80375,"style":682},[407,408,658],[363,80377,666],{"className":80378},[665],[363,80380,80382],{"className":80381},[638],[363,80383,80385],{"className":80384,"style":8315},[642],[363,80386],{},[363,80388,578],{"className":80389},[494],[363,80391,39012],{"className":80392},[407,408],[363,80394,605],{"className":80395},[501],[363,80397,666],{"className":80398},[665],[363,80400,80402],{"className":80401},[638],[363,80403,80405],{"className":80404,"style":25299},[642],[363,80406],{},[363,80408,666],{"className":80409},[665],[363,80411,80413],{"className":80412},[638],[363,80414,80416],{"className":80415,"style":80207},[642],[363,80417],{},[363,80419,80420,80423],{"style":79943},[363,80421],{"className":80422,"style":79836},[650],[363,80424,80426,80429,80432,80435,80438,80441,80529,80561,80564,80567,80570,80573,80613,80616,80645,80648,80651,80654,80657,80660,80663,80692,80695],{"className":80425},[407],[363,80427],{"className":80428},[407],[363,80430],{"className":80431,"style":3981},[505],[363,80433],{"className":80434,"style":2934},[505],[363,80436,2817],{"className":80437},[2938],[363,80439],{"className":80440,"style":2934},[505],[363,80442,80444,80447,80526],{"className":80443},[407],[363,80445],{"className":80446},[494,789],[363,80448,80450],{"className":80449},[586],[363,80451,80453,80518],{"className":80452},[633,634],[363,80454,80456,80515],{"className":80455},[638],[363,80457,80459,80470,80478],{"className":80458,"style":38070},[642],[363,80460,80461,80464],{"style":805},[363,80462],{"className":80463,"style":809},[650],[363,80465,80467],{"className":80466},[407],[363,80468,2810],{"className":80469},[407],[363,80471,80472,80475],{"style":821},[363,80473],{"className":80474,"style":809},[650],[363,80476],{"className":80477,"style":829},[828],[363,80479,80480,80483],{"style":832},[363,80481],{"className":80482,"style":809},[650],[363,80484,80486],{"className":80485},[407],[363,80487,80489,80492],{"className":80488},[407],[363,80490,39009],{"className":80491},[407,408],[363,80493,80495],{"className":80494},[629],[363,80496,80498],{"className":80497},[633],[363,80499,80501],{"className":80500},[638],[363,80502,80504],{"className":80503,"style":20375},[642],[363,80505,80506,80509],{"style":7212},[363,80507],{"className":80508,"style":651},[650],[363,80510,80512],{"className":80511},[655,656,657,658],[363,80513,2810],{"className":80514},[407,658],[363,80516,666],{"className":80517},[665],[363,80519,80521],{"className":80520},[638],[363,80522,80524],{"className":80523,"style":4125},[642],[363,80525],{},[363,80527],{"className":80528},[501,789],[363,80530,80532,80535],{"className":80531},[407],[363,80533,385],{"className":80534,"style":409},[407,408],[363,80536,80538],{"className":80537},[629],[363,80539,80541],{"className":80540},[633],[363,80542,80544],{"className":80543},[638],[363,80545,80547],{"className":80546,"style":29318},[642],[363,80548,80549,80552],{"style":8624},[363,80550],{"className":80551,"style":651},[650],[363,80553,80555],{"className":80554},[655,656,657,658],[363,80556,80558],{"className":80557},[407,658],[363,80559,22095],{"className":80560},[407,658],[363,80562,461],{"className":80563},[494],[363,80565,465],{"className":80566},[407],[363,80568,468],{"className":80569},[501],[363,80571],{"className":80572,"style":754},[505],[363,80574,80576,80579],{"className":80575},[407],[363,80577,571],{"className":80578},[407,714],[363,80580,80582],{"className":80581},[629],[363,80583,80585,80605],{"className":80584},[633,634],[363,80586,80588,80602],{"className":80587},[638],[363,80589,80591],{"className":80590,"style":727},[642],[363,80592,80593,80596],{"style":730},[363,80594],{"className":80595,"style":651},[650],[363,80597,80599],{"className":80598},[655,656,657,658],[363,80600,554],{"className":80601,"style":682},[407,408,658],[363,80603,666],{"className":80604},[665],[363,80606,80608],{"className":80607},[638],[363,80609,80611],{"className":80610,"style":8315},[642],[363,80612],{},[363,80614,578],{"className":80615},[494],[363,80617,80619,80622],{"className":80618},[407],[363,80620,39012],{"className":80621},[407,408],[363,80623,80625],{"className":80624},[629],[363,80626,80628],{"className":80627},[633],[363,80629,80631],{"className":80630},[638],[363,80632,80634],{"className":80633,"style":20082},[642],[363,80635,80636,80639],{"style":8624},[363,80637],{"className":80638,"style":651},[650],[363,80640,80642],{"className":80641},[655,656,657,658],[363,80643,2810],{"className":80644},[407,658],[363,80646,605],{"className":80647},[501],[363,80649],{"className":80650,"style":2934},[505],[363,80652,2817],{"className":80653},[2938],[363,80655],{"className":80656,"style":2934},[505],[363,80658,19568],{"className":80659,"style":625},[407,408],[363,80661,461],{"className":80662},[494],[363,80664,80666,80669],{"className":80665},[407],[363,80667,39009],{"className":80668},[407,408],[363,80670,80672],{"className":80671},[629],[363,80673,80675],{"className":80674},[633],[363,80676,80678],{"className":80677},[638],[363,80679,80681],{"className":80680,"style":20082},[642],[363,80682,80683,80686],{"style":8624},[363,80684],{"className":80685,"style":651},[650],[363,80687,80689],{"className":80688},[655,656,657,658],[363,80690,41082],{"className":80691},[407,658],[363,80693,468],{"className":80694},[501],[363,80696,4722],{"className":80697},[407],[363,80699,666],{"className":80700},[665],[363,80702,80704],{"className":80703},[638],[363,80705,80707],{"className":80706,"style":79959},[642],[363,80708],{},[11,80710,80711,23692,80795,16142,80880,80983,80984,81190,81191,16142,81361,80983,81533,81840,81841,81897,81898,82083,82084,82317,82318,82321,82322,82402],{},[1572,80712,80713,80714,80794],{},"这说明：在无穷小尺度上，所有 f-散度都只差一个常数 ",[363,80715,80717,80744],{"className":80716,"translate":367},[366],[363,80718,80720],{"className":80719},[371],[373,80721,80722],{"xmlns":375},[377,80723,80724,80742],{},[380,80725,80726,80736,80738,80740],{},[7161,80727,80728,80730],{},[383,80729,385],{},[380,80731,80732,80734],{},[458,80733,7167],{"mathvariant":557},[458,80735,7167],{"mathvariant":557},[458,80737,461],{"stretchy":460},[463,80739,465],{},[458,80741,468],{"stretchy":460},[387,80743,39881],{"encoding":389},[363,80745,80747],{"className":80746,"ariaHidden":394},[393],[363,80748,80750,80753,80785,80788,80791],{"className":80749},[398],[363,80751],{"className":80752,"style":7190},[402],[363,80754,80756,80759],{"className":80755},[407],[363,80757,385],{"className":80758,"style":409},[407,408],[363,80760,80762],{"className":80761},[629],[363,80763,80765],{"className":80764},[633],[363,80766,80768],{"className":80767},[638],[363,80769,80771],{"className":80770,"style":7209},[642],[363,80772,80773,80776],{"style":7212},[363,80774],{"className":80775,"style":651},[650],[363,80777,80779],{"className":80778},[655,656,657,658],[363,80780,80782],{"className":80781},[407,658],[363,80783,22095],{"className":80784},[407,658],[363,80786,461],{"className":80787},[494],[363,80789,465],{"className":80790},[407],[363,80792,468],{"className":80793},[501],"，形状完全一致。",[363,80796,80798,80827],{"className":80797,"translate":367},[366],[363,80799,80801],{"className":80800},[371],[373,80802,80803],{"xmlns":375},[377,80804,80805,80825],{},[380,80806,80807,80809,80811,80813,80815,80817,80819,80821,80823],{},[383,80808,385],{},[458,80810,461],{"stretchy":460},[383,80812,1116],{},[458,80814,468],{"stretchy":460},[458,80816,471],{},[383,80818,1116],{},[383,80820,4447],{},[458,80822,4450],{},[383,80824,1116],{},[387,80826,4455],{"encoding":389},[363,80828,80830,80857],{"className":80829,"ariaHidden":394},[393],[363,80831,80833,80836,80839,80842,80845,80848,80851,80854],{"className":80832},[398],[363,80834],{"className":80835,"style":487},[402],[363,80837,385],{"className":80838,"style":409},[407,408],[363,80840,461],{"className":80841},[494],[363,80843,1116],{"className":80844},[407,408],[363,80846,468],{"className":80847},[501],[363,80849],{"className":80850,"style":506},[505],[363,80852,471],{"className":80853},[510],[363,80855],{"className":80856,"style":506},[505],[363,80858,80860,80863,80866,80869,80874,80877],{"className":80859},[398],[363,80861],{"className":80862,"style":403},[402],[363,80864,1116],{"className":80865},[407,408],[363,80867],{"className":80868,"style":754},[505],[363,80870,4501,80872],{"className":80871},[1831],[363,80873,4505],{"style":4504},[363,80875],{"className":80876,"style":754},[505],[363,80878,1116],{"className":80879},[407,408],[363,80881,80883,80915],{"className":80882,"translate":367},[366],[363,80884,80886],{"className":80885},[371],[373,80887,80888],{"xmlns":375},[377,80889,80890,80912],{},[380,80891,80892,80902,80904,80906,80908,80910],{},[7161,80893,80894,80896],{},[383,80895,385],{},[380,80897,80898,80900],{},[458,80899,7167],{"mathvariant":557},[458,80901,7167],{"mathvariant":557},[458,80903,461],{"stretchy":460},[463,80905,465],{},[458,80907,468],{"stretchy":460},[458,80909,471],{},[463,80911,465],{},[387,80913,80914],{"encoding":389},"f''(1)=1",[363,80916,80918,80974],{"className":80917,"ariaHidden":394},[393],[363,80919,80921,80924,80956,80959,80962,80965,80968,80971],{"className":80920},[398],[363,80922],{"className":80923,"style":7190},[402],[363,80925,80927,80930],{"className":80926},[407],[363,80928,385],{"className":80929,"style":409},[407,408],[363,80931,80933],{"className":80932},[629],[363,80934,80936],{"className":80935},[633],[363,80937,80939],{"className":80938},[638],[363,80940,80942],{"className":80941,"style":7209},[642],[363,80943,80944,80947],{"style":7212},[363,80945],{"className":80946,"style":651},[650],[363,80948,80950],{"className":80949},[655,656,657,658],[363,80951,80953],{"className":80952},[407,658],[363,80954,22095],{"className":80955},[407,658],[363,80957,461],{"className":80958},[494],[363,80960,465],{"className":80961},[407],[363,80963,468],{"className":80964},[501],[363,80966],{"className":80967,"style":506},[505],[363,80969,471],{"className":80970},[510],[363,80972],{"className":80973,"style":506},[505],[363,80975,80977,80980],{"className":80976},[398],[363,80978],{"className":80979,"style":520},[402],[363,80981,465],{"className":80982},[407],"）即得 ",[363,80985,80987,81023],{"className":80986,"translate":367},[366],[363,80988,80990],{"className":80989},[371],[373,80991,80992],{"xmlns":375},[377,80993,80994,81020],{},[380,80995,80996,81006,81008,81014],{},[543,80997,80998,81000],{},[383,80999,547],{},[380,81001,81002,81004],{},[383,81003,11041],{},[383,81005,22240],{},[458,81007,33306],{},[586,81009,81010,81012],{},[463,81011,465],{},[463,81013,2810],{},[7161,81015,81016,81018],{},[383,81017,37796],{},[463,81019,2810],{},[387,81021,81022],{"encoding":389},"D_{KL}\\approx\\frac12\\chi^2",[363,81024,81026,81087],{"className":81025,"ariaHidden":394},[393],[363,81027,81029,81032,81078,81081,81084],{"className":81028},[398],[363,81030],{"className":81031,"style":16308},[402],[363,81033,81035,81038],{"className":81034},[407],[363,81036,547],{"className":81037,"style":625},[407,408],[363,81039,81041],{"className":81040},[629],[363,81042,81044,81070],{"className":81043},[633,634],[363,81045,81047,81067],{"className":81046},[638],[363,81048,81050],{"className":81049,"style":727},[642],[363,81051,81052,81055],{"style":646},[363,81053],{"className":81054,"style":651},[650],[363,81056,81058],{"className":81057},[655,656,657,658],[363,81059,81061,81064],{"className":81060},[407,658],[363,81062,11041],{"className":81063,"style":11129},[407,408,658],[363,81065,22240],{"className":81066},[407,408,658],[363,81068,666],{"className":81069},[665],[363,81071,81073],{"className":81072},[638],[363,81074,81076],{"className":81075,"style":8315},[642],[363,81077],{},[363,81079],{"className":81080,"style":506},[505],[363,81082,33306],{"className":81083},[510],[363,81085],{"className":81086,"style":506},[505],[363,81088,81090,81093,81161],{"className":81089},[398],[363,81091],{"className":81092,"style":2852},[402],[363,81094,81096,81099,81158],{"className":81095},[407],[363,81097],{"className":81098},[494,789],[363,81100,81102],{"className":81101},[586],[363,81103,81105,81150],{"className":81104},[633,634],[363,81106,81108,81147],{"className":81107},[638],[363,81109,81111,81125,81133],{"className":81110,"style":2871},[642],[363,81112,81113,81116],{"style":2874},[363,81114],{"className":81115,"style":809},[650],[363,81117,81119],{"className":81118},[655,656,657,658],[363,81120,81122],{"className":81121},[407,658],[363,81123,2810],{"className":81124},[407,658],[363,81126,81127,81130],{"style":821},[363,81128],{"className":81129,"style":809},[650],[363,81131],{"className":81132,"style":829},[828],[363,81134,81135,81138],{"style":2897},[363,81136],{"className":81137,"style":809},[650],[363,81139,81141],{"className":81140},[655,656,657,658],[363,81142,81144],{"className":81143},[407,658],[363,81145,465],{"className":81146},[407,658],[363,81148,666],{"className":81149},[665],[363,81151,81153],{"className":81152},[638],[363,81154,81156],{"className":81155,"style":2919},[642],[363,81157],{},[363,81159],{"className":81160},[501,789],[363,81162,81164,81167],{"className":81163},[407],[363,81165,37796],{"className":81166},[407,408],[363,81168,81170],{"className":81169},[629],[363,81171,81173],{"className":81172},[633],[363,81174,81176],{"className":81175},[638],[363,81177,81179],{"className":81178,"style":20375},[642],[363,81180,81181,81184],{"style":7212},[363,81182],{"className":81183,"style":651},[650],[363,81185,81187],{"className":81186},[655,656,657,658],[363,81188,2810],{"className":81189},[407,658],"；取 ",[363,81192,81194,81231],{"className":81193,"translate":367},[366],[363,81195,81197],{"className":81196},[371],[373,81198,81199],{"xmlns":375},[377,81200,81201,81229],{},[380,81202,81203,81205,81207,81209,81211,81213,81215,81219,81221,81223],{},[383,81204,385],{},[458,81206,461],{"stretchy":460},[383,81208,1116],{},[458,81210,468],{"stretchy":460},[458,81212,471],{},[458,81214,461],{"stretchy":460},[34686,81216,81217],{},[383,81218,1116],{},[458,81220,5160],{},[463,81222,465],{},[7161,81224,81225,81227],{},[458,81226,468],{"stretchy":460},[463,81228,2810],{},[387,81230,42977],{"encoding":389},[363,81232,81234,81261,81323],{"className":81233,"ariaHidden":394},[393],[363,81235,81237,81240,81243,81246,81249,81252,81255,81258],{"className":81236},[398],[363,81238],{"className":81239,"style":487},[402],[363,81241,385],{"className":81242,"style":409},[407,408],[363,81244,461],{"className":81245},[494],[363,81247,1116],{"className":81248},[407,408],[363,81250,468],{"className":81251},[501],[363,81253],{"className":81254,"style":506},[505],[363,81256,471],{"className":81257},[510],[363,81259],{"className":81260,"style":506},[505],[363,81262,81264,81267,81270,81314,81317,81320],{"className":81263},[398],[363,81265],{"className":81266,"style":43014},[402],[363,81268,461],{"className":81269},[494],[363,81271,81273],{"className":81272},[407,34714],[363,81274,81276,81306],{"className":81275},[633,634],[363,81277,81279,81303],{"className":81278},[638],[363,81280,81282,81291],{"className":81281,"style":43030},[642],[363,81283,81285,81288],{"className":81284,"style":12210},[6654],[363,81286],{"className":81287,"style":809},[650],[363,81289,1116],{"className":81290,"style":34734},[407,408],[363,81292,81293,81296],{"style":43042},[363,81294],{"className":81295,"style":809},[650],[363,81297,81299],{"className":81298,"style":34791},[34790],[6670,81300,81301],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,81302],{"d":34798},[363,81304,666],{"className":81305},[665],[363,81307,81309],{"className":81308},[638],[363,81310,81312],{"className":81311,"style":43062},[642],[363,81313],{},[363,81315],{"className":81316,"style":2934},[505],[363,81318,5160],{"className":81319},[2938],[363,81321],{"className":81322,"style":2934},[505],[363,81324,81326,81329,81332],{"className":81325},[398],[363,81327],{"className":81328,"style":20350},[402],[363,81330,465],{"className":81331},[407],[363,81333,81335,81338],{"className":81334},[501],[363,81336,468],{"className":81337},[501],[363,81339,81341],{"className":81340},[629],[363,81342,81344],{"className":81343},[633],[363,81345,81347],{"className":81346},[638],[363,81348,81350],{"className":81349,"style":20375},[642],[363,81351,81352,81355],{"style":7212},[363,81353],{"className":81354,"style":651},[650],[363,81356,81358],{"className":81357},[655,656,657,658],[363,81359,2810],{"className":81360},[407,658],[363,81362,81364,81400],{"className":81363,"translate":367},[366],[363,81365,81367],{"className":81366},[371],[373,81368,81369],{"xmlns":375},[377,81370,81371,81397],{},[380,81372,81373,81383,81385,81387,81389,81391],{},[7161,81374,81375,81377],{},[383,81376,385],{},[380,81378,81379,81381],{},[458,81380,7167],{"mathvariant":557},[458,81382,7167],{"mathvariant":557},[458,81384,461],{"stretchy":460},[463,81386,465],{},[458,81388,468],{"stretchy":460},[458,81390,471],{},[586,81392,81393,81395],{},[463,81394,465],{},[463,81396,2810],{},[387,81398,81399],{"encoding":389},"f''(1)=\\frac12",[363,81401,81403,81459],{"className":81402,"ariaHidden":394},[393],[363,81404,81406,81409,81441,81444,81447,81450,81453,81456],{"className":81405},[398],[363,81407],{"className":81408,"style":7190},[402],[363,81410,81412,81415],{"className":81411},[407],[363,81413,385],{"className":81414,"style":409},[407,408],[363,81416,81418],{"className":81417},[629],[363,81419,81421],{"className":81420},[633],[363,81422,81424],{"className":81423},[638],[363,81425,81427],{"className":81426,"style":7209},[642],[363,81428,81429,81432],{"style":7212},[363,81430],{"className":81431,"style":651},[650],[363,81433,81435],{"className":81434},[655,656,657,658],[363,81436,81438],{"className":81437},[407,658],[363,81439,22095],{"className":81440},[407,658],[363,81442,461],{"className":81443},[494],[363,81445,465],{"className":81446},[407],[363,81448,468],{"className":81449},[501],[363,81451],{"className":81452,"style":506},[505],[363,81454,471],{"className":81455},[510],[363,81457],{"className":81458,"style":506},[505],[363,81460,81462,81465],{"className":81461},[398],[363,81463],{"className":81464,"style":2852},[402],[363,81466,81468,81471,81530],{"className":81467},[407],[363,81469],{"className":81470},[494,789],[363,81472,81474],{"className":81473},[586],[363,81475,81477,81522],{"className":81476},[633,634],[363,81478,81480,81519],{"className":81479},[638],[363,81481,81483,81497,81505],{"className":81482,"style":2871},[642],[363,81484,81485,81488],{"style":2874},[363,81486],{"className":81487,"style":809},[650],[363,81489,81491],{"className":81490},[655,656,657,658],[363,81492,81494],{"className":81493},[407,658],[363,81495,2810],{"className":81496},[407,658],[363,81498,81499,81502],{"style":821},[363,81500],{"className":81501,"style":809},[650],[363,81503],{"className":81504,"style":829},[828],[363,81506,81507,81510],{"style":2897},[363,81508],{"className":81509,"style":809},[650],[363,81511,81513],{"className":81512},[655,656,657,658],[363,81514,81516],{"className":81515},[407,658],[363,81517,465],{"className":81518},[407,658],[363,81520,666],{"className":81521},[665],[363,81523,81525],{"className":81524},[638],[363,81526,81528],{"className":81527,"style":2919},[642],[363,81529],{},[363,81531],{"className":81532},[501,789],[363,81534,81536,81581],{"className":81535,"translate":367},[366],[363,81537,81539],{"className":81538},[371],[373,81540,81541],{"xmlns":375},[377,81542,81543,81579],{},[380,81544,81545,81547,81549,81553,81555,81559,81565,81567,81573],{},[458,81546,1634],{},[458,81548,461],{"stretchy":460},[34686,81550,81551],{},[383,81552,11],{},[458,81554,5160],{},[34686,81556,81557],{},[383,81558,1291],{},[7161,81560,81561,81563],{},[458,81562,468],{"stretchy":460},[463,81564,2810],{},[458,81566,33306],{},[586,81568,81569,81571],{},[463,81570,465],{},[463,81572,39336],{},[7161,81574,81575,81577],{},[383,81576,37796],{},[463,81578,2810],{},[387,81580,39345],{"encoding":389},[363,81582,81584,81649,81737],{"className":81583,"ariaHidden":394},[393],[363,81585,81587,81590,81593,81596,81640,81643,81646],{"className":81586},[398],[363,81588],{"className":81589,"style":39355},[402],[363,81591,1634],{"className":81592,"style":5964},[1831,1832,5963],[363,81594,461],{"className":81595},[494],[363,81597,81599],{"className":81598},[407,34714],[363,81600,81602,81632],{"className":81601},[633,634],[363,81603,81605,81629],{"className":81604},[638],[363,81606,81608,81617],{"className":81607,"style":39374},[642],[363,81609,81611,81614],{"className":81610,"style":12210},[6654],[363,81612],{"className":81613,"style":809},[650],[363,81615,11],{"className":81616,"style":34734},[407,408],[363,81618,81619,81622],{"style":39386},[363,81620],{"className":81621,"style":809},[650],[363,81623,81625],{"className":81624,"style":34791},[34790],[6670,81626,81627],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,81628],{"d":34798},[363,81630,666],{"className":81631},[665],[363,81633,81635],{"className":81634},[638],[363,81636,81638],{"className":81637,"style":39406},[642],[363,81639],{},[363,81641],{"className":81642,"style":2934},[505],[363,81644,5160],{"className":81645},[2938],[363,81647],{"className":81648,"style":2934},[505],[363,81650,81652,81655,81699,81728,81731,81734],{"className":81651},[398],[363,81653],{"className":81654,"style":39424},[402],[363,81656,81658],{"className":81657},[407,34714],[363,81659,81661,81691],{"className":81660},[633,634],[363,81662,81664,81688],{"className":81663},[638],[363,81665,81667,81676],{"className":81666,"style":39374},[642],[363,81668,81670,81673],{"className":81669,"style":12210},[6654],[363,81671],{"className":81672,"style":809},[650],[363,81674,1291],{"className":81675,"style":39446},[407,408],[363,81677,81678,81681],{"style":39386},[363,81679],{"className":81680,"style":809},[650],[363,81682,81684],{"className":81683,"style":34791},[34790],[6670,81685,81686],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,81687],{"d":34798},[363,81689,666],{"className":81690},[665],[363,81692,81694],{"className":81693},[638],[363,81695,81697],{"className":81696,"style":39406},[642],[363,81698],{},[363,81700,81702,81705],{"className":81701},[501],[363,81703,468],{"className":81704},[501],[363,81706,81708],{"className":81707},[629],[363,81709,81711],{"className":81710},[633],[363,81712,81714],{"className":81713},[638],[363,81715,81717],{"className":81716,"style":20375},[642],[363,81718,81719,81722],{"style":7212},[363,81720],{"className":81721,"style":651},[650],[363,81723,81725],{"className":81724},[655,656,657,658],[363,81726,2810],{"className":81727},[407,658],[363,81729],{"className":81730,"style":506},[505],[363,81732,33306],{"className":81733},[510],[363,81735],{"className":81736,"style":506},[505],[363,81738,81740,81743,81811],{"className":81739},[398],[363,81741],{"className":81742,"style":2852},[402],[363,81744,81746,81749,81808],{"className":81745},[407],[363,81747],{"className":81748},[494,789],[363,81750,81752],{"className":81751},[586],[363,81753,81755,81800],{"className":81754},[633,634],[363,81756,81758,81797],{"className":81757},[638],[363,81759,81761,81775,81783],{"className":81760,"style":2871},[642],[363,81762,81763,81766],{"style":2874},[363,81764],{"className":81765,"style":809},[650],[363,81767,81769],{"className":81768},[655,656,657,658],[363,81770,81772],{"className":81771},[407,658],[363,81773,39336],{"className":81774},[407,658],[363,81776,81777,81780],{"style":821},[363,81778],{"className":81779,"style":809},[650],[363,81781],{"className":81782,"style":829},[828],[363,81784,81785,81788],{"style":2897},[363,81786],{"className":81787,"style":809},[650],[363,81789,81791],{"className":81790},[655,656,657,658],[363,81792,81794],{"className":81793},[407,658],[363,81795,465],{"className":81796},[407,658],[363,81798,666],{"className":81799},[665],[363,81801,81803],{"className":81802},[638],[363,81804,81806],{"className":81805,"style":2919},[642],[363,81807],{},[363,81809],{"className":81810},[501,789],[363,81812,81814,81817],{"className":81813},[407],[363,81815,37796],{"className":81816},[407,408],[363,81818,81820],{"className":81819},[629],[363,81821,81823],{"className":81822},[633],[363,81824,81826],{"className":81825},[638],[363,81827,81829],{"className":81828,"style":20375},[642],[363,81830,81831,81834],{"style":7212},[363,81832],{"className":81833,"style":651},[650],[363,81835,81837],{"className":81836},[655,656,657,658],[363,81838,2810],{"className":81839},[407,658],"，除以 2 或换算成 ",[363,81842,81844,81864],{"className":81843,"translate":367},[366],[363,81845,81847],{"className":81846},[371],[373,81848,81849],{"xmlns":375},[377,81850,81851,81861],{},[380,81852,81853,81855,81857,81859],{},[463,81854,465],{},[458,81856,5160],{},[383,81858,39638],{},[383,81860,39641],{},[387,81862,81863],{"encoding":389},"1-BC",[363,81865,81867,81885],{"className":81866,"ariaHidden":394},[393],[363,81868,81870,81873,81876,81879,81882],{"className":81869},[398],[363,81871],{"className":81872,"style":12925},[402],[363,81874,465],{"className":81875},[407],[363,81877],{"className":81878,"style":2934},[505],[363,81880,5160],{"className":81881},[2938],[363,81883],{"className":81884,"style":2934},[505],[363,81886,81888,81891,81894],{"className":81887},[398],[363,81889],{"className":81890,"style":1011},[402],[363,81892,39638],{"className":81893,"style":39734},[407,408],[363,81895,39641],{"className":81896,"style":11129},[407,408]," 就是 3.4 节引用的 Bhattacharyya 约定 ",[363,81899,81901,81933],{"className":81900,"translate":367},[366],[363,81902,81904],{"className":81903},[371],[373,81905,81906],{"xmlns":375},[377,81907,81908,81930],{},[380,81909,81910,81916,81918,81924],{},[7161,81911,81912,81914],{},[383,81913,34231],{},[463,81915,2810],{},[458,81917,33306],{},[586,81919,81920,81922],{},[463,81921,465],{},[463,81923,39650],{},[7161,81925,81926,81928],{},[383,81927,37796],{},[463,81929,2810],{},[387,81931,81932],{"encoding":389},"H^2\\approx\\frac18\\chi^2",[363,81934,81936,81980],{"className":81935,"ariaHidden":394},[393],[363,81937,81939,81942,81971,81974,81977],{"className":81938},[398],[363,81940],{"className":81941,"style":20375},[402],[363,81943,81945,81948],{"className":81944},[407],[363,81946,34231],{"className":81947,"style":34385},[407,408],[363,81949,81951],{"className":81950},[629],[363,81952,81954],{"className":81953},[633],[363,81955,81957],{"className":81956},[638],[363,81958,81960],{"className":81959,"style":20375},[642],[363,81961,81962,81965],{"style":7212},[363,81963],{"className":81964,"style":651},[650],[363,81966,81968],{"className":81967},[655,656,657,658],[363,81969,2810],{"className":81970},[407,658],[363,81972],{"className":81973,"style":506},[505],[363,81975,33306],{"className":81976},[510],[363,81978],{"className":81979,"style":506},[505],[363,81981,81983,81986,82054],{"className":81982},[398],[363,81984],{"className":81985,"style":2852},[402],[363,81987,81989,81992,82051],{"className":81988},[407],[363,81990],{"className":81991},[494,789],[363,81993,81995],{"className":81994},[586],[363,81996,81998,82043],{"className":81997},[633,634],[363,81999,82001,82040],{"className":82000},[638],[363,82002,82004,82018,82026],{"className":82003,"style":2871},[642],[363,82005,82006,82009],{"style":2874},[363,82007],{"className":82008,"style":809},[650],[363,82010,82012],{"className":82011},[655,656,657,658],[363,82013,82015],{"className":82014},[407,658],[363,82016,39650],{"className":82017},[407,658],[363,82019,82020,82023],{"style":821},[363,82021],{"className":82022,"style":809},[650],[363,82024],{"className":82025,"style":829},[828],[363,82027,82028,82031],{"style":2897},[363,82029],{"className":82030,"style":809},[650],[363,82032,82034],{"className":82033},[655,656,657,658],[363,82035,82037],{"className":82036},[407,658],[363,82038,465],{"className":82039},[407,658],[363,82041,666],{"className":82042},[665],[363,82044,82046],{"className":82045},[638],[363,82047,82049],{"className":82048,"style":2919},[642],[363,82050],{},[363,82052],{"className":82053},[501,789],[363,82055,82057,82060],{"className":82056},[407],[363,82058,37796],{"className":82059},[407,408],[363,82061,82063],{"className":82062},[629],[363,82064,82066],{"className":82065},[633],[363,82067,82069],{"className":82068},[638],[363,82070,82072],{"className":82071,"style":20375},[642],[363,82073,82074,82077],{"style":7212},[363,82075],{"className":82076,"style":651},[650],[363,82078,82080],{"className":82079},[655,656,657,658],[363,82081,2810],{"className":82082},[407,658],"。共同因子 ",[363,82085,82087,82139],{"className":82086,"translate":367},[366],[363,82088,82090],{"className":82089},[371],[373,82091,82092],{"xmlns":375},[377,82093,82094,82136],{},[380,82095,82096,82102,82104,82110,82112,82114,82116,82122,82124,82130,82132,82134],{},[7161,82097,82098,82100],{},[383,82099,39009],{},[463,82101,2810],{},[458,82103,1634],{},[7161,82105,82106,82108],{},[383,82107,39012],{},[463,82109,2810],{},[383,82111,592],{},[383,82113,554],{},[458,82115,471],{},[7161,82117,82118,82120],{},[383,82119,37796],{},[463,82121,2810],{},[458,82123,461],{"stretchy":460},[543,82125,82126,82128],{},[383,82127,561],{},[383,82129,39009],{},[383,82131,558],{"mathvariant":557},[383,82133,554],{},[458,82135,468],{"stretchy":460},[387,82137,82138],{"encoding":389},"\\varepsilon^2\\int h^2 dP=\\chi^2(Q_\\varepsilon\\|P)",[363,82140,82142,82230],{"className":82141,"ariaHidden":394},[393],[363,82143,82145,82148,82177,82180,82183,82186,82215,82218,82221,82224,82227],{"className":82144},[398],[363,82146],{"className":82147,"style":50675},[402],[363,82149,82151,82154],{"className":82150},[407],[363,82152,39009],{"className":82153},[407,408],[363,82155,82157],{"className":82156},[629],[363,82158,82160],{"className":82159},[633],[363,82161,82163],{"className":82162},[638],[363,82164,82166],{"className":82165,"style":20375},[642],[363,82167,82168,82171],{"style":7212},[363,82169],{"className":82170,"style":651},[650],[363,82172,82174],{"className":82173},[655,656,657,658],[363,82175,2810],{"className":82176},[407,658],[363,82178],{"className":82179,"style":754},[505],[363,82181,1634],{"className":82182,"style":5964},[1831,1832,5963],[363,82184],{"className":82185,"style":754},[505],[363,82187,82189,82192],{"className":82188},[407],[363,82190,39012],{"className":82191},[407,408],[363,82193,82195],{"className":82194},[629],[363,82196,82198],{"className":82197},[633],[363,82199,82201],{"className":82200},[638],[363,82202,82204],{"className":82203,"style":20375},[642],[363,82205,82206,82209],{"style":7212},[363,82207],{"className":82208,"style":651},[650],[363,82210,82212],{"className":82211},[655,656,657,658],[363,82213,2810],{"className":82214},[407,658],[363,82216,592],{"className":82217},[407,408],[363,82219,554],{"className":82220,"style":682},[407,408],[363,82222],{"className":82223,"style":506},[505],[363,82225,471],{"className":82226},[510],[363,82228],{"className":82229,"style":506},[505],[363,82231,82233,82236,82265,82268,82308,82311,82314],{"className":82232},[398],[363,82234],{"className":82235,"style":20350},[402],[363,82237,82239,82242],{"className":82238},[407],[363,82240,37796],{"className":82241},[407,408],[363,82243,82245],{"className":82244},[629],[363,82246,82248],{"className":82247},[633],[363,82249,82251],{"className":82250},[638],[363,82252,82254],{"className":82253,"style":20375},[642],[363,82255,82256,82259],{"style":7212},[363,82257],{"className":82258,"style":651},[650],[363,82260,82262],{"className":82261},[655,656,657,658],[363,82263,2810],{"className":82264},[407,658],[363,82266,461],{"className":82267},[494],[363,82269,82271,82274],{"className":82270},[407],[363,82272,561],{"className":82273},[407,408],[363,82275,82277],{"className":82276},[629],[363,82278,82280,82300],{"className":82279},[633,634],[363,82281,82283,82297],{"className":82282},[638],[363,82284,82286],{"className":82285,"style":45276},[642],[363,82287,82288,82291],{"style":730},[363,82289],{"className":82290,"style":651},[650],[363,82292,82294],{"className":82293},[655,656,657,658],[363,82295,39009],{"className":82296},[407,408,658],[363,82298,666],{"className":82299},[665],[363,82301,82303],{"className":82302},[638],[363,82304,82306],{"className":82305,"style":8315},[642],[363,82307],{},[363,82309,558],{"className":82310},[407],[363,82312,554],{"className":82313,"style":682},[407,408],[363,82315,468],{"className":82316},[501]," 就是",[1572,82319,82320],{},"Fisher 信息度量","：它给出统计流形上的黎曼度量，而 ",[363,82323,82325,82352],{"className":82324,"translate":367},[366],[363,82326,82328],{"className":82327},[371],[373,82329,82330],{"xmlns":375},[377,82331,82332,82350],{},[380,82333,82334,82344,82346,82348],{},[7161,82335,82336,82338],{},[383,82337,385],{},[380,82339,82340,82342],{},[458,82341,7167],{"mathvariant":557},[458,82343,7167],{"mathvariant":557},[458,82345,461],{"stretchy":460},[463,82347,465],{},[458,82349,468],{"stretchy":460},[387,82351,39881],{"encoding":389},[363,82353,82355],{"className":82354,"ariaHidden":394},[393],[363,82356,82358,82361,82393,82396,82399],{"className":82357},[398],[363,82359],{"className":82360,"style":7190},[402],[363,82362,82364,82367],{"className":82363},[407],[363,82365,385],{"className":82366,"style":409},[407,408],[363,82368,82370],{"className":82369},[629],[363,82371,82373],{"className":82372},[633],[363,82374,82376],{"className":82375},[638],[363,82377,82379],{"className":82378,"style":7209},[642],[363,82380,82381,82384],{"style":7212},[363,82382],{"className":82383,"style":651},[650],[363,82385,82387],{"className":82386},[655,656,657,658],[363,82388,82390],{"className":82389},[407,658],[363,82391,22095],{"className":82392},[407,658],[363,82394,461],{"className":82395},[494],[363,82397,465],{"className":82398},[407],[363,82400,468],{"className":82401},[501]," 只是「单位选择」。这也解释了为什么 GAN 中「选 JS 还是选 KL」在小偏差区几乎无差别，差别只在远离平衡或支撑不重叠时才显现。",[2658,82404,82406],{"id":82405},"_47-不等式网络","4.7 不等式网络",[1340,82408,82410,82604,83110,83571],{"title":82409},"命题 4.6（不等式网络）",[11,82411,82412,82413,82603],{},"记 ",[363,82414,82416,82454],{"className":82415,"translate":367},[366],[363,82417,82419],{"className":82418},[371],[373,82420,82421],{"xmlns":375},[377,82422,82423,82451],{},[380,82424,82425,82431,82433,82441,82443,82445,82447,82449],{},[7161,82426,82427,82429],{},[383,82428,34231],{},[463,82430,2810],{},[458,82432,471],{},[7900,82434,82435,82437,82439],{},[383,82436,34231],{},[1644,82438,42484],{},[463,82440,2810],{},[458,82442,471],{},[463,82444,465],{},[458,82446,5160],{},[383,82448,39638],{},[383,82450,39641],{},[387,82452,82453],{"encoding":389},"H^2=H^2_{\\text{Bhattacharyya}}=1-BC",[363,82455,82457,82501,82573,82591],{"className":82456,"ariaHidden":394},[393],[363,82458,82460,82463,82492,82495,82498],{"className":82459},[398],[363,82461],{"className":82462,"style":20375},[402],[363,82464,82466,82469],{"className":82465},[407],[363,82467,34231],{"className":82468,"style":34385},[407,408],[363,82470,82472],{"className":82471},[629],[363,82473,82475],{"className":82474},[633],[363,82476,82478],{"className":82477},[638],[363,82479,82481],{"className":82480,"style":20375},[642],[363,82482,82483,82486],{"style":7212},[363,82484],{"className":82485,"style":651},[650],[363,82487,82489],{"className":82488},[655,656,657,658],[363,82490,2810],{"className":82491},[407,658],[363,82493],{"className":82494,"style":506},[505],[363,82496,471],{"className":82497},[510],[363,82499],{"className":82500,"style":506},[505],[363,82502,82504,82507,82564,82567,82570],{"className":82503},[398],[363,82505],{"className":82506,"style":43232},[402],[363,82508,82510,82513],{"className":82509},[407],[363,82511,34231],{"className":82512,"style":34385},[407,408],[363,82514,82516],{"className":82515},[629],[363,82517,82519,82556],{"className":82518},[633,634],[363,82520,82522,82553],{"className":82521},[638],[363,82523,82525,82542],{"className":82524,"style":20375},[642],[363,82526,82527,82530],{"style":43256},[363,82528],{"className":82529,"style":651},[650],[363,82531,82533],{"className":82532},[655,656,657,658],[363,82534,82536],{"className":82535},[407,658],[363,82537,82539],{"className":82538},[407,4945,658],[363,82540,42484],{"className":82541},[407,658],[363,82543,82544,82547],{"style":7212},[363,82545],{"className":82546,"style":651},[650],[363,82548,82550],{"className":82549},[655,656,657,658],[363,82551,2810],{"className":82552},[407,658],[363,82554,666],{"className":82555},[665],[363,82557,82559],{"className":82558},[638],[363,82560,82562],{"className":82561,"style":43292},[642],[363,82563],{},[363,82565],{"className":82566,"style":506},[505],[363,82568,471],{"className":82569},[510],[363,82571],{"className":82572,"style":506},[505],[363,82574,82576,82579,82582,82585,82588],{"className":82575},[398],[363,82577],{"className":82578,"style":12925},[402],[363,82580,465],{"className":82581},[407],[363,82583],{"className":82584,"style":2934},[505],[363,82586,5160],{"className":82587},[2938],[363,82589],{"className":82590,"style":2934},[505],[363,82592,82594,82597,82600],{"className":82593},[398],[363,82595],{"className":82596,"style":1011},[402],[363,82598,39638],{"className":82599,"style":39734},[407,408],[363,82601,39641],{"className":82602,"style":11129},[407,408],"，则对概率测度有",[363,82605,82607],{"className":82606,"translate":367},[528],[363,82608,82610,82731],{"className":82609,"translate":367},[366],[363,82611,82613],{"className":82612},[371],[373,82614,82615],{"xmlns":375,"display":537},[377,82616,82617,82728],{},[1590,82618,82619,82654],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,82620,82621,82627],{},[1599,82622,82623],{},[1602,82624,82625],{"scriptlevel":474,"displaystyle":394},[380,82626],{},[1599,82628,82629],{},[1602,82630,82631],{"scriptlevel":474,"displaystyle":394},[380,82632,82633,82635],{},[380,82634],{},[380,82636,82637,82639,82641,82644,82646,82648,82650,82652],{},[383,82638,554],{"mathvariant":557},[383,82640,12310],{"mathvariant":557},[383,82642,82643],{"mathvariant":557},"n",[383,82645,7908],{"mathvariant":557},[383,82647,7911],{"mathvariant":557},[383,82649,7914],{"mathvariant":557},[383,82651,16797],{"mathvariant":557},[458,82653,1362],{},[1596,82655,82656,82662],{},[1599,82657,82658],{},[1602,82659,82660],{"scriptlevel":474,"displaystyle":394},[380,82661],{},[1599,82663,82664],{},[1602,82665,82666],{"scriptlevel":474,"displaystyle":394},[380,82667,82668,82670,82672,82682,82684,82686,82688,82690,82692,82694,82726],{},[380,82669],{},[505,82671],{"width":3609},[543,82673,82674,82676],{},[383,82675,547],{},[380,82677,82678,82680],{},[383,82679,5739],{},[383,82681,35197],{},[458,82683,461],{"stretchy":460},[383,82685,554],{},[458,82687,898],{"separator":394},[383,82689,561],{},[458,82691,468],{"stretchy":460},[458,82693,10299],{},[34686,82695,82696],{},[380,82697,82698,82706,82716,82718,82720,82722,82724],{},[1602,82699,82700],{"scriptlevel":474,"displaystyle":460},[586,82701,82702,82704],{},[463,82703,465],{},[463,82705,2810],{},[543,82707,82708,82710],{},[383,82709,547],{},[380,82711,82712,82714],{},[383,82713,11041],{},[383,82715,22240],{},[458,82717,461],{"stretchy":460},[383,82719,554],{},[383,82721,558],{"mathvariant":557},[383,82723,561],{},[458,82725,468],{"stretchy":460},[458,82727,898],{"separator":394},[387,82729,82730],{"encoding":389},"\\begin{aligned}\n&\\mathrm{Pinsker:}\\\\\n&\\qquad D_{TV}(P,Q)\\le\n\\sqrt{\\tfrac12 D_{KL}(P\\|Q)},\n\\end{aligned}",[363,82732,82734],{"className":82733,"ariaHidden":394},[393],[363,82735,82737,82741],{"className":82736},[398],[363,82738],{"className":82739,"style":82740},[402],"height:3.34em;vertical-align:-1.42em;",[363,82742,82744],{"className":82743},[407],[363,82745,82747,82791],{"className":82746},[1590],[363,82748,82750],{"className":82749},[1707],[363,82751,82753,82782],{"className":82752},[633,634],[363,82754,82756,82779],{"className":82755},[638],[363,82757,82760,82770],{"className":82758,"style":82759},[642],"height:1.92em;",[363,82761,82763,82767],{"style":82762},"top:-4.3639em;",[363,82764],{"className":82765,"style":82766},[650],"height:3.2839em;",[363,82768],{"className":82769},[407],[363,82771,82773,82776],{"style":82772},"top:-2.42em;",[363,82774],{"className":82775,"style":82766},[650],[363,82777],{"className":82778},[407],[363,82780,666],{"className":82781},[665],[363,82783,82785],{"className":82784},[638],[363,82786,82789],{"className":82787,"style":82788},[642],"height:1.42em;",[363,82790],{},[363,82792,82794],{"className":82793},[1798],[363,82795,82797,83102],{"className":82796},[633,634],[363,82798,82800,83099],{"className":82799},[638],[363,82801,82803,82827],{"className":82802,"style":82759},[642],[363,82804,82805,82808],{"style":82762},[363,82806],{"className":82807,"style":82766},[650],[363,82809,82811,82814],{"className":82810},[407],[363,82812],{"className":82813},[407],[363,82815,82817,82821,82824],{"className":82816},[407],[363,82818,82820],{"className":82819},[407,33009],"Pinsker",[363,82822],{"className":82823,"style":506},[505],[363,82825,1362],{"className":82826},[510],[363,82828,82829,82832],{"style":82772},[363,82830],{"className":82831,"style":82766},[650],[363,82833,82835,82838,82841,82887,82890,82893,82896,82899,82902,82905,82908,82911,82914,83096],{"className":82834},[407],[363,82836],{"className":82837},[407],[363,82839],{"className":82840,"style":3981},[505],[363,82842,82844,82847],{"className":82843},[407],[363,82845,547],{"className":82846,"style":625},[407,408],[363,82848,82850],{"className":82849},[629],[363,82851,82853,82879],{"className":82852},[633,634],[363,82854,82856,82876],{"className":82855},[638],[363,82857,82859],{"className":82858,"style":727},[642],[363,82860,82861,82864],{"style":646},[363,82862],{"className":82863,"style":651},[650],[363,82865,82867],{"className":82866},[655,656,657,658],[363,82868,82870,82873],{"className":82869},[407,658],[363,82871,5739],{"className":82872,"style":682},[407,408,658],[363,82874,35197],{"className":82875,"style":2934},[407,408,658],[363,82877,666],{"className":82878},[665],[363,82880,82882],{"className":82881},[638],[363,82883,82885],{"className":82884,"style":8315},[642],[363,82886],{},[363,82888,461],{"className":82889},[494],[363,82891,554],{"className":82892,"style":682},[407,408],[363,82894,898],{"className":82895},[920],[363,82897],{"className":82898,"style":754},[505],[363,82900,561],{"className":82901},[407,408],[363,82903,468],{"className":82904},[501],[363,82906],{"className":82907,"style":506},[505],[363,82909,10299],{"className":82910},[510],[363,82912],{"className":82913,"style":506},[505],[363,82915,82917],{"className":82916},[407,34714],[363,82918,82920,83087],{"className":82919},[633,634],[363,82921,82923,83084],{"className":82922},[638],[363,82924,82927,83067],{"className":82925,"style":82926},[642],"height:1.2839em;",[363,82928,82931,82935],{"className":82929,"style":82930},[6654],"top:-3.8em;",[363,82932],{"className":82933,"style":82934},[650],"height:3.8em;",[363,82936,82938,83006,83052,83055,83058,83061,83064],{"className":82937,"style":41508},[407],[363,82939,82941,82944,83003],{"className":82940},[407],[363,82942],{"className":82943},[494,789],[363,82945,82947],{"className":82946},[586],[363,82948,82950,82995],{"className":82949},[633,634],[363,82951,82953,82992],{"className":82952},[638],[363,82954,82956,82970,82978],{"className":82955,"style":2871},[642],[363,82957,82958,82961],{"style":2874},[363,82959],{"className":82960,"style":809},[650],[363,82962,82964],{"className":82963},[655,656,657,658],[363,82965,82967],{"className":82966},[407,658],[363,82968,2810],{"className":82969},[407,658],[363,82971,82972,82975],{"style":821},[363,82973],{"className":82974,"style":809},[650],[363,82976],{"className":82977,"style":829},[828],[363,82979,82980,82983],{"style":2897},[363,82981],{"className":82982,"style":809},[650],[363,82984,82986],{"className":82985},[655,656,657,658],[363,82987,82989],{"className":82988},[407,658],[363,82990,465],{"className":82991},[407,658],[363,82993,666],{"className":82994},[665],[363,82996,82998],{"className":82997},[638],[363,82999,83001],{"className":83000,"style":2919},[642],[363,83002],{},[363,83004],{"className":83005},[501,789],[363,83007,83009,83012],{"className":83008},[407],[363,83010,547],{"className":83011,"style":625},[407,408],[363,83013,83015],{"className":83014},[629],[363,83016,83018,83044],{"className":83017},[633,634],[363,83019,83021,83041],{"className":83020},[638],[363,83022,83024],{"className":83023,"style":727},[642],[363,83025,83026,83029],{"style":646},[363,83027],{"className":83028,"style":651},[650],[363,83030,83032],{"className":83031},[655,656,657,658],[363,83033,83035,83038],{"className":83034},[407,658],[363,83036,11041],{"className":83037,"style":11129},[407,408,658],[363,83039,22240],{"className":83040},[407,408,658],[363,83042,666],{"className":83043},[665],[363,83045,83047],{"className":83046},[638],[363,83048,83050],{"className":83049,"style":8315},[642],[363,83051],{},[363,83053,461],{"className":83054},[494],[363,83056,554],{"className":83057,"style":682},[407,408],[363,83059,558],{"className":83060},[407],[363,83062,561],{"className":83063},[407,408],[363,83065,468],{"className":83066},[501],[363,83068,83070,83073],{"style":83069},"top:-3.2439em;",[363,83071],{"className":83072,"style":82934},[650],[363,83074,83077],{"className":83075,"style":83076},[34790],"min-width:1.02em;height:1.88em;",[6670,83078,83081],{"xmlns":6672,"width":6673,"height":83079,"viewBox":83080,"preserveAspectRatio":6676},"1.88em","0 0 400000 1944",[6678,83082],{"d":83083},"M983 90\nl0 -0\nc4,-6.7,10,-10,18,-10 H400000v40\nH1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7\ns-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744\nc-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30\nc26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722\nc56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5\nc53.7,-170.3,84.5,-266.8,92.5,-289.5z\nM1001 80h400000v40h-400000z",[363,83085,666],{"className":83086},[665],[363,83088,83090],{"className":83089},[638],[363,83091,83094],{"className":83092,"style":83093},[642],"height:0.5561em;",[363,83095],{},[363,83097,898],{"className":83098},[920],[363,83100,666],{"className":83101},[665],[363,83103,83105],{"className":83104},[638],[363,83106,83108],{"className":83107,"style":82788},[642],[363,83109],{},[363,83111,83113],{"className":83112,"translate":367},[528],[363,83114,83116,83250],{"className":83115,"translate":367},[366],[363,83117,83119],{"className":83118},[371],[373,83120,83121],{"xmlns":375,"display":537},[377,83122,83123,83247],{},[1590,83124,83125,83181],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,83126,83127,83133],{},[1599,83128,83129],{},[1602,83130,83131],{"scriptlevel":474,"displaystyle":394},[380,83132],{},[1599,83134,83135],{},[1602,83136,83137],{"scriptlevel":474,"displaystyle":394},[380,83138,83139,83141],{},[380,83140],{},[380,83142,83143,83145,83147,83149,83151,83153,83155,83157,83159,83161,83163,83165,83168,83170,83172,83175,83177,83179],{},[383,83144,39638],{"mathvariant":557},[383,83146,16797],{"mathvariant":557},[383,83148,7914],{"mathvariant":557},[383,83150,1116],{"mathvariant":557},[383,83152,45527],{"mathvariant":557},[383,83154,4505],{"mathvariant":557},[383,83156,82643],{"mathvariant":557},[383,83158,48009],{"mathvariant":557},[383,83160,48005],{"mathvariant":557},[383,83162,48005],{"mathvariant":557},[383,83164,7914],{"mathvariant":557},[1644,83166,83167],{},"–",[383,83169,34231],{"mathvariant":557},[383,83171,15747],{"mathvariant":557},[383,83173,83174],{"mathvariant":557},"b",[383,83176,7914],{"mathvariant":557},[383,83178,16797],{"mathvariant":557},[458,83180,1362],{},[1596,83182,83183,83189],{},[1599,83184,83185],{},[1602,83186,83187],{"scriptlevel":474,"displaystyle":394},[380,83188],{},[1599,83190,83191],{},[1602,83192,83193],{"scriptlevel":474,"displaystyle":394},[380,83194,83195,83197,83199,83205,83207,83209,83211,83213,83215,83217,83225,83235,83237,83239,83241,83243,83245],{},[380,83196],{},[505,83198],{"width":3609},[7161,83200,83201,83203],{},[383,83202,34231],{},[463,83204,2810],{},[458,83206,461],{"stretchy":460},[383,83208,554],{},[458,83210,898],{"separator":394},[383,83212,561],{},[458,83214,468],{"stretchy":460},[458,83216,10299],{},[1602,83218,83219],{"scriptlevel":474,"displaystyle":460},[586,83220,83221,83223],{},[463,83222,465],{},[463,83224,2810],{},[543,83226,83227,83229],{},[383,83228,547],{},[380,83230,83231,83233],{},[383,83232,11041],{},[383,83234,22240],{},[458,83236,461],{"stretchy":460},[383,83238,554],{},[383,83240,558],{"mathvariant":557},[383,83242,561],{},[458,83244,468],{"stretchy":460},[458,83246,898],{"separator":394},[387,83248,83249],{"encoding":389},"\\begin{aligned}\n&\\mathrm{Bretagnolle\\text{–}Huber:}\\\\\n&\\qquad H^2(P,Q)\\le \\tfrac12 D_{KL}(P\\|Q),\n\\end{aligned}",[363,83251,83253],{"className":83252,"ariaHidden":394},[393],[363,83254,83256,83260],{"className":83255},[398],[363,83257],{"className":83258,"style":83259},[402],"height:2.7241em;vertical-align:-1.1121em;",[363,83261,83263],{"className":83262},[407],[363,83264,83266,83310],{"className":83265},[1590],[363,83267,83269],{"className":83268},[1707],[363,83270,83272,83301],{"className":83271},[633,634],[363,83273,83275,83298],{"className":83274},[638],[363,83276,83279,83289],{"className":83277,"style":83278},[642],"height:1.6121em;",[363,83280,83282,83286],{"style":83281},"top:-3.6362em;",[363,83283],{"className":83284,"style":83285},[650],"height:2.8641em;",[363,83287],{"className":83288},[407],[363,83290,83292,83295],{"style":83291},"top:-2.1121em;",[363,83293],{"className":83294,"style":83285},[650],[363,83296],{"className":83297},[407],[363,83299,666],{"className":83300},[665],[363,83302,83304],{"className":83303},[638],[363,83305,83308],{"className":83306,"style":83307},[642],"height:1.1121em;",[363,83309],{},[363,83311,83313],{"className":83312},[1798],[363,83314,83316,83563],{"className":83315},[633,634],[363,83317,83319,83560],{"className":83318},[638],[363,83320,83322,83357],{"className":83321,"style":83278},[642],[363,83323,83325,83328],{"style":83324},"top:-3.7721em;",[363,83326],{"className":83327,"style":809},[650],[363,83329,83331,83334],{"className":83330},[407],[363,83332],{"className":83333},[407],[363,83335,83337,83341,83347,83351,83354],{"className":83336},[407],[363,83338,83340],{"className":83339},[407,33009],"Bretagnolle",[363,83342,83344],{"className":83343},[407,4945],[363,83345,83167],{"className":83346},[407],[363,83348,83350],{"className":83349},[407,33009],"Huber",[363,83352],{"className":83353,"style":506},[505],[363,83355,1362],{"className":83356},[510],[363,83358,83360,83363],{"style":83359},"top:-2.2479em;",[363,83361],{"className":83362,"style":809},[650],[363,83364,83366,83369,83372,83401,83404,83407,83410,83413,83416,83419,83422,83425,83428,83496,83542,83545,83548,83551,83554,83557],{"className":83365},[407],[363,83367],{"className":83368},[407],[363,83370],{"className":83371,"style":3981},[505],[363,83373,83375,83378],{"className":83374},[407],[363,83376,34231],{"className":83377,"style":34385},[407,408],[363,83379,83381],{"className":83380},[629],[363,83382,83384],{"className":83383},[633],[363,83385,83387],{"className":83386},[638],[363,83388,83390],{"className":83389,"style":20082},[642],[363,83391,83392,83395],{"style":8624},[363,83393],{"className":83394,"style":651},[650],[363,83396,83398],{"className":83397},[655,656,657,658],[363,83399,2810],{"className":83400},[407,658],[363,83402,461],{"className":83403},[494],[363,83405,554],{"className":83406,"style":682},[407,408],[363,83408,898],{"className":83409},[920],[363,83411],{"className":83412,"style":754},[505],[363,83414,561],{"className":83415},[407,408],[363,83417,468],{"className":83418},[501],[363,83420],{"className":83421,"style":506},[505],[363,83423,10299],{"className":83424},[510],[363,83426],{"className":83427,"style":506},[505],[363,83429,83431,83434,83493],{"className":83430},[407],[363,83432],{"className":83433},[494,789],[363,83435,83437],{"className":83436},[586],[363,83438,83440,83485],{"className":83439},[633,634],[363,83441,83443,83482],{"className":83442},[638],[363,83444,83446,83460,83468],{"className":83445,"style":2871},[642],[363,83447,83448,83451],{"style":2874},[363,83449],{"className":83450,"style":809},[650],[363,83452,83454],{"className":83453},[655,656,657,658],[363,83455,83457],{"className":83456},[407,658],[363,83458,2810],{"className":83459},[407,658],[363,83461,83462,83465],{"style":821},[363,83463],{"className":83464,"style":809},[650],[363,83466],{"className":83467,"style":829},[828],[363,83469,83470,83473],{"style":2897},[363,83471],{"className":83472,"style":809},[650],[363,83474,83476],{"className":83475},[655,656,657,658],[363,83477,83479],{"className":83478},[407,658],[363,83480,465],{"className":83481},[407,658],[363,83483,666],{"className":83484},[665],[363,83486,83488],{"className":83487},[638],[363,83489,83491],{"className":83490,"style":2919},[642],[363,83492],{},[363,83494],{"className":83495},[501,789],[363,83497,83499,83502],{"className":83498},[407],[363,83500,547],{"className":83501,"style":625},[407,408],[363,83503,83505],{"className":83504},[629],[363,83506,83508,83534],{"className":83507},[633,634],[363,83509,83511,83531],{"className":83510},[638],[363,83512,83514],{"className":83513,"style":727},[642],[363,83515,83516,83519],{"style":646},[363,83517],{"className":83518,"style":651},[650],[363,83520,83522],{"className":83521},[655,656,657,658],[363,83523,83525,83528],{"className":83524},[407,658],[363,83526,11041],{"className":83527,"style":11129},[407,408,658],[363,83529,22240],{"className":83530},[407,408,658],[363,83532,666],{"className":83533},[665],[363,83535,83537],{"className":83536},[638],[363,83538,83540],{"className":83539,"style":8315},[642],[363,83541],{},[363,83543,461],{"className":83544},[494],[363,83546,554],{"className":83547,"style":682},[407,408],[363,83549,558],{"className":83550},[407],[363,83552,561],{"className":83553},[407,408],[363,83555,468],{"className":83556},[501],[363,83558,898],{"className":83559},[920],[363,83561,666],{"className":83562},[665],[363,83564,83566],{"className":83565},[638],[363,83567,83569],{"className":83568,"style":83307},[642],[363,83570],{},[363,83572,83574],{"className":83573,"translate":367},[528],[363,83575,83577,83711],{"className":83576,"translate":367},[366],[363,83578,83580],{"className":83579},[371],[373,83581,83582],{"xmlns":375,"display":537},[377,83583,83584,83708],{},[1590,83585,83586,83662],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,83587,83588,83594],{},[1599,83589,83590],{},[1602,83591,83592],{"scriptlevel":474,"displaystyle":394},[380,83593],{},[1599,83595,83596],{},[1602,83597,83598],{"scriptlevel":474,"displaystyle":394},[380,83599,83600,83602,83612,83614,83616,83618,83620,83622,83624,83648,83650],{},[380,83601],{},[543,83603,83604,83606],{},[383,83605,547],{},[380,83607,83608,83610],{},[383,83609,5739],{},[383,83611,35197],{},[458,83613,461],{"stretchy":460},[383,83615,554],{},[458,83617,898],{"separator":394},[383,83619,561],{},[458,83621,468],{"stretchy":460},[458,83623,10299],{},[34686,83625,83626],{},[380,83627,83628,83634,83636,83638,83640,83646],{},[7161,83629,83630,83632],{},[383,83631,34231],{},[463,83633,2810],{},[458,83635,461],{"stretchy":460},[463,83637,2810],{},[458,83639,5160],{},[7161,83641,83642,83644],{},[383,83643,34231],{},[463,83645,2810],{},[458,83647,468],{"stretchy":460},[458,83649,10299],{},[34686,83651,83652],{},[380,83653,83654,83656],{},[463,83655,2810],{},[7161,83657,83658,83660],{},[383,83659,34231],{},[463,83661,2810],{},[1596,83663,83664,83670],{},[1599,83665,83666],{},[1602,83667,83668],{"scriptlevel":474,"displaystyle":394},[380,83669],{},[1599,83671,83672],{},[1602,83673,83674],{"scriptlevel":474,"displaystyle":394},[380,83675,83676,83678,83680,83682,83706],{},[380,83677],{},[505,83679],{"width":3609},[458,83681,10299],{},[34686,83683,83684],{},[380,83685,83686,83696,83698,83700,83702,83704],{},[543,83687,83688,83690],{},[383,83689,547],{},[380,83691,83692,83694],{},[383,83693,11041],{},[383,83695,22240],{},[458,83697,461],{"stretchy":460},[383,83699,554],{},[383,83701,558],{"mathvariant":557},[383,83703,561],{},[458,83705,468],{"stretchy":460},[383,83707,4722],{"mathvariant":557},[387,83709,83710],{"encoding":389},"\\begin{aligned}\n&D_{TV}(P,Q)\\le\\sqrt{H^2(2-H^2)}\n\\le\\sqrt{2H^2}\\\\\n&\\qquad\\le\\sqrt{D_{KL}(P\\|Q)} .\n\\end{aligned}",[363,83712,83714],{"className":83713,"ariaHidden":394},[393],[363,83715,83717,83721],{"className":83716},[398],[363,83718],{"className":83719,"style":83720},[402],"height:3.0078em;vertical-align:-1.2539em;",[363,83722,83724],{"className":83723},[407],[363,83725,83727,83771],{"className":83726},[1590],[363,83728,83730],{"className":83729},[1707],[363,83731,83733,83762],{"className":83732},[633,634],[363,83734,83736,83759],{"className":83735},[638],[363,83737,83740,83750],{"className":83738,"style":83739},[642],"height:1.7539em;",[363,83741,83743,83747],{"style":83742},"top:-3.7539em;",[363,83744],{"className":83745,"style":83746},[650],"height:3.0039em;",[363,83748],{"className":83749},[407],[363,83751,83753,83756],{"style":83752},"top:-2.11em;",[363,83754],{"className":83755,"style":83746},[650],[363,83757],{"className":83758},[407],[363,83760,666],{"className":83761},[665],[363,83763,83765],{"className":83764},[638],[363,83766,83769],{"className":83767,"style":83768},[642],"height:1.2539em;",[363,83770],{},[363,83772,83774],{"className":83773},[1798],[363,83775,83777,84217],{"className":83776},[633,634],[363,83778,83780,84214],{"className":83779},[638],[363,83781,83783,84083],{"className":83782,"style":83739},[642],[363,83784,83785,83788],{"style":83742},[363,83786],{"className":83787,"style":83746},[650],[363,83789,83791,83794,83840,83843,83846,83849,83852,83855,83858,83861,83864,83867,83995,83998,84001,84004],{"className":83790},[407],[363,83792],{"className":83793},[407],[363,83795,83797,83800],{"className":83796},[407],[363,83798,547],{"className":83799,"style":625},[407,408],[363,83801,83803],{"className":83802},[629],[363,83804,83806,83832],{"className":83805},[633,634],[363,83807,83809,83829],{"className":83808},[638],[363,83810,83812],{"className":83811,"style":727},[642],[363,83813,83814,83817],{"style":646},[363,83815],{"className":83816,"style":651},[650],[363,83818,83820],{"className":83819},[655,656,657,658],[363,83821,83823,83826],{"className":83822},[407,658],[363,83824,5739],{"className":83825,"style":682},[407,408,658],[363,83827,35197],{"className":83828,"style":2934},[407,408,658],[363,83830,666],{"className":83831},[665],[363,83833,83835],{"className":83834},[638],[363,83836,83838],{"className":83837,"style":8315},[642],[363,83839],{},[363,83841,461],{"className":83842},[494],[363,83844,554],{"className":83845,"style":682},[407,408],[363,83847,898],{"className":83848},[920],[363,83850],{"className":83851,"style":754},[505],[363,83853,561],{"className":83854},[407,408],[363,83856,468],{"className":83857},[501],[363,83859],{"className":83860,"style":506},[505],[363,83862,10299],{"className":83863},[510],[363,83865],{"className":83866,"style":506},[505],[363,83868,83870],{"className":83869},[407,34714],[363,83871,83873,83986],{"className":83872},[633,634],[363,83874,83876,83983],{"className":83875},[638],[363,83877,83880,83966],{"className":83878,"style":83879},[642],"height:0.9839em;",[363,83881,83884,83887],{"className":83882,"style":83883},[6654],"top:-3.2em;",[363,83885],{"className":83886,"style":15193},[650],[363,83888,83890,83919,83922,83925,83928,83931,83934,83963],{"className":83889,"style":41508},[407],[363,83891,83893,83896],{"className":83892},[407],[363,83894,34231],{"className":83895,"style":34385},[407,408],[363,83897,83899],{"className":83898},[629],[363,83900,83902],{"className":83901},[633],[363,83903,83905],{"className":83904},[638],[363,83906,83908],{"className":83907,"style":45379},[642],[363,83909,83910,83913],{"style":45382},[363,83911],{"className":83912,"style":651},[650],[363,83914,83916],{"className":83915},[655,656,657,658],[363,83917,2810],{"className":83918},[407,658],[363,83920,461],{"className":83921},[494],[363,83923,2810],{"className":83924},[407],[363,83926],{"className":83927,"style":2934},[505],[363,83929,5160],{"className":83930},[2938],[363,83932],{"className":83933,"style":2934},[505],[363,83935,83937,83940],{"className":83936},[407],[363,83938,34231],{"className":83939,"style":34385},[407,408],[363,83941,83943],{"className":83942},[629],[363,83944,83946],{"className":83945},[633],[363,83947,83949],{"className":83948},[638],[363,83950,83952],{"className":83951,"style":45379},[642],[363,83953,83954,83957],{"style":45382},[363,83955],{"className":83956,"style":651},[650],[363,83958,83960],{"className":83959},[655,656,657,658],[363,83961,2810],{"className":83962},[407,658],[363,83964,468],{"className":83965},[501],[363,83967,83969,83972],{"style":83968},"top:-2.9439em;",[363,83970],{"className":83971,"style":15193},[650],[363,83973,83976],{"className":83974,"style":83975},[34790],"min-width:1.02em;height:1.28em;",[6670,83977,83980],{"xmlns":6672,"width":6673,"height":83978,"viewBox":83979,"preserveAspectRatio":6676},"1.28em","0 0 400000 1296",[6678,83981],{"d":83982},"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z",[363,83984,666],{"className":83985},[665],[363,83987,83989],{"className":83988},[638],[363,83990,83993],{"className":83991,"style":83992},[642],"height:0.2561em;",[363,83994],{},[363,83996],{"className":83997,"style":506},[505],[363,83999,10299],{"className":84000},[510],[363,84002],{"className":84003,"style":506},[505],[363,84005,84007],{"className":84006},[407,34714],[363,84008,84010,84074],{"className":84009},[633,634],[363,84011,84013,84071],{"className":84012},[638],[363,84014,84017,84058],{"className":84015,"style":84016},[642],"height:1.0039em;",[363,84018,84020,84023],{"className":84019,"style":12210},[6654],[363,84021],{"className":84022,"style":809},[650],[363,84024,84026,84029],{"className":84025,"style":34734},[407],[363,84027,2810],{"className":84028},[407],[363,84030,84032,84035],{"className":84031},[407],[363,84033,34231],{"className":84034,"style":34385},[407,408],[363,84036,84038],{"className":84037},[629],[363,84039,84041],{"className":84040},[633],[363,84042,84044],{"className":84043},[638],[363,84045,84047],{"className":84046,"style":45379},[642],[363,84048,84049,84052],{"style":45382},[363,84050],{"className":84051,"style":651},[650],[363,84053,84055],{"className":84054},[655,656,657,658],[363,84056,2810],{"className":84057},[407,658],[363,84059,84061,84064],{"style":84060},"top:-2.9639em;",[363,84062],{"className":84063,"style":809},[650],[363,84065,84067],{"className":84066,"style":34791},[34790],[6670,84068,84069],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,84070],{"d":34798},[363,84072,666],{"className":84073},[665],[363,84075,84077],{"className":84076},[638],[363,84078,84081],{"className":84079,"style":84080},[642],"height:0.0361em;",[363,84082],{},[363,84084,84085,84088],{"style":83752},[363,84086],{"className":84087,"style":83746},[650],[363,84089,84091,84094,84097,84100,84103,84106,84211],{"className":84090},[407],[363,84092],{"className":84093},[407],[363,84095],{"className":84096,"style":3981},[505],[363,84098],{"className":84099,"style":506},[505],[363,84101,10299],{"className":84102},[510],[363,84104],{"className":84105,"style":506},[505],[363,84107,84109],{"className":84108},[407,34714],[363,84110,84112,84203],{"className":84111},[633,634],[363,84113,84115,84200],{"className":84114},[638],[363,84116,84118,84188],{"className":84117,"style":83879},[642],[363,84119,84121,84124],{"className":84120,"style":83883},[6654],[363,84122],{"className":84123,"style":15193},[650],[363,84125,84127,84173,84176,84179,84182,84185],{"className":84126,"style":41508},[407],[363,84128,84130,84133],{"className":84129},[407],[363,84131,547],{"className":84132,"style":625},[407,408],[363,84134,84136],{"className":84135},[629],[363,84137,84139,84165],{"className":84138},[633,634],[363,84140,84142,84162],{"className":84141},[638],[363,84143,84145],{"className":84144,"style":727},[642],[363,84146,84147,84150],{"style":646},[363,84148],{"className":84149,"style":651},[650],[363,84151,84153],{"className":84152},[655,656,657,658],[363,84154,84156,84159],{"className":84155},[407,658],[363,84157,11041],{"className":84158,"style":11129},[407,408,658],[363,84160,22240],{"className":84161},[407,408,658],[363,84163,666],{"className":84164},[665],[363,84166,84168],{"className":84167},[638],[363,84169,84171],{"className":84170,"style":8315},[642],[363,84172],{},[363,84174,461],{"className":84175},[494],[363,84177,554],{"className":84178,"style":682},[407,408],[363,84180,558],{"className":84181},[407],[363,84183,561],{"className":84184},[407,408],[363,84186,468],{"className":84187},[501],[363,84189,84190,84193],{"style":83968},[363,84191],{"className":84192,"style":15193},[650],[363,84194,84196],{"className":84195,"style":83975},[34790],[6670,84197,84198],{"xmlns":6672,"width":6673,"height":83978,"viewBox":83979,"preserveAspectRatio":6676},[6678,84199],{"d":83982},[363,84201,666],{"className":84202},[665],[363,84204,84206],{"className":84205},[638],[363,84207,84209],{"className":84208,"style":83992},[642],[363,84210],{},[363,84212,4722],{"className":84213},[407],[363,84215,666],{"className":84216},[665],[363,84218,84220],{"className":84219},[638],[363,84221,84223],{"className":84222,"style":83768},[642],[363,84224],{},[11,84226,84227,84230],{},[1572,84228,84229],{},"Pinsker 的完整推导（Vajda 型两步法）。"," 分三步：",[11,84232,84233,84236,84237,84265,84266,84374],{},[1572,84234,84235],{},"第 1 步（数据处理到二元划分）。"," 对任一事件 ",[363,84238,84240,84253],{"className":84239,"translate":367},[366],[363,84241,84243],{"className":84242},[371],[373,84244,84245],{"xmlns":375},[377,84246,84247,84251],{},[380,84248,84249],{},[383,84250,950],{},[387,84252,950],{"encoding":389},[363,84254,84256],{"className":84255,"ariaHidden":394},[393],[363,84257,84259,84262],{"className":84258},[398],[363,84260],{"className":84261,"style":1011},[402],[363,84263,950],{"className":84264},[407,408],"，把样本空间经确定性映射 ",[363,84267,84269,84297],{"className":84268,"translate":367},[366],[363,84270,84272],{"className":84271},[371],[373,84273,84274],{"xmlns":375},[377,84275,84276,84294],{},[380,84277,84278,84280,84282,84288,84290,84292],{},[383,84279,1121],{},[458,84281,9031],{},[543,84283,84284,84286],{},[463,84285,465],{"mathvariant":75560},[383,84287,950],{},[458,84289,461],{"stretchy":460},[383,84291,1121],{},[458,84293,468],{"stretchy":460},[387,84295,84296],{"encoding":389},"x\\mapsto\\mathbf 1_A(x)",[363,84298,84300,84319],{"className":84299,"ariaHidden":394},[393],[363,84301,84303,84307,84310,84313,84316],{"className":84302},[398],[363,84304],{"className":84305,"style":84306},[402],"height:0.522em;vertical-align:-0.011em;",[363,84308,1121],{"className":84309},[407,408],[363,84311],{"className":84312,"style":506},[505],[363,84314,9031],{"className":84315},[510],[363,84317],{"className":84318,"style":506},[505],[363,84320,84322,84325,84365,84368,84371],{"className":84321},[398],[363,84323],{"className":84324,"style":487},[402],[363,84326,84328,84331],{"className":84327},[407],[363,84329,465],{"className":84330},[407,75905],[363,84332,84334],{"className":84333},[629],[363,84335,84337,84357],{"className":84336},[633,634],[363,84338,84340,84354],{"className":84339},[638],[363,84341,84343],{"className":84342,"style":727},[642],[363,84344,84345,84348],{"style":730},[363,84346],{"className":84347,"style":651},[650],[363,84349,84351],{"className":84350},[655,656,657,658],[363,84352,950],{"className":84353},[407,408,658],[363,84355,666],{"className":84356},[665],[363,84358,84360],{"className":84359},[638],[363,84361,84363],{"className":84362,"style":8315},[642],[363,84364],{},[363,84366,461],{"className":84367},[494],[363,84369,1121],{"className":84370},[407,408],[363,84372,468],{"className":84373},[501]," 压成两个点，用 4.5 节的 DPI：",[363,84376,84378],{"className":84377,"translate":367},[528],[363,84379,84381,84506],{"className":84380,"translate":367},[366],[363,84382,84384],{"className":84383},[371],[373,84385,84386],{"xmlns":375,"display":537},[377,84387,84388,84503],{},[380,84389,84390,84400,84402,84404,84406,84408,84410,84412,84414,84416,84426,84428,84438,84440,84442,84444,84446,84448,84450,84460,84462,84465,84467,84469,84471,84473,84475,84477,84479,84481,84483,84485,84487,84489,84491,84493,84495,84497,84499,84501],{},[543,84391,84392,84394],{},[383,84393,547],{},[380,84395,84396,84398],{},[383,84397,11041],{},[383,84399,22240],{},[458,84401,461],{"stretchy":460},[383,84403,554],{},[383,84405,558],{"mathvariant":557},[383,84407,561],{},[458,84409,468],{"stretchy":460},[1644,84411,4630],{},[458,84413,7275],{},[1644,84415,4630],{},[543,84417,84418,84420],{},[383,84419,547],{},[380,84421,84422,84424],{},[383,84423,11041],{},[383,84425,22240],{},[458,84427,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[380,84429,84430,84432,84434,84436],{},[383,84431,39638],{"mathvariant":557},[383,84433,7914],{"mathvariant":557},[383,84435,16797],{"mathvariant":557},[383,84437,82643],{"mathvariant":557},[458,84439,461],{"stretchy":460},[383,84441,45101],{},[458,84443,468],{"stretchy":460},[1644,84445,1646],{},[383,84447,558],{"mathvariant":557},[1644,84449,1646],{},[380,84451,84452,84454,84456,84458],{},[383,84453,39638],{"mathvariant":557},[383,84455,7914],{"mathvariant":557},[383,84457,16797],{"mathvariant":557},[383,84459,82643],{"mathvariant":557},[458,84461,461],{"stretchy":460},[383,84463,84464],{},"β",[458,84466,468],{"stretchy":460},[458,84468,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,84470,898],{"separator":394},[505,84472],{"width":3609},[383,84474,45101],{},[458,84476,471],{},[383,84478,554],{},[458,84480,461],{"stretchy":460},[383,84482,950],{},[458,84484,468],{"stretchy":460},[458,84486,898],{"separator":394},[1644,84488,4630],{},[383,84490,84464],{},[458,84492,471],{},[383,84494,561],{},[458,84496,461],{"stretchy":460},[383,84498,950],{},[458,84500,468],{"stretchy":460},[383,84502,4722],{"mathvariant":557},[387,84504,84505],{"encoding":389},"D_{KL}(P\\|Q)\\ \\ge\\ \nD_{KL}\\big(\\mathrm{Bern}(\\alpha)\\,\\|\\,\n\\mathrm{Bern}(\\beta)\\big),\n\\qquad \\alpha=P(A),\\ \\beta=Q(A).",[363,84507,84509,84591,84717,84756],{"className":84508,"ariaHidden":394},[393],[363,84510,84512,84515,84561,84564,84567,84570,84573,84576,84579,84582,84585,84588],{"className":84511},[398],[363,84513],{"className":84514,"style":487},[402],[363,84516,84518,84521],{"className":84517},[407],[363,84519,547],{"className":84520,"style":625},[407,408],[363,84522,84524],{"className":84523},[629],[363,84525,84527,84553],{"className":84526},[633,634],[363,84528,84530,84550],{"className":84529},[638],[363,84531,84533],{"className":84532,"style":727},[642],[363,84534,84535,84538],{"style":646},[363,84536],{"className":84537,"style":651},[650],[363,84539,84541],{"className":84540},[655,656,657,658],[363,84542,84544,84547],{"className":84543},[407,658],[363,84545,11041],{"className":84546,"style":11129},[407,408,658],[363,84548,22240],{"className":84549},[407,408,658],[363,84551,666],{"className":84552},[665],[363,84554,84556],{"className":84555},[638],[363,84557,84559],{"className":84558,"style":8315},[642],[363,84560],{},[363,84562,461],{"className":84563},[494],[363,84565,554],{"className":84566,"style":682},[407,408],[363,84568,558],{"className":84569},[407],[363,84571,561],{"className":84572},[407,408],[363,84574,468],{"className":84575},[501],[363,84577,4630],{"className":84578},[505],[363,84580],{"className":84581,"style":506},[505],[363,84583,7275],{"className":84584},[510],[363,84586,4630],{"className":84587},[505],[363,84589],{"className":84590,"style":506},[505],[363,84592,84594,84597,84643,84649,84656,84659,84662,84665,84668,84671,84674,84680,84683,84687,84690,84696,84699,84702,84705,84708,84711,84714],{"className":84593},[398],[363,84595],{"className":84596,"style":20910},[402],[363,84598,84600,84603],{"className":84599},[407],[363,84601,547],{"className":84602,"style":625},[407,408],[363,84604,84606],{"className":84605},[629],[363,84607,84609,84635],{"className":84608},[633,634],[363,84610,84612,84632],{"className":84611},[638],[363,84613,84615],{"className":84614,"style":727},[642],[363,84616,84617,84620],{"style":646},[363,84618],{"className":84619,"style":651},[650],[363,84621,84623],{"className":84622},[655,656,657,658],[363,84624,84626,84629],{"className":84625},[407,658],[363,84627,11041],{"className":84628,"style":11129},[407,408,658],[363,84630,22240],{"className":84631},[407,408,658],[363,84633,666],{"className":84634},[665],[363,84636,84638],{"className":84637},[638],[363,84639,84641],{"className":84640,"style":8315},[642],[363,84642],{},[363,84644,84646],{"className":84645},[407],[363,84647,461],{"className":84648},[767,10021],[363,84650,84652],{"className":84651},[407],[363,84653,84655],{"className":84654},[407,33009],"Bern",[363,84657,461],{"className":84658},[494],[363,84660,45101],{"className":84661,"style":45131},[407,408],[363,84663,468],{"className":84664},[501],[363,84666],{"className":84667,"style":754},[505],[363,84669,558],{"className":84670},[407],[363,84672],{"className":84673,"style":754},[505],[363,84675,84677],{"className":84676},[407],[363,84678,84655],{"className":84679},[407,33009],[363,84681,461],{"className":84682},[494],[363,84684,84464],{"className":84685,"style":84686},[407,408],"margin-right:0.0528em;",[363,84688,468],{"className":84689},[501],[363,84691,84693],{"className":84692},[407],[363,84694,468],{"className":84695},[767,10021],[363,84697,898],{"className":84698},[920],[363,84700],{"className":84701,"style":3981},[505],[363,84703],{"className":84704,"style":754},[505],[363,84706,45101],{"className":84707,"style":45131},[407,408],[363,84709],{"className":84710,"style":506},[505],[363,84712,471],{"className":84713},[510],[363,84715],{"className":84716,"style":506},[505],[363,84718,84720,84723,84726,84729,84732,84735,84738,84741,84744,84747,84750,84753],{"className":84719},[398],[363,84721],{"className":84722,"style":487},[402],[363,84724,554],{"className":84725,"style":682},[407,408],[363,84727,461],{"className":84728},[494],[363,84730,950],{"className":84731},[407,408],[363,84733,468],{"className":84734},[501],[363,84736,898],{"className":84737},[920],[363,84739,4630],{"className":84740},[505],[363,84742],{"className":84743,"style":754},[505],[363,84745,84464],{"className":84746,"style":84686},[407,408],[363,84748],{"className":84749,"style":506},[505],[363,84751,471],{"className":84752},[510],[363,84754],{"className":84755,"style":506},[505],[363,84757,84759,84762,84765,84768,84771,84774],{"className":84758},[398],[363,84760],{"className":84761,"style":487},[402],[363,84763,561],{"className":84764},[407,408],[363,84766,461],{"className":84767},[494],[363,84769,950],{"className":84770},[407,408],[363,84772,468],{"className":84773},[501],[363,84775,4722],{"className":84776},[407],[11,84778,84779,84782,84783,84878,84879,84907,84908,5992,85041,85173,85174,5992,85247,85320],{},[1572,84780,84781],{},"第 2 步（二元问题的精确最小值）。"," 固定差 ",[363,84784,84786,84812],{"className":84785,"translate":367},[366],[363,84787,84789],{"className":84788},[371],[373,84790,84791],{"xmlns":375},[377,84792,84793,84809],{},[380,84794,84795,84797,84799,84801,84803,84805,84807],{},[383,84796,16059],{},[458,84798,471],{},[383,84800,45101],{},[458,84802,5160],{},[383,84804,84464],{},[458,84806,7275],{},[463,84808,474],{},[387,84810,84811],{"encoding":389},"\\delta=\\alpha-\\beta\\ge0",[363,84813,84815,84833,84851,84869],{"className":84814,"ariaHidden":394},[393],[363,84816,84818,84821,84824,84827,84830],{"className":84817},[398],[363,84819],{"className":84820,"style":12944},[402],[363,84822,16059],{"className":84823,"style":16108},[407,408],[363,84825],{"className":84826,"style":506},[505],[363,84828,471],{"className":84829},[510],[363,84831],{"className":84832,"style":506},[505],[363,84834,84836,84839,84842,84845,84848],{"className":84835},[398],[363,84837],{"className":84838,"style":4598},[402],[363,84840,45101],{"className":84841,"style":45131},[407,408],[363,84843],{"className":84844,"style":2934},[505],[363,84846,5160],{"className":84847},[2938],[363,84849],{"className":84850,"style":2934},[505],[363,84852,84854,84857,84860,84863,84866],{"className":84853},[398],[363,84855],{"className":84856,"style":403},[402],[363,84858,84464],{"className":84859,"style":84686},[407,408],[363,84861],{"className":84862,"style":506},[505],[363,84864,7275],{"className":84865},[510],[363,84867],{"className":84868,"style":506},[505],[363,84870,84872,84875],{"className":84871},[398],[363,84873],{"className":84874,"style":520},[402],[363,84876,474],{"className":84877},[407],"（目标 TV 值），对 ",[363,84880,84882,84895],{"className":84881,"translate":367},[366],[363,84883,84885],{"className":84884},[371],[373,84886,84887],{"xmlns":375},[377,84888,84889,84893],{},[380,84890,84891],{},[383,84892,45101],{},[387,84894,49437],{"encoding":389},[363,84896,84898],{"className":84897,"ariaHidden":394},[393],[363,84899,84901,84904],{"className":84900},[398],[363,84902],{"className":84903,"style":2692},[402],[363,84905,45101],{"className":84906,"style":45131},[407,408]," 最小化二元 KL。取对称中心 ",[363,84909,84911,84939],{"className":84910,"translate":367},[366],[363,84912,84914],{"className":84913},[371],[373,84915,84916],{"xmlns":375},[377,84917,84918,84936],{},[380,84919,84920,84922,84924],{},[383,84921,45101],{},[458,84923,471],{},[586,84925,84926,84934],{},[380,84927,84928,84930,84932],{},[463,84929,465],{},[458,84931,2817],{},[383,84933,16059],{},[463,84935,2810],{},[387,84937,84938],{"encoding":389},"\\alpha=\\frac{1+\\delta}{2}",[363,84940,84942,84960],{"className":84941,"ariaHidden":394},[393],[363,84943,84945,84948,84951,84954,84957],{"className":84944},[398],[363,84946],{"className":84947,"style":2692},[402],[363,84949,45101],{"className":84950,"style":45131},[407,408],[363,84952],{"className":84953,"style":506},[505],[363,84955,471],{"className":84956},[510],[363,84958],{"className":84959,"style":506},[505],[363,84961,84963,84967],{"className":84962},[398],[363,84964],{"className":84965,"style":84966},[402],"height:1.2251em;vertical-align:-0.345em;",[363,84968,84970,84973,85038],{"className":84969},[407],[363,84971],{"className":84972},[494,789],[363,84974,84976],{"className":84975},[586],[363,84977,84979,85030],{"className":84978},[633,634],[363,84980,84982,85027],{"className":84981},[638],[363,84983,84985,84999,85007],{"className":84984,"style":3034},[642],[363,84986,84987,84990],{"style":2874},[363,84988],{"className":84989,"style":809},[650],[363,84991,84993],{"className":84992},[655,656,657,658],[363,84994,84996],{"className":84995},[407,658],[363,84997,2810],{"className":84998},[407,658],[363,85000,85001,85004],{"style":821},[363,85002],{"className":85003,"style":809},[650],[363,85005],{"className":85006,"style":829},[828],[363,85008,85009,85012],{"style":2897},[363,85010],{"className":85011,"style":809},[650],[363,85013,85015],{"className":85014},[655,656,657,658],[363,85016,85018,85021,85024],{"className":85017},[407,658],[363,85019,465],{"className":85020},[407,658],[363,85022,2817],{"className":85023},[2938,658],[363,85025,16059],{"className":85026,"style":16108},[407,408,658],[363,85028,666],{"className":85029},[665],[363,85031,85033],{"className":85032},[638],[363,85034,85036],{"className":85035,"style":2919},[642],[363,85037],{},[363,85039],{"className":85040},[501,789],[363,85042,85044,85072],{"className":85043,"translate":367},[366],[363,85045,85047],{"className":85046},[371],[373,85048,85049],{"xmlns":375},[377,85050,85051,85069],{},[380,85052,85053,85055,85057],{},[383,85054,84464],{},[458,85056,471],{},[586,85058,85059,85067],{},[380,85060,85061,85063,85065],{},[463,85062,465],{},[458,85064,5160],{},[383,85066,16059],{},[463,85068,2810],{},[387,85070,85071],{"encoding":389},"\\beta=\\frac{1-\\delta}{2}",[363,85073,85075,85093],{"className":85074,"ariaHidden":394},[393],[363,85076,85078,85081,85084,85087,85090],{"className":85077},[398],[363,85079],{"className":85080,"style":403},[402],[363,85082,84464],{"className":85083,"style":84686},[407,408],[363,85085],{"className":85086,"style":506},[505],[363,85088,471],{"className":85089},[510],[363,85091],{"className":85092,"style":506},[505],[363,85094,85096,85099],{"className":85095},[398],[363,85097],{"className":85098,"style":84966},[402],[363,85100,85102,85105,85170],{"className":85101},[407],[363,85103],{"className":85104},[494,789],[363,85106,85108],{"className":85107},[586],[363,85109,85111,85162],{"className":85110},[633,634],[363,85112,85114,85159],{"className":85113},[638],[363,85115,85117,85131,85139],{"className":85116,"style":3034},[642],[363,85118,85119,85122],{"style":2874},[363,85120],{"className":85121,"style":809},[650],[363,85123,85125],{"className":85124},[655,656,657,658],[363,85126,85128],{"className":85127},[407,658],[363,85129,2810],{"className":85130},[407,658],[363,85132,85133,85136],{"style":821},[363,85134],{"className":85135,"style":809},[650],[363,85137],{"className":85138,"style":829},[828],[363,85140,85141,85144],{"style":2897},[363,85142],{"className":85143,"style":809},[650],[363,85145,85147],{"className":85146},[655,656,657,658],[363,85148,85150,85153,85156],{"className":85149},[407,658],[363,85151,465],{"className":85152},[407,658],[363,85154,5160],{"className":85155},[2938,658],[363,85157,16059],{"className":85158,"style":16108},[407,408,658],[363,85160,666],{"className":85161},[665],[363,85163,85165],{"className":85164},[638],[363,85166,85168],{"className":85167,"style":2919},[642],[363,85169],{},[363,85171],{"className":85172},[501,789],"，此时 ",[363,85175,85177,85199],{"className":85176,"translate":367},[366],[363,85178,85180],{"className":85179},[371],[373,85181,85182],{"xmlns":375},[377,85183,85184,85196],{},[380,85185,85186,85188,85190,85192,85194],{},[463,85187,465],{},[458,85189,5160],{},[383,85191,45101],{},[458,85193,471],{},[383,85195,84464],{},[387,85197,85198],{"encoding":389},"1-\\alpha=\\beta",[363,85200,85202,85220,85238],{"className":85201,"ariaHidden":394},[393],[363,85203,85205,85208,85211,85214,85217],{"className":85204},[398],[363,85206],{"className":85207,"style":12925},[402],[363,85209,465],{"className":85210},[407],[363,85212],{"className":85213,"style":2934},[505],[363,85215,5160],{"className":85216},[2938],[363,85218],{"className":85219,"style":2934},[505],[363,85221,85223,85226,85229,85232,85235],{"className":85222},[398],[363,85224],{"className":85225,"style":2692},[402],[363,85227,45101],{"className":85228,"style":45131},[407,408],[363,85230],{"className":85231,"style":506},[505],[363,85233,471],{"className":85234},[510],[363,85236],{"className":85237,"style":506},[505],[363,85239,85241,85244],{"className":85240},[398],[363,85242],{"className":85243,"style":403},[402],[363,85245,84464],{"className":85246,"style":84686},[407,408],[363,85248,85250,85272],{"className":85249,"translate":367},[366],[363,85251,85253],{"className":85252},[371],[373,85254,85255],{"xmlns":375},[377,85256,85257,85269],{},[380,85258,85259,85261,85263,85265,85267],{},[463,85260,465],{},[458,85262,5160],{},[383,85264,84464],{},[458,85266,471],{},[383,85268,45101],{},[387,85270,85271],{"encoding":389},"1-\\beta=\\alpha",[363,85273,85275,85293,85311],{"className":85274,"ariaHidden":394},[393],[363,85276,85278,85281,85284,85287,85290],{"className":85277},[398],[363,85279],{"className":85280,"style":12925},[402],[363,85282,465],{"className":85283},[407],[363,85285],{"className":85286,"style":2934},[505],[363,85288,5160],{"className":85289},[2938],[363,85291],{"className":85292,"style":2934},[505],[363,85294,85296,85299,85302,85305,85308],{"className":85295},[398],[363,85297],{"className":85298,"style":403},[402],[363,85300,84464],{"className":85301,"style":84686},[407,408],[363,85303],{"className":85304,"style":506},[505],[363,85306,471],{"className":85307},[510],[363,85309],{"className":85310,"style":506},[505],[363,85312,85314,85317],{"className":85313},[398],[363,85315],{"className":85316,"style":2692},[402],[363,85318,45101],{"className":85319,"style":45131},[407,408],"，算得",[363,85322,85324],{"className":85323,"translate":367},[528],[363,85325,85327,85583],{"className":85326,"translate":367},[366],[363,85328,85330],{"className":85329},[371],[373,85331,85332],{"xmlns":375,"display":537},[377,85333,85334,85580],{},[1590,85335,85336,85394,85444,85518],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,85337,85338,85344],{},[1599,85339,85340],{},[1602,85341,85342],{"scriptlevel":474,"displaystyle":394},[380,85343],{},[1599,85345,85346],{},[1602,85347,85348],{"scriptlevel":474,"displaystyle":394},[380,85349,85350,85352,85362,85364,85374,85376,85390,85392],{},[380,85351],{},[543,85353,85354,85356],{},[383,85355,547],{},[380,85357,85358,85360],{},[383,85359,11041],{},[383,85361,22240],{},[458,85363,461],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[380,85365,85366,85368,85370,85372],{},[383,85367,39638],{"mathvariant":557},[383,85369,7914],{"mathvariant":557},[383,85371,16797],{"mathvariant":557},[383,85373,82643],{"mathvariant":557},[458,85375,461],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[1602,85377,85378],{"scriptlevel":474,"displaystyle":460},[586,85379,85380,85388],{},[380,85381,85382,85384,85386],{},[463,85383,465],{},[458,85385,2817],{},[383,85387,16059],{},[463,85389,2810],{},[458,85391,468],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[458,85393,468],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[1596,85395,85396,85402],{},[1599,85397,85398],{},[1602,85399,85400],{"scriptlevel":474,"displaystyle":394},[380,85401],{},[1599,85403,85404],{},[1602,85405,85406],{"scriptlevel":474,"displaystyle":394},[380,85407,85408,85410,85412,85414,85424,85426,85440,85442],{},[380,85409],{},[505,85411],{"width":3609},[458,85413,558],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[380,85415,85416,85418,85420,85422],{},[383,85417,39638],{"mathvariant":557},[383,85419,7914],{"mathvariant":557},[383,85421,16797],{"mathvariant":557},[383,85423,82643],{"mathvariant":557},[458,85425,461],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[1602,85427,85428],{"scriptlevel":474,"displaystyle":460},[586,85429,85430,85438],{},[380,85431,85432,85434,85436],{},[463,85433,465],{},[458,85435,5160],{},[383,85437,16059],{},[463,85439,2810],{},[458,85441,468],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[458,85443,468],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[1596,85445,85446,85452],{},[1599,85447,85448],{},[1602,85449,85450],{"scriptlevel":474,"displaystyle":394},[380,85451],{},[1599,85453,85454],{},[1602,85455,85456],{"scriptlevel":474,"displaystyle":394},[380,85457,85458,85460,85462,85464,85466,85468,85476,85478,85480,85482,85484,85492,85494,85496,85498,85500,85502,85504,85506,85508,85510],{},[380,85459],{},[458,85461,471],{},[383,85463,45101],{},[383,85465,4447],{},[458,85467,4450],{},[1602,85469,85470],{"scriptlevel":474,"displaystyle":460},[586,85471,85472,85474],{},[383,85473,45101],{},[383,85475,84464],{},[458,85477,2817],{},[383,85479,84464],{},[383,85481,4447],{},[458,85483,4450],{},[1602,85485,85486],{"scriptlevel":474,"displaystyle":460},[586,85487,85488,85490],{},[383,85489,84464],{},[383,85491,45101],{},[458,85493,471],{},[458,85495,461],{"stretchy":460},[383,85497,45101],{},[458,85499,5160],{},[383,85501,84464],{},[458,85503,468],{"stretchy":460},[1644,85505,1646],{},[383,85507,4447],{},[458,85509,4450],{},[1602,85511,85512],{"scriptlevel":474,"displaystyle":460},[586,85513,85514,85516],{},[383,85515,45101],{},[383,85517,84464],{},[1596,85519,85520,85526],{},[1599,85521,85522],{},[1602,85523,85524],{"scriptlevel":474,"displaystyle":394},[380,85525],{},[1599,85527,85528],{},[1602,85529,85530],{"scriptlevel":474,"displaystyle":394},[380,85531,85532,85534,85536,85538,85540,85542,85544,85564,85566,85568,85570,85572,85574,85576,85578],{},[380,85533],{},[458,85535,471],{},[383,85537,16059],{},[1644,85539,1646],{},[383,85541,4447],{},[458,85543,4450],{},[1602,85545,85546],{"scriptlevel":474,"displaystyle":460},[586,85547,85548,85556],{},[380,85549,85550,85552,85554],{},[463,85551,465],{},[458,85553,2817],{},[383,85555,16059],{},[380,85557,85558,85560,85562],{},[463,85559,465],{},[458,85561,5160],{},[383,85563,16059],{},[458,85565,471],{},[458,85567,1362],{},[1644,85569,1646],{},[383,85571,39012],{},[458,85573,461],{"stretchy":460},[383,85575,16059],{},[458,85577,468],{"stretchy":460},[383,85579,4722],{"mathvariant":557},[387,85581,85582],{"encoding":389},"\\begin{aligned}\n&D_{KL}\\Big(\\mathrm{Bern}\n\\Big(\\tfrac{1+\\delta}2\\Big)\\Big)\\\\\n&\\qquad\\Big\\|\\mathrm{Bern}\n\\Big(\\tfrac{1-\\delta}2\\Big)\\Big)\\\\\n&=\\alpha\\log\\tfrac{\\alpha}{\\beta}\n+\\beta\\log\\tfrac{\\beta}{\\alpha}\n=(\\alpha-\\beta)\\,\\log\\tfrac{\\alpha}{\\beta}\\\\\n&=\\delta\\,\\log\\tfrac{1+\\delta}{1-\\delta}\n=:\\,h(\\delta).\n\\end{aligned}",[363,85584,85586],{"className":85585,"ariaHidden":394},[393],[363,85587,85589,85593],{"className":85588},[398],[363,85590],{"className":85591,"style":85592},[402],"height:7.1968em;vertical-align:-3.3484em;",[363,85594,85596],{"className":85595},[407],[363,85597,85599,85660],{"className":85598},[1590],[363,85600,85602],{"className":85601},[1707],[363,85603,85605,85651],{"className":85604},[633,634],[363,85606,85608,85648],{"className":85607},[638],[363,85609,85612,85621,85630,85639],{"className":85610,"style":85611},[642],"height:3.8484em;",[363,85613,85615,85618],{"style":85614},"top:-5.8484em;",[363,85616],{"className":85617,"style":17935},[650],[363,85619],{"className":85620},[407],[363,85622,85624,85627],{"style":85623},"top:-3.7484em;",[363,85625],{"className":85626,"style":17935},[650],[363,85628],{"className":85629},[407],[363,85631,85633,85636],{"style":85632},"top:-1.8661em;",[363,85634],{"className":85635,"style":17935},[650],[363,85637],{"className":85638},[407],[363,85640,85642,85645],{"style":85641},"top:-0.2049em;",[363,85643],{"className":85644,"style":17935},[650],[363,85646],{"className":85647},[407],[363,85649,666],{"className":85650},[665],[363,85652,85654],{"className":85653},[638],[363,85655,85658],{"className":85656,"style":85657},[642],"height:3.3484em;",[363,85659],{},[363,85661,85663],{"className":85662},[1798],[363,85664,85666,86440],{"className":85665},[633,634],[363,85667,85669,86437],{"className":85668},[638],[363,85670,85672,85833,85987,86293],{"className":85671,"style":85611},[642],[363,85673,85674,85677],{"style":85614},[363,85675],{"className":85676,"style":17935},[650],[363,85678,85680,85683,85729,85735,85741,85747,85821,85827],{"className":85679},[407],[363,85681],{"className":85682},[407],[363,85684,85686,85689],{"className":85685},[407],[363,85687,547],{"className":85688,"style":625},[407,408],[363,85690,85692],{"className":85691},[629],[363,85693,85695,85721],{"className":85694},[633,634],[363,85696,85698,85718],{"className":85697},[638],[363,85699,85701],{"className":85700,"style":727},[642],[363,85702,85703,85706],{"style":646},[363,85704],{"className":85705,"style":651},[650],[363,85707,85709],{"className":85708},[655,656,657,658],[363,85710,85712,85715],{"className":85711},[407,658],[363,85713,11041],{"className":85714,"style":11129},[407,408,658],[363,85716,22240],{"className":85717},[407,408,658],[363,85719,666],{"className":85720},[665],[363,85722,85724],{"className":85723},[638],[363,85725,85727],{"className":85726,"style":8315},[642],[363,85728],{},[363,85730,85732],{"className":85731},[407],[363,85733,461],{"className":85734},[767,4067],[363,85736,85738],{"className":85737},[407],[363,85739,84655],{"className":85740},[407,33009],[363,85742,85744],{"className":85743},[407],[363,85745,461],{"className":85746},[767,4067],[363,85748,85750,85753,85818],{"className":85749},[407],[363,85751],{"className":85752},[494,789],[363,85754,85756],{"className":85755},[586],[363,85757,85759,85810],{"className":85758},[633,634],[363,85760,85762,85807],{"className":85761},[638],[363,85763,85765,85779,85787],{"className":85764,"style":3034},[642],[363,85766,85767,85770],{"style":2874},[363,85768],{"className":85769,"style":809},[650],[363,85771,85773],{"className":85772},[655,656,657,658],[363,85774,85776],{"className":85775},[407,658],[363,85777,2810],{"className":85778},[407,658],[363,85780,85781,85784],{"style":821},[363,85782],{"className":85783,"style":809},[650],[363,85785],{"className":85786,"style":829},[828],[363,85788,85789,85792],{"style":2897},[363,85790],{"className":85791,"style":809},[650],[363,85793,85795],{"className":85794},[655,656,657,658],[363,85796,85798,85801,85804],{"className":85797},[407,658],[363,85799,465],{"className":85800},[407,658],[363,85802,2817],{"className":85803},[2938,658],[363,85805,16059],{"className":85806,"style":16108},[407,408,658],[363,85808,666],{"className":85809},[665],[363,85811,85813],{"className":85812},[638],[363,85814,85816],{"className":85815,"style":2919},[642],[363,85817],{},[363,85819],{"className":85820},[501,789],[363,85822,85824],{"className":85823},[407],[363,85825,468],{"className":85826},[767,4067],[363,85828,85830],{"className":85829},[407],[363,85831,468],{"className":85832},[767,4067],[363,85834,85835,85838],{"style":85623},[363,85836],{"className":85837,"style":17935},[650],[363,85839,85841,85844,85847,85889,85895,85901,85975,85981],{"className":85840},[407],[363,85842],{"className":85843},[407],[363,85845],{"className":85846,"style":3981},[505],[363,85848,85850],{"className":85849},[407],[363,85851,85853],{"className":85852},[767,15176],[363,85854,85856,85880],{"className":85855},[633,634],[363,85857,85859,85877],{"className":85858},[638],[363,85860,85863],{"className":85861,"style":85862},[642],"height:1.15em;",[363,85864,85865,85868],{"style":73871},[363,85866],{"className":85867,"style":82934},[650],[363,85869,85871],{"style":85870},"width:0.556em;height:1.8em;",[6670,85872,85874],{"xmlns":6672,"width":15199,"height":17786,"viewBox":85873},"0 0 556 1800",[6678,85875],{"d":85876},"M145 15 v585 v600 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v-600 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v600 v585 h43z\nM367 15 v585 v600 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v-600 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M410 15 H367 v585 v600 v585 h43z",[363,85878,666],{"className":85879},[665],[363,85881,85883],{"className":85882},[638],[363,85884,85887],{"className":85885,"style":85886},[642],"height:0.65em;",[363,85888],{},[363,85890,85892],{"className":85891},[407],[363,85893,84655],{"className":85894},[407,33009],[363,85896,85898],{"className":85897},[407],[363,85899,461],{"className":85900},[767,4067],[363,85902,85904,85907,85972],{"className":85903},[407],[363,85905],{"className":85906},[494,789],[363,85908,85910],{"className":85909},[586],[363,85911,85913,85964],{"className":85912},[633,634],[363,85914,85916,85961],{"className":85915},[638],[363,85917,85919,85933,85941],{"className":85918,"style":3034},[642],[363,85920,85921,85924],{"style":2874},[363,85922],{"className":85923,"style":809},[650],[363,85925,85927],{"className":85926},[655,656,657,658],[363,85928,85930],{"className":85929},[407,658],[363,85931,2810],{"className":85932},[407,658],[363,85934,85935,85938],{"style":821},[363,85936],{"className":85937,"style":809},[650],[363,85939],{"className":85940,"style":829},[828],[363,85942,85943,85946],{"style":2897},[363,85944],{"className":85945,"style":809},[650],[363,85947,85949],{"className":85948},[655,656,657,658],[363,85950,85952,85955,85958],{"className":85951},[407,658],[363,85953,465],{"className":85954},[407,658],[363,85956,5160],{"className":85957},[2938,658],[363,85959,16059],{"className":85960,"style":16108},[407,408,658],[363,85962,666],{"className":85963},[665],[363,85965,85967],{"className":85966},[638],[363,85968,85970],{"className":85969,"style":2919},[642],[363,85971],{},[363,85973],{"className":85974},[501,789],[363,85976,85978],{"className":85977},[407],[363,85979,468],{"className":85980},[767,4067],[363,85982,85984],{"className":85983},[407],[363,85985,468],{"className":85986},[767,4067],[363,85988,85989,85992],{"style":85632},[363,85990],{"className":85991,"style":17935},[650],[363,85993,85995,85998,86001,86004,86007,86010,86013,86018,86021,86090,86093,86096,86099,86102,86105,86110,86113,86181,86184,86187,86190,86193,86196,86199,86202,86205,86208,86211,86214,86217,86222,86225],{"className":85994},[407],[363,85996],{"className":85997},[407],[363,85999],{"className":86000,"style":506},[505],[363,86002,471],{"className":86003},[510],[363,86005],{"className":86006,"style":506},[505],[363,86008,45101],{"className":86009,"style":45131},[407,408],[363,86011],{"className":86012,"style":754},[505],[363,86014,4501,86016],{"className":86015},[1831],[363,86017,4505],{"style":4504},[363,86019],{"className":86020,"style":754},[505],[363,86022,86024,86027,86087],{"className":86023},[407],[363,86025],{"className":86026},[494,789],[363,86028,86030],{"className":86029},[586],[363,86031,86033,86079],{"className":86032},[633,634],[363,86034,86036,86076],{"className":86035},[638],[363,86037,86040,86054,86062],{"className":86038,"style":86039},[642],"height:0.6954em;",[363,86041,86042,86045],{"style":2874},[363,86043],{"className":86044,"style":809},[650],[363,86046,86048],{"className":86047},[655,656,657,658],[363,86049,86051],{"className":86050},[407,658],[363,86052,84464],{"className":86053,"style":84686},[407,408,658],[363,86055,86056,86059],{"style":821},[363,86057],{"className":86058,"style":809},[650],[363,86060],{"className":86061,"style":829},[828],[363,86063,86064,86067],{"style":2897},[363,86065],{"className":86066,"style":809},[650],[363,86068,86070],{"className":86069},[655,656,657,658],[363,86071,86073],{"className":86072},[407,658],[363,86074,45101],{"className":86075,"style":45131},[407,408,658],[363,86077,666],{"className":86078},[665],[363,86080,86082],{"className":86081},[638],[363,86083,86085],{"className":86084,"style":3086},[642],[363,86086],{},[363,86088],{"className":86089},[501,789],[363,86091],{"className":86092,"style":2934},[505],[363,86094,2817],{"className":86095},[2938],[363,86097],{"className":86098,"style":2934},[505],[363,86100,84464],{"className":86101,"style":84686},[407,408],[363,86103],{"className":86104,"style":754},[505],[363,86106,4501,86108],{"className":86107},[1831],[363,86109,4505],{"style":4504},[363,86111],{"className":86112,"style":754},[505],[363,86114,86116,86119,86178],{"className":86115},[407],[363,86117],{"className":86118},[494,789],[363,86120,86122],{"className":86121},[586],[363,86123,86125,86170],{"className":86124},[633,634],[363,86126,86128,86167],{"className":86127},[638],[363,86129,86131,86145,86153],{"className":86130,"style":3172},[642],[363,86132,86133,86136],{"style":2874},[363,86134],{"className":86135,"style":809},[650],[363,86137,86139],{"className":86138},[655,656,657,658],[363,86140,86142],{"className":86141},[407,658],[363,86143,45101],{"className":86144,"style":45131},[407,408,658],[363,86146,86147,86150],{"style":821},[363,86148],{"className":86149,"style":809},[650],[363,86151],{"className":86152,"style":829},[828],[363,86154,86155,86158],{"style":3200},[363,86156],{"className":86157,"style":809},[650],[363,86159,86161],{"className":86160},[655,656,657,658],[363,86162,86164],{"className":86163},[407,658],[363,86165,84464],{"className":86166,"style":84686},[407,408,658],[363,86168,666],{"className":86169},[665],[363,86171,86173],{"className":86172},[638],[363,86174,86176],{"className":86175,"style":2919},[642],[363,86177],{},[363,86179],{"className":86180},[501,789],[363,86182],{"className":86183,"style":506},[505],[363,86185,471],{"className":86186},[510],[363,86188],{"className":86189,"style":506},[505],[363,86191,461],{"className":86192},[494],[363,86194,45101],{"className":86195,"style":45131},[407,408],[363,86197],{"className":86198,"style":2934},[505],[363,86200,5160],{"className":86201},[2938],[363,86203],{"className":86204,"style":2934},[505],[363,86206,84464],{"className":86207,"style":84686},[407,408],[363,86209,468],{"className":86210},[501],[363,86212],{"className":86213,"style":754},[505],[363,86215],{"className":86216,"style":754},[505],[363,86218,4501,86220],{"className":86219},[1831],[363,86221,4505],{"style":4504},[363,86223],{"className":86224,"style":754},[505],[363,86226,86228,86231,86290],{"className":86227},[407],[363,86229],{"className":86230},[494,789],[363,86232,86234],{"className":86233},[586],[363,86235,86237,86282],{"className":86236},[633,634],[363,86238,86240,86279],{"className":86239},[638],[363,86241,86243,86257,86265],{"className":86242,"style":86039},[642],[363,86244,86245,86248],{"style":2874},[363,86246],{"className":86247,"style":809},[650],[363,86249,86251],{"className":86250},[655,656,657,658],[363,86252,86254],{"className":86253},[407,658],[363,86255,84464],{"className":86256,"style":84686},[407,408,658],[363,86258,86259,86262],{"style":821},[363,86260],{"className":86261,"style":809},[650],[363,86263],{"className":86264,"style":829},[828],[363,86266,86267,86270],{"style":2897},[363,86268],{"className":86269,"style":809},[650],[363,86271,86273],{"className":86272},[655,656,657,658],[363,86274,86276],{"className":86275},[407,658],[363,86277,45101],{"className":86278,"style":45131},[407,408,658],[363,86280,666],{"className":86281},[665],[363,86283,86285],{"className":86284},[638],[363,86286,86288],{"className":86287,"style":3086},[642],[363,86289],{},[363,86291],{"className":86292},[501,789],[363,86294,86295,86298],{"style":85641},[363,86296],{"className":86297,"style":17935},[650],[363,86299,86301,86304,86307,86310,86313,86316,86319,86322,86327,86330,86410,86413,86416,86419,86422,86425,86428,86431,86434],{"className":86300},[407],[363,86302],{"className":86303},[407],[363,86305],{"className":86306,"style":506},[505],[363,86308,471],{"className":86309},[510],[363,86311],{"className":86312,"style":506},[505],[363,86314,16059],{"className":86315,"style":16108},[407,408],[363,86317],{"className":86318,"style":754},[505],[363,86320],{"className":86321,"style":754},[505],[363,86323,4501,86325],{"className":86324},[1831],[363,86326,4505],{"style":4504},[363,86328],{"className":86329,"style":754},[505],[363,86331,86333,86336,86407],{"className":86332},[407],[363,86334],{"className":86335},[494,789],[363,86337,86339],{"className":86338},[586],[363,86340,86342,86399],{"className":86341},[633,634],[363,86343,86345,86396],{"className":86344},[638],[363,86346,86348,86368,86376],{"className":86347,"style":3034},[642],[363,86349,86350,86353],{"style":2874},[363,86351],{"className":86352,"style":809},[650],[363,86354,86356],{"className":86355},[655,656,657,658],[363,86357,86359,86362,86365],{"className":86358},[407,658],[363,86360,465],{"className":86361},[407,658],[363,86363,5160],{"className":86364},[2938,658],[363,86366,16059],{"className":86367,"style":16108},[407,408,658],[363,86369,86370,86373],{"style":821},[363,86371],{"className":86372,"style":809},[650],[363,86374],{"className":86375,"style":829},[828],[363,86377,86378,86381],{"style":2897},[363,86379],{"className":86380,"style":809},[650],[363,86382,86384],{"className":86383},[655,656,657,658],[363,86385,86387,86390,86393],{"className":86386},[407,658],[363,86388,465],{"className":86389},[407,658],[363,86391,2817],{"className":86392},[2938,658],[363,86394,16059],{"className":86395,"style":16108},[407,408,658],[363,86397,666],{"className":86398},[665],[363,86400,86402],{"className":86401},[638],[363,86403,86405],{"className":86404,"style":16776},[642],[363,86406],{},[363,86408],{"className":86409},[501,789],[363,86411],{"className":86412,"style":506},[505],[363,86414,24461],{"className":86415},[510],[363,86417],{"className":86418,"style":754},[505],[363,86420],{"className":86421,"style":506},[505],[363,86423,39012],{"className":86424},[407,408],[363,86426,461],{"className":86427},[494],[363,86429,16059],{"className":86430,"style":16108},[407,408],[363,86432,468],{"className":86433},[501],[363,86435,4722],{"className":86436},[407],[363,86438,666],{"className":86439},[665],[363,86441,86443],{"className":86442},[638],[363,86444,86446],{"className":86445,"style":85657},[642],[363,86447],{},[11,86449,86450,86451,86576,86577,86658,86659,20313,86687,86737,86738,86816,86817,86948,86949,86952,86953,87128,87129,4200,87308,87359,87360,87388],{},"由标签交换的对称性 ",[363,86452,86454,86492],{"className":86453,"translate":367},[366],[363,86455,86457],{"className":86456},[371],[373,86458,86459],{"xmlns":375},[377,86460,86461,86489],{},[380,86462,86463,86465,86467,86469,86471,86473,86475,86477,86479,86481,86483,86485,86487],{},[383,86464,31369],{},[458,86466,461],{"stretchy":460},[383,86468,45101],{},[458,86470,468],{"stretchy":460},[458,86472,471],{},[383,86474,31369],{},[458,86476,461],{"stretchy":460},[463,86478,465],{},[458,86480,5160],{},[383,86482,45101],{},[458,86484,2817],{},[383,86486,16059],{},[458,86488,468],{"stretchy":460},[387,86490,86491],{"encoding":389},"\\varphi(\\alpha)=\\varphi(1-\\alpha+\\delta)",[363,86493,86495,86522,86546,86564],{"className":86494,"ariaHidden":394},[393],[363,86496,86498,86501,86504,86507,86510,86513,86516,86519],{"className":86497},[398],[363,86499],{"className":86500,"style":487},[402],[363,86502,31369],{"className":86503},[407,408],[363,86505,461],{"className":86506},[494],[363,86508,45101],{"className":86509,"style":45131},[407,408],[363,86511,468],{"className":86512},[501],[363,86514],{"className":86515,"style":506},[505],[363,86517,471],{"className":86518},[510],[363,86520],{"className":86521,"style":506},[505],[363,86523,86525,86528,86531,86534,86537,86540,86543],{"className":86524},[398],[363,86526],{"className":86527,"style":487},[402],[363,86529,31369],{"className":86530},[407,408],[363,86532,461],{"className":86533},[494],[363,86535,465],{"className":86536},[407],[363,86538],{"className":86539,"style":2934},[505],[363,86541,5160],{"className":86542},[2938],[363,86544],{"className":86545,"style":2934},[505],[363,86547,86549,86552,86555,86558,86561],{"className":86548},[398],[363,86550],{"className":86551,"style":4598},[402],[363,86553,45101],{"className":86554,"style":45131},[407,408],[363,86556],{"className":86557,"style":2934},[505],[363,86559,2817],{"className":86560},[2938],[363,86562],{"className":86563,"style":2934},[505],[363,86565,86567,86570,86573],{"className":86566},[398],[363,86568],{"className":86569,"style":487},[402],[363,86571,16059],{"className":86572,"style":16108},[407,408],[363,86574,468],{"className":86575},[501],"、边界值更大（",[363,86578,86580,86602],{"className":86579,"translate":367},[366],[363,86581,86583],{"className":86582},[371],[373,86584,86585],{"xmlns":375},[377,86586,86587,86599],{},[380,86588,86589,86591,86593],{},[383,86590,45101],{},[458,86592,1376],{},[7161,86594,86595,86597],{},[383,86596,16059],{},[458,86598,2817],{},[387,86600,86601],{"encoding":389},"\\alpha\\to\\delta^+",[363,86603,86605,86623],{"className":86604,"ariaHidden":394},[393],[363,86606,86608,86611,86614,86617,86620],{"className":86607},[398],[363,86609],{"className":86610,"style":2692},[402],[363,86612,45101],{"className":86613,"style":45131},[407,408],[363,86615],{"className":86616,"style":506},[505],[363,86618,1376],{"className":86619},[510],[363,86621],{"className":86622,"style":506},[505],[363,86624,86626,86629],{"className":86625},[398],[363,86627],{"className":86628,"style":21356},[402],[363,86630,86632,86635],{"className":86631},[407],[363,86633,16059],{"className":86634,"style":16108},[407,408],[363,86636,86638],{"className":86637},[629],[363,86639,86641],{"className":86640},[633],[363,86642,86644],{"className":86643},[638],[363,86645,86647],{"className":86646,"style":21356},[642],[363,86648,86649,86652],{"style":7212},[363,86650],{"className":86651,"style":651},[650],[363,86653,86655],{"className":86654},[655,656,657,658],[363,86656,2817],{"className":86657},[2938,658]," 时不平衡质量挤出 ",[363,86660,86662,86675],{"className":86661,"translate":367},[366],[363,86663,86665],{"className":86664},[371],[373,86666,86667],{"xmlns":375},[377,86668,86669,86673],{},[380,86670,86671],{},[383,86672,1371],{"mathvariant":557},[387,86674,4217],{"encoding":389},[363,86676,86678],{"className":86677,"ariaHidden":394},[393],[363,86679,86681,86684],{"className":86680},[398],[363,86682],{"className":86683,"style":2692},[402],[363,86685,1371],{"className":86686},[407],[363,86688,86690,86707],{"className":86689,"translate":367},[366],[363,86691,86693],{"className":86692},[371],[373,86694,86695],{"xmlns":375},[377,86696,86697,86705],{},[380,86698,86699,86701,86703],{},[383,86700,45101],{},[458,86702,1376],{},[463,86704,465],{},[387,86706,47562],{"encoding":389},[363,86708,86710,86728],{"className":86709,"ariaHidden":394},[393],[363,86711,86713,86716,86719,86722,86725],{"className":86712},[398],[363,86714],{"className":86715,"style":2692},[402],[363,86717,45101],{"className":86718,"style":45131},[407,408],[363,86720],{"className":86721,"style":506},[505],[363,86723,1376],{"className":86724},[510],[363,86726],{"className":86727,"style":506},[505],[363,86729,86731,86734],{"className":86730},[398],[363,86732],{"className":86733,"style":520},[402],[363,86735,465],{"className":86736},[407]," 时值为 ",[363,86739,86741,86769],{"className":86740,"translate":367},[366],[363,86742,86744],{"className":86743},[371],[373,86745,86746],{"xmlns":375},[377,86747,86748,86766],{},[380,86749,86750,86752,86754,86756,86758,86760,86762,86764],{},[458,86751,5160],{},[383,86753,4447],{},[458,86755,4450],{},[458,86757,461],{"stretchy":460},[463,86759,465],{},[458,86761,5160],{},[383,86763,16059],{},[458,86765,468],{"stretchy":460},[387,86767,86768],{"encoding":389},"-\\log(1-\\delta)",[363,86770,86772,86804],{"className":86771,"ariaHidden":394},[393],[363,86773,86775,86778,86781,86784,86789,86792,86795,86798,86801],{"className":86774},[398],[363,86776],{"className":86777,"style":487},[402],[363,86779,5160],{"className":86780},[407],[363,86782],{"className":86783,"style":754},[505],[363,86785,4501,86787],{"className":86786},[1831],[363,86788,4505],{"style":4504},[363,86790,461],{"className":86791},[494],[363,86793,465],{"className":86794},[407],[363,86796],{"className":86797,"style":2934},[505],[363,86799,5160],{"className":86800},[2938],[363,86802],{"className":86803,"style":2934},[505],[363,86805,86807,86810,86813],{"className":86806},[398],[363,86808],{"className":86809,"style":487},[402],[363,86811,16059],{"className":86812,"style":16108},[407,408],[363,86814,468],{"className":86815},[501],"，均大于中心值）可得：唯一驻点在 ",[363,86818,86820,86847],{"className":86819,"translate":367},[366],[363,86821,86823],{"className":86822},[371],[373,86824,86825],{"xmlns":375},[377,86826,86827,86845],{},[380,86828,86829,86831,86833],{},[383,86830,45101],{},[458,86832,471],{},[586,86834,86835,86843],{},[380,86836,86837,86839,86841],{},[463,86838,465],{},[458,86840,2817],{},[383,86842,16059],{},[463,86844,2810],{},[387,86846,84938],{"encoding":389},[363,86848,86850,86868],{"className":86849,"ariaHidden":394},[393],[363,86851,86853,86856,86859,86862,86865],{"className":86852},[398],[363,86854],{"className":86855,"style":2692},[402],[363,86857,45101],{"className":86858,"style":45131},[407,408],[363,86860],{"className":86861,"style":506},[505],[363,86863,471],{"className":86864},[510],[363,86866],{"className":86867,"style":506},[505],[363,86869,86871,86874],{"className":86870},[398],[363,86872],{"className":86873,"style":84966},[402],[363,86875,86877,86880,86945],{"className":86876},[407],[363,86878],{"className":86879},[494,789],[363,86881,86883],{"className":86882},[586],[363,86884,86886,86937],{"className":86885},[633,634],[363,86887,86889,86934],{"className":86888},[638],[363,86890,86892,86906,86914],{"className":86891,"style":3034},[642],[363,86893,86894,86897],{"style":2874},[363,86895],{"className":86896,"style":809},[650],[363,86898,86900],{"className":86899},[655,656,657,658],[363,86901,86903],{"className":86902},[407,658],[363,86904,2810],{"className":86905},[407,658],[363,86907,86908,86911],{"style":821},[363,86909],{"className":86910,"style":809},[650],[363,86912],{"className":86913,"style":829},[828],[363,86915,86916,86919],{"style":2897},[363,86917],{"className":86918,"style":809},[650],[363,86920,86922],{"className":86921},[655,656,657,658],[363,86923,86925,86928,86931],{"className":86924},[407,658],[363,86926,465],{"className":86927},[407,658],[363,86929,2817],{"className":86930},[2938,658],[363,86932,16059],{"className":86933,"style":16108},[407,408,658],[363,86935,666],{"className":86936},[665],[363,86938,86940],{"className":86939},[638],[363,86941,86943],{"className":86942,"style":2919},[642],[363,86944],{},[363,86946],{"className":86947},[501,789],"，且是",[1572,86950,86951],{},"精确最小值","（Vajda 界）：",[363,86954,86956,87012],{"className":86955,"translate":367},[366],[363,86957,86959],{"className":86958},[371],[373,86960,86961],{"xmlns":375},[377,86962,86963,87009],{},[380,86964,86965,86975,86977,86979,86981,86983,86985,86987,86989,86991,86997,86999,87001,87003,87005,87007],{},[543,86966,86967,86969],{},[383,86968,547],{},[380,86970,86971,86973],{},[383,86972,11041],{},[383,86974,22240],{},[458,86976,461],{"stretchy":460},[383,86978,554],{},[383,86980,558],{"mathvariant":557},[383,86982,561],{},[458,86984,468],{"stretchy":460},[458,86986,7275],{},[383,86988,39012],{},[458,86990,461],{"stretchy":460},[380,86992,86993,86995],{},[383,86994,5739],{"mathvariant":557},[383,86996,35197],{"mathvariant":557},[458,86998,461],{"stretchy":460},[383,87000,554],{},[458,87002,898],{"separator":394},[383,87004,561],{},[458,87006,468],{"stretchy":460},[458,87008,468],{"stretchy":460},[387,87010,87011],{"encoding":389},"D_{KL}(P\\|Q)\\ge h(\\mathrm{TV}(P,Q))",[363,87013,87015,87091],{"className":87014,"ariaHidden":394},[393],[363,87016,87018,87021,87067,87070,87073,87076,87079,87082,87085,87088],{"className":87017},[398],[363,87019],{"className":87020,"style":487},[402],[363,87022,87024,87027],{"className":87023},[407],[363,87025,547],{"className":87026,"style":625},[407,408],[363,87028,87030],{"className":87029},[629],[363,87031,87033,87059],{"className":87032},[633,634],[363,87034,87036,87056],{"className":87035},[638],[363,87037,87039],{"className":87038,"style":727},[642],[363,87040,87041,87044],{"style":646},[363,87042],{"className":87043,"style":651},[650],[363,87045,87047],{"className":87046},[655,656,657,658],[363,87048,87050,87053],{"className":87049},[407,658],[363,87051,11041],{"className":87052,"style":11129},[407,408,658],[363,87054,22240],{"className":87055},[407,408,658],[363,87057,666],{"className":87058},[665],[363,87060,87062],{"className":87061},[638],[363,87063,87065],{"className":87064,"style":8315},[642],[363,87066],{},[363,87068,461],{"className":87069},[494],[363,87071,554],{"className":87072,"style":682},[407,408],[363,87074,558],{"className":87075},[407],[363,87077,561],{"className":87078},[407,408],[363,87080,468],{"className":87081},[501],[363,87083],{"className":87084,"style":506},[505],[363,87086,7275],{"className":87087},[510],[363,87089],{"className":87090,"style":506},[505],[363,87092,87094,87097,87100,87103,87110,87113,87116,87119,87122,87125],{"className":87093},[398],[363,87095],{"className":87096,"style":487},[402],[363,87098,39012],{"className":87099},[407,408],[363,87101,461],{"className":87102},[494],[363,87104,87106],{"className":87105},[407],[363,87107,87109],{"className":87108,"style":4504},[407,33009],"TV",[363,87111,461],{"className":87112},[494],[363,87114,554],{"className":87115,"style":682},[407,408],[363,87117,898],{"className":87118},[920],[363,87120],{"className":87121,"style":754},[505],[363,87123,561],{"className":87124},[407,408],[363,87126,19394],{"className":87127},[501],"，其中 ",[363,87130,87132,87178],{"className":87131,"translate":367},[366],[363,87133,87135],{"className":87134},[371],[373,87136,87137],{"xmlns":375},[377,87138,87139,87175],{},[380,87140,87141,87143,87145,87147,87149,87151,87153,87155,87157],{},[383,87142,39012],{},[458,87144,461],{"stretchy":460},[383,87146,16059],{},[458,87148,468],{"stretchy":460},[458,87150,471],{},[383,87152,16059],{},[383,87154,4447],{},[458,87156,4450],{},[586,87158,87159,87167],{},[380,87160,87161,87163,87165],{},[463,87162,465],{},[458,87164,2817],{},[383,87166,16059],{},[380,87168,87169,87171,87173],{},[463,87170,465],{},[458,87172,5160],{},[383,87174,16059],{},[387,87176,87177],{"encoding":389},"h(\\delta)=\\delta\\log\\frac{1+\\delta}{1-\\delta}",[363,87179,87181,87208],{"className":87180,"ariaHidden":394},[393],[363,87182,87184,87187,87190,87193,87196,87199,87202,87205],{"className":87183},[398],[363,87185],{"className":87186,"style":487},[402],[363,87188,39012],{"className":87189},[407,408],[363,87191,461],{"className":87192},[494],[363,87194,16059],{"className":87195,"style":16108},[407,408],[363,87197,468],{"className":87198},[501],[363,87200],{"className":87201,"style":506},[505],[363,87203,471],{"className":87204},[510],[363,87206],{"className":87207,"style":506},[505],[363,87209,87211,87214,87217,87220,87225,87228],{"className":87210},[398],[363,87212],{"className":87213,"style":16700},[402],[363,87215,16059],{"className":87216,"style":16108},[407,408],[363,87218],{"className":87219,"style":754},[505],[363,87221,4501,87223],{"className":87222},[1831],[363,87224,4505],{"style":4504},[363,87226],{"className":87227,"style":754},[505],[363,87229,87231,87234,87305],{"className":87230},[407],[363,87232],{"className":87233},[494,789],[363,87235,87237],{"className":87236},[586],[363,87238,87240,87297],{"className":87239},[633,634],[363,87241,87243,87294],{"className":87242},[638],[363,87244,87246,87266,87274],{"className":87245,"style":3034},[642],[363,87247,87248,87251],{"style":2874},[363,87249],{"className":87250,"style":809},[650],[363,87252,87254],{"className":87253},[655,656,657,658],[363,87255,87257,87260,87263],{"className":87256},[407,658],[363,87258,465],{"className":87259},[407,658],[363,87261,5160],{"className":87262},[2938,658],[363,87264,16059],{"className":87265,"style":16108},[407,408,658],[363,87267,87268,87271],{"style":821},[363,87269],{"className":87270,"style":809},[650],[363,87272],{"className":87273,"style":829},[828],[363,87275,87276,87279],{"style":2897},[363,87277],{"className":87278,"style":809},[650],[363,87280,87282],{"className":87281},[655,656,657,658],[363,87283,87285,87288,87291],{"className":87284},[407,658],[363,87286,465],{"className":87287},[407,658],[363,87289,2817],{"className":87290},[2938,658],[363,87292,16059],{"className":87293,"style":16108},[407,408,658],[363,87295,666],{"className":87296},[665],[363,87298,87300],{"className":87299},[638],[363,87301,87303],{"className":87302,"style":16776},[642],[363,87304],{},[363,87306],{"className":87307},[501,789],[363,87309,87311,87329],{"className":87310,"translate":367},[366],[363,87312,87314],{"className":87313},[371],[373,87315,87316],{"xmlns":375},[377,87317,87318,87326],{},[380,87319,87320,87322,87324],{},[383,87321,16059],{},[458,87323,1376],{},[463,87325,465],{},[387,87327,87328],{"encoding":389},"\\delta\\to1",[363,87330,87332,87350],{"className":87331,"ariaHidden":394},[393],[363,87333,87335,87338,87341,87344,87347],{"className":87334},[398],[363,87336],{"className":87337,"style":12944},[402],[363,87339,16059],{"className":87340,"style":16108},[407,408],[363,87342],{"className":87343,"style":506},[505],[363,87345,1376],{"className":87346},[510],[363,87348],{"className":87349,"style":506},[505],[363,87351,87353,87356],{"className":87352},[398],[363,87354],{"className":87355,"style":520},[402],[363,87357,465],{"className":87358},[407]," 时发散（与 KL 在支撑分离时为 ",[363,87361,87363,87376],{"className":87362,"translate":367},[366],[363,87364,87366],{"className":87365},[371],[373,87367,87368],{"xmlns":375},[377,87369,87370,87374],{},[380,87371,87372],{},[383,87373,1371],{"mathvariant":557},[387,87375,4217],{"encoding":389},[363,87377,87379],{"className":87378,"ariaHidden":394},[393],[363,87380,87382,87385],{"className":87381},[398],[363,87383],{"className":87384,"style":2692},[402],[363,87386,1371],{"className":87387},[407]," 一致）。",[11,87390,87391,87394],{},[1572,87392,87393],{},"第 3 步（初等放缩）。"," 由",[363,87396,87398],{"className":87397,"translate":367},[528],[363,87399,87401,87487],{"className":87400,"translate":367},[366],[363,87402,87404],{"className":87403},[371],[373,87405,87406],{"xmlns":375,"display":537},[377,87407,87408,87484],{},[380,87409,87410,87412,87414,87432,87434,87436,87476,87478,87480,87482],{},[383,87411,4447],{},[458,87413,4450],{},[586,87415,87416,87424],{},[380,87417,87418,87420,87422],{},[463,87419,465],{},[458,87421,2817],{},[383,87423,16059],{},[380,87425,87426,87428,87430],{},[463,87427,465],{},[458,87429,5160],{},[383,87431,16059],{},[458,87433,471],{},[463,87435,2810],{},[380,87437,87438,87440,87442,87444,87454,87456,87467,87469,87472,87474],{},[458,87439,461],{"fence":394},[383,87441,16059],{},[458,87443,2817],{},[586,87445,87446,87452],{},[7161,87447,87448,87450],{},[383,87449,16059],{},[463,87451,41082],{},[463,87453,41082],{},[458,87455,2817],{},[586,87457,87458,87465],{},[7161,87459,87460,87462],{},[383,87461,16059],{},[463,87463,87464],{},"5",[463,87466,87464],{},[458,87468,2817],{},[458,87470,87471],{},"⋯",[1644,87473,1646],{},[458,87475,468],{"fence":394},[458,87477,7275],{},[463,87479,2810],{},[383,87481,16059],{},[458,87483,898],{"separator":394},[387,87485,87486],{"encoding":389},"\\log\\frac{1+\\delta}{1-\\delta}\n=2\\left(\\delta+\\frac{\\delta^3}3\n+\\frac{\\delta^5}5+\\cdots\\right)\n\\ge 2\\delta,",[363,87488,87490,87599,87848],{"className":87489,"ariaHidden":394},[393],[363,87491,87493,87496,87501,87504,87590,87593,87596],{"className":87492},[398],[363,87494],{"className":87495,"style":18398},[402],[363,87497,4501,87499],{"className":87498},[1831],[363,87500,4505],{"style":4504},[363,87502],{"className":87503,"style":754},[505],[363,87505,87507,87510,87587],{"className":87506},[407],[363,87508],{"className":87509},[494,789],[363,87511,87513],{"className":87512},[586],[363,87514,87516,87579],{"className":87515},[633,634],[363,87517,87519,87576],{"className":87518},[638],[363,87520,87522,87545,87553],{"className":87521,"style":802},[642],[363,87523,87524,87527],{"style":805},[363,87525],{"className":87526,"style":809},[650],[363,87528,87530,87533,87536,87539,87542],{"className":87529},[407],[363,87531,465],{"className":87532},[407],[363,87534],{"className":87535,"style":2934},[505],[363,87537,5160],{"className":87538},[2938],[363,87540],{"className":87541,"style":2934},[505],[363,87543,16059],{"className":87544,"style":16108},[407,408],[363,87546,87547,87550],{"style":821},[363,87548],{"className":87549,"style":809},[650],[363,87551],{"className":87552,"style":829},[828],[363,87554,87555,87558],{"style":832},[363,87556],{"className":87557,"style":809},[650],[363,87559,87561,87564,87567,87570,87573],{"className":87560},[407],[363,87562,465],{"className":87563},[407],[363,87565],{"className":87566,"style":2934},[505],[363,87568,2817],{"className":87569},[2938],[363,87571],{"className":87572,"style":2934},[505],[363,87574,16059],{"className":87575,"style":16108},[407,408],[363,87577,666],{"className":87578},[665],[363,87580,87582],{"className":87581},[638],[363,87583,87585],{"className":87584,"style":17362},[642],[363,87586],{},[363,87588],{"className":87589},[501,789],[363,87591],{"className":87592,"style":506},[505],[363,87594,471],{"className":87595},[510],[363,87597],{"className":87598,"style":506},[505],[363,87600,87602,87606,87609,87612,87839,87842,87845],{"className":87601},[398],[363,87603],{"className":87604,"style":87605},[402],"height:2.4411em;vertical-align:-0.95em;",[363,87607,2810],{"className":87608},[407],[363,87610],{"className":87611,"style":754},[505],[363,87613,87615,87621,87624,87627,87630,87633,87721,87724,87727,87730,87818,87821,87824,87827,87830,87833],{"className":87614},[758],[363,87616,87618],{"className":87617,"style":763},[494,762],[363,87619,461],{"className":87620},[767,657],[363,87622,16059],{"className":87623,"style":16108},[407,408],[363,87625],{"className":87626,"style":2934},[505],[363,87628,2817],{"className":87629},[2938],[363,87631],{"className":87632,"style":2934},[505],[363,87634,87636,87639,87718],{"className":87635},[407],[363,87637],{"className":87638},[494,789],[363,87640,87642],{"className":87641},[586],[363,87643,87645,87710],{"className":87644},[633,634],[363,87646,87648,87707],{"className":87647},[638],[363,87649,87651,87662,87670],{"className":87650,"style":38070},[642],[363,87652,87653,87656],{"style":805},[363,87654],{"className":87655,"style":809},[650],[363,87657,87659],{"className":87658},[407],[363,87660,41082],{"className":87661},[407],[363,87663,87664,87667],{"style":821},[363,87665],{"className":87666,"style":809},[650],[363,87668],{"className":87669,"style":829},[828],[363,87671,87672,87675],{"style":832},[363,87673],{"className":87674,"style":809},[650],[363,87676,87678],{"className":87677},[407],[363,87679,87681,87684],{"className":87680},[407],[363,87682,16059],{"className":87683,"style":16108},[407,408],[363,87685,87687],{"className":87686},[629],[363,87688,87690],{"className":87689},[633],[363,87691,87693],{"className":87692},[638],[363,87694,87696],{"className":87695,"style":20375},[642],[363,87697,87698,87701],{"style":7212},[363,87699],{"className":87700,"style":651},[650],[363,87702,87704],{"className":87703},[655,656,657,658],[363,87705,41082],{"className":87706},[407,658],[363,87708,666],{"className":87709},[665],[363,87711,87713],{"className":87712},[638],[363,87714,87716],{"className":87715,"style":4125},[642],[363,87717],{},[363,87719],{"className":87720},[501,789],[363,87722],{"className":87723,"style":2934},[505],[363,87725,2817],{"className":87726},[2938],[363,87728],{"className":87729,"style":2934},[505],[363,87731,87733,87736,87815],{"className":87732},[407],[363,87734],{"className":87735},[494,789],[363,87737,87739],{"className":87738},[586],[363,87740,87742,87807],{"className":87741},[633,634],[363,87743,87745,87804],{"className":87744},[638],[363,87746,87748,87759,87767],{"className":87747,"style":38070},[642],[363,87749,87750,87753],{"style":805},[363,87751],{"className":87752,"style":809},[650],[363,87754,87756],{"className":87755},[407],[363,87757,87464],{"className":87758},[407],[363,87760,87761,87764],{"style":821},[363,87762],{"className":87763,"style":809},[650],[363,87765],{"className":87766,"style":829},[828],[363,87768,87769,87772],{"style":832},[363,87770],{"className":87771,"style":809},[650],[363,87773,87775],{"className":87774},[407],[363,87776,87778,87781],{"className":87777},[407],[363,87779,16059],{"className":87780,"style":16108},[407,408],[363,87782,87784],{"className":87783},[629],[363,87785,87787],{"className":87786},[633],[363,87788,87790],{"className":87789},[638],[363,87791,87793],{"className":87792,"style":20375},[642],[363,87794,87795,87798],{"style":7212},[363,87796],{"className":87797,"style":651},[650],[363,87799,87801],{"className":87800},[655,656,657,658],[363,87802,87464],{"className":87803},[407,658],[363,87805,666],{"className":87806},[665],[363,87808,87810],{"className":87809},[638],[363,87811,87813],{"className":87812,"style":4125},[642],[363,87814],{},[363,87816],{"className":87817},[501,789],[363,87819],{"className":87820,"style":2934},[505],[363,87822,2817],{"className":87823},[2938],[363,87825],{"className":87826,"style":2934},[505],[363,87828,87471],{"className":87829},[758],[363,87831],{"className":87832,"style":754},[505],[363,87834,87836],{"className":87835,"style":763},[501,762],[363,87837,468],{"className":87838},[767,657],[363,87840],{"className":87841,"style":506},[505],[363,87843,7275],{"className":87844},[510],[363,87846],{"className":87847,"style":506},[505],[363,87849,87851,87854,87857,87860],{"className":87850},[398],[363,87852],{"className":87853,"style":403},[402],[363,87855,2810],{"className":87856},[407],[363,87858,16059],{"className":87859,"style":16108},[407,408],[363,87861,898],{"className":87862},[920],[363,87864,87866],{"className":87865,"translate":367},[528],[363,87867,87869,88048],{"className":87868,"translate":367},[366],[363,87870,87872],{"className":87871},[371],[373,87873,87874],{"xmlns":375,"display":537},[377,87875,87876,88045],{},[1590,87877,87878,87964],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,87879,87880,87886],{},[1599,87881,87882],{},[1602,87883,87884],{"scriptlevel":474,"displaystyle":394},[380,87885],{},[1599,87887,87888],{},[1602,87889,87890],{"scriptlevel":474,"displaystyle":394},[380,87891,87892,87894,87904,87906,87908,87910,87912,87914,87916,87918,87920,87922,87924,87930,87932,87934,87936,87938,87940,87942,87948,87950,87952,87954,87956,87962],{},[380,87893],{},[543,87895,87896,87898],{},[383,87897,547],{},[380,87899,87900,87902],{},[383,87901,11041],{},[383,87903,22240],{},[458,87905,461],{"stretchy":460},[383,87907,554],{},[383,87909,558],{"mathvariant":557},[383,87911,561],{},[458,87913,468],{"stretchy":460},[1644,87915,4630],{},[458,87917,7275],{},[1644,87919,4630],{},[383,87921,39012],{},[458,87923,461],{"stretchy":460},[380,87925,87926,87928],{},[383,87927,5739],{"mathvariant":557},[383,87929,35197],{"mathvariant":557},[458,87931,468],{"stretchy":460},[1644,87933,4630],{},[458,87935,7275],{},[1644,87937,4630],{},[463,87939,2810],{},[1644,87941,1646],{},[380,87943,87944,87946],{},[383,87945,5739],{"mathvariant":557},[383,87947,35197],{"mathvariant":557},[458,87949,461],{"stretchy":460},[383,87951,554],{},[458,87953,898],{"separator":394},[383,87955,561],{},[7161,87957,87958,87960],{},[458,87959,468],{"stretchy":460},[463,87961,2810],{},[458,87963,898],{"separator":394},[1596,87965,87966,87972],{},[1599,87967,87968],{},[1602,87969,87970],{"scriptlevel":474,"displaystyle":394},[380,87971],{},[1599,87973,87974],{},[1602,87975,87976],{"scriptlevel":474,"displaystyle":394},[380,87977,87978,87980,87983,87985,87991,87993,87995,87997,87999,88001,88003,88005,88007,88039,88041,88043],{},[380,87979],{},[1644,87981,87982],{},"即",[505,87984],{"width":4662},[380,87986,87987,87989],{},[383,87988,5739],{"mathvariant":557},[383,87990,35197],{"mathvariant":557},[458,87992,461],{"stretchy":460},[383,87994,554],{},[458,87996,898],{"separator":394},[383,87998,561],{},[458,88000,468],{"stretchy":460},[1644,88002,4630],{},[458,88004,10299],{},[1644,88006,4630],{},[34686,88008,88009],{},[380,88010,88011,88019,88029,88031,88033,88035,88037],{},[1602,88012,88013],{"scriptlevel":474,"displaystyle":460},[586,88014,88015,88017],{},[463,88016,465],{},[463,88018,2810],{},[543,88020,88021,88023],{},[383,88022,547],{},[380,88024,88025,88027],{},[383,88026,11041],{},[383,88028,22240],{},[458,88030,461],{"stretchy":460},[383,88032,554],{},[383,88034,558],{"mathvariant":557},[383,88036,561],{},[458,88038,468],{"stretchy":460},[383,88040,4722],{"mathvariant":557},[1644,88042,4630],{},[383,88044,59599],{"mathvariant":557},[387,88046,88047],{"encoding":389},"\\begin{aligned}\n&D_{KL}(P\\|Q)\\ \\ge\\ h(\\mathrm{TV})\n\\ \\ge\\ 2\\,\\mathrm{TV}(P,Q)^2 ,\\\\[2pt]\n&\\text{即}\\quad\n\\mathrm{TV}(P,Q)\\ \\le\\\n\\sqrt{\\tfrac12 D_{KL}(P\\|Q)} .\\ \\square\n\\end{aligned}",[363,88049,88051],{"className":88050,"ariaHidden":394},[393],[363,88052,88054,88058],{"className":88053},[398],[363,88055],{"className":88056,"style":88057},[402],"height:3.5641em;vertical-align:-1.5321em;",[363,88059,88061],{"className":88060},[407],[363,88062,88064,88107],{"className":88063},[1590],[363,88065,88067],{"className":88066},[1707],[363,88068,88070,88098],{"className":88069},[633,634],[363,88071,88073,88095],{"className":88072},[638],[363,88074,88077,88086],{"className":88075,"style":88076},[642],"height:2.0321em;",[363,88078,88080,88083],{"style":88079},"top:-4.4519em;",[363,88081],{"className":88082,"style":82766},[650],[363,88084],{"className":88085},[407],[363,88087,88089,88092],{"style":88088},"top:-2.3079em;",[363,88090],{"className":88091,"style":82766},[650],[363,88093],{"className":88094},[407],[363,88096,666],{"className":88097},[665],[363,88099,88101],{"className":88100},[638],[363,88102,88105],{"className":88103,"style":88104},[642],"height:1.5321em;",[363,88106],{},[363,88108,88110],{"className":88109},[1798],[363,88111,88113,88540],{"className":88112},[633,634],[363,88114,88116,88537],{"className":88115},[638],[363,88117,88119,88295],{"className":88118,"style":88076},[642],[363,88120,88121,88124],{"style":88079},[363,88122],{"className":88123,"style":82766},[650],[363,88125,88127,88130,88176,88179,88182,88185,88188,88191,88194,88197,88200,88203,88206,88209,88212,88218,88221,88224,88227,88230,88233,88236,88239,88242,88248,88251,88254,88257,88260,88263,88292],{"className":88126},[407],[363,88128],{"className":88129},[407],[363,88131,88133,88136],{"className":88132},[407],[363,88134,547],{"className":88135,"style":625},[407,408],[363,88137,88139],{"className":88138},[629],[363,88140,88142,88168],{"className":88141},[633,634],[363,88143,88145,88165],{"className":88144},[638],[363,88146,88148],{"className":88147,"style":727},[642],[363,88149,88150,88153],{"style":646},[363,88151],{"className":88152,"style":651},[650],[363,88154,88156],{"className":88155},[655,656,657,658],[363,88157,88159,88162],{"className":88158},[407,658],[363,88160,11041],{"className":88161,"style":11129},[407,408,658],[363,88163,22240],{"className":88164},[407,408,658],[363,88166,666],{"className":88167},[665],[363,88169,88171],{"className":88170},[638],[363,88172,88174],{"className":88173,"style":8315},[642],[363,88175],{},[363,88177,461],{"className":88178},[494],[363,88180,554],{"className":88181,"style":682},[407,408],[363,88183,558],{"className":88184},[407],[363,88186,561],{"className":88187},[407,408],[363,88189,468],{"className":88190},[501],[363,88192,4630],{"className":88193},[505],[363,88195],{"className":88196,"style":506},[505],[363,88198,7275],{"className":88199},[510],[363,88201,4630],{"className":88202},[505],[363,88204],{"className":88205,"style":506},[505],[363,88207,39012],{"className":88208},[407,408],[363,88210,461],{"className":88211},[494],[363,88213,88215],{"className":88214},[407],[363,88216,87109],{"className":88217,"style":4504},[407,33009],[363,88219,468],{"className":88220},[501],[363,88222,4630],{"className":88223},[505],[363,88225],{"className":88226,"style":506},[505],[363,88228,7275],{"className":88229},[510],[363,88231,4630],{"className":88232},[505],[363,88234],{"className":88235,"style":506},[505],[363,88237,2810],{"className":88238},[407],[363,88240],{"className":88241,"style":754},[505],[363,88243,88245],{"className":88244},[407],[363,88246,87109],{"className":88247,"style":4504},[407,33009],[363,88249,461],{"className":88250},[494],[363,88252,554],{"className":88253,"style":682},[407,408],[363,88255,898],{"className":88256},[920],[363,88258],{"className":88259,"style":754},[505],[363,88261,561],{"className":88262},[407,408],[363,88264,88266,88269],{"className":88265},[501],[363,88267,468],{"className":88268},[501],[363,88270,88272],{"className":88271},[629],[363,88273,88275],{"className":88274},[633],[363,88276,88278],{"className":88277},[638],[363,88279,88281],{"className":88280,"style":20082},[642],[363,88282,88283,88286],{"style":8624},[363,88284],{"className":88285,"style":651},[650],[363,88287,88289],{"className":88288},[655,656,657,658],[363,88290,2810],{"className":88291},[407,658],[363,88293,898],{"className":88294},[920],[363,88296,88297,88300],{"style":88088},[363,88298],{"className":88299,"style":82766},[650],[363,88301,88303,88306,88312,88316,88322,88325,88328,88331,88334,88337,88340,88343,88346,88349,88352,88355,88528,88531,88534],{"className":88302},[407],[363,88304],{"className":88305},[407],[363,88307,88309],{"className":88308},[407,4945],[363,88310,87982],{"className":88311},[407,4949],[363,88313],{"className":88314,"style":88315},[505],"margin-right:1em;",[363,88317,88319],{"className":88318},[407],[363,88320,87109],{"className":88321,"style":4504},[407,33009],[363,88323,461],{"className":88324},[494],[363,88326,554],{"className":88327,"style":682},[407,408],[363,88329,898],{"className":88330},[920],[363,88332],{"className":88333,"style":754},[505],[363,88335,561],{"className":88336},[407,408],[363,88338,468],{"className":88339},[501],[363,88341,4630],{"className":88342},[505],[363,88344],{"className":88345,"style":506},[505],[363,88347,10299],{"className":88348},[510],[363,88350,4630],{"className":88351},[505],[363,88353],{"className":88354,"style":506},[505],[363,88356,88358],{"className":88357},[407,34714],[363,88359,88361,88520],{"className":88360},[633,634],[363,88362,88364,88517],{"className":88363},[638],[363,88365,88367,88505],{"className":88366,"style":82926},[642],[363,88368,88370,88373],{"className":88369,"style":82930},[6654],[363,88371],{"className":88372,"style":82934},[650],[363,88374,88376,88444,88490,88493,88496,88499,88502],{"className":88375,"style":41508},[407],[363,88377,88379,88382,88441],{"className":88378},[407],[363,88380],{"className":88381},[494,789],[363,88383,88385],{"className":88384},[586],[363,88386,88388,88433],{"className":88387},[633,634],[363,88389,88391,88430],{"className":88390},[638],[363,88392,88394,88408,88416],{"className":88393,"style":2871},[642],[363,88395,88396,88399],{"style":2874},[363,88397],{"className":88398,"style":809},[650],[363,88400,88402],{"className":88401},[655,656,657,658],[363,88403,88405],{"className":88404},[407,658],[363,88406,2810],{"className":88407},[407,658],[363,88409,88410,88413],{"style":821},[363,88411],{"className":88412,"style":809},[650],[363,88414],{"className":88415,"style":829},[828],[363,88417,88418,88421],{"style":2897},[363,88419],{"className":88420,"style":809},[650],[363,88422,88424],{"className":88423},[655,656,657,658],[363,88425,88427],{"className":88426},[407,658],[363,88428,465],{"className":88429},[407,658],[363,88431,666],{"className":88432},[665],[363,88434,88436],{"className":88435},[638],[363,88437,88439],{"className":88438,"style":2919},[642],[363,88440],{},[363,88442],{"className":88443},[501,789],[363,88445,88447,88450],{"className":88446},[407],[363,88448,547],{"className":88449,"style":625},[407,408],[363,88451,88453],{"className":88452},[629],[363,88454,88456,88482],{"className":88455},[633,634],[363,88457,88459,88479],{"className":88458},[638],[363,88460,88462],{"className":88461,"style":727},[642],[363,88463,88464,88467],{"style":646},[363,88465],{"className":88466,"style":651},[650],[363,88468,88470],{"className":88469},[655,656,657,658],[363,88471,88473,88476],{"className":88472},[407,658],[363,88474,11041],{"className":88475,"style":11129},[407,408,658],[363,88477,22240],{"className":88478},[407,408,658],[363,88480,666],{"className":88481},[665],[363,88483,88485],{"className":88484},[638],[363,88486,88488],{"className":88487,"style":8315},[642],[363,88489],{},[363,88491,461],{"className":88492},[494],[363,88494,554],{"className":88495,"style":682},[407,408],[363,88497,558],{"className":88498},[407],[363,88500,561],{"className":88501},[407,408],[363,88503,468],{"className":88504},[501],[363,88506,88507,88510],{"style":83069},[363,88508],{"className":88509,"style":82934},[650],[363,88511,88513],{"className":88512,"style":83076},[34790],[6670,88514,88515],{"xmlns":6672,"width":6673,"height":83079,"viewBox":83080,"preserveAspectRatio":6676},[6678,88516],{"d":83083},[363,88518,666],{"className":88519},[665],[363,88521,88523],{"className":88522},[638],[363,88524,88526],{"className":88525,"style":83093},[642],[363,88527],{},[363,88529,4722],{"className":88530},[407],[363,88532,4630],{"className":88533},[505],[363,88535,59599],{"className":88536},[407,60141],[363,88538,666],{"className":88539},[665],[363,88541,88543],{"className":88542},[638],[363,88544,88546],{"className":88545,"style":88104},[642],[363,88547],{},[11,88549,88550,88553,88554,88654,88655,88763,88764,88793,88794,16142,88903,88954],{},[1572,88551,88552],{},"关于常数："," Pinsker 不等式中的 ",[363,88555,88557,88577],{"className":88556,"translate":367},[366],[363,88558,88560],{"className":88559},[371],[373,88561,88562],{"xmlns":375},[377,88563,88564,88574],{},[380,88565,88566],{},[1602,88567,88568],{"scriptlevel":474,"displaystyle":460},[586,88569,88570,88572],{},[463,88571,465],{},[463,88573,2810],{},[387,88575,88576],{"encoding":389},"\\tfrac12",[363,88578,88580],{"className":88579,"ariaHidden":394},[393],[363,88581,88583,88586],{"className":88582},[398],[363,88584],{"className":88585,"style":2852},[402],[363,88587,88589,88592,88651],{"className":88588},[407],[363,88590],{"className":88591},[494,789],[363,88593,88595],{"className":88594},[586],[363,88596,88598,88643],{"className":88597},[633,634],[363,88599,88601,88640],{"className":88600},[638],[363,88602,88604,88618,88626],{"className":88603,"style":2871},[642],[363,88605,88606,88609],{"style":2874},[363,88607],{"className":88608,"style":809},[650],[363,88610,88612],{"className":88611},[655,656,657,658],[363,88613,88615],{"className":88614},[407,658],[363,88616,2810],{"className":88617},[407,658],[363,88619,88620,88623],{"style":821},[363,88621],{"className":88622,"style":809},[650],[363,88624],{"className":88625,"style":829},[828],[363,88627,88628,88631],{"style":2897},[363,88629],{"className":88630,"style":809},[650],[363,88632,88634],{"className":88633},[655,656,657,658],[363,88635,88637],{"className":88636},[407,658],[363,88638,465],{"className":88639},[407,658],[363,88641,666],{"className":88642},[665],[363,88644,88646],{"className":88645},[638],[363,88647,88649],{"className":88648,"style":2919},[642],[363,88650],{},[363,88652],{"className":88653},[501,789],"（即 ",[363,88656,88658,88692],{"className":88657,"translate":367},[366],[363,88659,88661],{"className":88660},[371],[373,88662,88663],{"xmlns":375},[377,88664,88665,88689],{},[380,88666,88667,88673,88675,88677,88679],{},[380,88668,88669,88671],{},[383,88670,11041],{"mathvariant":557},[383,88672,22240],{"mathvariant":557},[458,88674,7275],{},[463,88676,2810],{},[1644,88678,1646],{},[7161,88680,88681,88687],{},[380,88682,88683,88685],{},[383,88684,5739],{"mathvariant":557},[383,88686,35197],{"mathvariant":557},[463,88688,2810],{},[387,88690,88691],{"encoding":389},"\\mathrm{KL}\\ge2\\,\\mathrm{TV}^2",[363,88693,88695,88717],{"className":88694,"ariaHidden":394},[393],[363,88696,88698,88702,88708,88711,88714],{"className":88697},[398],[363,88699],{"className":88700,"style":88701},[402],"height:0.8193em;vertical-align:-0.136em;",[363,88703,88705],{"className":88704},[407],[363,88706,33010],{"className":88707},[407,33009],[363,88709],{"className":88710,"style":506},[505],[363,88712,7275],{"className":88713},[510],[363,88715],{"className":88716,"style":506},[505],[363,88718,88720,88724,88727,88730],{"className":88719},[398],[363,88721],{"className":88722,"style":88723},[402],"height:0.8873em;",[363,88725,2810],{"className":88726},[407],[363,88728],{"className":88729,"style":754},[505],[363,88731,88733,88739],{"className":88732},[407],[363,88734,88736],{"className":88735},[407],[363,88737,87109],{"className":88738,"style":4504},[407,33009],[363,88740,88742],{"className":88741},[629],[363,88743,88745],{"className":88744},[633],[363,88746,88748],{"className":88747},[638],[363,88749,88751],{"className":88750,"style":88723},[642],[363,88752,88754,88757],{"style":88753},"top:-3.1362em;margin-right:0.05em;",[363,88755],{"className":88756,"style":651},[650],[363,88758,88760],{"className":88759},[655,656,657,658],[363,88761,2810],{"className":88762},[407,658]," 的系数 2）是最优的：取两分布仅在极小 ",[363,88765,88767,88781],{"className":88766,"translate":367},[366],[363,88768,88770],{"className":88769},[371],[373,88771,88772],{"xmlns":375},[377,88773,88774,88778],{},[380,88775,88776],{},[383,88777,39009],{},[387,88779,88780],{"encoding":389},"\\varepsilon",[363,88782,88784],{"className":88783,"ariaHidden":394},[393],[363,88785,88787,88790],{"className":88786},[398],[363,88788],{"className":88789,"style":2692},[402],[363,88791,39009],{"className":88792},[407,408]," 上偏离最优对称配置，可让 ",[363,88795,88797,88829],{"className":88796,"translate":367},[366],[363,88798,88800],{"className":88799},[371],[373,88801,88802],{"xmlns":375},[377,88803,88804,88826],{},[380,88805,88806,88808,88810,88812,88814,88816,88822,88824],{},[383,88807,39012],{},[458,88809,461],{"stretchy":460},[383,88811,16059],{},[458,88813,468],{"stretchy":460},[458,88815,1288],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[7161,88817,88818,88820],{},[383,88819,16059],{},[463,88821,2810],{},[458,88823,1376],{},[463,88825,2810],{},[387,88827,88828],{"encoding":389},"h(\\delta)\\big\u002F\\delta^2\\to 2",[363,88830,88832,88894],{"className":88831,"ariaHidden":394},[393],[363,88833,88835,88838,88841,88844,88847,88850,88856,88885,88888,88891],{"className":88834},[398],[363,88836],{"className":88837,"style":20910},[402],[363,88839,39012],{"className":88840},[407,408],[363,88842,461],{"className":88843},[494],[363,88845,16059],{"className":88846,"style":16108},[407,408],[363,88848,468],{"className":88849},[501],[363,88851,88853],{"className":88852},[407],[363,88854,1288],{"className":88855},[767,10021],[363,88857,88859,88862],{"className":88858},[407],[363,88860,16059],{"className":88861,"style":16108},[407,408],[363,88863,88865],{"className":88864},[629],[363,88866,88868],{"className":88867},[633],[363,88869,88871],{"className":88870},[638],[363,88872,88874],{"className":88873,"style":20375},[642],[363,88875,88876,88879],{"style":7212},[363,88877],{"className":88878,"style":651},[650],[363,88880,88882],{"className":88881},[655,656,657,658],[363,88883,2810],{"className":88884},[407,658],[363,88886],{"className":88887,"style":506},[505],[363,88889,1376],{"className":88890},[510],[363,88892],{"className":88893,"style":506},[505],[363,88895,88897,88900],{"className":88896},[398],[363,88898],{"className":88899,"style":520},[402],[363,88901,2810],{"className":88902},[407],[363,88904,88906,88924],{"className":88905,"translate":367},[366],[363,88907,88909],{"className":88908},[371],[373,88910,88911],{"xmlns":375},[377,88912,88913,88921],{},[380,88914,88915,88917,88919],{},[383,88916,16059],{},[458,88918,1376],{},[463,88920,474],{},[387,88922,88923],{"encoding":389},"\\delta\\to0",[363,88925,88927,88945],{"className":88926,"ariaHidden":394},[393],[363,88928,88930,88933,88936,88939,88942],{"className":88929},[398],[363,88931],{"className":88932,"style":12944},[402],[363,88934,16059],{"className":88935,"style":16108},[407,408],[363,88937],{"className":88938,"style":506},[505],[363,88940,1376],{"className":88941},[510],[363,88943],{"className":88944,"style":506},[505],[363,88946,88948,88951],{"className":88947},[398],[363,88949],{"className":88950,"style":520},[402],[363,88952,474],{"className":88953},[407],"），故常数不能改进。",[11,88956,88957,88958,89027],{},"顺便指出：对一般 f-散度也有平行的\"固定 TV 时最小化 ",[363,88959,88961,88978],{"className":88960,"translate":367},[366],[363,88962,88964],{"className":88963},[371],[373,88965,88966],{"xmlns":375},[377,88967,88968,88976],{},[380,88969,88970],{},[543,88971,88972,88974],{},[383,88973,547],{},[383,88975,385],{},[387,88977,4369],{"encoding":389},[363,88979,88981],{"className":88980,"ariaHidden":394},[393],[363,88982,88984,88987],{"className":88983},[398],[363,88985],{"className":88986,"style":4379},[402],[363,88988,88990,88993],{"className":88989},[407],[363,88991,547],{"className":88992,"style":625},[407,408],[363,88994,88996],{"className":88995},[629],[363,88997,88999,89019],{"className":88998},[633,634],[363,89000,89002,89016],{"className":89001},[638],[363,89003,89005],{"className":89004,"style":643},[642],[363,89006,89007,89010],{"style":646},[363,89008],{"className":89009,"style":651},[650],[363,89011,89013],{"className":89012},[655,656,657,658],[363,89014,385],{"className":89015,"style":409},[407,408,658],[363,89017,666],{"className":89018},[665],[363,89020,89022],{"className":89021},[638],[363,89023,89025],{"className":89024,"style":673},[642],[363,89026],{},"\"函数（Fedotov–Harremoës 2003 给出完整刻画），即每个 f-散度都自带一个 TV 的下界函数；这是 4.7 末拓扑结论的定量基础。",[11,89029,89030,89033,89034,89062,89063,89066],{},[1572,89031,89032],{},"Bretagnolle–Huber 的推导。"," 由 Rényi 散度在阶数 ",[363,89035,89037,89050],{"className":89036,"translate":367},[366],[363,89038,89040],{"className":89039},[371],[373,89041,89042],{"xmlns":375},[377,89043,89044,89048],{},[380,89045,89046],{},[383,89047,45101],{},[387,89049,49437],{"encoding":389},[363,89051,89053],{"className":89052,"ariaHidden":394},[393],[363,89054,89056,89059],{"className":89055},[398],[363,89057],{"className":89058,"style":2692},[402],[363,89060,45101],{"className":89061,"style":45131},[407,408]," 上",[1572,89064,89065],{},"单调不减","（Hölder 不等式的直接推论），",[363,89068,89070],{"className":89069,"translate":367},[528],[363,89071,89073,89171],{"className":89072,"translate":367},[366],[363,89074,89076],{"className":89075},[371],[373,89077,89078],{"xmlns":375,"display":537},[377,89079,89080,89168],{},[380,89081,89082,89092,89094,89096,89098,89100,89102,89104,89112,89114,89116,89118,89120,89122,89124,89126,89128,89142,89144,89146,89148,89150,89152,89154,89156,89158,89160,89162,89164,89166],{},[543,89083,89084,89086],{},[383,89085,547],{},[380,89087,89088,89090],{},[383,89089,11041],{},[383,89091,22240],{},[458,89093,461],{"stretchy":460},[383,89095,554],{},[383,89097,558],{"mathvariant":557},[383,89099,561],{},[458,89101,468],{"stretchy":460},[458,89103,471],{},[7900,89105,89106,89108,89110],{},[383,89107,547],{},[463,89109,465],{},[383,89111,1379],{},[458,89113,461],{"stretchy":460},[383,89115,554],{},[383,89117,558],{"mathvariant":557},[383,89119,561],{},[458,89121,468],{"stretchy":460},[1644,89123,4630],{},[458,89125,7275],{},[1644,89127,4630],{},[7900,89129,89130,89132,89140],{},[383,89131,547],{},[380,89133,89134,89136,89138],{},[463,89135,465],{},[383,89137,1288],{"mathvariant":557},[463,89139,2810],{},[383,89141,1379],{},[458,89143,461],{"stretchy":460},[383,89145,554],{},[383,89147,558],{"mathvariant":557},[383,89149,561],{},[458,89151,468],{"stretchy":460},[458,89153,471],{},[458,89155,5160],{},[463,89157,2810],{},[383,89159,4447],{},[458,89161,4450],{},[383,89163,39638],{},[383,89165,39641],{},[383,89167,4722],{"mathvariant":557},[387,89169,89170],{"encoding":389},"D_{KL}(P\\|Q)=D^{R}_{1}(P\\|Q)\n\\ \\ge\\ D^{R}_{1\u002F2}(P\\|Q)=-2\\log BC .",[363,89172,89174,89250,89343,89433],{"className":89173,"ariaHidden":394},[393],[363,89175,89177,89180,89226,89229,89232,89235,89238,89241,89244,89247],{"className":89176},[398],[363,89178],{"className":89179,"style":487},[402],[363,89181,89183,89186],{"className":89182},[407],[363,89184,547],{"className":89185,"style":625},[407,408],[363,89187,89189],{"className":89188},[629],[363,89190,89192,89218],{"className":89191},[633,634],[363,89193,89195,89215],{"className":89194},[638],[363,89196,89198],{"className":89197,"style":727},[642],[363,89199,89200,89203],{"style":646},[363,89201],{"className":89202,"style":651},[650],[363,89204,89206],{"className":89205},[655,656,657,658],[363,89207,89209,89212],{"className":89208},[407,658],[363,89210,11041],{"className":89211,"style":11129},[407,408,658],[363,89213,22240],{"className":89214},[407,408,658],[363,89216,666],{"className":89217},[665],[363,89219,89221],{"className":89220},[638],[363,89222,89224],{"className":89223,"style":8315},[642],[363,89225],{},[363,89227,461],{"className":89228},[494],[363,89230,554],{"className":89231,"style":682},[407,408],[363,89233,558],{"className":89234},[407],[363,89236,561],{"className":89237},[407,408],[363,89239,468],{"className":89240},[501],[363,89242],{"className":89243,"style":506},[505],[363,89245,471],{"className":89246},[510],[363,89248],{"className":89249,"style":506},[505],[363,89251,89253,89256,89313,89316,89319,89322,89325,89328,89331,89334,89337,89340],{"className":89252},[398],[363,89254],{"className":89255,"style":51220},[402],[363,89257,89259,89262],{"className":89258},[407],[363,89260,547],{"className":89261,"style":625},[407,408],[363,89263,89265],{"className":89264},[629],[363,89266,89268,89305],{"className":89267},[633,634],[363,89269,89271,89302],{"className":89270},[638],[363,89272,89274,89288],{"className":89273,"style":38859},[642],[363,89275,89276,89279],{"style":49919},[363,89277],{"className":89278,"style":651},[650],[363,89280,89282],{"className":89281},[655,656,657,658],[363,89283,89285],{"className":89284},[407,658],[363,89286,465],{"className":89287},[407,658],[363,89289,89290,89293],{"style":8624},[363,89291],{"className":89292,"style":651},[650],[363,89294,89296],{"className":89295},[655,656,657,658],[363,89297,89299],{"className":89298},[407,658],[363,89300,1379],{"className":89301,"style":49946},[407,408,658],[363,89303,666],{"className":89304},[665],[363,89306,89308],{"className":89307},[638],[363,89309,89311],{"className":89310,"style":8646},[642],[363,89312],{},[363,89314,461],{"className":89315},[494],[363,89317,554],{"className":89318,"style":682},[407,408],[363,89320,558],{"className":89321},[407],[363,89323,561],{"className":89324},[407,408],[363,89326,468],{"className":89327},[501],[363,89329,4630],{"className":89330},[505],[363,89332],{"className":89333,"style":506},[505],[363,89335,7275],{"className":89336},[510],[363,89338,4630],{"className":89339},[505],[363,89341],{"className":89342,"style":506},[505],[363,89344,89346,89350,89409,89412,89415,89418,89421,89424,89427,89430],{"className":89345},[398],[363,89347],{"className":89348,"style":89349},[402],"height:1.3383em;vertical-align:-0.447em;",[363,89351,89353,89356],{"className":89352},[407],[363,89354,547],{"className":89355,"style":625},[407,408],[363,89357,89359],{"className":89358},[629],[363,89360,89362,89400],{"className":89361},[633,634],[363,89363,89365,89397],{"className":89364},[638],[363,89366,89368,89383],{"className":89367,"style":38859},[642],[363,89369,89371,89374],{"style":89370},"top:-2.428em;margin-left:-0.0278em;margin-right:0.05em;",[363,89372],{"className":89373,"style":651},[650],[363,89375,89377],{"className":89376},[655,656,657,658],[363,89378,89380],{"className":89379},[407,658],[363,89381,33986],{"className":89382},[407,658],[363,89384,89385,89388],{"style":8624},[363,89386],{"className":89387,"style":651},[650],[363,89389,89391],{"className":89390},[655,656,657,658],[363,89392,89394],{"className":89393},[407,658],[363,89395,1379],{"className":89396,"style":49946},[407,408,658],[363,89398,666],{"className":89399},[665],[363,89401,89403],{"className":89402},[638],[363,89404,89407],{"className":89405,"style":89406},[642],"height:0.447em;",[363,89408],{},[363,89410,461],{"className":89411},[494],[363,89413,554],{"className":89414,"style":682},[407,408],[363,89416,558],{"className":89417},[407],[363,89419,561],{"className":89420},[407,408],[363,89422,468],{"className":89423},[501],[363,89425],{"className":89426,"style":506},[505],[363,89428,471],{"className":89429},[510],[363,89431],{"className":89432,"style":506},[505],[363,89434,89436,89439,89442,89445,89448,89453,89456,89459,89462],{"className":89435},[398],[363,89437],{"className":89438,"style":403},[402],[363,89440,5160],{"className":89441},[407],[363,89443,2810],{"className":89444},[407],[363,89446],{"className":89447,"style":754},[505],[363,89449,4501,89451],{"className":89450},[1831],[363,89452,4505],{"style":4504},[363,89454],{"className":89455,"style":754},[505],[363,89457,39638],{"className":89458,"style":39734},[407,408],[363,89460,39641],{"className":89461,"style":11129},[407,408],[363,89463,4722],{"className":89464},[407],[11,89466,89467,89468,16142,89561,89612,89613,89793],{},"又由 ",[363,89469,89471,89499],{"className":89470,"translate":367},[366],[363,89472,89474],{"className":89473},[371],[373,89475,89476],{"xmlns":375},[377,89477,89478,89496],{},[380,89479,89480,89482,89484,89486,89488,89490,89492,89494],{},[458,89481,5160],{},[383,89483,4447],{},[458,89485,4450],{},[383,89487,1121],{},[458,89489,7275],{},[463,89491,465],{},[458,89493,5160],{},[383,89495,1121],{},[387,89497,89498],{"encoding":389},"-\\log x\\ge 1-x",[363,89500,89502,89534,89552],{"className":89501,"ariaHidden":394},[393],[363,89503,89505,89508,89511,89514,89519,89522,89525,89528,89531],{"className":89504},[398],[363,89506],{"className":89507,"style":403},[402],[363,89509,5160],{"className":89510},[407],[363,89512],{"className":89513,"style":754},[505],[363,89515,4501,89517],{"className":89516},[1831],[363,89518,4505],{"style":4504},[363,89520],{"className":89521,"style":754},[505],[363,89523,1121],{"className":89524},[407,408],[363,89526],{"className":89527,"style":506},[505],[363,89529,7275],{"className":89530},[510],[363,89532],{"className":89533,"style":506},[505],[363,89535,89537,89540,89543,89546,89549],{"className":89536},[398],[363,89538],{"className":89539,"style":12925},[402],[363,89541,465],{"className":89542},[407],[363,89544],{"className":89545,"style":2934},[505],[363,89547,5160],{"className":89548},[2938],[363,89550],{"className":89551,"style":2934},[505],[363,89553,89555,89558],{"className":89554},[398],[363,89556],{"className":89557,"style":2692},[402],[363,89559,1121],{"className":89560},[407,408],[363,89562,89564,89582],{"className":89563,"translate":367},[366],[363,89565,89567],{"className":89566},[371],[373,89568,89569],{"xmlns":375},[377,89570,89571,89579],{},[380,89572,89573,89575,89577],{},[383,89574,1121],{},[458,89576,3250],{},[463,89578,474],{},[387,89580,89581],{"encoding":389},"x>0",[363,89583,89585,89603],{"className":89584,"ariaHidden":394},[393],[363,89586,89588,89591,89594,89597,89600],{"className":89587},[398],[363,89589],{"className":89590,"style":6271},[402],[363,89592,1121],{"className":89593},[407,408],[363,89595],{"className":89596,"style":506},[505],[363,89598,3250],{"className":89599},[510],[363,89601],{"className":89602,"style":506},[505],[363,89604,89606,89609],{"className":89605},[398],[363,89607],{"className":89608,"style":520},[402],[363,89610,474],{"className":89611},[407],"），",[363,89614,89616,89666],{"className":89615,"translate":367},[366],[363,89617,89619],{"className":89618},[371],[373,89620,89621],{"xmlns":375},[377,89622,89623,89663],{},[380,89624,89625,89627,89629,89631,89633,89635,89637,89639,89641,89643,89645,89647,89649,89651,89653,89655,89657],{},[458,89626,5160],{},[463,89628,2810],{},[383,89630,4447],{},[458,89632,4450],{},[383,89634,39638],{},[383,89636,39641],{},[458,89638,7275],{},[463,89640,2810],{},[458,89642,461],{"stretchy":460},[463,89644,465],{},[458,89646,5160],{},[383,89648,39638],{},[383,89650,39641],{},[458,89652,468],{"stretchy":460},[458,89654,471],{},[463,89656,2810],{},[7161,89658,89659,89661],{},[383,89660,34231],{},[463,89662,2810],{},[387,89664,89665],{"encoding":389}," -2\\log BC\\ge 2(1-BC)=2H^2",[363,89667,89669,89707,89731,89755],{"className":89668,"ariaHidden":394},[393],[363,89670,89672,89675,89678,89681,89684,89689,89692,89695,89698,89701,89704],{"className":89671},[398],[363,89673],{"className":89674,"style":403},[402],[363,89676,5160],{"className":89677},[407],[363,89679,2810],{"className":89680},[407],[363,89682],{"className":89683,"style":754},[505],[363,89685,4501,89687],{"className":89686},[1831],[363,89688,4505],{"style":4504},[363,89690],{"className":89691,"style":754},[505],[363,89693,39638],{"className":89694,"style":39734},[407,408],[363,89696,39641],{"className":89697,"style":11129},[407,408],[363,89699],{"className":89700,"style":506},[505],[363,89702,7275],{"className":89703},[510],[363,89705],{"className":89706,"style":506},[505],[363,89708,89710,89713,89716,89719,89722,89725,89728],{"className":89709},[398],[363,89711],{"className":89712,"style":487},[402],[363,89714,2810],{"className":89715},[407],[363,89717,461],{"className":89718},[494],[363,89720,465],{"className":89721},[407],[363,89723],{"className":89724,"style":2934},[505],[363,89726,5160],{"className":89727},[2938],[363,89729],{"className":89730,"style":2934},[505],[363,89732,89734,89737,89740,89743,89746,89749,89752],{"className":89733},[398],[363,89735],{"className":89736,"style":487},[402],[363,89738,39638],{"className":89739,"style":39734},[407,408],[363,89741,39641],{"className":89742,"style":11129},[407,408],[363,89744,468],{"className":89745},[501],[363,89747],{"className":89748,"style":506},[505],[363,89750,471],{"className":89751},[510],[363,89753],{"className":89754,"style":506},[505],[363,89756,89758,89761,89764],{"className":89757},[398],[363,89759],{"className":89760,"style":20375},[402],[363,89762,2810],{"className":89763},[407],[363,89765,89767,89770],{"className":89766},[407],[363,89768,34231],{"className":89769,"style":34385},[407,408],[363,89771,89773],{"className":89772},[629],[363,89774,89776],{"className":89775},[633],[363,89777,89779],{"className":89778},[638],[363,89780,89782],{"className":89781,"style":20375},[642],[363,89783,89784,89787],{"style":7212},[363,89785],{"className":89786,"style":651},[650],[363,89788,89790],{"className":89789},[655,656,657,658],[363,89791,2810],{"className":89792},[407,658],"。合并即得",[363,89795,89797],{"className":89796,"translate":367},[528],[363,89798,89800,89854],{"className":89799,"translate":367},[366],[363,89801,89803],{"className":89802},[371],[373,89804,89805],{"xmlns":375,"display":537},[377,89806,89807,89851],{},[380,89808,89809,89815,89817,89825,89835,89837,89839,89841,89843,89845,89847,89849],{},[7161,89810,89811,89813],{},[383,89812,34231],{},[463,89814,2810],{},[458,89816,10299],{},[1602,89818,89819],{"scriptlevel":474,"displaystyle":460},[586,89820,89821,89823],{},[463,89822,465],{},[463,89824,2810],{},[543,89826,89827,89829],{},[383,89828,547],{},[380,89830,89831,89833],{},[383,89832,11041],{},[383,89834,22240],{},[458,89836,461],{"stretchy":460},[383,89838,554],{},[383,89840,558],{"mathvariant":557},[383,89842,561],{},[458,89844,468],{"stretchy":460},[383,89846,4722],{"mathvariant":557},[505,89848],{"width":3609},[383,89850,59599],{"mathvariant":557},[387,89852,89853],{"encoding":389},"H^2\\le \\tfrac12 D_{KL}(P\\|Q). \\qquad\\square",[363,89855,89857,89902],{"className":89856,"ariaHidden":394},[393],[363,89858,89860,89864,89893,89896,89899],{"className":89859},[398],[363,89861],{"className":89862,"style":89863},[402],"height:1.0001em;vertical-align:-0.136em;",[363,89865,89867,89870],{"className":89866},[407],[363,89868,34231],{"className":89869,"style":34385},[407,408],[363,89871,89873],{"className":89872},[629],[363,89874,89876],{"className":89875},[633],[363,89877,89879],{"className":89878},[638],[363,89880,89882],{"className":89881,"style":20082},[642],[363,89883,89884,89887],{"style":8624},[363,89885],{"className":89886,"style":651},[650],[363,89888,89890],{"className":89889},[655,656,657,658],[363,89891,2810],{"className":89892},[407,658],[363,89894],{"className":89895,"style":506},[505],[363,89897,10299],{"className":89898},[510],[363,89900],{"className":89901,"style":506},[505],[363,89903,89905,89908,89976,90022,90025,90028,90031,90034,90037,90040,90043],{"className":89904},[398],[363,89906],{"className":89907,"style":2852},[402],[363,89909,89911,89914,89973],{"className":89910},[407],[363,89912],{"className":89913},[494,789],[363,89915,89917],{"className":89916},[586],[363,89918,89920,89965],{"className":89919},[633,634],[363,89921,89923,89962],{"className":89922},[638],[363,89924,89926,89940,89948],{"className":89925,"style":2871},[642],[363,89927,89928,89931],{"style":2874},[363,89929],{"className":89930,"style":809},[650],[363,89932,89934],{"className":89933},[655,656,657,658],[363,89935,89937],{"className":89936},[407,658],[363,89938,2810],{"className":89939},[407,658],[363,89941,89942,89945],{"style":821},[363,89943],{"className":89944,"style":809},[650],[363,89946],{"className":89947,"style":829},[828],[363,89949,89950,89953],{"style":2897},[363,89951],{"className":89952,"style":809},[650],[363,89954,89956],{"className":89955},[655,656,657,658],[363,89957,89959],{"className":89958},[407,658],[363,89960,465],{"className":89961},[407,658],[363,89963,666],{"className":89964},[665],[363,89966,89968],{"className":89967},[638],[363,89969,89971],{"className":89970,"style":2919},[642],[363,89972],{},[363,89974],{"className":89975},[501,789],[363,89977,89979,89982],{"className":89978},[407],[363,89980,547],{"className":89981,"style":625},[407,408],[363,89983,89985],{"className":89984},[629],[363,89986,89988,90014],{"className":89987},[633,634],[363,89989,89991,90011],{"className":89990},[638],[363,89992,89994],{"className":89993,"style":727},[642],[363,89995,89996,89999],{"style":646},[363,89997],{"className":89998,"style":651},[650],[363,90000,90002],{"className":90001},[655,656,657,658],[363,90003,90005,90008],{"className":90004},[407,658],[363,90006,11041],{"className":90007,"style":11129},[407,408,658],[363,90009,22240],{"className":90010},[407,408,658],[363,90012,666],{"className":90013},[665],[363,90015,90017],{"className":90016},[638],[363,90018,90020],{"className":90019,"style":8315},[642],[363,90021],{},[363,90023,461],{"className":90024},[494],[363,90026,554],{"className":90027,"style":682},[407,408],[363,90029,558],{"className":90030},[407],[363,90032,561],{"className":90033},[407,408],[363,90035,468],{"className":90036},[501],[363,90038,4722],{"className":90039},[407],[363,90041],{"className":90042,"style":3981},[505],[363,90044,59599],{"className":90045},[407,60141],[11,90047,90048,90049,5992,90254,26626,90438,90791],{},"顺便验证与 4.6 节一致：小偏差时 ",[363,90050,90052,90087],{"className":90051,"translate":367},[366],[363,90053,90055],{"className":90054},[371],[373,90056,90057],{"xmlns":375},[377,90058,90059,90085],{},[380,90060,90061,90071,90073,90079],{},[543,90062,90063,90065],{},[383,90064,547],{},[380,90066,90067,90069],{},[383,90068,11041],{},[383,90070,22240],{},[458,90072,33306],{},[586,90074,90075,90077],{},[463,90076,465],{},[463,90078,2810],{},[7161,90080,90081,90083],{},[383,90082,37796],{},[463,90084,2810],{},[387,90086,81022],{"encoding":389},[363,90088,90090,90151],{"className":90089,"ariaHidden":394},[393],[363,90091,90093,90096,90142,90145,90148],{"className":90092},[398],[363,90094],{"className":90095,"style":16308},[402],[363,90097,90099,90102],{"className":90098},[407],[363,90100,547],{"className":90101,"style":625},[407,408],[363,90103,90105],{"className":90104},[629],[363,90106,90108,90134],{"className":90107},[633,634],[363,90109,90111,90131],{"className":90110},[638],[363,90112,90114],{"className":90113,"style":727},[642],[363,90115,90116,90119],{"style":646},[363,90117],{"className":90118,"style":651},[650],[363,90120,90122],{"className":90121},[655,656,657,658],[363,90123,90125,90128],{"className":90124},[407,658],[363,90126,11041],{"className":90127,"style":11129},[407,408,658],[363,90129,22240],{"className":90130},[407,408,658],[363,90132,666],{"className":90133},[665],[363,90135,90137],{"className":90136},[638],[363,90138,90140],{"className":90139,"style":8315},[642],[363,90141],{},[363,90143],{"className":90144,"style":506},[505],[363,90146,33306],{"className":90147},[510],[363,90149],{"className":90150,"style":506},[505],[363,90152,90154,90157,90225],{"className":90153},[398],[363,90155],{"className":90156,"style":2852},[402],[363,90158,90160,90163,90222],{"className":90159},[407],[363,90161],{"className":90162},[494,789],[363,90164,90166],{"className":90165},[586],[363,90167,90169,90214],{"className":90168},[633,634],[363,90170,90172,90211],{"className":90171},[638],[363,90173,90175,90189,90197],{"className":90174,"style":2871},[642],[363,90176,90177,90180],{"style":2874},[363,90178],{"className":90179,"style":809},[650],[363,90181,90183],{"className":90182},[655,656,657,658],[363,90184,90186],{"className":90185},[407,658],[363,90187,2810],{"className":90188},[407,658],[363,90190,90191,90194],{"style":821},[363,90192],{"className":90193,"style":809},[650],[363,90195],{"className":90196,"style":829},[828],[363,90198,90199,90202],{"style":2897},[363,90200],{"className":90201,"style":809},[650],[363,90203,90205],{"className":90204},[655,656,657,658],[363,90206,90208],{"className":90207},[407,658],[363,90209,465],{"className":90210},[407,658],[363,90212,666],{"className":90213},[665],[363,90215,90217],{"className":90216},[638],[363,90218,90220],{"className":90219,"style":2919},[642],[363,90221],{},[363,90223],{"className":90224},[501,789],[363,90226,90228,90231],{"className":90227},[407],[363,90229,37796],{"className":90230},[407,408],[363,90232,90234],{"className":90233},[629],[363,90235,90237],{"className":90236},[633],[363,90238,90240],{"className":90239},[638],[363,90241,90243],{"className":90242,"style":20375},[642],[363,90244,90245,90248],{"style":7212},[363,90246],{"className":90247,"style":651},[650],[363,90249,90251],{"className":90250},[655,656,657,658],[363,90252,2810],{"className":90253},[407,658],[363,90255,90257,90288],{"className":90256,"translate":367},[366],[363,90258,90260],{"className":90259},[371],[373,90261,90262],{"xmlns":375},[377,90263,90264,90286],{},[380,90265,90266,90272,90274,90280],{},[7161,90267,90268,90270],{},[383,90269,34231],{},[463,90271,2810],{},[458,90273,33306],{},[586,90275,90276,90278],{},[463,90277,465],{},[463,90279,39650],{},[7161,90281,90282,90284],{},[383,90283,37796],{},[463,90285,2810],{},[387,90287,81932],{"encoding":389},[363,90289,90291,90335],{"className":90290,"ariaHidden":394},[393],[363,90292,90294,90297,90326,90329,90332],{"className":90293},[398],[363,90295],{"className":90296,"style":20375},[402],[363,90298,90300,90303],{"className":90299},[407],[363,90301,34231],{"className":90302,"style":34385},[407,408],[363,90304,90306],{"className":90305},[629],[363,90307,90309],{"className":90308},[633],[363,90310,90312],{"className":90311},[638],[363,90313,90315],{"className":90314,"style":20375},[642],[363,90316,90317,90320],{"style":7212},[363,90318],{"className":90319,"style":651},[650],[363,90321,90323],{"className":90322},[655,656,657,658],[363,90324,2810],{"className":90325},[407,658],[363,90327],{"className":90328,"style":506},[505],[363,90330,33306],{"className":90331},[510],[363,90333],{"className":90334,"style":506},[505],[363,90336,90338,90341,90409],{"className":90337},[398],[363,90339],{"className":90340,"style":2852},[402],[363,90342,90344,90347,90406],{"className":90343},[407],[363,90345],{"className":90346},[494,789],[363,90348,90350],{"className":90349},[586],[363,90351,90353,90398],{"className":90352},[633,634],[363,90354,90356,90395],{"className":90355},[638],[363,90357,90359,90373,90381],{"className":90358,"style":2871},[642],[363,90360,90361,90364],{"style":2874},[363,90362],{"className":90363,"style":809},[650],[363,90365,90367],{"className":90366},[655,656,657,658],[363,90368,90370],{"className":90369},[407,658],[363,90371,39650],{"className":90372},[407,658],[363,90374,90375,90378],{"style":821},[363,90376],{"className":90377,"style":809},[650],[363,90379],{"className":90380,"style":829},[828],[363,90382,90383,90386],{"style":2897},[363,90384],{"className":90385,"style":809},[650],[363,90387,90389],{"className":90388},[655,656,657,658],[363,90390,90392],{"className":90391},[407,658],[363,90393,465],{"className":90394},[407,658],[363,90396,666],{"className":90397},[665],[363,90399,90401],{"className":90400},[638],[363,90402,90404],{"className":90403,"style":2919},[642],[363,90405],{},[363,90407],{"className":90408},[501,789],[363,90410,90412,90415],{"className":90411},[407],[363,90413,37796],{"className":90414},[407,408],[363,90416,90418],{"className":90417},[629],[363,90419,90421],{"className":90420},[633],[363,90422,90424],{"className":90423},[638],[363,90425,90427],{"className":90426,"style":20375},[642],[363,90428,90429,90432],{"style":7212},[363,90430],{"className":90431,"style":651},[650],[363,90433,90435],{"className":90434},[655,656,657,658],[363,90436,2810],{"className":90437},[407,658],[363,90439,90441,90495],{"className":90440,"translate":367},[366],[363,90442,90444],{"className":90443},[371],[373,90445,90446],{"xmlns":375},[377,90447,90448,90492],{},[380,90449,90450,90456,90458,90464,90474,90476,90482],{},[7161,90451,90452,90454],{},[383,90453,34231],{},[463,90455,2810],{},[458,90457,33306],{},[586,90459,90460,90462],{},[463,90461,465],{},[463,90463,39336],{},[543,90465,90466,90468],{},[383,90467,547],{},[380,90469,90470,90472],{},[383,90471,11041],{},[383,90473,22240],{},[458,90475,10299],{},[586,90477,90478,90480],{},[463,90479,465],{},[463,90481,2810],{},[543,90483,90484,90486],{},[383,90485,547],{},[380,90487,90488,90490],{},[383,90489,11041],{},[383,90491,22240],{},[387,90493,90494],{"encoding":389},"H^2\\approx\\frac14 D_{KL}\\le\\frac12 D_{KL}",[363,90496,90498,90542,90671],{"className":90497,"ariaHidden":394},[393],[363,90499,90501,90504,90533,90536,90539],{"className":90500},[398],[363,90502],{"className":90503,"style":20375},[402],[363,90505,90507,90510],{"className":90506},[407],[363,90508,34231],{"className":90509,"style":34385},[407,408],[363,90511,90513],{"className":90512},[629],[363,90514,90516],{"className":90515},[633],[363,90517,90519],{"className":90518},[638],[363,90520,90522],{"className":90521,"style":20375},[642],[363,90523,90524,90527],{"style":7212},[363,90525],{"className":90526,"style":651},[650],[363,90528,90530],{"className":90529},[655,656,657,658],[363,90531,2810],{"className":90532},[407,658],[363,90534],{"className":90535,"style":506},[505],[363,90537,33306],{"className":90538},[510],[363,90540],{"className":90541,"style":506},[505],[363,90543,90545,90548,90616,90662,90665,90668],{"className":90544},[398],[363,90546],{"className":90547,"style":2852},[402],[363,90549,90551,90554,90613],{"className":90550},[407],[363,90552],{"className":90553},[494,789],[363,90555,90557],{"className":90556},[586],[363,90558,90560,90605],{"className":90559},[633,634],[363,90561,90563,90602],{"className":90562},[638],[363,90564,90566,90580,90588],{"className":90565,"style":2871},[642],[363,90567,90568,90571],{"style":2874},[363,90569],{"className":90570,"style":809},[650],[363,90572,90574],{"className":90573},[655,656,657,658],[363,90575,90577],{"className":90576},[407,658],[363,90578,39336],{"className":90579},[407,658],[363,90581,90582,90585],{"style":821},[363,90583],{"className":90584,"style":809},[650],[363,90586],{"className":90587,"style":829},[828],[363,90589,90590,90593],{"style":2897},[363,90591],{"className":90592,"style":809},[650],[363,90594,90596],{"className":90595},[655,656,657,658],[363,90597,90599],{"className":90598},[407,658],[363,90600,465],{"className":90601},[407,658],[363,90603,666],{"className":90604},[665],[363,90606,90608],{"className":90607},[638],[363,90609,90611],{"className":90610,"style":2919},[642],[363,90612],{},[363,90614],{"className":90615},[501,789],[363,90617,90619,90622],{"className":90618},[407],[363,90620,547],{"className":90621,"style":625},[407,408],[363,90623,90625],{"className":90624},[629],[363,90626,90628,90654],{"className":90627},[633,634],[363,90629,90631,90651],{"className":90630},[638],[363,90632,90634],{"className":90633,"style":727},[642],[363,90635,90636,90639],{"style":646},[363,90637],{"className":90638,"style":651},[650],[363,90640,90642],{"className":90641},[655,656,657,658],[363,90643,90645,90648],{"className":90644},[407,658],[363,90646,11041],{"className":90647,"style":11129},[407,408,658],[363,90649,22240],{"className":90650},[407,408,658],[363,90652,666],{"className":90653},[665],[363,90655,90657],{"className":90656},[638],[363,90658,90660],{"className":90659,"style":8315},[642],[363,90661],{},[363,90663],{"className":90664,"style":506},[505],[363,90666,10299],{"className":90667},[510],[363,90669],{"className":90670,"style":506},[505],[363,90672,90674,90677,90745],{"className":90673},[398],[363,90675],{"className":90676,"style":2852},[402],[363,90678,90680,90683,90742],{"className":90679},[407],[363,90681],{"className":90682},[494,789],[363,90684,90686],{"className":90685},[586],[363,90687,90689,90734],{"className":90688},[633,634],[363,90690,90692,90731],{"className":90691},[638],[363,90693,90695,90709,90717],{"className":90694,"style":2871},[642],[363,90696,90697,90700],{"style":2874},[363,90698],{"className":90699,"style":809},[650],[363,90701,90703],{"className":90702},[655,656,657,658],[363,90704,90706],{"className":90705},[407,658],[363,90707,2810],{"className":90708},[407,658],[363,90710,90711,90714],{"style":821},[363,90712],{"className":90713,"style":809},[650],[363,90715],{"className":90716,"style":829},[828],[363,90718,90719,90722],{"style":2897},[363,90720],{"className":90721,"style":809},[650],[363,90723,90725],{"className":90724},[655,656,657,658],[363,90726,90728],{"className":90727},[407,658],[363,90729,465],{"className":90730},[407,658],[363,90732,666],{"className":90733},[665],[363,90735,90737],{"className":90736},[638],[363,90738,90740],{"className":90739,"style":2919},[642],[363,90741],{},[363,90743],{"className":90744},[501,789],[363,90746,90748,90751],{"className":90747},[407],[363,90749,547],{"className":90750,"style":625},[407,408],[363,90752,90754],{"className":90753},[629],[363,90755,90757,90783],{"className":90756},[633,634],[363,90758,90760,90780],{"className":90759},[638],[363,90761,90763],{"className":90762,"style":727},[642],[363,90764,90765,90768],{"style":646},[363,90766],{"className":90767,"style":651},[650],[363,90769,90771],{"className":90770},[655,656,657,658],[363,90772,90774,90777],{"className":90773},[407,658],[363,90775,11041],{"className":90776,"style":11129},[407,408,658],[363,90778,22240],{"className":90779},[407,408,658],[363,90781,666],{"className":90782},[665],[363,90784,90786],{"className":90785},[638],[363,90787,90789],{"className":90788,"style":8315},[642],[363,90790],{},"，不等式成立且留有余量。",[11,90793,90794,90856],{},[1572,90795,90796,90797,90855],{},"TV 与 ",[363,90798,90800,90817],{"className":90799,"translate":367},[366],[363,90801,90803],{"className":90802},[371],[373,90804,90805],{"xmlns":375},[377,90806,90807,90815],{},[380,90808,90809],{},[7161,90810,90811,90813],{},[383,90812,34231],{},[463,90814,2810],{},[387,90816,42417],{"encoding":389},[363,90818,90820],{"className":90819,"ariaHidden":394},[393],[363,90821,90823,90826],{"className":90822},[398],[363,90824],{"className":90825,"style":20375},[402],[363,90827,90829,90832],{"className":90828},[407],[363,90830,34231],{"className":90831,"style":34385},[407,408],[363,90833,90835],{"className":90834},[629],[363,90836,90838],{"className":90837},[633],[363,90839,90841],{"className":90840},[638],[363,90842,90844],{"className":90843,"style":20375},[642],[363,90845,90846,90849],{"style":7212},[363,90847],{"className":90848,"style":651},[650],[363,90850,90852],{"className":90851},[655,656,657,658],[363,90853,2810],{"className":90854},[407,658]," 的关系。"," 由 Cauchy–Schwarz，",[363,90858,90860],{"className":90859,"translate":367},[528],[363,90861,90863,91089],{"className":90862,"translate":367},[366],[363,90864,90866],{"className":90865},[371],[373,90867,90868],{"xmlns":375,"display":537},[377,90869,90870,91086],{},[1590,90871,90872,90938,91006],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,90873,90874,90890],{},[1599,90875,90876],{},[1602,90877,90878],{"scriptlevel":474,"displaystyle":394},[380,90879,90880,90882,90884],{},[463,90881,2810],{},[1644,90883,1646],{},[380,90885,90886,90888],{},[383,90887,5739],{"mathvariant":557},[383,90889,35197],{"mathvariant":557},[1599,90891,90892],{},[1602,90893,90894],{"scriptlevel":474,"displaystyle":394},[380,90895,90896,90898,90900,90902,90904,90908,90910,90914,90916,90918,90920,90924,90926,90930,90932,90934,90936],{},[380,90897],{},[458,90899,471],{},[458,90901,1634],{},[383,90903,5155],{"mathvariant":557},[34686,90905,90906],{},[383,90907,11],{},[458,90909,5160],{},[34686,90911,90912],{},[383,90913,1291],{},[383,90915,5155],{"mathvariant":557},[1644,90917,16251],{},[383,90919,5155],{"mathvariant":557},[34686,90921,90922],{},[383,90923,11],{},[458,90925,2817],{},[34686,90927,90928],{},[383,90929,1291],{},[383,90931,5155],{"mathvariant":557},[1644,90933,1646],{},[383,90935,592],{},[383,90937,1121],{},[1596,90939,90940,90946],{},[1599,90941,90942],{},[1602,90943,90944],{"scriptlevel":474,"displaystyle":394},[380,90945],{},[1599,90947,90948],{},[1602,90949,90950],{"scriptlevel":474,"displaystyle":394},[380,90951,90952,90954,90956,90980,90982],{},[380,90953],{},[458,90955,10299],{},[34686,90957,90958],{},[380,90959,90960,90962,90964,90968,90970,90974],{},[458,90961,1634],{},[458,90963,461],{"stretchy":460},[34686,90965,90966],{},[383,90967,11],{},[458,90969,5160],{},[34686,90971,90972],{},[383,90973,1291],{},[7161,90975,90976,90978],{},[458,90977,468],{"stretchy":460},[463,90979,2810],{},[458,90981,3646],{},[34686,90983,90984],{},[380,90985,90986,90988,90990,90994,90996,91000],{},[458,90987,1634],{},[458,90989,461],{"stretchy":460},[34686,90991,90992],{},[383,90993,11],{},[458,90995,2817],{},[34686,90997,90998],{},[383,90999,1291],{},[7161,91001,91002,91004],{},[458,91003,468],{"stretchy":460},[463,91005,2810],{},[1596,91007,91008,91014],{},[1599,91009,91010],{},[1602,91011,91012],{"scriptlevel":474,"displaystyle":394},[380,91013],{},[1599,91015,91016],{},[1602,91017,91018],{"scriptlevel":474,"displaystyle":394},[380,91019,91020,91022,91024,91036,91038,91056,91058,91084],{},[380,91021],{},[458,91023,471],{},[34686,91025,91026],{},[380,91027,91028,91030],{},[463,91029,2810],{},[7161,91031,91032,91034],{},[383,91033,34231],{},[463,91035,2810],{},[458,91037,3646],{},[34686,91039,91040],{},[380,91041,91042,91044,91046,91048,91050,91052,91054],{},[463,91043,2810],{},[458,91045,461],{"stretchy":460},[463,91047,465],{},[458,91049,2817],{},[383,91051,39638],{},[383,91053,39641],{},[458,91055,468],{"stretchy":460},[458,91057,471],{},[34686,91059,91060],{},[380,91061,91062,91064,91070,91072,91074,91076,91082],{},[463,91063,39336],{},[7161,91065,91066,91068],{},[383,91067,34231],{},[463,91069,2810],{},[458,91071,461],{"stretchy":460},[463,91073,2810],{},[458,91075,5160],{},[7161,91077,91078,91080],{},[383,91079,34231],{},[463,91081,2810],{},[458,91083,468],{"stretchy":460},[458,91085,898],{"separator":394},[387,91087,91088],{"encoding":389},"\\begin{aligned}\n2\\,\\mathrm{TV}\n&=\\int|\\sqrt p-\\sqrt q|\\;|\\sqrt p+\\sqrt q|\\,dx\\\\\n&\\le\\sqrt{\\int(\\sqrt p-\\sqrt q)^2}\n\\cdot\\sqrt{\\int(\\sqrt p+\\sqrt q)^2}\\\\\n&=\\sqrt{2H^2}\\cdot\\sqrt{2(1+BC)}\n=\\sqrt{4H^2(2-H^2)},\n\\end{aligned}",[363,91090,91092],{"className":91091,"ariaHidden":394},[393],[363,91093,91095,91099],{"className":91094},[398],[363,91096],{"className":91097,"style":91098},[402],"height:7.2262em;vertical-align:-3.3631em;",[363,91100,91102],{"className":91101},[407],[363,91103,91105,91170],{"className":91104},[1590],[363,91106,91108],{"className":91107},[1707],[363,91109,91111,91161],{"className":91110},[633,634],[363,91112,91114,91158],{"className":91113},[638],[363,91115,91118,91140,91149],{"className":91116,"style":91117},[642],"height:3.8631em;",[363,91119,91121,91125],{"style":91120},"top:-6.3858em;",[363,91122],{"className":91123,"style":91124},[650],"height:3.8828em;",[363,91126,91128,91131,91134],{"className":91127},[407],[363,91129,2810],{"className":91130},[407],[363,91132],{"className":91133,"style":754},[505],[363,91135,91137],{"className":91136},[407],[363,91138,87109],{"className":91139,"style":4504},[407,33009],[363,91141,91143,91146],{"style":91142},"top:-3.3408em;",[363,91144],{"className":91145,"style":91124},[650],[363,91147],{"className":91148},[407],[363,91150,91152,91155],{"style":91151},"top:-0.8797em;",[363,91153],{"className":91154,"style":91124},[650],[363,91156],{"className":91157},[407],[363,91159,666],{"className":91160},[665],[363,91162,91164],{"className":91163},[638],[363,91165,91168],{"className":91166,"style":91167},[642],"height:3.3631em;",[363,91169],{},[363,91171,91173],{"className":91172},[1798],[363,91174,91176,92130],{"className":91175},[633,634],[363,91177,91179,92127],{"className":91178},[638],[363,91180,91182,91426,91816],{"className":91181,"style":91117},[642],[363,91183,91184,91187],{"style":91120},[363,91185],{"className":91186,"style":91124},[650],[363,91188,91190,91193,91196,91199,91202,91205,91208,91211,91255,91258,91261,91264,91308,91311,91314,91317,91361,91364,91367,91370,91414,91417,91420,91423],{"className":91189},[407],[363,91191],{"className":91192},[407],[363,91194],{"className":91195,"style":506},[505],[363,91197,471],{"className":91198},[510],[363,91200],{"className":91201,"style":506},[505],[363,91203,1634],{"className":91204,"style":1834},[1831,1832,1833],[363,91206],{"className":91207,"style":754},[505],[363,91209,5155],{"className":91210},[407],[363,91212,91214],{"className":91213},[407,34714],[363,91215,91217,91247],{"className":91216},[633,634],[363,91218,91220,91244],{"className":91219},[638],[363,91221,91223,91232],{"className":91222,"style":7209},[642],[363,91224,91226,91229],{"className":91225,"style":12210},[6654],[363,91227],{"className":91228,"style":809},[650],[363,91230,11],{"className":91231,"style":34734},[407,408],[363,91233,91234,91237],{"style":41697},[363,91235],{"className":91236,"style":809},[650],[363,91238,91240],{"className":91239,"style":34791},[34790],[6670,91241,91242],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,91243],{"d":34798},[363,91245,666],{"className":91246},[665],[363,91248,91250],{"className":91249},[638],[363,91251,91253],{"className":91252,"style":41717},[642],[363,91254],{},[363,91256],{"className":91257,"style":2934},[505],[363,91259,5160],{"className":91260},[2938],[363,91262],{"className":91263,"style":2934},[505],[363,91265,91267],{"className":91266},[407,34714],[363,91268,91270,91300],{"className":91269},[633,634],[363,91271,91273,91297],{"className":91272},[638],[363,91274,91276,91285],{"className":91275,"style":7209},[642],[363,91277,91279,91282],{"className":91278,"style":12210},[6654],[363,91280],{"className":91281,"style":809},[650],[363,91283,1291],{"className":91284,"style":39446},[407,408],[363,91286,91287,91290],{"style":41697},[363,91288],{"className":91289,"style":809},[650],[363,91291,91293],{"className":91292,"style":34791},[34790],[6670,91294,91295],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,91296],{"d":34798},[363,91298,666],{"className":91299},[665],[363,91301,91303],{"className":91302},[638],[363,91304,91306],{"className":91305,"style":41717},[642],[363,91307],{},[363,91309,5155],{"className":91310},[407],[363,91312],{"className":91313,"style":506},[505],[363,91315,5155],{"className":91316},[407],[363,91318,91320],{"className":91319},[407,34714],[363,91321,91323,91353],{"className":91322},[633,634],[363,91324,91326,91350],{"className":91325},[638],[363,91327,91329,91338],{"className":91328,"style":7209},[642],[363,91330,91332,91335],{"className":91331,"style":12210},[6654],[363,91333],{"className":91334,"style":809},[650],[363,91336,11],{"className":91337,"style":34734},[407,408],[363,91339,91340,91343],{"style":41697},[363,91341],{"className":91342,"style":809},[650],[363,91344,91346],{"className":91345,"style":34791},[34790],[6670,91347,91348],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,91349],{"d":34798},[363,91351,666],{"className":91352},[665],[363,91354,91356],{"className":91355},[638],[363,91357,91359],{"className":91358,"style":41717},[642],[363,91360],{},[363,91362],{"className":91363,"style":2934},[505],[363,91365,2817],{"className":91366},[2938],[363,91368],{"className":91369,"style":2934},[505],[363,91371,91373],{"className":91372},[407,34714],[363,91374,91376,91406],{"className":91375},[633,634],[363,91377,91379,91403],{"className":91378},[638],[363,91380,91382,91391],{"className":91381,"style":7209},[642],[363,91383,91385,91388],{"className":91384,"style":12210},[6654],[363,91386],{"className":91387,"style":809},[650],[363,91389,1291],{"className":91390,"style":39446},[407,408],[363,91392,91393,91396],{"style":41697},[363,91394],{"className":91395,"style":809},[650],[363,91397,91399],{"className":91398,"style":34791},[34790],[6670,91400,91401],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,91402],{"d":34798},[363,91404,666],{"className":91405},[665],[363,91407,91409],{"className":91408},[638],[363,91410,91412],{"className":91411,"style":41717},[642],[363,91413],{},[363,91415,5155],{"className":91416},[407],[363,91418],{"className":91419,"style":754},[505],[363,91421,592],{"className":91422},[407,408],[363,91424,1121],{"className":91425},[407,408],[363,91427,91428,91431],{"style":91142},[363,91429],{"className":91430,"style":91124},[650],[363,91432,91434,91437,91440,91443,91446,91631,91634,91637,91640],{"className":91433},[407],[363,91435],{"className":91436},[407],[363,91438],{"className":91439,"style":506},[505],[363,91441,10299],{"className":91442},[510],[363,91444],{"className":91445,"style":506},[505],[363,91447,91449],{"className":91448},[407,34714],[363,91450,91452,91622],{"className":91451},[633,634],[363,91453,91455,91619],{"className":91454},[638],[363,91456,91459,91602],{"className":91457,"style":91458},[642],"height:1.8828em;",[363,91460,91463,91467],{"className":91461,"style":91462},[6654],"top:-5em;",[363,91464],{"className":91465,"style":91466},[650],"height:5em;",[363,91468,91470,91473,91476,91520,91523,91526,91529,91573],{"className":91469,"style":41508},[407],[363,91471,1634],{"className":91472,"style":1834},[1831,1832,1833],[363,91474,461],{"className":91475},[494],[363,91477,91479],{"className":91478},[407,34714],[363,91480,91482,91512],{"className":91481},[633,634],[363,91483,91485,91509],{"className":91484},[638],[363,91486,91488,91497],{"className":91487,"style":7209},[642],[363,91489,91491,91494],{"className":91490,"style":12210},[6654],[363,91492],{"className":91493,"style":809},[650],[363,91495,11],{"className":91496,"style":34734},[407,408],[363,91498,91499,91502],{"style":41697},[363,91500],{"className":91501,"style":809},[650],[363,91503,91505],{"className":91504,"style":34791},[34790],[6670,91506,91507],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,91508],{"d":34798},[363,91510,666],{"className":91511},[665],[363,91513,91515],{"className":91514},[638],[363,91516,91518],{"className":91517,"style":41717},[642],[363,91519],{},[363,91521],{"className":91522,"style":2934},[505],[363,91524,5160],{"className":91525},[2938],[363,91527],{"className":91528,"style":2934},[505],[363,91530,91532],{"className":91531},[407,34714],[363,91533,91535,91565],{"className":91534},[633,634],[363,91536,91538,91562],{"className":91537},[638],[363,91539,91541,91550],{"className":91540,"style":7209},[642],[363,91542,91544,91547],{"className":91543,"style":12210},[6654],[363,91545],{"className":91546,"style":809},[650],[363,91548,1291],{"className":91549,"style":39446},[407,408],[363,91551,91552,91555],{"style":41697},[363,91553],{"className":91554,"style":809},[650],[363,91556,91558],{"className":91557,"style":34791},[34790],[6670,91559,91560],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,91561],{"d":34798},[363,91563,666],{"className":91564},[665],[363,91566,91568],{"className":91567},[638],[363,91569,91571],{"className":91570,"style":41717},[642],[363,91572],{},[363,91574,91576,91579],{"className":91575},[501],[363,91577,468],{"className":91578},[501],[363,91580,91582],{"className":91581},[629],[363,91583,91585],{"className":91584},[633],[363,91586,91588],{"className":91587},[638],[363,91589,91591],{"className":91590,"style":45379},[642],[363,91592,91593,91596],{"style":45382},[363,91594],{"className":91595,"style":651},[650],[363,91597,91599],{"className":91598},[655,656,657,658],[363,91600,2810],{"className":91601},[407,658],[363,91603,91605,91608],{"style":91604},"top:-3.8428em;",[363,91606],{"className":91607,"style":91466},[650],[363,91609,91612],{"className":91610,"style":91611},[34790],"min-width:1.02em;height:3.08em;",[6670,91613,91616],{"xmlns":6672,"width":6673,"height":91614,"viewBox":91615,"preserveAspectRatio":6676},"3.08em","0 0 400000 3240",[6678,91617],{"d":91618},"M473,2793\nc339.3,-1799.3,509.3,-2700,510,-2702 l0 -0\nc3.3,-7.3,9.3,-11,18,-11 H400000v40H1017.7\ns-90.5,478,-276.2,1466c-185.7,988,-279.5,1483,-281.5,1485c-2,6,-10,9,-24,9\nc-8,0,-12,-0.7,-12,-2c0,-1.3,-5.3,-32,-16,-92c-50.7,-293.3,-119.7,-693.3,-207,-1200\nc0,-1.3,-5.3,8.7,-16,30c-10.7,21.3,-21.3,42.7,-32,64s-16,33,-16,33s-26,-26,-26,-26\ns76,-153,76,-153s77,-151,77,-151c0.7,0.7,35.7,202,105,604c67.3,400.7,102,602.7,104,\n606zM1001 80h400000v40H1017.7z",[363,91620,666],{"className":91621},[665],[363,91623,91625],{"className":91624},[638],[363,91626,91629],{"className":91627,"style":91628},[642],"height:1.1572em;",[363,91630],{},[363,91632],{"className":91633,"style":2934},[505],[363,91635,3646],{"className":91636},[2938],[363,91638],{"className":91639,"style":2934},[505],[363,91641,91643],{"className":91642},[407,34714],[363,91644,91646,91808],{"className":91645},[633,634],[363,91647,91649,91805],{"className":91648},[638],[363,91650,91652,91793],{"className":91651,"style":91458},[642],[363,91653,91655,91658],{"className":91654,"style":91462},[6654],[363,91656],{"className":91657,"style":91466},[650],[363,91659,91661,91664,91667,91711,91714,91717,91720,91764],{"className":91660,"style":41508},[407],[363,91662,1634],{"className":91663,"style":1834},[1831,1832,1833],[363,91665,461],{"className":91666},[494],[363,91668,91670],{"className":91669},[407,34714],[363,91671,91673,91703],{"className":91672},[633,634],[363,91674,91676,91700],{"className":91675},[638],[363,91677,91679,91688],{"className":91678,"style":7209},[642],[363,91680,91682,91685],{"className":91681,"style":12210},[6654],[363,91683],{"className":91684,"style":809},[650],[363,91686,11],{"className":91687,"style":34734},[407,408],[363,91689,91690,91693],{"style":41697},[363,91691],{"className":91692,"style":809},[650],[363,91694,91696],{"className":91695,"style":34791},[34790],[6670,91697,91698],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,91699],{"d":34798},[363,91701,666],{"className":91702},[665],[363,91704,91706],{"className":91705},[638],[363,91707,91709],{"className":91708,"style":41717},[642],[363,91710],{},[363,91712],{"className":91713,"style":2934},[505],[363,91715,2817],{"className":91716},[2938],[363,91718],{"className":91719,"style":2934},[505],[363,91721,91723],{"className":91722},[407,34714],[363,91724,91726,91756],{"className":91725},[633,634],[363,91727,91729,91753],{"className":91728},[638],[363,91730,91732,91741],{"className":91731,"style":7209},[642],[363,91733,91735,91738],{"className":91734,"style":12210},[6654],[363,91736],{"className":91737,"style":809},[650],[363,91739,1291],{"className":91740,"style":39446},[407,408],[363,91742,91743,91746],{"style":41697},[363,91744],{"className":91745,"style":809},[650],[363,91747,91749],{"className":91748,"style":34791},[34790],[6670,91750,91751],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,91752],{"d":34798},[363,91754,666],{"className":91755},[665],[363,91757,91759],{"className":91758},[638],[363,91760,91762],{"className":91761,"style":41717},[642],[363,91763],{},[363,91765,91767,91770],{"className":91766},[501],[363,91768,468],{"className":91769},[501],[363,91771,91773],{"className":91772},[629],[363,91774,91776],{"className":91775},[633],[363,91777,91779],{"className":91778},[638],[363,91780,91782],{"className":91781,"style":45379},[642],[363,91783,91784,91787],{"style":45382},[363,91785],{"className":91786,"style":651},[650],[363,91788,91790],{"className":91789},[655,656,657,658],[363,91791,2810],{"className":91792},[407,658],[363,91794,91795,91798],{"style":91604},[363,91796],{"className":91797,"style":91466},[650],[363,91799,91801],{"className":91800,"style":91611},[34790],[6670,91802,91803],{"xmlns":6672,"width":6673,"height":91614,"viewBox":91615,"preserveAspectRatio":6676},[6678,91804],{"d":91618},[363,91806,666],{"className":91807},[665],[363,91809,91811],{"className":91810},[638],[363,91812,91814],{"className":91813,"style":91628},[642],[363,91815],{},[363,91817,91818,91821],{"style":91151},[363,91819],{"className":91820,"style":91124},[650],[363,91822,91824,91827,91830,91833,91836,91912,91915,91918,91921,91992,91995,91998,92001,92124],{"className":91823},[407],[363,91825],{"className":91826},[407],[363,91828],{"className":91829,"style":506},[505],[363,91831,471],{"className":91832},[510],[363,91834],{"className":91835,"style":506},[505],[363,91837,91839],{"className":91838},[407,34714],[363,91840,91842,91904],{"className":91841},[633,634],[363,91843,91845,91901],{"className":91844},[638],[363,91846,91848,91889],{"className":91847,"style":84016},[642],[363,91849,91851,91854],{"className":91850,"style":12210},[6654],[363,91852],{"className":91853,"style":809},[650],[363,91855,91857,91860],{"className":91856,"style":34734},[407],[363,91858,2810],{"className":91859},[407],[363,91861,91863,91866],{"className":91862},[407],[363,91864,34231],{"className":91865,"style":34385},[407,408],[363,91867,91869],{"className":91868},[629],[363,91870,91872],{"className":91871},[633],[363,91873,91875],{"className":91874},[638],[363,91876,91878],{"className":91877,"style":45379},[642],[363,91879,91880,91883],{"style":45382},[363,91881],{"className":91882,"style":651},[650],[363,91884,91886],{"className":91885},[655,656,657,658],[363,91887,2810],{"className":91888},[407,658],[363,91890,91891,91894],{"style":84060},[363,91892],{"className":91893,"style":809},[650],[363,91895,91897],{"className":91896,"style":34791},[34790],[6670,91898,91899],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,91900],{"d":34798},[363,91902,666],{"className":91903},[665],[363,91905,91907],{"className":91906},[638],[363,91908,91910],{"className":91909,"style":84080},[642],[363,91911],{},[363,91913],{"className":91914,"style":2934},[505],[363,91916,3646],{"className":91917},[2938],[363,91919],{"className":91920,"style":2934},[505],[363,91922,91924],{"className":91923},[407,34714],[363,91925,91927,91984],{"className":91926},[633,634],[363,91928,91930,91981],{"className":91929},[638],[363,91931,91933,91969],{"className":91932,"style":83879},[642],[363,91934,91936,91939],{"className":91935,"style":83883},[6654],[363,91937],{"className":91938,"style":15193},[650],[363,91940,91942,91945,91948,91951,91954,91957,91960,91963,91966],{"className":91941,"style":41508},[407],[363,91943,2810],{"className":91944},[407],[363,91946,461],{"className":91947},[494],[363,91949,465],{"className":91950},[407],[363,91952],{"className":91953,"style":2934},[505],[363,91955,2817],{"className":91956},[2938],[363,91958],{"className":91959,"style":2934},[505],[363,91961,39638],{"className":91962,"style":39734},[407,408],[363,91964,39641],{"className":91965,"style":11129},[407,408],[363,91967,468],{"className":91968},[501],[363,91970,91971,91974],{"style":83968},[363,91972],{"className":91973,"style":15193},[650],[363,91975,91977],{"className":91976,"style":83975},[34790],[6670,91978,91979],{"xmlns":6672,"width":6673,"height":83978,"viewBox":83979,"preserveAspectRatio":6676},[6678,91980],{"d":83982},[363,91982,666],{"className":91983},[665],[363,91985,91987],{"className":91986},[638],[363,91988,91990],{"className":91989,"style":83992},[642],[363,91991],{},[363,91993],{"className":91994,"style":506},[505],[363,91996,471],{"className":91997},[510],[363,91999],{"className":92000,"style":506},[505],[363,92002,92004],{"className":92003},[407,34714],[363,92005,92007,92116],{"className":92006},[633,634],[363,92008,92010,92113],{"className":92009},[638],[363,92011,92013,92101],{"className":92012,"style":83879},[642],[363,92014,92016,92019],{"className":92015,"style":83883},[6654],[363,92017],{"className":92018,"style":15193},[650],[363,92020,92022,92025,92054,92057,92060,92063,92066,92069,92098],{"className":92021,"style":41508},[407],[363,92023,39336],{"className":92024},[407],[363,92026,92028,92031],{"className":92027},[407],[363,92029,34231],{"className":92030,"style":34385},[407,408],[363,92032,92034],{"className":92033},[629],[363,92035,92037],{"className":92036},[633],[363,92038,92040],{"className":92039},[638],[363,92041,92043],{"className":92042,"style":45379},[642],[363,92044,92045,92048],{"style":45382},[363,92046],{"className":92047,"style":651},[650],[363,92049,92051],{"className":92050},[655,656,657,658],[363,92052,2810],{"className":92053},[407,658],[363,92055,461],{"className":92056},[494],[363,92058,2810],{"className":92059},[407],[363,92061],{"className":92062,"style":2934},[505],[363,92064,5160],{"className":92065},[2938],[363,92067],{"className":92068,"style":2934},[505],[363,92070,92072,92075],{"className":92071},[407],[363,92073,34231],{"className":92074,"style":34385},[407,408],[363,92076,92078],{"className":92077},[629],[363,92079,92081],{"className":92080},[633],[363,92082,92084],{"className":92083},[638],[363,92085,92087],{"className":92086,"style":45379},[642],[363,92088,92089,92092],{"style":45382},[363,92090],{"className":92091,"style":651},[650],[363,92093,92095],{"className":92094},[655,656,657,658],[363,92096,2810],{"className":92097},[407,658],[363,92099,468],{"className":92100},[501],[363,92102,92103,92106],{"style":83968},[363,92104],{"className":92105,"style":15193},[650],[363,92107,92109],{"className":92108,"style":83975},[34790],[6670,92110,92111],{"xmlns":6672,"width":6673,"height":83978,"viewBox":83979,"preserveAspectRatio":6676},[6678,92112],{"d":83982},[363,92114,666],{"className":92115},[665],[363,92117,92119],{"className":92118},[638],[363,92120,92122],{"className":92121,"style":83992},[642],[363,92123],{},[363,92125,898],{"className":92126},[920],[363,92128,666],{"className":92129},[665],[363,92131,92133],{"className":92132},[638],[363,92134,92136],{"className":92135,"style":91167},[642],[363,92137],{},[11,92139,92140,92141,92342,92343,92550,92551,92706,92707,1338],{},"故 ",[363,92142,92144,92188],{"className":92143,"translate":367},[366],[363,92145,92147],{"className":92146},[371],[373,92148,92149],{"xmlns":375},[377,92150,92151,92185],{},[380,92152,92153,92159,92161],{},[380,92154,92155,92157],{},[383,92156,5739],{"mathvariant":557},[383,92158,35197],{"mathvariant":557},[458,92160,10299],{},[34686,92162,92163],{},[380,92164,92165,92171,92173,92175,92177,92183],{},[7161,92166,92167,92169],{},[383,92168,34231],{},[463,92170,2810],{},[458,92172,461],{"stretchy":460},[463,92174,2810],{},[458,92176,5160],{},[7161,92178,92179,92181],{},[383,92180,34231],{},[463,92182,2810],{},[458,92184,468],{"stretchy":460},[387,92186,92187],{"encoding":389},"\\mathrm{TV}\\le\\sqrt{H^2(2-H^2)}",[363,92189,92191,92212],{"className":92190,"ariaHidden":394},[393],[363,92192,92194,92197,92203,92206,92209],{"className":92193},[398],[363,92195],{"className":92196,"style":88701},[402],[363,92198,92200],{"className":92199},[407],[363,92201,87109],{"className":92202,"style":4504},[407,33009],[363,92204],{"className":92205,"style":506},[505],[363,92207,10299],{"className":92208},[510],[363,92210],{"className":92211,"style":506},[505],[363,92213,92215,92219],{"className":92214},[398],[363,92216],{"className":92217,"style":92218},[402],"height:1.24em;vertical-align:-0.305em;",[363,92220,92222],{"className":92221},[407,34714],[363,92223,92225,92333],{"className":92224},[633,634],[363,92226,92228,92330],{"className":92227},[638],[363,92229,92232,92317],{"className":92230,"style":92231},[642],"height:0.935em;",[363,92233,92235,92238],{"className":92234,"style":83883},[6654],[363,92236],{"className":92237,"style":15193},[650],[363,92239,92241,92270,92273,92276,92279,92282,92285,92314],{"className":92240,"style":41508},[407],[363,92242,92244,92247],{"className":92243},[407],[363,92245,34231],{"className":92246,"style":34385},[407,408],[363,92248,92250],{"className":92249},[629],[363,92251,92253],{"className":92252},[633],[363,92254,92256],{"className":92255},[638],[363,92257,92259],{"className":92258,"style":45379},[642],[363,92260,92261,92264],{"style":45382},[363,92262],{"className":92263,"style":651},[650],[363,92265,92267],{"className":92266},[655,656,657,658],[363,92268,2810],{"className":92269},[407,658],[363,92271,461],{"className":92272},[494],[363,92274,2810],{"className":92275},[407],[363,92277],{"className":92278,"style":2934},[505],[363,92280,5160],{"className":92281},[2938],[363,92283],{"className":92284,"style":2934},[505],[363,92286,92288,92291],{"className":92287},[407],[363,92289,34231],{"className":92290,"style":34385},[407,408],[363,92292,92294],{"className":92293},[629],[363,92295,92297],{"className":92296},[633],[363,92298,92300],{"className":92299},[638],[363,92301,92303],{"className":92302,"style":45379},[642],[363,92304,92305,92308],{"style":45382},[363,92306],{"className":92307,"style":651},[650],[363,92309,92311],{"className":92310},[655,656,657,658],[363,92312,2810],{"className":92313},[407,658],[363,92315,468],{"className":92316},[501],[363,92318,92320,92323],{"style":92319},"top:-2.895em;",[363,92321],{"className":92322,"style":15193},[650],[363,92324,92326],{"className":92325,"style":83975},[34790],[6670,92327,92328],{"xmlns":6672,"width":6673,"height":83978,"viewBox":83979,"preserveAspectRatio":6676},[6678,92329],{"d":83982},[363,92331,666],{"className":92332},[665],[363,92334,92336],{"className":92335},[638],[363,92337,92340],{"className":92338,"style":92339},[642],"height:0.305em;",[363,92341],{},"，再与 ",[363,92344,92346,92382],{"className":92345,"translate":367},[366],[363,92347,92349],{"className":92348},[371],[373,92350,92351],{"xmlns":375},[377,92352,92353,92379],{},[380,92354,92355,92361,92363,92369],{},[7161,92356,92357,92359],{},[383,92358,34231],{},[463,92360,2810],{},[458,92362,10299],{},[586,92364,92365,92367],{},[463,92366,465],{},[463,92368,2810],{},[543,92370,92371,92373],{},[383,92372,547],{},[380,92374,92375,92377],{},[383,92376,11041],{},[383,92378,22240],{},[387,92380,92381],{"encoding":389},"H^2\\le\\frac12 D_{KL}",[363,92383,92385,92430],{"className":92384,"ariaHidden":394},[393],[363,92386,92388,92392,92421,92424,92427],{"className":92387},[398],[363,92389],{"className":92390,"style":92391},[402],"height:0.9501em;vertical-align:-0.136em;",[363,92393,92395,92398],{"className":92394},[407],[363,92396,34231],{"className":92397,"style":34385},[407,408],[363,92399,92401],{"className":92400},[629],[363,92402,92404],{"className":92403},[633],[363,92405,92407],{"className":92406},[638],[363,92408,92410],{"className":92409,"style":20375},[642],[363,92411,92412,92415],{"style":7212},[363,92413],{"className":92414,"style":651},[650],[363,92416,92418],{"className":92417},[655,656,657,658],[363,92419,2810],{"className":92420},[407,658],[363,92422],{"className":92423,"style":506},[505],[363,92425,10299],{"className":92426},[510],[363,92428],{"className":92429,"style":506},[505],[363,92431,92433,92436,92504],{"className":92432},[398],[363,92434],{"className":92435,"style":2852},[402],[363,92437,92439,92442,92501],{"className":92438},[407],[363,92440],{"className":92441},[494,789],[363,92443,92445],{"className":92444},[586],[363,92446,92448,92493],{"className":92447},[633,634],[363,92449,92451,92490],{"className":92450},[638],[363,92452,92454,92468,92476],{"className":92453,"style":2871},[642],[363,92455,92456,92459],{"style":2874},[363,92457],{"className":92458,"style":809},[650],[363,92460,92462],{"className":92461},[655,656,657,658],[363,92463,92465],{"className":92464},[407,658],[363,92466,2810],{"className":92467},[407,658],[363,92469,92470,92473],{"style":821},[363,92471],{"className":92472,"style":809},[650],[363,92474],{"className":92475,"style":829},[828],[363,92477,92478,92481],{"style":2897},[363,92479],{"className":92480,"style":809},[650],[363,92482,92484],{"className":92483},[655,656,657,658],[363,92485,92487],{"className":92486},[407,658],[363,92488,465],{"className":92489},[407,658],[363,92491,666],{"className":92492},[665],[363,92494,92496],{"className":92495},[638],[363,92497,92499],{"className":92498,"style":2919},[642],[363,92500],{},[363,92502],{"className":92503},[501,789],[363,92505,92507,92510],{"className":92506},[407],[363,92508,547],{"className":92509,"style":625},[407,408],[363,92511,92513],{"className":92512},[629],[363,92514,92516,92542],{"className":92515},[633,634],[363,92517,92519,92539],{"className":92518},[638],[363,92520,92522],{"className":92521,"style":727},[642],[363,92523,92524,92527],{"style":646},[363,92525],{"className":92526,"style":651},[650],[363,92528,92530],{"className":92529},[655,656,657,658],[363,92531,92533,92536],{"className":92532},[407,658],[363,92534,11041],{"className":92535,"style":11129},[407,408,658],[363,92537,22240],{"className":92538},[407,408,658],[363,92540,666],{"className":92541},[665],[363,92543,92545],{"className":92544},[638],[363,92546,92548],{"className":92547,"style":8315},[642],[363,92549],{}," 串起来就有 ",[363,92552,92554,92586],{"className":92553,"translate":367},[366],[363,92555,92557],{"className":92556},[371],[373,92558,92559],{"xmlns":375},[377,92560,92561,92583],{},[380,92562,92563,92569,92571],{},[380,92564,92565,92567],{},[383,92566,5739],{"mathvariant":557},[383,92568,35197],{"mathvariant":557},[458,92570,10299],{},[34686,92572,92573],{},[543,92574,92575,92577],{},[383,92576,547],{},[380,92578,92579,92581],{},[383,92580,11041],{},[383,92582,22240],{},[387,92584,92585],{"encoding":389},"\\mathrm{TV}\\le\\sqrt{D_{KL}}",[363,92587,92589,92610],{"className":92588,"ariaHidden":394},[393],[363,92590,92592,92595,92601,92604,92607],{"className":92591},[398],[363,92593],{"className":92594,"style":88701},[402],[363,92596,92598],{"className":92597},[407],[363,92599,87109],{"className":92600,"style":4504},[407,33009],[363,92602],{"className":92603,"style":506},[505],[363,92605,10299],{"className":92606},[510],[363,92608],{"className":92609,"style":506},[505],[363,92611,92613,92616],{"className":92612},[398],[363,92614],{"className":92615,"style":34710},[402],[363,92617,92619],{"className":92618},[407,34714],[363,92620,92622,92698],{"className":92621},[633,634],[363,92623,92625,92695],{"className":92624},[638],[363,92626,92628,92683],{"className":92627,"style":34724},[642],[363,92629,92631,92634],{"className":92630,"style":12210},[6654],[363,92632],{"className":92633,"style":809},[650],[363,92635,92637],{"className":92636,"style":34734},[407],[363,92638,92640,92643],{"className":92639},[407],[363,92641,547],{"className":92642,"style":625},[407,408],[363,92644,92646],{"className":92645},[629],[363,92647,92649,92675],{"className":92648},[633,634],[363,92650,92652,92672],{"className":92651},[638],[363,92653,92655],{"className":92654,"style":727},[642],[363,92656,92657,92660],{"style":646},[363,92658],{"className":92659,"style":651},[650],[363,92661,92663],{"className":92662},[655,656,657,658],[363,92664,92666,92669],{"className":92665},[407,658],[363,92667,11041],{"className":92668,"style":11129},[407,408,658],[363,92670,22240],{"className":92671},[407,408,658],[363,92673,666],{"className":92674},[665],[363,92676,92678],{"className":92677},[638],[363,92679,92681],{"className":92680,"style":8315},[642],[363,92682],{},[363,92684,92685,92688],{"style":34783},[363,92686],{"className":92687,"style":809},[650],[363,92689,92691],{"className":92690,"style":34791},[34790],[6670,92692,92693],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,92694],{"d":34798},[363,92696,666],{"className":92697},[665],[363,92699,92701],{"className":92700},[638],[363,92702,92704],{"className":92703,"style":34808},[642],[363,92705],{},"（比 Pinsker 常数差一个 ",[363,92708,92710,92726],{"className":92709,"translate":367},[366],[363,92711,92713],{"className":92712},[371],[373,92714,92715],{"xmlns":375},[377,92716,92717,92723],{},[380,92718,92719],{},[34686,92720,92721],{},[463,92722,2810],{},[387,92724,92725],{"encoding":389},"\\sqrt2",[363,92727,92729],{"className":92728,"ariaHidden":394},[393],[363,92730,92732,92736],{"className":92731},[398],[363,92733],{"className":92734,"style":92735},[402],"height:1.04em;vertical-align:-0.1328em;",[363,92737,92739],{"className":92738},[407,34714],[363,92740,92742,92774],{"className":92741},[633,634],[363,92743,92745,92771],{"className":92744},[638],[363,92746,92749,92758],{"className":92747,"style":92748},[642],"height:0.9072em;",[363,92750,92752,92755],{"className":92751,"style":12210},[6654],[363,92753],{"className":92754,"style":809},[650],[363,92756,2810],{"className":92757,"style":34734},[407],[363,92759,92761,92764],{"style":92760},"top:-2.8672em;",[363,92762],{"className":92763,"style":809},[650],[363,92765,92767],{"className":92766,"style":34791},[34790],[6670,92768,92769],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,92770],{"d":34798},[363,92772,666],{"className":92773},[665],[363,92775,92777],{"className":92776},[638],[363,92778,92781],{"className":92779,"style":92780},[642],"height:0.1328em;",[363,92782],{},[1340,92784,92786,92936,94464,95956,96343,96909],{"title":92785},"定理 4.2（拓扑关系的准确版）",[11,92787,881,92788,92816,92817,92882,92883,92935],{},[363,92789,92791,92804],{"className":92790,"translate":367},[366],[363,92792,92794],{"className":92793},[371],[373,92795,92796],{"xmlns":375},[377,92797,92798,92802],{},[380,92799,92800],{},[383,92801,385],{},[387,92803,385],{"encoding":389},[363,92805,92807],{"className":92806,"ariaHidden":394},[393],[363,92808,92810,92813],{"className":92809},[398],[363,92811],{"className":92812,"style":403},[402],[363,92814,385],{"className":92815,"style":409},[407,408]," 凸、",[363,92818,92820,92843],{"className":92819,"translate":367},[366],[363,92821,92823],{"className":92822},[371],[373,92824,92825],{"xmlns":375},[377,92826,92827,92841],{},[380,92828,92829,92831,92833,92835,92837,92839],{},[383,92830,385],{},[458,92832,461],{"stretchy":460},[463,92834,465],{},[458,92836,468],{"stretchy":460},[458,92838,471],{},[463,92840,474],{},[387,92842,477],{"encoding":389},[363,92844,92846,92873],{"className":92845,"ariaHidden":394},[393],[363,92847,92849,92852,92855,92858,92861,92864,92867,92870],{"className":92848},[398],[363,92850],{"className":92851,"style":487},[402],[363,92853,385],{"className":92854,"style":409},[407,408],[363,92856,461],{"className":92857},[494],[363,92859,465],{"className":92860},[407],[363,92862,468],{"className":92863},[501],[363,92865],{"className":92866,"style":506},[505],[363,92868,471],{"className":92869},[510],[363,92871],{"className":92872,"style":506},[505],[363,92874,92876,92879],{"className":92875},[398],[363,92877],{"className":92878,"style":520},[402],[363,92880,474],{"className":92881},[407]," 且在 ",[363,92884,92886,92908],{"className":92885,"translate":367},[366],[363,92887,92889],{"className":92888},[371],[373,92890,92891],{"xmlns":375},[377,92892,92893,92905],{},[380,92894,92895,92897,92899,92901,92903],{},[458,92896,461],{"stretchy":460},[463,92898,474],{},[458,92900,898],{"separator":394},[383,92902,1371],{"mathvariant":557},[458,92904,468],{"stretchy":460},[387,92906,92907],{"encoding":389},"(0,\\infty)",[363,92909,92911],{"className":92910,"ariaHidden":394},[393],[363,92912,92914,92917,92920,92923,92926,92929,92932],{"className":92913},[398],[363,92915],{"className":92916,"style":487},[402],[363,92918,461],{"className":92919},[494],[363,92921,474],{"className":92922},[407],[363,92924,898],{"className":92925},[920],[363,92927],{"className":92928,"style":754},[505],[363,92930,1371],{"className":92931},[407],[363,92933,468],{"className":92934},[501]," 上连续。",[11,92937,92938,6841,92941,93274,93275,93346,93347,5992,93454,93603,93604,93759,93760,93910,93911,93969,93970,94098,94099,94156,94157,94463],{},[1572,92939,92940],{},"(a)（\"下来\"方向，一般成立）",[363,92942,92944,93014],{"className":92943,"translate":367},[366],[363,92945,92947],{"className":92946},[371],[373,92948,92949],{"xmlns":375},[377,92950,92951,93011],{},[380,92952,92953,92959,92961,92967,92969,92971,92973,92975,92977,92979,92981,92983,92993,92995,93001,93003,93005,93007,93009],{},[543,92954,92955,92957],{},[383,92956,547],{},[383,92958,385],{},[458,92960,461],{"stretchy":460},[543,92962,92963,92965],{},[383,92964,554],{},[383,92966,82643],{},[383,92968,558],{"mathvariant":557},[383,92970,561],{},[458,92972,468],{"stretchy":460},[458,92974,1376],{},[463,92976,474],{},[1644,92978,4630],{},[458,92980,4633],{},[1644,92982,4630],{},[543,92984,92985,92987],{},[383,92986,547],{},[380,92988,92989,92991],{},[383,92990,5739],{},[383,92992,35197],{},[458,92994,461],{"stretchy":460},[543,92996,92997,92999],{},[383,92998,554],{},[383,93000,82643],{},[458,93002,898],{"separator":394},[383,93004,561],{},[458,93006,468],{"stretchy":460},[458,93008,1376],{},[463,93010,474],{},[387,93012,93013],{"encoding":389},"D_f(P_n\\|Q)\\to0\\ \\Longrightarrow\\ D_{TV}(P_n,Q)\\to0",[363,93015,93017,93124,93149,93265],{"className":93016,"ariaHidden":394},[393],[363,93018,93020,93023,93063,93066,93106,93109,93112,93115,93118,93121],{"className":93019},[398],[363,93021],{"className":93022,"style":618},[402],[363,93024,93026,93029],{"className":93025},[407],[363,93027,547],{"className":93028,"style":625},[407,408],[363,93030,93032],{"className":93031},[629],[363,93033,93035,93055],{"className":93034},[633,634],[363,93036,93038,93052],{"className":93037},[638],[363,93039,93041],{"className":93040,"style":643},[642],[363,93042,93043,93046],{"style":646},[363,93044],{"className":93045,"style":651},[650],[363,93047,93049],{"className":93048},[655,656,657,658],[363,93050,385],{"className":93051,"style":409},[407,408,658],[363,93053,666],{"className":93054},[665],[363,93056,93058],{"className":93057},[638],[363,93059,93061],{"className":93060,"style":673},[642],[363,93062],{},[363,93064,461],{"className":93065},[494],[363,93067,93069,93072],{"className":93068},[407],[363,93070,554],{"className":93071,"style":682},[407,408],[363,93073,93075],{"className":93074},[629],[363,93076,93078,93098],{"className":93077},[633,634],[363,93079,93081,93095],{"className":93080},[638],[363,93082,93084],{"className":93083,"style":45276},[642],[363,93085,93086,93089],{"style":11483},[363,93087],{"className":93088,"style":651},[650],[363,93090,93092],{"className":93091},[655,656,657,658],[363,93093,82643],{"className":93094},[407,408,658],[363,93096,666],{"className":93097},[665],[363,93099,93101],{"className":93100},[638],[363,93102,93104],{"className":93103,"style":8315},[642],[363,93105],{},[363,93107,558],{"className":93108},[407],[363,93110,561],{"className":93111},[407,408],[363,93113,468],{"className":93114},[501],[363,93116],{"className":93117,"style":506},[505],[363,93119,1376],{"className":93120},[510],[363,93122],{"className":93123,"style":506},[505],[363,93125,93127,93131,93134,93137,93140,93143,93146],{"className":93126},[398],[363,93128],{"className":93129,"style":93130},[402],"height:0.6684em;vertical-align:-0.024em;",[363,93132,474],{"className":93133},[407],[363,93135,4630],{"className":93136},[505],[363,93138],{"className":93139,"style":506},[505],[363,93141,4633],{"className":93142},[510],[363,93144,4630],{"className":93145},[505],[363,93147],{"className":93148,"style":506},[505],[363,93150,93152,93155,93201,93204,93244,93247,93250,93253,93256,93259,93262],{"className":93151},[398],[363,93153],{"className":93154,"style":487},[402],[363,93156,93158,93161],{"className":93157},[407],[363,93159,547],{"className":93160,"style":625},[407,408],[363,93162,93164],{"className":93163},[629],[363,93165,93167,93193],{"className":93166},[633,634],[363,93168,93170,93190],{"className":93169},[638],[363,93171,93173],{"className":93172,"style":727},[642],[363,93174,93175,93178],{"style":646},[363,93176],{"className":93177,"style":651},[650],[363,93179,93181],{"className":93180},[655,656,657,658],[363,93182,93184,93187],{"className":93183},[407,658],[363,93185,5739],{"className":93186,"style":682},[407,408,658],[363,93188,35197],{"className":93189,"style":2934},[407,408,658],[363,93191,666],{"className":93192},[665],[363,93194,93196],{"className":93195},[638],[363,93197,93199],{"className":93198,"style":8315},[642],[363,93200],{},[363,93202,461],{"className":93203},[494],[363,93205,93207,93210],{"className":93206},[407],[363,93208,554],{"className":93209,"style":682},[407,408],[363,93211,93213],{"className":93212},[629],[363,93214,93216,93236],{"className":93215},[633,634],[363,93217,93219,93233],{"className":93218},[638],[363,93220,93222],{"className":93221,"style":45276},[642],[363,93223,93224,93227],{"style":11483},[363,93225],{"className":93226,"style":651},[650],[363,93228,93230],{"className":93229},[655,656,657,658],[363,93231,82643],{"className":93232},[407,408,658],[363,93234,666],{"className":93235},[665],[363,93237,93239],{"className":93238},[638],[363,93240,93242],{"className":93241,"style":8315},[642],[363,93243],{},[363,93245,898],{"className":93246},[920],[363,93248],{"className":93249,"style":754},[505],[363,93251,561],{"className":93252},[407,408],[363,93254,468],{"className":93255},[501],[363,93257],{"className":93258,"style":506},[505],[363,93260,1376],{"className":93261},[510],[363,93263],{"className":93264,"style":506},[505],[363,93266,93268,93271],{"className":93267},[398],[363,93269],{"className":93270,"style":520},[402],[363,93272,474],{"className":93273},[407],"。每个适度正则的 f-散度都自带一个连续的 TV 下界函数 ",[363,93276,93278,93296],{"className":93277,"translate":367},[366],[363,93279,93281],{"className":93280},[371],[373,93282,93283],{"xmlns":375},[377,93284,93285,93293],{},[380,93286,93287],{},[543,93288,93289,93291],{},[383,93290,4505],{},[383,93292,385],{},[387,93294,93295],{"encoding":389},"g_f",[363,93297,93299],{"className":93298,"ariaHidden":394},[393],[363,93300,93302,93306],{"className":93301},[398],[363,93303],{"className":93304,"style":93305},[402],"height:0.7167em;vertical-align:-0.2861em;",[363,93307,93309,93312],{"className":93308},[407],[363,93310,4505],{"className":93311,"style":1328},[407,408],[363,93313,93315],{"className":93314},[629],[363,93316,93318,93338],{"className":93317},[633,634],[363,93319,93321,93335],{"className":93320},[638],[363,93322,93324],{"className":93323,"style":643},[642],[363,93325,93326,93329],{"style":19190},[363,93327],{"className":93328,"style":651},[650],[363,93330,93332],{"className":93331},[655,656,657,658],[363,93333,385],{"className":93334,"style":409},[407,408,658],[363,93336,666],{"className":93337},[665],[363,93339,93341],{"className":93340},[638],[363,93342,93344],{"className":93343,"style":673},[642],[363,93345],{},"（Vajda \u002F Fedotov–Harremoës），",[363,93348,93350,93378],{"className":93349,"translate":367},[366],[363,93351,93353],{"className":93352},[371],[373,93354,93355],{"xmlns":375},[377,93356,93357,93375],{},[380,93358,93359,93365,93367,93369,93371,93373],{},[543,93360,93361,93363],{},[383,93362,4505],{},[383,93364,385],{},[458,93366,461],{"stretchy":460},[463,93368,474],{},[458,93370,468],{"stretchy":460},[458,93372,471],{},[463,93374,474],{},[387,93376,93377],{"encoding":389},"g_f(0)=0",[363,93379,93381,93445],{"className":93380,"ariaHidden":394},[393],[363,93382,93384,93387,93427,93430,93433,93436,93439,93442],{"className":93383},[398],[363,93385],{"className":93386,"style":618},[402],[363,93388,93390,93393],{"className":93389},[407],[363,93391,4505],{"className":93392,"style":1328},[407,408],[363,93394,93396],{"className":93395},[629],[363,93397,93399,93419],{"className":93398},[633,634],[363,93400,93402,93416],{"className":93401},[638],[363,93403,93405],{"className":93404,"style":643},[642],[363,93406,93407,93410],{"style":19190},[363,93408],{"className":93409,"style":651},[650],[363,93411,93413],{"className":93412},[655,656,657,658],[363,93414,385],{"className":93415,"style":409},[407,408,658],[363,93417,666],{"className":93418},[665],[363,93420,93422],{"className":93421},[638],[363,93423,93425],{"className":93424,"style":673},[642],[363,93426],{},[363,93428,461],{"className":93429},[494],[363,93431,474],{"className":93432},[407],[363,93434,468],{"className":93435},[501],[363,93437],{"className":93438,"style":506},[505],[363,93440,471],{"className":93441},[510],[363,93443],{"className":93444,"style":506},[505],[363,93446,93448,93451],{"className":93447},[398],[363,93449],{"className":93450,"style":520},[402],[363,93452,474],{"className":93453},[407],[363,93455,93457,93497],{"className":93456,"translate":367},[366],[363,93458,93460],{"className":93459},[371],[373,93461,93462],{"xmlns":375},[377,93463,93464,93494],{},[380,93465,93466,93472,93474,93476,93478,93480,93482,93484,93486,93488,93490,93492],{},[543,93467,93468,93470],{},[383,93469,4505],{},[383,93471,385],{},[458,93473,461],{"stretchy":460},[383,93475,1116],{},[458,93477,468],{"stretchy":460},[458,93479,3250],{},[463,93481,474],{},[1644,93483,4630],{},[458,93485,461],{"stretchy":460},[383,93487,1116],{},[458,93489,3250],{},[463,93491,474],{},[458,93493,468],{"stretchy":460},[387,93495,93496],{"encoding":389},"g_f(t)>0\\ (t>0)",[363,93498,93500,93564,93591],{"className":93499,"ariaHidden":394},[393],[363,93501,93503,93506,93546,93549,93552,93555,93558,93561],{"className":93502},[398],[363,93504],{"className":93505,"style":618},[402],[363,93507,93509,93512],{"className":93508},[407],[363,93510,4505],{"className":93511,"style":1328},[407,408],[363,93513,93515],{"className":93514},[629],[363,93516,93518,93538],{"className":93517},[633,634],[363,93519,93521,93535],{"className":93520},[638],[363,93522,93524],{"className":93523,"style":643},[642],[363,93525,93526,93529],{"style":19190},[363,93527],{"className":93528,"style":651},[650],[363,93530,93532],{"className":93531},[655,656,657,658],[363,93533,385],{"className":93534,"style":409},[407,408,658],[363,93536,666],{"className":93537},[665],[363,93539,93541],{"className":93540},[638],[363,93542,93544],{"className":93543,"style":673},[642],[363,93545],{},[363,93547,461],{"className":93548},[494],[363,93550,1116],{"className":93551},[407,408],[363,93553,468],{"className":93554},[501],[363,93556],{"className":93557,"style":506},[505],[363,93559,3250],{"className":93560},[510],[363,93562],{"className":93563,"style":506},[505],[363,93565,93567,93570,93573,93576,93579,93582,93585,93588],{"className":93566},[398],[363,93568],{"className":93569,"style":487},[402],[363,93571,474],{"className":93572},[407],[363,93574,4630],{"className":93575},[505],[363,93577,461],{"className":93578},[494],[363,93580,1116],{"className":93581},[407,408],[363,93583],{"className":93584,"style":506},[505],[363,93586,3250],{"className":93587},[510],[363,93589],{"className":93590,"style":506},[505],[363,93592,93594,93597,93600],{"className":93593},[398],[363,93595],{"className":93596,"style":487},[402],[363,93598,474],{"className":93599},[407],[363,93601,468],{"className":93602},[501],"，使 ",[363,93605,93607,93643],{"className":93606,"translate":367},[366],[363,93608,93610],{"className":93609},[371],[373,93611,93612],{"xmlns":375},[377,93613,93614,93640],{},[380,93615,93616,93622,93624,93630,93632,93638],{},[543,93617,93618,93620],{},[383,93619,547],{},[383,93621,385],{},[458,93623,7275],{},[543,93625,93626,93628],{},[383,93627,4505],{},[383,93629,385],{},[458,93631,461],{"stretchy":460},[380,93633,93634,93636],{},[383,93635,5739],{"mathvariant":557},[383,93637,35197],{"mathvariant":557},[458,93639,468],{"stretchy":460},[387,93641,93642],{"encoding":389},"D_f\\ge g_f(\\mathrm{TV})",[363,93644,93646,93701],{"className":93645,"ariaHidden":394},[393],[363,93647,93649,93652,93692,93695,93698],{"className":93648},[398],[363,93650],{"className":93651,"style":4379},[402],[363,93653,93655,93658],{"className":93654},[407],[363,93656,547],{"className":93657,"style":625},[407,408],[363,93659,93661],{"className":93660},[629],[363,93662,93664,93684],{"className":93663},[633,634],[363,93665,93667,93681],{"className":93666},[638],[363,93668,93670],{"className":93669,"style":643},[642],[363,93671,93672,93675],{"style":646},[363,93673],{"className":93674,"style":651},[650],[363,93676,93678],{"className":93677},[655,656,657,658],[363,93679,385],{"className":93680,"style":409},[407,408,658],[363,93682,666],{"className":93683},[665],[363,93685,93687],{"className":93686},[638],[363,93688,93690],{"className":93689,"style":673},[642],[363,93691],{},[363,93693],{"className":93694,"style":506},[505],[363,93696,7275],{"className":93697},[510],[363,93699],{"className":93700,"style":506},[505],[363,93702,93704,93707,93747,93750,93756],{"className":93703},[398],[363,93705],{"className":93706,"style":618},[402],[363,93708,93710,93713],{"className":93709},[407],[363,93711,4505],{"className":93712,"style":1328},[407,408],[363,93714,93716],{"className":93715},[629],[363,93717,93719,93739],{"className":93718},[633,634],[363,93720,93722,93736],{"className":93721},[638],[363,93723,93725],{"className":93724,"style":643},[642],[363,93726,93727,93730],{"style":19190},[363,93728],{"className":93729,"style":651},[650],[363,93731,93733],{"className":93732},[655,656,657,658],[363,93734,385],{"className":93735,"style":409},[407,408,658],[363,93737,666],{"className":93738},[665],[363,93740,93742],{"className":93741},[638],[363,93743,93745],{"className":93744,"style":673},[642],[363,93746],{},[363,93748,461],{"className":93749},[494],[363,93751,93753],{"className":93752},[407],[363,93754,87109],{"className":93755,"style":4504},[407,33009],[363,93757,468],{"className":93758},[501],"；常用成员的具体形式：KL 给 ",[363,93761,93763,93801],{"className":93762,"translate":367},[366],[363,93764,93766],{"className":93765},[371],[373,93767,93768],{"xmlns":375},[377,93769,93770,93798],{},[380,93771,93772,93774,93776,93786,93788],{},[463,93773,2810],{},[1644,93775,1646],{},[7161,93777,93778,93784],{},[380,93779,93780,93782],{},[383,93781,5739],{"mathvariant":557},[383,93783,35197],{"mathvariant":557},[463,93785,2810],{},[458,93787,10299],{},[543,93789,93790,93792],{},[383,93791,547],{},[380,93793,93794,93796],{},[383,93795,11041],{},[383,93797,22240],{},[387,93799,93800],{"encoding":389},"2\\,\\mathrm{TV}^2\\le D_{KL}",[363,93802,93804,93858],{"className":93803,"ariaHidden":394},[393],[363,93805,93807,93811,93814,93817,93849,93852,93855],{"className":93806},[398],[363,93808],{"className":93809,"style":93810},[402],"height:1.0233em;vertical-align:-0.136em;",[363,93812,2810],{"className":93813},[407],[363,93815],{"className":93816,"style":754},[505],[363,93818,93820,93826],{"className":93819},[407],[363,93821,93823],{"className":93822},[407],[363,93824,87109],{"className":93825,"style":4504},[407,33009],[363,93827,93829],{"className":93828},[629],[363,93830,93832],{"className":93831},[633],[363,93833,93835],{"className":93834},[638],[363,93836,93838],{"className":93837,"style":88723},[642],[363,93839,93840,93843],{"style":88753},[363,93841],{"className":93842,"style":651},[650],[363,93844,93846],{"className":93845},[655,656,657,658],[363,93847,2810],{"className":93848},[407,658],[363,93850],{"className":93851,"style":506},[505],[363,93853,10299],{"className":93854},[510],[363,93856],{"className":93857,"style":506},[505],[363,93859,93861,93864],{"className":93860},[398],[363,93862],{"className":93863,"style":16308},[402],[363,93865,93867,93870],{"className":93866},[407],[363,93868,547],{"className":93869,"style":625},[407,408],[363,93871,93873],{"className":93872},[629],[363,93874,93876,93902],{"className":93875},[633,634],[363,93877,93879,93899],{"className":93878},[638],[363,93880,93882],{"className":93881,"style":727},[642],[363,93883,93884,93887],{"style":646},[363,93885],{"className":93886,"style":651},[650],[363,93888,93890],{"className":93889},[655,656,657,658],[363,93891,93893,93896],{"className":93892},[407,658],[363,93894,11041],{"className":93895,"style":11129},[407,408,658],[363,93897,22240],{"className":93898},[407,408,658],[363,93900,666],{"className":93901},[665],[363,93903,93905],{"className":93904},[638],[363,93906,93908],{"className":93907,"style":8315},[642],[363,93909],{},"（Pinsker），",[363,93912,93914,93931],{"className":93913,"translate":367},[366],[363,93915,93917],{"className":93916},[371],[373,93918,93919],{"xmlns":375},[377,93920,93921,93929],{},[380,93922,93923],{},[7161,93924,93925,93927],{},[383,93926,37796],{},[463,93928,2810],{},[387,93930,40741],{"encoding":389},[363,93932,93934],{"className":93933,"ariaHidden":394},[393],[363,93935,93937,93940],{"className":93936},[398],[363,93938],{"className":93939,"style":40751},[402],[363,93941,93943,93946],{"className":93942},[407],[363,93944,37796],{"className":93945},[407,408],[363,93947,93949],{"className":93948},[629],[363,93950,93952],{"className":93951},[633],[363,93953,93955],{"className":93954},[638],[363,93956,93958],{"className":93957,"style":20375},[642],[363,93959,93960,93963],{"style":7212},[363,93961],{"className":93962,"style":651},[650],[363,93964,93966],{"className":93965},[655,656,657,658],[363,93967,2810],{"className":93968},[407,658]," 给 ",[363,93971,93973,94007],{"className":93972,"translate":367},[366],[363,93974,93976],{"className":93975},[371],[373,93977,93978],{"xmlns":375},[377,93979,93980,94004],{},[380,93981,93982,93988,93990,93992,93994],{},[7161,93983,93984,93986],{},[383,93985,37796],{},[463,93987,2810],{},[458,93989,7275],{},[463,93991,39336],{},[1644,93993,1646],{},[7161,93995,93996,94002],{},[380,93997,93998,94000],{},[383,93999,5739],{"mathvariant":557},[383,94001,35197],{"mathvariant":557},[463,94003,2810],{},[387,94005,94006],{"encoding":389},"\\chi^2\\ge4\\,\\mathrm{TV}^2",[363,94008,94010,94054],{"className":94009,"ariaHidden":394},[393],[363,94011,94013,94016,94045,94048,94051],{"className":94012},[398],[363,94014],{"className":94015,"style":40751},[402],[363,94017,94019,94022],{"className":94018},[407],[363,94020,37796],{"className":94021},[407,408],[363,94023,94025],{"className":94024},[629],[363,94026,94028],{"className":94027},[633],[363,94029,94031],{"className":94030},[638],[363,94032,94034],{"className":94033,"style":20375},[642],[363,94035,94036,94039],{"style":7212},[363,94037],{"className":94038,"style":651},[650],[363,94040,94042],{"className":94041},[655,656,657,658],[363,94043,2810],{"className":94044},[407,658],[363,94046],{"className":94047,"style":506},[505],[363,94049,7275],{"className":94050},[510],[363,94052],{"className":94053,"style":506},[505],[363,94055,94057,94060,94063,94066],{"className":94056},[398],[363,94058],{"className":94059,"style":88723},[402],[363,94061,39336],{"className":94062},[407],[363,94064],{"className":94065,"style":754},[505],[363,94067,94069,94075],{"className":94068},[407],[363,94070,94072],{"className":94071},[407],[363,94073,87109],{"className":94074,"style":4504},[407,33009],[363,94076,94078],{"className":94077},[629],[363,94079,94081],{"className":94080},[633],[363,94082,94084],{"className":94083},[638],[363,94085,94087],{"className":94086,"style":88723},[642],[363,94088,94089,94092],{"style":88753},[363,94090],{"className":94091,"style":651},[650],[363,94093,94095],{"className":94094},[655,656,657,658],[363,94096,2810],{"className":94097},[407,658],"，Hellinger",[363,94100,94102,94119],{"className":94101,"translate":367},[366],[363,94103,94105],{"className":94104},[371],[373,94106,94107],{"xmlns":375},[377,94108,94109,94117],{},[380,94110,94111],{},[7161,94112,94113,94115],{},[380,94114],{},[463,94116,2810],{},[387,94118,44616],{"encoding":389},[363,94120,94122],{"className":94121,"ariaHidden":394},[393],[363,94123,94125,94128],{"className":94124},[398],[363,94126],{"className":94127,"style":20375},[402],[363,94129,94131,94133],{"className":94130},[407],[363,94132],{},[363,94134,94136],{"className":94135},[629],[363,94137,94139],{"className":94138},[633],[363,94140,94142],{"className":94141},[638],[363,94143,94145],{"className":94144,"style":20375},[642],[363,94146,94147,94150],{"style":7212},[363,94148],{"className":94149,"style":651},[650],[363,94151,94153],{"className":94152},[655,656,657,658],[363,94154,2810],{"className":94155},[407,658]," 经由 ",[363,94158,94160,94218],{"className":94159,"translate":367},[366],[363,94161,94163],{"className":94162},[371],[373,94164,94165],{"xmlns":375},[377,94166,94167,94215],{},[380,94168,94169,94175,94177,94201,94203],{},[380,94170,94171,94173],{},[383,94172,5739],{"mathvariant":557},[383,94174,35197],{"mathvariant":557},[458,94176,10299],{},[34686,94178,94179],{},[380,94180,94181,94187,94189,94191,94193,94199],{},[7161,94182,94183,94185],{},[383,94184,34231],{},[463,94186,2810],{},[458,94188,461],{"stretchy":460},[463,94190,2810],{},[458,94192,5160],{},[7161,94194,94195,94197],{},[383,94196,34231],{},[463,94198,2810],{},[458,94200,468],{"stretchy":460},[458,94202,10299],{},[34686,94204,94205],{},[380,94206,94207,94209],{},[463,94208,2810],{},[7161,94210,94211,94213],{},[383,94212,34231],{},[463,94214,2810],{},[387,94216,94217],{"encoding":389},"\\mathrm{TV}\\le\\sqrt{H^2(2-H^2)}\\le\\sqrt{2H^2}",[363,94219,94221,94242,94377],{"className":94220,"ariaHidden":394},[393],[363,94222,94224,94227,94233,94236,94239],{"className":94223},[398],[363,94225],{"className":94226,"style":88701},[402],[363,94228,94230],{"className":94229},[407],[363,94231,87109],{"className":94232,"style":4504},[407,33009],[363,94234],{"className":94235,"style":506},[505],[363,94237,10299],{"className":94238},[510],[363,94240],{"className":94241,"style":506},[505],[363,94243,94245,94248,94368,94371,94374],{"className":94244},[398],[363,94246],{"className":94247,"style":92218},[402],[363,94249,94251],{"className":94250},[407,34714],[363,94252,94254,94360],{"className":94253},[633,634],[363,94255,94257,94357],{"className":94256},[638],[363,94258,94260,94345],{"className":94259,"style":92231},[642],[363,94261,94263,94266],{"className":94262,"style":83883},[6654],[363,94264],{"className":94265,"style":15193},[650],[363,94267,94269,94298,94301,94304,94307,94310,94313,94342],{"className":94268,"style":41508},[407],[363,94270,94272,94275],{"className":94271},[407],[363,94273,34231],{"className":94274,"style":34385},[407,408],[363,94276,94278],{"className":94277},[629],[363,94279,94281],{"className":94280},[633],[363,94282,94284],{"className":94283},[638],[363,94285,94287],{"className":94286,"style":45379},[642],[363,94288,94289,94292],{"style":45382},[363,94290],{"className":94291,"style":651},[650],[363,94293,94295],{"className":94294},[655,656,657,658],[363,94296,2810],{"className":94297},[407,658],[363,94299,461],{"className":94300},[494],[363,94302,2810],{"className":94303},[407],[363,94305],{"className":94306,"style":2934},[505],[363,94308,5160],{"className":94309},[2938],[363,94311],{"className":94312,"style":2934},[505],[363,94314,94316,94319],{"className":94315},[407],[363,94317,34231],{"className":94318,"style":34385},[407,408],[363,94320,94322],{"className":94321},[629],[363,94323,94325],{"className":94324},[633],[363,94326,94328],{"className":94327},[638],[363,94329,94331],{"className":94330,"style":45379},[642],[363,94332,94333,94336],{"style":45382},[363,94334],{"className":94335,"style":651},[650],[363,94337,94339],{"className":94338},[655,656,657,658],[363,94340,2810],{"className":94341},[407,658],[363,94343,468],{"className":94344},[501],[363,94346,94347,94350],{"style":92319},[363,94348],{"className":94349,"style":15193},[650],[363,94351,94353],{"className":94352,"style":83975},[34790],[6670,94354,94355],{"xmlns":6672,"width":6673,"height":83978,"viewBox":83979,"preserveAspectRatio":6676},[6678,94356],{"d":83982},[363,94358,666],{"className":94359},[665],[363,94361,94363],{"className":94362},[638],[363,94364,94366],{"className":94365,"style":92339},[642],[363,94367],{},[363,94369],{"className":94370,"style":506},[505],[363,94372,10299],{"className":94373},[510],[363,94375],{"className":94376,"style":506},[505],[363,94378,94380,94384],{"className":94379},[398],[363,94381],{"className":94382,"style":94383},[402],"height:1.04em;vertical-align:-0.0849em;",[363,94385,94387],{"className":94386},[407,34714],[363,94388,94390,94454],{"className":94389},[633,634],[363,94391,94393,94451],{"className":94392},[638],[363,94394,94397,94438],{"className":94395,"style":94396},[642],"height:0.9551em;",[363,94398,94400,94403],{"className":94399,"style":12210},[6654],[363,94401],{"className":94402,"style":809},[650],[363,94404,94406,94409],{"className":94405,"style":34734},[407],[363,94407,2810],{"className":94408},[407],[363,94410,94412,94415],{"className":94411},[407],[363,94413,34231],{"className":94414,"style":34385},[407,408],[363,94416,94418],{"className":94417},[629],[363,94419,94421],{"className":94420},[633],[363,94422,94424],{"className":94423},[638],[363,94425,94427],{"className":94426,"style":45379},[642],[363,94428,94429,94432],{"style":45382},[363,94430],{"className":94431,"style":651},[650],[363,94433,94435],{"className":94434},[655,656,657,658],[363,94436,2810],{"className":94437},[407,658],[363,94439,94441,94444],{"style":94440},"top:-2.9151em;",[363,94442],{"className":94443,"style":809},[650],[363,94445,94447],{"className":94446,"style":34791},[34790],[6670,94448,94449],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,94450],{"d":34798},[363,94452,666],{"className":94453},[665],[363,94455,94457],{"className":94456},[638],[363,94458,94461],{"className":94459,"style":94460},[642],"height:0.0849em;",[363,94462],{},"，TV 本身平凡。",[11,94465,94466,6841,94469,94801,94802,94805,94806,94857,94858,3092,94911,95238,95239,5992,95421,95553,95554,95744,95745,95955],{},[1572,94467,94468],{},"(b)（\"上去\"方向，需要条件）",[363,94470,94472,94542],{"className":94471,"translate":367},[366],[363,94473,94475],{"className":94474},[371],[373,94476,94477],{"xmlns":375},[377,94478,94479,94539],{},[380,94480,94481,94491,94493,94499,94501,94503,94505,94507,94509,94511,94513,94515,94521,94523,94529,94531,94533,94535,94537],{},[543,94482,94483,94485],{},[383,94484,547],{},[380,94486,94487,94489],{},[383,94488,5739],{},[383,94490,35197],{},[458,94492,461],{"stretchy":460},[543,94494,94495,94497],{},[383,94496,554],{},[383,94498,82643],{},[458,94500,898],{"separator":394},[383,94502,561],{},[458,94504,468],{"stretchy":460},[458,94506,1376],{},[463,94508,474],{},[1644,94510,4630],{},[458,94512,4633],{},[1644,94514,4630],{},[543,94516,94517,94519],{},[383,94518,547],{},[383,94520,385],{},[458,94522,461],{"stretchy":460},[543,94524,94525,94527],{},[383,94526,554],{},[383,94528,82643],{},[383,94530,558],{"mathvariant":557},[383,94532,561],{},[458,94534,468],{"stretchy":460},[458,94536,1376],{},[463,94538,474],{},[387,94540,94541],{"encoding":389},"D_{TV}(P_n,Q)\\to0\\ \\Longrightarrow\\ D_f(P_n\\|Q)\\to0",[363,94543,94545,94661,94685,94792],{"className":94544,"ariaHidden":394},[393],[363,94546,94548,94551,94597,94600,94640,94643,94646,94649,94652,94655,94658],{"className":94547},[398],[363,94549],{"className":94550,"style":487},[402],[363,94552,94554,94557],{"className":94553},[407],[363,94555,547],{"className":94556,"style":625},[407,408],[363,94558,94560],{"className":94559},[629],[363,94561,94563,94589],{"className":94562},[633,634],[363,94564,94566,94586],{"className":94565},[638],[363,94567,94569],{"className":94568,"style":727},[642],[363,94570,94571,94574],{"style":646},[363,94572],{"className":94573,"style":651},[650],[363,94575,94577],{"className":94576},[655,656,657,658],[363,94578,94580,94583],{"className":94579},[407,658],[363,94581,5739],{"className":94582,"style":682},[407,408,658],[363,94584,35197],{"className":94585,"style":2934},[407,408,658],[363,94587,666],{"className":94588},[665],[363,94590,94592],{"className":94591},[638],[363,94593,94595],{"className":94594,"style":8315},[642],[363,94596],{},[363,94598,461],{"className":94599},[494],[363,94601,94603,94606],{"className":94602},[407],[363,94604,554],{"className":94605,"style":682},[407,408],[363,94607,94609],{"className":94608},[629],[363,94610,94612,94632],{"className":94611},[633,634],[363,94613,94615,94629],{"className":94614},[638],[363,94616,94618],{"className":94617,"style":45276},[642],[363,94619,94620,94623],{"style":11483},[363,94621],{"className":94622,"style":651},[650],[363,94624,94626],{"className":94625},[655,656,657,658],[363,94627,82643],{"className":94628},[407,408,658],[363,94630,666],{"className":94631},[665],[363,94633,94635],{"className":94634},[638],[363,94636,94638],{"className":94637,"style":8315},[642],[363,94639],{},[363,94641,898],{"className":94642},[920],[363,94644],{"className":94645,"style":754},[505],[363,94647,561],{"className":94648},[407,408],[363,94650,468],{"className":94651},[501],[363,94653],{"className":94654,"style":506},[505],[363,94656,1376],{"className":94657},[510],[363,94659],{"className":94660,"style":506},[505],[363,94662,94664,94667,94670,94673,94676,94679,94682],{"className":94663},[398],[363,94665],{"className":94666,"style":93130},[402],[363,94668,474],{"className":94669},[407],[363,94671,4630],{"className":94672},[505],[363,94674],{"className":94675,"style":506},[505],[363,94677,4633],{"className":94678},[510],[363,94680,4630],{"className":94681},[505],[363,94683],{"className":94684,"style":506},[505],[363,94686,94688,94691,94731,94734,94774,94777,94780,94783,94786,94789],{"className":94687},[398],[363,94689],{"className":94690,"style":618},[402],[363,94692,94694,94697],{"className":94693},[407],[363,94695,547],{"className":94696,"style":625},[407,408],[363,94698,94700],{"className":94699},[629],[363,94701,94703,94723],{"className":94702},[633,634],[363,94704,94706,94720],{"className":94705},[638],[363,94707,94709],{"className":94708,"style":643},[642],[363,94710,94711,94714],{"style":646},[363,94712],{"className":94713,"style":651},[650],[363,94715,94717],{"className":94716},[655,656,657,658],[363,94718,385],{"className":94719,"style":409},[407,408,658],[363,94721,666],{"className":94722},[665],[363,94724,94726],{"className":94725},[638],[363,94727,94729],{"className":94728,"style":673},[642],[363,94730],{},[363,94732,461],{"className":94733},[494],[363,94735,94737,94740],{"className":94736},[407],[363,94738,554],{"className":94739,"style":682},[407,408],[363,94741,94743],{"className":94742},[629],[363,94744,94746,94766],{"className":94745},[633,634],[363,94747,94749,94763],{"className":94748},[638],[363,94750,94752],{"className":94751,"style":45276},[642],[363,94753,94754,94757],{"style":11483},[363,94755],{"className":94756,"style":651},[650],[363,94758,94760],{"className":94759},[655,656,657,658],[363,94761,82643],{"className":94762},[407,408,658],[363,94764,666],{"className":94765},[665],[363,94767,94769],{"className":94768},[638],[363,94770,94772],{"className":94771,"style":8315},[642],[363,94773],{},[363,94775,558],{"className":94776},[407],[363,94778,561],{"className":94779},[407,408],[363,94781,468],{"className":94782},[501],[363,94784],{"className":94785,"style":506},[505],[363,94787,1376],{"className":94788},[510],[363,94790],{"className":94791,"style":506},[505],[363,94793,94795,94798],{"className":94794},[398],[363,94796],{"className":94797,"style":520},[402],[363,94799,474],{"className":94800},[407]," 一般",[1572,94803,94804],{},"不成立","。反例：在 ",[363,94807,94809,94830],{"className":94808,"translate":367},[366],[363,94810,94812],{"className":94811},[371],[373,94813,94814],{"xmlns":375},[377,94815,94816,94828],{},[380,94817,94818,94820,94822,94824,94826],{},[458,94819,578],{"stretchy":460},[463,94821,474],{},[458,94823,898],{"separator":394},[463,94825,465],{},[458,94827,605],{"stretchy":460},[387,94829,37161],{"encoding":389},[363,94831,94833],{"className":94832,"ariaHidden":394},[393],[363,94834,94836,94839,94842,94845,94848,94851,94854],{"className":94835},[398],[363,94837],{"className":94838,"style":487},[402],[363,94840,578],{"className":94841},[494],[363,94843,474],{"className":94844},[407],[363,94846,898],{"className":94847},[920],[363,94849],{"className":94850,"style":754},[505],[363,94852,465],{"className":94853},[407],[363,94855,605],{"className":94856},[501]," 上取 ",[363,94859,94861,94880],{"className":94860,"translate":367},[366],[363,94862,94864],{"className":94863},[371],[373,94865,94866],{"xmlns":375},[377,94867,94868,94877],{},[380,94869,94870,94872,94875],{},[383,94871,11],{},[458,94873,94874],{},"≡",[463,94876,465],{},[387,94878,94879],{"encoding":389},"p\\equiv1",[363,94881,94883,94902],{"className":94882,"ariaHidden":394},[393],[363,94884,94886,94890,94893,94896,94899],{"className":94885},[398],[363,94887],{"className":94888,"style":94889},[402],"height:0.6582em;vertical-align:-0.1944em;",[363,94891,11],{"className":94892},[407,408],[363,94894],{"className":94895,"style":506},[505],[363,94897,94874],{"className":94898},[510],[363,94900],{"className":94901,"style":506},[505],[363,94903,94905,94908],{"className":94904},[398],[363,94906],{"className":94907,"style":520},[402],[363,94909,465],{"className":94910},[407],[363,94912,94914,94985],{"className":94913,"translate":367},[366],[363,94915,94917],{"className":94916},[371],[373,94918,94919],{"xmlns":375},[377,94920,94921,94982],{},[380,94922,94923,94929,94931,94933,94935,94937,94943,94945,94947,94949,94955,94957,94968,94970,94972,94974,94980],{},[543,94924,94925,94927],{},[383,94926,1291],{},[383,94928,82643],{},[458,94930,471],{},[458,94932,461],{"stretchy":460},[463,94934,465],{},[458,94936,5160],{},[543,94938,94939,94941],{},[383,94940,16059],{},[383,94942,82643],{},[458,94944,468],{"stretchy":460},[383,94946,11],{},[458,94948,2817],{},[543,94950,94951,94953],{},[383,94952,16059],{},[383,94954,82643],{},[1644,94956,1646],{},[380,94958,94959,94962,94964,94966],{},[383,94960,94961],{"mathvariant":557},"U",[383,94963,82643],{"mathvariant":557},[383,94965,12310],{"mathvariant":557},[383,94967,385],{"mathvariant":557},[458,94969,578],{"stretchy":460},[463,94971,474],{},[458,94973,898],{"separator":394},[543,94975,94976,94978],{},[383,94977,39009],{},[383,94979,82643],{},[458,94981,605],{"stretchy":460},[387,94983,94984],{"encoding":389},"q_n=(1-\\delta_n)p+\\delta_n\\,\\mathrm{Unif}[0,\\varepsilon_n]",[363,94986,94988,95043,95064,95126],{"className":94987,"ariaHidden":394},[393],[363,94989,94991,94994,95034,95037,95040],{"className":94990},[398],[363,94992],{"className":94993,"style":2623},[402],[363,94995,94997,95000],{"className":94996},[407],[363,94998,1291],{"className":94999,"style":1328},[407,408],[363,95001,95003],{"className":95002},[629],[363,95004,95006,95026],{"className":95005},[633,634],[363,95007,95009,95023],{"className":95008},[638],[363,95010,95012],{"className":95011,"style":45276},[642],[363,95013,95014,95017],{"style":19190},[363,95015],{"className":95016,"style":651},[650],[363,95018,95020],{"className":95019},[655,656,657,658],[363,95021,82643],{"className":95022},[407,408,658],[363,95024,666],{"className":95025},[665],[363,95027,95029],{"className":95028},[638],[363,95030,95032],{"className":95031,"style":8315},[642],[363,95033],{},[363,95035],{"className":95036,"style":506},[505],[363,95038,471],{"className":95039},[510],[363,95041],{"className":95042,"style":506},[505],[363,95044,95046,95049,95052,95055,95058,95061],{"className":95045},[398],[363,95047],{"className":95048,"style":487},[402],[363,95050,461],{"className":95051},[494],[363,95053,465],{"className":95054},[407],[363,95056],{"className":95057,"style":2934},[505],[363,95059,5160],{"className":95060},[2938],[363,95062],{"className":95063,"style":2934},[505],[363,95065,95067,95070,95111,95114,95117,95120,95123],{"className":95066},[398],[363,95068],{"className":95069,"style":487},[402],[363,95071,95073,95076],{"className":95072},[407],[363,95074,16059],{"className":95075,"style":16108},[407,408],[363,95077,95079],{"className":95078},[629],[363,95080,95082,95103],{"className":95081},[633,634],[363,95083,95085,95100],{"className":95084},[638],[363,95086,95088],{"className":95087,"style":45276},[642],[363,95089,95091,95094],{"style":95090},"top:-2.55em;margin-left:-0.0379em;margin-right:0.05em;",[363,95092],{"className":95093,"style":651},[650],[363,95095,95097],{"className":95096},[655,656,657,658],[363,95098,82643],{"className":95099},[407,408,658],[363,95101,666],{"className":95102},[665],[363,95104,95106],{"className":95105},[638],[363,95107,95109],{"className":95108,"style":8315},[642],[363,95110],{},[363,95112,468],{"className":95113},[501],[363,95115,11],{"className":95116},[407,408],[363,95118],{"className":95119,"style":2934},[505],[363,95121,2817],{"className":95122},[2938],[363,95124],{"className":95125,"style":2934},[505],[363,95127,95129,95132,95172,95175,95183,95186,95189,95192,95195,95235],{"className":95128},[398],[363,95130],{"className":95131,"style":487},[402],[363,95133,95135,95138],{"className":95134},[407],[363,95136,16059],{"className":95137,"style":16108},[407,408],[363,95139,95141],{"className":95140},[629],[363,95142,95144,95164],{"className":95143},[633,634],[363,95145,95147,95161],{"className":95146},[638],[363,95148,95150],{"className":95149,"style":45276},[642],[363,95151,95152,95155],{"style":95090},[363,95153],{"className":95154,"style":651},[650],[363,95156,95158],{"className":95157},[655,656,657,658],[363,95159,82643],{"className":95160},[407,408,658],[363,95162,666],{"className":95163},[665],[363,95165,95167],{"className":95166},[638],[363,95168,95170],{"className":95169,"style":8315},[642],[363,95171],{},[363,95173],{"className":95174,"style":754},[505],[363,95176,95178],{"className":95177},[407],[363,95179,95182],{"className":95180,"style":95181},[407,33009],"margin-right:0.0778em;","Unif",[363,95184,578],{"className":95185},[494],[363,95187,474],{"className":95188},[407],[363,95190,898],{"className":95191},[920],[363,95193],{"className":95194,"style":754},[505],[363,95196,95198,95201],{"className":95197},[407],[363,95199,39009],{"className":95200},[407,408],[363,95202,95204],{"className":95203},[629],[363,95205,95207,95227],{"className":95206},[633,634],[363,95208,95210,95224],{"className":95209},[638],[363,95211,95213],{"className":95212,"style":45276},[642],[363,95214,95215,95218],{"style":730},[363,95216],{"className":95217,"style":651},[650],[363,95219,95221],{"className":95220},[655,656,657,658],[363,95222,82643],{"className":95223},[407,408,658],[363,95225,666],{"className":95226},[665],[363,95228,95230],{"className":95229},[638],[363,95231,95233],{"className":95232,"style":8315},[642],[363,95234],{},[363,95236,605],{"className":95237},[501],"，取 ",[363,95240,95242,95277],{"className":95241,"translate":367},[366],[363,95243,95245],{"className":95244},[371],[373,95246,95247],{"xmlns":375},[377,95248,95249,95274],{},[380,95250,95251,95257,95259],{},[543,95252,95253,95255],{},[383,95254,16059],{},[383,95256,82643],{},[458,95258,471],{},[1602,95260,95261],{"scriptlevel":474,"displaystyle":460},[586,95262,95263,95265],{},[463,95264,465],{},[380,95266,95267,95270,95272],{},[383,95268,95269],{},"ln",[458,95271,4450],{},[383,95273,82643],{},[387,95275,95276],{"encoding":389},"\\delta_n=\\tfrac1{\\ln n}",[363,95278,95280,95335],{"className":95279,"ariaHidden":394},[393],[363,95281,95283,95286,95326,95329,95332],{"className":95282},[398],[363,95284],{"className":95285,"style":11821},[402],[363,95287,95289,95292],{"className":95288},[407],[363,95290,16059],{"className":95291,"style":16108},[407,408],[363,95293,95295],{"className":95294},[629],[363,95296,95298,95318],{"className":95297},[633,634],[363,95299,95301,95315],{"className":95300},[638],[363,95302,95304],{"className":95303,"style":45276},[642],[363,95305,95306,95309],{"style":95090},[363,95307],{"className":95308,"style":651},[650],[363,95310,95312],{"className":95311},[655,656,657,658],[363,95313,82643],{"className":95314},[407,408,658],[363,95316,666],{"className":95317},[665],[363,95319,95321],{"className":95320},[638],[363,95322,95324],{"className":95323,"style":8315},[642],[363,95325],{},[363,95327],{"className":95328,"style":506},[505],[363,95330,471],{"className":95331},[510],[363,95333],{"className":95334,"style":506},[505],[363,95336,95338,95341],{"className":95337},[398],[363,95339],{"className":95340,"style":2852},[402],[363,95342,95344,95347,95418],{"className":95343},[407],[363,95345],{"className":95346},[494,789],[363,95348,95350],{"className":95349},[586],[363,95351,95353,95410],{"className":95352},[633,634],[363,95354,95356,95407],{"className":95355},[638],[363,95357,95359,95385,95393],{"className":95358,"style":2871},[642],[363,95360,95361,95364],{"style":2874},[363,95362],{"className":95363,"style":809},[650],[363,95365,95367],{"className":95366},[655,656,657,658],[363,95368,95370,95379,95382],{"className":95369},[407,658],[363,95371,95373,95376],{"className":95372},[1831,658],[363,95374,48005],{"className":95375},[658],[363,95377,82643],{"className":95378},[658],[363,95380],{"className":95381,"style":42713},[505,658],[363,95383,82643],{"className":95384},[407,408,658],[363,95386,95387,95390],{"style":821},[363,95388],{"className":95389,"style":809},[650],[363,95391],{"className":95392,"style":829},[828],[363,95394,95395,95398],{"style":2897},[363,95396],{"className":95397,"style":809},[650],[363,95399,95401],{"className":95400},[655,656,657,658],[363,95402,95404],{"className":95403},[407,658],[363,95405,465],{"className":95406},[407,658],[363,95408,666],{"className":95409},[665],[363,95411,95413],{"className":95412},[638],[363,95414,95416],{"className":95415,"style":2919},[642],[363,95417],{},[363,95419],{"className":95420},[501,789],[363,95422,95424,95454],{"className":95423,"translate":367},[366],[363,95425,95427],{"className":95426},[371],[373,95428,95429],{"xmlns":375},[377,95430,95431,95451],{},[380,95432,95433,95439,95441],{},[543,95434,95435,95437],{},[383,95436,39009],{},[383,95438,82643],{},[458,95440,471],{},[7161,95442,95443,95445],{},[383,95444,7914],{},[380,95446,95447,95449],{},[458,95448,5160],{},[383,95450,82643],{},[387,95452,95453],{"encoding":389},"\\varepsilon_n=e^{-n}",[363,95455,95457,95512],{"className":95456,"ariaHidden":394},[393],[363,95458,95460,95463,95503,95506,95509],{"className":95459},[398],[363,95461],{"className":95462,"style":13721},[402],[363,95464,95466,95469],{"className":95465},[407],[363,95467,39009],{"className":95468},[407,408],[363,95470,95472],{"className":95471},[629],[363,95473,95475,95495],{"className":95474},[633,634],[363,95476,95478,95492],{"className":95477},[638],[363,95479,95481],{"className":95480,"style":45276},[642],[363,95482,95483,95486],{"style":730},[363,95484],{"className":95485,"style":651},[650],[363,95487,95489],{"className":95488},[655,656,657,658],[363,95490,82643],{"className":95491},[407,408,658],[363,95493,666],{"className":95494},[665],[363,95496,95498],{"className":95497},[638],[363,95499,95501],{"className":95500,"style":8315},[642],[363,95502],{},[363,95504],{"className":95505,"style":506},[505],[363,95507,471],{"className":95508},[510],[363,95510],{"className":95511,"style":506},[505],[363,95513,95515,95518],{"className":95514},[398],[363,95516],{"className":95517,"style":21356},[402],[363,95519,95521,95524],{"className":95520},[407],[363,95522,7914],{"className":95523},[407,408],[363,95525,95527],{"className":95526},[629],[363,95528,95530],{"className":95529},[633],[363,95531,95533],{"className":95532},[638],[363,95534,95536],{"className":95535,"style":21356},[642],[363,95537,95538,95541],{"style":7212},[363,95539],{"className":95540,"style":651},[650],[363,95542,95544],{"className":95543},[655,656,657,658],[363,95545,95547,95550],{"className":95546},[407,658],[363,95548,5160],{"className":95549},[407,658],[363,95551,82643],{"className":95552},[407,408,658],"。则 ",[363,95555,95557,95601],{"className":95556,"translate":367},[366],[363,95558,95560],{"className":95559},[371],[373,95561,95562],{"xmlns":375},[377,95563,95564,95598],{},[380,95565,95566,95572,95574,95580,95582,95584,95586,95588,95594,95596],{},[380,95567,95568,95570],{},[383,95569,5739],{"mathvariant":557},[383,95571,35197],{"mathvariant":557},[458,95573,461],{"stretchy":460},[543,95575,95576,95578],{},[383,95577,1291],{},[383,95579,82643],{},[458,95581,898],{"separator":394},[383,95583,11],{},[458,95585,468],{"stretchy":460},[458,95587,33306],{},[543,95589,95590,95592],{},[383,95591,16059],{},[383,95593,82643],{},[458,95595,1376],{},[463,95597,474],{},[387,95599,95600],{"encoding":389},"\\mathrm{TV}(q_n,p)\\approx\\delta_n\\to0",[363,95602,95604,95680,95735],{"className":95603,"ariaHidden":394},[393],[363,95605,95607,95610,95616,95619,95659,95662,95665,95668,95671,95674,95677],{"className":95606},[398],[363,95608],{"className":95609,"style":487},[402],[363,95611,95613],{"className":95612},[407],[363,95614,87109],{"className":95615,"style":4504},[407,33009],[363,95617,461],{"className":95618},[494],[363,95620,95622,95625],{"className":95621},[407],[363,95623,1291],{"className":95624,"style":1328},[407,408],[363,95626,95628],{"className":95627},[629],[363,95629,95631,95651],{"className":95630},[633,634],[363,95632,95634,95648],{"className":95633},[638],[363,95635,95637],{"className":95636,"style":45276},[642],[363,95638,95639,95642],{"style":19190},[363,95640],{"className":95641,"style":651},[650],[363,95643,95645],{"className":95644},[655,656,657,658],[363,95646,82643],{"className":95647},[407,408,658],[363,95649,666],{"className":95650},[665],[363,95652,95654],{"className":95653},[638],[363,95655,95657],{"className":95656,"style":8315},[642],[363,95658],{},[363,95660,898],{"className":95661},[920],[363,95663],{"className":95664,"style":754},[505],[363,95666,11],{"className":95667},[407,408],[363,95669,468],{"className":95670},[501],[363,95672],{"className":95673,"style":506},[505],[363,95675,33306],{"className":95676},[510],[363,95678],{"className":95679,"style":506},[505],[363,95681,95683,95686,95726,95729,95732],{"className":95682},[398],[363,95684],{"className":95685,"style":11821},[402],[363,95687,95689,95692],{"className":95688},[407],[363,95690,16059],{"className":95691,"style":16108},[407,408],[363,95693,95695],{"className":95694},[629],[363,95696,95698,95718],{"className":95697},[633,634],[363,95699,95701,95715],{"className":95700},[638],[363,95702,95704],{"className":95703,"style":45276},[642],[363,95705,95706,95709],{"style":95090},[363,95707],{"className":95708,"style":651},[650],[363,95710,95712],{"className":95711},[655,656,657,658],[363,95713,82643],{"className":95714},[407,408,658],[363,95716,666],{"className":95717},[665],[363,95719,95721],{"className":95720},[638],[363,95722,95724],{"className":95723,"style":8315},[642],[363,95725],{},[363,95727],{"className":95728,"style":506},[505],[363,95730,1376],{"className":95731},[510],[363,95733],{"className":95734,"style":506},[505],[363,95736,95738,95741],{"className":95737},[398],[363,95739],{"className":95740,"style":520},[402],[363,95742,474],{"className":95743},[407],"，但 ",[363,95746,95748,95797],{"className":95747,"translate":367},[366],[363,95749,95751],{"className":95750},[371],[373,95752,95753],{"xmlns":375},[377,95754,95755,95794],{},[380,95756,95757,95763,95765,95771,95773,95775,95777,95780,95786,95788,95790,95792],{},[380,95758,95759,95761],{},[383,95760,11041],{"mathvariant":557},[383,95762,22240],{"mathvariant":557},[458,95764,461],{"stretchy":460},[543,95766,95767,95769],{},[383,95768,1291],{},[383,95770,82643],{},[383,95772,558],{"mathvariant":557},[383,95774,11],{},[458,95776,468],{"stretchy":460},[458,95778,95779],{},"≳",[543,95781,95782,95784],{},[383,95783,16059],{},[383,95785,82643],{},[458,95787,3646],{},[383,95789,82643],{},[458,95791,1376],{},[383,95793,1371],{"mathvariant":557},[387,95795,95796],{"encoding":389},"\\mathrm{KL}(q_n\\|p)\\gtrsim \\delta_n\\cdot n\\to\\infty",[363,95798,95800,95873,95928,95946],{"className":95799,"ariaHidden":394},[393],[363,95801,95803,95806,95812,95815,95855,95858,95861,95864,95867,95870],{"className":95802},[398],[363,95804],{"className":95805,"style":487},[402],[363,95807,95809],{"className":95808},[407],[363,95810,33010],{"className":95811},[407,33009],[363,95813,461],{"className":95814},[494],[363,95816,95818,95821],{"className":95817},[407],[363,95819,1291],{"className":95820,"style":1328},[407,408],[363,95822,95824],{"className":95823},[629],[363,95825,95827,95847],{"className":95826},[633,634],[363,95828,95830,95844],{"className":95829},[638],[363,95831,95833],{"className":95832,"style":45276},[642],[363,95834,95835,95838],{"style":19190},[363,95836],{"className":95837,"style":651},[650],[363,95839,95841],{"className":95840},[655,656,657,658],[363,95842,82643],{"className":95843},[407,408,658],[363,95845,666],{"className":95846},[665],[363,95848,95850],{"className":95849},[638],[363,95851,95853],{"className":95852,"style":8315},[642],[363,95854],{},[363,95856,558],{"className":95857},[407],[363,95859,11],{"className":95860},[407,408],[363,95862,468],{"className":95863},[501],[363,95865],{"className":95866,"style":506},[505],[363,95868,95779],{"className":95869},[510,60141],[363,95871],{"className":95872,"style":506},[505],[363,95874,95876,95879,95919,95922,95925],{"className":95875},[398],[363,95877],{"className":95878,"style":11821},[402],[363,95880,95882,95885],{"className":95881},[407],[363,95883,16059],{"className":95884,"style":16108},[407,408],[363,95886,95888],{"className":95887},[629],[363,95889,95891,95911],{"className":95890},[633,634],[363,95892,95894,95908],{"className":95893},[638],[363,95895,95897],{"className":95896,"style":45276},[642],[363,95898,95899,95902],{"style":95090},[363,95900],{"className":95901,"style":651},[650],[363,95903,95905],{"className":95904},[655,656,657,658],[363,95906,82643],{"className":95907},[407,408,658],[363,95909,666],{"className":95910},[665],[363,95912,95914],{"className":95913},[638],[363,95915,95917],{"className":95916,"style":8315},[642],[363,95918],{},[363,95920],{"className":95921,"style":2934},[505],[363,95923,3646],{"className":95924},[2938],[363,95926],{"className":95927,"style":2934},[505],[363,95929,95931,95934,95937,95940,95943],{"className":95930},[398],[363,95932],{"className":95933,"style":2692},[402],[363,95935,82643],{"className":95936},[407,408],[363,95938],{"className":95939,"style":506},[505],[363,95941,1376],{"className":95942},[510],[363,95944],{"className":95945,"style":506},[505],[363,95947,95949,95952],{"className":95948},[398],[363,95950],{"className":95951,"style":2692},[402],[363,95953,1371],{"className":95954},[407],"。反例的机制很典型：TV 只控制\"总质量差\"，控制不了小测度集合上密度的巨大尖峰，而 KL 对小分母极其敏感——这正是 KL\u002Fχ² \"无界\"分歧的拓扑体现。",[11,95957,95958,95961,95962,95990,95991,60411,96057,96122,96123,23971],{},[1572,95959,95960],{},"(c)（有限字母表\u002F一致比值界下，全部等价）"," 若似然比一致有界（例如：",[363,95963,95965,95978],{"className":95964,"translate":367},[366],[363,95966,95968],{"className":95967},[371],[373,95969,95970],{"xmlns":375},[377,95971,95972,95976],{},[380,95973,95974],{},[383,95975,561],{},[387,95977,561],{"encoding":389},[363,95979,95981],{"className":95980,"ariaHidden":394},[393],[363,95982,95984,95987],{"className":95983},[398],[363,95985],{"className":95986,"style":913},[402],[363,95988,561],{"className":95989},[407,408]," 在有限字母表上且 ",[363,95992,95994,96018],{"className":95993,"translate":367},[366],[363,95995,95997],{"className":95996},[371],[373,95998,95999],{"xmlns":375},[377,96000,96001,96015],{},[380,96002,96003,96005,96007,96009,96011,96013],{},[383,96004,1291],{},[458,96006,461],{"stretchy":460},[383,96008,1121],{},[458,96010,468],{"stretchy":460},[458,96012,3250],{},[463,96014,474],{},[387,96016,96017],{"encoding":389},"q(x)>0",[363,96019,96021,96048],{"className":96020,"ariaHidden":394},[393],[363,96022,96024,96027,96030,96033,96036,96039,96042,96045],{"className":96023},[398],[363,96025],{"className":96026,"style":487},[402],[363,96028,1291],{"className":96029,"style":1328},[407,408],[363,96031,461],{"className":96032},[494],[363,96034,1121],{"className":96035},[407,408],[363,96037,468],{"className":96038},[501],[363,96040],{"className":96041,"style":506},[505],[363,96043,3250],{"className":96044},[510],[363,96046],{"className":96047,"style":506},[505],[363,96049,96051,96054],{"className":96050},[398],[363,96052],{"className":96053,"style":520},[402],[363,96055,474],{"className":96056},[407],[363,96058,96060,96083],{"className":96059,"translate":367},[366],[363,96061,96063],{"className":96062},[371],[373,96064,96065],{"xmlns":375},[377,96066,96067,96080],{},[380,96068,96069,96071,96073,96076,96078],{},[383,96070,1121],{},[458,96072,6256],{},[383,96074,96075],{"mathvariant":557},"supp",[458,96077,4450],{},[383,96079,554],{},[387,96081,96082],{"encoding":389},"x\\in\\operatorname{supp}P",[363,96084,96086,96104],{"className":96085,"ariaHidden":394},[393],[363,96087,96089,96092,96095,96098,96101],{"className":96088},[398],[363,96090],{"className":96091,"style":6271},[402],[363,96093,1121],{"className":96094},[407,408],[363,96096],{"className":96097,"style":506},[505],[363,96099,6256],{"className":96100},[510],[363,96102],{"className":96103,"style":506},[505],[363,96105,96107,96110,96116,96119],{"className":96106},[398],[363,96108],{"className":96109,"style":913},[402],[363,96111,96113],{"className":96112},[1831],[363,96114,96075],{"className":96115},[407,33009],[363,96117],{"className":96118,"style":754},[505],[363,96120,554],{"className":96121,"style":682},[407,408],"——此时 ",[363,96124,96126,96162],{"className":96125,"translate":367},[366],[363,96127,96129],{"className":96128},[371],[373,96130,96131],{"xmlns":375},[377,96132,96133,96159],{},[380,96134,96135,96137,96139,96145,96147,96155,96157],{},[383,96136,1116],{},[458,96138,471],{},[586,96140,96141,96143],{},[383,96142,11],{},[383,96144,1291],{},[458,96146,10299],{},[543,96148,96149,96151,96153],{},[383,96150,1116],{},[383,96152,52734],{},[458,96154,4450],{},[458,96156,7598],{},[383,96158,1371],{"mathvariant":557},[387,96160,96161],{"encoding":389},"t=\\frac{p}{q}\\le t_{\\max}\u003C\\infty",[363,96163,96165,96183,96266,96334],{"className":96164,"ariaHidden":394},[393],[363,96166,96168,96171,96174,96177,96180],{"className":96167},[398],[363,96169],{"className":96170,"style":5690},[402],[363,96172,1116],{"className":96173},[407,408],[363,96175],{"className":96176,"style":506},[505],[363,96178,471],{"className":96179},[510],[363,96181],{"className":96182,"style":506},[505],[363,96184,96186,96189,96257,96260,96263],{"className":96185},[398],[363,96187],{"className":96188,"style":3431},[402],[363,96190,96192,96195,96254],{"className":96191},[407],[363,96193],{"className":96194},[494,789],[363,96196,96198],{"className":96197},[586],[363,96199,96201,96246],{"className":96200},[633,634],[363,96202,96204,96243],{"className":96203},[638],[363,96205,96207,96221,96229],{"className":96206,"style":3450},[642],[363,96208,96209,96212],{"style":2874},[363,96210],{"className":96211,"style":809},[650],[363,96213,96215],{"className":96214},[655,656,657,658],[363,96216,96218],{"className":96217},[407,658],[363,96219,1291],{"className":96220,"style":1328},[407,408,658],[363,96222,96223,96226],{"style":821},[363,96224],{"className":96225,"style":809},[650],[363,96227],{"className":96228,"style":829},[828],[363,96230,96231,96234],{"style":3200},[363,96232],{"className":96233,"style":809},[650],[363,96235,96237],{"className":96236},[655,656,657,658],[363,96238,96240],{"className":96239},[407,658],[363,96241,11],{"className":96242},[407,408,658],[363,96244,666],{"className":96245},[665],[363,96247,96249],{"className":96248},[638],[363,96250,96252],{"className":96251,"style":3086},[642],[363,96253],{},[363,96255],{"className":96256},[501,789],[363,96258],{"className":96259,"style":506},[505],[363,96261,10299],{"className":96262},[510],[363,96264],{"className":96265,"style":506},[505],[363,96267,96269,96273,96325,96328,96331],{"className":96268},[398],[363,96270],{"className":96271,"style":96272},[402],"height:0.7651em;vertical-align:-0.15em;",[363,96274,96276,96279],{"className":96275},[407],[363,96277,1116],{"className":96278},[407,408],[363,96280,96282],{"className":96281},[629],[363,96283,96285,96317],{"className":96284},[633,634],[363,96286,96288,96314],{"className":96287},[638],[363,96289,96291],{"className":96290,"style":45276},[642],[363,96292,96293,96296],{"style":730},[363,96294],{"className":96295,"style":651},[650],[363,96297,96299],{"className":96298},[655,656,657,658],[363,96300,96302],{"className":96301},[407,658],[363,96303,96305,96308,96311],{"className":96304},[1831,658],[363,96306,26670],{"className":96307},[658],[363,96309,45527],{"className":96310},[658],[363,96312,1121],{"className":96313},[658],[363,96315,666],{"className":96316},[665],[363,96318,96320],{"className":96319},[638],[363,96321,96323],{"className":96322,"style":8315},[642],[363,96324],{},[363,96326],{"className":96327,"style":506},[505],[363,96329,7598],{"className":96330},[510],[363,96332],{"className":96333,"style":506},[505],[363,96335,96337,96340],{"className":96336},[398],[363,96338],{"className":96339,"style":2692},[402],[363,96341,1371],{"className":96342},[407],[363,96344,96346],{"className":96345,"translate":367},[528],[363,96347,96349,96484],{"className":96348,"translate":367},[366],[363,96350,96352],{"className":96351},[371],[373,96353,96354],{"xmlns":375,"display":537},[377,96355,96356,96481],{},[1590,96357,96358,96429],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,96359,96360,96366],{},[1599,96361,96362],{},[1602,96363,96364],{"scriptlevel":474,"displaystyle":394},[380,96365],{},[1599,96367,96368],{},[1602,96369,96370],{"scriptlevel":474,"displaystyle":394},[380,96371,96372,96374,96380,96382,96388,96390,96392,96394,96396,96398,96400,96403,96405,96411,96413,96419,96421,96423,96425,96427],{},[380,96373],{},[543,96375,96376,96378],{},[383,96377,547],{},[383,96379,385],{},[458,96381,461],{"stretchy":460},[543,96383,96384,96386],{},[383,96385,554],{},[383,96387,82643],{},[383,96389,558],{"mathvariant":557},[383,96391,561],{},[458,96393,468],{"stretchy":460},[458,96395,1376],{},[463,96397,474],{},[1644,96399,16251],{},[458,96401,96402],{},"⟺",[1644,96404,16251],{},[380,96406,96407,96409],{},[383,96408,5739],{"mathvariant":557},[383,96410,35197],{"mathvariant":557},[458,96412,461],{"stretchy":460},[543,96414,96415,96417],{},[383,96416,554],{},[383,96418,82643],{},[458,96420,898],{"separator":394},[383,96422,561],{},[458,96424,468],{"stretchy":460},[458,96426,1376],{},[463,96428,474],{},[1596,96430,96431,96437],{},[1599,96432,96433],{},[1602,96434,96435],{"scriptlevel":474,"displaystyle":394},[380,96436],{},[1599,96438,96439],{},[1602,96440,96441],{"scriptlevel":474,"displaystyle":394},[380,96442,96443,96445,96447,96449,96451,96453,96463,96465,96471,96473,96475,96477,96479],{},[380,96444],{},[505,96446],{"width":3609},[1644,96448,16251],{},[458,96450,96402],{},[1644,96452,16251],{},[543,96454,96455,96457],{},[383,96456,547],{},[380,96458,96459,96461],{},[383,96460,11041],{},[383,96462,22240],{},[458,96464,461],{"stretchy":460},[543,96466,96467,96469],{},[383,96468,554],{},[383,96470,82643],{},[383,96472,558],{"mathvariant":557},[383,96474,561],{},[458,96476,468],{"stretchy":460},[458,96478,1376],{},[463,96480,474],{},[387,96482,96483],{"encoding":389},"\\begin{aligned}\n&D_f(P_n\\|Q)\\to0\n\\iff\\mathrm{TV}(P_n,Q)\\to0\\\\\n&\\qquad\\iff D_{KL}(P_n\\|Q)\\to0\n\\end{aligned}",[363,96485,96487],{"className":96486,"ariaHidden":394},[393],[363,96488,96490,96494],{"className":96489},[398],[363,96491],{"className":96492,"style":96493},[402],"height:2.7em;vertical-align:-1.1em;",[363,96495,96497],{"className":96496},[407],[363,96498,96500,96543],{"className":96499},[1590],[363,96501,96503],{"className":96502},[1707],[363,96504,96506,96534],{"className":96505},[633,634],[363,96507,96509,96531],{"className":96508},[638],[363,96510,96513,96523],{"className":96511,"style":96512},[642],"height:1.6em;",[363,96514,96516,96520],{"style":96515},"top:-3.6em;",[363,96517],{"className":96518,"style":96519},[650],"height:2.84em;",[363,96521],{"className":96522},[407],[363,96524,96525,96528],{"style":2250},[363,96526],{"className":96527,"style":96519},[650],[363,96529],{"className":96530},[407],[363,96532,666],{"className":96533},[665],[363,96535,96537],{"className":96536},[638],[363,96538,96541],{"className":96539,"style":96540},[642],"height:1.1em;",[363,96542],{},[363,96544,96546],{"className":96545},[1798],[363,96547,96549,96901],{"className":96548},[633,634],[363,96550,96552,96898],{"className":96551},[638],[363,96553,96555,96759],{"className":96554,"style":96512},[642],[363,96556,96558,96561],{"style":96557},"top:-3.76em;",[363,96559],{"className":96560,"style":809},[650],[363,96562,96564,96567,96607,96610,96650,96653,96656,96659,96662,96665,96668,96671,96674,96677,96680,96683,96686,96692,96695,96735,96738,96741,96744,96747,96750,96753,96756],{"className":96563},[407],[363,96565],{"className":96566},[407],[363,96568,96570,96573],{"className":96569},[407],[363,96571,547],{"className":96572,"style":625},[407,408],[363,96574,96576],{"className":96575},[629],[363,96577,96579,96599],{"className":96578},[633,634],[363,96580,96582,96596],{"className":96581},[638],[363,96583,96585],{"className":96584,"style":643},[642],[363,96586,96587,96590],{"style":646},[363,96588],{"className":96589,"style":651},[650],[363,96591,96593],{"className":96592},[655,656,657,658],[363,96594,385],{"className":96595,"style":409},[407,408,658],[363,96597,666],{"className":96598},[665],[363,96600,96602],{"className":96601},[638],[363,96603,96605],{"className":96604,"style":673},[642],[363,96606],{},[363,96608,461],{"className":96609},[494],[363,96611,96613,96616],{"className":96612},[407],[363,96614,554],{"className":96615,"style":682},[407,408],[363,96617,96619],{"className":96618},[629],[363,96620,96622,96642],{"className":96621},[633,634],[363,96623,96625,96639],{"className":96624},[638],[363,96626,96628],{"className":96627,"style":45276},[642],[363,96629,96630,96633],{"style":11483},[363,96631],{"className":96632,"style":651},[650],[363,96634,96636],{"className":96635},[655,656,657,658],[363,96637,82643],{"className":96638},[407,408,658],[363,96640,666],{"className":96641},[665],[363,96643,96645],{"className":96644},[638],[363,96646,96648],{"className":96647,"style":8315},[642],[363,96649],{},[363,96651,558],{"className":96652},[407],[363,96654,561],{"className":96655},[407,408],[363,96657,468],{"className":96658},[501],[363,96660],{"className":96661,"style":506},[505],[363,96663,1376],{"className":96664},[510],[363,96666],{"className":96667,"style":506},[505],[363,96669,474],{"className":96670},[407],[363,96672],{"className":96673,"style":506},[505],[363,96675],{"className":96676,"style":506},[505],[363,96678,96402],{"className":96679},[510],[363,96681],{"className":96682,"style":506},[505],[363,96684],{"className":96685,"style":506},[505],[363,96687,96689],{"className":96688},[407],[363,96690,87109],{"className":96691,"style":4504},[407,33009],[363,96693,461],{"className":96694},[494],[363,96696,96698,96701],{"className":96697},[407],[363,96699,554],{"className":96700,"style":682},[407,408],[363,96702,96704],{"className":96703},[629],[363,96705,96707,96727],{"className":96706},[633,634],[363,96708,96710,96724],{"className":96709},[638],[363,96711,96713],{"className":96712,"style":45276},[642],[363,96714,96715,96718],{"style":11483},[363,96716],{"className":96717,"style":651},[650],[363,96719,96721],{"className":96720},[655,656,657,658],[363,96722,82643],{"className":96723},[407,408,658],[363,96725,666],{"className":96726},[665],[363,96728,96730],{"className":96729},[638],[363,96731,96733],{"className":96732,"style":8315},[642],[363,96734],{},[363,96736,898],{"className":96737},[920],[363,96739],{"className":96740,"style":754},[505],[363,96742,561],{"className":96743},[407,408],[363,96745,468],{"className":96746},[501],[363,96748],{"className":96749,"style":506},[505],[363,96751,1376],{"className":96752},[510],[363,96754],{"className":96755,"style":506},[505],[363,96757,474],{"className":96758},[407],[363,96760,96761,96764],{"style":25083},[363,96762],{"className":96763,"style":809},[650],[363,96765,96767,96770,96773,96776,96779,96782,96785,96788,96834,96837,96877,96880,96883,96886,96889,96892,96895],{"className":96766},[407],[363,96768],{"className":96769},[407],[363,96771],{"className":96772,"style":3981},[505],[363,96774],{"className":96775,"style":506},[505],[363,96777],{"className":96778,"style":506},[505],[363,96780,96402],{"className":96781},[510],[363,96783],{"className":96784,"style":506},[505],[363,96786],{"className":96787,"style":506},[505],[363,96789,96791,96794],{"className":96790},[407],[363,96792,547],{"className":96793,"style":625},[407,408],[363,96795,96797],{"className":96796},[629],[363,96798,96800,96826],{"className":96799},[633,634],[363,96801,96803,96823],{"className":96802},[638],[363,96804,96806],{"className":96805,"style":727},[642],[363,96807,96808,96811],{"style":646},[363,96809],{"className":96810,"style":651},[650],[363,96812,96814],{"className":96813},[655,656,657,658],[363,96815,96817,96820],{"className":96816},[407,658],[363,96818,11041],{"className":96819,"style":11129},[407,408,658],[363,96821,22240],{"className":96822},[407,408,658],[363,96824,666],{"className":96825},[665],[363,96827,96829],{"className":96828},[638],[363,96830,96832],{"className":96831,"style":8315},[642],[363,96833],{},[363,96835,461],{"className":96836},[494],[363,96838,96840,96843],{"className":96839},[407],[363,96841,554],{"className":96842,"style":682},[407,408],[363,96844,96846],{"className":96845},[629],[363,96847,96849,96869],{"className":96848},[633,634],[363,96850,96852,96866],{"className":96851},[638],[363,96853,96855],{"className":96854,"style":45276},[642],[363,96856,96857,96860],{"style":11483},[363,96858],{"className":96859,"style":651},[650],[363,96861,96863],{"className":96862},[655,656,657,658],[363,96864,82643],{"className":96865},[407,408,658],[363,96867,666],{"className":96868},[665],[363,96870,96872],{"className":96871},[638],[363,96873,96875],{"className":96874,"style":8315},[642],[363,96876],{},[363,96878,558],{"className":96879},[407],[363,96881,561],{"className":96882},[407,408],[363,96884,468],{"className":96885},[501],[363,96887],{"className":96888,"style":506},[505],[363,96890,1376],{"className":96891},[510],[363,96893],{"className":96894,"style":506},[505],[363,96896,474],{"className":96897},[407],[363,96899,666],{"className":96900},[665],[363,96902,96904],{"className":96903},[638],[363,96905,96907],{"className":96906,"style":96540},[642],[363,96908],{},[11,96910,96911,96912,96940,96941,97088,97089,97286],{},"对一切上述 ",[363,96913,96915,96928],{"className":96914,"translate":367},[366],[363,96916,96918],{"className":96917},[371],[373,96919,96920],{"xmlns":375},[377,96921,96922,96926],{},[380,96923,96924],{},[383,96925,385],{},[387,96927,385],{"encoding":389},[363,96929,96931],{"className":96930,"ariaHidden":394},[393],[363,96932,96934,96937],{"className":96933},[398],[363,96935],{"className":96936,"style":403},[402],[363,96938,385],{"className":96939,"style":409},[407,408]," 同时成立（上界方向由 ",[363,96942,96944,96992],{"className":96943,"translate":367},[366],[363,96945,96947],{"className":96946},[371],[373,96948,96949],{"xmlns":375},[377,96950,96951,96989],{},[380,96952,96953,96955,96957,96959,96961,96963,96965,96967,96969,96971,96973,96975,96977,96979,96981,96983,96985,96987],{},[383,96954,5155],{"mathvariant":557},[383,96956,385],{},[458,96958,461],{"stretchy":460},[383,96960,1116],{},[458,96962,468],{"stretchy":460},[458,96964,5160],{},[383,96966,385],{},[458,96968,461],{"stretchy":460},[463,96970,465],{},[458,96972,468],{"stretchy":460},[383,96974,5155],{"mathvariant":557},[458,96976,10299],{},[383,96978,39641],{},[383,96980,5155],{"mathvariant":557},[383,96982,1116],{},[458,96984,5160],{},[463,96986,465],{},[383,96988,5155],{"mathvariant":557},[387,96990,96991],{"encoding":389},"|f(t)-f(1)|\\le C|t-1|",[363,96993,96995,97025,97055,97079],{"className":96994,"ariaHidden":394},[393],[363,96996,96998,97001,97004,97007,97010,97013,97016,97019,97022],{"className":96997},[398],[363,96999],{"className":97000,"style":487},[402],[363,97002,5155],{"className":97003},[407],[363,97005,385],{"className":97006,"style":409},[407,408],[363,97008,461],{"className":97009},[494],[363,97011,1116],{"className":97012},[407,408],[363,97014,468],{"className":97015},[501],[363,97017],{"className":97018,"style":2934},[505],[363,97020,5160],{"className":97021},[2938],[363,97023],{"className":97024,"style":2934},[505],[363,97026,97028,97031,97034,97037,97040,97043,97046,97049,97052],{"className":97027},[398],[363,97029],{"className":97030,"style":487},[402],[363,97032,385],{"className":97033,"style":409},[407,408],[363,97035,461],{"className":97036},[494],[363,97038,465],{"className":97039},[407],[363,97041,468],{"className":97042},[501],[363,97044,5155],{"className":97045},[407],[363,97047],{"className":97048,"style":506},[505],[363,97050,10299],{"className":97051},[510],[363,97053],{"className":97054,"style":506},[505],[363,97056,97058,97061,97064,97067,97070,97073,97076],{"className":97057},[398],[363,97059],{"className":97060,"style":487},[402],[363,97062,39641],{"className":97063,"style":11129},[407,408],[363,97065,5155],{"className":97066},[407],[363,97068,1116],{"className":97069},[407,408],[363,97071],{"className":97072,"style":2934},[505],[363,97074,5160],{"className":97075},[2938],[363,97077],{"className":97078,"style":2934},[505],[363,97080,97082,97085],{"className":97081},[398],[363,97083],{"className":97084,"style":487},[402],[363,97086,35026],{"className":97087},[407]," 于 ",[363,97090,97092,97136],{"className":97091,"translate":367},[366],[363,97093,97095],{"className":97094},[371],[373,97096,97097],{"xmlns":375},[377,97098,97099,97133],{},[380,97100,97101,97103,97105,97107,97109,97111,97119,97121,97123,97131],{},[383,97102,1116],{},[458,97104,6256],{},[458,97106,578],{"stretchy":460},[463,97108,465],{},[383,97110,1288],{"mathvariant":557},[543,97112,97113,97115,97117],{},[383,97114,1116],{},[383,97116,51955],{},[458,97118,4450],{},[458,97120,898],{"separator":394},[1644,97122,1646],{},[543,97124,97125,97127,97129],{},[383,97126,1116],{},[383,97128,52734],{},[458,97130,4450],{},[458,97132,605],{"stretchy":460},[387,97134,97135],{"encoding":389},"t\\in[1\u002Ft_{\\min},\\,t_{\\max}]",[363,97137,97139,97157],{"className":97138,"ariaHidden":394},[393],[363,97140,97142,97145,97148,97151,97154],{"className":97141},[398],[363,97143],{"className":97144,"style":7613},[402],[363,97146,1116],{"className":97147},[407,408],[363,97149],{"className":97150,"style":506},[505],[363,97152,6256],{"className":97153},[510],[363,97155],{"className":97156,"style":506},[505],[363,97158,97160,97163,97166,97169,97222,97225,97228,97231,97283],{"className":97159},[398],[363,97161],{"className":97162,"style":487},[402],[363,97164,578],{"className":97165},[494],[363,97167,8936],{"className":97168},[407],[363,97170,97172,97175],{"className":97171},[407],[363,97173,1116],{"className":97174},[407,408],[363,97176,97178],{"className":97177},[629],[363,97179,97181,97214],{"className":97180},[633,634],[363,97182,97184,97211],{"className":97183},[638],[363,97185,97188],{"className":97186,"style":97187},[642],"height:0.3175em;",[363,97189,97190,97193],{"style":730},[363,97191],{"className":97192,"style":651},[650],[363,97194,97196],{"className":97195},[655,656,657,658],[363,97197,97199],{"className":97198},[407,658],[363,97200,97202,97205,97208],{"className":97201},[1831,658],[363,97203,26670],{"className":97204},[658],[363,97206,12310],{"className":97207},[658],[363,97209,82643],{"className":97210},[658],[363,97212,666],{"className":97213},[665],[363,97215,97217],{"className":97216},[638],[363,97218,97220],{"className":97219,"style":8315},[642],[363,97221],{},[363,97223,898],{"className":97224},[920],[363,97226],{"className":97227,"style":754},[505],[363,97229],{"className":97230,"style":754},[505],[363,97232,97234,97237],{"className":97233},[407],[363,97235,1116],{"className":97236},[407,408],[363,97238,97240],{"className":97239},[629],[363,97241,97243,97275],{"className":97242},[633,634],[363,97244,97246,97272],{"className":97245},[638],[363,97247,97249],{"className":97248,"style":45276},[642],[363,97250,97251,97254],{"style":730},[363,97252],{"className":97253,"style":651},[650],[363,97255,97257],{"className":97256},[655,656,657,658],[363,97258,97260],{"className":97259},[407,658],[363,97261,97263,97266,97269],{"className":97262},[1831,658],[363,97264,26670],{"className":97265},[658],[363,97267,45527],{"className":97268},[658],[363,97270,1121],{"className":97271},[658],[363,97273,666],{"className":97274},[665],[363,97276,97278],{"className":97277},[638],[363,97279,97281],{"className":97280,"style":8315},[642],[363,97282],{},[363,97284,605],{"className":97285},[501]," 的一致 Lipschitz 性给出）。",[11,97288,97289,97290,97293],{},"也就是说，",[1572,97291,97292],{},"\"所有 f-散度诱导同一拓扑\"必须在有限\u002F紧设定或一致比值界下读","：此时它们都等价于全变差拓扑（也叫强拓扑），只是\"度量标尺\"不同；而在一般测度空间上，KL 型拓扑严格强于 TV 拓扑。这一分层对理解第 6 节 f-散度与 Wasserstein 的真正差异很重要：f-散度族的内部差异是\"强度\"差异，而它们与 Wasserstein 的差异是\"性质\"差异。",[2658,97295,97297],{"id":97296},"_48-一般不是度量","4.8 一般不是度量",[11,97299,97300],{},"f-散度一般不对称，也不满足三角不等式，因此通常不是距离度量。但某些特殊形式可以诱导出度量：",[10374,97302,97303,98815],{},[7012,97304,97305,97308,97309,97981,97984,97985,98013,98014,98087,98088,98348,98349,98754,98755,98814],{},[1572,97306,97307],{},"Hellinger 距离","是度量：",[363,97310,97312],{"className":97311,"translate":367},[528],[363,97313,97315,97419],{"className":97314,"translate":367},[366],[363,97316,97318],{"className":97317},[371],[373,97319,97320],{"xmlns":375,"display":537},[377,97321,97322,97416],{},[380,97323,97324,97330,97332,97334,97336,97338,97340,97342,97380,97382,97394,97396,97414],{},[543,97325,97326,97328],{},[383,97327,44907],{},[383,97329,34231],{},[458,97331,461],{"stretchy":460},[383,97333,554],{},[458,97335,898],{"separator":394},[383,97337,561],{},[458,97339,468],{"stretchy":460},[458,97341,471],{},[34686,97343,97344],{},[380,97345,97346,97354,97356,97358,97362,97364,97368,97374,97376,97378],{},[1602,97347,97348],{"scriptlevel":474,"displaystyle":460},[586,97349,97350,97352],{},[463,97351,465],{},[463,97353,2810],{},[458,97355,1634],{},[458,97357,461],{"stretchy":460},[34686,97359,97360],{},[383,97361,11],{},[458,97363,5160],{},[34686,97365,97366],{},[383,97367,1291],{},[7161,97369,97370,97372],{},[458,97371,468],{"stretchy":460},[463,97373,2810],{},[1644,97375,1646],{},[383,97377,592],{},[383,97379,1121],{},[458,97381,471],{},[34686,97383,97384],{},[380,97385,97386,97388,97390,97392],{},[463,97387,465],{},[458,97389,5160],{},[383,97391,39638],{},[383,97393,39641],{},[458,97395,471],{},[34686,97397,97398],{},[380,97399,97400,97402,97404,97406],{},[463,97401,2810],{},[458,97403,5160],{},[463,97405,2810],{},[7900,97407,97408,97410,97412],{},[383,97409,34231],{},[1644,97411,42484],{},[463,97413,2810],{},[383,97415,4722],{"mathvariant":557},[387,97417,97418],{"encoding":389},"\\rho_H(P,Q)\n=\\sqrt{\\tfrac12\\int(\\sqrt p-\\sqrt q)^2\\,dx}\n=\\sqrt{1-BC}\n=\\sqrt{2-2H^2_{\\text{Bhattacharyya}}}.",[363,97420,97422,97495,97767,97848],{"className":97421,"ariaHidden":394},[393],[363,97423,97425,97428,97468,97471,97474,97477,97480,97483,97486,97489,97492],{"className":97424},[398],[363,97426],{"className":97427,"style":487},[402],[363,97429,97431,97434],{"className":97430},[407],[363,97432,44907],{"className":97433},[407,408],[363,97435,97437],{"className":97436},[629],[363,97438,97440,97460],{"className":97439},[633,634],[363,97441,97443,97457],{"className":97442},[638],[363,97444,97446],{"className":97445,"style":727},[642],[363,97447,97448,97451],{"style":730},[363,97449],{"className":97450,"style":651},[650],[363,97452,97454],{"className":97453},[655,656,657,658],[363,97455,34231],{"className":97456,"style":34385},[407,408,658],[363,97458,666],{"className":97459},[665],[363,97461,97463],{"className":97462},[638],[363,97464,97466],{"className":97465,"style":8315},[642],[363,97467],{},[363,97469,461],{"className":97470},[494],[363,97472,554],{"className":97473,"style":682},[407,408],[363,97475,898],{"className":97476},[920],[363,97478],{"className":97479,"style":754},[505],[363,97481,561],{"className":97482},[407,408],[363,97484,468],{"className":97485},[501],[363,97487],{"className":97488,"style":506},[505],[363,97490,471],{"className":97491},[510],[363,97493],{"className":97494,"style":506},[505],[363,97496,97498,97502,97758,97761,97764],{"className":97497},[398],[363,97499],{"className":97500,"style":97501},[402],"height:3.04em;vertical-align:-1.1572em;",[363,97503,97505],{"className":97504},[407,34714],[363,97506,97508,97750],{"className":97507},[633,634],[363,97509,97511,97747],{"className":97510},[638],[363,97512,97514,97735],{"className":97513,"style":91458},[642],[363,97515,97517,97520],{"className":97516,"style":91462},[6654],[363,97518],{"className":97519,"style":91466},[650],[363,97521,97523,97591,97594,97597,97600,97644,97647,97650,97653,97697,97726,97729,97732],{"className":97522,"style":41508},[407],[363,97524,97526,97529,97588],{"className":97525},[407],[363,97527],{"className":97528},[494,789],[363,97530,97532],{"className":97531},[586],[363,97533,97535,97580],{"className":97534},[633,634],[363,97536,97538,97577],{"className":97537},[638],[363,97539,97541,97555,97563],{"className":97540,"style":2871},[642],[363,97542,97543,97546],{"style":2874},[363,97544],{"className":97545,"style":809},[650],[363,97547,97549],{"className":97548},[655,656,657,658],[363,97550,97552],{"className":97551},[407,658],[363,97553,2810],{"className":97554},[407,658],[363,97556,97557,97560],{"style":821},[363,97558],{"className":97559,"style":809},[650],[363,97561],{"className":97562,"style":829},[828],[363,97564,97565,97568],{"style":2897},[363,97566],{"className":97567,"style":809},[650],[363,97569,97571],{"className":97570},[655,656,657,658],[363,97572,97574],{"className":97573},[407,658],[363,97575,465],{"className":97576},[407,658],[363,97578,666],{"className":97579},[665],[363,97581,97583],{"className":97582},[638],[363,97584,97586],{"className":97585,"style":2919},[642],[363,97587],{},[363,97589],{"className":97590},[501,789],[363,97592],{"className":97593,"style":754},[505],[363,97595,1634],{"className":97596,"style":1834},[1831,1832,1833],[363,97598,461],{"className":97599},[494],[363,97601,97603],{"className":97602},[407,34714],[363,97604,97606,97636],{"className":97605},[633,634],[363,97607,97609,97633],{"className":97608},[638],[363,97610,97612,97621],{"className":97611,"style":7209},[642],[363,97613,97615,97618],{"className":97614,"style":12210},[6654],[363,97616],{"className":97617,"style":809},[650],[363,97619,11],{"className":97620,"style":34734},[407,408],[363,97622,97623,97626],{"style":41697},[363,97624],{"className":97625,"style":809},[650],[363,97627,97629],{"className":97628,"style":34791},[34790],[6670,97630,97631],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,97632],{"d":34798},[363,97634,666],{"className":97635},[665],[363,97637,97639],{"className":97638},[638],[363,97640,97642],{"className":97641,"style":41717},[642],[363,97643],{},[363,97645],{"className":97646,"style":2934},[505],[363,97648,5160],{"className":97649},[2938],[363,97651],{"className":97652,"style":2934},[505],[363,97654,97656],{"className":97655},[407,34714],[363,97657,97659,97689],{"className":97658},[633,634],[363,97660,97662,97686],{"className":97661},[638],[363,97663,97665,97674],{"className":97664,"style":7209},[642],[363,97666,97668,97671],{"className":97667,"style":12210},[6654],[363,97669],{"className":97670,"style":809},[650],[363,97672,1291],{"className":97673,"style":39446},[407,408],[363,97675,97676,97679],{"style":41697},[363,97677],{"className":97678,"style":809},[650],[363,97680,97682],{"className":97681,"style":34791},[34790],[6670,97683,97684],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,97685],{"d":34798},[363,97687,666],{"className":97688},[665],[363,97690,97692],{"className":97691},[638],[363,97693,97695],{"className":97694,"style":41717},[642],[363,97696],{},[363,97698,97700,97703],{"className":97699},[501],[363,97701,468],{"className":97702},[501],[363,97704,97706],{"className":97705},[629],[363,97707,97709],{"className":97708},[633],[363,97710,97712],{"className":97711},[638],[363,97713,97715],{"className":97714,"style":45379},[642],[363,97716,97717,97720],{"style":45382},[363,97718],{"className":97719,"style":651},[650],[363,97721,97723],{"className":97722},[655,656,657,658],[363,97724,2810],{"className":97725},[407,658],[363,97727],{"className":97728,"style":754},[505],[363,97730,592],{"className":97731},[407,408],[363,97733,1121],{"className":97734},[407,408],[363,97736,97737,97740],{"style":91604},[363,97738],{"className":97739,"style":91466},[650],[363,97741,97743],{"className":97742,"style":91611},[34790],[6670,97744,97745],{"xmlns":6672,"width":6673,"height":91614,"viewBox":91615,"preserveAspectRatio":6676},[6678,97746],{"d":91618},[363,97748,666],{"className":97749},[665],[363,97751,97753],{"className":97752},[638],[363,97754,97756],{"className":97755,"style":91628},[642],[363,97757],{},[363,97759],{"className":97760,"style":506},[505],[363,97762,471],{"className":97763},[510],[363,97765],{"className":97766,"style":506},[505],[363,97768,97770,97774,97839,97842,97845],{"className":97769},[398],[363,97771],{"className":97772,"style":97773},[402],"height:1.04em;vertical-align:-0.1061em;",[363,97775,97777],{"className":97776},[407,34714],[363,97778,97780,97830],{"className":97779},[633,634],[363,97781,97783,97827],{"className":97782},[638],[363,97784,97787,97814],{"className":97785,"style":97786},[642],"height:0.9339em;",[363,97788,97790,97793],{"className":97789,"style":12210},[6654],[363,97791],{"className":97792,"style":809},[650],[363,97794,97796,97799,97802,97805,97808,97811],{"className":97795,"style":34734},[407],[363,97797,465],{"className":97798},[407],[363,97800],{"className":97801,"style":2934},[505],[363,97803,5160],{"className":97804},[2938],[363,97806],{"className":97807,"style":2934},[505],[363,97809,39638],{"className":97810,"style":39734},[407,408],[363,97812,39641],{"className":97813,"style":11129},[407,408],[363,97815,97817,97820],{"style":97816},"top:-2.8939em;",[363,97818],{"className":97819,"style":809},[650],[363,97821,97823],{"className":97822,"style":34791},[34790],[6670,97824,97825],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,97826],{"d":34798},[363,97828,666],{"className":97829},[665],[363,97831,97833],{"className":97832},[638],[363,97834,97837],{"className":97835,"style":97836},[642],"height:0.1061em;",[363,97838],{},[363,97840],{"className":97841,"style":506},[505],[363,97843,471],{"className":97844},[510],[363,97846],{"className":97847,"style":506},[505],[363,97849,97851,97855,97978],{"className":97850},[398],[363,97852],{"className":97853,"style":97854},[402],"height:1.84em;vertical-align:-0.6269em;",[363,97856,97858],{"className":97857},[407,34714],[363,97859,97861,97969],{"className":97860},[633,634],[363,97862,97864,97966],{"className":97863},[638],[363,97865,97868,97953],{"className":97866,"style":97867},[642],"height:1.2131em;",[363,97869,97871,97874],{"className":97870,"style":82930},[6654],[363,97872],{"className":97873,"style":82934},[650],[363,97875,97877,97880,97883,97886,97889,97892],{"className":97876,"style":41508},[407],[363,97878,2810],{"className":97879},[407],[363,97881],{"className":97882,"style":2934},[505],[363,97884,5160],{"className":97885},[2938],[363,97887],{"className":97888,"style":2934},[505],[363,97890,2810],{"className":97891},[407],[363,97893,97895,97898],{"className":97894},[407],[363,97896,34231],{"className":97897,"style":34385},[407,408],[363,97899,97901],{"className":97900},[629],[363,97902,97904,97944],{"className":97903},[633,634],[363,97905,97907,97941],{"className":97906},[638],[363,97908,97911,97929],{"className":97909,"style":97910},[642],"height:0.7959em;",[363,97912,97914,97917],{"style":97913},"top:-2.3987em;margin-left:-0.0813em;margin-right:0.05em;",[363,97915],{"className":97916,"style":651},[650],[363,97918,97920],{"className":97919},[655,656,657,658],[363,97921,97923],{"className":97922},[407,658],[363,97924,97926],{"className":97925},[407,4945,658],[363,97927,42484],{"className":97928},[407,658],[363,97930,97932,97935],{"style":97931},"top:-3.0448em;margin-right:0.05em;",[363,97933],{"className":97934,"style":651},[650],[363,97936,97938],{"className":97937},[655,656,657,658],[363,97939,2810],{"className":97940},[407,658],[363,97942,666],{"className":97943},[665],[363,97945,97947],{"className":97946},[638],[363,97948,97951],{"className":97949,"style":97950},[642],"height:0.4374em;",[363,97952],{},[363,97954,97956,97959],{"style":97955},"top:-3.1731em;",[363,97957],{"className":97958,"style":82934},[650],[363,97960,97962],{"className":97961,"style":83076},[34790],[6670,97963,97964],{"xmlns":6672,"width":6673,"height":83079,"viewBox":83080,"preserveAspectRatio":6676},[6678,97965],{"d":83083},[363,97967,666],{"className":97968},[665],[363,97970,97972],{"className":97971},[638],[363,97973,97976],{"className":97974,"style":97975},[642],"height:0.6269em;",[363,97977],{},[363,97979,4722],{"className":97980},[407],[97982,97983],"br",{},"它有一个特别漂亮的几何解释：把分布 ",[363,97986,97988,98001],{"className":97987,"translate":367},[366],[363,97989,97991],{"className":97990},[371],[373,97992,97993],{"xmlns":375},[377,97994,97995,97999],{},[380,97996,97997],{},[383,97998,554],{},[387,98000,554],{"encoding":389},[363,98002,98004],{"className":98003,"ariaHidden":394},[393],[363,98005,98007,98010],{"className":98006},[398],[363,98008],{"className":98009,"style":1011},[402],[363,98011,554],{"className":98012,"style":682},[407,408]," 映到单位球面上的点 ",[363,98015,98017,98033],{"className":98016,"translate":367},[366],[363,98018,98020],{"className":98019},[371],[373,98021,98022],{"xmlns":375},[377,98023,98024,98030],{},[380,98025,98026],{},[34686,98027,98028],{},[383,98029,11],{},[387,98031,98032],{"encoding":389},"\\sqrt p",[363,98034,98036],{"className":98035,"ariaHidden":394},[393],[363,98037,98039,98043],{"className":98038},[398],[363,98040],{"className":98041,"style":98042},[402],"height:1.04em;vertical-align:-0.3369em;",[363,98044,98046],{"className":98045},[407,34714],[363,98047,98049,98079],{"className":98048},[633,634],[363,98050,98052,98076],{"className":98051},[638],[363,98053,98055,98064],{"className":98054,"style":39374},[642],[363,98056,98058,98061],{"className":98057,"style":12210},[6654],[363,98059],{"className":98060,"style":809},[650],[363,98062,11],{"className":98063,"style":34734},[407,408],[363,98065,98066,98069],{"style":39386},[363,98067],{"className":98068,"style":809},[650],[363,98070,98072],{"className":98071,"style":34791},[34790],[6670,98073,98074],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,98075],{"d":34798},[363,98077,666],{"className":98078},[665],[363,98080,98082],{"className":98081},[638],[363,98083,98085],{"className":98084,"style":39406},[642],[363,98086],{},"（因 ",[363,98089,98091,98127],{"className":98090,"translate":367},[366],[363,98092,98094],{"className":98093},[371],[373,98095,98096],{"xmlns":375},[377,98097,98098,98124],{},[380,98099,98100,98102,98106,98114,98116,98118,98120,98122],{},[458,98101,558],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[34686,98103,98104],{},[383,98105,11],{},[7900,98107,98108,98110,98112],{},[458,98109,558],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[463,98111,2810],{},[463,98113,2810],{},[458,98115,471],{},[458,98117,1634],{},[383,98119,11],{},[458,98121,471],{},[463,98123,465],{},[387,98125,98126],{"encoding":389},"\\big\\lVert\\sqrt p\\big\\rVert_2^2=\\int p=1",[363,98128,98130,98315,98339],{"className":98129,"ariaHidden":394},[393],[363,98131,98133,98137,98174,98218,98306,98309,98312],{"className":98132},[398],[363,98134],{"className":98135,"style":98136},[402],"height:1.4537em;vertical-align:-0.3997em;",[363,98138,98140],{"className":98139},[407],[363,98141,98143],{"className":98142},[767,15176],[363,98144,98146,98166],{"className":98145},[633,634],[363,98147,98149,98163],{"className":98148},[638],[363,98150,98152],{"className":98151,"style":15186},[642],[363,98153,98154,98157],{"style":15189},[363,98155],{"className":98156,"style":15193},[650],[363,98158,98159],{"style":15196},[6670,98160,98161],{"xmlns":6672,"width":15199,"height":9797,"viewBox":15200},[6678,98162],{"d":15203},[363,98164,666],{"className":98165},[665],[363,98167,98169],{"className":98168},[638],[363,98170,98172],{"className":98171,"style":15213},[642],[363,98173],{},[363,98175,98177],{"className":98176},[407,34714],[363,98178,98180,98210],{"className":98179},[633,634],[363,98181,98183,98207],{"className":98182},[638],[363,98184,98186,98195],{"className":98185,"style":39374},[642],[363,98187,98189,98192],{"className":98188,"style":12210},[6654],[363,98190],{"className":98191,"style":809},[650],[363,98193,11],{"className":98194,"style":34734},[407,408],[363,98196,98197,98200],{"style":39386},[363,98198],{"className":98199,"style":809},[650],[363,98201,98203],{"className":98202,"style":34791},[34790],[6670,98204,98205],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,98206],{"d":34798},[363,98208,666],{"className":98209},[665],[363,98211,98213],{"className":98212},[638],[363,98214,98216],{"className":98215,"style":39406},[642],[363,98217],{},[363,98219,98221,98258],{"className":98220},[407],[363,98222,98224],{"className":98223},[407],[363,98225,98227],{"className":98226},[767,15176],[363,98228,98230,98250],{"className":98229},[633,634],[363,98231,98233,98247],{"className":98232},[638],[363,98234,98236],{"className":98235,"style":15186},[642],[363,98237,98238,98241],{"style":15189},[363,98239],{"className":98240,"style":15193},[650],[363,98242,98243],{"style":15196},[6670,98244,98245],{"xmlns":6672,"width":15199,"height":9797,"viewBox":15200},[6678,98246],{"d":15203},[363,98248,666],{"className":98249},[665],[363,98251,98253],{"className":98252},[638],[363,98254,98256],{"className":98255,"style":15213},[642],[363,98257],{},[363,98259,98261],{"className":98260},[629],[363,98262,98264,98297],{"className":98263},[633,634],[363,98265,98267,98294],{"className":98266},[638],[363,98268,98271,98283],{"className":98269,"style":98270},[642],"height:1.054em;",[363,98272,98274,98277],{"style":98273},"top:-2.3003em;margin-right:0.05em;",[363,98275],{"className":98276,"style":651},[650],[363,98278,98280],{"className":98279},[655,656,657,658],[363,98281,2810],{"className":98282},[407,658],[363,98284,98285,98288],{"style":51782},[363,98286],{"className":98287,"style":651},[650],[363,98289,98291],{"className":98290},[655,656,657,658],[363,98292,2810],{"className":98293},[407,658],[363,98295,666],{"className":98296},[665],[363,98298,98300],{"className":98299},[638],[363,98301,98304],{"className":98302,"style":98303},[642],"height:0.3997em;",[363,98305],{},[363,98307],{"className":98308,"style":506},[505],[363,98310,471],{"className":98311},[510],[363,98313],{"className":98314,"style":506},[505],[363,98316,98318,98321,98324,98327,98330,98333,98336],{"className":98317},[398],[363,98319],{"className":98320,"style":5959},[402],[363,98322,1634],{"className":98323,"style":5964},[1831,1832,5963],[363,98325],{"className":98326,"style":754},[505],[363,98328,11],{"className":98329},[407,408],[363,98331],{"className":98332,"style":506},[505],[363,98334,471],{"className":98335},[510],[363,98337],{"className":98338,"style":506},[505],[363,98340,98342,98345],{"className":98341},[398],[363,98343],{"className":98344,"style":520},[402],[363,98346,465],{"className":98347},[407],"），则 ",[363,98350,98352,98410],{"className":98351,"translate":367},[366],[363,98353,98355],{"className":98354},[371],[373,98356,98357],{"xmlns":375},[377,98358,98359,98407],{},[380,98360,98361,98367,98369,98371,98373,98375,98377,98379,98389,98391,98395,98397,98401],{},[543,98362,98363,98365],{},[383,98364,44907],{},[383,98366,34231],{},[458,98368,461],{"stretchy":460},[383,98370,554],{},[458,98372,898],{"separator":394},[383,98374,561],{},[458,98376,468],{"stretchy":460},[458,98378,471],{},[1602,98380,98381],{"scriptlevel":474,"displaystyle":460},[586,98382,98383,98385],{},[463,98384,465],{},[34686,98386,98387],{},[463,98388,2810],{},[458,98390,558],{"stretchy":460},[34686,98392,98393],{},[383,98394,11],{},[458,98396,5160],{},[34686,98398,98399],{},[383,98400,1291],{},[543,98402,98403,98405],{},[458,98404,558],{"stretchy":460},[463,98406,2810],{},[387,98408,98409],{"encoding":389},"\\rho_H(P,Q)=\\tfrac{1}{\\sqrt2}\\lVert\\sqrt p-\\sqrt q\\rVert_2",[363,98411,98413,98486,98663],{"className":98412,"ariaHidden":394},[393],[363,98414,98416,98419,98459,98462,98465,98468,98471,98474,98477,98480,98483],{"className":98415},[398],[363,98417],{"className":98418,"style":487},[402],[363,98420,98422,98425],{"className":98421},[407],[363,98423,44907],{"className":98424},[407,408],[363,98426,98428],{"className":98427},[629],[363,98429,98431,98451],{"className":98430},[633,634],[363,98432,98434,98448],{"className":98433},[638],[363,98435,98437],{"className":98436,"style":727},[642],[363,98438,98439,98442],{"style":730},[363,98440],{"className":98441,"style":651},[650],[363,98443,98445],{"className":98444},[655,656,657,658],[363,98446,34231],{"className":98447,"style":34385},[407,408,658],[363,98449,666],{"className":98450},[665],[363,98452,98454],{"className":98453},[638],[363,98455,98457],{"className":98456,"style":8315},[642],[363,98458],{},[363,98460,461],{"className":98461},[494],[363,98463,554],{"className":98464,"style":682},[407,408],[363,98466,898],{"className":98467},[920],[363,98469],{"className":98470,"style":754},[505],[363,98472,561],{"className":98473},[407,408],[363,98475,468],{"className":98476},[501],[363,98478],{"className":98479,"style":506},[505],[363,98481,471],{"className":98482},[510],[363,98484],{"className":98485,"style":506},[505],[363,98487,98489,98493,98607,98610,98654,98657,98660],{"className":98488},[398],[363,98490],{"className":98491,"style":98492},[402],"height:1.3831em;vertical-align:-0.538em;",[363,98494,98496,98499,98604],{"className":98495},[407],[363,98497],{"className":98498},[494,789],[363,98500,98502],{"className":98501},[586],[363,98503,98505,98595],{"className":98504},[633,634],[363,98506,98508,98592],{"className":98507},[638],[363,98509,98511,98570,98578],{"className":98510,"style":2871},[642],[363,98512,98514,98517],{"style":98513},"top:-2.551em;",[363,98515],{"className":98516,"style":809},[650],[363,98518,98520],{"className":98519},[655,656,657,658],[363,98521,98523],{"className":98522},[407,658],[363,98524,98526],{"className":98525},[407,34714,658],[363,98527,98529,98561],{"className":98528},[633,634],[363,98530,98532,98558],{"className":98531},[638],[363,98533,98536,98545],{"className":98534,"style":98535},[642],"height:0.9128em;",[363,98537,98539,98542],{"className":98538,"style":12210},[6654],[363,98540],{"className":98541,"style":809},[650],[363,98543,2810],{"className":98544,"style":34734},[407,658],[363,98546,98548,98551],{"style":98547},"top:-2.8728em;",[363,98549],{"className":98550,"style":809},[650],[363,98552,98554],{"className":98553,"style":34791},[34790,658],[6670,98555,98556],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,98557],{"d":34798},[363,98559,666],{"className":98560},[665],[363,98562,98564],{"className":98563},[638],[363,98565,98568],{"className":98566,"style":98567},[642],"height:0.1272em;",[363,98569],{},[363,98571,98572,98575],{"style":821},[363,98573],{"className":98574,"style":809},[650],[363,98576],{"className":98577,"style":829},[828],[363,98579,98580,98583],{"style":2897},[363,98581],{"className":98582,"style":809},[650],[363,98584,98586],{"className":98585},[655,656,657,658],[363,98587,98589],{"className":98588},[407,658],[363,98590,465],{"className":98591},[407,658],[363,98593,666],{"className":98594},[665],[363,98596,98598],{"className":98597},[638],[363,98599,98602],{"className":98600,"style":98601},[642],"height:0.538em;",[363,98603],{},[363,98605],{"className":98606},[501,789],[363,98608,558],{"className":98609},[494],[363,98611,98613],{"className":98612},[407,34714],[363,98614,98616,98646],{"className":98615},[633,634],[363,98617,98619,98643],{"className":98618},[638],[363,98620,98622,98631],{"className":98621,"style":39374},[642],[363,98623,98625,98628],{"className":98624,"style":12210},[6654],[363,98626],{"className":98627,"style":809},[650],[363,98629,11],{"className":98630,"style":34734},[407,408],[363,98632,98633,98636],{"style":39386},[363,98634],{"className":98635,"style":809},[650],[363,98637,98639],{"className":98638,"style":34791},[34790],[6670,98640,98641],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,98642],{"d":34798},[363,98644,666],{"className":98645},[665],[363,98647,98649],{"className":98648},[638],[363,98650,98652],{"className":98651,"style":39406},[642],[363,98653],{},[363,98655],{"className":98656,"style":2934},[505],[363,98658,5160],{"className":98659},[2938],[363,98661],{"className":98662,"style":2934},[505],[363,98664,98666,98670,98714],{"className":98665},[398],[363,98667],{"className":98668,"style":98669},[402],"height:1.0869em;vertical-align:-0.3369em;",[363,98671,98673],{"className":98672},[407,34714],[363,98674,98676,98706],{"className":98675},[633,634],[363,98677,98679,98703],{"className":98678},[638],[363,98680,98682,98691],{"className":98681,"style":39374},[642],[363,98683,98685,98688],{"className":98684,"style":12210},[6654],[363,98686],{"className":98687,"style":809},[650],[363,98689,1291],{"className":98690,"style":39446},[407,408],[363,98692,98693,98696],{"style":39386},[363,98694],{"className":98695,"style":809},[650],[363,98697,98699],{"className":98698,"style":34791},[34790],[6670,98700,98701],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,98702],{"d":34798},[363,98704,666],{"className":98705},[665],[363,98707,98709],{"className":98708},[638],[363,98710,98712],{"className":98711,"style":39406},[642],[363,98713],{},[363,98715,98717,98720],{"className":98716},[501],[363,98718,558],{"className":98719},[501],[363,98721,98723],{"className":98722},[629],[363,98724,98726,98746],{"className":98725},[633,634],[363,98727,98729,98743],{"className":98728},[638],[363,98730,98732],{"className":98731,"style":11480},[642],[363,98733,98734,98737],{"style":730},[363,98735],{"className":98736,"style":651},[650],[363,98738,98740],{"className":98739},[655,656,657,658],[363,98741,2810],{"className":98742},[407,658],[363,98744,666],{"className":98745},[665],[363,98747,98749],{"className":98748},[638],[363,98750,98752],{"className":98751,"style":8315},[642],[363,98753],{}," 就是单位球面上的欧氏距离——度量公理（对称、三角不等式）由 ",[363,98756,98758,98776],{"className":98757,"translate":367},[366],[363,98759,98761],{"className":98760},[371],[373,98762,98763],{"xmlns":375},[377,98764,98765,98773],{},[380,98766,98767],{},[7161,98768,98769,98771],{},[383,98770,22240],{},[463,98772,2810],{},[387,98774,98775],{"encoding":389},"L^2",[363,98777,98779],{"className":98778,"ariaHidden":394},[393],[363,98780,98782,98785],{"className":98781},[398],[363,98783],{"className":98784,"style":20375},[402],[363,98786,98788,98791],{"className":98787},[407],[363,98789,22240],{"className":98790},[407,408],[363,98792,98794],{"className":98793},[629],[363,98795,98797],{"className":98796},[633],[363,98798,98800],{"className":98799},[638],[363,98801,98803],{"className":98802,"style":20375},[642],[363,98804,98805,98808],{"style":7212},[363,98806],{"className":98807,"style":651},[650],[363,98809,98811],{"className":98810},[655,656,657,658],[363,98812,2810],{"className":98813},[407,658]," 距离直接继承，非退化由\"开平方是单射\"保证；",[7012,98816,98817,99133,99134,99213],{},[1572,98818,98819,98957,98958,99132],{},[363,98820,98822,98852],{"className":98821,"translate":367},[366],[363,98823,98825],{"className":98824},[371],[373,98826,98827],{"xmlns":375},[377,98828,98829,98849],{},[380,98830,98831],{},[34686,98832,98833],{},[380,98834,98835,98837,98839],{},[463,98836,2810],{},[1644,98838,1646],{},[543,98840,98841,98843],{},[383,98842,547],{},[380,98844,98845,98847],{},[383,98846,24090],{},[383,98848,26084],{},[387,98850,98851],{"encoding":389},"\\sqrt{2\\,D_{JS}}",[363,98853,98855],{"className":98854,"ariaHidden":394},[393],[363,98856,98858,98861],{"className":98857},[398],[363,98859],{"className":98860,"style":34710},[402],[363,98862,98864],{"className":98863},[407,34714],[363,98865,98867,98949],{"className":98866},[633,634],[363,98868,98870,98946],{"className":98869},[638],[363,98871,98873,98934],{"className":98872,"style":34724},[642],[363,98874,98876,98879],{"className":98875,"style":12210},[6654],[363,98877],{"className":98878,"style":809},[650],[363,98880,98882,98885,98888],{"className":98881,"style":34734},[407],[363,98883,2810],{"className":98884},[407],[363,98886],{"className":98887,"style":754},[505],[363,98889,98891,98894],{"className":98890},[407],[363,98892,547],{"className":98893,"style":625},[407,408],[363,98895,98897],{"className":98896},[629],[363,98898,98900,98926],{"className":98899},[633,634],[363,98901,98903,98923],{"className":98902},[638],[363,98904,98906],{"className":98905,"style":727},[642],[363,98907,98908,98911],{"style":646},[363,98909],{"className":98910,"style":651},[650],[363,98912,98914],{"className":98913},[655,656,657,658],[363,98915,98917,98920],{"className":98916},[407,658],[363,98918,24090],{"className":98919,"style":24500},[407,408,658],[363,98921,26084],{"className":98922,"style":26208},[407,408,658],[363,98924,666],{"className":98925},[665],[363,98927,98929],{"className":98928},[638],[363,98930,98932],{"className":98931,"style":8315},[642],[363,98933],{},[363,98935,98936,98939],{"style":34783},[363,98937],{"className":98938,"style":809},[650],[363,98940,98942],{"className":98941,"style":34791},[34790],[6670,98943,98944],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,98945],{"d":34798},[363,98947,666],{"className":98948},[665],[363,98950,98952],{"className":98951},[638],[363,98953,98955],{"className":98954,"style":34808},[642],[363,98956],{},"（等价地 ",[363,98959,98961,98989],{"className":98960,"translate":367},[366],[363,98962,98964],{"className":98963},[371],[373,98965,98966],{"xmlns":375},[377,98967,98968,98986],{},[380,98969,98970],{},[34686,98971,98972],{},[543,98973,98974,98976],{},[383,98975,547],{},[543,98977,98978,98980],{},[383,98979,385],{},[380,98981,98982,98984],{},[383,98983,24090],{},[383,98985,26084],{},[387,98987,98988],{"encoding":389},"\\sqrt{D_{f_{JS}}}",[363,98990,98992],{"className":98991,"ariaHidden":394},[393],[363,98993,98995,98999],{"className":98994},[398],[363,98996],{"className":98997,"style":98998},[402],"height:1.24em;vertical-align:-0.3564em;",[363,99000,99002],{"className":99001},[407,34714],[363,99003,99005,99123],{"className":99004},[633,634],[363,99006,99008,99120],{"className":99007},[638],[363,99009,99012,99107],{"className":99010,"style":99011},[642],"height:0.8836em;",[363,99013,99015,99018],{"className":99014,"style":83883},[6654],[363,99016],{"className":99017,"style":15193},[650],[363,99019,99021],{"className":99020,"style":41508},[407],[363,99022,99024,99027],{"className":99023},[407],[363,99025,547],{"className":99026,"style":625},[407,408],[363,99028,99030],{"className":99029},[629],[363,99031,99033,99099],{"className":99032},[633,634],[363,99034,99036,99096],{"className":99035},[638],[363,99037,99039],{"className":99038,"style":643},[642],[363,99040,99041,99044],{"style":646},[363,99042],{"className":99043,"style":651},[650],[363,99045,99047],{"className":99046},[655,656,657,658],[363,99048,99050],{"className":99049},[407,658],[363,99051,99053,99056],{"className":99052},[407,658],[363,99054,385],{"className":99055,"style":409},[407,408,658],[363,99057,99059],{"className":99058},[629],[363,99060,99062,99088],{"className":99061},[633,634],[363,99063,99065,99085],{"className":99064},[638],[363,99066,99068],{"className":99067,"style":6445},[642],[363,99069,99070,99073],{"style":30549},[363,99071],{"className":99072,"style":30553},[650],[363,99074,99076],{"className":99075},[655,30557,10021,658],[363,99077,99079,99082],{"className":99078},[407,658],[363,99080,24090],{"className":99081,"style":24500},[407,408,658],[363,99083,26084],{"className":99084,"style":26208},[407,408,658],[363,99086,666],{"className":99087},[665],[363,99089,99091],{"className":99090},[638],[363,99092,99094],{"className":99093,"style":30576},[642],[363,99095],{},[363,99097,666],{"className":99098},[665],[363,99100,99102],{"className":99101},[638],[363,99103,99105],{"className":99104,"style":673},[642],[363,99106],{},[363,99108,99110,99113],{"style":99109},"top:-2.8436em;",[363,99111],{"className":99112,"style":15193},[650],[363,99114,99116],{"className":99115,"style":83975},[34790],[6670,99117,99118],{"xmlns":6672,"width":6673,"height":83978,"viewBox":83979,"preserveAspectRatio":6676},[6678,99119],{"d":83982},[363,99121,666],{"className":99122},[665],[363,99124,99126],{"className":99125},[638],[363,99127,99130],{"className":99128,"style":99129},[642],"height:0.3564em;",[363,99131],{}," 规范化后）是度量","（Endres–Schindelin 的结论），其证明用到了 ",[363,99135,99137,99158],{"className":99136,"translate":367},[366],[363,99138,99140],{"className":99139},[371],[373,99141,99142],{"xmlns":375},[377,99143,99144,99156],{},[380,99145,99146],{},[543,99147,99148,99150],{},[383,99149,385],{},[380,99151,99152,99154],{},[383,99153,24090],{},[383,99155,26084],{},[387,99157,31102],{"encoding":389},[363,99159,99161],{"className":99160,"ariaHidden":394},[393],[363,99162,99164,99167],{"className":99163},[398],[363,99165],{"className":99166,"style":403},[402],[363,99168,99170,99173],{"className":99169},[407],[363,99171,385],{"className":99172,"style":409},[407,408],[363,99174,99176],{"className":99175},[629],[363,99177,99179,99205],{"className":99178},[633,634],[363,99180,99182,99202],{"className":99181},[638],[363,99183,99185],{"className":99184,"style":727},[642],[363,99186,99187,99190],{"style":27856},[363,99188],{"className":99189,"style":651},[650],[363,99191,99193],{"className":99192},[655,656,657,658],[363,99194,99196,99199],{"className":99195},[407,658],[363,99197,24090],{"className":99198,"style":24500},[407,408,658],[363,99200,26084],{"className":99201,"style":26208},[407,408,658],[363,99203,666],{"className":99204},[665],[363,99206,99208],{"className":99207},[638],[363,99209,99211],{"className":99210,"style":8315},[642],[363,99212],{}," 对应生成元的\"负定型\"性质。",[11,99215,99216,99217,99333,99334,99414,99415,99443,99444,99472],{},"反过来，不对称显然排除度量；即使对称，",[363,99218,99220,99240],{"className":99219,"translate":367},[366],[363,99221,99223],{"className":99222},[371],[373,99224,99225],{"xmlns":375},[377,99226,99227,99237],{},[380,99228,99229],{},[34686,99230,99231],{},[543,99232,99233,99235],{},[383,99234,547],{},[383,99236,385],{},[387,99238,99239],{"encoding":389},"\\sqrt{D_f}",[363,99241,99243],{"className":99242,"ariaHidden":394},[393],[363,99244,99246,99249],{"className":99245},[398],[363,99247],{"className":99248,"style":98998},[402],[363,99250,99252],{"className":99251},[407,34714],[363,99253,99255,99325],{"className":99254},[633,634],[363,99256,99258,99322],{"className":99257},[638],[363,99259,99261,99310],{"className":99260,"style":99011},[642],[363,99262,99264,99267],{"className":99263,"style":83883},[6654],[363,99265],{"className":99266,"style":15193},[650],[363,99268,99270],{"className":99269,"style":41508},[407],[363,99271,99273,99276],{"className":99272},[407],[363,99274,547],{"className":99275,"style":625},[407,408],[363,99277,99279],{"className":99278},[629],[363,99280,99282,99302],{"className":99281},[633,634],[363,99283,99285,99299],{"className":99284},[638],[363,99286,99288],{"className":99287,"style":643},[642],[363,99289,99290,99293],{"style":646},[363,99291],{"className":99292,"style":651},[650],[363,99294,99296],{"className":99295},[655,656,657,658],[363,99297,385],{"className":99298,"style":409},[407,408,658],[363,99300,666],{"className":99301},[665],[363,99303,99305],{"className":99304},[638],[363,99306,99308],{"className":99307,"style":673},[642],[363,99309],{},[363,99311,99312,99315],{"style":99109},[363,99313],{"className":99314,"style":15193},[650],[363,99316,99318],{"className":99317,"style":83975},[34790],[6670,99319,99320],{"xmlns":6672,"width":6673,"height":83978,"viewBox":83979,"preserveAspectRatio":6676},[6678,99321],{"d":83982},[363,99323,666],{"className":99324},[665],[363,99326,99328],{"className":99327},[638],[363,99329,99331],{"className":99330,"style":99129},[642],[363,99332],{}," 也不自动是度量。例如全变差 ",[363,99335,99337,99359],{"className":99336,"translate":367},[366],[363,99338,99340],{"className":99339},[371],[373,99341,99342],{"xmlns":375},[377,99343,99344,99356],{},[380,99345,99346],{},[543,99347,99348,99350],{},[383,99349,547],{},[380,99351,99352,99354],{},[383,99353,5739],{},[383,99355,35197],{},[387,99357,99358],{"encoding":389},"D_{TV}",[363,99360,99362],{"className":99361,"ariaHidden":394},[393],[363,99363,99365,99368],{"className":99364},[398],[363,99366],{"className":99367,"style":16308},[402],[363,99369,99371,99374],{"className":99370},[407],[363,99372,547],{"className":99373,"style":625},[407,408],[363,99375,99377],{"className":99376},[629],[363,99378,99380,99406],{"className":99379},[633,634],[363,99381,99383,99403],{"className":99382},[638],[363,99384,99386],{"className":99385,"style":727},[642],[363,99387,99388,99391],{"style":646},[363,99389],{"className":99390,"style":651},[650],[363,99392,99394],{"className":99393},[655,656,657,658],[363,99395,99397,99400],{"className":99396},[407,658],[363,99398,5739],{"className":99399,"style":682},[407,408,658],[363,99401,35197],{"className":99402,"style":2934},[407,408,658],[363,99404,666],{"className":99405},[665],[363,99407,99409],{"className":99408},[638],[363,99410,99412],{"className":99411,"style":8315},[642],[363,99413],{}," 本身就是度量，但若取某凸积 ",[363,99416,99418,99431],{"className":99417,"translate":367},[366],[363,99419,99421],{"className":99420},[371],[373,99422,99423],{"xmlns":375},[377,99424,99425,99429],{},[380,99426,99427],{},[383,99428,385],{},[387,99430,385],{"encoding":389},[363,99432,99434],{"className":99433,"ariaHidden":394},[393],[363,99435,99437,99440],{"className":99436},[398],[363,99438],{"className":99439,"style":403},[402],[363,99441,385],{"className":99442,"style":409},[407,408]," 的散度再做开方，三角不等式可能失效——这依赖 ",[363,99445,99447,99460],{"className":99446,"translate":367},[366],[363,99448,99450],{"className":99449},[371],[373,99451,99452],{"xmlns":375},[377,99453,99454,99458],{},[380,99455,99456],{},[383,99457,385],{},[387,99459,385],{"encoding":389},[363,99461,99463],{"className":99462,"ariaHidden":394},[393],[363,99464,99466,99469],{"className":99465},[398],[363,99467],{"className":99468,"style":403},[402],[363,99470,385],{"className":99471,"style":409},[407,408]," 是否落在\"负定（negative type）\"函数类中；不是自动成立的。",[11,99474,99475,99478,99479,99481,99482,99532,99533,99561,99562,99641],{},[1572,99476,99477],{},"与度量的对照结论："," f-散度的正确身份是",[1572,99480,52850],{},"（divergence）：非负、在 ",[363,99483,99485,99502],{"className":99484,"translate":367},[366],[363,99486,99488],{"className":99487},[371],[373,99489,99490],{"xmlns":375},[377,99491,99492,99500],{},[380,99493,99494,99496,99498],{},[383,99495,554],{},[458,99497,471],{},[383,99499,561],{},[387,99501,10618],{"encoding":389},[363,99503,99505,99523],{"className":99504,"ariaHidden":394},[393],[363,99506,99508,99511,99514,99517,99520],{"className":99507},[398],[363,99509],{"className":99510,"style":1011},[402],[363,99512,554],{"className":99513,"style":682},[407,408],[363,99515],{"className":99516,"style":506},[505],[363,99518,471],{"className":99519},[510],[363,99521],{"className":99522,"style":506},[505],[363,99524,99526,99529],{"className":99525},[398],[363,99527],{"className":99528,"style":913},[402],[363,99530,561],{"className":99531},[407,408]," 处取零，但不要求对称与三角不等式。当我们需要真距离时（例如做收敛分析、中心化、 ",[363,99534,99536,99549],{"className":99535,"translate":367},[366],[363,99537,99539],{"className":99538},[371],[373,99540,99541],{"xmlns":375},[377,99542,99543,99547],{},[380,99544,99545],{},[383,99546,7911],{},[387,99548,7911],{"encoding":389},[363,99550,99552],{"className":99551,"ariaHidden":394},[393],[363,99553,99555,99558],{"className":99554},[398],[363,99556],{"className":99557,"style":12944},[402],[363,99559,7911],{"className":99560,"style":8614},[407,408],"-中心聚类），就从 f-散度族里挑那些 ",[363,99563,99565,99581],{"className":99564,"translate":367},[366],[363,99566,99568],{"className":99567},[371],[373,99569,99570],{"xmlns":375},[377,99571,99572,99578],{},[380,99573,99574],{},[34686,99575,99576],{},[458,99577,3646],{"lspace":1594,"rspace":1594},[387,99579,99580],{"encoding":389},"\\sqrt{\\cdot}",[363,99582,99584],{"className":99583,"ariaHidden":394},[393],[363,99585,99587,99591],{"className":99586},[398],[363,99588],{"className":99589,"style":99590},[402],"height:1.04em;vertical-align:-0.2328em;",[363,99592,99594],{"className":99593},[407,34714],[363,99595,99597,99632],{"className":99596},[633,634],[363,99598,99600,99629],{"className":99599},[638],[363,99601,99604,99616],{"className":99602,"style":99603},[642],"height:0.8072em;",[363,99605,99607,99610],{"className":99606,"style":12210},[6654],[363,99608],{"className":99609,"style":809},[650],[363,99611,99613],{"className":99612,"style":34734},[407],[363,99614,3646],{"className":99615},[407],[363,99617,99619,99622],{"style":99618},"top:-2.7672em;",[363,99620],{"className":99621,"style":809},[650],[363,99623,99625],{"className":99624,"style":34791},[34790],[6670,99626,99627],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,99628],{"d":34798},[363,99630,666],{"className":99631},[665],[363,99633,99635],{"className":99634},[638],[363,99636,99639],{"className":99637,"style":99638},[642],"height:0.2328em;",[363,99640],{}," 后成为度量的成员（Hellinger、JS、TV），或干脆换成真正的度量类（第 6 节的 IPM）。",[18,99643,99645],{"id":99644},"_5-变分表示与-f-gan","5. 变分表示与 f-GAN",[2658,99647,99649],{"id":99648},"_51-可训练目标","5.1 可训练目标",[11,99651,99652],{},"4.4 节给出精确对偶：",[363,99654,99656],{"className":99655,"translate":367},[528],[363,99657,99659,99753],{"className":99658,"translate":367},[366],[363,99660,99662],{"className":99661},[371],[373,99663,99664],{"xmlns":375,"display":537},[377,99665,99666,99750],{},[380,99667,99668,99674,99676,99678,99680,99682,99684,99686,99696,99698,99704,99706,99708,99710,99712,99714,99716,99718,99724,99726,99732,99734,99736,99738,99740,99742,99744,99746,99748],{},[543,99669,99670,99672],{},[383,99671,547],{},[383,99673,385],{},[458,99675,461],{"stretchy":460},[383,99677,554],{},[383,99679,558],{"mathvariant":557},[383,99681,561],{},[458,99683,468],{"stretchy":460},[458,99685,471],{},[6363,99687,99688,99694],{},[380,99689,99690,99692],{},[383,99691,35779],{},[458,99693,4450],{},[383,99695,4505],{},[458,99697,3245],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[543,99699,99700,99702],{},[383,99701,571],{"mathvariant":570},[383,99703,554],{},[458,99705,578],{"stretchy":460},[383,99707,4505],{},[458,99709,461],{"stretchy":460},[383,99711,945],{},[458,99713,468],{"stretchy":460},[458,99715,605],{"stretchy":460},[458,99717,5160],{},[543,99719,99720,99722],{},[383,99721,571],{"mathvariant":570},[383,99723,561],{},[458,99725,578],{"stretchy":460},[7161,99727,99728,99730],{},[383,99729,385],{},[458,99731,7920],{},[458,99733,461],{"stretchy":460},[383,99735,4505],{},[458,99737,461],{"stretchy":460},[383,99739,945],{},[458,99741,468],{"stretchy":460},[458,99743,468],{"stretchy":460},[458,99745,605],{"stretchy":460},[458,99747,3255],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[383,99749,4722],{"mathvariant":557},[387,99751,99752],{"encoding":389},"D_f(P\\|Q)\n=\\sup_{g}\\Big\\{\\mathbb E_P[g(X)]\n-\\mathbb E_Q[f^*(g(X))]\\Big\\}.",[363,99754,99756,99826,99953],{"className":99755,"ariaHidden":394},[393],[363,99757,99759,99762,99802,99805,99808,99811,99814,99817,99820,99823],{"className":99758},[398],[363,99760],{"className":99761,"style":618},[402],[363,99763,99765,99768],{"className":99764},[407],[363,99766,547],{"className":99767,"style":625},[407,408],[363,99769,99771],{"className":99770},[629],[363,99772,99774,99794],{"className":99773},[633,634],[363,99775,99777,99791],{"className":99776},[638],[363,99778,99780],{"className":99779,"style":643},[642],[363,99781,99782,99785],{"style":646},[363,99783],{"className":99784,"style":651},[650],[363,99786,99788],{"className":99787},[655,656,657,658],[363,99789,385],{"className":99790,"style":409},[407,408,658],[363,99792,666],{"className":99793},[665],[363,99795,99797],{"className":99796},[638],[363,99798,99800],{"className":99799,"style":673},[642],[363,99801],{},[363,99803,461],{"className":99804},[494],[363,99806,554],{"className":99807,"style":682},[407,408],[363,99809,558],{"className":99810},[407],[363,99812,561],{"className":99813},[407,408],[363,99815,468],{"className":99816},[501],[363,99818],{"className":99819,"style":506},[505],[363,99821,471],{"className":99822},[510],[363,99824],{"className":99825,"style":506},[505],[363,99827,99829,99833,99880,99883,99889,99929,99932,99935,99938,99941,99944,99947,99950],{"className":99828},[398],[363,99830],{"className":99831,"style":99832},[402],"height:2.1805em;vertical-align:-1.0305em;",[363,99834,99836],{"className":99835},[1831,14063],[363,99837,99839,99872],{"className":99838},[633,634],[363,99840,99842,99869],{"className":99841},[638],[363,99843,99845,99859],{"className":99844,"style":2692},[642],[363,99846,99847,99850],{"style":61537},[363,99848],{"className":99849,"style":809},[650],[363,99851,99853],{"className":99852},[655,656,657,658],[363,99854,99856],{"className":99855},[407,658],[363,99857,4505],{"className":99858,"style":1328},[407,408,658],[363,99860,99861,99864],{"style":12210},[363,99862],{"className":99863,"style":809},[650],[363,99865,99866],{},[363,99867,35779],{"className":99868},[1831],[363,99870,666],{"className":99871},[665],[363,99873,99875],{"className":99874},[638],[363,99876,99878],{"className":99877,"style":61569},[642],[363,99879],{},[363,99881],{"className":99882,"style":754},[505],[363,99884,99886],{"className":99885},[407],[363,99887,3245],{"className":99888},[767,4067],[363,99890,99892,99895],{"className":99891},[407],[363,99893,571],{"className":99894},[407,714],[363,99896,99898],{"className":99897},[629],[363,99899,99901,99921],{"className":99900},[633,634],[363,99902,99904,99918],{"className":99903},[638],[363,99905,99907],{"className":99906,"style":727},[642],[363,99908,99909,99912],{"style":730},[363,99910],{"className":99911,"style":651},[650],[363,99913,99915],{"className":99914},[655,656,657,658],[363,99916,554],{"className":99917,"style":682},[407,408,658],[363,99919,666],{"className":99920},[665],[363,99922,99924],{"className":99923},[638],[363,99925,99927],{"className":99926,"style":8315},[642],[363,99928],{},[363,99930,578],{"className":99931},[494],[363,99933,4505],{"className":99934,"style":1328},[407,408],[363,99936,461],{"className":99937},[494],[363,99939,945],{"className":99940,"style":9234},[407,408],[363,99942,20737],{"className":99943},[501],[363,99945],{"className":99946,"style":2934},[505],[363,99948,5160],{"className":99949},[2938],[363,99951],{"className":99952,"style":2934},[505],[363,99954,99956,99959,99999,100002,100031,100034,100037,100040,100043,100047,100053],{"className":99955},[398],[363,99957],{"className":99958,"style":68464},[402],[363,99960,99962,99965],{"className":99961},[407],[363,99963,571],{"className":99964},[407,714],[363,99966,99968],{"className":99967},[629],[363,99969,99971,99991],{"className":99970},[633,634],[363,99972,99974,99988],{"className":99973},[638],[363,99975,99977],{"className":99976,"style":727},[642],[363,99978,99979,99982],{"style":730},[363,99980],{"className":99981,"style":651},[650],[363,99983,99985],{"className":99984},[655,656,657,658],[363,99986,561],{"className":99987},[407,408,658],[363,99989,666],{"className":99990},[665],[363,99992,99994],{"className":99993},[638],[363,99995,99997],{"className":99996,"style":673},[642],[363,99998],{},[363,100000,578],{"className":100001},[494],[363,100003,100005,100008],{"className":100004},[407],[363,100006,385],{"className":100007,"style":409},[407,408],[363,100009,100011],{"className":100010},[629],[363,100012,100014],{"className":100013},[633],[363,100015,100017],{"className":100016},[638],[363,100018,100020],{"className":100019,"style":8595},[642],[363,100021,100022,100025],{"style":8624},[363,100023],{"className":100024,"style":651},[650],[363,100026,100028],{"className":100027},[655,656,657,658],[363,100029,7920],{"className":100030},[2938,658],[363,100032,461],{"className":100033},[494],[363,100035,4505],{"className":100036,"style":1328},[407,408],[363,100038,461],{"className":100039},[494],[363,100041,945],{"className":100042,"style":9234},[407,408],[363,100044,100046],{"className":100045},[501],"))]",[363,100048,100050],{"className":100049},[407],[363,100051,3255],{"className":100052},[767,4067],[363,100054,4722],{"className":100055},[407],[11,100057,68479,100058,100086,100087,100115,100116,100185,100186,100189,100190,100261],{},[363,100059,100061,100074],{"className":100060,"translate":367},[366],[363,100062,100064],{"className":100063},[371],[373,100065,100066],{"xmlns":375},[377,100067,100068,100072],{},[380,100069,100070],{},[383,100071,554],{},[387,100073,554],{"encoding":389},[363,100075,100077],{"className":100076,"ariaHidden":394},[393],[363,100078,100080,100083],{"className":100079},[398],[363,100081],{"className":100082,"style":1011},[402],[363,100084,554],{"className":100085,"style":682},[407,408]," 是数据分布、",[363,100088,100090,100103],{"className":100089,"translate":367},[366],[363,100091,100093],{"className":100092},[371],[373,100094,100095],{"xmlns":375},[377,100096,100097,100101],{},[380,100098,100099],{},[383,100100,561],{},[387,100102,561],{"encoding":389},[363,100104,100106],{"className":100105,"ariaHidden":394},[393],[363,100107,100109,100112],{"className":100108},[398],[363,100110],{"className":100111,"style":913},[402],[363,100113,561],{"className":100114},[407,408]," 是生成分布时，右端可直接用两批样本做蒙特卡洛估计，得到 ",[363,100117,100119,100136],{"className":100118,"translate":367},[366],[363,100120,100122],{"className":100121},[371],[373,100123,100124],{"xmlns":375},[377,100125,100126,100134],{},[380,100127,100128],{},[543,100129,100130,100132],{},[383,100131,547],{},[383,100133,385],{},[387,100135,4369],{"encoding":389},[363,100137,100139],{"className":100138,"ariaHidden":394},[393],[363,100140,100142,100145],{"className":100141},[398],[363,100143],{"className":100144,"style":4379},[402],[363,100146,100148,100151],{"className":100147},[407],[363,100149,547],{"className":100150,"style":625},[407,408],[363,100152,100154],{"className":100153},[629],[363,100155,100157,100177],{"className":100156},[633,634],[363,100158,100160,100174],{"className":100159},[638],[363,100161,100163],{"className":100162,"style":643},[642],[363,100164,100165,100168],{"style":646},[363,100166],{"className":100167,"style":651},[650],[363,100169,100171],{"className":100170},[655,656,657,658],[363,100172,385],{"className":100173,"style":409},[407,408,658],[363,100175,666],{"className":100176},[665],[363,100178,100180],{"className":100179},[638],[363,100181,100183],{"className":100182,"style":673},[642],[363,100184],{}," 的一个",[1572,100187,100188],{},"下界","，并用一个网络 ",[363,100191,100193,100212],{"className":100192,"translate":367},[366],[363,100194,100196],{"className":100195},[371],[373,100197,100198],{"xmlns":375},[377,100199,100200,100209],{},[380,100201,100202],{},[543,100203,100204,100206],{},[383,100205,4505],{},[383,100207,100208],{},"ω",[387,100210,100211],{"encoding":389},"g_\\omega",[363,100213,100215],{"className":100214,"ariaHidden":394},[393],[363,100216,100218,100221],{"className":100217},[398],[363,100219],{"className":100220,"style":2623},[402],[363,100222,100224,100227],{"className":100223},[407],[363,100225,4505],{"className":100226,"style":1328},[407,408],[363,100228,100230],{"className":100229},[629],[363,100231,100233,100253],{"className":100232},[633,634],[363,100234,100236,100250],{"className":100235},[638],[363,100237,100239],{"className":100238,"style":45276},[642],[363,100240,100241,100244],{"style":19190},[363,100242],{"className":100243,"style":651},[650],[363,100245,100247],{"className":100246},[655,656,657,658],[363,100248,100208],{"className":100249,"style":1328},[407,408,658],[363,100251,666],{"className":100252},[665],[363,100254,100256],{"className":100255},[638],[363,100257,100259],{"className":100258,"style":8315},[642],[363,100260],{}," 逼近最优解。于是",[363,100263,100265],{"className":100264,"translate":367},[528],[363,100266,100268,100398],{"className":100267,"translate":367},[366],[363,100269,100271],{"className":100270},[371],[373,100272,100273],{"xmlns":375,"display":537},[377,100274,100275,100395],{},[380,100276,100277,100288,100290,100292,100294,100296,100298,100304,100306,100308,100314,100328,100334,100336,100342,100344,100346,100352,100367,100373,100375,100381,100383,100389,100391,100393],{},[543,100278,100279,100286],{},[12158,100280,100281,100283],{"accent":394},[383,100282,547],{},[458,100284,100285],{"stretchy":394},"^",[383,100287,385],{},[458,100289,461],{"stretchy":460},[383,100291,554],{},[383,100293,558],{"mathvariant":557},[383,100295,561],{},[458,100297,34222],{"separator":394},[543,100299,100300,100302],{},[383,100301,4505],{},[383,100303,100208],{},[458,100305,468],{"stretchy":460},[458,100307,471],{},[586,100309,100310,100312],{},[463,100311,465],{},[383,100313,82643],{},[48667,100315,100316,100318,100326],{},[458,100317,13808],{},[380,100319,100320,100322,100324],{},[383,100321,12310],{},[458,100323,471],{},[463,100325,465],{},[383,100327,82643],{},[543,100329,100330,100332],{},[383,100331,4505],{},[383,100333,100208],{},[458,100335,461],{"stretchy":460},[543,100337,100338,100340],{},[383,100339,1121],{},[383,100341,12310],{},[458,100343,468],{"stretchy":460},[458,100345,5160],{},[586,100347,100348,100350],{},[463,100349,465],{},[383,100351,26670],{},[48667,100353,100354,100356,100365],{},[458,100355,13808],{},[380,100357,100358,100361,100363],{},[383,100359,100360],{},"j",[458,100362,471],{},[463,100364,465],{},[383,100366,26670],{},[7161,100368,100369,100371],{},[383,100370,385],{},[458,100372,7920],{},[458,100374,461],{"stretchy":460},[543,100376,100377,100379],{},[383,100378,4505],{},[383,100380,100208],{},[458,100382,461],{"stretchy":460},[543,100384,100385,100387],{},[383,100386,40584],{},[383,100388,100360],{},[458,100390,468],{"stretchy":460},[458,100392,468],{"stretchy":460},[383,100394,4722],{"mathvariant":557},[387,100396,100397],{"encoding":389},"\\widehat D_f(P\\|Q;g_\\omega)\n=\\frac1n\\sum_{i=1}^n g_\\omega(x_i)\n-\\frac1m\\sum_{j=1}^m f^*(g_\\omega(y_j)).",[363,100399,100401,100554,100790],{"className":100400,"ariaHidden":394},[393],[363,100402,100404,100408,100484,100487,100490,100493,100496,100499,100502,100542,100545,100548,100551],{"className":100403},[398],[363,100405],{"className":100406,"style":100407},[402],"height:1.2094em;vertical-align:-0.2861em;",[363,100409,100411,100450],{"className":100410},[407],[363,100412,100414],{"className":100413},[407,12198],[363,100415,100417],{"className":100416},[633],[363,100418,100420],{"className":100419},[638],[363,100421,100424,100432],{"className":100422,"style":100423},[642],"height:0.9233em;",[363,100425,100426,100429],{"style":12210},[363,100427],{"className":100428,"style":809},[650],[363,100430,547],{"className":100431,"style":625},[407,408],[363,100433,100436,100439],{"className":100434,"style":100435},[6654],"width:calc(100% - 0.1111em);margin-left:0.1111em;top:-3.6833em;",[363,100437],{"className":100438,"style":809},[650],[363,100440,100442],{"style":100441},"height:0.24em;",[6670,100443,100447],{"xmlns":6672,"width":76225,"height":100444,"viewBox":100445,"preserveAspectRatio":100446},"0.24em","0 0 1062 239","none",[6678,100448],{"d":100449},"M529 0h5l519 115c5 1 9 5 9 10 0 1-1 2-1 3l-4 22\nc-1 5-5 9-11 9h-2L532 67 19 159h-2c-5 0-9-4-11-9l-5-22c-1-6 2-12 8-13z",[363,100451,100453],{"className":100452},[629],[363,100454,100456,100476],{"className":100455},[633,634],[363,100457,100459,100473],{"className":100458},[638],[363,100460,100462],{"className":100461,"style":643},[642],[363,100463,100464,100467],{"style":646},[363,100465],{"className":100466,"style":651},[650],[363,100468,100470],{"className":100469},[655,656,657,658],[363,100471,385],{"className":100472,"style":409},[407,408,658],[363,100474,666],{"className":100475},[665],[363,100477,100479],{"className":100478},[638],[363,100480,100482],{"className":100481,"style":673},[642],[363,100483],{},[363,100485,461],{"className":100486},[494],[363,100488,554],{"className":100489,"style":682},[407,408],[363,100491,558],{"className":100492},[407],[363,100494,561],{"className":100495},[407,408],[363,100497,34222],{"className":100498},[920],[363,100500],{"className":100501,"style":754},[505],[363,100503,100505,100508],{"className":100504},[407],[363,100506,4505],{"className":100507,"style":1328},[407,408],[363,100509,100511],{"className":100510},[629],[363,100512,100514,100534],{"className":100513},[633,634],[363,100515,100517,100531],{"className":100516},[638],[363,100518,100520],{"className":100519,"style":45276},[642],[363,100521,100522,100525],{"style":19190},[363,100523],{"className":100524,"style":651},[650],[363,100526,100528],{"className":100527},[655,656,657,658],[363,100529,100208],{"className":100530,"style":1328},[407,408,658],[363,100532,666],{"className":100533},[665],[363,100535,100537],{"className":100536},[638],[363,100538,100540],{"className":100539,"style":8315},[642],[363,100541],{},[363,100543,468],{"className":100544},[501],[363,100546],{"className":100547,"style":506},[505],[363,100549,471],{"className":100550},[510],[363,100552],{"className":100553,"style":506},[505],[363,100555,100557,100561,100623,100626,100692,100695,100735,100738,100778,100781,100784,100787],{"className":100556},[398],[363,100558],{"className":100559,"style":100560},[402],"height:2.9291em;vertical-align:-1.2777em;",[363,100562,100564,100567,100620],{"className":100563},[407],[363,100565],{"className":100566},[494,789],[363,100568,100570],{"className":100569},[586],[363,100571,100573,100612],{"className":100572},[633,634],[363,100574,100576,100609],{"className":100575},[638],[363,100577,100579,100590,100598],{"className":100578,"style":23236},[642],[363,100580,100581,100584],{"style":805},[363,100582],{"className":100583,"style":809},[650],[363,100585,100587],{"className":100586},[407],[363,100588,82643],{"className":100589},[407,408],[363,100591,100592,100595],{"style":821},[363,100593],{"className":100594,"style":809},[650],[363,100596],{"className":100597,"style":829},[828],[363,100599,100600,100603],{"style":832},[363,100601],{"className":100602,"style":809},[650],[363,100604,100606],{"className":100605},[407],[363,100607,465],{"className":100608},[407],[363,100610,666],{"className":100611},[665],[363,100613,100615],{"className":100614},[638],[363,100616,100618],{"className":100617,"style":4125},[642],[363,100619],{},[363,100621],{"className":100622},[501,789],[363,100624],{"className":100625,"style":754},[505],[363,100627,100629],{"className":100628},[1831,14063],[363,100630,100632,100684],{"className":100631},[633,634],[363,100633,100635,100681],{"className":100634},[638],[363,100636,100639,100659,100669],{"className":100637,"style":100638},[642],"height:1.6514em;",[363,100640,100641,100644],{"style":14076},[363,100642],{"className":100643,"style":14080},[650],[363,100645,100647],{"className":100646},[655,656,657,658],[363,100648,100650,100653,100656],{"className":100649},[407,658],[363,100651,12310],{"className":100652},[407,408,658],[363,100654,471],{"className":100655},[510,658],[363,100657,465],{"className":100658},[407,658],[363,100660,100661,100664],{"style":14089},[363,100662],{"className":100663,"style":14080},[650],[363,100665,100666],{},[363,100667,13808],{"className":100668},[1831,1832,1833],[363,100670,100672,100675],{"style":100671},"top:-4.3em;margin-left:0em;",[363,100673],{"className":100674,"style":14080},[650],[363,100676,100678],{"className":100677},[655,656,657,658],[363,100679,82643],{"className":100680},[407,408,658],[363,100682,666],{"className":100683},[665],[363,100685,100687],{"className":100686},[638],[363,100688,100690],{"className":100689,"style":14107},[642],[363,100691],{},[363,100693],{"className":100694,"style":754},[505],[363,100696,100698,100701],{"className":100697},[407],[363,100699,4505],{"className":100700,"style":1328},[407,408],[363,100702,100704],{"className":100703},[629],[363,100705,100707,100727],{"className":100706},[633,634],[363,100708,100710,100724],{"className":100709},[638],[363,100711,100713],{"className":100712,"style":45276},[642],[363,100714,100715,100718],{"style":19190},[363,100716],{"className":100717,"style":651},[650],[363,100719,100721],{"className":100720},[655,656,657,658],[363,100722,100208],{"className":100723,"style":1328},[407,408,658],[363,100725,666],{"className":100726},[665],[363,100728,100730],{"className":100729},[638],[363,100731,100733],{"className":100732,"style":8315},[642],[363,100734],{},[363,100736,461],{"className":100737},[494],[363,100739,100741,100744],{"className":100740},[407],[363,100742,1121],{"className":100743},[407,408],[363,100745,100747],{"className":100746},[629],[363,100748,100750,100770],{"className":100749},[633,634],[363,100751,100753,100767],{"className":100752},[638],[363,100754,100756],{"className":100755,"style":12529},[642],[363,100757,100758,100761],{"style":730},[363,100759],{"className":100760,"style":651},[650],[363,100762,100764],{"className":100763},[655,656,657,658],[363,100765,12310],{"className":100766},[407,408,658],[363,100768,666],{"className":100769},[665],[363,100771,100773],{"className":100772},[638],[363,100774,100776],{"className":100775,"style":8315},[642],[363,100777],{},[363,100779,468],{"className":100780},[501],[363,100782],{"className":100783,"style":2934},[505],[363,100785,5160],{"className":100786},[2938],[363,100788],{"className":100789,"style":2934},[505],[363,100791,100793,100797,100859,100862,100928,100931,100960,100963,101003,101006,101046,101049],{"className":100792},[398],[363,100794],{"className":100795,"style":100796},[402],"height:3.0652em;vertical-align:-1.4138em;",[363,100798,100800,100803,100856],{"className":100799},[407],[363,100801],{"className":100802},[494,789],[363,100804,100806],{"className":100805},[586],[363,100807,100809,100848],{"className":100808},[633,634],[363,100810,100812,100845],{"className":100811},[638],[363,100813,100815,100826,100834],{"className":100814,"style":23236},[642],[363,100816,100817,100820],{"style":805},[363,100818],{"className":100819,"style":809},[650],[363,100821,100823],{"className":100822},[407],[363,100824,26670],{"className":100825},[407,408],[363,100827,100828,100831],{"style":821},[363,100829],{"className":100830,"style":809},[650],[363,100832],{"className":100833,"style":829},[828],[363,100835,100836,100839],{"style":832},[363,100837],{"className":100838,"style":809},[650],[363,100840,100842],{"className":100841},[407],[363,100843,465],{"className":100844},[407],[363,100846,666],{"className":100847},[665],[363,100849,100851],{"className":100850},[638],[363,100852,100854],{"className":100853,"style":4125},[642],[363,100855],{},[363,100857],{"className":100858},[501,789],[363,100860],{"className":100861,"style":754},[505],[363,100863,100865],{"className":100864},[1831,14063],[363,100866,100868,100919],{"className":100867},[633,634],[363,100869,100871,100916],{"className":100870},[638],[363,100872,100874,100895,100905],{"className":100873,"style":100638},[642],[363,100875,100876,100879],{"style":14076},[363,100877],{"className":100878,"style":14080},[650],[363,100880,100882],{"className":100881},[655,656,657,658],[363,100883,100885,100889,100892],{"className":100884},[407,658],[363,100886,100360],{"className":100887,"style":100888},[407,408,658],"margin-right:0.0572em;",[363,100890,471],{"className":100891},[510,658],[363,100893,465],{"className":100894},[407,658],[363,100896,100897,100900],{"style":14089},[363,100898],{"className":100899,"style":14080},[650],[363,100901,100902],{},[363,100903,13808],{"className":100904},[1831,1832,1833],[363,100906,100907,100910],{"style":100671},[363,100908],{"className":100909,"style":14080},[650],[363,100911,100913],{"className":100912},[655,656,657,658],[363,100914,26670],{"className":100915},[407,408,658],[363,100917,666],{"className":100918},[665],[363,100920,100922],{"className":100921},[638],[363,100923,100926],{"className":100924,"style":100925},[642],"height:1.4138em;",[363,100927],{},[363,100929],{"className":100930,"style":754},[505],[363,100932,100934,100937],{"className":100933},[407],[363,100935,385],{"className":100936,"style":409},[407,408],[363,100938,100940],{"className":100939},[629],[363,100941,100943],{"className":100942},[633],[363,100944,100946],{"className":100945},[638],[363,100947,100949],{"className":100948,"style":8595},[642],[363,100950,100951,100954],{"style":8624},[363,100952],{"className":100953,"style":651},[650],[363,100955,100957],{"className":100956},[655,656,657,658],[363,100958,7920],{"className":100959},[2938,658],[363,100961,461],{"className":100962},[494],[363,100964,100966,100969],{"className":100965},[407],[363,100967,4505],{"className":100968,"style":1328},[407,408],[363,100970,100972],{"className":100971},[629],[363,100973,100975,100995],{"className":100974},[633,634],[363,100976,100978,100992],{"className":100977},[638],[363,100979,100981],{"className":100980,"style":45276},[642],[363,100982,100983,100986],{"style":19190},[363,100984],{"className":100985,"style":651},[650],[363,100987,100989],{"className":100988},[655,656,657,658],[363,100990,100208],{"className":100991,"style":1328},[407,408,658],[363,100993,666],{"className":100994},[665],[363,100996,100998],{"className":100997},[638],[363,100999,101001],{"className":101000,"style":8315},[642],[363,101002],{},[363,101004,461],{"className":101005},[494],[363,101007,101009,101012],{"className":101008},[407],[363,101010,40584],{"className":101011,"style":1328},[407,408],[363,101013,101015],{"className":101014},[629],[363,101016,101018,101038],{"className":101017},[633,634],[363,101019,101021,101035],{"className":101020},[638],[363,101022,101024],{"className":101023,"style":12529},[642],[363,101025,101026,101029],{"style":19190},[363,101027],{"className":101028,"style":651},[650],[363,101030,101032],{"className":101031},[655,656,657,658],[363,101033,100360],{"className":101034,"style":100888},[407,408,658],[363,101036,666],{"className":101037},[665],[363,101039,101041],{"className":101040},[638],[363,101042,101044],{"className":101043,"style":673},[642],[363,101045],{},[363,101047,19394],{"className":101048},[501],[363,101050,4722],{"className":101051},[407],[11,101053,14608,101054,101083,101084,101177],{},[363,101055,101057,101071],{"className":101056,"translate":367},[366],[363,101058,101060],{"className":101059},[371],[373,101061,101062],{"xmlns":375},[377,101063,101064,101068],{},[380,101065,101066],{},[383,101067,100208],{},[387,101069,101070],{"encoding":389},"\\omega",[363,101072,101074],{"className":101073,"ariaHidden":394},[393],[363,101075,101077,101080],{"className":101076},[398],[363,101078],{"className":101079,"style":2692},[402],[363,101081,100208],{"className":101082,"style":1328},[407,408]," 极大化即得估计；把 ",[363,101085,101087,101110],{"className":101086,"translate":367},[366],[363,101088,101090],{"className":101089},[371],[373,101091,101092],{"xmlns":375},[377,101093,101094,101107],{},[380,101095,101096,101098,101100],{},[383,101097,561],{},[458,101099,471],{},[543,101101,101102,101104],{},[383,101103,561],{},[383,101105,101106],{},"θ",[387,101108,101109],{"encoding":389},"Q=Q_\\theta",[363,101111,101113,101131],{"className":101112,"ariaHidden":394},[393],[363,101114,101116,101119,101122,101125,101128],{"className":101115},[398],[363,101117],{"className":101118,"style":913},[402],[363,101120,561],{"className":101121},[407,408],[363,101123],{"className":101124,"style":506},[505],[363,101126,471],{"className":101127},[510],[363,101129],{"className":101130,"style":506},[505],[363,101132,101134,101137],{"className":101133},[398],[363,101135],{"className":101136,"style":913},[402],[363,101138,101140,101143],{"className":101139},[407],[363,101141,561],{"className":101142},[407,408],[363,101144,101146],{"className":101145},[629],[363,101147,101149,101169],{"className":101148},[633,634],[363,101150,101152,101166],{"className":101151},[638],[363,101153,101155],{"className":101154,"style":643},[642],[363,101156,101157,101160],{"style":730},[363,101158],{"className":101159,"style":651},[650],[363,101161,101163],{"className":101162},[655,656,657,658],[363,101164,101106],{"className":101165,"style":625},[407,408,658],[363,101167,666],{"className":101168},[665],[363,101170,101172],{"className":101171},[638],[363,101173,101175],{"className":101174,"style":8315},[642],[363,101176],{},"（生成器）同时放进去，就得到 f-GAN 的 minimax 目标：",[363,101179,101181],{"className":101180,"translate":367},[528],[363,101182,101184,101286],{"className":101183,"translate":367},[366],[363,101185,101187],{"className":101186},[371],[373,101188,101189],{"xmlns":375,"display":537},[377,101190,101191,101283],{},[380,101192,101193,101203,101205,101215,101217,101219,101225,101227,101233,101235,101237,101239,101241,101243,101253,101255,101261,101263,101269,101271,101273,101275,101277,101279,101281],{},[6363,101194,101195,101201],{},[380,101196,101197,101199],{},[383,101198,51955],{},[458,101200,4450],{},[383,101202,101106],{},[1644,101204,4630],{},[6363,101206,101207,101213],{},[380,101208,101209,101211],{},[383,101210,52734],{},[458,101212,4450],{},[383,101214,100208],{},[1644,101216,4630],{},[458,101218,3245],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[543,101220,101221,101223],{},[383,101222,571],{"mathvariant":570},[383,101224,554],{},[458,101226,578],{"stretchy":460},[543,101228,101229,101231],{},[383,101230,4505],{},[383,101232,100208],{},[458,101234,461],{"stretchy":460},[383,101236,945],{},[458,101238,468],{"stretchy":460},[458,101240,605],{"stretchy":460},[458,101242,5160],{},[543,101244,101245,101247],{},[383,101246,571],{"mathvariant":570},[543,101248,101249,101251],{},[383,101250,561],{},[383,101252,101106],{},[458,101254,578],{"stretchy":460},[7161,101256,101257,101259],{},[383,101258,385],{},[458,101260,7920],{},[458,101262,461],{"stretchy":460},[543,101264,101265,101267],{},[383,101266,4505],{},[383,101268,100208],{},[458,101270,461],{"stretchy":460},[383,101272,945],{},[458,101274,468],{"stretchy":460},[458,101276,468],{"stretchy":460},[458,101278,605],{"stretchy":460},[458,101280,3255],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[383,101282,4722],{"mathvariant":557},[387,101284,101285],{"encoding":389},"\\min_\\theta\\ \\max_\\omega\\\n\\Big\\{\\mathbb E_{P}[g_\\omega(X)]\n-\\mathbb E_{Q_\\theta}[f^*(g_\\omega(X))]\\Big\\}.",[363,101287,101289,101509],{"className":101288,"ariaHidden":394},[393],[363,101290,101292,101296,101341,101344,101347,101393,101396,101399,101405,101448,101451,101491,101494,101497,101500,101503,101506],{"className":101291},[398],[363,101293],{"className":101294,"style":101295},[402],"height:1.9021em;vertical-align:-0.7521em;",[363,101297,101299],{"className":101298},[1831,14063],[363,101300,101302,101332],{"className":101301},[633,634],[363,101303,101305,101329],{"className":101304},[638],[363,101306,101308,101319],{"className":101307,"style":52240},[642],[363,101309,101310,101313],{"style":52243},[363,101311],{"className":101312,"style":809},[650],[363,101314,101316],{"className":101315},[655,656,657,658],[363,101317,101106],{"className":101318,"style":625},[407,408,658],[363,101320,101321,101324],{"style":12210},[363,101322],{"className":101323,"style":809},[650],[363,101325,101326],{},[363,101327,51955],{"className":101328},[1831],[363,101330,666],{"className":101331},[665],[363,101333,101335],{"className":101334},[638],[363,101336,101339],{"className":101337,"style":101338},[642],"height:0.7521em;",[363,101340],{},[363,101342,4630],{"className":101343},[505],[363,101345],{"className":101346,"style":754},[505],[363,101348,101350],{"className":101349},[1831,14063],[363,101351,101353,101384],{"className":101352},[633,634],[363,101354,101356,101381],{"className":101355},[638],[363,101357,101359,101371],{"className":101358,"style":2692},[642],[363,101360,101362,101365],{"style":101361},"top:-2.4em;margin-left:0em;",[363,101363],{"className":101364,"style":809},[650],[363,101366,101368],{"className":101367},[655,656,657,658],[363,101369,100208],{"className":101370,"style":1328},[407,408,658],[363,101372,101373,101376],{"style":12210},[363,101374],{"className":101375,"style":809},[650],[363,101377,101378],{},[363,101379,52734],{"className":101380},[1831],[363,101382,666],{"className":101383},[665],[363,101385,101387],{"className":101386},[638],[363,101388,101391],{"className":101389,"style":101390},[642],"height:0.7em;",[363,101392],{},[363,101394,4630],{"className":101395},[505],[363,101397],{"className":101398,"style":754},[505],[363,101400,101402],{"className":101401},[407],[363,101403,3245],{"className":101404},[767,4067],[363,101406,101408,101411],{"className":101407},[407],[363,101409,571],{"className":101410},[407,714],[363,101412,101414],{"className":101413},[629],[363,101415,101417,101440],{"className":101416},[633,634],[363,101418,101420,101437],{"className":101419},[638],[363,101421,101423],{"className":101422,"style":727},[642],[363,101424,101425,101428],{"style":730},[363,101426],{"className":101427,"style":651},[650],[363,101429,101431],{"className":101430},[655,656,657,658],[363,101432,101434],{"className":101433},[407,658],[363,101435,554],{"className":101436,"style":682},[407,408,658],[363,101438,666],{"className":101439},[665],[363,101441,101443],{"className":101442},[638],[363,101444,101446],{"className":101445,"style":8315},[642],[363,101447],{},[363,101449,578],{"className":101450},[494],[363,101452,101454,101457],{"className":101453},[407],[363,101455,4505],{"className":101456,"style":1328},[407,408],[363,101458,101460],{"className":101459},[629],[363,101461,101463,101483],{"className":101462},[633,634],[363,101464,101466,101480],{"className":101465},[638],[363,101467,101469],{"className":101468,"style":45276},[642],[363,101470,101471,101474],{"style":19190},[363,101472],{"className":101473,"style":651},[650],[363,101475,101477],{"className":101476},[655,656,657,658],[363,101478,100208],{"className":101479,"style":1328},[407,408,658],[363,101481,666],{"className":101482},[665],[363,101484,101486],{"className":101485},[638],[363,101487,101489],{"className":101488,"style":8315},[642],[363,101490],{},[363,101492,461],{"className":101493},[494],[363,101495,945],{"className":101496,"style":9234},[407,408],[363,101498,20737],{"className":101499},[501],[363,101501],{"className":101502,"style":2934},[505],[363,101504,5160],{"className":101505},[2938],[363,101507],{"className":101508,"style":2934},[505],[363,101510,101512,101515,101597,101600,101629,101632,101672,101675,101678,101681,101687],{"className":101511},[398],[363,101513],{"className":101514,"style":68464},[402],[363,101516,101518,101521],{"className":101517},[407],[363,101519,571],{"className":101520},[407,714],[363,101522,101524],{"className":101523},[629],[363,101525,101527,101589],{"className":101526},[633,634],[363,101528,101530,101586],{"className":101529},[638],[363,101531,101533],{"className":101532,"style":727},[642],[363,101534,101535,101538],{"style":730},[363,101536],{"className":101537,"style":651},[650],[363,101539,101541],{"className":101540},[655,656,657,658],[363,101542,101544],{"className":101543},[407,658],[363,101545,101547,101550],{"className":101546},[407,658],[363,101548,561],{"className":101549},[407,408,658],[363,101551,101553],{"className":101552},[629],[363,101554,101556,101577],{"className":101555},[633,634],[363,101557,101559,101574],{"className":101558},[638],[363,101560,101562],{"className":101561,"style":6445},[642],[363,101563,101565,101568],{"style":101564},"top:-2.3488em;margin-left:0em;margin-right:0.0714em;",[363,101566],{"className":101567,"style":30553},[650],[363,101569,101571],{"className":101570},[655,30557,10021,658],[363,101572,101106],{"className":101573,"style":625},[407,408,658],[363,101575,666],{"className":101576},[665],[363,101578,101580],{"className":101579},[638],[363,101581,101584],{"className":101582,"style":101583},[642],"height:0.1512em;",[363,101585],{},[363,101587,666],{"className":101588},[665],[363,101590,101592],{"className":101591},[638],[363,101593,101595],{"className":101594,"style":673},[642],[363,101596],{},[363,101598,578],{"className":101599},[494],[363,101601,101603,101606],{"className":101602},[407],[363,101604,385],{"className":101605,"style":409},[407,408],[363,101607,101609],{"className":101608},[629],[363,101610,101612],{"className":101611},[633],[363,101613,101615],{"className":101614},[638],[363,101616,101618],{"className":101617,"style":8595},[642],[363,101619,101620,101623],{"style":8624},[363,101621],{"className":101622,"style":651},[650],[363,101624,101626],{"className":101625},[655,656,657,658],[363,101627,7920],{"className":101628},[2938,658],[363,101630,461],{"className":101631},[494],[363,101633,101635,101638],{"className":101634},[407],[363,101636,4505],{"className":101637,"style":1328},[407,408],[363,101639,101641],{"className":101640},[629],[363,101642,101644,101664],{"className":101643},[633,634],[363,101645,101647,101661],{"className":101646},[638],[363,101648,101650],{"className":101649,"style":45276},[642],[363,101651,101652,101655],{"style":19190},[363,101653],{"className":101654,"style":651},[650],[363,101656,101658],{"className":101657},[655,656,657,658],[363,101659,100208],{"className":101660,"style":1328},[407,408,658],[363,101662,666],{"className":101663},[665],[363,101665,101667],{"className":101666},[638],[363,101668,101670],{"className":101669,"style":8315},[642],[363,101671],{},[363,101673,461],{"className":101674},[494],[363,101676,945],{"className":101677,"style":9234},[407,408],[363,101679,100046],{"className":101680},[501],[363,101682,101684],{"className":101683},[407],[363,101685,3255],{"className":101686},[767,4067],[363,101688,4722],{"className":101689},[407],[2658,101691,101693],{"id":101692},"_52-最优判别器","5.2 最优判别器",[1340,101695,101697,101771,102042],{"title":101696},"命题 5.1（最优判别器）",[11,101698,101699,101700,101741,101742,101770],{},"在 5.1 节的 minimax 目标中，固定 ",[363,101701,101703,101720],{"className":101702,"translate":367},[366],[363,101704,101706],{"className":101705},[371],[373,101707,101708],{"xmlns":375},[377,101709,101710,101718],{},[380,101711,101712,101714,101716],{},[383,101713,554],{},[458,101715,898],{"separator":394},[383,101717,561],{},[387,101719,903],{"encoding":389},[363,101721,101723],{"className":101722,"ariaHidden":394},[393],[363,101724,101726,101729,101732,101735,101738],{"className":101725},[398],[363,101727],{"className":101728,"style":913},[402],[363,101730,554],{"className":101731,"style":682},[407,408],[363,101733,898],{"className":101734},[920],[363,101736],{"className":101737,"style":754},[505],[363,101739,561],{"className":101740},[407,408]," 时内层对 ",[363,101743,101745,101758],{"className":101744,"translate":367},[366],[363,101746,101748],{"className":101747},[371],[373,101749,101750],{"xmlns":375},[377,101751,101752,101756],{},[380,101753,101754],{},[383,101755,4505],{},[387,101757,4505],{"encoding":389},[363,101759,101761],{"className":101760,"ariaHidden":394},[393],[363,101762,101764,101767],{"className":101763},[398],[363,101765],{"className":101766,"style":2623},[402],[363,101768,4505],{"className":101769,"style":1328},[407,408]," 的最优解为",[363,101772,101774],{"className":101773,"translate":367},[528],[363,101775,101777,101841],{"className":101776,"translate":367},[366],[363,101778,101780],{"className":101779},[371],[373,101781,101782],{"xmlns":375,"display":537},[377,101783,101784,101838],{},[380,101785,101786,101792,101794,101796,101798,101800,101806,101808,101836],{},[7161,101787,101788,101790],{},[383,101789,4505],{},[458,101791,7920],{},[458,101793,461],{"stretchy":460},[383,101795,1121],{},[458,101797,468],{"stretchy":460},[458,101799,471],{},[7161,101801,101802,101804],{},[383,101803,385],{},[458,101805,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[1644,101807,1651],{},[380,101809,101810,101812,101834],{},[458,101811,461],{"fence":394},[586,101813,101814,101824],{},[380,101815,101816,101818,101820,101822],{},[383,101817,11],{},[458,101819,461],{"stretchy":460},[383,101821,1121],{},[458,101823,468],{"stretchy":460},[380,101825,101826,101828,101830,101832],{},[383,101827,1291],{},[458,101829,461],{"stretchy":460},[383,101831,1121],{},[458,101833,468],{"stretchy":460},[458,101835,468],{"fence":394},[458,101837,898],{"separator":394},[387,101839,101840],{"encoding":389},"g^*(x)=f'\\!\\left(\\frac{p(x)}{q(x)}\\right),",[363,101842,101844,101897],{"className":101843,"ariaHidden":394},[393],[363,101845,101847,101850,101879,101882,101885,101888,101891,101894],{"className":101846},[398],[363,101848],{"className":101849,"style":487},[402],[363,101851,101853,101856],{"className":101852},[407],[363,101854,4505],{"className":101855,"style":1328},[407,408],[363,101857,101859],{"className":101858},[629],[363,101860,101862],{"className":101861},[633],[363,101863,101865],{"className":101864},[638],[363,101866,101868],{"className":101867,"style":8595},[642],[363,101869,101870,101873],{"style":8624},[363,101871],{"className":101872,"style":651},[650],[363,101874,101876],{"className":101875},[655,656,657,658],[363,101877,7920],{"className":101878},[2938,658],[363,101880,461],{"className":101881},[494],[363,101883,1121],{"className":101884},[407,408],[363,101886,468],{"className":101887},[501],[363,101889],{"className":101890,"style":506},[505],[363,101892,471],{"className":101893},[510],[363,101895],{"className":101896,"style":506},[505],[363,101898,101900,101903,101935,101938,101941,102036,102039],{"className":101899},[398],[363,101901],{"className":101902,"style":707},[402],[363,101904,101906,101909],{"className":101905},[407],[363,101907,385],{"className":101908,"style":409},[407,408],[363,101910,101912],{"className":101911},[629],[363,101913,101915],{"className":101914},[633],[363,101916,101918],{"className":101917},[638],[363,101919,101921],{"className":101920,"style":29318},[642],[363,101922,101923,101926],{"style":8624},[363,101924],{"className":101925,"style":651},[650],[363,101927,101929],{"className":101928},[655,656,657,658],[363,101930,101932],{"className":101931},[407,658],[363,101933,7167],{"className":101934},[407,658],[363,101936],{"className":101937,"style":1859},[505],[363,101939],{"className":101940,"style":754},[505],[363,101942,101944,101950,102030],{"className":101943},[758],[363,101945,101947],{"className":101946,"style":763},[494,762],[363,101948,461],{"className":101949},[767,657],[363,101951,101953,101956,102027],{"className":101952},[407],[363,101954],{"className":101955},[494,789],[363,101957,101959],{"className":101958},[586],[363,101960,101962,102019],{"className":101961},[633,634],[363,101963,101965,102016],{"className":101964},[638],[363,101966,101968,101988,101996],{"className":101967,"style":1890},[642],[363,101969,101970,101973],{"style":805},[363,101971],{"className":101972,"style":809},[650],[363,101974,101976,101979,101982,101985],{"className":101975},[407],[363,101977,1291],{"className":101978,"style":1328},[407,408],[363,101980,461],{"className":101981},[494],[363,101983,1121],{"className":101984},[407,408],[363,101986,468],{"className":101987},[501],[363,101989,101990,101993],{"style":821},[363,101991],{"className":101992,"style":809},[650],[363,101994],{"className":101995,"style":829},[828],[363,101997,101998,102001],{"style":832},[363,101999],{"className":102000,"style":809},[650],[363,102002,102004,102007,102010,102013],{"className":102003},[407],[363,102005,11],{"className":102006},[407,408],[363,102008,461],{"className":102009},[494],[363,102011,1121],{"className":102012},[407,408],[363,102014,468],{"className":102015},[501],[363,102017,666],{"className":102018},[665],[363,102020,102022],{"className":102021},[638],[363,102023,102025],{"className":102024,"style":1948},[642],[363,102026],{},[363,102028],{"className":102029},[501,789],[363,102031,102033],{"className":102032,"style":763},[501,762],[363,102034,468],{"className":102035},[767,657],[363,102037],{"className":102038,"style":754},[505],[363,102040,898],{"className":102041},[920],[11,102043,102044,102045,102107],{},"即判别器学到的量是似然比经 ",[363,102046,102048,102066],{"className":102047,"translate":367},[366],[363,102049,102051],{"className":102050},[371],[373,102052,102053],{"xmlns":375},[377,102054,102055,102063],{},[380,102056,102057],{},[7161,102058,102059,102061],{},[383,102060,385],{},[458,102062,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[387,102064,102065],{"encoding":389},"f'",[363,102067,102069],{"className":102068,"ariaHidden":394},[393],[363,102070,102072,102075],{"className":102071},[398],[363,102073],{"className":102074,"style":64508},[402],[363,102076,102078,102081],{"className":102077},[407],[363,102079,385],{"className":102080,"style":409},[407,408],[363,102082,102084],{"className":102083},[629],[363,102085,102087],{"className":102086},[633],[363,102088,102090],{"className":102089},[638],[363,102091,102093],{"className":102092,"style":7209},[642],[363,102094,102095,102098],{"style":7212},[363,102096],{"className":102097,"style":651},[650],[363,102099,102101],{"className":102100},[655,656,657,658],[363,102102,102104],{"className":102103},[407,658],[363,102105,7167],{"className":102106},[407,658]," 之后的取值。",[11,102109,102110,102112,102113,102157,102158,102321,102322,102365],{},[1572,102111,55818],{}," 目标对 ",[363,102114,102116,102136],{"className":102115,"translate":367},[366],[363,102117,102119],{"className":102118},[371],[373,102120,102121],{"xmlns":375},[377,102122,102123,102133],{},[380,102124,102125,102127,102129,102131],{},[383,102126,4505],{},[458,102128,461],{"stretchy":460},[383,102130,1121],{},[458,102132,468],{"stretchy":460},[387,102134,102135],{"encoding":389},"g(x)",[363,102137,102139],{"className":102138,"ariaHidden":394},[393],[363,102140,102142,102145,102148,102151,102154],{"className":102141},[398],[363,102143],{"className":102144,"style":487},[402],[363,102146,4505],{"className":102147,"style":1328},[407,408],[363,102149,461],{"className":102150},[494],[363,102152,1121],{"className":102153},[407,408],[363,102155,468],{"className":102156},[501]," 的逐点依赖是 ",[363,102159,102161,102217],{"className":102160,"translate":367},[366],[363,102162,102164],{"className":102163},[371],[373,102165,102166],{"xmlns":375},[377,102167,102168,102214],{},[380,102169,102170,102172,102174,102176,102178,102180,102182,102184,102186,102188,102190,102192,102194,102196,102202,102204,102206,102208,102210,102212],{},[383,102171,11],{},[458,102173,461],{"stretchy":460},[383,102175,1121],{},[458,102177,468],{"stretchy":460},[383,102179,4505],{},[458,102181,461],{"stretchy":460},[383,102183,1121],{},[458,102185,468],{"stretchy":460},[458,102187,5160],{},[383,102189,1291],{},[458,102191,461],{"stretchy":460},[383,102193,1121],{},[458,102195,468],{"stretchy":460},[7161,102197,102198,102200],{},[383,102199,385],{},[458,102201,7920],{},[458,102203,461],{"stretchy":460},[383,102205,4505],{},[458,102207,461],{"stretchy":460},[383,102209,1121],{},[458,102211,468],{"stretchy":460},[458,102213,468],{"stretchy":460},[387,102215,102216],{"encoding":389},"p(x)g(x)-q(x)f^*(g(x))",[363,102218,102220,102259],{"className":102219,"ariaHidden":394},[393],[363,102221,102223,102226,102229,102232,102235,102238,102241,102244,102247,102250,102253,102256],{"className":102222},[398],[363,102224],{"className":102225,"style":487},[402],[363,102227,11],{"className":102228},[407,408],[363,102230,461],{"className":102231},[494],[363,102233,1121],{"className":102234},[407,408],[363,102236,468],{"className":102237},[501],[363,102239,4505],{"className":102240,"style":1328},[407,408],[363,102242,461],{"className":102243},[494],[363,102245,1121],{"className":102246},[407,408],[363,102248,468],{"className":102249},[501],[363,102251],{"className":102252,"style":2934},[505],[363,102254,5160],{"className":102255},[2938],[363,102257],{"className":102258,"style":2934},[505],[363,102260,102262,102265,102268,102271,102274,102277,102306,102309,102312,102315,102318],{"className":102261},[398],[363,102263],{"className":102264,"style":487},[402],[363,102266,1291],{"className":102267,"style":1328},[407,408],[363,102269,461],{"className":102270},[494],[363,102272,1121],{"className":102273},[407,408],[363,102275,468],{"className":102276},[501],[363,102278,102280,102283],{"className":102279},[407],[363,102281,385],{"className":102282,"style":409},[407,408],[363,102284,102286],{"className":102285},[629],[363,102287,102289],{"className":102288},[633],[363,102290,102292],{"className":102291},[638],[363,102293,102295],{"className":102294,"style":8846},[642],[363,102296,102297,102300],{"style":7212},[363,102298],{"className":102299,"style":651},[650],[363,102301,102303],{"className":102302},[655,656,657,658],[363,102304,7920],{"className":102305},[2938,658],[363,102307,461],{"className":102308},[494],[363,102310,4505],{"className":102311,"style":1328},[407,408],[363,102313,461],{"className":102314},[494],[363,102316,1121],{"className":102317},[407,408],[363,102319,19394],{"className":102320},[501],"，对 ",[363,102323,102325,102344],{"className":102324,"translate":367},[366],[363,102326,102328],{"className":102327},[371],[373,102329,102330],{"xmlns":375},[377,102331,102332,102342],{},[380,102333,102334,102336,102338,102340],{},[383,102335,4505],{},[458,102337,461],{"stretchy":460},[383,102339,1121],{},[458,102341,468],{"stretchy":460},[387,102343,102135],{"encoding":389},[363,102345,102347],{"className":102346,"ariaHidden":394},[393],[363,102348,102350,102353,102356,102359,102362],{"className":102349},[398],[363,102351],{"className":102352,"style":487},[402],[363,102354,4505],{"className":102355,"style":1328},[407,408],[363,102357,461],{"className":102358},[494],[363,102360,1121],{"className":102361},[407,408],[363,102363,468],{"className":102364},[501]," 求导：",[363,102367,102369],{"className":102368,"translate":367},[528],[363,102370,102372,102492],{"className":102371,"translate":367},[366],[363,102373,102375],{"className":102374},[371],[373,102376,102377],{"xmlns":375,"display":537},[377,102378,102379,102489],{},[380,102380,102381,102383,102385,102387,102389,102391,102393,102395,102397,102399,102401,102411,102413,102415,102417,102419,102421,102423,102425,102427,102429,102431,102433,102443,102445,102451,102453,102455,102457,102459,102461,102483,102485,102487],{},[383,102382,11],{},[458,102384,461],{"stretchy":460},[383,102386,1121],{},[458,102388,468],{"stretchy":460},[458,102390,5160],{},[383,102392,1291],{},[458,102394,461],{"stretchy":460},[383,102396,1121],{},[458,102398,468],{"stretchy":460},[1644,102400,1646],{},[7161,102402,102403,102405],{},[383,102404,385],{},[380,102406,102407,102409],{},[458,102408,7920],{},[458,102410,7167],{"mathvariant":557},[458,102412,461],{"stretchy":460},[383,102414,4505],{},[458,102416,461],{"stretchy":460},[383,102418,1121],{},[458,102420,468],{"stretchy":460},[458,102422,468],{"stretchy":460},[458,102424,471],{},[463,102426,474],{},[1644,102428,4630],{},[458,102430,4633],{},[1644,102432,4630],{},[7161,102434,102435,102437],{},[383,102436,385],{},[380,102438,102439,102441],{},[458,102440,7920],{},[458,102442,7167],{"mathvariant":557},[458,102444,461],{"stretchy":460},[7161,102446,102447,102449],{},[383,102448,4505],{},[458,102450,7920],{},[458,102452,461],{"stretchy":460},[383,102454,1121],{},[458,102456,468],{"stretchy":460},[458,102458,468],{"stretchy":460},[458,102460,471],{},[586,102462,102463,102473],{},[380,102464,102465,102467,102469,102471],{},[383,102466,11],{},[458,102468,461],{"stretchy":460},[383,102470,1121],{},[458,102472,468],{"stretchy":460},[380,102474,102475,102477,102479,102481],{},[383,102476,1291],{},[458,102478,461],{"stretchy":460},[383,102480,1121],{},[458,102482,468],{"stretchy":460},[458,102484,471],{},[383,102486,1116],{},[383,102488,4722],{"mathvariant":557},[387,102490,102491],{"encoding":389},"p(x)-q(x)\\,f^{*\\prime}(g(x))=0\n\\ \\Longrightarrow\\\nf^{*\\prime}(g^*(x))=\\frac{p(x)}{q(x)}=t .",[363,102493,102495,102522,102603,102627,102718,102814],{"className":102494,"ariaHidden":394},[393],[363,102496,102498,102501,102504,102507,102510,102513,102516,102519],{"className":102497},[398],[363,102499],{"className":102500,"style":487},[402],[363,102502,11],{"className":102503},[407,408],[363,102505,461],{"className":102506},[494],[363,102508,1121],{"className":102509},[407,408],[363,102511,468],{"className":102512},[501],[363,102514],{"className":102515,"style":2934},[505],[363,102517,5160],{"className":102518},[2938],[363,102520],{"className":102521,"style":2934},[505],[363,102523,102525,102529,102532,102535,102538,102541,102544,102579,102582,102585,102588,102591,102594,102597,102600],{"className":102524},[398],[363,102526],{"className":102527,"style":102528},[402],"height:1.0519em;vertical-align:-0.25em;",[363,102530,1291],{"className":102531,"style":1328},[407,408],[363,102533,461],{"className":102534},[494],[363,102536,1121],{"className":102537},[407,408],[363,102539,468],{"className":102540},[501],[363,102542],{"className":102543,"style":754},[505],[363,102545,102547,102550],{"className":102546},[407],[363,102548,385],{"className":102549,"style":409},[407,408],[363,102551,102553],{"className":102552},[629],[363,102554,102556],{"className":102555},[633],[363,102557,102559],{"className":102558},[638],[363,102560,102562],{"className":102561,"style":29318},[642],[363,102563,102564,102567],{"style":8624},[363,102565],{"className":102566,"style":651},[650],[363,102568,102570],{"className":102569},[655,656,657,658],[363,102571,102573,102576],{"className":102572},[407,658],[363,102574,7920],{"className":102575},[407,658],[363,102577,7167],{"className":102578},[407,658],[363,102580,461],{"className":102581},[494],[363,102583,4505],{"className":102584,"style":1328},[407,408],[363,102586,461],{"className":102587},[494],[363,102589,1121],{"className":102590},[407,408],[363,102592,19394],{"className":102593},[501],[363,102595],{"className":102596,"style":506},[505],[363,102598,471],{"className":102599},[510],[363,102601],{"className":102602,"style":506},[505],[363,102604,102606,102609,102612,102615,102618,102621,102624],{"className":102605},[398],[363,102607],{"className":102608,"style":93130},[402],[363,102610,474],{"className":102611},[407],[363,102613,4630],{"className":102614},[505],[363,102616],{"className":102617,"style":506},[505],[363,102619,4633],{"className":102620},[510],[363,102622,4630],{"className":102623},[505],[363,102625],{"className":102626,"style":506},[505],[363,102628,102630,102633,102668,102671,102700,102703,102706,102709,102712,102715],{"className":102629},[398],[363,102631],{"className":102632,"style":102528},[402],[363,102634,102636,102639],{"className":102635},[407],[363,102637,385],{"className":102638,"style":409},[407,408],[363,102640,102642],{"className":102641},[629],[363,102643,102645],{"className":102644},[633],[363,102646,102648],{"className":102647},[638],[363,102649,102651],{"className":102650,"style":29318},[642],[363,102652,102653,102656],{"style":8624},[363,102654],{"className":102655,"style":651},[650],[363,102657,102659],{"className":102658},[655,656,657,658],[363,102660,102662,102665],{"className":102661},[407,658],[363,102663,7920],{"className":102664},[407,658],[363,102666,7167],{"className":102667},[407,658],[363,102669,461],{"className":102670},[494],[363,102672,102674,102677],{"className":102673},[407],[363,102675,4505],{"className":102676,"style":1328},[407,408],[363,102678,102680],{"className":102679},[629],[363,102681,102683],{"className":102682},[633],[363,102684,102686],{"className":102685},[638],[363,102687,102689],{"className":102688,"style":8595},[642],[363,102690,102691,102694],{"style":8624},[363,102692],{"className":102693,"style":651},[650],[363,102695,102697],{"className":102696},[655,656,657,658],[363,102698,7920],{"className":102699},[2938,658],[363,102701,461],{"className":102702},[494],[363,102704,1121],{"className":102705},[407,408],[363,102707,19394],{"className":102708},[501],[363,102710],{"className":102711,"style":506},[505],[363,102713,471],{"className":102714},[510],[363,102716],{"className":102717,"style":506},[505],[363,102719,102721,102725,102805,102808,102811],{"className":102720},[398],[363,102722],{"className":102723,"style":102724},[402],"height:2.363em;vertical-align:-0.936em;",[363,102726,102728,102731,102802],{"className":102727},[407],[363,102729],{"className":102730},[494,789],[363,102732,102734],{"className":102733},[586],[363,102735,102737,102794],{"className":102736},[633,634],[363,102738,102740,102791],{"className":102739},[638],[363,102741,102743,102763,102771],{"className":102742,"style":1890},[642],[363,102744,102745,102748],{"style":805},[363,102746],{"className":102747,"style":809},[650],[363,102749,102751,102754,102757,102760],{"className":102750},[407],[363,102752,1291],{"className":102753,"style":1328},[407,408],[363,102755,461],{"className":102756},[494],[363,102758,1121],{"className":102759},[407,408],[363,102761,468],{"className":102762},[501],[363,102764,102765,102768],{"style":821},[363,102766],{"className":102767,"style":809},[650],[363,102769],{"className":102770,"style":829},[828],[363,102772,102773,102776],{"style":832},[363,102774],{"className":102775,"style":809},[650],[363,102777,102779,102782,102785,102788],{"className":102778},[407],[363,102780,11],{"className":102781},[407,408],[363,102783,461],{"className":102784},[494],[363,102786,1121],{"className":102787},[407,408],[363,102789,468],{"className":102790},[501],[363,102792,666],{"className":102793},[665],[363,102795,102797],{"className":102796},[638],[363,102798,102800],{"className":102799,"style":1948},[642],[363,102801],{},[363,102803],{"className":102804},[501,789],[363,102806],{"className":102807,"style":506},[505],[363,102809,471],{"className":102810},[510],[363,102812],{"className":102813,"style":506},[505],[363,102815,102817,102820,102823],{"className":102816},[398],[363,102818],{"className":102819,"style":5690},[402],[363,102821,1116],{"className":102822},[407,408],[363,102824,4722],{"className":102825},[407],[11,102827,34439,102828,103035,103036,103192,103193,103251,103252,103346,103347,103350,103351,103420,103421,103502,103503,103531],{},[363,102829,102831,102877],{"className":102830,"translate":367},[366],[363,102832,102834],{"className":102833},[371],[373,102835,102836],{"xmlns":375},[377,102837,102838,102874],{},[380,102839,102840,102842,102848,102854,102856,102858,102864],{},[458,102841,461],{"stretchy":460},[7161,102843,102844,102846],{},[383,102845,385],{},[458,102847,7920],{},[7161,102849,102850,102852],{},[458,102851,468],{"stretchy":460},[458,102853,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,102855,471],{},[458,102857,461],{"stretchy":460},[7161,102859,102860,102862],{},[383,102861,385],{},[458,102863,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[7161,102865,102866,102868],{},[458,102867,468],{"stretchy":460},[380,102869,102870,102872],{},[458,102871,5160],{},[463,102873,465],{},[387,102875,102876],{"encoding":389},"(f^*)'=(f')^{-1}",[363,102878,102880,102959],{"className":102879,"ariaHidden":394},[393],[363,102881,102883,102886,102889,102918,102950,102953,102956],{"className":102882},[398],[363,102884],{"className":102885,"style":7190},[402],[363,102887,461],{"className":102888},[494],[363,102890,102892,102895],{"className":102891},[407],[363,102893,385],{"className":102894,"style":409},[407,408],[363,102896,102898],{"className":102897},[629],[363,102899,102901],{"className":102900},[633],[363,102902,102904],{"className":102903},[638],[363,102905,102907],{"className":102906,"style":8846},[642],[363,102908,102909,102912],{"style":7212},[363,102910],{"className":102911,"style":651},[650],[363,102913,102915],{"className":102914},[655,656,657,658],[363,102916,7920],{"className":102917},[2938,658],[363,102919,102921,102924],{"className":102920},[501],[363,102922,468],{"className":102923},[501],[363,102925,102927],{"className":102926},[629],[363,102928,102930],{"className":102929},[633],[363,102931,102933],{"className":102932},[638],[363,102934,102936],{"className":102935,"style":7209},[642],[363,102937,102938,102941],{"style":7212},[363,102939],{"className":102940,"style":651},[650],[363,102942,102944],{"className":102943},[655,656,657,658],[363,102945,102947],{"className":102946},[407,658],[363,102948,7167],{"className":102949},[407,658],[363,102951],{"className":102952,"style":506},[505],[363,102954,471],{"className":102955},[510],[363,102957],{"className":102958,"style":506},[505],[363,102960,102962,102965,102968,103000],{"className":102961},[398],[363,102963],{"className":102964,"style":20350},[402],[363,102966,461],{"className":102967},[494],[363,102969,102971,102974],{"className":102970},[407],[363,102972,385],{"className":102973,"style":409},[407,408],[363,102975,102977],{"className":102976},[629],[363,102978,102980],{"className":102979},[633],[363,102981,102983],{"className":102982},[638],[363,102984,102986],{"className":102985,"style":7209},[642],[363,102987,102988,102991],{"style":7212},[363,102989],{"className":102990,"style":651},[650],[363,102992,102994],{"className":102993},[655,656,657,658],[363,102995,102997],{"className":102996},[407,658],[363,102998,7167],{"className":102999},[407,658],[363,103001,103003,103006],{"className":103002},[501],[363,103004,468],{"className":103005},[501],[363,103007,103009],{"className":103008},[629],[363,103010,103012],{"className":103011},[633],[363,103013,103015],{"className":103014},[638],[363,103016,103018],{"className":103017,"style":20375},[642],[363,103019,103020,103023],{"style":7212},[363,103021],{"className":103022,"style":651},[650],[363,103024,103026],{"className":103025},[655,656,657,658],[363,103027,103029,103032],{"className":103028},[407,658],[363,103030,5160],{"className":103031},[407,658],[363,103033,465],{"className":103034},[407,658],"（Fenchel 的互逆关系），即得 ",[363,103037,103039,103083],{"className":103038,"translate":367},[366],[363,103040,103042],{"className":103041},[371],[373,103043,103044],{"xmlns":375},[377,103045,103046,103080],{},[380,103047,103048,103054,103056,103058,103060,103062,103068,103070,103072,103074,103076,103078],{},[7161,103049,103050,103052],{},[383,103051,4505],{},[458,103053,7920],{},[458,103055,461],{"stretchy":460},[383,103057,1121],{},[458,103059,468],{"stretchy":460},[458,103061,471],{},[7161,103063,103064,103066],{},[383,103065,385],{},[458,103067,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,103069,461],{"stretchy":460},[383,103071,1116],{},[458,103073,461],{"stretchy":460},[383,103075,1121],{},[458,103077,468],{"stretchy":460},[458,103079,468],{"stretchy":460},[387,103081,103082],{"encoding":389},"g^*(x)=f'(t(x))",[363,103084,103086,103139],{"className":103085,"ariaHidden":394},[393],[363,103087,103089,103092,103121,103124,103127,103130,103133,103136],{"className":103088},[398],[363,103090],{"className":103091,"style":487},[402],[363,103093,103095,103098],{"className":103094},[407],[363,103096,4505],{"className":103097,"style":1328},[407,408],[363,103099,103101],{"className":103100},[629],[363,103102,103104],{"className":103103},[633],[363,103105,103107],{"className":103106},[638],[363,103108,103110],{"className":103109,"style":8846},[642],[363,103111,103112,103115],{"style":7212},[363,103113],{"className":103114,"style":651},[650],[363,103116,103118],{"className":103117},[655,656,657,658],[363,103119,7920],{"className":103120},[2938,658],[363,103122,461],{"className":103123},[494],[363,103125,1121],{"className":103126},[407,408],[363,103128,468],{"className":103129},[501],[363,103131],{"className":103132,"style":506},[505],[363,103134,471],{"className":103135},[510],[363,103137],{"className":103138,"style":506},[505],[363,103140,103142,103145,103177,103180,103183,103186,103189],{"className":103141},[398],[363,103143],{"className":103144,"style":7190},[402],[363,103146,103148,103151],{"className":103147},[407],[363,103149,385],{"className":103150,"style":409},[407,408],[363,103152,103154],{"className":103153},[629],[363,103155,103157],{"className":103156},[633],[363,103158,103160],{"className":103159},[638],[363,103161,103163],{"className":103162,"style":7209},[642],[363,103164,103165,103168],{"style":7212},[363,103166],{"className":103167,"style":651},[650],[363,103169,103171],{"className":103170},[655,656,657,658],[363,103172,103174],{"className":103173},[407,658],[363,103175,7167],{"className":103176},[407,658],[363,103178,461],{"className":103179},[494],[363,103181,1116],{"className":103182},[407,408],[363,103184,461],{"className":103185},[494],[363,103187,1121],{"className":103188},[407,408],[363,103190,19394],{"className":103191},[501],"。把 ",[363,103194,103196,103213],{"className":103195,"translate":367},[366],[363,103197,103199],{"className":103198},[371],[373,103200,103201],{"xmlns":375},[377,103202,103203,103211],{},[380,103204,103205],{},[7161,103206,103207,103209],{},[383,103208,4505],{},[458,103210,7920],{},[387,103212,64352],{"encoding":389},[363,103214,103216],{"className":103215,"ariaHidden":394},[393],[363,103217,103219,103222],{"className":103218},[398],[363,103220],{"className":103221,"style":64362},[402],[363,103223,103225,103228],{"className":103224},[407],[363,103226,4505],{"className":103227,"style":1328},[407,408],[363,103229,103231],{"className":103230},[629],[363,103232,103234],{"className":103233},[633],[363,103235,103237],{"className":103236},[638],[363,103238,103240],{"className":103239,"style":8846},[642],[363,103241,103242,103245],{"style":7212},[363,103243],{"className":103244,"style":651},[650],[363,103246,103248],{"className":103247},[655,656,657,658],[363,103249,7920],{"className":103250},[2938,658]," 代回即得 ",[363,103253,103255,103282],{"className":103254,"translate":367},[366],[363,103256,103258],{"className":103257},[371],[373,103259,103260],{"xmlns":375},[377,103261,103262,103280],{},[380,103263,103264,103270,103272,103274,103276,103278],{},[543,103265,103266,103268],{},[383,103267,547],{},[383,103269,385],{},[458,103271,461],{"stretchy":460},[383,103273,554],{},[383,103275,558],{"mathvariant":557},[383,103277,561],{},[458,103279,468],{"stretchy":460},[387,103281,5586],{"encoding":389},[363,103283,103285],{"className":103284,"ariaHidden":394},[393],[363,103286,103288,103291,103331,103334,103337,103340,103343],{"className":103287},[398],[363,103289],{"className":103290,"style":618},[402],[363,103292,103294,103297],{"className":103293},[407],[363,103295,547],{"className":103296,"style":625},[407,408],[363,103298,103300],{"className":103299},[629],[363,103301,103303,103323],{"className":103302},[633,634],[363,103304,103306,103320],{"className":103305},[638],[363,103307,103309],{"className":103308,"style":643},[642],[363,103310,103311,103314],{"style":646},[363,103312],{"className":103313,"style":651},[650],[363,103315,103317],{"className":103316},[655,656,657,658],[363,103318,385],{"className":103319,"style":409},[407,408,658],[363,103321,666],{"className":103322},[665],[363,103324,103326],{"className":103325},[638],[363,103327,103329],{"className":103328,"style":673},[642],[363,103330],{},[363,103332,461],{"className":103333},[494],[363,103335,554],{"className":103336,"style":682},[407,408],[363,103338,558],{"className":103339},[407],[363,103341,561],{"className":103342},[407,408],[363,103344,468],{"className":103345},[501],"（这正是定理 4.1 所给的最优解）。",[1572,103348,103349],{},"实践含义："," 判别器网络 ",[363,103352,103354,103371],{"className":103353,"translate":367},[366],[363,103355,103357],{"className":103356},[371],[373,103358,103359],{"xmlns":375},[377,103360,103361,103369],{},[380,103362,103363],{},[543,103364,103365,103367],{},[383,103366,4505],{},[383,103368,100208],{},[387,103370,100211],{"encoding":389},[363,103372,103374],{"className":103373,"ariaHidden":394},[393],[363,103375,103377,103380],{"className":103376},[398],[363,103378],{"className":103379,"style":2623},[402],[363,103381,103383,103386],{"className":103382},[407],[363,103384,4505],{"className":103385,"style":1328},[407,408],[363,103387,103389],{"className":103388},[629],[363,103390,103392,103412],{"className":103391},[633,634],[363,103393,103395,103409],{"className":103394},[638],[363,103396,103398],{"className":103397,"style":45276},[642],[363,103399,103400,103403],{"style":19190},[363,103401],{"className":103402,"style":651},[650],[363,103404,103406],{"className":103405},[655,656,657,658],[363,103407,100208],{"className":103408,"style":1328},[407,408,658],[363,103410,666],{"className":103411},[665],[363,103413,103415],{"className":103414},[638],[363,103416,103418],{"className":103417,"style":8315},[642],[363,103419],{}," 学的是 ",[363,103422,103424,103449],{"className":103423,"translate":367},[366],[363,103425,103427],{"className":103426},[371],[373,103428,103429],{"xmlns":375},[377,103430,103431,103446],{},[380,103432,103433,103439,103441,103444],{},[7161,103434,103435,103437],{},[383,103436,385],{},[458,103438,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,103440,461],{"stretchy":460},[1644,103442,103443],{},"似然比",[458,103445,468],{"stretchy":460},[387,103447,103448],{"encoding":389},"f'(\\text{似然比})",[363,103450,103452],{"className":103451,"ariaHidden":394},[393],[363,103453,103455,103458,103490,103493,103499],{"className":103454},[398],[363,103456],{"className":103457,"style":7190},[402],[363,103459,103461,103464],{"className":103460},[407],[363,103462,385],{"className":103463,"style":409},[407,408],[363,103465,103467],{"className":103466},[629],[363,103468,103470],{"className":103469},[633],[363,103471,103473],{"className":103472},[638],[363,103474,103476],{"className":103475,"style":7209},[642],[363,103477,103478,103481],{"style":7212},[363,103479],{"className":103480,"style":651},[650],[363,103482,103484],{"className":103483},[655,656,657,658],[363,103485,103487],{"className":103486},[407,658],[363,103488,7167],{"className":103489},[407,658],[363,103491,461],{"className":103492},[494],[363,103494,103496],{"className":103495},[407,4945],[363,103497,103443],{"className":103498},[407,4949],[363,103500,468],{"className":103501},[501],"，而不是似然比本身；不同 ",[363,103504,103506,103519],{"className":103505,"translate":367},[366],[363,103507,103509],{"className":103508},[371],[373,103510,103511],{"xmlns":375},[377,103512,103513,103517],{},[380,103514,103515],{},[383,103516,385],{},[387,103518,385],{"encoding":389},[363,103520,103522],{"className":103521,"ariaHidden":394},[393],[363,103523,103525,103528],{"className":103524},[398],[363,103526],{"className":103527,"style":403},[402],[363,103529,385],{"className":103530,"style":409},[407,408]," 等价于对似然比做了不同的单调「整形」，因此决定了梯度的尺度与饱和方式。",[2658,103533,103535],{"id":103534},"_53-各散度的-gan-目标","5.3 各散度的 GAN 目标",[11,103537,103538,103539,9747],{},"取上表的 ",[363,103540,103542,103559],{"className":103541,"translate":367},[366],[363,103543,103545],{"className":103544},[371],[373,103546,103547],{"xmlns":375},[377,103548,103549,103557],{},[380,103550,103551],{},[7161,103552,103553,103555],{},[383,103554,385],{},[458,103556,7920],{},[387,103558,61055],{"encoding":389},[363,103560,103562],{"className":103561,"ariaHidden":394},[393],[363,103563,103565,103568],{"className":103564},[398],[363,103566],{"className":103567,"style":403},[402],[363,103569,103571,103574],{"className":103570},[407],[363,103572,385],{"className":103573,"style":409},[407,408],[363,103575,103577],{"className":103576},[629],[363,103578,103580],{"className":103579},[633],[363,103581,103583],{"className":103582},[638],[363,103584,103586],{"className":103585,"style":8846},[642],[363,103587,103588,103591],{"style":7212},[363,103589],{"className":103590,"style":651},[650],[363,103592,103594],{"className":103593},[655,656,657,658],[363,103595,7920],{"className":103596},[2938,658],[10374,103598,103599],{},[7012,103600,103601,16142,103603,45955],{},[1572,103602,33010],{},[363,103604,103606,103638],{"className":103605,"translate":367},[366],[363,103607,103609],{"className":103608},[371],[373,103610,103611],{"xmlns":375},[377,103612,103613,103635],{},[380,103614,103615,103621,103623],{},[7161,103616,103617,103619],{},[383,103618,385],{},[458,103620,7920],{},[458,103622,471],{},[7161,103624,103625,103627],{},[383,103626,7914],{},[380,103628,103629,103631,103633],{},[383,103630,40584],{},[458,103632,5160],{},[463,103634,465],{},[387,103636,103637],{"encoding":389},"f^*=e^{y-1}",[363,103639,103641,103685],{"className":103640,"ariaHidden":394},[393],[363,103642,103644,103647,103676,103679,103682],{"className":103643},[398],[363,103645],{"className":103646,"style":403},[402],[363,103648,103650,103653],{"className":103649},[407],[363,103651,385],{"className":103652,"style":409},[407,408],[363,103654,103656],{"className":103655},[629],[363,103657,103659],{"className":103658},[633],[363,103660,103662],{"className":103661},[638],[363,103663,103665],{"className":103664,"style":8846},[642],[363,103666,103667,103670],{"style":7212},[363,103668],{"className":103669,"style":651},[650],[363,103671,103673],{"className":103672},[655,656,657,658],[363,103674,7920],{"className":103675},[2938,658],[363,103677],{"className":103678,"style":506},[505],[363,103680,471],{"className":103681},[510],[363,103683],{"className":103684,"style":506},[505],[363,103686,103688,103691],{"className":103687},[398],[363,103689],{"className":103690,"style":20375},[402],[363,103692,103694,103697],{"className":103693},[407],[363,103695,7914],{"className":103696},[407,408],[363,103698,103700],{"className":103699},[629],[363,103701,103703],{"className":103702},[633],[363,103704,103706],{"className":103705},[638],[363,103707,103709],{"className":103708,"style":20375},[642],[363,103710,103711,103714],{"style":7212},[363,103712],{"className":103713,"style":651},[650],[363,103715,103717],{"className":103716},[655,656,657,658],[363,103718,103720,103723,103726],{"className":103719},[407,658],[363,103721,40584],{"className":103722,"style":1328},[407,408,658],[363,103724,5160],{"className":103725},[2938,658],[363,103727,465],{"className":103728},[407,658],[363,103730,103732],{"className":103731,"translate":367},[528],[363,103733,103735,103821],{"className":103734,"translate":367},[366],[363,103736,103738],{"className":103737},[371],[373,103739,103740],{"xmlns":375,"display":537},[377,103741,103742,103818],{},[380,103743,103744,103754,103756,103758,103760,103762,103764,103766,103776,103778,103784,103786,103788,103790,103792,103798,103800,103812,103814,103816],{},[543,103745,103746,103748],{},[383,103747,547],{},[380,103749,103750,103752],{},[383,103751,11041],{},[383,103753,22240],{},[458,103755,461],{"stretchy":460},[383,103757,554],{},[383,103759,558],{"mathvariant":557},[383,103761,561],{},[458,103763,468],{"stretchy":460},[458,103765,471],{},[6363,103767,103768,103774],{},[380,103769,103770,103772],{},[383,103771,35779],{},[458,103773,4450],{},[383,103775,4505],{},[458,103777,3245],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[543,103779,103780,103782],{},[383,103781,571],{"mathvariant":570},[383,103783,554],{},[458,103785,578],{"stretchy":460},[383,103787,4505],{},[458,103789,605],{"stretchy":460},[458,103791,5160],{},[543,103793,103794,103796],{},[383,103795,571],{"mathvariant":570},[383,103797,561],{},[458,103799,578],{"stretchy":460},[7161,103801,103802,103804],{},[383,103803,7914],{},[380,103805,103806,103808,103810],{},[383,103807,4505],{},[458,103809,5160],{},[463,103811,465],{},[458,103813,605],{"stretchy":460},[458,103815,3255],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[383,103817,4722],{"mathvariant":557},[387,103819,103820],{"encoding":389},"D_{KL}(P\\|Q)\n=\\sup_g\\Big\\{\\mathbb E_P[g]\n-\\mathbb E_Q[e^{g-1}]\\Big\\}.",[363,103822,103824,103900,104017],{"className":103823,"ariaHidden":394},[393],[363,103825,103827,103830,103876,103879,103882,103885,103888,103891,103894,103897],{"className":103826},[398],[363,103828],{"className":103829,"style":487},[402],[363,103831,103833,103836],{"className":103832},[407],[363,103834,547],{"className":103835,"style":625},[407,408],[363,103837,103839],{"className":103838},[629],[363,103840,103842,103868],{"className":103841},[633,634],[363,103843,103845,103865],{"className":103844},[638],[363,103846,103848],{"className":103847,"style":727},[642],[363,103849,103850,103853],{"style":646},[363,103851],{"className":103852,"style":651},[650],[363,103854,103856],{"className":103855},[655,656,657,658],[363,103857,103859,103862],{"className":103858},[407,658],[363,103860,11041],{"className":103861,"style":11129},[407,408,658],[363,103863,22240],{"className":103864},[407,408,658],[363,103866,666],{"className":103867},[665],[363,103869,103871],{"className":103870},[638],[363,103872,103874],{"className":103873,"style":8315},[642],[363,103875],{},[363,103877,461],{"className":103878},[494],[363,103880,554],{"className":103881,"style":682},[407,408],[363,103883,558],{"className":103884},[407],[363,103886,561],{"className":103887},[407,408],[363,103889,468],{"className":103890},[501],[363,103892],{"className":103893,"style":506},[505],[363,103895,471],{"className":103896},[510],[363,103898],{"className":103899,"style":506},[505],[363,103901,103903,103906,103950,103953,103959,103999,104002,104005,104008,104011,104014],{"className":103902},[398],[363,103904],{"className":103905,"style":99832},[402],[363,103907,103909],{"className":103908},[1831,14063],[363,103910,103912,103942],{"className":103911},[633,634],[363,103913,103915,103939],{"className":103914},[638],[363,103916,103918,103929],{"className":103917,"style":2692},[642],[363,103919,103920,103923],{"style":61537},[363,103921],{"className":103922,"style":809},[650],[363,103924,103926],{"className":103925},[655,656,657,658],[363,103927,4505],{"className":103928,"style":1328},[407,408,658],[363,103930,103931,103934],{"style":12210},[363,103932],{"className":103933,"style":809},[650],[363,103935,103936],{},[363,103937,35779],{"className":103938},[1831],[363,103940,666],{"className":103941},[665],[363,103943,103945],{"className":103944},[638],[363,103946,103948],{"className":103947,"style":61569},[642],[363,103949],{},[363,103951],{"className":103952,"style":754},[505],[363,103954,103956],{"className":103955},[407],[363,103957,3245],{"className":103958},[767,4067],[363,103960,103962,103965],{"className":103961},[407],[363,103963,571],{"className":103964},[407,714],[363,103966,103968],{"className":103967},[629],[363,103969,103971,103991],{"className":103970},[633,634],[363,103972,103974,103988],{"className":103973},[638],[363,103975,103977],{"className":103976,"style":727},[642],[363,103978,103979,103982],{"style":730},[363,103980],{"className":103981,"style":651},[650],[363,103983,103985],{"className":103984},[655,656,657,658],[363,103986,554],{"className":103987,"style":682},[407,408,658],[363,103989,666],{"className":103990},[665],[363,103992,103994],{"className":103993},[638],[363,103995,103997],{"className":103996,"style":8315},[642],[363,103998],{},[363,104000,578],{"className":104001},[494],[363,104003,4505],{"className":104004,"style":1328},[407,408],[363,104006,605],{"className":104007},[501],[363,104009],{"className":104010,"style":2934},[505],[363,104012,5160],{"className":104013},[2938],[363,104015],{"className":104016,"style":2934},[505],[363,104018,104020,104023,104063,104066,104104,104107,104113],{"className":104019},[398],[363,104021],{"className":104022,"style":68464},[402],[363,104024,104026,104029],{"className":104025},[407],[363,104027,571],{"className":104028},[407,714],[363,104030,104032],{"className":104031},[629],[363,104033,104035,104055],{"className":104034},[633,634],[363,104036,104038,104052],{"className":104037},[638],[363,104039,104041],{"className":104040,"style":727},[642],[363,104042,104043,104046],{"style":730},[363,104044],{"className":104045,"style":651},[650],[363,104047,104049],{"className":104048},[655,656,657,658],[363,104050,561],{"className":104051},[407,408,658],[363,104053,666],{"className":104054},[665],[363,104056,104058],{"className":104057},[638],[363,104059,104061],{"className":104060,"style":673},[642],[363,104062],{},[363,104064,578],{"className":104065},[494],[363,104067,104069,104072],{"className":104068},[407],[363,104070,7914],{"className":104071},[407,408],[363,104073,104075],{"className":104074},[629],[363,104076,104078],{"className":104077},[633],[363,104079,104081],{"className":104080},[638],[363,104082,104084],{"className":104083,"style":20082},[642],[363,104085,104086,104089],{"style":8624},[363,104087],{"className":104088,"style":651},[650],[363,104090,104092],{"className":104091},[655,656,657,658],[363,104093,104095,104098,104101],{"className":104094},[407,658],[363,104096,4505],{"className":104097,"style":1328},[407,408,658],[363,104099,5160],{"className":104100},[2938,658],[363,104102,465],{"className":104103},[407,658],[363,104105,605],{"className":104106},[501],[363,104108,104110],{"className":104109},[407],[363,104111,3255],{"className":104112},[767,4067],[363,104114,4722],{"className":104115},[407],[11,104117,104118,104119,104327,104328,104401,104402,104434,104435,104463],{},"（这是「MINE-f」式下界。经典 Donsker–Varadhan 下界是 ",[363,104120,104122,104168],{"className":104121,"translate":367},[366],[363,104123,104125],{"className":104124},[371],[373,104126,104127],{"xmlns":375},[377,104128,104129,104165],{},[380,104130,104131,104137,104139,104141,104143,104145,104147,104149,104155,104157,104163],{},[543,104132,104133,104135],{},[383,104134,571],{"mathvariant":570},[383,104136,554],{},[458,104138,578],{"stretchy":460},[383,104140,4505],{},[458,104142,605],{"stretchy":460},[458,104144,5160],{},[383,104146,4447],{},[458,104148,4450],{},[543,104150,104151,104153],{},[383,104152,571],{"mathvariant":570},[383,104154,561],{},[458,104156,578],{"stretchy":460},[7161,104158,104159,104161],{},[383,104160,7914],{},[383,104162,4505],{},[458,104164,605],{"stretchy":460},[387,104166,104167],{"encoding":389},"\\mathbb E_P[g]-\\log\\mathbb E_Q[e^{g}]",[363,104169,104171,104235],{"className":104170,"ariaHidden":394},[393],[363,104172,104174,104177,104217,104220,104223,104226,104229,104232],{"className":104173},[398],[363,104175],{"className":104176,"style":487},[402],[363,104178,104180,104183],{"className":104179},[407],[363,104181,571],{"className":104182},[407,714],[363,104184,104186],{"className":104185},[629],[363,104187,104189,104209],{"className":104188},[633,634],[363,104190,104192,104206],{"className":104191},[638],[363,104193,104195],{"className":104194,"style":727},[642],[363,104196,104197,104200],{"style":730},[363,104198],{"className":104199,"style":651},[650],[363,104201,104203],{"className":104202},[655,656,657,658],[363,104204,554],{"className":104205,"style":682},[407,408,658],[363,104207,666],{"className":104208},[665],[363,104210,104212],{"className":104211},[638],[363,104213,104215],{"className":104214,"style":8315},[642],[363,104216],{},[363,104218,578],{"className":104219},[494],[363,104221,4505],{"className":104222,"style":1328},[407,408],[363,104224,605],{"className":104225},[501],[363,104227],{"className":104228,"style":2934},[505],[363,104230,5160],{"className":104231},[2938],[363,104233],{"className":104234,"style":2934},[505],[363,104236,104238,104241,104246,104249,104289,104292,104324],{"className":104237},[398],[363,104239],{"className":104240,"style":618},[402],[363,104242,4501,104244],{"className":104243},[1831],[363,104245,4505],{"style":4504},[363,104247],{"className":104248,"style":754},[505],[363,104250,104252,104255],{"className":104251},[407],[363,104253,571],{"className":104254},[407,714],[363,104256,104258],{"className":104257},[629],[363,104259,104261,104281],{"className":104260},[633,634],[363,104262,104264,104278],{"className":104263},[638],[363,104265,104267],{"className":104266,"style":727},[642],[363,104268,104269,104272],{"style":730},[363,104270],{"className":104271,"style":651},[650],[363,104273,104275],{"className":104274},[655,656,657,658],[363,104276,561],{"className":104277},[407,408,658],[363,104279,666],{"className":104280},[665],[363,104282,104284],{"className":104283},[638],[363,104285,104287],{"className":104286,"style":673},[642],[363,104288],{},[363,104290,578],{"className":104291},[494],[363,104293,104295,104298],{"className":104294},[407],[363,104296,7914],{"className":104297},[407,408],[363,104299,104301],{"className":104300},[629],[363,104302,104304],{"className":104303},[633],[363,104305,104307],{"className":104306},[638],[363,104308,104310],{"className":104309,"style":50700},[642],[363,104311,104312,104315],{"style":7212},[363,104313],{"className":104314,"style":651},[650],[363,104316,104318],{"className":104317},[655,656,657,658],[363,104319,104321],{"className":104320},[407,658],[363,104322,4505],{"className":104323,"style":1328},[407,408,658],[363,104325,605],{"className":104326},[501],"，二者同源但第二项不同：",[363,104329,104331,104354],{"className":104330,"translate":367},[366],[363,104332,104334],{"className":104333},[371],[373,104335,104336],{"xmlns":375},[377,104337,104338,104352],{},[380,104339,104340],{},[7161,104341,104342,104344],{},[383,104343,7914],{},[380,104345,104346,104348,104350],{},[383,104347,40584],{},[458,104349,5160],{},[463,104351,465],{},[387,104353,65249],{"encoding":389},[363,104355,104357],{"className":104356,"ariaHidden":394},[393],[363,104358,104360,104363],{"className":104359},[398],[363,104361],{"className":104362,"style":20375},[402],[363,104364,104366,104369],{"className":104365},[407],[363,104367,7914],{"className":104368},[407,408],[363,104370,104372],{"className":104371},[629],[363,104373,104375],{"className":104374},[633],[363,104376,104378],{"className":104377},[638],[363,104379,104381],{"className":104380,"style":20375},[642],[363,104382,104383,104386],{"style":7212},[363,104384],{"className":104385,"style":651},[650],[363,104387,104389],{"className":104388},[655,656,657,658],[363,104390,104392,104395,104398],{"className":104391},[407,658],[363,104393,40584],{"className":104394,"style":1328},[407,408,658],[363,104396,5160],{"className":104397},[2938,658],[363,104399,465],{"className":104400},[407,658]," 是把 ",[363,104403,104405,104420],{"className":104404,"translate":367},[366],[363,104406,104408],{"className":104407},[371],[373,104409,104410],{"xmlns":375},[377,104411,104412,104418],{},[380,104413,104414,104416],{},[383,104415,4447],{},[458,104417,4450],{},[387,104419,21930],{"encoding":389},[363,104421,104423],{"className":104422,"ariaHidden":394},[393],[363,104424,104426,104429],{"className":104425},[398],[363,104427],{"className":104428,"style":403},[402],[363,104430,4501,104432],{"className":104431},[1831],[363,104433,4505],{"style":4504}," 移到最外层并做 ",[363,104436,104438,104451],{"className":104437,"translate":367},[366],[363,104439,104441],{"className":104440},[371],[373,104442,104443],{"xmlns":375},[377,104444,104445,104449],{},[380,104446,104447],{},[383,104448,385],{},[387,104450,385],{"encoding":389},[363,104452,104454],{"className":104453,"ariaHidden":394},[393],[363,104455,104457,104460],{"className":104456},[398],[363,104458],{"className":104459,"style":403},[402],[363,104461,385],{"className":104462,"style":409},[407,408],"-散度对偶后的结果。）",[10374,104465,104466,104692,105085,105516],{},[7012,104467,104468,104471,104472,49519,104505,104533,104534,104589,104590,104640,104641,104691],{},[1572,104469,104470],{},"反向 KL \u002F α-GAN","：把 α 从 ",[363,104473,104475,104490],{"className":104474,"translate":367},[366],[363,104476,104478],{"className":104477},[371],[373,104479,104480],{"xmlns":375},[377,104481,104482,104488],{},[380,104483,104484,104486],{},[458,104485,5160],{},[463,104487,465],{},[387,104489,49503],{"encoding":389},[363,104491,104493],{"className":104492,"ariaHidden":394},[393],[363,104494,104496,104499,104502],{"className":104495},[398],[363,104497],{"className":104498,"style":12925},[402],[363,104500,5160],{"className":104501},[407],[363,104503,465],{"className":104504},[407],[363,104506,104508,104521],{"className":104507,"translate":367},[366],[363,104509,104511],{"className":104510},[371],[373,104512,104513],{"xmlns":375},[377,104514,104515,104519],{},[380,104516,104517],{},[463,104518,465],{},[387,104520,465],{"encoding":389},[363,104522,104524],{"className":104523,"ariaHidden":394},[393],[363,104525,104527,104530],{"className":104526},[398],[363,104528],{"className":104529,"style":520},[402],[363,104531,465],{"className":104532},[407],"，散度从反向 KL（",[363,104535,104537,104556],{"className":104536,"translate":367},[366],[363,104538,104540],{"className":104539},[371],[373,104541,104542],{"xmlns":375},[377,104543,104544,104554],{},[380,104545,104546,104548,104550,104552],{},[383,104547,45101],{},[458,104549,1376],{},[458,104551,5160],{},[463,104553,465],{},[387,104555,49386],{"encoding":389},[363,104557,104559,104577],{"className":104558,"ariaHidden":394},[393],[363,104560,104562,104565,104568,104571,104574],{"className":104561},[398],[363,104563],{"className":104564,"style":2692},[402],[363,104566,45101],{"className":104567,"style":45131},[407,408],[363,104569],{"className":104570,"style":506},[505],[363,104572,1376],{"className":104573},[510],[363,104575],{"className":104576,"style":506},[505],[363,104578,104580,104583,104586],{"className":104579},[398],[363,104581],{"className":104582,"style":12925},[402],[363,104584,5160],{"className":104585},[407],[363,104587,465],{"className":104588},[407],"，zero-forcing、模式崩塌倾向）经 Hellinger 型对称散度（",[363,104591,104593,104610],{"className":104592,"translate":367},[366],[363,104594,104596],{"className":104595},[371],[373,104597,104598],{"xmlns":375},[377,104599,104600,104608],{},[380,104601,104602,104604,104606],{},[383,104603,45101],{},[458,104605,471],{},[463,104607,474],{},[387,104609,46835],{"encoding":389},[363,104611,104613,104631],{"className":104612,"ariaHidden":394},[393],[363,104614,104616,104619,104622,104625,104628],{"className":104615},[398],[363,104617],{"className":104618,"style":2692},[402],[363,104620,45101],{"className":104621,"style":45131},[407,408],[363,104623],{"className":104624,"style":506},[505],[363,104626,471],{"className":104627},[510],[363,104629],{"className":104630,"style":506},[505],[363,104632,104634,104637],{"className":104633},[398],[363,104635],{"className":104636,"style":520},[402],[363,104638,474],{"className":104639},[407],"）过渡到正向 KL（",[363,104642,104644,104661],{"className":104643,"translate":367},[366],[363,104645,104647],{"className":104646},[371],[373,104648,104649],{"xmlns":375},[377,104650,104651,104659],{},[380,104652,104653,104655,104657],{},[383,104654,45101],{},[458,104656,1376],{},[463,104658,465],{},[387,104660,47562],{"encoding":389},[363,104662,104664,104682],{"className":104663,"ariaHidden":394},[393],[363,104665,104667,104670,104673,104676,104679],{"className":104666},[398],[363,104668],{"className":104669,"style":2692},[402],[363,104671,45101],{"className":104672,"style":45131},[407,408],[363,104674],{"className":104675,"style":506},[505],[363,104677,1376],{"className":104678},[510],[363,104680],{"className":104681,"style":506},[505],[363,104683,104685,104688],{"className":104684},[398],[363,104686],{"className":104687,"style":520},[402],[363,104689,465],{"className":104690},[407],"，zero-avoiding、模式覆盖倾向），可以在\"崩塌—覆盖\"之间连续调节（见 3.6 节的两端极限）。",[7012,104693,104694,9747,104696,3092,104940,105080,105081,105084],{},[1572,104695,53471],{},[363,104697,104699,104749],{"className":104698,"translate":367},[366],[363,104700,104702],{"className":104701},[371],[373,104703,104704],{"xmlns":375},[377,104705,104706,104746],{},[380,104707,104708,104714,104716,104718,104724,104726,104728,104730,104732,104734,104744],{},[7161,104709,104710,104712],{},[383,104711,385],{},[458,104713,7920],{},[458,104715,471],{},[458,104717,5160],{},[586,104719,104720,104722],{},[463,104721,465],{},[463,104723,2810],{},[383,104725,4447],{},[458,104727,4450],{},[458,104729,461],{"stretchy":460},[463,104731,2810],{},[458,104733,5160],{},[7161,104735,104736,104738],{},[383,104737,7914],{},[380,104739,104740,104742],{},[463,104741,2810],{},[383,104743,40584],{},[458,104745,468],{"stretchy":460},[387,104747,104748],{"encoding":389},"f^*=-\\frac12\\log(2-e^{2y})",[363,104750,104752,104796,104896],{"className":104751,"ariaHidden":394},[393],[363,104753,104755,104758,104787,104790,104793],{"className":104754},[398],[363,104756],{"className":104757,"style":403},[402],[363,104759,104761,104764],{"className":104760},[407],[363,104762,385],{"className":104763,"style":409},[407,408],[363,104765,104767],{"className":104766},[629],[363,104768,104770],{"className":104769},[633],[363,104771,104773],{"className":104772},[638],[363,104774,104776],{"className":104775,"style":8846},[642],[363,104777,104778,104781],{"style":7212},[363,104779],{"className":104780,"style":651},[650],[363,104782,104784],{"className":104783},[655,656,657,658],[363,104785,7920],{"className":104786},[2938,658],[363,104788],{"className":104789,"style":506},[505],[363,104791,471],{"className":104792},[510],[363,104794],{"className":104795,"style":506},[505],[363,104797,104799,104802,104805,104873,104876,104881,104884,104887,104890,104893],{"className":104798},[398],[363,104800],{"className":104801,"style":2852},[402],[363,104803,5160],{"className":104804},[407],[363,104806,104808,104811,104870],{"className":104807},[407],[363,104809],{"className":104810},[494,789],[363,104812,104814],{"className":104813},[586],[363,104815,104817,104862],{"className":104816},[633,634],[363,104818,104820,104859],{"className":104819},[638],[363,104821,104823,104837,104845],{"className":104822,"style":2871},[642],[363,104824,104825,104828],{"style":2874},[363,104826],{"className":104827,"style":809},[650],[363,104829,104831],{"className":104830},[655,656,657,658],[363,104832,104834],{"className":104833},[407,658],[363,104835,2810],{"className":104836},[407,658],[363,104838,104839,104842],{"style":821},[363,104840],{"className":104841,"style":809},[650],[363,104843],{"className":104844,"style":829},[828],[363,104846,104847,104850],{"style":2897},[363,104848],{"className":104849,"style":809},[650],[363,104851,104853],{"className":104852},[655,656,657,658],[363,104854,104856],{"className":104855},[407,658],[363,104857,465],{"className":104858},[407,658],[363,104860,666],{"className":104861},[665],[363,104863,104865],{"className":104864},[638],[363,104866,104868],{"className":104867,"style":2919},[642],[363,104869],{},[363,104871],{"className":104872},[501,789],[363,104874],{"className":104875,"style":754},[505],[363,104877,4501,104879],{"className":104878},[1831],[363,104880,4505],{"style":4504},[363,104882,461],{"className":104883},[494],[363,104885,2810],{"className":104886},[407],[363,104888],{"className":104889,"style":2934},[505],[363,104891,5160],{"className":104892},[2938],[363,104894],{"className":104895,"style":2934},[505],[363,104897,104899,104902,104937],{"className":104898},[398],[363,104900],{"className":104901,"style":20350},[402],[363,104903,104905,104908],{"className":104904},[407],[363,104906,7914],{"className":104907},[407,408],[363,104909,104911],{"className":104910},[629],[363,104912,104914],{"className":104913},[633],[363,104915,104917],{"className":104916},[638],[363,104918,104920],{"className":104919,"style":20375},[642],[363,104921,104922,104925],{"style":7212},[363,104923],{"className":104924,"style":651},[650],[363,104926,104928],{"className":104927},[655,656,657,658],[363,104929,104931,104934],{"className":104930},[407,658],[363,104932,2810],{"className":104933},[407,658],[363,104935,40584],{"className":104936,"style":1328},[407,408,658],[363,104938,468],{"className":104939},[501],[363,104941,104943,104970],{"className":104942,"translate":367},[366],[363,104944,104946],{"className":104945},[371],[373,104947,104948],{"xmlns":375},[377,104949,104950,104968],{},[380,104951,104952,104954,104956],{},[383,104953,40584],{},[458,104955,7598],{},[586,104957,104958,104966],{},[380,104959,104960,104962,104964],{},[383,104961,4447],{},[458,104963,4450],{},[463,104965,2810],{},[463,104967,2810],{},[387,104969,66090],{"encoding":389},[363,104971,104973,104991],{"className":104972,"ariaHidden":394},[393],[363,104974,104976,104979,104982,104985,104988],{"className":104975},[398],[363,104977],{"className":104978,"style":32039},[402],[363,104980,40584],{"className":104981,"style":1328},[407,408],[363,104983],{"className":104984,"style":506},[505],[363,104986,7598],{"className":104987},[510],[363,104989],{"className":104990,"style":506},[505],[363,104992,104994,104997],{"className":104993},[398],[363,104995],{"className":104996,"style":66118},[402],[363,104998,105000,105003,105077],{"className":104999},[407],[363,105001],{"className":105002},[494,789],[363,105004,105006],{"className":105005},[586],[363,105007,105009,105069],{"className":105008},[633,634],[363,105010,105012,105066],{"className":105011},[638],[363,105013,105015,105029,105037],{"className":105014,"style":3172},[642],[363,105016,105017,105020],{"style":2874},[363,105018],{"className":105019,"style":809},[650],[363,105021,105023],{"className":105022},[655,656,657,658],[363,105024,105026],{"className":105025},[407,658],[363,105027,2810],{"className":105028},[407,658],[363,105030,105031,105034],{"style":821},[363,105032],{"className":105033,"style":809},[650],[363,105035],{"className":105036,"style":829},[828],[363,105038,105039,105042],{"style":3200},[363,105040],{"className":105041,"style":809},[650],[363,105043,105045],{"className":105044},[655,656,657,658],[363,105046,105048,105060,105063],{"className":105047},[407,658],[363,105049,105051,105054,105057],{"className":105050},[1831,658],[363,105052,48005],{"className":105053},[658],[363,105055,48009],{"className":105056},[658],[363,105058,4505],{"className":105059,"style":4504},[658],[363,105061],{"className":105062,"style":42713},[505,658],[363,105064,2810],{"className":105065},[407,658],[363,105067,666],{"className":105068},[665],[363,105070,105072],{"className":105071},[638],[363,105073,105075],{"className":105074,"style":2919},[642],[363,105076],{},[363,105078],{"className":105079},[501,789],"。代回即",[1572,105082,105083],{},"原始 GAN 的对抗目标","（见 5.4）。",[7012,105086,105087,9747,105148,105288,105289,105511,105512,105515],{},[1572,105088,105089,105147],{},[363,105090,105092,105109],{"className":105091,"translate":367},[366],[363,105093,105095],{"className":105094},[371],[373,105096,105097],{"xmlns":375},[377,105098,105099,105107],{},[380,105100,105101],{},[7161,105102,105103,105105],{},[383,105104,37796],{},[463,105106,2810],{},[387,105108,40741],{"encoding":389},[363,105110,105112],{"className":105111,"ariaHidden":394},[393],[363,105113,105115,105118],{"className":105114},[398],[363,105116],{"className":105117,"style":40751},[402],[363,105119,105121,105124],{"className":105120},[407],[363,105122,37796],{"className":105123},[407,408],[363,105125,105127],{"className":105126},[629],[363,105128,105130],{"className":105129},[633],[363,105131,105133],{"className":105132},[638],[363,105134,105136],{"className":105135,"style":20375},[642],[363,105137,105138,105141],{"style":7212},[363,105139],{"className":105140,"style":651},[650],[363,105142,105144],{"className":105143},[655,656,657,658],[363,105145,2810],{"className":105146},[407,658],"（LSGAN）",[363,105149,105151,105185],{"className":105150,"translate":367},[366],[363,105152,105154],{"className":105153},[371],[373,105155,105156],{"xmlns":375},[377,105157,105158,105182],{},[380,105159,105160,105166,105168,105170,105172,105178,105180],{},[7161,105161,105162,105164],{},[383,105163,385],{},[458,105165,7920],{},[458,105167,471],{},[383,105169,40584],{},[458,105171,2817],{},[7161,105173,105174,105176],{},[383,105175,40584],{},[463,105177,2810],{},[383,105179,1288],{"mathvariant":557},[463,105181,39336],{},[387,105183,105184],{"encoding":389},"f^*=y+y^2\u002F4",[363,105186,105188,105232,105250],{"className":105187,"ariaHidden":394},[393],[363,105189,105191,105194,105223,105226,105229],{"className":105190},[398],[363,105192],{"className":105193,"style":403},[402],[363,105195,105197,105200],{"className":105196},[407],[363,105198,385],{"className":105199,"style":409},[407,408],[363,105201,105203],{"className":105202},[629],[363,105204,105206],{"className":105205},[633],[363,105207,105209],{"className":105208},[638],[363,105210,105212],{"className":105211,"style":8846},[642],[363,105213,105214,105217],{"style":7212},[363,105215],{"className":105216,"style":651},[650],[363,105218,105220],{"className":105219},[655,656,657,658],[363,105221,7920],{"className":105222},[2938,658],[363,105224],{"className":105225,"style":506},[505],[363,105227,471],{"className":105228},[510],[363,105230],{"className":105231,"style":506},[505],[363,105233,105235,105238,105241,105244,105247],{"className":105234},[398],[363,105236],{"className":105237,"style":40668},[402],[363,105239,40584],{"className":105240,"style":1328},[407,408],[363,105242],{"className":105243,"style":2934},[505],[363,105245,2817],{"className":105246},[2938],[363,105248],{"className":105249,"style":2934},[505],[363,105251,105253,105256,105285],{"className":105252},[398],[363,105254],{"className":105255,"style":20350},[402],[363,105257,105259,105262],{"className":105258},[407],[363,105260,40584],{"className":105261,"style":1328},[407,408],[363,105263,105265],{"className":105264},[629],[363,105266,105268],{"className":105267},[633],[363,105269,105271],{"className":105270},[638],[363,105272,105274],{"className":105273,"style":20375},[642],[363,105275,105276,105279],{"style":7212},[363,105277],{"className":105278,"style":651},[650],[363,105280,105282],{"className":105281},[655,656,657,658],[363,105283,2810],{"className":105284},[407,658],[363,105286,40719],{"className":105287},[407],"，目标变为 ",[363,105290,105292,105342],{"className":105291,"translate":367},[366],[363,105293,105295],{"className":105294},[371],[373,105296,105297],{"xmlns":375},[377,105298,105299,105339],{},[380,105300,105301,105307,105309,105311,105313,105315,105321,105323,105325,105327,105333,105335,105337],{},[543,105302,105303,105305],{},[383,105304,571],{"mathvariant":570},[383,105306,554],{},[458,105308,578],{"stretchy":460},[383,105310,4505],{},[458,105312,605],{"stretchy":460},[458,105314,5160],{},[543,105316,105317,105319],{},[383,105318,571],{"mathvariant":570},[383,105320,561],{},[458,105322,578],{"stretchy":460},[383,105324,4505],{},[458,105326,2817],{},[7161,105328,105329,105331],{},[383,105330,4505],{},[463,105332,2810],{},[383,105334,1288],{"mathvariant":557},[463,105336,39336],{},[458,105338,605],{"stretchy":460},[387,105340,105341],{"encoding":389},"\\mathbb E_P[g]-\\mathbb E_Q[g+g^2\u002F4]",[363,105343,105345,105409,105470],{"className":105344,"ariaHidden":394},[393],[363,105346,105348,105351,105391,105394,105397,105400,105403,105406],{"className":105347},[398],[363,105349],{"className":105350,"style":487},[402],[363,105352,105354,105357],{"className":105353},[407],[363,105355,571],{"className":105356},[407,714],[363,105358,105360],{"className":105359},[629],[363,105361,105363,105383],{"className":105362},[633,634],[363,105364,105366,105380],{"className":105365},[638],[363,105367,105369],{"className":105368,"style":727},[642],[363,105370,105371,105374],{"style":730},[363,105372],{"className":105373,"style":651},[650],[363,105375,105377],{"className":105376},[655,656,657,658],[363,105378,554],{"className":105379,"style":682},[407,408,658],[363,105381,666],{"className":105382},[665],[363,105384,105386],{"className":105385},[638],[363,105387,105389],{"className":105388,"style":8315},[642],[363,105390],{},[363,105392,578],{"className":105393},[494],[363,105395,4505],{"className":105396,"style":1328},[407,408],[363,105398,605],{"className":105399},[501],[363,105401],{"className":105402,"style":2934},[505],[363,105404,5160],{"className":105405},[2938],[363,105407],{"className":105408,"style":2934},[505],[363,105410,105412,105415,105455,105458,105461,105464,105467],{"className":105411},[398],[363,105413],{"className":105414,"style":618},[402],[363,105416,105418,105421],{"className":105417},[407],[363,105419,571],{"className":105420},[407,714],[363,105422,105424],{"className":105423},[629],[363,105425,105427,105447],{"className":105426},[633,634],[363,105428,105430,105444],{"className":105429},[638],[363,105431,105433],{"className":105432,"style":727},[642],[363,105434,105435,105438],{"style":730},[363,105436],{"className":105437,"style":651},[650],[363,105439,105441],{"className":105440},[655,656,657,658],[363,105442,561],{"className":105443},[407,408,658],[363,105445,666],{"className":105446},[665],[363,105448,105450],{"className":105449},[638],[363,105451,105453],{"className":105452,"style":673},[642],[363,105454],{},[363,105456,578],{"className":105457},[494],[363,105459,4505],{"className":105460,"style":1328},[407,408],[363,105462],{"className":105463,"style":2934},[505],[363,105465,2817],{"className":105466},[2938],[363,105468],{"className":105469,"style":2934},[505],[363,105471,105473,105476,105505,105508],{"className":105472},[398],[363,105474],{"className":105475,"style":20350},[402],[363,105477,105479,105482],{"className":105478},[407],[363,105480,4505],{"className":105481,"style":1328},[407,408],[363,105483,105485],{"className":105484},[629],[363,105486,105488],{"className":105487},[633],[363,105489,105491],{"className":105490},[638],[363,105492,105494],{"className":105493,"style":20375},[642],[363,105495,105496,105499],{"style":7212},[363,105497],{"className":105498,"style":651},[650],[363,105500,105502],{"className":105501},[655,656,657,658],[363,105503,2810],{"className":105504},[407,658],[363,105506,40719],{"className":105507},[407],[363,105509,605],{"className":105510},[501],"，即对判别器输出做",[1572,105513,105514],{},"最小二乘","回归，梯度不会像 sigmoid 那样饱和。",[7012,105517,105518,9747,105521,3092,105644,10527],{},[1572,105519,105520],{},"Hellinger²",[363,105522,105524,105558],{"className":105523,"translate":367},[366],[363,105525,105527],{"className":105526},[371],[373,105528,105529],{"xmlns":375},[377,105530,105531,105555],{},[380,105532,105533,105539,105541,105543,105545,105547,105549,105551,105553],{},[7161,105534,105535,105537],{},[383,105536,385],{},[458,105538,7920],{},[458,105540,471],{},[383,105542,40584],{},[383,105544,1288],{"mathvariant":557},[458,105546,461],{"stretchy":460},[463,105548,465],{},[458,105550,5160],{},[383,105552,40584],{},[458,105554,468],{"stretchy":460},[387,105556,105557],{"encoding":389},"f^*=y\u002F(1-y)",[363,105559,105561,105605,105632],{"className":105560,"ariaHidden":394},[393],[363,105562,105564,105567,105596,105599,105602],{"className":105563},[398],[363,105565],{"className":105566,"style":403},[402],[363,105568,105570,105573],{"className":105569},[407],[363,105571,385],{"className":105572,"style":409},[407,408],[363,105574,105576],{"className":105575},[629],[363,105577,105579],{"className":105578},[633],[363,105580,105582],{"className":105581},[638],[363,105583,105585],{"className":105584,"style":8846},[642],[363,105586,105587,105590],{"style":7212},[363,105588],{"className":105589,"style":651},[650],[363,105591,105593],{"className":105592},[655,656,657,658],[363,105594,7920],{"className":105595},[2938,658],[363,105597],{"className":105598,"style":506},[505],[363,105600,471],{"className":105601},[510],[363,105603],{"className":105604,"style":506},[505],[363,105606,105608,105611,105614,105617,105620,105623,105626,105629],{"className":105607},[398],[363,105609],{"className":105610,"style":487},[402],[363,105612,40584],{"className":105613,"style":1328},[407,408],[363,105615,1288],{"className":105616},[407],[363,105618,461],{"className":105619},[494],[363,105621,465],{"className":105622},[407],[363,105624],{"className":105625,"style":2934},[505],[363,105627,5160],{"className":105628},[2938],[363,105630],{"className":105631,"style":2934},[505],[363,105633,105635,105638,105641],{"className":105634},[398],[363,105636],{"className":105637,"style":487},[402],[363,105639,40584],{"className":105640,"style":1328},[407,408],[363,105642,468],{"className":105643},[501],[363,105645,105647,105664],{"className":105646,"translate":367},[366],[363,105648,105650],{"className":105649},[371],[373,105651,105652],{"xmlns":375},[377,105653,105654,105662],{},[380,105655,105656,105658,105660],{},[383,105657,40584],{},[458,105659,7598],{},[463,105661,465],{},[387,105663,67120],{"encoding":389},[363,105665,105667,105685],{"className":105666,"ariaHidden":394},[393],[363,105668,105670,105673,105676,105679,105682],{"className":105669},[398],[363,105671],{"className":105672,"style":32039},[402],[363,105674,40584],{"className":105675,"style":1328},[407,408],[363,105677],{"className":105678,"style":506},[505],[363,105680,7598],{"className":105681},[510],[363,105683],{"className":105684,"style":506},[505],[363,105686,105688,105691],{"className":105687},[398],[363,105689],{"className":105690,"style":520},[402],[363,105692,465],{"className":105693},[407],[2658,105695,105697],{"id":105696},"_54-原始-gan-与-js-散度","5.4 原始 GAN 与 JS 散度",[11,105699,105700,105701,105883],{},"原始 GAN 的判别器输出经 sigmoid 得 ",[363,105702,105704,105756],{"className":105703,"translate":367},[366],[363,105705,105707],{"className":105706},[371],[373,105708,105709],{"xmlns":375},[377,105710,105711,105753],{},[380,105712,105713,105715,105717,105719,105721,105723,105725,105727,105729,105735,105737,105739,105741,105743,105745,105747,105749,105751],{},[383,105714,2679],{},[458,105716,461],{"stretchy":460},[383,105718,547],{},[458,105720,461],{"stretchy":460},[383,105722,1121],{},[458,105724,468],{"stretchy":460},[458,105726,468],{"stretchy":460},[458,105728,471],{},[543,105730,105731,105733],{},[383,105732,547],{},[383,105734,7908],{},[458,105736,461],{"stretchy":460},[383,105738,1121],{},[458,105740,468],{"stretchy":460},[458,105742,6256],{},[458,105744,461],{"stretchy":460},[463,105746,474],{},[458,105748,898],{"separator":394},[463,105750,465],{},[458,105752,468],{"stretchy":460},[387,105754,105755],{"encoding":389},"\\sigma(D(x))=D_{s}(x)\\in(0,1)",[363,105757,105759,105792,105859],{"className":105758,"ariaHidden":394},[393],[363,105760,105762,105765,105768,105771,105774,105777,105780,105783,105786,105789],{"className":105761},[398],[363,105763],{"className":105764,"style":487},[402],[363,105766,2679],{"className":105767,"style":1328},[407,408],[363,105769,461],{"className":105770},[494],[363,105772,547],{"className":105773,"style":625},[407,408],[363,105775,461],{"className":105776},[494],[363,105778,1121],{"className":105779},[407,408],[363,105781,19394],{"className":105782},[501],[363,105784],{"className":105785,"style":506},[505],[363,105787,471],{"className":105788},[510],[363,105790],{"className":105791,"style":506},[505],[363,105793,105795,105798,105841,105844,105847,105850,105853,105856],{"className":105794},[398],[363,105796],{"className":105797,"style":487},[402],[363,105799,105801,105804],{"className":105800},[407],[363,105802,547],{"className":105803,"style":625},[407,408],[363,105805,105807],{"className":105806},[629],[363,105808,105810,105833],{"className":105809},[633,634],[363,105811,105813,105830],{"className":105812},[638],[363,105814,105816],{"className":105815,"style":45276},[642],[363,105817,105818,105821],{"style":646},[363,105819],{"className":105820,"style":651},[650],[363,105822,105824],{"className":105823},[655,656,657,658],[363,105825,105827],{"className":105826},[407,658],[363,105828,7908],{"className":105829},[407,408,658],[363,105831,666],{"className":105832},[665],[363,105834,105836],{"className":105835},[638],[363,105837,105839],{"className":105838,"style":8315},[642],[363,105840],{},[363,105842,461],{"className":105843},[494],[363,105845,1121],{"className":105846},[407,408],[363,105848,468],{"className":105849},[501],[363,105851],{"className":105852,"style":506},[505],[363,105854,6256],{"className":105855},[510],[363,105857],{"className":105858,"style":506},[505],[363,105860,105862,105865,105868,105871,105874,105877,105880],{"className":105861},[398],[363,105863],{"className":105864,"style":487},[402],[363,105866,461],{"className":105867},[494],[363,105869,474],{"className":105870},[407],[363,105872,898],{"className":105873},[920],[363,105875],{"className":105876,"style":754},[505],[363,105878,465],{"className":105879},[407],[363,105881,468],{"className":105882},[501],"，其目标等价于最小化 JS 散度下的对抗博弈。判别器写成 logit",[363,105885,105887],{"className":105886,"translate":367},[528],[363,105888,105890,105968],{"className":105889,"translate":367},[366],[363,105891,105893],{"className":105892},[371],[373,105894,105895],{"xmlns":375,"display":537},[377,105896,105897,105965],{},[380,105898,105899,105901,105903,105905,105907,105909,105911,105913,105919,105921,105923,105925,105927,105929,105931,105933,105935,105937,105943,105945,105947,105949,105951,105953,105955,105957,105963],{},[383,105900,4505],{},[458,105902,461],{"stretchy":460},[383,105904,1121],{},[458,105906,468],{"stretchy":460},[458,105908,471],{},[383,105910,4447],{},[458,105912,4450],{},[543,105914,105915,105917],{},[383,105916,547],{},[383,105918,7908],{},[458,105920,461],{"stretchy":460},[383,105922,1121],{},[458,105924,468],{"stretchy":460},[458,105926,5160],{},[383,105928,4447],{},[458,105930,4450],{},[458,105932,461],{"stretchy":460},[463,105934,465],{},[458,105936,5160],{},[543,105938,105939,105941],{},[383,105940,547],{},[383,105942,7908],{},[458,105944,461],{"stretchy":460},[383,105946,1121],{},[458,105948,468],{"stretchy":460},[458,105950,468],{"stretchy":460},[458,105952,471],{},[383,105954,4447],{},[458,105956,4450],{},[586,105958,105959,105961],{},[383,105960,11],{},[383,105962,1291],{},[458,105964,898],{"separator":394},[387,105966,105967],{"encoding":389},"g(x)=\\log D_s(x)-\\log(1-D_s(x))\n=\\log\\frac{p}{q},",[363,105969,105971,105998,106070,106096,106160],{"className":105970,"ariaHidden":394},[393],[363,105972,105974,105977,105980,105983,105986,105989,105992,105995],{"className":105973},[398],[363,105975],{"className":105976,"style":487},[402],[363,105978,4505],{"className":105979,"style":1328},[407,408],[363,105981,461],{"className":105982},[494],[363,105984,1121],{"className":105985},[407,408],[363,105987,468],{"className":105988},[501],[363,105990],{"className":105991,"style":506},[505],[363,105993,471],{"className":105994},[510],[363,105996],{"className":105997,"style":506},[505],[363,105999,106001,106004,106009,106012,106052,106055,106058,106061,106064,106067],{"className":106000},[398],[363,106002],{"className":106003,"style":487},[402],[363,106005,4501,106007],{"className":106006},[1831],[363,106008,4505],{"style":4504},[363,106010],{"className":106011,"style":754},[505],[363,106013,106015,106018],{"className":106014},[407],[363,106016,547],{"className":106017,"style":625},[407,408],[363,106019,106021],{"className":106020},[629],[363,106022,106024,106044],{"className":106023},[633,634],[363,106025,106027,106041],{"className":106026},[638],[363,106028,106030],{"className":106029,"style":45276},[642],[363,106031,106032,106035],{"style":646},[363,106033],{"className":106034,"style":651},[650],[363,106036,106038],{"className":106037},[655,656,657,658],[363,106039,7908],{"className":106040},[407,408,658],[363,106042,666],{"className":106043},[665],[363,106045,106047],{"className":106046},[638],[363,106048,106050],{"className":106049,"style":8315},[642],[363,106051],{},[363,106053,461],{"className":106054},[494],[363,106056,1121],{"className":106057},[407,408],[363,106059,468],{"className":106060},[501],[363,106062],{"className":106063,"style":2934},[505],[363,106065,5160],{"className":106066},[2938],[363,106068],{"className":106069,"style":2934},[505],[363,106071,106073,106076,106081,106084,106087,106090,106093],{"className":106072},[398],[363,106074],{"className":106075,"style":487},[402],[363,106077,4501,106079],{"className":106078},[1831],[363,106080,4505],{"style":4504},[363,106082,461],{"className":106083},[494],[363,106085,465],{"className":106086},[407],[363,106088],{"className":106089,"style":2934},[505],[363,106091,5160],{"className":106092},[2938],[363,106094],{"className":106095,"style":2934},[505],[363,106097,106099,106102,106142,106145,106148,106151,106154,106157],{"className":106098},[398],[363,106100],{"className":106101,"style":487},[402],[363,106103,106105,106108],{"className":106104},[407],[363,106106,547],{"className":106107,"style":625},[407,408],[363,106109,106111],{"className":106110},[629],[363,106112,106114,106134],{"className":106113},[633,634],[363,106115,106117,106131],{"className":106116},[638],[363,106118,106120],{"className":106119,"style":45276},[642],[363,106121,106122,106125],{"style":646},[363,106123],{"className":106124,"style":651},[650],[363,106126,106128],{"className":106127},[655,656,657,658],[363,106129,7908],{"className":106130},[407,408,658],[363,106132,666],{"className":106133},[665],[363,106135,106137],{"className":106136},[638],[363,106138,106140],{"className":106139,"style":8315},[642],[363,106141],{},[363,106143,461],{"className":106144},[494],[363,106146,1121],{"className":106147},[407,408],[363,106149,19394],{"className":106150},[501],[363,106152],{"className":106153,"style":506},[505],[363,106155,471],{"className":106156},[510],[363,106158],{"className":106159,"style":506},[505],[363,106161,106163,106166,106171,106174,106236],{"className":106162},[398],[363,106164],{"className":106165,"style":22357},[402],[363,106167,4501,106169],{"className":106168},[1831],[363,106170,4505],{"style":4504},[363,106172],{"className":106173,"style":754},[505],[363,106175,106177,106180,106233],{"className":106176},[407],[363,106178],{"className":106179},[494,789],[363,106181,106183],{"className":106182},[586],[363,106184,106186,106225],{"className":106185},[633,634],[363,106187,106189,106222],{"className":106188},[638],[363,106190,106192,106203,106211],{"className":106191,"style":3901},[642],[363,106193,106194,106197],{"style":805},[363,106195],{"className":106196,"style":809},[650],[363,106198,106200],{"className":106199},[407],[363,106201,1291],{"className":106202,"style":1328},[407,408],[363,106204,106205,106208],{"style":821},[363,106206],{"className":106207,"style":809},[650],[363,106209],{"className":106210,"style":829},[828],[363,106212,106213,106216],{"style":832},[363,106214],{"className":106215,"style":809},[650],[363,106217,106219],{"className":106218},[407],[363,106220,11],{"className":106221},[407,408],[363,106223,666],{"className":106224},[665],[363,106226,106228],{"className":106227},[638],[363,106229,106231],{"className":106230,"style":854},[642],[363,106232],{},[363,106234],{"className":106235},[501,789],[363,106237,898],{"className":106238},[920],[11,106240,106241],{},"它与 5.2 节的最优解",[363,106243,106245],{"className":106244,"translate":367},[528],[363,106246,106248,106330],{"className":106247,"translate":367},[366],[363,106249,106251],{"className":106250},[371],[373,106252,106253],{"xmlns":375,"display":537},[377,106254,106255,106327],{},[380,106256,106257,106269,106271,106273,106275,106277,106289,106291,106297,106299,106301,106307,106309,106311],{},[7900,106258,106259,106261,106267],{},[383,106260,4505],{},[380,106262,106263,106265],{},[383,106264,24090],{},[383,106266,26084],{},[458,106268,7920],{},[458,106270,461],{"stretchy":460},[383,106272,1121],{},[458,106274,468],{"stretchy":460},[458,106276,471],{},[7900,106278,106279,106281,106287],{},[383,106280,385],{},[380,106282,106283,106285],{},[383,106284,24090],{},[383,106286,26084],{},[458,106288,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,106290,461],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[586,106292,106293,106295],{},[383,106294,11],{},[383,106296,1291],{},[458,106298,468],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[458,106300,471],{},[586,106302,106303,106305],{},[463,106304,465],{},[463,106306,2810],{},[383,106308,4447],{},[458,106310,4450],{},[586,106312,106313,106319],{},[380,106314,106315,106317],{},[463,106316,2810],{},[383,106318,1116],{},[380,106320,106321,106323,106325],{},[383,106322,1116],{},[458,106324,2817],{},[463,106326,465],{},[387,106328,106329],{"encoding":389},"g_{JS}^*(x)=f_{JS}'\\Big(\\frac{p}{q}\\Big)\n=\\frac12\\log\\frac{2t}{t+1}",[363,106331,106333,106415,106564],{"className":106332,"ariaHidden":394},[393],[363,106334,106336,106339,106397,106400,106403,106406,106409,106412],{"className":106335},[398],[363,106337],{"className":106338,"style":487},[402],[363,106340,106342,106345],{"className":106341},[407],[363,106343,4505],{"className":106344,"style":1328},[407,408],[363,106346,106348],{"className":106347},[629],[363,106349,106351,106389],{"className":106350},[633,634],[363,106352,106354,106386],{"className":106353},[638],[363,106355,106357,106375],{"className":106356,"style":8595},[642],[363,106358,106360,106363],{"style":106359},"top:-2.453em;margin-left:-0.0359em;margin-right:0.05em;",[363,106361],{"className":106362,"style":651},[650],[363,106364,106366],{"className":106365},[655,656,657,658],[363,106367,106369,106372],{"className":106368},[407,658],[363,106370,24090],{"className":106371,"style":24500},[407,408,658],[363,106373,26084],{"className":106374,"style":26208},[407,408,658],[363,106376,106377,106380],{"style":8624},[363,106378],{"className":106379,"style":651},[650],[363,106381,106383],{"className":106382},[655,656,657,658],[363,106384,7920],{"className":106385},[2938,658],[363,106387,666],{"className":106388},[665],[363,106390,106392],{"className":106391},[638],[363,106393,106395],{"className":106394,"style":8646},[642],[363,106396],{},[363,106398,461],{"className":106399},[494],[363,106401,1121],{"className":106402},[407,408],[363,106404,468],{"className":106405},[501],[363,106407],{"className":106408,"style":506},[505],[363,106410,471],{"className":106411},[510],[363,106413],{"className":106414,"style":506},[505],[363,106416,106418,106421,106481,106487,106549,106555,106558,106561],{"className":106417},[398],[363,106419],{"className":106420,"style":48312},[402],[363,106422,106424,106427],{"className":106423},[407],[363,106425,385],{"className":106426,"style":409},[407,408],[363,106428,106430],{"className":106429},[629],[363,106431,106433,106473],{"className":106432},[633,634],[363,106434,106436,106470],{"className":106435},[638],[363,106437,106439,106456],{"className":106438,"style":29318},[642],[363,106440,106441,106444],{"style":8598},[363,106442],{"className":106443,"style":651},[650],[363,106445,106447],{"className":106446},[655,656,657,658],[363,106448,106450,106453],{"className":106449},[407,658],[363,106451,24090],{"className":106452,"style":24500},[407,408,658],[363,106454,26084],{"className":106455,"style":26208},[407,408,658],[363,106457,106458,106461],{"style":8624},[363,106459],{"className":106460,"style":651},[650],[363,106462,106464],{"className":106463},[655,656,657,658],[363,106465,106467],{"className":106466},[407,658],[363,106468,7167],{"className":106469},[407,658],[363,106471,666],{"className":106472},[665],[363,106474,106476],{"className":106475},[638],[363,106477,106479],{"className":106478,"style":8646},[642],[363,106480],{},[363,106482,106484],{"className":106483},[407],[363,106485,461],{"className":106486},[767,4067],[363,106488,106490,106493,106546],{"className":106489},[407],[363,106491],{"className":106492},[494,789],[363,106494,106496],{"className":106495},[586],[363,106497,106499,106538],{"className":106498},[633,634],[363,106500,106502,106535],{"className":106501},[638],[363,106503,106505,106516,106524],{"className":106504,"style":3901},[642],[363,106506,106507,106510],{"style":805},[363,106508],{"className":106509,"style":809},[650],[363,106511,106513],{"className":106512},[407],[363,106514,1291],{"className":106515,"style":1328},[407,408],[363,106517,106518,106521],{"style":821},[363,106519],{"className":106520,"style":809},[650],[363,106522],{"className":106523,"style":829},[828],[363,106525,106526,106529],{"style":832},[363,106527],{"className":106528,"style":809},[650],[363,106530,106532],{"className":106531},[407],[363,106533,11],{"className":106534},[407,408],[363,106536,666],{"className":106537},[665],[363,106539,106541],{"className":106540},[638],[363,106542,106544],{"className":106543,"style":854},[642],[363,106545],{},[363,106547],{"className":106548},[501,789],[363,106550,106552],{"className":106551},[407],[363,106553,468],{"className":106554},[767,4067],[363,106556],{"className":106557,"style":506},[505],[363,106559,471],{"className":106560},[510],[363,106562],{"className":106563,"style":506},[505],[363,106565,106567,106570,106632,106635,106640,106643],{"className":106566},[398],[363,106568],{"className":106569,"style":26963},[402],[363,106571,106573,106576,106629],{"className":106572},[407],[363,106574],{"className":106575},[494,789],[363,106577,106579],{"className":106578},[586],[363,106580,106582,106621],{"className":106581},[633,634],[363,106583,106585,106618],{"className":106584},[638],[363,106586,106588,106599,106607],{"className":106587,"style":23236},[642],[363,106589,106590,106593],{"style":805},[363,106591],{"className":106592,"style":809},[650],[363,106594,106596],{"className":106595},[407],[363,106597,2810],{"className":106598},[407],[363,106600,106601,106604],{"style":821},[363,106602],{"className":106603,"style":809},[650],[363,106605],{"className":106606,"style":829},[828],[363,106608,106609,106612],{"style":832},[363,106610],{"className":106611,"style":809},[650],[363,106613,106615],{"className":106614},[407],[363,106616,465],{"className":106617},[407],[363,106619,666],{"className":106620},[665],[363,106622,106624],{"className":106623},[638],[363,106625,106627],{"className":106626,"style":4125},[642],[363,106628],{},[363,106630],{"className":106631},[501,789],[363,106633],{"className":106634,"style":754},[505],[363,106636,4501,106638],{"className":106637},[1831],[363,106639,4505],{"style":4504},[363,106641],{"className":106642,"style":754},[505],[363,106644,106646,106649,106717],{"className":106645},[407],[363,106647],{"className":106648},[494,789],[363,106650,106652],{"className":106651},[586],[363,106653,106655,106709],{"className":106654},[633,634],[363,106656,106658,106706],{"className":106657},[638],[363,106659,106661,106684,106692],{"className":106660,"style":23236},[642],[363,106662,106663,106666],{"style":805},[363,106664],{"className":106665,"style":809},[650],[363,106667,106669,106672,106675,106678,106681],{"className":106668},[407],[363,106670,1116],{"className":106671},[407,408],[363,106673],{"className":106674,"style":2934},[505],[363,106676,2817],{"className":106677},[2938],[363,106679],{"className":106680,"style":2934},[505],[363,106682,465],{"className":106683},[407],[363,106685,106686,106689],{"style":821},[363,106687],{"className":106688,"style":809},[650],[363,106690],{"className":106691,"style":829},[828],[363,106693,106694,106697],{"style":832},[363,106695],{"className":106696,"style":809},[650],[363,106698,106700,106703],{"className":106699},[407],[363,106701,2810],{"className":106702},[407],[363,106704,1116],{"className":106705},[407,408],[363,106707,666],{"className":106708},[665],[363,106710,106712],{"className":106711},[638],[363,106713,106715],{"className":106714,"style":17362},[642],[363,106716],{},[363,106718],{"className":106719},[501,789],[11,106721,106722,106723,107109],{},"通过重参数化 ",[363,106724,106726,106786],{"className":106725,"translate":367},[366],[363,106727,106729],{"className":106728},[371],[373,106730,106731],{"xmlns":375},[377,106732,106733,106783],{},[380,106734,106735,106743,106745,106769,106771],{},[7900,106736,106737,106739,106741],{},[383,106738,547],{},[383,106740,7908],{},[458,106742,7920],{},[458,106744,471],{},[586,106746,106747,106767],{},[7161,106748,106749,106751],{},[383,106750,7914],{},[380,106752,106753,106755],{},[463,106754,2810],{},[7900,106756,106757,106759,106765],{},[383,106758,4505],{},[380,106760,106761,106763],{},[383,106762,24090],{},[383,106764,26084],{},[458,106766,7920],{},[463,106768,2810],{},[458,106770,471],{},[586,106772,106773,106775],{},[383,106774,11],{},[380,106776,106777,106779,106781],{},[383,106778,11],{},[458,106780,2817],{},[383,106782,1291],{},[387,106784,106785],{"encoding":389},"D_s^*=\\frac{e^{2g_{JS}^*}}{2}=\\frac{p}{p+q}",[363,106787,106789,106856,107029],{"className":106788,"ariaHidden":394},[393],[363,106790,106792,106796,106847,106850,106853],{"className":106791},[398],[363,106793],{"className":106794,"style":106795},[402],"height:0.9357em;vertical-align:-0.247em;",[363,106797,106799,106802],{"className":106798},[407],[363,106800,547],{"className":106801,"style":625},[407,408],[363,106803,106805],{"className":106804},[629],[363,106806,106808,106839],{"className":106807},[633,634],[363,106809,106811,106836],{"className":106810},[638],[363,106812,106814,106825],{"className":106813,"style":8846},[642],[363,106815,106816,106819],{"style":49919},[363,106817],{"className":106818,"style":651},[650],[363,106820,106822],{"className":106821},[655,656,657,658],[363,106823,7908],{"className":106824},[407,408,658],[363,106826,106827,106830],{"style":7212},[363,106828],{"className":106829,"style":651},[650],[363,106831,106833],{"className":106832},[655,656,657,658],[363,106834,7920],{"className":106835},[2938,658],[363,106837,666],{"className":106838},[665],[363,106840,106842],{"className":106841},[638],[363,106843,106845],{"className":106844,"style":8646},[642],[363,106846],{},[363,106848],{"className":106849,"style":506},[505],[363,106851,471],{"className":106852},[510],[363,106854],{"className":106855,"style":506},[505],[363,106857,106859,106863,107020,107023,107026],{"className":106858},[398],[363,106860],{"className":106861,"style":106862},[402],"height:1.4753em;vertical-align:-0.345em;",[363,106864,106866,106869,107017],{"className":106865},[407],[363,106867],{"className":106868},[494,789],[363,106870,106872],{"className":106871},[586],[363,106873,106875,107009],{"className":106874},[633,634],[363,106876,106878,107006],{"className":106877},[638],[363,106879,106882,106896,106904],{"className":106880,"style":106881},[642],"height:1.1303em;",[363,106883,106884,106887],{"style":2874},[363,106885],{"className":106886,"style":809},[650],[363,106888,106890],{"className":106889},[655,656,657,658],[363,106891,106893],{"className":106892},[407,658],[363,106894,2810],{"className":106895},[407,658],[363,106897,106898,106901],{"style":821},[363,106899],{"className":106900,"style":809},[650],[363,106902],{"className":106903,"style":829},[828],[363,106905,106906,106909],{"style":2897},[363,106907],{"className":106908,"style":809},[650],[363,106910,106912],{"className":106911},[655,656,657,658],[363,106913,106915],{"className":106914},[407,658],[363,106916,106918,106921],{"className":106917},[407,658],[363,106919,7914],{"className":106920},[407,408,658],[363,106922,106924],{"className":106923},[629],[363,106925,106927],{"className":106926},[633],[363,106928,106930],{"className":106929},[638],[363,106931,106934],{"className":106932,"style":106933},[642],"height:1.0519em;",[363,106935,106937,106941],{"style":106936},"top:-3.0519em;margin-right:0.0714em;",[363,106938],{"className":106939,"style":106940},[650],"height:2.6209em;",[363,106942,106944],{"className":106943},[655,30557,10021,658],[363,106945,106947,106950],{"className":106946},[407,658],[363,106948,2810],{"className":106949},[407,658],[363,106951,106953,106956],{"className":106952},[407,658],[363,106954,4505],{"className":106955,"style":1328},[407,408,658],[363,106957,106959],{"className":106958},[629],[363,106960,106962,106997],{"className":106961},[633,634],[363,106963,106965,106994],{"className":106964},[638],[363,106966,106969,106985],{"className":106967,"style":106968},[642],"height:0.8693em;",[363,106970,106972,106976],{"style":106971},"top:-2.2427em;margin-left:-0.0359em;margin-right:0.1em;",[363,106973],{"className":106974,"style":106975},[650],"height:2.6833em;",[363,106977,106979,106982],{"className":106978},[407,658],[363,106980,24090],{"className":106981,"style":24500},[407,408,658],[363,106983,26084],{"className":106984,"style":26208},[407,408,658],[363,106986,106988,106991],{"style":106987},"top:-3.0873em;margin-right:0.1em;",[363,106989],{"className":106990,"style":106975},[650],[363,106992,7920],{"className":106993},[2938,658],[363,106995,666],{"className":106996},[665],[363,106998,107000],{"className":106999},[638],[363,107001,107004],{"className":107002,"style":107003},[642],"height:0.4406em;",[363,107005],{},[363,107007,666],{"className":107008},[665],[363,107010,107012],{"className":107011},[638],[363,107013,107015],{"className":107014,"style":2919},[642],[363,107016],{},[363,107018],{"className":107019},[501,789],[363,107021],{"className":107022,"style":506},[505],[363,107024,471],{"className":107025},[510],[363,107027],{"className":107028,"style":506},[505],[363,107030,107032,107035],{"className":107031},[398],[363,107033],{"className":107034,"style":3431},[402],[363,107036,107038,107041,107106],{"className":107037},[407],[363,107039],{"className":107040},[494,789],[363,107042,107044],{"className":107043},[586],[363,107045,107047,107098],{"className":107046},[633,634],[363,107048,107050,107095],{"className":107049},[638],[363,107051,107053,107073,107081],{"className":107052,"style":3450},[642],[363,107054,107055,107058],{"style":2874},[363,107056],{"className":107057,"style":809},[650],[363,107059,107061],{"className":107060},[655,656,657,658],[363,107062,107064,107067,107070],{"className":107063},[407,658],[363,107065,11],{"className":107066},[407,408,658],[363,107068,2817],{"className":107069},[2938,658],[363,107071,1291],{"className":107072,"style":1328},[407,408,658],[363,107074,107075,107078],{"style":821},[363,107076],{"className":107077,"style":809},[650],[363,107079],{"className":107080,"style":829},[828],[363,107082,107083,107086],{"style":3200},[363,107084],{"className":107085,"style":809},[650],[363,107087,107089],{"className":107088},[655,656,657,658],[363,107090,107092],{"className":107091},[407,658],[363,107093,11],{"className":107094},[407,408,658],[363,107096,666],{"className":107097},[665],[363,107099,107101],{"className":107100},[638],[363,107102,107104],{"className":107103,"style":3086},[642],[363,107105],{},[363,107107],{"className":107108},[501,789]," 相联系（常数平移在共轭表示中自由），故在最优判别器处可直接代入：",[363,107111,107113],{"className":107112,"translate":367},[528],[363,107114,107116,107223],{"className":107115,"translate":367},[366],[363,107117,107119],{"className":107118},[371],[373,107120,107121],{"xmlns":375,"display":537},[377,107122,107123,107220],{},[380,107124,107125,107131,107133,107135,107137,107143,107145,107147,107153,107155,107157,107159,107161,107163,107165,107171,107173,107175,107177,107179,107181,107191,107193,107209,107211,107213,107215,107217],{},[543,107126,107127,107129],{},[383,107128,571],{"mathvariant":570},[383,107130,554],{},[458,107132,578],{"stretchy":460},[383,107134,4447],{},[458,107136,4450],{},[543,107138,107139,107141],{},[383,107140,547],{},[383,107142,7908],{},[458,107144,605],{"stretchy":460},[458,107146,2817],{},[543,107148,107149,107151],{},[383,107150,571],{"mathvariant":570},[383,107152,561],{},[458,107154,578],{"stretchy":460},[383,107156,4447],{},[458,107158,4450],{},[458,107160,461],{"stretchy":460},[463,107162,465],{},[458,107164,5160],{},[543,107166,107167,107169],{},[383,107168,547],{},[383,107170,7908],{},[458,107172,468],{"stretchy":460},[458,107174,605],{"stretchy":460},[458,107176,471],{},[463,107178,2810],{},[1644,107180,1646],{},[543,107182,107183,107185],{},[383,107184,547],{},[380,107186,107187,107189],{},[383,107188,24090],{},[383,107190,26084],{},[1644,107192,1651],{},[380,107194,107195,107197,107199,107201,107203,107205,107207],{},[458,107196,461],{"fence":394},[383,107198,554],{},[1644,107200,4630],{},[458,107202,558],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[1644,107204,4630],{},[383,107206,561],{},[458,107208,468],{"fence":394},[458,107210,5160],{},[463,107212,2810],{},[383,107214,4447],{},[458,107216,4450],{},[463,107218,107219],{},"2.",[387,107221,107222],{"encoding":389},"\\mathbb E_P[\\log D_s]+\\mathbb E_Q[\\log(1-D_s)]\n=2\\,D_{JS}\\!\\left(P\\ \\Big\\|\\ Q\\right)-2\\log 2 .",[363,107224,107226,107335,107404,107462,107599],{"className":107225,"ariaHidden":394},[393],[363,107227,107229,107232,107272,107275,107280,107283,107323,107326,107329,107332],{"className":107228},[398],[363,107230],{"className":107231,"style":487},[402],[363,107233,107235,107238],{"className":107234},[407],[363,107236,571],{"className":107237},[407,714],[363,107239,107241],{"className":107240},[629],[363,107242,107244,107264],{"className":107243},[633,634],[363,107245,107247,107261],{"className":107246},[638],[363,107248,107250],{"className":107249,"style":727},[642],[363,107251,107252,107255],{"style":730},[363,107253],{"className":107254,"style":651},[650],[363,107256,107258],{"className":107257},[655,656,657,658],[363,107259,554],{"className":107260,"style":682},[407,408,658],[363,107262,666],{"className":107263},[665],[363,107265,107267],{"className":107266},[638],[363,107268,107270],{"className":107269,"style":8315},[642],[363,107271],{},[363,107273,578],{"className":107274},[494],[363,107276,4501,107278],{"className":107277},[1831],[363,107279,4505],{"style":4504},[363,107281],{"className":107282,"style":754},[505],[363,107284,107286,107289],{"className":107285},[407],[363,107287,547],{"className":107288,"style":625},[407,408],[363,107290,107292],{"className":107291},[629],[363,107293,107295,107315],{"className":107294},[633,634],[363,107296,107298,107312],{"className":107297},[638],[363,107299,107301],{"className":107300,"style":45276},[642],[363,107302,107303,107306],{"style":646},[363,107304],{"className":107305,"style":651},[650],[363,107307,107309],{"className":107308},[655,656,657,658],[363,107310,7908],{"className":107311},[407,408,658],[363,107313,666],{"className":107314},[665],[363,107316,107318],{"className":107317},[638],[363,107319,107321],{"className":107320,"style":8315},[642],[363,107322],{},[363,107324,605],{"className":107325},[501],[363,107327],{"className":107328,"style":2934},[505],[363,107330,2817],{"className":107331},[2938],[363,107333],{"className":107334,"style":2934},[505],[363,107336,107338,107341,107381,107384,107389,107392,107395,107398,107401],{"className":107337},[398],[363,107339],{"className":107340,"style":618},[402],[363,107342,107344,107347],{"className":107343},[407],[363,107345,571],{"className":107346},[407,714],[363,107348,107350],{"className":107349},[629],[363,107351,107353,107373],{"className":107352},[633,634],[363,107354,107356,107370],{"className":107355},[638],[363,107357,107359],{"className":107358,"style":727},[642],[363,107360,107361,107364],{"style":730},[363,107362],{"className":107363,"style":651},[650],[363,107365,107367],{"className":107366},[655,656,657,658],[363,107368,561],{"className":107369},[407,408,658],[363,107371,666],{"className":107372},[665],[363,107374,107376],{"className":107375},[638],[363,107377,107379],{"className":107378,"style":673},[642],[363,107380],{},[363,107382,578],{"className":107383},[494],[363,107385,4501,107387],{"className":107386},[1831],[363,107388,4505],{"style":4504},[363,107390,461],{"className":107391},[494],[363,107393,465],{"className":107394},[407],[363,107396],{"className":107397,"style":2934},[505],[363,107399,5160],{"className":107400},[2938],[363,107402],{"className":107403,"style":2934},[505],[363,107405,107407,107410,107450,107453,107456,107459],{"className":107406},[398],[363,107408],{"className":107409,"style":487},[402],[363,107411,107413,107416],{"className":107412},[407],[363,107414,547],{"className":107415,"style":625},[407,408],[363,107417,107419],{"className":107418},[629],[363,107420,107422,107442],{"className":107421},[633,634],[363,107423,107425,107439],{"className":107424},[638],[363,107426,107428],{"className":107427,"style":45276},[642],[363,107429,107430,107433],{"style":646},[363,107431],{"className":107432,"style":651},[650],[363,107434,107436],{"className":107435},[655,656,657,658],[363,107437,7908],{"className":107438},[407,408,658],[363,107440,666],{"className":107441},[665],[363,107443,107445],{"className":107444},[638],[363,107446,107448],{"className":107447,"style":8315},[642],[363,107449],{},[363,107451,20737],{"className":107452},[501],[363,107454],{"className":107455,"style":506},[505],[363,107457,471],{"className":107458},[510],[363,107460],{"className":107461,"style":506},[505],[363,107463,107465,107468,107471,107474,107520,107523,107526,107590,107593,107596],{"className":107464},[398],[363,107466],{"className":107467,"style":68464},[402],[363,107469,2810],{"className":107470},[407],[363,107472],{"className":107473,"style":754},[505],[363,107475,107477,107480],{"className":107476},[407],[363,107478,547],{"className":107479,"style":625},[407,408],[363,107481,107483],{"className":107482},[629],[363,107484,107486,107512],{"className":107485},[633,634],[363,107487,107489,107509],{"className":107488},[638],[363,107490,107492],{"className":107491,"style":727},[642],[363,107493,107494,107497],{"style":646},[363,107495],{"className":107496,"style":651},[650],[363,107498,107500],{"className":107499},[655,656,657,658],[363,107501,107503,107506],{"className":107502},[407,658],[363,107504,24090],{"className":107505,"style":24500},[407,408,658],[363,107507,26084],{"className":107508,"style":26208},[407,408,658],[363,107510,666],{"className":107511},[665],[363,107513,107515],{"className":107514},[638],[363,107516,107518],{"className":107517,"style":8315},[642],[363,107519],{},[363,107521],{"className":107522,"style":1859},[505],[363,107524],{"className":107525,"style":754},[505],[363,107527,107529,107535,107538,107541,107578,107581,107584],{"className":107528},[758],[363,107530,107532],{"className":107531,"style":763},[494,762],[363,107533,461],{"className":107534},[767,4067],[363,107536,554],{"className":107537,"style":682},[407,408],[363,107539,4630],{"className":107540},[505],[363,107542,107544],{"className":107543},[407],[363,107545,107547],{"className":107546},[767,15176],[363,107548,107550,107570],{"className":107549},[633,634],[363,107551,107553,107567],{"className":107552},[638],[363,107554,107556],{"className":107555,"style":85862},[642],[363,107557,107558,107561],{"style":73871},[363,107559],{"className":107560,"style":82934},[650],[363,107562,107563],{"style":85870},[6670,107564,107565],{"xmlns":6672,"width":15199,"height":17786,"viewBox":85873},[6678,107566],{"d":85876},[363,107568,666],{"className":107569},[665],[363,107571,107573],{"className":107572},[638],[363,107574,107576],{"className":107575,"style":85886},[642],[363,107577],{},[363,107579,4630],{"className":107580},[505],[363,107582,561],{"className":107583},[407,408],[363,107585,107587],{"className":107586,"style":763},[501,762],[363,107588,468],{"className":107589},[767,4067],[363,107591],{"className":107592,"style":2934},[505],[363,107594,5160],{"className":107595},[2938],[363,107597],{"className":107598,"style":2934},[505],[363,107600,107602,107605,107608,107611,107616,107619],{"className":107601},[398],[363,107603],{"className":107604,"style":403},[402],[363,107606,2810],{"className":107607},[407],[363,107609],{"className":107610,"style":754},[505],[363,107612,4501,107614],{"className":107613},[1831],[363,107615,4505],{"style":4504},[363,107617],{"className":107618,"style":754},[505],[363,107620,107219],{"className":107621},[407],[11,107623,107624,107625,33148],{},"推导：",[363,107626,107628,107686],{"className":107627,"translate":367},[366],[363,107629,107631],{"className":107630},[371],[373,107632,107633],{"xmlns":375},[377,107634,107635,107683],{},[380,107636,107637,107639,107641,107657,107659,107661,107663,107675,107677,107679,107681],{},[383,107638,4447],{},[458,107640,4450],{},[586,107642,107643,107649],{},[380,107644,107645,107647],{},[463,107646,2810],{},[383,107648,11],{},[380,107650,107651,107653,107655],{},[383,107652,11],{},[458,107654,2817],{},[383,107656,1291],{},[458,107658,471],{},[383,107660,4447],{},[458,107662,4450],{},[586,107664,107665,107667],{},[383,107666,11],{},[380,107668,107669,107671,107673],{},[383,107670,11],{},[458,107672,2817],{},[383,107674,1291],{},[458,107676,2817],{},[383,107678,4447],{},[458,107680,4450],{},[463,107682,2810],{},[387,107684,107685],{"encoding":389},"\\log\\frac{2p}{p+q}=\\log\\frac{p}{p+q}+\\log2",[363,107687,107689,107791,107888],{"className":107688,"ariaHidden":394},[393],[363,107690,107692,107696,107701,107704,107782,107785,107788],{"className":107691},[398],[363,107693],{"className":107694,"style":107695},[402],"height:1.3783em;vertical-align:-0.4811em;",[363,107697,4501,107699],{"className":107698},[1831],[363,107700,4505],{"style":4504},[363,107702],{"className":107703,"style":754},[505],[363,107705,107707,107710,107779],{"className":107706},[407],[363,107708],{"className":107709},[494,789],[363,107711,107713],{"className":107712},[586],[363,107714,107716,107771],{"className":107715},[633,634],[363,107717,107719,107768],{"className":107718},[638],[363,107720,107723,107743,107751],{"className":107721,"style":107722},[642],"height:0.8972em;",[363,107724,107725,107728],{"style":2874},[363,107726],{"className":107727,"style":809},[650],[363,107729,107731],{"className":107730},[655,656,657,658],[363,107732,107734,107737,107740],{"className":107733},[407,658],[363,107735,11],{"className":107736},[407,408,658],[363,107738,2817],{"className":107739},[2938,658],[363,107741,1291],{"className":107742,"style":1328},[407,408,658],[363,107744,107745,107748],{"style":821},[363,107746],{"className":107747,"style":809},[650],[363,107749],{"className":107750,"style":829},[828],[363,107752,107753,107756],{"style":3200},[363,107754],{"className":107755,"style":809},[650],[363,107757,107759],{"className":107758},[655,656,657,658],[363,107760,107762,107765],{"className":107761},[407,658],[363,107763,2810],{"className":107764},[407,658],[363,107766,11],{"className":107767},[407,408,658],[363,107769,666],{"className":107770},[665],[363,107772,107774],{"className":107773},[638],[363,107775,107777],{"className":107776,"style":3086},[642],[363,107778],{},[363,107780],{"className":107781},[501,789],[363,107783],{"className":107784,"style":506},[505],[363,107786,471],{"className":107787},[510],[363,107789],{"className":107790,"style":506},[505],[363,107792,107794,107797,107802,107805,107879,107882,107885],{"className":107793},[398],[363,107795],{"className":107796,"style":3431},[402],[363,107798,4501,107800],{"className":107799},[1831],[363,107801,4505],{"style":4504},[363,107803],{"className":107804,"style":754},[505],[363,107806,107808,107811,107876],{"className":107807},[407],[363,107809],{"className":107810},[494,789],[363,107812,107814],{"className":107813},[586],[363,107815,107817,107868],{"className":107816},[633,634],[363,107818,107820,107865],{"className":107819},[638],[363,107821,107823,107843,107851],{"className":107822,"style":3450},[642],[363,107824,107825,107828],{"style":2874},[363,107826],{"className":107827,"style":809},[650],[363,107829,107831],{"className":107830},[655,656,657,658],[363,107832,107834,107837,107840],{"className":107833},[407,658],[363,107835,11],{"className":107836},[407,408,658],[363,107838,2817],{"className":107839},[2938,658],[363,107841,1291],{"className":107842,"style":1328},[407,408,658],[363,107844,107845,107848],{"style":821},[363,107846],{"className":107847,"style":809},[650],[363,107849],{"className":107850,"style":829},[828],[363,107852,107853,107856],{"style":3200},[363,107854],{"className":107855,"style":809},[650],[363,107857,107859],{"className":107858},[655,656,657,658],[363,107860,107862],{"className":107861},[407,658],[363,107863,11],{"className":107864},[407,408,658],[363,107866,666],{"className":107867},[665],[363,107869,107871],{"className":107870},[638],[363,107872,107874],{"className":107873,"style":3086},[642],[363,107875],{},[363,107877],{"className":107878},[501,789],[363,107880],{"className":107881,"style":2934},[505],[363,107883,2817],{"className":107884},[2938],[363,107886],{"className":107887,"style":2934},[505],[363,107889,107891,107894,107899,107902],{"className":107890},[398],[363,107892],{"className":107893,"style":403},[402],[363,107895,4501,107897],{"className":107896},[1831],[363,107898,4505],{"style":4504},[363,107900],{"className":107901,"style":754},[505],[363,107903,2810],{"className":107904},[407],[363,107906,107908],{"className":107907,"translate":367},[528],[363,107909,107911,108003],{"className":107910,"translate":367},[366],[363,107912,107914],{"className":107913},[371],[373,107915,107916],{"xmlns":375,"display":537},[377,107917,107918,108000],{},[380,107919,107920,107926,107928,107930,107932,107934,107936,107938,107944,107946,107948,107950,107966,107968,107970,107976,107978,107980,107982,107988,107990,107992,107994,107996,107998],{},[380,107921,107922,107924],{},[383,107923,11041],{"mathvariant":557},[383,107925,22240],{"mathvariant":557},[458,107927,461],{"stretchy":460},[383,107929,554],{},[383,107931,558],{"mathvariant":557},[383,107933,25914],{},[458,107935,468],{"stretchy":460},[458,107937,471],{},[543,107939,107940,107942],{},[383,107941,571],{"mathvariant":570},[383,107943,554],{},[458,107945,578],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[383,107947,4447],{},[458,107949,4450],{},[586,107951,107952,107958],{},[380,107953,107954,107956],{},[463,107955,2810],{},[383,107957,11],{},[380,107959,107960,107962,107964],{},[383,107961,11],{},[458,107963,2817],{},[383,107965,1291],{},[458,107967,605],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[458,107969,471],{},[543,107971,107972,107974],{},[383,107973,571],{"mathvariant":570},[383,107975,554],{},[458,107977,578],{"stretchy":460},[383,107979,4447],{},[458,107981,4450],{},[543,107983,107984,107986],{},[383,107985,547],{},[383,107987,7908],{},[458,107989,605],{"stretchy":460},[458,107991,2817],{},[383,107993,4447],{},[458,107995,4450],{},[463,107997,2810],{},[458,107999,898],{"separator":394},[387,108001,108002],{"encoding":389},"\\mathrm{KL}(P\\|M)\n=\\mathbb E_P\\Big[\\log\\frac{2p}{p+q}\\Big]\n=\\mathbb E_P[\\log D_s]+\\log2,",[363,108004,108006,108042,108197,108306],{"className":108005,"ariaHidden":394},[393],[363,108007,108009,108012,108018,108021,108024,108027,108030,108033,108036,108039],{"className":108008},[398],[363,108010],{"className":108011,"style":487},[402],[363,108013,108015],{"className":108014},[407],[363,108016,33010],{"className":108017},[407,33009],[363,108019,461],{"className":108020},[494],[363,108022,554],{"className":108023,"style":682},[407,408],[363,108025,558],{"className":108026},[407],[363,108028,25914],{"className":108029,"style":25948},[407,408],[363,108031,468],{"className":108032},[501],[363,108034],{"className":108035,"style":506},[505],[363,108037,471],{"className":108038},[510],[363,108040],{"className":108041,"style":506},[505],[363,108043,108045,108048,108088,108094,108097,108102,108105,108182,108188,108191,108194],{"className":108044},[398],[363,108046],{"className":108047,"style":31650},[402],[363,108049,108051,108054],{"className":108050},[407],[363,108052,571],{"className":108053},[407,714],[363,108055,108057],{"className":108056},[629],[363,108058,108060,108080],{"className":108059},[633,634],[363,108061,108063,108077],{"className":108062},[638],[363,108064,108066],{"className":108065,"style":727},[642],[363,108067,108068,108071],{"style":730},[363,108069],{"className":108070,"style":651},[650],[363,108072,108074],{"className":108073},[655,656,657,658],[363,108075,554],{"className":108076,"style":682},[407,408,658],[363,108078,666],{"className":108079},[665],[363,108081,108083],{"className":108082},[638],[363,108084,108086],{"className":108085,"style":8315},[642],[363,108087],{},[363,108089,108091],{"className":108090},[407],[363,108092,578],{"className":108093},[767,4067],[363,108095],{"className":108096,"style":754},[505],[363,108098,4501,108100],{"className":108099},[1831],[363,108101,4505],{"style":4504},[363,108103],{"className":108104,"style":754},[505],[363,108106,108108,108111,108179],{"className":108107},[407],[363,108109],{"className":108110},[494,789],[363,108112,108114],{"className":108113},[586],[363,108115,108117,108171],{"className":108116},[633,634],[363,108118,108120,108168],{"className":108119},[638],[363,108121,108123,108146,108154],{"className":108122,"style":23236},[642],[363,108124,108125,108128],{"style":805},[363,108126],{"className":108127,"style":809},[650],[363,108129,108131,108134,108137,108140,108143],{"className":108130},[407],[363,108132,11],{"className":108133},[407,408],[363,108135],{"className":108136,"style":2934},[505],[363,108138,2817],{"className":108139},[2938],[363,108141],{"className":108142,"style":2934},[505],[363,108144,1291],{"className":108145,"style":1328},[407,408],[363,108147,108148,108151],{"style":821},[363,108149],{"className":108150,"style":809},[650],[363,108152],{"className":108153,"style":829},[828],[363,108155,108156,108159],{"style":832},[363,108157],{"className":108158,"style":809},[650],[363,108160,108162,108165],{"className":108161},[407],[363,108163,2810],{"className":108164},[407],[363,108166,11],{"className":108167},[407,408],[363,108169,666],{"className":108170},[665],[363,108172,108174],{"className":108173},[638],[363,108175,108177],{"className":108176,"style":854},[642],[363,108178],{},[363,108180],{"className":108181},[501,789],[363,108183,108185],{"className":108184},[407],[363,108186,605],{"className":108187},[767,4067],[363,108189],{"className":108190,"style":506},[505],[363,108192,471],{"className":108193},[510],[363,108195],{"className":108196,"style":506},[505],[363,108198,108200,108203,108243,108246,108251,108254,108294,108297,108300,108303],{"className":108199},[398],[363,108201],{"className":108202,"style":487},[402],[363,108204,108206,108209],{"className":108205},[407],[363,108207,571],{"className":108208},[407,714],[363,108210,108212],{"className":108211},[629],[363,108213,108215,108235],{"className":108214},[633,634],[363,108216,108218,108232],{"className":108217},[638],[363,108219,108221],{"className":108220,"style":727},[642],[363,108222,108223,108226],{"style":730},[363,108224],{"className":108225,"style":651},[650],[363,108227,108229],{"className":108228},[655,656,657,658],[363,108230,554],{"className":108231,"style":682},[407,408,658],[363,108233,666],{"className":108234},[665],[363,108236,108238],{"className":108237},[638],[363,108239,108241],{"className":108240,"style":8315},[642],[363,108242],{},[363,108244,578],{"className":108245},[494],[363,108247,4501,108249],{"className":108248},[1831],[363,108250,4505],{"style":4504},[363,108252],{"className":108253,"style":754},[505],[363,108255,108257,108260],{"className":108256},[407],[363,108258,547],{"className":108259,"style":625},[407,408],[363,108261,108263],{"className":108262},[629],[363,108264,108266,108286],{"className":108265},[633,634],[363,108267,108269,108283],{"className":108268},[638],[363,108270,108272],{"className":108271,"style":45276},[642],[363,108273,108274,108277],{"style":646},[363,108275],{"className":108276,"style":651},[650],[363,108278,108280],{"className":108279},[655,656,657,658],[363,108281,7908],{"className":108282},[407,408,658],[363,108284,666],{"className":108285},[665],[363,108287,108289],{"className":108288},[638],[363,108290,108292],{"className":108291,"style":8315},[642],[363,108293],{},[363,108295,605],{"className":108296},[501],[363,108298],{"className":108299,"style":2934},[505],[363,108301,2817],{"className":108302},[2938],[363,108304],{"className":108305,"style":2934},[505],[363,108307,108309,108312,108317,108320,108323],{"className":108308},[398],[363,108310],{"className":108311,"style":403},[402],[363,108313,4501,108315],{"className":108314},[1831],[363,108316,4505],{"style":4504},[363,108318],{"className":108319,"style":754},[505],[363,108321,2810],{"className":108322},[407],[363,108324,898],{"className":108325},[920],[11,108327,14608,108328,108356,108357,108411,108412,108526,108527,108585],{},[363,108329,108331,108344],{"className":108330,"translate":367},[366],[363,108332,108334],{"className":108333},[371],[373,108335,108336],{"xmlns":375},[377,108337,108338,108342],{},[380,108339,108340],{},[383,108341,561],{},[387,108343,561],{"encoding":389},[363,108345,108347],{"className":108346,"ariaHidden":394},[393],[363,108348,108350,108353],{"className":108349},[398],[363,108351],{"className":108352,"style":913},[402],[363,108354,561],{"className":108355},[407,408]," 同理，两式相加即得。于是「最小化 JS」与「在最优判别器下最大化 GAN 目标」是同一件事，而常数 ",[363,108358,108360,108382],{"className":108359,"translate":367},[366],[363,108361,108363],{"className":108362},[371],[373,108364,108365],{"xmlns":375},[377,108366,108367,108379],{},[380,108368,108369,108371,108373,108375,108377],{},[458,108370,5160],{},[463,108372,2810],{},[383,108374,4447],{},[458,108376,4450],{},[463,108378,2810],{},[387,108380,108381],{"encoding":389},"-2\\log2",[363,108383,108385],{"className":108384,"ariaHidden":394},[393],[363,108386,108388,108391,108394,108397,108400,108405,108408],{"className":108387},[398],[363,108389],{"className":108390,"style":403},[402],[363,108392,5160],{"className":108393},[407],[363,108395,2810],{"className":108396},[407],[363,108398],{"className":108399,"style":754},[505],[363,108401,4501,108403],{"className":108402},[1831],[363,108404,4505],{"style":4504},[363,108406],{"className":108407,"style":754},[505],[363,108409,2810],{"className":108410},[407]," 与生成器无关。这解释了「GAN 训练不收敛」的来源：JS 有界，一旦支撑集几近不重叠，",[363,108413,108415,108445],{"className":108414,"translate":367},[366],[363,108416,108418],{"className":108417},[371],[373,108419,108420],{"xmlns":375},[377,108421,108422,108442],{},[380,108423,108424,108434,108436,108438,108440],{},[543,108425,108426,108428],{},[383,108427,547],{},[380,108429,108430,108432],{},[383,108431,24090],{},[383,108433,26084],{},[458,108435,1376],{},[383,108437,4447],{},[458,108439,4450],{},[463,108441,2810],{},[387,108443,108444],{"encoding":389},"D_{JS}\\to\\log2",[363,108446,108448,108509],{"className":108447,"ariaHidden":394},[393],[363,108449,108451,108454,108500,108503,108506],{"className":108450},[398],[363,108452],{"className":108453,"style":16308},[402],[363,108455,108457,108460],{"className":108456},[407],[363,108458,547],{"className":108459,"style":625},[407,408],[363,108461,108463],{"className":108462},[629],[363,108464,108466,108492],{"className":108465},[633,634],[363,108467,108469,108489],{"className":108468},[638],[363,108470,108472],{"className":108471,"style":727},[642],[363,108473,108474,108477],{"style":646},[363,108475],{"className":108476,"style":651},[650],[363,108478,108480],{"className":108479},[655,656,657,658],[363,108481,108483,108486],{"className":108482},[407,658],[363,108484,24090],{"className":108485,"style":24500},[407,408,658],[363,108487,26084],{"className":108488,"style":26208},[407,408,658],[363,108490,666],{"className":108491},[665],[363,108493,108495],{"className":108494},[638],[363,108496,108498],{"className":108497,"style":8315},[642],[363,108499],{},[363,108501],{"className":108502,"style":506},[505],[363,108504,1376],{"className":108505},[510],[363,108507],{"className":108508,"style":506},[505],[363,108510,108512,108515,108520,108523],{"className":108511},[398],[363,108513],{"className":108514,"style":403},[402],[363,108516,4501,108518],{"className":108517},[1831],[363,108519,4505],{"style":4504},[363,108521],{"className":108522,"style":754},[505],[363,108524,2810],{"className":108525},[407],"，判别器梯度饱和，生成器梯度消失。反过来，换成 LSGAN（",[363,108528,108530,108547],{"className":108529,"translate":367},[366],[363,108531,108533],{"className":108532},[371],[373,108534,108535],{"xmlns":375},[377,108536,108537,108545],{},[380,108538,108539],{},[7161,108540,108541,108543],{},[383,108542,37796],{},[463,108544,2810],{},[387,108546,40741],{"encoding":389},[363,108548,108550],{"className":108549,"ariaHidden":394},[393],[363,108551,108553,108556],{"className":108552},[398],[363,108554],{"className":108555,"style":40751},[402],[363,108557,108559,108562],{"className":108558},[407],[363,108560,37796],{"className":108561},[407,408],[363,108563,108565],{"className":108564},[629],[363,108566,108568],{"className":108567},[633],[363,108569,108571],{"className":108570},[638],[363,108572,108574],{"className":108573,"style":20375},[642],[363,108575,108576,108579],{"style":7212},[363,108577],{"className":108578,"style":651},[650],[363,108580,108582],{"className":108581},[655,656,657,658],[363,108583,2810],{"className":108584},[407,658],"）、Wasserstein（非 f-散度）或 α-GAN 就能改变这一点。",[2658,108587,108589],{"id":108588},"_55-估计性质","5.5 估计性质",[11,108591,108592],{},"用 5.1 的 Monte Carlo 下界做估计时：",[10374,108594,108595,108740,108895],{},[7012,108596,108597,108598,34172,108667,108669,108670,108739],{},"它是 ",[363,108599,108601,108618],{"className":108600,"translate":367},[366],[363,108602,108604],{"className":108603},[371],[373,108605,108606],{"xmlns":375},[377,108607,108608,108616],{},[380,108609,108610],{},[543,108611,108612,108614],{},[383,108613,547],{},[383,108615,385],{},[387,108617,4369],{"encoding":389},[363,108619,108621],{"className":108620,"ariaHidden":394},[393],[363,108622,108624,108627],{"className":108623},[398],[363,108625],{"className":108626,"style":4379},[402],[363,108628,108630,108633],{"className":108629},[407],[363,108631,547],{"className":108632,"style":625},[407,408],[363,108634,108636],{"className":108635},[629],[363,108637,108639,108659],{"className":108638},[633,634],[363,108640,108642,108656],{"className":108641},[638],[363,108643,108645],{"className":108644,"style":643},[642],[363,108646,108647,108650],{"style":646},[363,108648],{"className":108649,"style":651},[650],[363,108651,108653],{"className":108652},[655,656,657,658],[363,108654,385],{"className":108655,"style":409},[407,408,658],[363,108657,666],{"className":108658},[665],[363,108660,108662],{"className":108661},[638],[363,108663,108665],{"className":108664,"style":673},[642],[363,108666],{},[1572,108668,100188],{},"（偏差向下），且偏差来自 ",[363,108671,108673,108690],{"className":108672,"translate":367},[366],[363,108674,108676],{"className":108675},[371],[373,108677,108678],{"xmlns":375},[377,108679,108680,108688],{},[380,108681,108682],{},[543,108683,108684,108686],{},[383,108685,4505],{},[383,108687,100208],{},[387,108689,100211],{"encoding":389},[363,108691,108693],{"className":108692,"ariaHidden":394},[393],[363,108694,108696,108699],{"className":108695},[398],[363,108697],{"className":108698,"style":2623},[402],[363,108700,108702,108705],{"className":108701},[407],[363,108703,4505],{"className":108704,"style":1328},[407,408],[363,108706,108708],{"className":108707},[629],[363,108709,108711,108731],{"className":108710},[633,634],[363,108712,108714,108728],{"className":108713},[638],[363,108715,108717],{"className":108716,"style":45276},[642],[363,108718,108719,108722],{"style":19190},[363,108720],{"className":108721,"style":651},[650],[363,108723,108725],{"className":108724},[655,656,657,658],[363,108726,100208],{"className":108727,"style":1328},[407,408,658],[363,108729,666],{"className":108730},[665],[363,108732,108734],{"className":108733},[638],[363,108735,108737],{"className":108736,"style":8315},[642],[363,108738],{}," 未达到最优 + 样本有限；",[7012,108741,68479,108742,108772,108773,108831,108832,108894],{},[363,108743,108745,108760],{"className":108744,"translate":367},[366],[363,108746,108748],{"className":108747},[371],[373,108749,108750],{"xmlns":375},[377,108751,108752,108758],{},[380,108753,108754,108756],{},[383,108755,35779],{},[458,108757,4450],{},[387,108759,57494],{"encoding":389},[363,108761,108763],{"className":108762,"ariaHidden":394},[393],[363,108764,108766,108769],{"className":108765},[398],[363,108767],{"className":108768,"style":2623},[402],[363,108770,35779],{"className":108771},[1831]," 取到极值时，估计量方差随 ",[363,108774,108776,108793],{"className":108775,"translate":367},[366],[363,108777,108779],{"className":108778},[371],[373,108780,108781],{"xmlns":375},[377,108782,108783,108791],{},[380,108784,108785],{},[7161,108786,108787,108789],{},[383,108788,385],{},[458,108790,7920],{},[387,108792,61055],{"encoding":389},[363,108794,108796],{"className":108795,"ariaHidden":394},[393],[363,108797,108799,108802],{"className":108798},[398],[363,108800],{"className":108801,"style":403},[402],[363,108803,108805,108808],{"className":108804},[407],[363,108806,385],{"className":108807,"style":409},[407,408],[363,108809,108811],{"className":108810},[629],[363,108812,108814],{"className":108813},[633],[363,108815,108817],{"className":108816},[638],[363,108818,108820],{"className":108819,"style":8846},[642],[363,108821,108822,108825],{"style":7212},[363,108823],{"className":108824,"style":651},[650],[363,108826,108828],{"className":108827},[655,656,657,658],[363,108829,7920],{"className":108830},[2938,658]," 增长而增大（如 KL 的 ",[363,108833,108835,108853],{"className":108834,"translate":367},[366],[363,108836,108838],{"className":108837},[371],[373,108839,108840],{"xmlns":375},[377,108841,108842,108850],{},[380,108843,108844],{},[7161,108845,108846,108848],{},[383,108847,7914],{},[383,108849,4505],{},[387,108851,108852],{"encoding":389},"e^{g}",[363,108854,108856],{"className":108855,"ariaHidden":394},[393],[363,108857,108859,108862],{"className":108858},[398],[363,108860],{"className":108861,"style":50700},[402],[363,108863,108865,108868],{"className":108864},[407],[363,108866,7914],{"className":108867},[407,408],[363,108869,108871],{"className":108870},[629],[363,108872,108874],{"className":108873},[633],[363,108875,108877],{"className":108876},[638],[363,108878,108880],{"className":108879,"style":50700},[642],[363,108881,108882,108885],{"style":7212},[363,108883],{"className":108884,"style":651},[650],[363,108886,108888],{"className":108887},[655,656,657,658],[363,108889,108891],{"className":108890},[407,658],[363,108892,4505],{"className":108893,"style":1328},[407,408,658]," 会重尾）；",[7012,108896,108897,108898,108926],{},"一个常用替代是「对称化」或「有界化」",[363,108899,108901,108914],{"className":108900,"translate":367},[366],[363,108902,108904],{"className":108903},[371],[373,108905,108906],{"xmlns":375},[377,108907,108908,108912],{},[380,108909,108910],{},[383,108911,385],{},[387,108913,385],{"encoding":389},[363,108915,108917],{"className":108916,"ariaHidden":394},[393],[363,108918,108920,108923],{"className":108919},[398],[363,108921],{"className":108922,"style":403},[402],[363,108924,385],{"className":108925,"style":409},[407,408],"（如 JS、TV），牺牲敏感性换取稳定梯度。这与第 6 节讨论的「有界\u002F无界」准确性—稳健性权衡是同一件事。",[18,108928,108930],{"id":108929},"_6-与其他散度的比较","6. 与其他散度的比较",[2658,108932,108934],{"id":108933},"_61-汇总","6.1 汇总",[52839,108936,108937,109067],{},[52842,108938,108939],{},[52845,108940,108941,108943,108988,109063,109065],{},[52848,108942,52850],{},[52848,108944,108945],{},[363,108946,108948,108967],{"className":108947,"translate":367},[366],[363,108949,108951],{"className":108950},[371],[373,108952,108953],{"xmlns":375},[377,108954,108955,108965],{},[380,108956,108957,108959,108961,108963],{},[383,108958,385],{},[458,108960,461],{"stretchy":460},[383,108962,1116],{},[458,108964,468],{"stretchy":460},[387,108966,52875],{"encoding":389},[363,108968,108970],{"className":108969,"ariaHidden":394},[393],[363,108971,108973,108976,108979,108982,108985],{"className":108972},[398],[363,108974],{"className":108975,"style":487},[402],[363,108977,385],{"className":108978,"style":409},[407,408],[363,108980,461],{"className":108981},[494],[363,108983,1116],{"className":108984},[407,408],[363,108986,468],{"className":108987},[501],[52848,108989,108990],{},[363,108991,108993,109016],{"className":108992,"translate":367},[366],[363,108994,108996],{"className":108995},[371],[373,108997,108998],{"xmlns":375},[377,108999,109000,109014],{},[380,109001,109002,109008,109010,109012],{},[7161,109003,109004,109006],{},[383,109005,385],{},[458,109007,7920],{},[458,109009,461],{"stretchy":460},[383,109011,40584],{},[458,109013,468],{"stretchy":460},[387,109015,65042],{"encoding":389},[363,109017,109019],{"className":109018,"ariaHidden":394},[393],[363,109020,109022,109025,109054,109057,109060],{"className":109021},[398],[363,109023],{"className":109024,"style":487},[402],[363,109026,109028,109031],{"className":109027},[407],[363,109029,385],{"className":109030,"style":409},[407,408],[363,109032,109034],{"className":109033},[629],[363,109035,109037],{"className":109036},[633],[363,109038,109040],{"className":109039},[638],[363,109041,109043],{"className":109042,"style":8846},[642],[363,109044,109045,109048],{"style":7212},[363,109046],{"className":109047,"style":651},[650],[363,109049,109051],{"className":109050},[655,656,657,658],[363,109052,7920],{"className":109053},[2938,658],[363,109055,461],{"className":109056},[494],[363,109058,40584],{"className":109059,"style":1328},[407,408],[363,109061,468],{"className":109062},[501],[52848,109064,30033],{},[52848,109066,52901],{},[52937,109068,109069,109202,109342,109832,110136,110445,110862,111173],{},[52845,109070,109071,109073,109123,109198,109200],{},[52942,109072,33010],{},[52942,109074,109075],{},[363,109076,109078,109097],{"className":109077,"translate":367},[366],[363,109079,109081],{"className":109080},[371],[373,109082,109083],{"xmlns":375},[377,109084,109085,109095],{},[380,109086,109087,109089,109091,109093],{},[383,109088,1116],{},[383,109090,4447],{},[458,109092,4450],{},[383,109094,1116],{},[387,109096,53073],{"encoding":389},[363,109098,109100],{"className":109099,"ariaHidden":394},[393],[363,109101,109103,109106,109109,109112,109117,109120],{"className":109102},[398],[363,109104],{"className":109105,"style":403},[402],[363,109107,1116],{"className":109108},[407,408],[363,109110],{"className":109111,"style":754},[505],[363,109113,4501,109115],{"className":109114},[1831],[363,109116,4505],{"style":4504},[363,109118],{"className":109119,"style":754},[505],[363,109121,1116],{"className":109122},[407,408],[52942,109124,109125],{},[363,109126,109128,109151],{"className":109127,"translate":367},[366],[363,109129,109131],{"className":109130},[371],[373,109132,109133],{"xmlns":375},[377,109134,109135,109149],{},[380,109136,109137],{},[7161,109138,109139,109141],{},[383,109140,7914],{},[380,109142,109143,109145,109147],{},[383,109144,40584],{},[458,109146,5160],{},[463,109148,465],{},[387,109150,65249],{"encoding":389},[363,109152,109154],{"className":109153,"ariaHidden":394},[393],[363,109155,109157,109160],{"className":109156},[398],[363,109158],{"className":109159,"style":20375},[402],[363,109161,109163,109166],{"className":109162},[407],[363,109164,7914],{"className":109165},[407,408],[363,109167,109169],{"className":109168},[629],[363,109170,109172],{"className":109171},[633],[363,109173,109175],{"className":109174},[638],[363,109176,109178],{"className":109177,"style":20375},[642],[363,109179,109180,109183],{"style":7212},[363,109181],{"className":109182,"style":651},[650],[363,109184,109186],{"className":109185},[655,656,657,658],[363,109187,109189,109192,109195],{"className":109188},[407,658],[363,109190,40584],{"className":109191,"style":1328},[407,408,658],[363,109193,5160],{"className":109194},[2938,658],[363,109196,465],{"className":109197},[407,658],[52942,109199,53102],{},[52942,109201,53102],{},[52845,109203,109204,109207,109257,109338,109340],{},[52942,109205,109206],{},"反向 KL",[52942,109208,109209],{},[363,109210,109212,109231],{"className":109211,"translate":367},[366],[363,109213,109215],{"className":109214},[371],[373,109216,109217],{"xmlns":375},[377,109218,109219,109229],{},[380,109220,109221,109223,109225,109227],{},[458,109222,5160],{},[383,109224,4447],{},[458,109226,4450],{},[383,109228,1116],{},[387,109230,53273],{"encoding":389},[363,109232,109234],{"className":109233,"ariaHidden":394},[393],[363,109235,109237,109240,109243,109246,109251,109254],{"className":109236},[398],[363,109238],{"className":109239,"style":403},[402],[363,109241,5160],{"className":109242},[407],[363,109244],{"className":109245,"style":754},[505],[363,109247,4501,109249],{"className":109248},[1831],[363,109250,4505],{"style":4504},[363,109252],{"className":109253,"style":754},[505],[363,109255,1116],{"className":109256},[407,408],[52942,109258,109259],{},[363,109260,109262,109291],{"className":109261,"translate":367},[366],[363,109263,109265],{"className":109264},[371],[373,109266,109267],{"xmlns":375},[377,109268,109269,109289],{},[380,109270,109271,109273,109275,109277,109279,109281,109283,109285,109287],{},[458,109272,5160],{},[463,109274,465],{},[458,109276,5160],{},[383,109278,4447],{},[458,109280,4450],{},[458,109282,461],{"stretchy":460},[458,109284,5160],{},[383,109286,40584],{},[458,109288,468],{"stretchy":460},[387,109290,65418],{"encoding":389},[363,109292,109294,109315],{"className":109293,"ariaHidden":394},[393],[363,109295,109297,109300,109303,109306,109309,109312],{"className":109296},[398],[363,109298],{"className":109299,"style":12925},[402],[363,109301,5160],{"className":109302},[407],[363,109304,465],{"className":109305},[407],[363,109307],{"className":109308,"style":2934},[505],[363,109310,5160],{"className":109311},[2938],[363,109313],{"className":109314,"style":2934},[505],[363,109316,109318,109321,109326,109329,109332,109335],{"className":109317},[398],[363,109319],{"className":109320,"style":487},[402],[363,109322,4501,109324],{"className":109323},[1831],[363,109325,4505],{"style":4504},[363,109327,461],{"className":109328},[494],[363,109330,5160],{"className":109331},[407],[363,109333,40584],{"className":109334,"style":1328},[407,408],[363,109336,468],{"className":109337},[501],[52942,109339,53102],{},[52942,109341,53102],{},[52845,109343,109344,109346,109635,109828,109830],{},[52942,109345,53471],{},[52942,109347,109348],{},[363,109349,109351,109408],{"className":109350,"translate":367},[366],[363,109352,109354],{"className":109353},[371],[373,109355,109356],{"xmlns":375},[377,109357,109358,109406],{},[380,109359,109360,109366,109368,109370,109372,109374,109376,109378,109380,109382,109384,109386,109388,109390,109392,109404],{},[586,109361,109362,109364],{},[463,109363,465],{},[463,109365,2810],{},[458,109367,578],{"stretchy":460},[383,109369,1116],{},[383,109371,4447],{},[458,109373,4450],{},[383,109375,1116],{},[458,109377,5160],{},[458,109379,461],{"stretchy":460},[383,109381,1116],{},[458,109383,2817],{},[463,109385,465],{},[458,109387,468],{"stretchy":460},[383,109389,4447],{},[458,109391,4450],{},[586,109393,109394,109402],{},[380,109395,109396,109398,109400],{},[383,109397,1116],{},[458,109399,2817],{},[463,109401,465],{},[463,109403,2810],{},[458,109405,605],{"stretchy":460},[387,109407,53534],{"encoding":389},[363,109409,109411,109514,109535],{"className":109410,"ariaHidden":394},[393],[363,109412,109414,109417,109485,109488,109491,109494,109499,109502,109505,109508,109511],{"className":109413},[398],[363,109415],{"className":109416,"style":2852},[402],[363,109418,109420,109423,109482],{"className":109419},[407],[363,109421],{"className":109422},[494,789],[363,109424,109426],{"className":109425},[586],[363,109427,109429,109474],{"className":109428},[633,634],[363,109430,109432,109471],{"className":109431},[638],[363,109433,109435,109449,109457],{"className":109434,"style":2871},[642],[363,109436,109437,109440],{"style":2874},[363,109438],{"className":109439,"style":809},[650],[363,109441,109443],{"className":109442},[655,656,657,658],[363,109444,109446],{"className":109445},[407,658],[363,109447,2810],{"className":109448},[407,658],[363,109450,109451,109454],{"style":821},[363,109452],{"className":109453,"style":809},[650],[363,109455],{"className":109456,"style":829},[828],[363,109458,109459,109462],{"style":2897},[363,109460],{"className":109461,"style":809},[650],[363,109463,109465],{"className":109464},[655,656,657,658],[363,109466,109468],{"className":109467},[407,658],[363,109469,465],{"className":109470},[407,658],[363,109472,666],{"className":109473},[665],[363,109475,109477],{"className":109476},[638],[363,109478,109480],{"className":109479,"style":2919},[642],[363,109481],{},[363,109483],{"className":109484},[501,789],[363,109486,578],{"className":109487},[494],[363,109489,1116],{"className":109490},[407,408],[363,109492],{"className":109493,"style":754},[505],[363,109495,4501,109497],{"className":109496},[1831],[363,109498,4505],{"style":4504},[363,109500],{"className":109501,"style":754},[505],[363,109503,1116],{"className":109504},[407,408],[363,109506],{"className":109507,"style":2934},[505],[363,109509,5160],{"className":109510},[2938],[363,109512],{"className":109513,"style":2934},[505],[363,109515,109517,109520,109523,109526,109529,109532],{"className":109516},[398],[363,109518],{"className":109519,"style":487},[402],[363,109521,461],{"className":109522},[494],[363,109524,1116],{"className":109525},[407,408],[363,109527],{"className":109528,"style":2934},[505],[363,109530,2817],{"className":109531},[2938],[363,109533],{"className":109534,"style":2934},[505],[363,109536,109538,109541,109544,109547,109550,109555,109558,109632],{"className":109537},[398],[363,109539],{"className":109540,"style":2852},[402],[363,109542,465],{"className":109543},[407],[363,109545,468],{"className":109546},[501],[363,109548],{"className":109549,"style":754},[505],[363,109551,4501,109553],{"className":109552},[1831],[363,109554,4505],{"style":4504},[363,109556],{"className":109557,"style":754},[505],[363,109559,109561,109564,109629],{"className":109560},[407],[363,109562],{"className":109563},[494,789],[363,109565,109567],{"className":109566},[586],[363,109568,109570,109621],{"className":109569},[633,634],[363,109571,109573,109618],{"className":109572},[638],[363,109574,109576,109590,109598],{"className":109575,"style":2871},[642],[363,109577,109578,109581],{"style":2874},[363,109579],{"className":109580,"style":809},[650],[363,109582,109584],{"className":109583},[655,656,657,658],[363,109585,109587],{"className":109586},[407,658],[363,109588,2810],{"className":109589},[407,658],[363,109591,109592,109595],{"style":821},[363,109593],{"className":109594,"style":809},[650],[363,109596],{"className":109597,"style":829},[828],[363,109599,109600,109603],{"style":2897},[363,109601],{"className":109602,"style":809},[650],[363,109604,109606],{"className":109605},[655,656,657,658],[363,109607,109609,109612,109615],{"className":109608},[407,658],[363,109610,1116],{"className":109611},[407,408,658],[363,109613,2817],{"className":109614},[2938,658],[363,109616,465],{"className":109617},[407,658],[363,109619,666],{"className":109620},[665],[363,109622,109624],{"className":109623},[638],[363,109625,109627],{"className":109626,"style":2919},[642],[363,109628],{},[363,109630],{"className":109631},[501,789],[363,109633,605],{"className":109634},[501],[52942,109636,109637],{},[363,109638,109640,109681],{"className":109639,"translate":367},[366],[363,109641,109643],{"className":109642},[371],[373,109644,109645],{"xmlns":375},[377,109646,109647,109679],{},[380,109648,109649,109651,109657,109659,109661,109663,109665,109667,109677],{},[458,109650,5160],{},[586,109652,109653,109655],{},[463,109654,465],{},[463,109656,2810],{},[383,109658,4447],{},[458,109660,4450],{},[458,109662,461],{"stretchy":460},[463,109664,2810],{},[458,109666,5160],{},[7161,109668,109669,109671],{},[383,109670,7914],{},[380,109672,109673,109675],{},[463,109674,2810],{},[383,109676,40584],{},[458,109678,468],{"stretchy":460},[387,109680,65910],{"encoding":389},[363,109682,109684,109784],{"className":109683,"ariaHidden":394},[393],[363,109685,109687,109690,109693,109761,109764,109769,109772,109775,109778,109781],{"className":109686},[398],[363,109688],{"className":109689,"style":2852},[402],[363,109691,5160],{"className":109692},[407],[363,109694,109696,109699,109758],{"className":109695},[407],[363,109697],{"className":109698},[494,789],[363,109700,109702],{"className":109701},[586],[363,109703,109705,109750],{"className":109704},[633,634],[363,109706,109708,109747],{"className":109707},[638],[363,109709,109711,109725,109733],{"className":109710,"style":2871},[642],[363,109712,109713,109716],{"style":2874},[363,109714],{"className":109715,"style":809},[650],[363,109717,109719],{"className":109718},[655,656,657,658],[363,109720,109722],{"className":109721},[407,658],[363,109723,2810],{"className":109724},[407,658],[363,109726,109727,109730],{"style":821},[363,109728],{"className":109729,"style":809},[650],[363,109731],{"className":109732,"style":829},[828],[363,109734,109735,109738],{"style":2897},[363,109736],{"className":109737,"style":809},[650],[363,109739,109741],{"className":109740},[655,656,657,658],[363,109742,109744],{"className":109743},[407,658],[363,109745,465],{"className":109746},[407,658],[363,109748,666],{"className":109749},[665],[363,109751,109753],{"className":109752},[638],[363,109754,109756],{"className":109755,"style":2919},[642],[363,109757],{},[363,109759],{"className":109760},[501,789],[363,109762],{"className":109763,"style":754},[505],[363,109765,4501,109767],{"className":109766},[1831],[363,109768,4505],{"style":4504},[363,109770,461],{"className":109771},[494],[363,109773,2810],{"className":109774},[407],[363,109776],{"className":109777,"style":2934},[505],[363,109779,5160],{"className":109780},[2938],[363,109782],{"className":109783,"style":2934},[505],[363,109785,109787,109790,109825],{"className":109786},[398],[363,109788],{"className":109789,"style":20350},[402],[363,109791,109793,109796],{"className":109792},[407],[363,109794,7914],{"className":109795},[407,408],[363,109797,109799],{"className":109798},[629],[363,109800,109802],{"className":109801},[633],[363,109803,109805],{"className":109804},[638],[363,109806,109808],{"className":109807,"style":20375},[642],[363,109809,109810,109813],{"style":7212},[363,109811],{"className":109812,"style":651},[650],[363,109814,109816],{"className":109815},[655,656,657,658],[363,109817,109819,109822],{"className":109818},[407,658],[363,109820,2810],{"className":109821},[407,658],[363,109823,40584],{"className":109824,"style":1328},[407,408,658],[363,109826,468],{"className":109827},[501],[52942,109829,53429],{},[52942,109831,53429],{},[52845,109833,109834,109837,109973,110132,110134],{},[52942,109835,109836],{},"全变差",[52942,109838,109839],{},[363,109840,109842,109869],{"className":109841,"translate":367},[366],[363,109843,109845],{"className":109844},[371],[373,109846,109847],{"xmlns":375},[377,109848,109849,109867],{},[380,109850,109851,109857,109859,109861,109863,109865],{},[586,109852,109853,109855],{},[463,109854,465],{},[463,109856,2810],{},[458,109858,5155],{"stretchy":460},[383,109860,1116],{},[458,109862,5160],{},[463,109864,465],{},[458,109866,5155],{"stretchy":460},[387,109868,53902],{"encoding":389},[363,109870,109872,109961],{"className":109871,"ariaHidden":394},[393],[363,109873,109875,109878,109946,109949,109952,109955,109958],{"className":109874},[398],[363,109876],{"className":109877,"style":2852},[402],[363,109879,109881,109884,109943],{"className":109880},[407],[363,109882],{"className":109883},[494,789],[363,109885,109887],{"className":109886},[586],[363,109888,109890,109935],{"className":109889},[633,634],[363,109891,109893,109932],{"className":109892},[638],[363,109894,109896,109910,109918],{"className":109895,"style":2871},[642],[363,109897,109898,109901],{"style":2874},[363,109899],{"className":109900,"style":809},[650],[363,109902,109904],{"className":109903},[655,656,657,658],[363,109905,109907],{"className":109906},[407,658],[363,109908,2810],{"className":109909},[407,658],[363,109911,109912,109915],{"style":821},[363,109913],{"className":109914,"style":809},[650],[363,109916],{"className":109917,"style":829},[828],[363,109919,109920,109923],{"style":2897},[363,109921],{"className":109922,"style":809},[650],[363,109924,109926],{"className":109925},[655,656,657,658],[363,109927,109929],{"className":109928},[407,658],[363,109930,465],{"className":109931},[407,658],[363,109933,666],{"className":109934},[665],[363,109936,109938],{"className":109937},[638],[363,109939,109941],{"className":109940,"style":2919},[642],[363,109942],{},[363,109944],{"className":109945},[501,789],[363,109947,5155],{"className":109948},[494],[363,109950,1116],{"className":109951},[407,408],[363,109953],{"className":109954,"style":2934},[505],[363,109956,5160],{"className":109957},[2938],[363,109959],{"className":109960,"style":2934},[505],[363,109962,109964,109967,109970],{"className":109963},[398],[363,109965],{"className":109966,"style":487},[402],[363,109968,465],{"className":109969},[407],[363,109971,5155],{"className":109972},[501],[52942,109974,109975,16142,110003,53822],{},[363,109976,109978,109991],{"className":109977,"translate":367},[366],[363,109979,109981],{"className":109980},[371],[373,109982,109983],{"xmlns":375},[377,109984,109985,109989],{},[380,109986,109987],{},[383,109988,40584],{},[387,109990,40584],{"encoding":389},[363,109992,109994],{"className":109993,"ariaHidden":394},[393],[363,109995,109997,110000],{"className":109996},[398],[363,109998],{"className":109999,"style":2623},[402],[363,110001,40584],{"className":110002,"style":1328},[407,408],[363,110004,110006,110031],{"className":110005,"translate":367},[366],[363,110007,110009],{"className":110008},[371],[373,110010,110011],{"xmlns":375},[377,110012,110013,110029],{},[380,110014,110015,110017,110019,110021,110023],{},[458,110016,5155],{"stretchy":460},[383,110018,40584],{},[458,110020,5155],{"stretchy":460},[458,110022,10299],{},[586,110024,110025,110027],{},[463,110026,465],{},[463,110028,2810],{},[387,110030,66404],{"encoding":389},[363,110032,110034,110058],{"className":110033,"ariaHidden":394},[393],[363,110035,110037,110040,110043,110046,110049,110052,110055],{"className":110036},[398],[363,110038],{"className":110039,"style":487},[402],[363,110041,5155],{"className":110042},[494],[363,110044,40584],{"className":110045,"style":1328},[407,408],[363,110047,5155],{"className":110048},[501],[363,110050],{"className":110051,"style":506},[505],[363,110053,10299],{"className":110054},[510],[363,110056],{"className":110057,"style":506},[505],[363,110059,110061,110064],{"className":110060},[398],[363,110062],{"className":110063,"style":2852},[402],[363,110065,110067,110070,110129],{"className":110066},[407],[363,110068],{"className":110069},[494,789],[363,110071,110073],{"className":110072},[586],[363,110074,110076,110121],{"className":110075},[633,634],[363,110077,110079,110118],{"className":110078},[638],[363,110080,110082,110096,110104],{"className":110081,"style":2871},[642],[363,110083,110084,110087],{"style":2874},[363,110085],{"className":110086,"style":809},[650],[363,110088,110090],{"className":110089},[655,656,657,658],[363,110091,110093],{"className":110092},[407,658],[363,110094,2810],{"className":110095},[407,658],[363,110097,110098,110101],{"style":821},[363,110099],{"className":110100,"style":809},[650],[363,110102],{"className":110103,"style":829},[828],[363,110105,110106,110109],{"style":2897},[363,110107],{"className":110108,"style":809},[650],[363,110110,110112],{"className":110111},[655,656,657,658],[363,110113,110115],{"className":110114},[407,658],[363,110116,465],{"className":110117},[407,658],[363,110119,666],{"className":110120},[665],[363,110122,110124],{"className":110123},[638],[363,110125,110127],{"className":110126,"style":2919},[642],[363,110128],{},[363,110130],{"className":110131},[501,789],[52942,110133,53429],{},[52942,110135,53429],{},[52845,110137,110138,110198,110290,110441,110443],{},[52942,110139,54088,110140],{},[363,110141,110143,110160],{"className":110142,"translate":367},[366],[363,110144,110146],{"className":110145},[371],[373,110147,110148],{"xmlns":375},[377,110149,110150,110158],{},[380,110151,110152],{},[7161,110153,110154,110156],{},[383,110155,37796],{},[463,110157,2810],{},[387,110159,40741],{"encoding":389},[363,110161,110163],{"className":110162,"ariaHidden":394},[393],[363,110164,110166,110169],{"className":110165},[398],[363,110167],{"className":110168,"style":40751},[402],[363,110170,110172,110175],{"className":110171},[407],[363,110173,37796],{"className":110174},[407,408],[363,110176,110178],{"className":110177},[629],[363,110179,110181],{"className":110180},[633],[363,110182,110184],{"className":110183},[638],[363,110185,110187],{"className":110186,"style":20375},[642],[363,110188,110189,110192],{"style":7212},[363,110190],{"className":110191,"style":651},[650],[363,110193,110195],{"className":110194},[655,656,657,658],[363,110196,2810],{"className":110197},[407,658],[52942,110199,110200],{},[363,110201,110203,110228],{"className":110202,"translate":367},[366],[363,110204,110206],{"className":110205},[371],[373,110207,110208],{"xmlns":375},[377,110209,110210,110226],{},[380,110211,110212,110214,110216,110218,110220],{},[458,110213,461],{"stretchy":460},[383,110215,1116],{},[458,110217,5160],{},[463,110219,465],{},[7161,110221,110222,110224],{},[458,110223,468],{"stretchy":460},[463,110225,2810],{},[387,110227,54177],{"encoding":389},[363,110229,110231,110252],{"className":110230,"ariaHidden":394},[393],[363,110232,110234,110237,110240,110243,110246,110249],{"className":110233},[398],[363,110235],{"className":110236,"style":487},[402],[363,110238,461],{"className":110239},[494],[363,110241,1116],{"className":110242},[407,408],[363,110244],{"className":110245,"style":2934},[505],[363,110247,5160],{"className":110248},[2938],[363,110250],{"className":110251,"style":2934},[505],[363,110253,110255,110258,110261],{"className":110254},[398],[363,110256],{"className":110257,"style":20350},[402],[363,110259,465],{"className":110260},[407],[363,110262,110264,110267],{"className":110263},[501],[363,110265,468],{"className":110266},[501],[363,110268,110270],{"className":110269},[629],[363,110271,110273],{"className":110272},[633],[363,110274,110276],{"className":110275},[638],[363,110277,110279],{"className":110278,"style":20375},[642],[363,110280,110281,110284],{"style":7212},[363,110282],{"className":110283,"style":651},[650],[363,110285,110287],{"className":110286},[655,656,657,658],[363,110288,2810],{"className":110289},[407,658],[52942,110291,110292],{},[363,110293,110295,110320],{"className":110294,"translate":367},[366],[363,110296,110298],{"className":110297},[371],[373,110299,110300],{"xmlns":375},[377,110301,110302,110318],{},[380,110303,110304,110306,110308],{},[383,110305,40584],{},[458,110307,2817],{},[586,110309,110310,110316],{},[7161,110311,110312,110314],{},[383,110313,40584],{},[463,110315,2810],{},[463,110317,39336],{},[387,110319,66691],{"encoding":389},[363,110321,110323,110341],{"className":110322,"ariaHidden":394},[393],[363,110324,110326,110329,110332,110335,110338],{"className":110325},[398],[363,110327],{"className":110328,"style":40668},[402],[363,110330,40584],{"className":110331,"style":1328},[407,408],[363,110333],{"className":110334,"style":2934},[505],[363,110336,2817],{"className":110337},[2938],[363,110339],{"className":110340,"style":2934},[505],[363,110342,110344,110347],{"className":110343},[398],[363,110345],{"className":110346,"style":66719},[402],[363,110348,110350,110353,110438],{"className":110349},[407],[363,110351],{"className":110352},[494,789],[363,110354,110356],{"className":110355},[586],[363,110357,110359,110430],{"className":110358},[633,634],[363,110360,110362,110427],{"className":110361},[638],[363,110363,110365,110379,110387],{"className":110364,"style":66738},[642],[363,110366,110367,110370],{"style":2874},[363,110368],{"className":110369,"style":809},[650],[363,110371,110373],{"className":110372},[655,656,657,658],[363,110374,110376],{"className":110375},[407,658],[363,110377,39336],{"className":110378},[407,658],[363,110380,110381,110384],{"style":821},[363,110382],{"className":110383,"style":809},[650],[363,110385],{"className":110386,"style":829},[828],[363,110388,110389,110392],{"style":3200},[363,110390],{"className":110391,"style":809},[650],[363,110393,110395],{"className":110394},[655,656,657,658],[363,110396,110398],{"className":110397},[407,658],[363,110399,110401,110404],{"className":110400},[407,658],[363,110402,40584],{"className":110403,"style":1328},[407,408,658],[363,110405,110407],{"className":110406},[629],[363,110408,110410],{"className":110409},[633],[363,110411,110413],{"className":110412},[638],[363,110414,110416],{"className":110415,"style":38859},[642],[363,110417,110418,110421],{"style":38862},[363,110419],{"className":110420,"style":30553},[650],[363,110422,110424],{"className":110423},[655,30557,10021,658],[363,110425,2810],{"className":110426},[407,658],[363,110428,666],{"className":110429},[665],[363,110431,110433],{"className":110432},[638],[363,110434,110436],{"className":110435,"style":2919},[642],[363,110437],{},[363,110439],{"className":110440},[501,789],[52942,110442,53102],{},[52942,110444,53102],{},[52845,110446,110447,110531,110682,110858,110860],{},[52942,110448,54283,110449],{},[363,110450,110452,110471],{"className":110451,"translate":367},[366],[363,110453,110455],{"className":110454},[371],[373,110456,110457],{"xmlns":375},[377,110458,110459,110469],{},[380,110460,110461],{},[7900,110462,110463,110465,110467],{},[383,110464,37796],{},[383,110466,38631],{},[463,110468,2810],{},[387,110470,54306],{"encoding":389},[363,110472,110474],{"className":110473,"ariaHidden":394},[393],[363,110475,110477,110480],{"className":110476},[398],[363,110478],{"className":110479,"style":38686},[402],[363,110481,110483,110486],{"className":110482},[407],[363,110484,37796],{"className":110485},[407,408],[363,110487,110489],{"className":110488},[629],[363,110490,110492,110523],{"className":110491},[633,634],[363,110493,110495,110520],{"className":110494},[638],[363,110496,110498,110509],{"className":110497,"style":20375},[642],[363,110499,110500,110503],{"style":38707},[363,110501],{"className":110502,"style":651},[650],[363,110504,110506],{"className":110505},[655,656,657,658],[363,110507,38631],{"className":110508,"style":25948},[407,408,658],[363,110510,110511,110514],{"style":7212},[363,110512],{"className":110513,"style":651},[650],[363,110515,110517],{"className":110516},[655,656,657,658],[363,110518,2810],{"className":110519},[407,658],[363,110521,666],{"className":110522},[665],[363,110524,110526],{"className":110525},[638],[363,110527,110529],{"className":110528,"style":38737},[642],[363,110530],{},[52942,110532,110533],{},[363,110534,110536,110567],{"className":110535,"translate":367},[366],[363,110537,110539],{"className":110538},[371],[373,110540,110541],{"xmlns":375},[377,110542,110543,110565],{},[380,110544,110545],{},[586,110546,110547,110563],{},[380,110548,110549,110551,110553,110555,110557],{},[458,110550,461],{"stretchy":460},[383,110552,1116],{},[458,110554,5160],{},[463,110556,465],{},[7161,110558,110559,110561],{},[458,110560,468],{"stretchy":460},[463,110562,2810],{},[383,110564,1116],{},[387,110566,54403],{"encoding":389},[363,110568,110570],{"className":110569,"ariaHidden":394},[393],[363,110571,110573,110576],{"className":110572},[398],[363,110574],{"className":110575,"style":54413},[402],[363,110577,110579,110582,110679],{"className":110578},[407],[363,110580],{"className":110581},[494,789],[363,110583,110585],{"className":110584},[586],[363,110586,110588,110671],{"className":110587},[633,634],[363,110589,110591,110668],{"className":110590},[638],[363,110592,110594,110608,110616],{"className":110593,"style":38795},[642],[363,110595,110596,110599],{"style":2874},[363,110597],{"className":110598,"style":809},[650],[363,110600,110602],{"className":110601},[655,656,657,658],[363,110603,110605],{"className":110604},[407,658],[363,110606,1116],{"className":110607},[407,408,658],[363,110609,110610,110613],{"style":821},[363,110611],{"className":110612,"style":809},[650],[363,110614],{"className":110615,"style":829},[828],[363,110617,110618,110621],{"style":26765},[363,110619],{"className":110620,"style":809},[650],[363,110622,110624],{"className":110623},[655,656,657,658],[363,110625,110627,110630,110633,110636,110639],{"className":110626},[407,658],[363,110628,461],{"className":110629},[494,658],[363,110631,1116],{"className":110632},[407,408,658],[363,110634,5160],{"className":110635},[2938,658],[363,110637,465],{"className":110638},[407,658],[363,110640,110642,110645],{"className":110641},[501,658],[363,110643,468],{"className":110644},[501,658],[363,110646,110648],{"className":110647},[629],[363,110649,110651],{"className":110650},[633],[363,110652,110654],{"className":110653},[638],[363,110655,110657],{"className":110656,"style":38859},[642],[363,110658,110659,110662],{"style":38862},[363,110660],{"className":110661,"style":30553},[650],[363,110663,110665],{"className":110664},[655,30557,10021,658],[363,110666,2810],{"className":110667},[407,658],[363,110669,666],{"className":110670},[665],[363,110672,110674],{"className":110673},[638],[363,110675,110677],{"className":110676,"style":2919},[642],[363,110678],{},[363,110680],{"className":110681},[501,789],[52942,110683,110684,16142,110808,53822],{},[363,110685,110687,110715],{"className":110686,"translate":367},[366],[363,110688,110690],{"className":110689},[371],[373,110691,110692],{"xmlns":375},[377,110693,110694,110712],{},[380,110695,110696,110698,110700,110702],{},[463,110697,2810],{},[458,110699,5160],{},[463,110701,2810],{},[34686,110703,110704],{},[380,110705,110706,110708,110710],{},[463,110707,465],{},[458,110709,5160],{},[383,110711,40584],{},[387,110713,110714],{"encoding":389},"2-2\\sqrt{1-y}",[363,110716,110718,110736],{"className":110717,"ariaHidden":394},[393],[363,110719,110721,110724,110727,110730,110733],{"className":110720},[398],[363,110722],{"className":110723,"style":12925},[402],[363,110725,2810],{"className":110726},[407],[363,110728],{"className":110729,"style":2934},[505],[363,110731,5160],{"className":110732},[2938],[363,110734],{"className":110735,"style":2934},[505],[363,110737,110739,110743,110746],{"className":110738},[398],[363,110740],{"className":110741,"style":110742},[402],"height:1.04em;vertical-align:-0.23em;",[363,110744,2810],{"className":110745},[407],[363,110747,110749],{"className":110748},[407,34714],[363,110750,110752,110799],{"className":110751},[633,634],[363,110753,110755,110796],{"className":110754},[638],[363,110756,110759,110783],{"className":110757,"style":110758},[642],"height:0.81em;",[363,110760,110762,110765],{"className":110761,"style":12210},[6654],[363,110763],{"className":110764,"style":809},[650],[363,110766,110768,110771,110774,110777,110780],{"className":110767,"style":34734},[407],[363,110769,465],{"className":110770},[407],[363,110772],{"className":110773,"style":2934},[505],[363,110775,5160],{"className":110776},[2938],[363,110778],{"className":110779,"style":2934},[505],[363,110781,40584],{"className":110782,"style":1328},[407,408],[363,110784,110786,110789],{"style":110785},"top:-2.77em;",[363,110787],{"className":110788,"style":809},[650],[363,110790,110792],{"className":110791,"style":34791},[34790],[6670,110793,110794],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,110795],{"d":34798},[363,110797,666],{"className":110798},[665],[363,110800,110802],{"className":110801},[638],[363,110803,110806],{"className":110804,"style":110805},[642],"height:0.23em;",[363,110807],{},[363,110809,110811,110828],{"className":110810,"translate":367},[366],[363,110812,110814],{"className":110813},[371],[373,110815,110816],{"xmlns":375},[377,110817,110818,110826],{},[380,110819,110820,110822,110824],{},[383,110821,40584],{},[458,110823,7598],{},[463,110825,465],{},[387,110827,67120],{"encoding":389},[363,110829,110831,110849],{"className":110830,"ariaHidden":394},[393],[363,110832,110834,110837,110840,110843,110846],{"className":110833},[398],[363,110835],{"className":110836,"style":32039},[402],[363,110838,40584],{"className":110839,"style":1328},[407,408],[363,110841],{"className":110842,"style":506},[505],[363,110844,7598],{"className":110845},[510],[363,110847],{"className":110848,"style":506},[505],[363,110850,110852,110855],{"className":110851},[398],[363,110853],{"className":110854,"style":520},[402],[363,110856,465],{"className":110857},[407],[52942,110859,53102],{},[52942,110861,53102],{},[52845,110863,110864,110923,111058,111169,111171],{},[52942,110865,54563,110866],{},[363,110867,110869,110886],{"className":110868,"translate":367},[366],[363,110870,110872],{"className":110871},[371],[373,110873,110874],{"xmlns":375},[377,110875,110876,110884],{},[380,110877,110878],{},[7161,110879,110880,110882],{},[380,110881],{},[463,110883,2810],{},[387,110885,44616],{"encoding":389},[363,110887,110889],{"className":110888,"ariaHidden":394},[393],[363,110890,110892,110895],{"className":110891},[398],[363,110893],{"className":110894,"style":20375},[402],[363,110896,110898,110900],{"className":110897},[407],[363,110899],{},[363,110901,110903],{"className":110902},[629],[363,110904,110906],{"className":110905},[633],[363,110907,110909],{"className":110908},[638],[363,110910,110912],{"className":110911,"style":20375},[642],[363,110913,110914,110917],{"style":7212},[363,110915],{"className":110916,"style":651},[650],[363,110918,110920],{"className":110919},[655,656,657,658],[363,110921,2810],{"className":110922},[407,658],[52942,110924,110925],{},[363,110926,110928,110955],{"className":110927,"translate":367},[366],[363,110929,110931],{"className":110930},[371],[373,110932,110933],{"xmlns":375},[377,110934,110935,110953],{},[380,110936,110937,110939,110943,110945,110947],{},[458,110938,461],{"stretchy":460},[34686,110940,110941],{},[383,110942,1116],{},[458,110944,5160],{},[463,110946,465],{},[7161,110948,110949,110951],{},[458,110950,468],{"stretchy":460},[463,110952,2810],{},[387,110954,54654],{"encoding":389},[363,110956,110958,111020],{"className":110957,"ariaHidden":394},[393],[363,110959,110961,110964,110967,111011,111014,111017],{"className":110960},[398],[363,110962],{"className":110963,"style":43014},[402],[363,110965,461],{"className":110966},[494],[363,110968,110970],{"className":110969},[407,34714],[363,110971,110973,111003],{"className":110972},[633,634],[363,110974,110976,111000],{"className":110975},[638],[363,110977,110979,110988],{"className":110978,"style":43030},[642],[363,110980,110982,110985],{"className":110981,"style":12210},[6654],[363,110983],{"className":110984,"style":809},[650],[363,110986,1116],{"className":110987,"style":34734},[407,408],[363,110989,110990,110993],{"style":43042},[363,110991],{"className":110992,"style":809},[650],[363,110994,110996],{"className":110995,"style":34791},[34790],[6670,110997,110998],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,110999],{"d":34798},[363,111001,666],{"className":111002},[665],[363,111004,111006],{"className":111005},[638],[363,111007,111009],{"className":111008,"style":43062},[642],[363,111010],{},[363,111012],{"className":111013,"style":2934},[505],[363,111015,5160],{"className":111016},[2938],[363,111018],{"className":111019,"style":2934},[505],[363,111021,111023,111026,111029],{"className":111022},[398],[363,111024],{"className":111025,"style":20350},[402],[363,111027,465],{"className":111028},[407],[363,111030,111032,111035],{"className":111031},[501],[363,111033,468],{"className":111034},[501],[363,111036,111038],{"className":111037},[629],[363,111039,111041],{"className":111040},[633],[363,111042,111044],{"className":111043},[638],[363,111045,111047],{"className":111046,"style":20375},[642],[363,111048,111049,111052],{"style":7212},[363,111050],{"className":111051,"style":651},[650],[363,111053,111055],{"className":111054},[655,656,657,658],[363,111056,2810],{"className":111057},[407,658],[52942,111059,111060],{},[363,111061,111063,111086],{"className":111062,"translate":367},[366],[363,111064,111066],{"className":111065},[371],[373,111067,111068],{"xmlns":375},[377,111069,111070,111084],{},[380,111071,111072],{},[586,111073,111074,111076],{},[383,111075,40584],{},[380,111077,111078,111080,111082],{},[463,111079,465],{},[458,111081,5160],{},[383,111083,40584],{},[387,111085,67014],{"encoding":389},[363,111087,111089],{"className":111088,"ariaHidden":394},[393],[363,111090,111092,111095],{"className":111091},[398],[363,111093],{"className":111094,"style":3431},[402],[363,111096,111098,111101,111166],{"className":111097},[407],[363,111099],{"className":111100},[494,789],[363,111102,111104],{"className":111103},[586],[363,111105,111107,111158],{"className":111106},[633,634],[363,111108,111110,111155],{"className":111109},[638],[363,111111,111113,111133,111141],{"className":111112,"style":3450},[642],[363,111114,111115,111118],{"style":2874},[363,111116],{"className":111117,"style":809},[650],[363,111119,111121],{"className":111120},[655,656,657,658],[363,111122,111124,111127,111130],{"className":111123},[407,658],[363,111125,465],{"className":111126},[407,658],[363,111128,5160],{"className":111129},[2938,658],[363,111131,40584],{"className":111132,"style":1328},[407,408,658],[363,111134,111135,111138],{"style":821},[363,111136],{"className":111137,"style":809},[650],[363,111139],{"className":111140,"style":829},[828],[363,111142,111143,111146],{"style":3200},[363,111144],{"className":111145,"style":809},[650],[363,111147,111149],{"className":111148},[655,656,657,658],[363,111150,111152],{"className":111151},[407,658],[363,111153,40584],{"className":111154,"style":1328},[407,408,658],[363,111156,666],{"className":111157},[665],[363,111159,111161],{"className":111160},[638],[363,111162,111164],{"className":111163,"style":3086},[642],[363,111165],{},[363,111167],{"className":111168},[501,789],[52942,111170,53429],{},[52942,111172,53429],{},[52845,111174,111175,111177,111417,111891,111893],{},[52942,111176,46337],{},[52942,111178,111179],{},[363,111180,111182,111237],{"className":111181,"translate":367},[366],[363,111183,111185],{"className":111184},[371],[373,111186,111187],{"xmlns":375},[377,111188,111189,111235],{},[380,111190,111191,111207,111209,111211,111213,111233],{},[586,111192,111193,111195],{},[463,111194,39336],{},[380,111196,111197,111199,111201],{},[463,111198,465],{},[458,111200,5160],{},[7161,111202,111203,111205],{},[383,111204,45101],{},[463,111206,2810],{},[458,111208,461],{"stretchy":460},[463,111210,465],{},[458,111212,5160],{},[7161,111214,111215,111217],{},[383,111216,1116],{},[380,111218,111219,111221,111223,111225,111227,111229,111231],{},[458,111220,461],{"stretchy":460},[463,111222,465],{},[458,111224,2817],{},[383,111226,45101],{},[458,111228,468],{"stretchy":460},[383,111230,1288],{"mathvariant":557},[463,111232,2810],{},[458,111234,468],{"stretchy":460},[387,111236,54978],{"encoding":389},[363,111238,111240,111361],{"className":111239,"ariaHidden":394},[393],[363,111241,111243,111246,111346,111349,111352,111355,111358],{"className":111242},[398],[363,111244],{"className":111245,"style":45752},[402],[363,111247,111249,111252,111343],{"className":111248},[407],[363,111250],{"className":111251},[494,789],[363,111253,111255],{"className":111254},[586],[363,111256,111258,111335],{"className":111257},[633,634],[363,111259,111261,111332],{"className":111260},[638],[363,111262,111264,111310,111318],{"className":111263,"style":2871},[642],[363,111265,111266,111269],{"style":2874},[363,111267],{"className":111268,"style":809},[650],[363,111270,111272],{"className":111271},[655,656,657,658],[363,111273,111275,111278,111281],{"className":111274},[407,658],[363,111276,465],{"className":111277},[407,658],[363,111279,5160],{"className":111280},[2938,658],[363,111282,111284,111287],{"className":111283},[407,658],[363,111285,45101],{"className":111286,"style":45131},[407,408,658],[363,111288,111290],{"className":111289},[629],[363,111291,111293],{"className":111292},[633],[363,111294,111296],{"className":111295},[638],[363,111297,111299],{"className":111298,"style":45806},[642],[363,111300,111301,111304],{"style":45809},[363,111302],{"className":111303,"style":30553},[650],[363,111305,111307],{"className":111306},[655,30557,10021,658],[363,111308,2810],{"className":111309},[407,658],[363,111311,111312,111315],{"style":821},[363,111313],{"className":111314,"style":809},[650],[363,111316],{"className":111317,"style":829},[828],[363,111319,111320,111323],{"style":2897},[363,111321],{"className":111322,"style":809},[650],[363,111324,111326],{"className":111325},[655,656,657,658],[363,111327,111329],{"className":111328},[407,658],[363,111330,39336],{"className":111331},[407,658],[363,111333,666],{"className":111334},[665],[363,111336,111338],{"className":111337},[638],[363,111339,111341],{"className":111340,"style":16776},[642],[363,111342],{},[363,111344],{"className":111345},[501,789],[363,111347,461],{"className":111348},[494],[363,111350,465],{"className":111351},[407],[363,111353],{"className":111354,"style":2934},[505],[363,111356,5160],{"className":111357},[2938],[363,111359],{"className":111360,"style":2934},[505],[363,111362,111364,111367,111414],{"className":111363},[398],[363,111365],{"className":111366,"style":55109},[402],[363,111368,111370,111373],{"className":111369},[407],[363,111371,1116],{"className":111372},[407,408],[363,111374,111376],{"className":111375},[629],[363,111377,111379],{"className":111378},[633],[363,111380,111382],{"className":111381},[638],[363,111383,111385],{"className":111384,"style":55128},[642],[363,111386,111387,111390],{"style":7212},[363,111388],{"className":111389,"style":651},[650],[363,111391,111393],{"className":111392},[655,656,657,658],[363,111394,111396,111399,111402,111405,111408,111411],{"className":111395},[407,658],[363,111397,461],{"className":111398},[494,658],[363,111400,465],{"className":111401},[407,658],[363,111403,2817],{"className":111404},[2938,658],[363,111406,45101],{"className":111407,"style":45131},[407,408,658],[363,111409,468],{"className":111410},[501,658],[363,111412,45497],{"className":111413},[407,658],[363,111415,468],{"className":111416},[501],[52942,111418,111419,3092,111841],{},[363,111420,111422,111498],{"className":111421,"translate":367},[366],[363,111423,111425],{"className":111424},[371],[373,111426,111427],{"xmlns":375},[377,111428,111429,111495],{},[380,111430,111431,111437,111439,111441,111443,111445,111447,111449,111451,111453,111455,111457,111459,111479,111481,111493],{},[586,111432,111433,111435],{},[463,111434,465],{},[383,111436,45527],{},[458,111438,578],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,111440,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,111442,461],{"stretchy":460},[463,111444,465],{},[458,111446,5160],{},[383,111448,45527],{},[458,111450,468],{"stretchy":460},[458,111452,461],{"stretchy":460},[458,111454,5160],{},[383,111456,40584],{},[458,111458,468],{"stretchy":460},[7161,111460,111461,111463],{},[458,111462,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[380,111464,111465,111467],{},[458,111466,5160],{},[586,111468,111469,111471],{},[383,111470,45527],{},[380,111472,111473,111475,111477],{},[463,111474,465],{},[458,111476,5160],{},[383,111478,45527],{},[458,111480,5160],{},[586,111482,111483,111485],{},[463,111484,465],{},[380,111486,111487,111489,111491],{},[463,111488,465],{},[458,111490,5160],{},[383,111492,45527],{},[458,111494,605],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[387,111496,111497],{"encoding":389},"\\frac{1}{a}\\big[\\big((1-a)(-y)\\big)^{-\\frac{a}{1-a}}-\\frac{1}{1-a}\\big]",[363,111499,111501,111602,111754],{"className":111500,"ariaHidden":394},[393],[363,111502,111504,111507,111575,111581,111587,111590,111593,111596,111599],{"className":111503},[398],[363,111505],{"className":111506,"style":20910},[402],[363,111508,111510,111513,111572],{"className":111509},[407],[363,111511],{"className":111512},[494,789],[363,111514,111516],{"className":111515},[586],[363,111517,111519,111564],{"className":111518},[633,634],[363,111520,111522,111561],{"className":111521},[638],[363,111523,111525,111539,111547],{"className":111524,"style":2871},[642],[363,111526,111527,111530],{"style":2874},[363,111528],{"className":111529,"style":809},[650],[363,111531,111533],{"className":111532},[655,656,657,658],[363,111534,111536],{"className":111535},[407,658],[363,111537,45527],{"className":111538},[407,408,658],[363,111540,111541,111544],{"style":821},[363,111542],{"className":111543,"style":809},[650],[363,111545],{"className":111546,"style":829},[828],[363,111548,111549,111552],{"style":2897},[363,111550],{"className":111551,"style":809},[650],[363,111553,111555],{"className":111554},[655,656,657,658],[363,111556,111558],{"className":111557},[407,658],[363,111559,465],{"className":111560},[407,658],[363,111562,666],{"className":111563},[665],[363,111565,111567],{"className":111566},[638],[363,111568,111570],{"className":111569,"style":2919},[642],[363,111571],{},[363,111573],{"className":111574},[501,789],[363,111576,111578],{"className":111577},[407],[363,111579,578],{"className":111580},[767,10021],[363,111582,111584],{"className":111583},[407],[363,111585,461],{"className":111586},[767,10021],[363,111588,461],{"className":111589},[494],[363,111591,465],{"className":111592},[407],[363,111594],{"className":111595,"style":2934},[505],[363,111597,5160],{"className":111598},[2938],[363,111600],{"className":111601,"style":2934},[505],[363,111603,111605,111609,111612,111615,111618,111621,111624,111627,111745,111748,111751],{"className":111604},[398],[363,111606],{"className":111607,"style":111608},[402],"height:1.437em;vertical-align:-0.35em;",[363,111610,45527],{"className":111611},[407,408],[363,111613,468],{"className":111614},[501],[363,111616,461],{"className":111617},[494],[363,111619,5160],{"className":111620},[407],[363,111622,40584],{"className":111623,"style":1328},[407,408],[363,111625,468],{"className":111626},[501],[363,111628,111630,111636],{"className":111629},[407],[363,111631,111633],{"className":111632},[407],[363,111634,468],{"className":111635},[767,10021],[363,111637,111639],{"className":111638},[629],[363,111640,111642],{"className":111641},[633],[363,111643,111645],{"className":111644},[638],[363,111646,111649],{"className":111647,"style":111648},[642],"height:1.087em;",[363,111650,111652,111655],{"style":111651},"top:-3.6029em;margin-right:0.05em;",[363,111653],{"className":111654,"style":809},[650],[363,111656,111658],{"className":111657},[655,656,657,658],[363,111659,111661,111664],{"className":111660},[407,658],[363,111662,5160],{"className":111663},[407,658],[363,111665,111667,111671,111742],{"className":111666},[407,658],[363,111668],{"className":111669},[494,789,655,30557,111670],"size6",[363,111672,111674],{"className":111673},[586],[363,111675,111677,111733],{"className":111676},[633,634],[363,111678,111680,111730],{"className":111679},[638],[363,111681,111684,111705,111715],{"className":111682,"style":111683},[642],"height:0.6915em;",[363,111685,111687,111690],{"style":111686},"top:-2.656em;",[363,111688],{"className":111689,"style":809},[650],[363,111691,111693],{"className":111692},[655,30557,10021,658],[363,111694,111696,111699,111702],{"className":111695},[407,658],[363,111697,465],{"className":111698},[407,658],[363,111700,5160],{"className":111701},[2938,658],[363,111703,45527],{"className":111704},[407,408,658],[363,111706,111708,111711],{"style":111707},"top:-3.2255em;",[363,111709],{"className":111710,"style":809},[650],[363,111712],{"className":111713,"style":111714},[828,658],"border-bottom-width:0.049em;",[363,111716,111718,111721],{"style":111717},"top:-3.384em;",[363,111719],{"className":111720,"style":809},[650],[363,111722,111724],{"className":111723},[655,30557,10021,658],[363,111725,111727],{"className":111726},[407,658],[363,111728,45527],{"className":111729},[407,408,658],[363,111731,666],{"className":111732},[665],[363,111734,111736],{"className":111735},[638],[363,111737,111740],{"className":111738,"style":111739},[642],"height:0.4035em;",[363,111741],{},[363,111743],{"className":111744},[501,789,655,30557,111670],[363,111746],{"className":111747,"style":2934},[505],[363,111749,5160],{"className":111750},[2938],[363,111752],{"className":111753,"style":2934},[505],[363,111755,111757,111761,111835],{"className":111756},[398],[363,111758],{"className":111759,"style":111760},[402],"height:1.2533em;vertical-align:-0.4033em;",[363,111762,111764,111767,111832],{"className":111763},[407],[363,111765],{"className":111766},[494,789],[363,111768,111770],{"className":111769},[586],[363,111771,111773,111824],{"className":111772},[633,634],[363,111774,111776,111821],{"className":111775},[638],[363,111777,111779,111799,111807],{"className":111778,"style":2871},[642],[363,111780,111781,111784],{"style":2874},[363,111782],{"className":111783,"style":809},[650],[363,111785,111787],{"className":111786},[655,656,657,658],[363,111788,111790,111793,111796],{"className":111789},[407,658],[363,111791,465],{"className":111792},[407,658],[363,111794,5160],{"className":111795},[2938,658],[363,111797,45527],{"className":111798},[407,408,658],[363,111800,111801,111804],{"style":821},[363,111802],{"className":111803,"style":809},[650],[363,111805],{"className":111806,"style":829},[828],[363,111808,111809,111812],{"style":2897},[363,111810],{"className":111811,"style":809},[650],[363,111813,111815],{"className":111814},[655,656,657,658],[363,111816,111818],{"className":111817},[407,658],[363,111819,465],{"className":111820},[407,658],[363,111822,666],{"className":111823},[665],[363,111825,111827],{"className":111826},[638],[363,111828,111830],{"className":111829,"style":16776},[642],[363,111831],{},[363,111833],{"className":111834},[501,789],[363,111836,111838],{"className":111837},[407],[363,111839,605],{"className":111840},[767,10021],[363,111842,111844,111861],{"className":111843,"translate":367},[366],[363,111845,111847],{"className":111846},[371],[373,111848,111849],{"xmlns":375},[377,111850,111851,111859],{},[380,111852,111853,111855,111857],{},[383,111854,40584],{},[458,111856,7598],{},[463,111858,474],{},[387,111860,65488],{"encoding":389},[363,111862,111864,111882],{"className":111863,"ariaHidden":394},[393],[363,111865,111867,111870,111873,111876,111879],{"className":111866},[398],[363,111868],{"className":111869,"style":32039},[402],[363,111871,40584],{"className":111872,"style":1328},[407,408],[363,111874],{"className":111875,"style":506},[505],[363,111877,7598],{"className":111878},[510],[363,111880],{"className":111881,"style":506},[505],[363,111883,111885,111888],{"className":111884},[398],[363,111886],{"className":111887,"style":520},[402],[363,111889,474],{"className":111890},[407],[52942,111892,53102],{},[52942,111894,53102],{},[11,111896,111897,111898,3092,112220,112531,112532,93969,112726,16142,112908,112958,112959,113502,113503,113679,113680,67461,114028,93969,114229,16142,114472,114522,114523,88654,114643,3092,114693,114824,114825,114953],{},"（Neyman 一行的验证：",[363,111899,111901,111959],{"className":111900,"translate":367},[366],[363,111902,111904],{"className":111903},[371],[373,111905,111906],{"xmlns":375},[377,111907,111908,111956],{},[380,111909,111910,111912,111914,111916,111918,111920,111940,111942,111944,111946,111948,111950],{},[383,111911,385],{},[458,111913,461],{"stretchy":460},[383,111915,1116],{},[458,111917,468],{"stretchy":460},[458,111919,471],{},[586,111921,111922,111938],{},[380,111923,111924,111926,111928,111930,111932],{},[458,111925,461],{"stretchy":460},[383,111927,1116],{},[458,111929,5160],{},[463,111931,465],{},[7161,111933,111934,111936],{},[458,111935,468],{"stretchy":460},[463,111937,2810],{},[383,111939,1116],{},[458,111941,471],{},[383,111943,1116],{},[458,111945,5160],{},[463,111947,2810],{},[458,111949,2817],{},[586,111951,111952,111954],{},[463,111953,465],{},[383,111955,1116],{},[387,111957,111958],{"encoding":389},"f(t)=\\frac{(t-1)^2}{t}=t-2+\\frac1t",[363,111960,111962,111989,112110,112128,112146],{"className":111961,"ariaHidden":394},[393],[363,111963,111965,111968,111971,111974,111977,111980,111983,111986],{"className":111964},[398],[363,111966],{"className":111967,"style":487},[402],[363,111969,385],{"className":111970,"style":409},[407,408],[363,111972,461],{"className":111973},[494],[363,111975,1116],{"className":111976},[407,408],[363,111978,468],{"className":111979},[501],[363,111981],{"className":111982,"style":506},[505],[363,111984,471],{"className":111985},[510],[363,111987],{"className":111988,"style":506},[505],[363,111990,111992,111995,112101,112104,112107],{"className":111991},[398],[363,111993],{"className":111994,"style":54413},[402],[363,111996,111998,112001,112098],{"className":111997},[407],[363,111999],{"className":112000},[494,789],[363,112002,112004],{"className":112003},[586],[363,112005,112007,112090],{"className":112006},[633,634],[363,112008,112010,112087],{"className":112009},[638],[363,112011,112013,112027,112035],{"className":112012,"style":38795},[642],[363,112014,112015,112018],{"style":2874},[363,112016],{"className":112017,"style":809},[650],[363,112019,112021],{"className":112020},[655,656,657,658],[363,112022,112024],{"className":112023},[407,658],[363,112025,1116],{"className":112026},[407,408,658],[363,112028,112029,112032],{"style":821},[363,112030],{"className":112031,"style":809},[650],[363,112033],{"className":112034,"style":829},[828],[363,112036,112037,112040],{"style":26765},[363,112038],{"className":112039,"style":809},[650],[363,112041,112043],{"className":112042},[655,656,657,658],[363,112044,112046,112049,112052,112055,112058],{"className":112045},[407,658],[363,112047,461],{"className":112048},[494,658],[363,112050,1116],{"className":112051},[407,408,658],[363,112053,5160],{"className":112054},[2938,658],[363,112056,465],{"className":112057},[407,658],[363,112059,112061,112064],{"className":112060},[501,658],[363,112062,468],{"className":112063},[501,658],[363,112065,112067],{"className":112066},[629],[363,112068,112070],{"className":112069},[633],[363,112071,112073],{"className":112072},[638],[363,112074,112076],{"className":112075,"style":38859},[642],[363,112077,112078,112081],{"style":38862},[363,112079],{"className":112080,"style":30553},[650],[363,112082,112084],{"className":112083},[655,30557,10021,658],[363,112085,2810],{"className":112086},[407,658],[363,112088,666],{"className":112089},[665],[363,112091,112093],{"className":112092},[638],[363,112094,112096],{"className":112095,"style":2919},[642],[363,112097],{},[363,112099],{"className":112100},[501,789],[363,112102],{"className":112103,"style":506},[505],[363,112105,471],{"className":112106},[510],[363,112108],{"className":112109,"style":506},[505],[363,112111,112113,112116,112119,112122,112125],{"className":112112},[398],[363,112114],{"className":112115,"style":67965},[402],[363,112117,1116],{"className":112118},[407,408],[363,112120],{"className":112121,"style":2934},[505],[363,112123,5160],{"className":112124},[2938],[363,112126],{"className":112127,"style":2934},[505],[363,112129,112131,112134,112137,112140,112143],{"className":112130},[398],[363,112132],{"className":112133,"style":12925},[402],[363,112135,2810],{"className":112136},[407],[363,112138],{"className":112139,"style":2934},[505],[363,112141,2817],{"className":112142},[2938],[363,112144],{"className":112145,"style":2934},[505],[363,112147,112149,112152],{"className":112148},[398],[363,112150],{"className":112151,"style":2852},[402],[363,112153,112155,112158,112217],{"className":112154},[407],[363,112156],{"className":112157},[494,789],[363,112159,112161],{"className":112160},[586],[363,112162,112164,112209],{"className":112163},[633,634],[363,112165,112167,112206],{"className":112166},[638],[363,112168,112170,112184,112192],{"className":112169,"style":2871},[642],[363,112171,112172,112175],{"style":2874},[363,112173],{"className":112174,"style":809},[650],[363,112176,112178],{"className":112177},[655,656,657,658],[363,112179,112181],{"className":112180},[407,658],[363,112182,1116],{"className":112183},[407,408,658],[363,112185,112186,112189],{"style":821},[363,112187],{"className":112188,"style":809},[650],[363,112190],{"className":112191,"style":829},[828],[363,112193,112194,112197],{"style":2897},[363,112195],{"className":112196,"style":809},[650],[363,112198,112200],{"className":112199},[655,656,657,658],[363,112201,112203],{"className":112202},[407,658],[363,112204,465],{"className":112205},[407,658],[363,112207,666],{"className":112208},[665],[363,112210,112212],{"className":112211},[638],[363,112213,112215],{"className":112214,"style":2919},[642],[363,112216],{},[363,112218],{"className":112219},[501,789],[363,112221,112223,112289],{"className":112222,"translate":367},[366],[363,112224,112226],{"className":112225},[371],[373,112227,112228],{"xmlns":375},[377,112229,112230,112286],{},[380,112231,112232,112238,112240,112242,112244,112246,112262,112264,112266,112268,112270,112272,112274,112276,112278,112284],{},[7161,112233,112234,112236],{},[383,112235,385],{},[458,112237,7920],{},[458,112239,461],{"stretchy":460},[383,112241,40584],{},[458,112243,468],{"stretchy":460},[458,112245,471],{},[543,112247,112248,112254],{},[380,112249,112250,112252],{},[383,112251,35779],{},[458,112253,4450],{},[380,112255,112256,112258,112260],{},[383,112257,1116],{},[458,112259,3250],{},[463,112261,474],{},[458,112263,3245],{"stretchy":460},[383,112265,40584],{},[383,112267,1116],{},[458,112269,5160],{},[383,112271,1116],{},[458,112273,2817],{},[463,112275,2810],{},[458,112277,5160],{},[586,112279,112280,112282],{},[463,112281,465],{},[383,112283,1116],{},[458,112285,3255],{"stretchy":460},[387,112287,112288],{"encoding":389},"f^*(y)=\\sup_{t>0}\\{yt-t+2-\\frac1t\\}",[363,112290,112292,112345,112418,112436,112454],{"className":112291,"ariaHidden":394},[393],[363,112293,112295,112298,112327,112330,112333,112336,112339,112342],{"className":112294},[398],[363,112296],{"className":112297,"style":487},[402],[363,112299,112301,112304],{"className":112300},[407],[363,112302,385],{"className":112303,"style":409},[407,408],[363,112305,112307],{"className":112306},[629],[363,112308,112310],{"className":112309},[633],[363,112311,112313],{"className":112312},[638],[363,112314,112316],{"className":112315,"style":8846},[642],[363,112317,112318,112321],{"style":7212},[363,112319],{"className":112320,"style":651},[650],[363,112322,112324],{"className":112323},[655,656,657,658],[363,112325,7920],{"className":112326},[2938,658],[363,112328,461],{"className":112329},[494],[363,112331,40584],{"className":112332,"style":1328},[407,408],[363,112334,468],{"className":112335},[501],[363,112337],{"className":112338,"style":506},[505],[363,112340,471],{"className":112341},[510],[363,112343],{"className":112344,"style":506},[505],[363,112346,112348,112351,112400,112403,112406,112409,112412,112415],{"className":112347},[398],[363,112349],{"className":112350,"style":35903},[402],[363,112352,112354,112357],{"className":112353},[1831],[363,112355,35779],{"className":112356},[1831],[363,112358,112360],{"className":112359},[629],[363,112361,112363,112392],{"className":112362},[633,634],[363,112364,112366,112389],{"className":112365},[638],[363,112367,112369],{"className":112368,"style":71997},[642],[363,112370,112371,112374],{"style":35925},[363,112372],{"className":112373,"style":651},[650],[363,112375,112377],{"className":112376},[655,656,657,658],[363,112378,112380,112383,112386],{"className":112379},[407,658],[363,112381,1116],{"className":112382},[407,408,658],[363,112384,3250],{"className":112385},[510,658],[363,112387,474],{"className":112388},[407,658],[363,112390,666],{"className":112391},[665],[363,112393,112395],{"className":112394},[638],[363,112396,112398],{"className":112397,"style":35953},[642],[363,112399],{},[363,112401,3245],{"className":112402},[494],[363,112404,40584],{"className":112405,"style":1328},[407,408],[363,112407,1116],{"className":112408},[407,408],[363,112410],{"className":112411,"style":2934},[505],[363,112413,5160],{"className":112414},[2938],[363,112416],{"className":112417,"style":2934},[505],[363,112419,112421,112424,112427,112430,112433],{"className":112420},[398],[363,112422],{"className":112423,"style":67965},[402],[363,112425,1116],{"className":112426},[407,408],[363,112428],{"className":112429,"style":2934},[505],[363,112431,2817],{"className":112432},[2938],[363,112434],{"className":112435,"style":2934},[505],[363,112437,112439,112442,112445,112448,112451],{"className":112438},[398],[363,112440],{"className":112441,"style":12925},[402],[363,112443,2810],{"className":112444},[407],[363,112446],{"className":112447,"style":2934},[505],[363,112449,5160],{"className":112450},[2938],[363,112452],{"className":112453,"style":2934},[505],[363,112455,112457,112460,112528],{"className":112456},[398],[363,112458],{"className":112459,"style":2852},[402],[363,112461,112463,112466,112525],{"className":112462},[407],[363,112464],{"className":112465},[494,789],[363,112467,112469],{"className":112468},[586],[363,112470,112472,112517],{"className":112471},[633,634],[363,112473,112475,112514],{"className":112474},[638],[363,112476,112478,112492,112500],{"className":112477,"style":2871},[642],[363,112479,112480,112483],{"style":2874},[363,112481],{"className":112482,"style":809},[650],[363,112484,112486],{"className":112485},[655,656,657,658],[363,112487,112489],{"className":112488},[407,658],[363,112490,1116],{"className":112491},[407,408,658],[363,112493,112494,112497],{"style":821},[363,112495],{"className":112496,"style":809},[650],[363,112498],{"className":112499,"style":829},[828],[363,112501,112502,112505],{"style":2897},[363,112503],{"className":112504,"style":809},[650],[363,112506,112508],{"className":112507},[655,656,657,658],[363,112509,112511],{"className":112510},[407,658],[363,112512,465],{"className":112513},[407,658],[363,112515,666],{"className":112516},[665],[363,112518,112520],{"className":112519},[638],[363,112521,112523],{"className":112522,"style":2919},[642],[363,112524],{},[363,112526],{"className":112527},[501,789],[363,112529,3255],{"className":112530},[501],"，驻点条件 ",[363,112533,112535,112569],{"className":112534,"translate":367},[366],[363,112536,112538],{"className":112537},[371],[373,112539,112540],{"xmlns":375},[377,112541,112542,112566],{},[380,112543,112544,112546,112548,112550,112552,112562,112564],{},[383,112545,40584],{},[458,112547,5160],{},[463,112549,465],{},[458,112551,2817],{},[586,112553,112554,112556],{},[463,112555,465],{},[7161,112557,112558,112560],{},[383,112559,1116],{},[463,112561,2810],{},[458,112563,471],{},[463,112565,474],{},[387,112567,112568],{"encoding":389},"y-1+\\frac1{t^2}=0",[363,112570,112572,112590,112608,112717],{"className":112571,"ariaHidden":394},[393],[363,112573,112575,112578,112581,112584,112587],{"className":112574},[398],[363,112576],{"className":112577,"style":40668},[402],[363,112579,40584],{"className":112580,"style":1328},[407,408],[363,112582],{"className":112583,"style":2934},[505],[363,112585,5160],{"className":112586},[2938],[363,112588],{"className":112589,"style":2934},[505],[363,112591,112593,112596,112599,112602,112605],{"className":112592},[398],[363,112594],{"className":112595,"style":12925},[402],[363,112597,465],{"className":112598},[407],[363,112600],{"className":112601,"style":2934},[505],[363,112603,2817],{"className":112604},[2938],[363,112606],{"className":112607,"style":2934},[505],[363,112609,112611,112614,112708,112711,112714],{"className":112610},[398],[363,112612],{"className":112613,"style":2852},[402],[363,112615,112617,112620,112705],{"className":112616},[407],[363,112618],{"className":112619},[494,789],[363,112621,112623],{"className":112622},[586],[363,112624,112626,112697],{"className":112625},[633,634],[363,112627,112629,112694],{"className":112628},[638],[363,112630,112632,112672,112680],{"className":112631,"style":2871},[642],[363,112633,112634,112637],{"style":2874},[363,112635],{"className":112636,"style":809},[650],[363,112638,112640],{"className":112639},[655,656,657,658],[363,112641,112643],{"className":112642},[407,658],[363,112644,112646,112649],{"className":112645},[407,658],[363,112647,1116],{"className":112648},[407,408,658],[363,112650,112652],{"className":112651},[629],[363,112653,112655],{"className":112654},[633],[363,112656,112658],{"className":112657},[638],[363,112659,112661],{"className":112660,"style":45806},[642],[363,112662,112663,112666],{"style":45809},[363,112664],{"className":112665,"style":30553},[650],[363,112667,112669],{"className":112668},[655,30557,10021,658],[363,112670,2810],{"className":112671},[407,658],[363,112673,112674,112677],{"style":821},[363,112675],{"className":112676,"style":809},[650],[363,112678],{"className":112679,"style":829},[828],[363,112681,112682,112685],{"style":2897},[363,112683],{"className":112684,"style":809},[650],[363,112686,112688],{"className":112687},[655,656,657,658],[363,112689,112691],{"className":112690},[407,658],[363,112692,465],{"className":112693},[407,658],[363,112695,666],{"className":112696},[665],[363,112698,112700],{"className":112699},[638],[363,112701,112703],{"className":112702,"style":2919},[642],[363,112704],{},[363,112706],{"className":112707},[501,789],[363,112709],{"className":112710,"style":506},[505],[363,112712,471],{"className":112713},[510],[363,112715],{"className":112716,"style":506},[505],[363,112718,112720,112723],{"className":112719},[398],[363,112721],{"className":112722,"style":520},[402],[363,112724,474],{"className":112725},[407],[363,112727,112729,112759],{"className":112728,"translate":367},[366],[363,112730,112732],{"className":112731},[371],[373,112733,112734],{"xmlns":375},[377,112735,112736,112756],{},[380,112737,112738,112740,112742],{},[383,112739,1116],{},[458,112741,471],{},[586,112743,112744,112746],{},[463,112745,465],{},[34686,112747,112748],{},[380,112749,112750,112752,112754],{},[463,112751,465],{},[458,112753,5160],{},[383,112755,40584],{},[387,112757,112758],{"encoding":389},"t=\\frac{1}{\\sqrt{1-y}}",[363,112760,112762,112780],{"className":112761,"ariaHidden":394},[393],[363,112763,112765,112768,112771,112774,112777],{"className":112764},[398],[363,112766],{"className":112767,"style":5690},[402],[363,112769,1116],{"className":112770},[407,408],[363,112772],{"className":112773,"style":506},[505],[363,112775,471],{"className":112776},[510],[363,112778],{"className":112779,"style":506},[505],[363,112781,112783,112786],{"className":112782},[398],[363,112784],{"className":112785,"style":98492},[402],[363,112787,112789,112792,112905],{"className":112788},[407],[363,112790],{"className":112791},[494,789],[363,112793,112795],{"className":112794},[586],[363,112796,112798,112897],{"className":112797},[633,634],[363,112799,112801,112894],{"className":112800},[638],[363,112802,112804,112872,112880],{"className":112803,"style":2871},[642],[363,112805,112807,112810],{"style":112806},"top:-2.6191em;",[363,112808],{"className":112809,"style":809},[650],[363,112811,112813],{"className":112812},[655,656,657,658],[363,112814,112816],{"className":112815},[407,658],[363,112817,112819],{"className":112818},[407,34714,658],[363,112820,112822,112863],{"className":112821},[633,634],[363,112823,112825,112860],{"className":112824},[638],[363,112826,112829,112847],{"className":112827,"style":112828},[642],"height:0.8156em;",[363,112830,112832,112835],{"className":112831,"style":12210},[6654],[363,112833],{"className":112834,"style":809},[650],[363,112836,112838,112841,112844],{"className":112837,"style":34734},[407,658],[363,112839,465],{"className":112840},[407,658],[363,112842,5160],{"className":112843},[2938,658],[363,112845,40584],{"className":112846,"style":1328},[407,408,658],[363,112848,112850,112853],{"style":112849},"top:-2.7756em;",[363,112851],{"className":112852,"style":809},[650],[363,112854,112856],{"className":112855,"style":34791},[34790,658],[6670,112857,112858],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,112859],{"d":34798},[363,112861,666],{"className":112862},[665],[363,112864,112866],{"className":112865},[638],[363,112867,112870],{"className":112868,"style":112869},[642],"height:0.2244em;",[363,112871],{},[363,112873,112874,112877],{"style":821},[363,112875],{"className":112876,"style":809},[650],[363,112878],{"className":112879,"style":829},[828],[363,112881,112882,112885],{"style":2897},[363,112883],{"className":112884,"style":809},[650],[363,112886,112888],{"className":112887},[655,656,657,658],[363,112889,112891],{"className":112890},[407,658],[363,112892,465],{"className":112893},[407,658],[363,112895,666],{"className":112896},[665],[363,112898,112900],{"className":112899},[638],[363,112901,112903],{"className":112902,"style":98601},[642],[363,112904],{},[363,112906],{"className":112907},[501,789],[363,112909,112911,112928],{"className":112910,"translate":367},[366],[363,112912,112914],{"className":112913},[371],[373,112915,112916],{"xmlns":375},[377,112917,112918,112926],{},[380,112919,112920,112922,112924],{},[383,112921,40584],{},[458,112923,7598],{},[463,112925,465],{},[387,112927,67120],{"encoding":389},[363,112929,112931,112949],{"className":112930,"ariaHidden":394},[393],[363,112932,112934,112937,112940,112943,112946],{"className":112933},[398],[363,112935],{"className":112936,"style":32039},[402],[363,112938,40584],{"className":112939,"style":1328},[407,408],[363,112941],{"className":112942,"style":506},[505],[363,112944,7598],{"className":112945},[510],[363,112947],{"className":112948,"style":506},[505],[363,112950,112952,112955],{"className":112951},[398],[363,112953],{"className":112954,"style":520},[402],[363,112956,465],{"className":112957},[407],"），代回得 ",[363,112960,112962,113054],{"className":112961,"translate":367},[366],[363,112963,112965],{"className":112964},[371],[373,112966,112967],{"xmlns":375},[377,112968,112969,113051],{},[380,112970,112971,112977,112979,112981,112983,112985,112987,112989,112991,112993,112995,112997,113003,113005,113007,113017,113019,113021,113023,113033,113035,113037,113039,113041],{},[7161,112972,112973,112975],{},[383,112974,385],{},[458,112976,7920],{},[458,112978,471],{},[383,112980,1116],{},[458,112982,461],{"stretchy":460},[383,112984,40584],{},[458,112986,5160],{},[463,112988,465],{},[458,112990,468],{"stretchy":460},[458,112992,2817],{},[463,112994,2810],{},[458,112996,5160],{},[586,112998,112999,113001],{},[463,113000,465],{},[383,113002,1116],{},[458,113004,471],{},[458,113006,5160],{},[34686,113008,113009],{},[380,113010,113011,113013,113015],{},[463,113012,465],{},[458,113014,5160],{},[383,113016,40584],{},[458,113018,2817],{},[463,113020,2810],{},[458,113022,5160],{},[34686,113024,113025],{},[380,113026,113027,113029,113031],{},[463,113028,465],{},[458,113030,5160],{},[383,113032,40584],{},[458,113034,471],{},[463,113036,2810],{},[458,113038,5160],{},[463,113040,2810],{},[34686,113042,113043],{},[380,113044,113045,113047,113049],{},[463,113046,465],{},[458,113048,5160],{},[383,113050,40584],{},[387,113052,113053],{"encoding":389},"f^*=t(y-1)+2-\\frac1t=-\\sqrt{1-y}+2-\\sqrt{1-y}=2-2\\sqrt{1-y}",[363,113055,113057,113101,113125,113146,113164,113247,113324,113342,113416,113434],{"className":113056,"ariaHidden":394},[393],[363,113058,113060,113063,113092,113095,113098],{"className":113059},[398],[363,113061],{"className":113062,"style":403},[402],[363,113064,113066,113069],{"className":113065},[407],[363,113067,385],{"className":113068,"style":409},[407,408],[363,113070,113072],{"className":113071},[629],[363,113073,113075],{"className":113074},[633],[363,113076,113078],{"className":113077},[638],[363,113079,113081],{"className":113080,"style":8846},[642],[363,113082,113083,113086],{"style":7212},[363,113084],{"className":113085,"style":651},[650],[363,113087,113089],{"className":113088},[655,656,657,658],[363,113090,7920],{"className":113091},[2938,658],[363,113093],{"className":113094,"style":506},[505],[363,113096,471],{"className":113097},[510],[363,113099],{"className":113100,"style":506},[505],[363,113102,113104,113107,113110,113113,113116,113119,113122],{"className":113103},[398],[363,113105],{"className":113106,"style":487},[402],[363,113108,1116],{"className":113109},[407,408],[363,113111,461],{"className":113112},[494],[363,113114,40584],{"className":113115,"style":1328},[407,408],[363,113117],{"className":113118,"style":2934},[505],[363,113120,5160],{"className":113121},[2938],[363,113123],{"className":113124,"style":2934},[505],[363,113126,113128,113131,113134,113137,113140,113143],{"className":113127},[398],[363,113129],{"className":113130,"style":487},[402],[363,113132,465],{"className":113133},[407],[363,113135,468],{"className":113136},[501],[363,113138],{"className":113139,"style":2934},[505],[363,113141,2817],{"className":113142},[2938],[363,113144],{"className":113145,"style":2934},[505],[363,113147,113149,113152,113155,113158,113161],{"className":113148},[398],[363,113150],{"className":113151,"style":12925},[402],[363,113153,2810],{"className":113154},[407],[363,113156],{"className":113157,"style":2934},[505],[363,113159,5160],{"className":113160},[2938],[363,113162],{"className":113163,"style":2934},[505],[363,113165,113167,113170,113238,113241,113244],{"className":113166},[398],[363,113168],{"className":113169,"style":2852},[402],[363,113171,113173,113176,113235],{"className":113172},[407],[363,113174],{"className":113175},[494,789],[363,113177,113179],{"className":113178},[586],[363,113180,113182,113227],{"className":113181},[633,634],[363,113183,113185,113224],{"className":113184},[638],[363,113186,113188,113202,113210],{"className":113187,"style":2871},[642],[363,113189,113190,113193],{"style":2874},[363,113191],{"className":113192,"style":809},[650],[363,113194,113196],{"className":113195},[655,656,657,658],[363,113197,113199],{"className":113198},[407,658],[363,113200,1116],{"className":113201},[407,408,658],[363,113203,113204,113207],{"style":821},[363,113205],{"className":113206,"style":809},[650],[363,113208],{"className":113209,"style":829},[828],[363,113211,113212,113215],{"style":2897},[363,113213],{"className":113214,"style":809},[650],[363,113216,113218],{"className":113217},[655,656,657,658],[363,113219,113221],{"className":113220},[407,658],[363,113222,465],{"className":113223},[407,658],[363,113225,666],{"className":113226},[665],[363,113228,113230],{"className":113229},[638],[363,113231,113233],{"className":113232,"style":2919},[642],[363,113234],{},[363,113236],{"className":113237},[501,789],[363,113239],{"className":113240,"style":506},[505],[363,113242,471],{"className":113243},[510],[363,113245],{"className":113246,"style":506},[505],[363,113248,113250,113253,113256,113315,113318,113321],{"className":113249},[398],[363,113251],{"className":113252,"style":110742},[402],[363,113254,5160],{"className":113255},[407],[363,113257,113259],{"className":113258},[407,34714],[363,113260,113262,113307],{"className":113261},[633,634],[363,113263,113265,113304],{"className":113264},[638],[363,113266,113268,113292],{"className":113267,"style":110758},[642],[363,113269,113271,113274],{"className":113270,"style":12210},[6654],[363,113272],{"className":113273,"style":809},[650],[363,113275,113277,113280,113283,113286,113289],{"className":113276,"style":34734},[407],[363,113278,465],{"className":113279},[407],[363,113281],{"className":113282,"style":2934},[505],[363,113284,5160],{"className":113285},[2938],[363,113287],{"className":113288,"style":2934},[505],[363,113290,40584],{"className":113291,"style":1328},[407,408],[363,113293,113294,113297],{"style":110785},[363,113295],{"className":113296,"style":809},[650],[363,113298,113300],{"className":113299,"style":34791},[34790],[6670,113301,113302],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,113303],{"d":34798},[363,113305,666],{"className":113306},[665],[363,113308,113310],{"className":113309},[638],[363,113311,113313],{"className":113312,"style":110805},[642],[363,113314],{},[363,113316],{"className":113317,"style":2934},[505],[363,113319,2817],{"className":113320},[2938],[363,113322],{"className":113323,"style":2934},[505],[363,113325,113327,113330,113333,113336,113339],{"className":113326},[398],[363,113328],{"className":113329,"style":12925},[402],[363,113331,2810],{"className":113332},[407],[363,113334],{"className":113335,"style":2934},[505],[363,113337,5160],{"className":113338},[2938],[363,113340],{"className":113341,"style":2934},[505],[363,113343,113345,113348,113407,113410,113413],{"className":113344},[398],[363,113346],{"className":113347,"style":110742},[402],[363,113349,113351],{"className":113350},[407,34714],[363,113352,113354,113399],{"className":113353},[633,634],[363,113355,113357,113396],{"className":113356},[638],[363,113358,113360,113384],{"className":113359,"style":110758},[642],[363,113361,113363,113366],{"className":113362,"style":12210},[6654],[363,113364],{"className":113365,"style":809},[650],[363,113367,113369,113372,113375,113378,113381],{"className":113368,"style":34734},[407],[363,113370,465],{"className":113371},[407],[363,113373],{"className":113374,"style":2934},[505],[363,113376,5160],{"className":113377},[2938],[363,113379],{"className":113380,"style":2934},[505],[363,113382,40584],{"className":113383,"style":1328},[407,408],[363,113385,113386,113389],{"style":110785},[363,113387],{"className":113388,"style":809},[650],[363,113390,113392],{"className":113391,"style":34791},[34790],[6670,113393,113394],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,113395],{"d":34798},[363,113397,666],{"className":113398},[665],[363,113400,113402],{"className":113401},[638],[363,113403,113405],{"className":113404,"style":110805},[642],[363,113406],{},[363,113408],{"className":113409,"style":506},[505],[363,113411,471],{"className":113412},[510],[363,113414],{"className":113415,"style":506},[505],[363,113417,113419,113422,113425,113428,113431],{"className":113418},[398],[363,113420],{"className":113421,"style":12925},[402],[363,113423,2810],{"className":113424},[407],[363,113426],{"className":113427,"style":2934},[505],[363,113429,5160],{"className":113430},[2938],[363,113432],{"className":113433,"style":2934},[505],[363,113435,113437,113440,113443],{"className":113436},[398],[363,113438],{"className":113439,"style":110742},[402],[363,113441,2810],{"className":113442},[407],[363,113444,113446],{"className":113445},[407,34714],[363,113447,113449,113494],{"className":113448},[633,634],[363,113450,113452,113491],{"className":113451},[638],[363,113453,113455,113479],{"className":113454,"style":110758},[642],[363,113456,113458,113461],{"className":113457,"style":12210},[6654],[363,113459],{"className":113460,"style":809},[650],[363,113462,113464,113467,113470,113473,113476],{"className":113463,"style":34734},[407],[363,113465,465],{"className":113466},[407],[363,113468],{"className":113469,"style":2934},[505],[363,113471,5160],{"className":113472},[2938],[363,113474],{"className":113475,"style":2934},[505],[363,113477,40584],{"className":113478,"style":1328},[407,408],[363,113480,113481,113484],{"style":110785},[363,113482],{"className":113483,"style":809},[650],[363,113485,113487],{"className":113486,"style":34791},[34790],[6670,113488,113489],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,113490],{"d":34798},[363,113492,666],{"className":113493},[665],[363,113495,113497],{"className":113496},[638],[363,113498,113500],{"className":113499,"style":110805},[642],[363,113501],{},"。α 一行取 ",[363,113504,113506,113545],{"className":113505,"translate":367},[366],[363,113507,113509],{"className":113508},[371],[373,113510,113511],{"xmlns":375},[377,113512,113513,113543],{},[380,113514,113515,113517,113519,113531,113533,113535,113537,113539,113541],{},[383,113516,45527],{},[458,113518,471],{},[586,113520,113521,113529],{},[380,113522,113523,113525,113527],{},[463,113524,465],{},[458,113526,2817],{},[383,113528,45101],{},[463,113530,2810],{},[458,113532,6256],{},[458,113534,461],{"stretchy":460},[463,113536,474],{},[458,113538,898],{"separator":394},[463,113540,465],{},[458,113542,468],{"stretchy":460},[387,113544,45556],{"encoding":389},[363,113546,113548,113566,113655],{"className":113547,"ariaHidden":394},[393],[363,113549,113551,113554,113557,113560,113563],{"className":113550},[398],[363,113552],{"className":113553,"style":2692},[402],[363,113555,45527],{"className":113556},[407,408],[363,113558],{"className":113559,"style":506},[505],[363,113561,471],{"className":113562},[510],[363,113564],{"className":113565,"style":506},[505],[363,113567,113569,113572,113646,113649,113652],{"className":113568},[398],[363,113570],{"className":113571,"style":2852},[402],[363,113573,113575,113578,113643],{"className":113574},[407],[363,113576],{"className":113577},[494,789],[363,113579,113581],{"className":113580},[586],[363,113582,113584,113635],{"className":113583},[633,634],[363,113585,113587,113632],{"className":113586},[638],[363,113588,113590,113604,113612],{"className":113589,"style":2871},[642],[363,113591,113592,113595],{"style":2874},[363,113593],{"className":113594,"style":809},[650],[363,113596,113598],{"className":113597},[655,656,657,658],[363,113599,113601],{"className":113600},[407,658],[363,113602,2810],{"className":113603},[407,658],[363,113605,113606,113609],{"style":821},[363,113607],{"className":113608,"style":809},[650],[363,113610],{"className":113611,"style":829},[828],[363,113613,113614,113617],{"style":2897},[363,113615],{"className":113616,"style":809},[650],[363,113618,113620],{"className":113619},[655,656,657,658],[363,113621,113623,113626,113629],{"className":113622},[407,658],[363,113624,465],{"className":113625},[407,658],[363,113627,2817],{"className":113628},[2938,658],[363,113630,45101],{"className":113631,"style":45131},[407,408,658],[363,113633,666],{"className":113634},[665],[363,113636,113638],{"className":113637},[638],[363,113639,113641],{"className":113640,"style":2919},[642],[363,113642],{},[363,113644],{"className":113645},[501,789],[363,113647],{"className":113648,"style":506},[505],[363,113650,6256],{"className":113651},[510],[363,113653],{"className":113654,"style":506},[505],[363,113656,113658,113661,113664,113667,113670,113673,113676],{"className":113657},[398],[363,113659],{"className":113660,"style":487},[402],[363,113662,461],{"className":113663},[494],[363,113665,474],{"className":113666},[407],[363,113668,898],{"className":113669},[920],[363,113671],{"className":113672,"style":754},[505],[363,113674,465],{"className":113675},[407],[363,113677,468],{"className":113678},[501],"，验证：",[363,113681,113683,113759],{"className":113682,"translate":367},[366],[363,113684,113686],{"className":113685},[371],[373,113687,113688],{"xmlns":375},[377,113689,113690,113756],{},[380,113691,113692,113700,113702,113704,113706,113708,113718,113720,113722,113724,113726,113754],{},[7900,113693,113694,113696,113698],{},[383,113695,385],{},[383,113697,45101],{},[458,113699,7920],{},[458,113701,461],{"stretchy":460},[383,113703,40584],{},[458,113705,468],{"stretchy":460},[458,113707,471],{},[543,113709,113710,113716],{},[380,113711,113712,113714],{},[383,113713,35779],{},[458,113715,4450],{},[383,113717,1116],{},[458,113719,3245],{"stretchy":460},[383,113721,1116],{},[383,113723,40584],{},[458,113725,5160],{},[586,113727,113728,113740],{},[380,113729,113730,113732,113734],{},[463,113731,465],{},[458,113733,5160],{},[7161,113735,113736,113738],{},[383,113737,1116],{},[383,113739,45527],{},[380,113741,113742,113744,113746,113748,113750,113752],{},[383,113743,45527],{},[458,113745,461],{"stretchy":460},[463,113747,465],{},[458,113749,5160],{},[383,113751,45527],{},[458,113753,468],{"stretchy":460},[458,113755,3255],{"stretchy":460},[387,113757,113758],{"encoding":389},"f_\\alpha^*(y)=\\sup_t\\{ty-\\frac{1-t^a}{a(1-a)}\\}",[363,113760,113762,113837,113901],{"className":113761,"ariaHidden":394},[393],[363,113763,113765,113768,113819,113822,113825,113828,113831,113834],{"className":113764},[398],[363,113766],{"className":113767,"style":487},[402],[363,113769,113771,113774],{"className":113770},[407],[363,113772,385],{"className":113773,"style":409},[407,408],[363,113775,113777],{"className":113776},[629],[363,113778,113780,113811],{"className":113779},[633,634],[363,113781,113783,113808],{"className":113782},[638],[363,113784,113786,113797],{"className":113785,"style":8846},[642],[363,113787,113788,113791],{"style":8598},[363,113789],{"className":113790,"style":651},[650],[363,113792,113794],{"className":113793},[655,656,657,658],[363,113795,45101],{"className":113796,"style":45131},[407,408,658],[363,113798,113799,113802],{"style":7212},[363,113800],{"className":113801,"style":651},[650],[363,113803,113805],{"className":113804},[655,656,657,658],[363,113806,7920],{"className":113807},[2938,658],[363,113809,666],{"className":113810},[665],[363,113812,113814],{"className":113813},[638],[363,113815,113817],{"className":113816,"style":8646},[642],[363,113818],{},[363,113820,461],{"className":113821},[494],[363,113823,40584],{"className":113824,"style":1328},[407,408],[363,113826,468],{"className":113827},[501],[363,113829],{"className":113830,"style":506},[505],[363,113832,471],{"className":113833},[510],[363,113835],{"className":113836,"style":506},[505],[363,113838,113840,113843,113883,113886,113889,113892,113895,113898],{"className":113839},[398],[363,113841],{"className":113842,"style":487},[402],[363,113844,113846,113849],{"className":113845},[1831],[363,113847,35779],{"className":113848},[1831],[363,113850,113852],{"className":113851},[629],[363,113853,113855,113875],{"className":113854},[633,634],[363,113856,113858,113872],{"className":113857},[638],[363,113859,113861],{"className":113860,"style":67358},[642],[363,113862,113863,113866],{"style":35925},[363,113864],{"className":113865,"style":651},[650],[363,113867,113869],{"className":113868},[655,656,657,658],[363,113870,1116],{"className":113871},[407,408,658],[363,113873,666],{"className":113874},[665],[363,113876,113878],{"className":113877},[638],[363,113879,113881],{"className":113880,"style":37367},[642],[363,113882],{},[363,113884,3245],{"className":113885},[494],[363,113887,1116],{"className":113888},[407,408],[363,113890,40584],{"className":113891,"style":1328},[407,408],[363,113893],{"className":113894,"style":2934},[505],[363,113896,5160],{"className":113897},[2938],[363,113899],{"className":113900,"style":2934},[505],[363,113902,113904,113908,114025],{"className":113903},[398],[363,113905],{"className":113906,"style":113907},[402],"height:1.431em;vertical-align:-0.52em;",[363,113909,113911,113914,114022],{"className":113910},[407],[363,113912],{"className":113913},[494,789],[363,113915,113917],{"className":113916},[586],[363,113918,113920,114014],{"className":113919},[633,634],[363,113921,113923,114011],{"className":113922},[638],[363,113924,113927,113956,113964],{"className":113925,"style":113926},[642],"height:0.911em;",[363,113928,113929,113932],{"style":2874},[363,113930],{"className":113931,"style":809},[650],[363,113933,113935],{"className":113934},[655,656,657,658],[363,113936,113938,113941,113944,113947,113950,113953],{"className":113937},[407,658],[363,113939,45527],{"className":113940},[407,408,658],[363,113942,461],{"className":113943},[494,658],[363,113945,465],{"className":113946},[407,658],[363,113948,5160],{"className":113949},[2938,658],[363,113951,45527],{"className":113952},[407,408,658],[363,113954,468],{"className":113955},[501,658],[363,113957,113958,113961],{"style":821},[363,113959],{"className":113960,"style":809},[650],[363,113962],{"className":113963,"style":829},[828],[363,113965,113966,113969],{"style":2897},[363,113967],{"className":113968,"style":809},[650],[363,113970,113972],{"className":113971},[655,656,657,658],[363,113973,113975,113978,113981],{"className":113974},[407,658],[363,113976,465],{"className":113977},[407,658],[363,113979,5160],{"className":113980},[2938,658],[363,113982,113984,113987],{"className":113983},[407,658],[363,113985,1116],{"className":113986},[407,408,658],[363,113988,113990],{"className":113989},[629],[363,113991,113993],{"className":113992},[633],[363,113994,113996],{"className":113995},[638],[363,113997,114000],{"className":113998,"style":113999},[642],"height:0.7385em;",[363,114001,114002,114005],{"style":38862},[363,114003],{"className":114004,"style":30553},[650],[363,114006,114008],{"className":114007},[655,30557,10021,658],[363,114009,45527],{"className":114010},[407,408,658],[363,114012,666],{"className":114013},[665],[363,114015,114017],{"className":114016},[638],[363,114018,114020],{"className":114019,"style":45949},[642],[363,114021],{},[363,114023],{"className":114024},[501,789],[363,114026,3255],{"className":114027},[501],[363,114029,114031,114073],{"className":114030,"translate":367},[366],[363,114032,114034],{"className":114033},[371],[373,114035,114036],{"xmlns":375},[377,114037,114038,114070],{},[380,114039,114040,114042,114044,114066,114068],{},[383,114041,40584],{},[458,114043,2817],{},[586,114045,114046,114058],{},[7161,114047,114048,114050],{},[383,114049,1116],{},[380,114051,114052,114054,114056],{},[383,114053,45527],{},[458,114055,5160],{},[463,114057,465],{},[380,114059,114060,114062,114064],{},[463,114061,465],{},[458,114063,5160],{},[383,114065,45527],{},[458,114067,471],{},[463,114069,474],{},[387,114071,114072],{"encoding":389},"y+\\frac{t^{a-1}}{1-a}=0",[363,114074,114076,114094,114220],{"className":114075,"ariaHidden":394},[393],[363,114077,114079,114082,114085,114088,114091],{"className":114078},[398],[363,114080],{"className":114081,"style":40668},[402],[363,114083,40584],{"className":114084,"style":1328},[407,408],[363,114086],{"className":114087,"style":2934},[505],[363,114089,2817],{"className":114090},[2938],[363,114092],{"className":114093,"style":2934},[505],[363,114095,114097,114101,114211,114214,114217],{"className":114096},[398],[363,114098],{"className":114099,"style":114100},[402],"height:1.4213em;vertical-align:-0.4033em;",[363,114102,114104,114107,114208],{"className":114103},[407],[363,114105],{"className":114106},[494,789],[363,114108,114110],{"className":114109},[586],[363,114111,114113,114200],{"className":114112},[633,634],[363,114114,114116,114197],{"className":114115},[638],[363,114117,114120,114140,114148],{"className":114118,"style":114119},[642],"height:1.0179em;",[363,114121,114122,114125],{"style":2874},[363,114123],{"className":114124,"style":809},[650],[363,114126,114128],{"className":114127},[655,656,657,658],[363,114129,114131,114134,114137],{"className":114130},[407,658],[363,114132,465],{"className":114133},[407,658],[363,114135,5160],{"className":114136},[2938,658],[363,114138,45527],{"className":114139},[407,408,658],[363,114141,114142,114145],{"style":821},[363,114143],{"className":114144,"style":809},[650],[363,114146],{"className":114147,"style":829},[828],[363,114149,114150,114153],{"style":2897},[363,114151],{"className":114152,"style":809},[650],[363,114154,114156],{"className":114155},[655,656,657,658],[363,114157,114159],{"className":114158},[407,658],[363,114160,114162,114165],{"className":114161},[407,658],[363,114163,1116],{"className":114164},[407,408,658],[363,114166,114168],{"className":114167},[629],[363,114169,114171],{"className":114170},[633],[363,114172,114174],{"className":114173},[638],[363,114175,114177],{"className":114176,"style":38859},[642],[363,114178,114179,114182],{"style":38862},[363,114180],{"className":114181,"style":30553},[650],[363,114183,114185],{"className":114184},[655,30557,10021,658],[363,114186,114188,114191,114194],{"className":114187},[407,658],[363,114189,45527],{"className":114190},[407,408,658],[363,114192,5160],{"className":114193},[2938,658],[363,114195,465],{"className":114196},[407,658],[363,114198,666],{"className":114199},[665],[363,114201,114203],{"className":114202},[638],[363,114204,114206],{"className":114205,"style":16776},[642],[363,114207],{},[363,114209],{"className":114210},[501,789],[363,114212],{"className":114213,"style":506},[505],[363,114215,471],{"className":114216},[510],[363,114218],{"className":114219,"style":506},[505],[363,114221,114223,114226],{"className":114222},[398],[363,114224],{"className":114225,"style":520},[402],[363,114227,474],{"className":114228},[407],[363,114230,114232,114288],{"className":114231,"translate":367},[366],[363,114233,114235],{"className":114234},[371],[373,114236,114237],{"xmlns":375},[377,114238,114239,114285],{},[380,114240,114241,114243,114245,114247,114249,114251,114253,114255,114257,114259,114261,114263,114265],{},[383,114242,1116],{},[458,114244,471],{},[458,114246,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,114248,461],{"stretchy":460},[463,114250,465],{},[458,114252,5160],{},[383,114254,45527],{},[458,114256,468],{"stretchy":460},[458,114258,461],{"stretchy":460},[458,114260,5160],{},[383,114262,40584],{},[458,114264,468],{"stretchy":460},[7161,114266,114267,114269],{},[458,114268,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[380,114270,114271,114273],{},[458,114272,5160],{},[586,114274,114275,114277],{},[463,114276,465],{},[380,114278,114279,114281,114283],{},[463,114280,465],{},[458,114282,5160],{},[383,114284,45527],{},[387,114286,114287],{"encoding":389},"t=\\big((1-a)(-y)\\big)^{-\\frac{1}{1-a}}",[363,114289,114291,114309,114336],{"className":114290,"ariaHidden":394},[393],[363,114292,114294,114297,114300,114303,114306],{"className":114293},[398],[363,114295],{"className":114296,"style":5690},[402],[363,114298,1116],{"className":114299},[407,408],[363,114301],{"className":114302,"style":506},[505],[363,114304,471],{"className":114305},[510],[363,114307],{"className":114308,"style":506},[505],[363,114310,114312,114315,114321,114324,114327,114330,114333],{"className":114311},[398],[363,114313],{"className":114314,"style":20910},[402],[363,114316,114318],{"className":114317},[407],[363,114319,461],{"className":114320},[767,10021],[363,114322,461],{"className":114323},[494],[363,114325,465],{"className":114326},[407],[363,114328],{"className":114329,"style":2934},[505],[363,114331,5160],{"className":114332},[2938],[363,114334],{"className":114335,"style":2934},[505],[363,114337,114339,114343,114346,114349,114352,114355,114358,114361],{"className":114338},[398],[363,114340],{"className":114341,"style":114342},[402],"height:1.5439em;vertical-align:-0.35em;",[363,114344,45527],{"className":114345},[407,408],[363,114347,468],{"className":114348},[501],[363,114350,461],{"className":114351},[494],[363,114353,5160],{"className":114354},[407],[363,114356,40584],{"className":114357,"style":1328},[407,408],[363,114359,468],{"className":114360},[501],[363,114362,114364,114370],{"className":114363},[407],[363,114365,114367],{"className":114366},[407],[363,114368,468],{"className":114369},[767,10021],[363,114371,114373],{"className":114372},[629],[363,114374,114376],{"className":114375},[633],[363,114377,114379],{"className":114378},[638],[363,114380,114383],{"className":114381,"style":114382},[642],"height:1.1939em;",[363,114384,114385,114388],{"style":111651},[363,114386],{"className":114387,"style":809},[650],[363,114389,114391],{"className":114390},[655,656,657,658],[363,114392,114394,114397],{"className":114393},[407,658],[363,114395,5160],{"className":114396},[407,658],[363,114398,114400,114403,114469],{"className":114399},[407,658],[363,114401],{"className":114402},[494,789,655,30557,111670],[363,114404,114406],{"className":114405},[586],[363,114407,114409,114461],{"className":114408},[633,634],[363,114410,114412,114458],{"className":114411},[638],[363,114413,114416,114436,114444],{"className":114414,"style":114415},[642],"height:0.8443em;",[363,114417,114418,114421],{"style":111686},[363,114419],{"className":114420,"style":809},[650],[363,114422,114424],{"className":114423},[655,30557,10021,658],[363,114425,114427,114430,114433],{"className":114426},[407,658],[363,114428,465],{"className":114429},[407,658],[363,114431,5160],{"className":114432},[2938,658],[363,114434,45527],{"className":114435},[407,408,658],[363,114437,114438,114441],{"style":111707},[363,114439],{"className":114440,"style":809},[650],[363,114442],{"className":114443,"style":111714},[828,658],[363,114445,114446,114449],{"style":111717},[363,114447],{"className":114448,"style":809},[650],[363,114450,114452],{"className":114451},[655,30557,10021,658],[363,114453,114455],{"className":114454},[407,658],[363,114456,465],{"className":114457},[407,658],[363,114459,666],{"className":114460},[665],[363,114462,114464],{"className":114463},[638],[363,114465,114467],{"className":114466,"style":111739},[642],[363,114468],{},[363,114470],{"className":114471},[501,789,655,30557,111670],[363,114473,114475,114492],{"className":114474,"translate":367},[366],[363,114476,114478],{"className":114477},[371],[373,114479,114480],{"xmlns":375},[377,114481,114482,114490],{},[380,114483,114484,114486,114488],{},[383,114485,40584],{},[458,114487,7598],{},[463,114489,474],{},[387,114491,65488],{"encoding":389},[363,114493,114495,114513],{"className":114494,"ariaHidden":394},[393],[363,114496,114498,114501,114504,114507,114510],{"className":114497},[398],[363,114499],{"className":114500,"style":32039},[402],[363,114502,40584],{"className":114503,"style":1328},[407,408],[363,114505],{"className":114506,"style":506},[505],[363,114508,7598],{"className":114509},[510],[363,114511],{"className":114512,"style":506},[505],[363,114514,114516,114519],{"className":114515},[398],[363,114517],{"className":114518,"style":520},[402],[363,114520,474],{"className":114521},[407],"），代回即得上式；",[363,114524,114526,114548],{"className":114525,"translate":367},[366],[363,114527,114529],{"className":114528},[371],[373,114530,114531],{"xmlns":375},[377,114532,114533,114545],{},[380,114534,114535,114537,114539],{},[383,114536,45527],{},[458,114538,471],{},[586,114540,114541,114543],{},[463,114542,465],{},[463,114544,2810],{},[387,114546,114547],{"encoding":389},"a=\\frac12",[363,114549,114551,114569],{"className":114550,"ariaHidden":394},[393],[363,114552,114554,114557,114560,114563,114566],{"className":114553},[398],[363,114555],{"className":114556,"style":2692},[402],[363,114558,45527],{"className":114559},[407,408],[363,114561],{"className":114562,"style":506},[505],[363,114564,471],{"className":114565},[510],[363,114567],{"className":114568,"style":506},[505],[363,114570,114572,114575],{"className":114571},[398],[363,114573],{"className":114574,"style":2852},[402],[363,114576,114578,114581,114640],{"className":114577},[407],[363,114579],{"className":114580},[494,789],[363,114582,114584],{"className":114583},[586],[363,114585,114587,114632],{"className":114586},[633,634],[363,114588,114590,114629],{"className":114589},[638],[363,114591,114593,114607,114615],{"className":114592,"style":2871},[642],[363,114594,114595,114598],{"style":2874},[363,114596],{"className":114597,"style":809},[650],[363,114599,114601],{"className":114600},[655,656,657,658],[363,114602,114604],{"className":114603},[407,658],[363,114605,2810],{"className":114606},[407,658],[363,114608,114609,114612],{"style":821},[363,114610],{"className":114611,"style":809},[650],[363,114613],{"className":114614,"style":829},[828],[363,114616,114617,114620],{"style":2897},[363,114618],{"className":114619,"style":809},[650],[363,114621,114623],{"className":114622},[655,656,657,658],[363,114624,114626],{"className":114625},[407,658],[363,114627,465],{"className":114628},[407,658],[363,114630,666],{"className":114631},[665],[363,114633,114635],{"className":114634},[638],[363,114636,114638],{"className":114637,"style":2919},[642],[363,114639],{},[363,114641],{"className":114642},[501,789],[363,114644,114646,114663],{"className":114645,"translate":367},[366],[363,114647,114649],{"className":114648},[371],[373,114650,114651],{"xmlns":375},[377,114652,114653,114661],{},[380,114654,114655,114657,114659],{},[383,114656,45101],{},[458,114658,471],{},[463,114660,474],{},[387,114662,46835],{"encoding":389},[363,114664,114666,114684],{"className":114665,"ariaHidden":394},[393],[363,114667,114669,114672,114675,114678,114681],{"className":114668},[398],[363,114670],{"className":114671,"style":2692},[402],[363,114673,45101],{"className":114674,"style":45131},[407,408],[363,114676],{"className":114677,"style":506},[505],[363,114679,471],{"className":114680},[510],[363,114682],{"className":114683,"style":506},[505],[363,114685,114687,114690],{"className":114686},[398],[363,114688],{"className":114689,"style":520},[402],[363,114691,474],{"className":114692},[407],[363,114694,114696,114726],{"className":114695,"translate":367},[366],[363,114697,114699],{"className":114698},[371],[373,114700,114701],{"xmlns":375},[377,114702,114703,114723],{},[380,114704,114705,114707,114709,114711,114713,114715,114717,114721],{},[383,114706,385],{},[458,114708,471],{},[463,114710,39336],{},[458,114712,461],{"stretchy":460},[463,114714,465],{},[458,114716,5160],{},[34686,114718,114719],{},[383,114720,1116],{},[458,114722,468],{"stretchy":460},[387,114724,114725],{"encoding":389},"f=4(1-\\sqrt t)",[363,114727,114729,114747,114771],{"className":114728,"ariaHidden":394},[393],[363,114730,114732,114735,114738,114741,114744],{"className":114731},[398],[363,114733],{"className":114734,"style":403},[402],[363,114736,385],{"className":114737,"style":409},[407,408],[363,114739],{"className":114740,"style":506},[505],[363,114742,471],{"className":114743},[510],[363,114745],{"className":114746,"style":506},[505],[363,114748,114750,114753,114756,114759,114762,114765,114768],{"className":114749},[398],[363,114751],{"className":114752,"style":487},[402],[363,114754,39336],{"className":114755},[407],[363,114757,461],{"className":114758},[494],[363,114760,465],{"className":114761},[407],[363,114763],{"className":114764,"style":2934},[505],[363,114766,5160],{"className":114767},[2938],[363,114769],{"className":114770,"style":2934},[505],[363,114772,114774,114777,114821],{"className":114773},[398],[363,114775],{"className":114776,"style":43014},[402],[363,114778,114780],{"className":114779},[407,34714],[363,114781,114783,114813],{"className":114782},[633,634],[363,114784,114786,114810],{"className":114785},[638],[363,114787,114789,114798],{"className":114788,"style":43030},[642],[363,114790,114792,114795],{"className":114791,"style":12210},[6654],[363,114793],{"className":114794,"style":809},[650],[363,114796,1116],{"className":114797,"style":34734},[407,408],[363,114799,114800,114803],{"style":43042},[363,114801],{"className":114802,"style":809},[650],[363,114804,114806],{"className":114805,"style":34791},[34790],[6670,114807,114808],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,114809],{"d":34798},[363,114811,666],{"className":114812},[665],[363,114814,114816],{"className":114815},[638],[363,114817,114819],{"className":114818,"style":43062},[642],[363,114820],{},[363,114822,468],{"className":114823},[501],"）时公式给出 ",[363,114826,114828,114854],{"className":114827,"translate":367},[366],[363,114829,114831],{"className":114830},[371],[373,114832,114833],{"xmlns":375},[377,114834,114835,114851],{},[380,114836,114837,114847,114849],{},[586,114838,114839,114841],{},[463,114840,39336],{},[380,114842,114843,114845],{},[458,114844,5160],{},[383,114846,40584],{},[458,114848,5160],{},[463,114850,39336],{},[387,114852,114853],{"encoding":389},"\\frac{4}{-y}-4",[363,114855,114857,114944],{"className":114856,"ariaHidden":394},[393],[363,114858,114860,114864,114935,114938,114941],{"className":114859},[398],[363,114861],{"className":114862,"style":114863},[402],"height:1.3262em;vertical-align:-0.4811em;",[363,114865,114867,114870,114932],{"className":114866},[407],[363,114868],{"className":114869},[494,789],[363,114871,114873],{"className":114872},[586],[363,114874,114876,114924],{"className":114875},[633,634],[363,114877,114879,114921],{"className":114878},[638],[363,114880,114882,114899,114907],{"className":114881,"style":2871},[642],[363,114883,114884,114887],{"style":2874},[363,114885],{"className":114886,"style":809},[650],[363,114888,114890],{"className":114889},[655,656,657,658],[363,114891,114893,114896],{"className":114892},[407,658],[363,114894,5160],{"className":114895},[407,658],[363,114897,40584],{"className":114898,"style":1328},[407,408,658],[363,114900,114901,114904],{"style":821},[363,114902],{"className":114903,"style":809},[650],[363,114905],{"className":114906,"style":829},[828],[363,114908,114909,114912],{"style":2897},[363,114910],{"className":114911,"style":809},[650],[363,114913,114915],{"className":114914},[655,656,657,658],[363,114916,114918],{"className":114917},[407,658],[363,114919,39336],{"className":114920},[407,658],[363,114922,666],{"className":114923},[665],[363,114925,114927],{"className":114926},[638],[363,114928,114930],{"className":114929,"style":3086},[642],[363,114931],{},[363,114933],{"className":114934},[501,789],[363,114936],{"className":114937,"style":2934},[505],[363,114939,5160],{"className":114940},[2938],[363,114942],{"className":114943,"style":2934},[505],[363,114945,114947,114950],{"className":114946},[398],[363,114948],{"className":114949,"style":520},[402],[363,114951,39336],{"className":114952},[407],"，可与直接展开互相验证。）",[11,114955,114956],{},"可见，f-散度族统一了「不对称\u002F对称」「有界\u002F无界」的多种散度。",[2658,114958,114960],{"id":114959},"_62-积分概率度量ipm","6.2 积分概率度量（IPM）",[11,114962,114963,114964,115013],{},"f-散度只依赖似然比 ",[363,114965,114967,114989],{"className":114966,"translate":367},[366],[363,114968,114970],{"className":114969},[371],[373,114971,114972],{"xmlns":375},[377,114973,114974,114986],{},[380,114975,114976,114978,114980,114982,114984],{},[383,114977,592],{},[383,114979,554],{},[383,114981,1288],{"mathvariant":557},[383,114983,592],{},[383,114985,561],{},[387,114987,114988],{"encoding":389},"dP\u002FdQ",[363,114990,114992],{"className":114991,"ariaHidden":394},[393],[363,114993,114995,114998,115001,115004,115007,115010],{"className":114994},[398],[363,114996],{"className":114997,"style":487},[402],[363,114999,592],{"className":115000},[407,408],[363,115002,554],{"className":115003,"style":682},[407,408],[363,115005,1288],{"className":115006},[407],[363,115008,592],{"className":115009},[407,408],[363,115011,561],{"className":115012},[407,408],"，因此把两个分布同时「搬到别处」值不变。这带来一个根本局限：",[363,115015,115017],{"className":115016,"translate":367},[528],[363,115018,115020,115075],{"className":115019,"translate":367},[366],[363,115021,115023],{"className":115022},[371],[373,115024,115025],{"xmlns":375,"display":537},[377,115026,115027,115072],{},[380,115028,115029,115031,115033,115035,115037,115039,115041,115044,115046,115048,115054,115056,115058,115060,115062,115068,115070],{},[1644,115030,4685],{},[383,115032,554],{},[458,115034,33894],{},[383,115036,561],{},[1644,115038,4630],{},[458,115040,461],{"stretchy":460},[1644,115042,115043],{},"支撑集不重叠，如 ",[383,115045,554],{},[458,115047,471],{},[543,115049,115050,115052],{},[383,115051,16059],{},[463,115053,474],{},[458,115055,898],{"separator":394},[1644,115057,4630],{},[383,115059,561],{},[458,115061,471],{},[543,115063,115064,115066],{},[383,115065,16059],{},[463,115067,465],{},[458,115069,468],{"stretchy":460},[458,115071,898],{"separator":394},[387,115073,115074],{"encoding":389},"\\text{若 } P\\perp Q\\\n(\\text{支撑集不重叠，如 } P=\\delta_0,\\ Q=\\delta_1),",[363,115076,115078,115105,115142,115209],{"className":115077,"ariaHidden":394},[393],[363,115079,115081,115084,115093,115096,115099,115102],{"className":115080},[398],[363,115082],{"className":115083,"style":12944},[402],[363,115085,115087,115090],{"className":115086},[407,4945],[363,115088,4996],{"className":115089},[407,4949],[363,115091,4630],{"className":115092},[407],[363,115094,554],{"className":115095,"style":682},[407,408],[363,115097],{"className":115098,"style":506},[505],[363,115100,33894],{"className":115101},[510],[363,115103],{"className":115104,"style":506},[505],[363,115106,115108,115111,115114,115117,115120,115130,115133,115136,115139],{"className":115107},[398],[363,115109],{"className":115110,"style":487},[402],[363,115112,561],{"className":115113},[407,408],[363,115115,4630],{"className":115116},[505],[363,115118,461],{"className":115119},[494],[363,115121,115123,115127],{"className":115122},[407,4945],[363,115124,115126],{"className":115125},[407,4949],"支撑集不重叠，如",[363,115128,4630],{"className":115129},[407],[363,115131,554],{"className":115132,"style":682},[407,408],[363,115134],{"className":115135,"style":506},[505],[363,115137,471],{"className":115138},[510],[363,115140],{"className":115141,"style":506},[505],[363,115143,115145,115148,115188,115191,115194,115197,115200,115203,115206],{"className":115144},[398],[363,115146],{"className":115147,"style":403},[402],[363,115149,115151,115154],{"className":115150},[407],[363,115152,16059],{"className":115153,"style":16108},[407,408],[363,115155,115157],{"className":115156},[629],[363,115158,115160,115180],{"className":115159},[633,634],[363,115161,115163,115177],{"className":115162},[638],[363,115164,115166],{"className":115165,"style":11480},[642],[363,115167,115168,115171],{"style":95090},[363,115169],{"className":115170,"style":651},[650],[363,115172,115174],{"className":115173},[655,656,657,658],[363,115175,474],{"className":115176},[407,658],[363,115178,666],{"className":115179},[665],[363,115181,115183],{"className":115182},[638],[363,115184,115186],{"className":115185,"style":8315},[642],[363,115187],{},[363,115189,898],{"className":115190},[920],[363,115192,4630],{"className":115193},[505],[363,115195],{"className":115196,"style":754},[505],[363,115198,561],{"className":115199},[407,408],[363,115201],{"className":115202,"style":506},[505],[363,115204,471],{"className":115205},[510],[363,115207],{"className":115208,"style":506},[505],[363,115210,115212,115215,115255,115258],{"className":115211},[398],[363,115213],{"className":115214,"style":487},[402],[363,115216,115218,115221],{"className":115217},[407],[363,115219,16059],{"className":115220,"style":16108},[407,408],[363,115222,115224],{"className":115223},[629],[363,115225,115227,115247],{"className":115226},[633,634],[363,115228,115230,115244],{"className":115229},[638],[363,115231,115233],{"className":115232,"style":11480},[642],[363,115234,115235,115238],{"style":95090},[363,115236],{"className":115237,"style":651},[650],[363,115239,115241],{"className":115240},[655,656,657,658],[363,115242,465],{"className":115243},[407,658],[363,115245,666],{"className":115246},[665],[363,115248,115250],{"className":115249},[638],[363,115251,115253],{"className":115252,"style":8315},[642],[363,115254],{},[363,115256,468],{"className":115257},[501],[363,115259,898],{"className":115260},[920],[363,115262,115264],{"className":115263,"translate":367},[528],[363,115265,115267,115317],{"className":115266,"translate":367},[366],[363,115268,115270],{"className":115269},[371],[373,115271,115272],{"xmlns":375,"display":537},[377,115273,115274,115314],{},[380,115275,115276,115286,115288,115290,115292,115294,115296,115298,115308,115310,115312],{},[543,115277,115278,115280],{},[383,115279,547],{},[380,115281,115282,115284],{},[383,115283,24090],{},[383,115285,26084],{},[458,115287,471],{},[383,115289,4447],{},[458,115291,4450],{},[463,115293,2810],{},[458,115295,898],{"separator":394},[505,115297],{"width":4662},[543,115299,115300,115302],{},[383,115301,547],{},[380,115303,115304,115306],{},[383,115305,5739],{},[383,115307,35197],{},[458,115309,471],{},[463,115311,465],{},[458,115313,898],{"separator":394},[387,115315,115316],{"encoding":389},"D_{JS}=\\log2,\\quad D_{TV}=1,",[363,115318,115320,115381,115462],{"className":115319,"ariaHidden":394},[393],[363,115321,115323,115326,115372,115375,115378],{"className":115322},[398],[363,115324],{"className":115325,"style":16308},[402],[363,115327,115329,115332],{"className":115328},[407],[363,115330,547],{"className":115331,"style":625},[407,408],[363,115333,115335],{"className":115334},[629],[363,115336,115338,115364],{"className":115337},[633,634],[363,115339,115341,115361],{"className":115340},[638],[363,115342,115344],{"className":115343,"style":727},[642],[363,115345,115346,115349],{"style":646},[363,115347],{"className":115348,"style":651},[650],[363,115350,115352],{"className":115351},[655,656,657,658],[363,115353,115355,115358],{"className":115354},[407,658],[363,115356,24090],{"className":115357,"style":24500},[407,408,658],[363,115359,26084],{"className":115360,"style":26208},[407,408,658],[363,115362,666],{"className":115363},[665],[363,115365,115367],{"className":115366},[638],[363,115368,115370],{"className":115369,"style":8315},[642],[363,115371],{},[363,115373],{"className":115374,"style":506},[505],[363,115376,471],{"className":115377},[510],[363,115379],{"className":115380,"style":506},[505],[363,115382,115384,115387,115392,115395,115398,115401,115404,115407,115453,115456,115459],{"className":115383},[398],[363,115385],{"className":115386,"style":403},[402],[363,115388,4501,115390],{"className":115389},[1831],[363,115391,4505],{"style":4504},[363,115393],{"className":115394,"style":754},[505],[363,115396,2810],{"className":115397},[407],[363,115399,898],{"className":115400},[920],[363,115402],{"className":115403,"style":88315},[505],[363,115405],{"className":115406,"style":754},[505],[363,115408,115410,115413],{"className":115409},[407],[363,115411,547],{"className":115412,"style":625},[407,408],[363,115414,115416],{"className":115415},[629],[363,115417,115419,115445],{"className":115418},[633,634],[363,115420,115422,115442],{"className":115421},[638],[363,115423,115425],{"className":115424,"style":727},[642],[363,115426,115427,115430],{"style":646},[363,115428],{"className":115429,"style":651},[650],[363,115431,115433],{"className":115432},[655,656,657,658],[363,115434,115436,115439],{"className":115435},[407,658],[363,115437,5739],{"className":115438,"style":682},[407,408,658],[363,115440,35197],{"className":115441,"style":2934},[407,408,658],[363,115443,666],{"className":115444},[665],[363,115446,115448],{"className":115447},[638],[363,115449,115451],{"className":115450,"style":8315},[642],[363,115452],{},[363,115454],{"className":115455,"style":506},[505],[363,115457,471],{"className":115458},[510],[363,115460],{"className":115461,"style":506},[505],[363,115463,115465,115468,115471],{"className":115464},[398],[363,115466],{"className":115467,"style":9705},[402],[363,115469,465],{"className":115470},[407],[363,115472,898],{"className":115473},[920],[11,115475,115476,115477,115480,115481,115545,115546,115596,115597,9747],{},"也就是说，f-散度在支撑分离时",[1572,115478,115479],{},"饱和到常数上界，对生成器参数的微小改动失去梯度","：因为被积分的量 ",[363,115482,115484,115512],{"className":115483,"translate":367},[366],[363,115485,115487],{"className":115486},[371],[373,115488,115489],{"xmlns":375},[377,115490,115491,115509],{},[380,115492,115493,115495,115497,115499,115501,115503,115505,115507],{},[383,115494,1291],{},[1644,115496,1646],{},[383,115498,385],{},[458,115500,461],{"stretchy":460},[383,115502,11],{},[383,115504,1288],{"mathvariant":557},[383,115506,1291],{},[458,115508,468],{"stretchy":460},[387,115510,115511],{"encoding":389},"q\\,f(p\u002Fq)",[363,115513,115515],{"className":115514,"ariaHidden":394},[393],[363,115516,115518,115521,115524,115527,115530,115533,115536,115539,115542],{"className":115517},[398],[363,115519],{"className":115520,"style":487},[402],[363,115522,1291],{"className":115523,"style":1328},[407,408],[363,115525],{"className":115526,"style":754},[505],[363,115528,385],{"className":115529,"style":409},[407,408],[363,115531,461],{"className":115532},[494],[363,115534,11],{"className":115535},[407,408],[363,115537,1288],{"className":115538},[407],[363,115540,1291],{"className":115541,"style":1328},[407,408],[363,115543,468],{"className":115544},[501]," 只在 ",[363,115547,115549,115566],{"className":115548,"translate":367},[366],[363,115550,115552],{"className":115551},[371],[373,115553,115554],{"xmlns":375},[377,115555,115556,115564],{},[380,115557,115558,115560,115562],{},[383,115559,1291],{},[458,115561,3250],{},[463,115563,474],{},[387,115565,32029],{"encoding":389},[363,115567,115569,115587],{"className":115568,"ariaHidden":394},[393],[363,115570,115572,115575,115578,115581,115584],{"className":115571},[398],[363,115573],{"className":115574,"style":32039},[402],[363,115576,1291],{"className":115577,"style":1328},[407,408],[363,115579],{"className":115580,"style":506},[505],[363,115582,3250],{"className":115583},[510],[363,115585],{"className":115586,"style":506},[505],[363,115588,115590,115593],{"className":115589},[398],[363,115591],{"className":115592,"style":520},[402],[363,115594,474],{"className":115595},[407]," 处有定义，当两个支撑几乎不重叠时，极小化散度的博弈只剩\"常数项 − 常数项\"，梯度信息全部丢失（这正是原 GAN 训练崩溃的理论根源）。Wasserstein 距离与 MMD 属于另一族——",[1572,115598,115599],{},"积分概率度量",[363,115601,115603],{"className":115602,"translate":367},[528],[363,115604,115606,115681],{"className":115605,"translate":367},[366],[363,115607,115609],{"className":115608},[371],[373,115610,115611],{"xmlns":375,"display":537},[377,115612,115613,115678],{},[380,115614,115615,115622,115624,115626,115628,115630,115632,115634,115650,115652,115654,115656,115658,115660,115662,115664,115666,115668,115670,115672,115674,115676],{},[543,115616,115617,115620],{},[1644,115618,115619],{},"IPM",[383,115621,37230],{"mathvariant":944},[458,115623,461],{"stretchy":460},[383,115625,554],{},[458,115627,898],{"separator":394},[383,115629,561],{},[458,115631,468],{"stretchy":460},[458,115633,471],{},[6363,115635,115636,115642],{},[380,115637,115638,115640],{},[383,115639,35779],{},[458,115641,4450],{},[380,115643,115644,115646,115648],{},[383,115645,39012],{},[458,115647,6256],{},[383,115649,37230],{"mathvariant":944},[458,115651,5155],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[458,115653,1634],{},[383,115655,39012],{},[1644,115657,1646],{},[383,115659,592],{},[383,115661,554],{},[458,115663,5160],{},[458,115665,1634],{},[383,115667,39012],{},[1644,115669,1646],{},[383,115671,592],{},[383,115673,561],{},[458,115675,5155],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[383,115677,4722],{"mathvariant":557},[387,115679,115680],{"encoding":389},"\\text{IPM}_{\\mathcal F}(P,Q)\n=\\sup_{h\\in\\mathcal F}\\Big|\\int h\\,dP\n-\\int h\\,dQ\\Big| .",[363,115682,115684,115764,115897],{"className":115683,"ariaHidden":394},[393],[363,115685,115687,115690,115737,115740,115743,115746,115749,115752,115755,115758,115761],{"className":115686},[398],[363,115688],{"className":115689,"style":487},[402],[363,115691,115693,115699],{"className":115692},[407],[363,115694,115696],{"className":115695},[407,4945],[363,115697,115619],{"className":115698},[407],[363,115700,115702],{"className":115701},[629],[363,115703,115705,115729],{"className":115704},[633,634],[363,115706,115708,115726],{"className":115707},[638],[363,115709,115711],{"className":115710,"style":727},[642],[363,115712,115713,115716],{"style":52793},[363,115714],{"className":115715,"style":651},[650],[363,115717,115719],{"className":115718},[655,656,657,658],[363,115720,115722],{"className":115721},[407,658],[363,115723,37230],{"className":115724,"style":115725},[407,971,658],"margin-right:0.0993em;",[363,115727,666],{"className":115728},[665],[363,115730,115732],{"className":115731},[638],[363,115733,115735],{"className":115734,"style":8315},[642],[363,115736],{},[363,115738,461],{"className":115739},[494],[363,115741,554],{"className":115742,"style":682},[407,408],[363,115744,898],{"className":115745},[920],[363,115747],{"className":115748,"style":754},[505],[363,115750,561],{"className":115751},[407,408],[363,115753,468],{"className":115754},[501],[363,115756],{"className":115757,"style":506},[505],[363,115759,471],{"className":115760},[510],[363,115762],{"className":115763,"style":506},[505],[363,115765,115767,115771,115824,115827,115867,115870,115873,115876,115879,115882,115885,115888,115891,115894],{"className":115766},[398],[363,115768],{"className":115769,"style":115770},[402],"height:2.3339em;vertical-align:-0.9739em;",[363,115772,115774],{"className":115773},[1831,14063],[363,115775,115777,115816],{"className":115776},[633,634],[363,115778,115780,115813],{"className":115779},[638],[363,115781,115783,115803],{"className":115782,"style":2692},[642],[363,115784,115785,115788],{"style":52053},[363,115786],{"className":115787,"style":809},[650],[363,115789,115791],{"className":115790},[655,656,657,658],[363,115792,115794,115797,115800],{"className":115793},[407,658],[363,115795,39012],{"className":115796},[407,408,658],[363,115798,6256],{"className":115799},[510,658],[363,115801,37230],{"className":115802,"style":115725},[407,971,658],[363,115804,115805,115808],{"style":12210},[363,115806],{"className":115807,"style":809},[650],[363,115809,115810],{},[363,115811,35779],{"className":115812},[1831],[363,115814,666],{"className":115815},[665],[363,115817,115819],{"className":115818},[638],[363,115820,115822],{"className":115821,"style":52097},[642],[363,115823],{},[363,115825],{"className":115826,"style":754},[505],[363,115828,115830],{"className":115829},[407],[363,115831,115833],{"className":115832},[767,15176],[363,115834,115836,115859],{"className":115835},[633,634],[363,115837,115839,115856],{"className":115838},[638],[363,115840,115842],{"className":115841,"style":85862},[642],[363,115843,115844,115847],{"style":73871},[363,115845],{"className":115846,"style":82934},[650],[363,115848,115850],{"style":115849},"width:0.333em;height:1.8em;",[6670,115851,115853],{"xmlns":6672,"width":35398,"height":17786,"viewBox":115852},"0 0 333 1800",[6678,115854],{"d":115855},"M145 15 v585 v600 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v-600 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v600 v585 h43z",[363,115857,666],{"className":115858},[665],[363,115860,115862],{"className":115861},[638],[363,115863,115865],{"className":115864,"style":85886},[642],[363,115866],{},[363,115868],{"className":115869,"style":754},[505],[363,115871,1634],{"className":115872,"style":1834},[1831,1832,1833],[363,115874],{"className":115875,"style":754},[505],[363,115877,39012],{"className":115878},[407,408],[363,115880],{"className":115881,"style":754},[505],[363,115883,592],{"className":115884},[407,408],[363,115886,554],{"className":115887,"style":682},[407,408],[363,115889],{"className":115890,"style":2934},[505],[363,115892,5160],{"className":115893},[2938],[363,115895],{"className":115896,"style":2934},[505],[363,115898,115900,115903,115906,115909,115912,115915,115918,115921,115958],{"className":115899},[398],[363,115901],{"className":115902,"style":6124},[402],[363,115904,1634],{"className":115905,"style":1834},[1831,1832,1833],[363,115907],{"className":115908,"style":754},[505],[363,115910,39012],{"className":115911},[407,408],[363,115913],{"className":115914,"style":754},[505],[363,115916,592],{"className":115917},[407,408],[363,115919,561],{"className":115920},[407,408],[363,115922,115924],{"className":115923},[407],[363,115925,115927],{"className":115926},[767,15176],[363,115928,115930,115950],{"className":115929},[633,634],[363,115931,115933,115947],{"className":115932},[638],[363,115934,115936],{"className":115935,"style":85862},[642],[363,115937,115938,115941],{"style":73871},[363,115939],{"className":115940,"style":82934},[650],[363,115942,115943],{"style":115849},[6670,115944,115945],{"xmlns":6672,"width":35398,"height":17786,"viewBox":115852},[6678,115946],{"d":115855},[363,115948,666],{"className":115949},[665],[363,115951,115953],{"className":115952},[638],[363,115954,115956],{"className":115955,"style":85886},[642],[363,115957],{},[363,115959,4722],{"className":115960},[407],[11,115962,115963,115964,115993,115994,116045,116046,116075,116076,116126,116127,116155,116156,116206,116207,116235],{},"它们比较的是「在函数类 ",[363,115965,115967,115981],{"className":115966,"translate":367},[366],[363,115968,115970],{"className":115969},[371],[373,115971,115972],{"xmlns":375},[377,115973,115974,115978],{},[380,115975,115976],{},[383,115977,37230],{"mathvariant":944},[387,115979,115980],{"encoding":389},"\\mathcal F",[363,115982,115984],{"className":115983,"ariaHidden":394},[393],[363,115985,115987,115990],{"className":115986},[398],[363,115988],{"className":115989,"style":1011},[402],[363,115991,37230],{"className":115992,"style":115725},[407,971]," 上积分的差」，而不是似然比，因此利用了样本空间的度量\u002F几何结构。KS 距离（",[363,115995,115997,116015],{"className":115996,"translate":367},[366],[363,115998,116000],{"className":115999},[371],[373,116001,116002],{"xmlns":375},[377,116003,116004,116012],{},[380,116005,116006,116008,116010],{},[383,116007,37230],{"mathvariant":944},[458,116009,471],{},[458,116011,3245],{"stretchy":460},[387,116013,116014],{"encoding":389},"\\mathcal F=\\{",[363,116016,116018,116036],{"className":116017,"ariaHidden":394},[393],[363,116019,116021,116024,116027,116030,116033],{"className":116020},[398],[363,116022],{"className":116023,"style":1011},[402],[363,116025,37230],{"className":116026,"style":115725},[407,971],[363,116028],{"className":116029,"style":506},[505],[363,116031,471],{"className":116032},[510],[363,116034],{"className":116035,"style":506},[505],[363,116037,116039,116042],{"className":116038},[398],[363,116040],{"className":116041,"style":487},[402],[363,116043,3245],{"className":116044},[494],"一维区间指示函数",[363,116047,116049,116063],{"className":116048,"translate":367},[366],[363,116050,116052],{"className":116051},[371],[373,116053,116054],{"xmlns":375},[377,116055,116056,116060],{},[380,116057,116058],{},[458,116059,3255],{"stretchy":460},[387,116061,116062],{"encoding":389},"\\}",[363,116064,116066],{"className":116065,"ariaHidden":394},[393],[363,116067,116069,116072],{"className":116068},[398],[363,116070],{"className":116071,"style":487},[402],[363,116073,3255],{"className":116074},[501],"）、Wasserstein（",[363,116077,116079,116096],{"className":116078,"translate":367},[366],[363,116080,116082],{"className":116081},[371],[373,116083,116084],{"xmlns":375},[377,116085,116086,116094],{},[380,116087,116088,116090,116092],{},[383,116089,37230],{"mathvariant":944},[458,116091,471],{},[458,116093,3245],{"stretchy":460},[387,116095,116014],{"encoding":389},[363,116097,116099,116117],{"className":116098,"ariaHidden":394},[393],[363,116100,116102,116105,116108,116111,116114],{"className":116101},[398],[363,116103],{"className":116104,"style":1011},[402],[363,116106,37230],{"className":116107,"style":115725},[407,971],[363,116109],{"className":116110,"style":506},[505],[363,116112,471],{"className":116113},[510],[363,116115],{"className":116116,"style":506},[505],[363,116118,116120,116123],{"className":116119},[398],[363,116121],{"className":116122,"style":487},[402],[363,116124,3245],{"className":116125},[494],"1-Lipschitz 函数",[363,116128,116130,116143],{"className":116129,"translate":367},[366],[363,116131,116133],{"className":116132},[371],[373,116134,116135],{"xmlns":375},[377,116136,116137,116141],{},[380,116138,116139],{},[458,116140,3255],{"stretchy":460},[387,116142,116062],{"encoding":389},[363,116144,116146],{"className":116145,"ariaHidden":394},[393],[363,116147,116149,116152],{"className":116148},[398],[363,116150],{"className":116151,"style":487},[402],[363,116153,3255],{"className":116154},[501],"）、MMD（",[363,116157,116159,116176],{"className":116158,"translate":367},[366],[363,116160,116162],{"className":116161},[371],[373,116163,116164],{"xmlns":375},[377,116165,116166,116174],{},[380,116167,116168,116170,116172],{},[383,116169,37230],{"mathvariant":944},[458,116171,471],{},[458,116173,3245],{"stretchy":460},[387,116175,116014],{"encoding":389},[363,116177,116179,116197],{"className":116178,"ariaHidden":394},[393],[363,116180,116182,116185,116188,116191,116194],{"className":116181},[398],[363,116183],{"className":116184,"style":1011},[402],[363,116186,37230],{"className":116187,"style":115725},[407,971],[363,116189],{"className":116190,"style":506},[505],[363,116192,471],{"className":116193},[510],[363,116195],{"className":116196,"style":506},[505],[363,116198,116200,116203],{"className":116199},[398],[363,116201],{"className":116202,"style":487},[402],[363,116204,3245],{"className":116205},[494],"RKHS 单位球",[363,116208,116210,116223],{"className":116209,"translate":367},[366],[363,116211,116213],{"className":116212},[371],[373,116214,116215],{"xmlns":375},[377,116216,116217,116221],{},[380,116218,116219],{},[458,116220,3255],{"stretchy":460},[387,116222,116062],{"encoding":389},[363,116224,116226],{"className":116225,"ariaHidden":394},[393],[363,116227,116229,116232],{"className":116228},[398],[363,116230],{"className":116231,"style":487},[402],[363,116233,3255],{"className":116234},[501],"）都是 IPM。上面对 f-散度的变分表示其实是「带惩罚的 IPM」：",[363,116237,116239],{"className":116238,"translate":367},[528],[363,116240,116242,116324],{"className":116241,"translate":367},[366],[363,116243,116245],{"className":116244},[371],[373,116246,116247],{"xmlns":375,"display":537},[377,116248,116249,116321],{},[380,116250,116251,116257,116259,116261,116263,116265,116267,116269,116279,116281,116287,116289,116291,116293,116295,116301,116303,116309,116311,116313,116315,116317,116319],{},[543,116252,116253,116255],{},[383,116254,547],{},[383,116256,385],{},[458,116258,461],{"stretchy":460},[383,116260,554],{},[383,116262,558],{"mathvariant":557},[383,116264,561],{},[458,116266,468],{"stretchy":460},[458,116268,471],{},[6363,116270,116271,116277],{},[380,116272,116273,116275],{},[383,116274,35779],{},[458,116276,4450],{},[383,116278,4505],{},[458,116280,3245],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[543,116282,116283,116285],{},[383,116284,571],{"mathvariant":570},[383,116286,554],{},[458,116288,578],{"stretchy":460},[383,116290,4505],{},[458,116292,605],{"stretchy":460},[458,116294,5160],{},[543,116296,116297,116299],{},[383,116298,571],{"mathvariant":570},[383,116300,561],{},[458,116302,578],{"stretchy":460},[7161,116304,116305,116307],{},[383,116306,385],{},[458,116308,7920],{},[458,116310,461],{"stretchy":460},[383,116312,4505],{},[458,116314,468],{"stretchy":460},[458,116316,605],{"stretchy":460},[458,116318,3255],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[458,116320,898],{"separator":394},[387,116322,116323],{"encoding":389},"D_f(P\\|Q)\n=\\sup_{g}\\Big\\{\\mathbb E_P[g]\n-\\mathbb E_Q[f^*(g)]\\Big\\},",[363,116325,116327,116397,116517],{"className":116326,"ariaHidden":394},[393],[363,116328,116330,116333,116373,116376,116379,116382,116385,116388,116391,116394],{"className":116329},[398],[363,116331],{"className":116332,"style":618},[402],[363,116334,116336,116339],{"className":116335},[407],[363,116337,547],{"className":116338,"style":625},[407,408],[363,116340,116342],{"className":116341},[629],[363,116343,116345,116365],{"className":116344},[633,634],[363,116346,116348,116362],{"className":116347},[638],[363,116349,116351],{"className":116350,"style":643},[642],[363,116352,116353,116356],{"style":646},[363,116354],{"className":116355,"style":651},[650],[363,116357,116359],{"className":116358},[655,656,657,658],[363,116360,385],{"className":116361,"style":409},[407,408,658],[363,116363,666],{"className":116364},[665],[363,116366,116368],{"className":116367},[638],[363,116369,116371],{"className":116370,"style":673},[642],[363,116372],{},[363,116374,461],{"className":116375},[494],[363,116377,554],{"className":116378,"style":682},[407,408],[363,116380,558],{"className":116381},[407],[363,116383,561],{"className":116384},[407,408],[363,116386,468],{"className":116387},[501],[363,116389],{"className":116390,"style":506},[505],[363,116392,471],{"className":116393},[510],[363,116395],{"className":116396,"style":506},[505],[363,116398,116400,116403,116450,116453,116459,116499,116502,116505,116508,116511,116514],{"className":116399},[398],[363,116401],{"className":116402,"style":99832},[402],[363,116404,116406],{"className":116405},[1831,14063],[363,116407,116409,116442],{"className":116408},[633,634],[363,116410,116412,116439],{"className":116411},[638],[363,116413,116415,116429],{"className":116414,"style":2692},[642],[363,116416,116417,116420],{"style":61537},[363,116418],{"className":116419,"style":809},[650],[363,116421,116423],{"className":116422},[655,656,657,658],[363,116424,116426],{"className":116425},[407,658],[363,116427,4505],{"className":116428,"style":1328},[407,408,658],[363,116430,116431,116434],{"style":12210},[363,116432],{"className":116433,"style":809},[650],[363,116435,116436],{},[363,116437,35779],{"className":116438},[1831],[363,116440,666],{"className":116441},[665],[363,116443,116445],{"className":116444},[638],[363,116446,116448],{"className":116447,"style":61569},[642],[363,116449],{},[363,116451],{"className":116452,"style":754},[505],[363,116454,116456],{"className":116455},[407],[363,116457,3245],{"className":116458},[767,4067],[363,116460,116462,116465],{"className":116461},[407],[363,116463,571],{"className":116464},[407,714],[363,116466,116468],{"className":116467},[629],[363,116469,116471,116491],{"className":116470},[633,634],[363,116472,116474,116488],{"className":116473},[638],[363,116475,116477],{"className":116476,"style":727},[642],[363,116478,116479,116482],{"style":730},[363,116480],{"className":116481,"style":651},[650],[363,116483,116485],{"className":116484},[655,656,657,658],[363,116486,554],{"className":116487,"style":682},[407,408,658],[363,116489,666],{"className":116490},[665],[363,116492,116494],{"className":116493},[638],[363,116495,116497],{"className":116496,"style":8315},[642],[363,116498],{},[363,116500,578],{"className":116501},[494],[363,116503,4505],{"className":116504,"style":1328},[407,408],[363,116506,605],{"className":116507},[501],[363,116509],{"className":116510,"style":2934},[505],[363,116512,5160],{"className":116513},[2938],[363,116515],{"className":116516,"style":2934},[505],[363,116518,116520,116523,116563,116566,116595,116598,116601,116604,116610],{"className":116519},[398],[363,116521],{"className":116522,"style":68464},[402],[363,116524,116526,116529],{"className":116525},[407],[363,116527,571],{"className":116528},[407,714],[363,116530,116532],{"className":116531},[629],[363,116533,116535,116555],{"className":116534},[633,634],[363,116536,116538,116552],{"className":116537},[638],[363,116539,116541],{"className":116540,"style":727},[642],[363,116542,116543,116546],{"style":730},[363,116544],{"className":116545,"style":651},[650],[363,116547,116549],{"className":116548},[655,656,657,658],[363,116550,561],{"className":116551},[407,408,658],[363,116553,666],{"className":116554},[665],[363,116556,116558],{"className":116557},[638],[363,116559,116561],{"className":116560,"style":673},[642],[363,116562],{},[363,116564,578],{"className":116565},[494],[363,116567,116569,116572],{"className":116568},[407],[363,116570,385],{"className":116571,"style":409},[407,408],[363,116573,116575],{"className":116574},[629],[363,116576,116578],{"className":116577},[633],[363,116579,116581],{"className":116580},[638],[363,116582,116584],{"className":116583,"style":8595},[642],[363,116585,116586,116589],{"style":8624},[363,116587],{"className":116588,"style":651},[650],[363,116590,116592],{"className":116591},[655,656,657,658],[363,116593,7920],{"className":116594},[2938,658],[363,116596,461],{"className":116597},[494],[363,116599,4505],{"className":116600,"style":1328},[407,408],[363,116602,20737],{"className":116603},[501],[363,116605,116607],{"className":116606},[407],[363,116608,3255],{"className":116609},[767,4067],[363,116611,898],{"className":116612},[920],[11,116614,116615,116616,116690,116691,116733],{},"它的被估计量是 ",[363,116617,116619,116643],{"className":116618,"translate":367},[366],[363,116620,116622],{"className":116621},[371],[373,116623,116624],{"xmlns":375},[377,116625,116626,116640],{},[380,116627,116628,116634,116636,116638],{},[7161,116629,116630,116632],{},[383,116631,385],{},[458,116633,7920],{},[458,116635,461],{"stretchy":460},[383,116637,4505],{},[458,116639,468],{"stretchy":460},[387,116641,116642],{"encoding":389},"f^*(g)",[363,116644,116646],{"className":116645,"ariaHidden":394},[393],[363,116647,116649,116652,116681,116684,116687],{"className":116648},[398],[363,116650],{"className":116651,"style":487},[402],[363,116653,116655,116658],{"className":116654},[407],[363,116656,385],{"className":116657,"style":409},[407,408],[363,116659,116661],{"className":116660},[629],[363,116662,116664],{"className":116663},[633],[363,116665,116667],{"className":116666},[638],[363,116668,116670],{"className":116669,"style":8846},[642],[363,116671,116672,116675],{"style":7212},[363,116673],{"className":116674,"style":651},[650],[363,116676,116678],{"className":116677},[655,656,657,658],[363,116679,7920],{"className":116680},[2938,658],[363,116682,461],{"className":116683},[494],[363,116685,4505],{"className":116686,"style":1328},[407,408],[363,116688,468],{"className":116689},[501],"，而不是 ",[363,116692,116694,116712],{"className":116693,"translate":367},[366],[363,116695,116697],{"className":116696},[371],[373,116698,116699],{"xmlns":375},[377,116700,116701,116709],{},[380,116702,116703,116705,116707],{},[383,116704,5155],{"mathvariant":557},[458,116706,3646],{"lspace":1594,"rspace":1594},[383,116708,5155],{"mathvariant":557},[387,116710,116711],{"encoding":389},"|{\\cdot}|",[363,116713,116715],{"className":116714,"ariaHidden":394},[393],[363,116716,116718,116721,116724,116730],{"className":116717},[398],[363,116719],{"className":116720,"style":487},[402],[363,116722,5155],{"className":116723},[407],[363,116725,116727],{"className":116726},[407],[363,116728,3646],{"className":116729},[407],[363,116731,5155],{"className":116732},[407],"，所以是「非对称 IPM」。",[11,116735,116736,116738],{},[1572,116737,6840],{}," Wasserstein\u002FMMD 不是 f-散度，也不能写成 f-散度；它们的关键区别在于是否利用几何、是否在支撑分离时仍给梯度、以及是否满足数据处理不等式（Wasserstein 一般不满足数据处理不等式，因为传输方案可以随条件分布\"重新安排\"质量；MMD 由核特征映射的条件期望是收缩算子，沿核的具体结构可证其满足数据处理不等式）。",[2658,116740,116742],{"id":116741},"_63-支撑不重叠的极限","6.3 支撑不重叠的极限",[52839,116744,116745,116825],{},[52842,116746,116747],{},[52845,116748,116749,116752,116754,116756,116758,116760,116820,116822],{},[52848,116750,116751],{},"情形",[52848,116753,33010],{},[52848,116755,109206],{},[52848,116757,53471],{},[52848,116759,87109],{},[52848,116761,116762],{},[363,116763,116765,116782],{"className":116764,"translate":367},[366],[363,116766,116768],{"className":116767},[371],[373,116769,116770],{"xmlns":375},[377,116771,116772,116780],{},[380,116773,116774],{},[7161,116775,116776,116778],{},[383,116777,37796],{},[463,116779,2810],{},[387,116781,40741],{"encoding":389},[363,116783,116785],{"className":116784,"ariaHidden":394},[393],[363,116786,116788,116791],{"className":116787},[398],[363,116789],{"className":116790,"style":40751},[402],[363,116792,116794,116797],{"className":116793},[407],[363,116795,37796],{"className":116796},[407,408],[363,116798,116800],{"className":116799},[629],[363,116801,116803],{"className":116802},[633],[363,116804,116806],{"className":116805},[638],[363,116807,116809],{"className":116808,"style":20375},[642],[363,116810,116811,116814],{"style":7212},[363,116812],{"className":116813,"style":651},[650],[363,116815,116817],{"className":116816},[655,656,657,658],[363,116818,2810],{"className":116819},[407,658],[52848,116821,105520],{},[52848,116823,116824],{},"Wasserstein",[52937,116826,116827,117237],{},[52845,116828,116829,117000,117035,117070,117112,117142,117177,117207],{},[52942,116830,116831,116999],{},[363,116832,116834,116868],{"className":116833,"translate":367},[366],[363,116835,116837],{"className":116836},[371],[373,116838,116839],{"xmlns":375},[377,116840,116841,116865],{},[380,116842,116843,116845,116847,116853,116855,116857,116859],{},[383,116844,554],{},[458,116846,471],{},[543,116848,116849,116851],{},[383,116850,16059],{},[463,116852,474],{},[458,116854,898],{"separator":394},[383,116856,561],{},[458,116858,471],{},[543,116860,116861,116863],{},[383,116862,16059],{},[463,116864,465],{},[387,116866,116867],{"encoding":389},"P=\\delta_0,Q=\\delta_1",[363,116869,116871,116889,116953],{"className":116870,"ariaHidden":394},[393],[363,116872,116874,116877,116880,116883,116886],{"className":116873},[398],[363,116875],{"className":116876,"style":1011},[402],[363,116878,554],{"className":116879,"style":682},[407,408],[363,116881],{"className":116882,"style":506},[505],[363,116884,471],{"className":116885},[510],[363,116887],{"className":116888,"style":506},[505],[363,116890,116892,116895,116935,116938,116941,116944,116947,116950],{"className":116891},[398],[363,116893],{"className":116894,"style":403},[402],[363,116896,116898,116901],{"className":116897},[407],[363,116899,16059],{"className":116900,"style":16108},[407,408],[363,116902,116904],{"className":116903},[629],[363,116905,116907,116927],{"className":116906},[633,634],[363,116908,116910,116924],{"className":116909},[638],[363,116911,116913],{"className":116912,"style":11480},[642],[363,116914,116915,116918],{"style":95090},[363,116916],{"className":116917,"style":651},[650],[363,116919,116921],{"className":116920},[655,656,657,658],[363,116922,474],{"className":116923},[407,658],[363,116925,666],{"className":116926},[665],[363,116928,116930],{"className":116929},[638],[363,116931,116933],{"className":116932,"style":8315},[642],[363,116934],{},[363,116936,898],{"className":116937},[920],[363,116939],{"className":116940,"style":754},[505],[363,116942,561],{"className":116943},[407,408],[363,116945],{"className":116946,"style":506},[505],[363,116948,471],{"className":116949},[510],[363,116951],{"className":116952,"style":506},[505],[363,116954,116956,116959],{"className":116955},[398],[363,116957],{"className":116958,"style":11821},[402],[363,116960,116962,116965],{"className":116961},[407],[363,116963,16059],{"className":116964,"style":16108},[407,408],[363,116966,116968],{"className":116967},[629],[363,116969,116971,116991],{"className":116970},[633,634],[363,116972,116974,116988],{"className":116973},[638],[363,116975,116977],{"className":116976,"style":11480},[642],[363,116978,116979,116982],{"style":95090},[363,116980],{"className":116981,"style":651},[650],[363,116983,116985],{"className":116984},[655,656,657,658],[363,116986,465],{"className":116987},[407,658],[363,116989,666],{"className":116990},[665],[363,116992,116994],{"className":116993},[638],[363,116995,116997],{"className":116996,"style":8315},[642],[363,116998],{},"（约）",[52942,117001,117002],{},[363,117003,117005,117020],{"className":117004,"translate":367},[366],[363,117006,117008],{"className":117007},[371],[373,117009,117010],{"xmlns":375},[377,117011,117012,117018],{},[380,117013,117014,117016],{},[458,117015,2817],{},[383,117017,1371],{"mathvariant":557},[387,117019,4588],{"encoding":389},[363,117021,117023],{"className":117022,"ariaHidden":394},[393],[363,117024,117026,117029,117032],{"className":117025},[398],[363,117027],{"className":117028,"style":4598},[402],[363,117030,2817],{"className":117031},[407],[363,117033,1371],{"className":117034},[407],[52942,117036,117037],{},[363,117038,117040,117055],{"className":117039,"translate":367},[366],[363,117041,117043],{"className":117042},[371],[373,117044,117045],{"xmlns":375},[377,117046,117047,117053],{},[380,117048,117049,117051],{},[458,117050,2817],{},[383,117052,1371],{"mathvariant":557},[387,117054,4588],{"encoding":389},[363,117056,117058],{"className":117057,"ariaHidden":394},[393],[363,117059,117061,117064,117067],{"className":117060},[398],[363,117062],{"className":117063,"style":4598},[402],[363,117065,2817],{"className":117066},[407],[363,117068,1371],{"className":117069},[407],[52942,117071,117072],{},[363,117073,117075,117092],{"className":117074,"translate":367},[366],[363,117076,117078],{"className":117077},[371],[373,117079,117080],{"xmlns":375},[377,117081,117082,117090],{},[380,117083,117084,117086,117088],{},[383,117085,4447],{},[458,117087,4450],{},[463,117089,2810],{},[387,117091,34832],{"encoding":389},[363,117093,117095],{"className":117094,"ariaHidden":394},[393],[363,117096,117098,117101,117106,117109],{"className":117097},[398],[363,117099],{"className":117100,"style":403},[402],[363,117102,4501,117104],{"className":117103},[1831],[363,117105,4505],{"style":4504},[363,117107],{"className":117108,"style":754},[505],[363,117110,2810],{"className":117111},[407],[52942,117113,117114],{},[363,117115,117117,117130],{"className":117116,"translate":367},[366],[363,117118,117120],{"className":117119},[371],[373,117121,117122],{"xmlns":375},[377,117123,117124,117128],{},[380,117125,117126],{},[463,117127,465],{},[387,117129,465],{"encoding":389},[363,117131,117133],{"className":117132,"ariaHidden":394},[393],[363,117134,117136,117139],{"className":117135},[398],[363,117137],{"className":117138,"style":520},[402],[363,117140,465],{"className":117141},[407],[52942,117143,117144],{},[363,117145,117147,117162],{"className":117146,"translate":367},[366],[363,117148,117150],{"className":117149},[371],[373,117151,117152],{"xmlns":375},[377,117153,117154,117160],{},[380,117155,117156,117158],{},[458,117157,2817],{},[383,117159,1371],{"mathvariant":557},[387,117161,4588],{"encoding":389},[363,117163,117165],{"className":117164,"ariaHidden":394},[393],[363,117166,117168,117171,117174],{"className":117167},[398],[363,117169],{"className":117170,"style":4598},[402],[363,117172,2817],{"className":117173},[407],[363,117175,1371],{"className":117176},[407],[52942,117178,117179],{},[363,117180,117182,117195],{"className":117181,"translate":367},[366],[363,117183,117185],{"className":117184},[371],[373,117186,117187],{"xmlns":375},[377,117188,117189,117193],{},[380,117190,117191],{},[463,117192,2810],{},[387,117194,2810],{"encoding":389},[363,117196,117198],{"className":117197,"ariaHidden":394},[393],[363,117199,117201,117204],{"className":117200},[398],[363,117202],{"className":117203,"style":520},[402],[363,117205,2810],{"className":117206},[407],[52942,117208,117209],{},[363,117210,117212,117225],{"className":117211,"translate":367},[366],[363,117213,117215],{"className":117214},[371],[373,117216,117217],{"xmlns":375},[377,117218,117219,117223],{},[380,117220,117221],{},[463,117222,465],{},[387,117224,465],{"encoding":389},[363,117226,117228],{"className":117227,"ariaHidden":394},[393],[363,117229,117231,117234],{"className":117230},[398],[363,117232],{"className":117233,"style":520},[402],[363,117235,465],{"className":117236},[407],[52845,117238,117239,117384,117430,117474,117532,117577,117690,117735],{},[52942,117240,117241],{},[363,117242,117244,117291],{"className":117243,"translate":367},[366],[363,117245,117247],{"className":117246},[371],[373,117248,117249],{"xmlns":375},[377,117250,117251,117288],{},[380,117252,117253,117255,117257,117259,117261,117263,117265,117267,117269,117271,117273,117275,117277,117279,117282,117284,117286],{},[383,117254,554],{},[458,117256,471],{},[383,117258,38631],{},[458,117260,461],{"stretchy":460},[463,117262,474],{},[458,117264,898],{"separator":394},[463,117266,465],{},[458,117268,468],{"stretchy":460},[458,117270,898],{"separator":394},[383,117272,561],{},[458,117274,471],{},[383,117276,38631],{},[458,117278,461],{"stretchy":460},[463,117280,117281],{},"100",[458,117283,898],{"separator":394},[463,117285,465],{},[458,117287,468],{"stretchy":460},[387,117289,117290],{"encoding":389},"P=N(0,1),Q=N(100,1)",[363,117292,117294,117312,117357],{"className":117293,"ariaHidden":394},[393],[363,117295,117297,117300,117303,117306,117309],{"className":117296},[398],[363,117298],{"className":117299,"style":1011},[402],[363,117301,554],{"className":117302,"style":682},[407,408],[363,117304],{"className":117305,"style":506},[505],[363,117307,471],{"className":117308},[510],[363,117310],{"className":117311,"style":506},[505],[363,117313,117315,117318,117321,117324,117327,117330,117333,117336,117339,117342,117345,117348,117351,117354],{"className":117314},[398],[363,117316],{"className":117317,"style":487},[402],[363,117319,38631],{"className":117320,"style":25948},[407,408],[363,117322,461],{"className":117323},[494],[363,117325,474],{"className":117326},[407],[363,117328,898],{"className":117329},[920],[363,117331],{"className":117332,"style":754},[505],[363,117334,465],{"className":117335},[407],[363,117337,468],{"className":117338},[501],[363,117340,898],{"className":117341},[920],[363,117343],{"className":117344,"style":754},[505],[363,117346,561],{"className":117347},[407,408],[363,117349],{"className":117350,"style":506},[505],[363,117352,471],{"className":117353},[510],[363,117355],{"className":117356,"style":506},[505],[363,117358,117360,117363,117366,117369,117372,117375,117378,117381],{"className":117359},[398],[363,117361],{"className":117362,"style":487},[402],[363,117364,38631],{"className":117365,"style":25948},[407,408],[363,117367,461],{"className":117368},[494],[363,117370,117281],{"className":117371},[407],[363,117373,898],{"className":117374},[920],[363,117376],{"className":117377,"style":754},[505],[363,117379,465],{"className":117380},[407],[363,117382,468],{"className":117383},[501],[52942,117385,117386],{},[363,117387,117389,117406],{"className":117388,"translate":367},[366],[363,117390,117392],{"className":117391},[371],[373,117393,117394],{"xmlns":375},[377,117395,117396,117403],{},[380,117397,117398,117400],{},[458,117399,471],{},[463,117401,117402],{},"5000",[387,117404,117405],{"encoding":389},"=5000",[363,117407,117409,117421],{"className":117408,"ariaHidden":394},[393],[363,117410,117412,117415,117418],{"className":117411},[398],[363,117413],{"className":117414,"style":11350},[402],[363,117416,471],{"className":117417},[510],[363,117419],{"className":117420,"style":506},[505],[363,117422,117424,117427],{"className":117423},[398],[363,117425],{"className":117426,"style":520},[402],[363,117428,117402],{"className":117429},[407],[52942,117431,117432],{},[363,117433,117435,117450],{"className":117434,"translate":367},[366],[363,117436,117438],{"className":117437},[371],[373,117439,117440],{"xmlns":375},[377,117441,117442,117448],{},[380,117443,117444,117446],{},[458,117445,471],{},[463,117447,117402],{},[387,117449,117405],{"encoding":389},[363,117451,117453,117465],{"className":117452,"ariaHidden":394},[393],[363,117454,117456,117459,117462],{"className":117455},[398],[363,117457],{"className":117458,"style":11350},[402],[363,117460,471],{"className":117461},[510],[363,117463],{"className":117464,"style":506},[505],[363,117466,117468,117471],{"className":117467},[398],[363,117469],{"className":117470,"style":520},[402],[363,117472,117402],{"className":117473},[407],[52942,117475,117476],{},[363,117477,117479,117499],{"className":117478,"translate":367},[366],[363,117480,117482],{"className":117481},[371],[373,117483,117484],{"xmlns":375},[377,117485,117486,117496],{},[380,117487,117488,117490,117492,117494],{},[458,117489,33306],{},[383,117491,4447],{},[458,117493,4450],{},[463,117495,2810],{},[387,117497,117498],{"encoding":389},"\\approx\\log2",[363,117500,117502,117515],{"className":117501,"ariaHidden":394},[393],[363,117503,117505,117509,117512],{"className":117504},[398],[363,117506],{"className":117507,"style":117508},[402],"height:0.4831em;",[363,117510,33306],{"className":117511},[510],[363,117513],{"className":117514,"style":506},[505],[363,117516,117518,117521,117526,117529],{"className":117517},[398],[363,117519],{"className":117520,"style":403},[402],[363,117522,4501,117524],{"className":117523},[1831],[363,117525,4505],{"style":4504},[363,117527],{"className":117528,"style":754},[505],[363,117530,2810],{"className":117531},[407],[52942,117533,117534],{},[363,117535,117537,117553],{"className":117536,"translate":367},[366],[363,117538,117540],{"className":117539},[371],[373,117541,117542],{"xmlns":375},[377,117543,117544,117550],{},[380,117545,117546,117548],{},[458,117547,33306],{},[463,117549,465],{},[387,117551,117552],{"encoding":389},"\\approx1",[363,117554,117556,117568],{"className":117555,"ariaHidden":394},[393],[363,117557,117559,117562,117565],{"className":117558},[398],[363,117560],{"className":117561,"style":117508},[402],[363,117563,33306],{"className":117564},[510],[363,117566],{"className":117567,"style":506},[505],[363,117569,117571,117574],{"className":117570},[398],[363,117572],{"className":117573,"style":520},[402],[363,117575,465],{"className":117576},[407],[52942,117578,117579],{},[363,117580,117582,117607],{"className":117581,"translate":367},[366],[363,117583,117585],{"className":117584},[371],[373,117586,117587],{"xmlns":375},[377,117588,117589,117604],{},[380,117590,117591,117593],{},[458,117592,33306],{},[7161,117594,117595,117597],{},[383,117596,7914],{},[7161,117598,117599,117602],{},[463,117600,117601],{},"10",[463,117603,39336],{},[387,117605,117606],{"encoding":389},"\\approx e^{10^4}",[363,117608,117610,117622],{"className":117609,"ariaHidden":394},[393],[363,117611,117613,117616,117619],{"className":117612},[398],[363,117614],{"className":117615,"style":117508},[402],[363,117617,33306],{"className":117618},[510],[363,117620],{"className":117621,"style":506},[505],[363,117623,117625,117629],{"className":117624},[398],[363,117626],{"className":117627,"style":117628},[402],"height:0.9869em;",[363,117630,117632,117635],{"className":117631},[407],[363,117633,7914],{"className":117634},[407,408],[363,117636,117638],{"className":117637},[629],[363,117639,117641],{"className":117640},[633],[363,117642,117644],{"className":117643},[638],[363,117645,117647],{"className":117646,"style":117628},[642],[363,117648,117649,117652],{"style":7212},[363,117650],{"className":117651,"style":651},[650],[363,117653,117655],{"className":117654},[655,656,657,658],[363,117656,117658,117661],{"className":117657},[407,658],[363,117659,465],{"className":117660},[407,658],[363,117662,117664,117667],{"className":117663},[407,658],[363,117665,474],{"className":117666},[407,658],[363,117668,117670],{"className":117669},[629],[363,117671,117673],{"className":117672},[633],[363,117674,117676],{"className":117675},[638],[363,117677,117679],{"className":117678,"style":38859},[642],[363,117680,117681,117684],{"style":38862},[363,117682],{"className":117683,"style":30553},[650],[363,117685,117687],{"className":117686},[655,30557,10021,658],[363,117688,39336],{"className":117689},[407,658],[52942,117691,117692],{},[363,117693,117695,117711],{"className":117694,"translate":367},[366],[363,117696,117698],{"className":117697},[371],[373,117699,117700],{"xmlns":375},[377,117701,117702,117708],{},[380,117703,117704,117706],{},[458,117705,33306],{},[463,117707,2810],{},[387,117709,117710],{"encoding":389},"\\approx2",[363,117712,117714,117726],{"className":117713,"ariaHidden":394},[393],[363,117715,117717,117720,117723],{"className":117716},[398],[363,117718],{"className":117719,"style":117508},[402],[363,117721,33306],{"className":117722},[510],[363,117724],{"className":117725,"style":506},[505],[363,117727,117729,117732],{"className":117728},[398],[363,117730],{"className":117731,"style":520},[402],[363,117733,2810],{"className":117734},[407],[52942,117736,117737],{},[363,117738,117740,117756],{"className":117739,"translate":367},[366],[363,117741,117743],{"className":117742},[371],[373,117744,117745],{"xmlns":375},[377,117746,117747,117753],{},[380,117748,117749,117751],{},[458,117750,471],{},[463,117752,117281],{},[387,117754,117755],{"encoding":389},"=100",[363,117757,117759,117771],{"className":117758,"ariaHidden":394},[393],[363,117760,117762,117765,117768],{"className":117761},[398],[363,117763],{"className":117764,"style":11350},[402],[363,117766,471],{"className":117767},[510],[363,117769],{"className":117770,"style":506},[505],[363,117772,117774,117777],{"className":117773},[398],[363,117775],{"className":117776,"style":520},[402],[363,117778,117281],{"className":117779},[407],[11,117781,117782],{},"f-散度在第二行全部「饱和到下界\u002F上界」，而 Wasserstein 随距离线性增长——这正是词嵌入、最优传输、Wasserstein GAN 的动机。",[18,117784,117786],{"id":117785},"_7-机器学习应用","7. 机器学习应用",[11,117788,117789],{},"f-散度族之所以重要，是因为：",[7009,117791,117792,117798,117808,117843],{},[7012,117793,117794,117797],{},[1572,117795,117796],{},"统一框架","：许多生成模型的目标函数可以写成 f-散度。",[7012,117799,117800,117803,117804,117807],{},[1572,117801,117802],{},"变分估计","：通过凸共轭，可以用神经网络估计 f-散度，这就是 ",[1572,117805,117806],{},"f-GAN"," 的核心思想。",[7012,117809,117810,117813,117814,117842],{},[1572,117811,117812],{},"灵活选择","：不同 ",[363,117815,117817,117830],{"className":117816,"translate":367},[366],[363,117818,117820],{"className":117819},[371],[373,117821,117822],{"xmlns":375},[377,117823,117824,117828],{},[380,117825,117826],{},[383,117827,385],{},[387,117829,385],{"encoding":389},[363,117831,117833],{"className":117832,"ariaHidden":394},[393],[363,117834,117836,117839],{"className":117835},[398],[363,117837],{"className":117838,"style":403},[402],[363,117840,385],{"className":117841,"style":409},[407,408]," 对应不同训练性质。例如 JS 有界但可能梯度消失，KL 无界但敏感。",[7012,117844,117845,117848],{},[1572,117846,117847],{},"理论分析","：数据处理不等式、凸性、对偶表示等为收敛性和泛化分析提供工具。",[11,117850,117851],{},"下面把这几条落到具体场景。",[2658,117853,117855],{"id":117854},"_71-f-gan","7.1 f-GAN",[11,117857,117858,117859,117987,117988,118016,118017,118045],{},"见第 5 节。核心是：",[363,117860,117862,117894],{"className":117861,"translate":367},[366],[363,117863,117865],{"className":117864},[371],[373,117866,117867],{"xmlns":375},[377,117868,117869,117891],{},[380,117870,117871,117881],{},[543,117872,117873,117879],{},[380,117874,117875,117877],{},[383,117876,51955],{},[458,117878,4450],{},[383,117880,101106],{},[543,117882,117883,117889],{},[380,117884,117885,117887],{},[383,117886,52734],{},[458,117888,4450],{},[383,117890,100208],{},[387,117892,117893],{"encoding":389},"\\min_\\theta\\max_\\omega",[363,117895,117897],{"className":117896,"ariaHidden":394},[393],[363,117898,117900,117904,117944,117947],{"className":117899},[398],[363,117901],{"className":117902,"style":117903},[402],"height:0.8179em;vertical-align:-0.15em;",[363,117905,117907,117910],{"className":117906},[1831],[363,117908,51955],{"className":117909},[1831],[363,117911,117913],{"className":117912},[629],[363,117914,117916,117936],{"className":117915},[633,634],[363,117917,117919,117933],{"className":117918},[638],[363,117920,117922],{"className":117921,"style":643},[642],[363,117923,117924,117927],{"style":52793},[363,117925],{"className":117926,"style":651},[650],[363,117928,117930],{"className":117929},[655,656,657,658],[363,117931,101106],{"className":117932,"style":625},[407,408,658],[363,117934,666],{"className":117935},[665],[363,117937,117939],{"className":117938},[638],[363,117940,117942],{"className":117941,"style":8315},[642],[363,117943],{},[363,117945],{"className":117946,"style":754},[505],[363,117948,117950,117953],{"className":117949},[1831],[363,117951,52734],{"className":117952},[1831],[363,117954,117956],{"className":117955},[629],[363,117957,117959,117979],{"className":117958},[633,634],[363,117960,117962,117976],{"className":117961},[638],[363,117963,117965],{"className":117964,"style":45276},[642],[363,117966,117967,117970],{"style":52793},[363,117968],{"className":117969,"style":651},[650],[363,117971,117973],{"className":117972},[655,656,657,658],[363,117974,100208],{"className":117975,"style":1328},[407,408,658],[363,117977,666],{"className":117978},[665],[363,117980,117982],{"className":117981},[638],[363,117983,117985],{"className":117984,"style":8315},[642],[363,117986],{}," 的对抗目标 = 对 ",[363,117989,117991,118004],{"className":117990,"translate":367},[366],[363,117992,117994],{"className":117993},[371],[373,117995,117996],{"xmlns":375},[377,117997,117998,118002],{},[380,117999,118000],{},[383,118001,385],{},[387,118003,385],{"encoding":389},[363,118005,118007],{"className":118006,"ariaHidden":394},[393],[363,118008,118010,118013],{"className":118009},[398],[363,118011],{"className":118012,"style":403},[402],[363,118014,385],{"className":118015,"style":409},[407,408]," 做对偶后的 f-散度估计。选择 ",[363,118018,118020,118033],{"className":118019,"translate":367},[366],[363,118021,118023],{"className":118022},[371],[373,118024,118025],{"xmlns":375},[377,118026,118027,118031],{},[380,118028,118029],{},[383,118030,385],{},[387,118032,385],{"encoding":389},[363,118034,118036],{"className":118035,"ariaHidden":394},[393],[363,118037,118039,118042],{"className":118038},[398],[363,118040],{"className":118041,"style":403},[402],[363,118043,385],{"className":118044,"style":409},[407,408]," 就是选择「用哪种散度训练生成器」，这直接决定模式崩塌、梯度消失与训练稳定性的权衡。",[2658,118047,118049],{"id":118048},"_72-变分推断与-elbo","7.2 变分推断与 ELBO",[11,118051,118052],{},"变分推断里最大化证据下界",[363,118054,118056],{"className":118055,"translate":367},[528],[363,118057,118059,118218],{"className":118058,"translate":367},[366],[363,118060,118062],{"className":118061},[371],[373,118063,118064],{"xmlns":375,"display":537},[377,118065,118066,118215],{},[1590,118067,118068,118145],{"rowspacing":1592,"columnalign":1593,"columnspacing":1594},[1596,118069,118070,118084],{},[1599,118071,118072],{},[1602,118073,118074],{"scriptlevel":474,"displaystyle":394},[380,118075,118076,118078,118080,118082],{},[383,118077,22240],{"mathvariant":944},[458,118079,461],{"stretchy":460},[383,118081,1291],{},[458,118083,468],{"stretchy":460},[1599,118085,118086],{},[1602,118087,118088],{"scriptlevel":474,"displaystyle":394},[380,118089,118090,118092,118094,118100,118102,118104,118106,118108,118110,118112,118114,118117,118119,118121,118123,118129,118131,118133,118135,118137,118139,118141,118143],{},[380,118091],{},[458,118093,471],{},[543,118095,118096,118098],{},[383,118097,571],{"mathvariant":570},[383,118099,1291],{},[458,118101,578],{"stretchy":460},[383,118103,4447],{},[458,118105,4450],{},[383,118107,11],{},[458,118109,461],{"stretchy":460},[383,118111,1121],{},[458,118113,898],{"separator":394},[383,118115,118116],{},"z",[458,118118,468],{"stretchy":460},[458,118120,605],{"stretchy":460},[458,118122,5160],{},[543,118124,118125,118127],{},[383,118126,571],{"mathvariant":570},[383,118128,1291],{},[458,118130,578],{"stretchy":460},[383,118132,4447],{},[458,118134,4450],{},[383,118136,1291],{},[458,118138,461],{"stretchy":460},[383,118140,118116],{},[458,118142,468],{"stretchy":460},[458,118144,605],{"stretchy":460},[1596,118146,118147,118153],{},[1599,118148,118149],{},[1602,118150,118151],{"scriptlevel":474,"displaystyle":394},[380,118152],{},[1599,118154,118155],{},[1602,118156,118157],{"scriptlevel":474,"displaystyle":394},[380,118158,118159,118161,118163,118165,118167,118169,118171,118173,118175,118177,118183,118185,118187,118189,118191,118193,118195,118197,118199,118201,118203,118205,118207,118209,118211,118213],{},[380,118160],{},[458,118162,471],{},[383,118164,4447],{},[458,118166,4450],{},[383,118168,11],{},[458,118170,461],{"stretchy":460},[383,118172,1121],{},[458,118174,468],{"stretchy":460},[458,118176,5160],{},[380,118178,118179,118181],{},[383,118180,11041],{"mathvariant":557},[383,118182,22240],{"mathvariant":557},[458,118184,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,118186,1291],{},[458,118188,461],{"stretchy":460},[383,118190,118116],{},[458,118192,468],{"stretchy":460},[1644,118194,1646],{},[383,118196,558],{"mathvariant":557},[1644,118198,1646],{},[383,118200,11],{},[458,118202,461],{"stretchy":460},[383,118204,118116],{},[383,118206,5155],{"mathvariant":557},[383,118208,1121],{},[458,118210,468],{"stretchy":460},[458,118212,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,118214,898],{"separator":394},[387,118216,118217],{"encoding":389},"\\begin{aligned}\n\\mathcal L(q)\n&=\\mathbb E_q[\\log p(x,z)]\n-\\mathbb E_q[\\log q(z)]\\\\\n&=\\log p(x)\n-\\mathrm{KL}\\big(q(z)\\,\\|\\,p(z|x)\\big),\n\\end{aligned}",[363,118219,118221],{"className":118220,"ariaHidden":394},[393],[363,118222,118224,118227],{"className":118223},[398],[363,118225],{"className":118226,"style":14933},[402],[363,118228,118230],{"className":118229},[407],[363,118231,118233,118285],{"className":118232},[1590],[363,118234,118236],{"className":118235},[1707],[363,118237,118239,118277],{"className":118238},[633,634],[363,118240,118242,118274],{"className":118241},[638],[363,118243,118245,118266],{"className":118244,"style":14952},[642],[363,118246,118248,118251],{"style":118247},"top:-3.765em;",[363,118249],{"className":118250,"style":809},[650],[363,118252,118254,118257,118260,118263],{"className":118253},[407],[363,118255,22240],{"className":118256},[407,971],[363,118258,461],{"className":118259},[494],[363,118261,1291],{"className":118262,"style":1328},[407,408],[363,118264,468],{"className":118265},[501],[363,118267,118268,118271],{"style":15340},[363,118269],{"className":118270,"style":809},[650],[363,118272],{"className":118273},[407],[363,118275,666],{"className":118276},[665],[363,118278,118280],{"className":118279},[638],[363,118281,118283],{"className":118282,"style":14981},[642],[363,118284],{},[363,118286,118288],{"className":118287},[1798],[363,118289,118291,118574],{"className":118290},[633,634],[363,118292,118294,118571],{"className":118293},[638],[363,118295,118297,118462],{"className":118296,"style":14952},[642],[363,118298,118299,118302],{"style":118247},[363,118300],{"className":118301,"style":809},[650],[363,118303,118305,118308,118311,118314,118317,118357,118360,118365,118368,118371,118374,118377,118380,118383,118387,118390,118393,118396,118399,118439,118442,118447,118450,118453,118456,118459],{"className":118304},[407],[363,118306],{"className":118307},[407],[363,118309],{"className":118310,"style":506},[505],[363,118312,471],{"className":118313},[510],[363,118315],{"className":118316,"style":506},[505],[363,118318,118320,118323],{"className":118319},[407],[363,118321,571],{"className":118322},[407,714],[363,118324,118326],{"className":118325},[629],[363,118327,118329,118349],{"className":118328},[633,634],[363,118330,118332,118346],{"className":118331},[638],[363,118333,118335],{"className":118334,"style":45276},[642],[363,118336,118337,118340],{"style":730},[363,118338],{"className":118339,"style":651},[650],[363,118341,118343],{"className":118342},[655,656,657,658],[363,118344,1291],{"className":118345,"style":1328},[407,408,658],[363,118347,666],{"className":118348},[665],[363,118350,118352],{"className":118351},[638],[363,118353,118355],{"className":118354,"style":673},[642],[363,118356],{},[363,118358,578],{"className":118359},[494],[363,118361,4501,118363],{"className":118362},[1831],[363,118364,4505],{"style":4504},[363,118366],{"className":118367,"style":754},[505],[363,118369,11],{"className":118370},[407,408],[363,118372,461],{"className":118373},[494],[363,118375,1121],{"className":118376},[407,408],[363,118378,898],{"className":118379},[920],[363,118381],{"className":118382,"style":754},[505],[363,118384,118116],{"className":118385,"style":118386},[407,408],"margin-right:0.044em;",[363,118388,20737],{"className":118389},[501],[363,118391],{"className":118392,"style":2934},[505],[363,118394,5160],{"className":118395},[2938],[363,118397],{"className":118398,"style":2934},[505],[363,118400,118402,118405],{"className":118401},[407],[363,118403,571],{"className":118404},[407,714],[363,118406,118408],{"className":118407},[629],[363,118409,118411,118431],{"className":118410},[633,634],[363,118412,118414,118428],{"className":118413},[638],[363,118415,118417],{"className":118416,"style":45276},[642],[363,118418,118419,118422],{"style":730},[363,118420],{"className":118421,"style":651},[650],[363,118423,118425],{"className":118424},[655,656,657,658],[363,118426,1291],{"className":118427,"style":1328},[407,408,658],[363,118429,666],{"className":118430},[665],[363,118432,118434],{"className":118433},[638],[363,118435,118437],{"className":118436,"style":673},[642],[363,118438],{},[363,118440,578],{"className":118441},[494],[363,118443,4501,118445],{"className":118444},[1831],[363,118446,4505],{"style":4504},[363,118448],{"className":118449,"style":754},[505],[363,118451,1291],{"className":118452,"style":1328},[407,408],[363,118454,461],{"className":118455},[494],[363,118457,118116],{"className":118458,"style":118386},[407,408],[363,118460,20737],{"className":118461},[501],[363,118463,118464,118467],{"style":15340},[363,118465],{"className":118466,"style":809},[650],[363,118468,118470,118473,118476,118479,118482,118487,118490,118493,118496,118499,118502,118505,118508,118511,118517,118523,118526,118529,118532,118535,118538,118541,118544,118547,118550,118553,118556,118559,118562,118568],{"className":118469},[407],[363,118471],{"className":118472},[407],[363,118474],{"className":118475,"style":506},[505],[363,118477,471],{"className":118478},[510],[363,118480],{"className":118481,"style":506},[505],[363,118483,4501,118485],{"className":118484},[1831],[363,118486,4505],{"style":4504},[363,118488],{"className":118489,"style":754},[505],[363,118491,11],{"className":118492},[407,408],[363,118494,461],{"className":118495},[494],[363,118497,1121],{"className":118498},[407,408],[363,118500,468],{"className":118501},[501],[363,118503],{"className":118504,"style":2934},[505],[363,118506,5160],{"className":118507},[2938],[363,118509],{"className":118510,"style":2934},[505],[363,118512,118514],{"className":118513},[407],[363,118515,33010],{"className":118516},[407,33009],[363,118518,118520],{"className":118519},[407],[363,118521,461],{"className":118522},[767,10021],[363,118524,1291],{"className":118525,"style":1328},[407,408],[363,118527,461],{"className":118528},[494],[363,118530,118116],{"className":118531,"style":118386},[407,408],[363,118533,468],{"className":118534},[501],[363,118536],{"className":118537,"style":754},[505],[363,118539,558],{"className":118540},[407],[363,118542],{"className":118543,"style":754},[505],[363,118545,11],{"className":118546},[407,408],[363,118548,461],{"className":118549},[494],[363,118551,118116],{"className":118552,"style":118386},[407,408],[363,118554,5155],{"className":118555},[407],[363,118557,1121],{"className":118558},[407,408],[363,118560,468],{"className":118561},[501],[363,118563,118565],{"className":118564},[407],[363,118566,468],{"className":118567},[767,10021],[363,118569,898],{"className":118570},[920],[363,118572,666],{"className":118573},[665],[363,118575,118577],{"className":118576},[638],[363,118578,118580],{"className":118579,"style":14981},[642],[363,118581],{},[11,118583,2597,118584,118645,118646,118717,118718,118819,118820,118848,118849,118907,118908,118936],{},[363,118585,118587,118615],{"className":118586,"translate":367},[366],[363,118588,118590],{"className":118589},[371],[373,118591,118592],{"xmlns":375},[377,118593,118594,118612],{},[380,118595,118596,118602,118604,118606,118608,118610],{},[380,118597,118598,118600],{},[383,118599,11041],{"mathvariant":557},[383,118601,22240],{"mathvariant":557},[458,118603,461],{"stretchy":460},[383,118605,1291],{},[383,118607,558],{"mathvariant":557},[383,118609,11],{},[458,118611,468],{"stretchy":460},[387,118613,118614],{"encoding":389},"\\mathrm{KL}(q\\|p)",[363,118616,118618],{"className":118617,"ariaHidden":394},[393],[363,118619,118621,118624,118630,118633,118636,118639,118642],{"className":118620},[398],[363,118622],{"className":118623,"style":487},[402],[363,118625,118627],{"className":118626},[407],[363,118628,33010],{"className":118629},[407,33009],[363,118631,461],{"className":118632},[494],[363,118634,1291],{"className":118635,"style":1328},[407,408],[363,118637,558],{"className":118638},[407],[363,118640,11],{"className":118641},[407,408],[363,118643,468],{"className":118644},[501]," 是 f-散度（",[363,118647,118649,118673],{"className":118648,"translate":367},[366],[363,118650,118652],{"className":118651},[371],[373,118653,118654],{"xmlns":375},[377,118655,118656,118670],{},[380,118657,118658,118660,118662,118664,118666,118668],{},[383,118659,385],{},[458,118661,471],{},[383,118663,1116],{},[383,118665,4447],{},[458,118667,4450],{},[383,118669,1116],{},[387,118671,118672],{"encoding":389},"f=t\\log t",[363,118674,118676,118694],{"className":118675,"ariaHidden":394},[393],[363,118677,118679,118682,118685,118688,118691],{"className":118678},[398],[363,118680],{"className":118681,"style":403},[402],[363,118683,385],{"className":118684,"style":409},[407,408],[363,118686],{"className":118687,"style":506},[505],[363,118689,471],{"className":118690},[510],[363,118692],{"className":118693,"style":506},[505],[363,118695,118697,118700,118703,118706,118711,118714],{"className":118696},[398],[363,118698],{"className":118699,"style":403},[402],[363,118701,1116],{"className":118702},[407,408],[363,118704],{"className":118705,"style":754},[505],[363,118707,4501,118709],{"className":118708},[1831],[363,118710,4505],{"style":4504},[363,118712],{"className":118713,"style":754},[505],[363,118715,1116],{"className":118716},[407,408],"）。反过来，任何以 ",[363,118719,118721,118753],{"className":118720,"translate":367},[366],[363,118722,118724],{"className":118723},[371],[373,118725,118726],{"xmlns":375},[377,118727,118728,118750],{},[380,118729,118730,118736,118738,118740,118742,118744,118746,118748],{},[543,118731,118732,118734],{},[383,118733,571],{"mathvariant":570},[383,118735,1291],{},[458,118737,578],{"stretchy":460},[383,118739,4447],{},[458,118741,4450],{},[458,118743,461],{"stretchy":460},[458,118745,3646],{},[458,118747,468],{"stretchy":460},[458,118749,605],{"stretchy":460},[387,118751,118752],{"encoding":389},"\\mathbb E_q[\\log(\\cdot)]",[363,118754,118756],{"className":118755,"ariaHidden":394},[393],[363,118757,118759,118762,118802,118805,118810,118813,118816],{"className":118758},[398],[363,118760],{"className":118761,"style":618},[402],[363,118763,118765,118768],{"className":118764},[407],[363,118766,571],{"className":118767},[407,714],[363,118769,118771],{"className":118770},[629],[363,118772,118774,118794],{"className":118773},[633,634],[363,118775,118777,118791],{"className":118776},[638],[363,118778,118780],{"className":118779,"style":45276},[642],[363,118781,118782,118785],{"style":730},[363,118783],{"className":118784,"style":651},[650],[363,118786,118788],{"className":118787},[655,656,657,658],[363,118789,1291],{"className":118790,"style":1328},[407,408,658],[363,118792,666],{"className":118793},[665],[363,118795,118797],{"className":118796},[638],[363,118798,118800],{"className":118799,"style":673},[642],[363,118801],{},[363,118803,578],{"className":118804},[494],[363,118806,4501,118808],{"className":118807},[1831],[363,118809,4505],{"style":4504},[363,118811,461],{"className":118812},[494],[363,118814,3646],{"className":118815},[407],[363,118817,20737],{"className":118818},[501]," 为组成部分的目标都可以用 f-散度的语言重写；",[363,118821,118823,118836],{"className":118822,"translate":367},[366],[363,118824,118826],{"className":118825},[371],[373,118827,118828],{"xmlns":375},[377,118829,118830,118834],{},[380,118831,118832],{},[383,118833,45101],{},[387,118835,49437],{"encoding":389},[363,118837,118839],{"className":118838,"ariaHidden":394},[393],[363,118840,118842,118845],{"className":118841},[398],[363,118843],{"className":118844,"style":2692},[402],[363,118846,45101],{"className":118847,"style":45131},[407,408],"-VI、",[363,118850,118852,118869],{"className":118851,"translate":367},[366],[363,118853,118855],{"className":118854},[371],[373,118856,118857],{"xmlns":375},[377,118858,118859,118867],{},[380,118860,118861],{},[7161,118862,118863,118865],{},[383,118864,37796],{},[463,118866,2810],{},[387,118868,40741],{"encoding":389},[363,118870,118872],{"className":118871,"ariaHidden":394},[393],[363,118873,118875,118878],{"className":118874},[398],[363,118876],{"className":118877,"style":40751},[402],[363,118879,118881,118884],{"className":118880},[407],[363,118882,37796],{"className":118883},[407,408],[363,118885,118887],{"className":118886},[629],[363,118888,118890],{"className":118889},[633],[363,118891,118893],{"className":118892},[638],[363,118894,118896],{"className":118895,"style":20375},[642],[363,118897,118898,118901],{"style":7212},[363,118899],{"className":118900,"style":651},[650],[363,118902,118904],{"className":118903},[655,656,657,658],[363,118905,2810],{"className":118906},[407,658],"-VI 等就换用别的 ",[363,118909,118911,118924],{"className":118910,"translate":367},[366],[363,118912,118914],{"className":118913},[371],[373,118915,118916],{"xmlns":375},[377,118917,118918,118922],{},[380,118919,118920],{},[383,118921,385],{},[387,118923,385],{"encoding":389},[363,118925,118927],{"className":118926,"ariaHidden":394},[393],[363,118928,118930,118933],{"className":118929},[398],[363,118931],{"className":118932,"style":403},[402],[363,118934,385],{"className":118935,"style":409},[407,408],"，在 3.1 节所说的「零回避」（mass-covering）与「零强制」（mode-seeking）两种极端行为之间取舍。",[2658,118938,118940],{"id":118939},"_73-互信息估计","7.3 互信息估计",[11,118942,118943],{},"互信息可写成",[363,118945,118947],{"className":118946,"translate":367},[528],[363,118948,118950,119065],{"className":118949,"translate":367},[366],[363,118951,118953],{"className":118952},[371],[373,118954,118955],{"xmlns":375,"display":537},[377,118956,118957,119062],{},[380,118958,118959,118961,118963,118965,118967,118969,118971,118973,118979,118981,118991,118993,118995,118997,119003,119006,119012,119014,119016,119030,119032,119042,119044,119050,119052,119058,119060],{},[383,118960,34215],{},[458,118962,461],{"stretchy":460},[383,118964,945],{},[458,118966,34222],{"separator":394},[383,118968,5748],{},[458,118970,468],{"stretchy":460},[458,118972,471],{},[380,118974,118975,118977],{},[383,118976,11041],{"mathvariant":557},[383,118978,22240],{"mathvariant":557},[458,118980,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[543,118982,118983,118985],{},[383,118984,554],{},[380,118986,118987,118989],{},[383,118988,945],{},[383,118990,5748],{},[1644,118992,1646],{},[383,118994,558],{"mathvariant":557},[1644,118996,1646],{},[543,118998,118999,119001],{},[383,119000,554],{},[383,119002,945],{},[458,119004,119005],{},"⊗",[543,119007,119008,119010],{},[383,119009,554],{},[383,119011,5748],{},[458,119013,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,119015,471],{},[543,119017,119018,119020],{},[383,119019,547],{},[380,119021,119022,119024,119026,119028],{},[383,119023,1116],{},[383,119025,4447],{},[458,119027,4450],{},[383,119029,1116],{},[458,119031,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[543,119033,119034,119036],{},[383,119035,554],{},[380,119037,119038,119040],{},[383,119039,945],{},[383,119041,5748],{},[383,119043,558],{"mathvariant":557},[543,119045,119046,119048],{},[383,119047,554],{},[383,119049,945],{},[458,119051,119005],{},[543,119053,119054,119056],{},[383,119055,554],{},[383,119057,5748],{},[458,119059,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,119061,898],{"separator":394},[387,119063,119064],{"encoding":389},"I(X;Y)\n=\\mathrm{KL}\\big(P_{XY}\\,\\|\\,P_X\\otimes P_Y\\big)\n=D_{t\\log t}\\big(P_{XY}\\|P_X\\otimes P_Y\\big),",[363,119066,119068,119104,119226,119287,119461],{"className":119067,"ariaHidden":394},[393],[363,119069,119071,119074,119077,119080,119083,119086,119089,119092,119095,119098,119101],{"className":119070},[398],[363,119072],{"className":119073,"style":487},[402],[363,119075,34215],{"className":119076,"style":9234},[407,408],[363,119078,461],{"className":119079},[494],[363,119081,945],{"className":119082,"style":9234},[407,408],[363,119084,34222],{"className":119085},[920],[363,119087],{"className":119088,"style":754},[505],[363,119090,5748],{"className":119091,"style":2934},[407,408],[363,119093,468],{"className":119094},[501],[363,119096],{"className":119097,"style":506},[505],[363,119099,471],{"className":119100},[510],[363,119102],{"className":119103,"style":506},[505],[363,119105,119107,119110,119116,119122,119168,119171,119174,119177,119217,119220,119223],{"className":119106},[398],[363,119108],{"className":119109,"style":20910},[402],[363,119111,119113],{"className":119112},[407],[363,119114,33010],{"className":119115},[407,33009],[363,119117,119119],{"className":119118},[407],[363,119120,461],{"className":119121},[767,10021],[363,119123,119125,119128],{"className":119124},[407],[363,119126,554],{"className":119127,"style":682},[407,408],[363,119129,119131],{"className":119130},[629],[363,119132,119134,119160],{"className":119133},[633,634],[363,119135,119137,119157],{"className":119136},[638],[363,119138,119140],{"className":119139,"style":727},[642],[363,119141,119142,119145],{"style":11483},[363,119143],{"className":119144,"style":651},[650],[363,119146,119148],{"className":119147},[655,656,657,658],[363,119149,119151,119154],{"className":119150},[407,658],[363,119152,945],{"className":119153,"style":9234},[407,408,658],[363,119155,5748],{"className":119156,"style":2934},[407,408,658],[363,119158,666],{"className":119159},[665],[363,119161,119163],{"className":119162},[638],[363,119164,119166],{"className":119165,"style":8315},[642],[363,119167],{},[363,119169],{"className":119170,"style":754},[505],[363,119172,558],{"className":119173},[407],[363,119175],{"className":119176,"style":754},[505],[363,119178,119180,119183],{"className":119179},[407],[363,119181,554],{"className":119182,"style":682},[407,408],[363,119184,119186],{"className":119185},[629],[363,119187,119189,119209],{"className":119188},[633,634],[363,119190,119192,119206],{"className":119191},[638],[363,119193,119195],{"className":119194,"style":727},[642],[363,119196,119197,119200],{"style":11483},[363,119198],{"className":119199,"style":651},[650],[363,119201,119203],{"className":119202},[655,656,657,658],[363,119204,945],{"className":119205,"style":9234},[407,408,658],[363,119207,666],{"className":119208},[665],[363,119210,119212],{"className":119211},[638],[363,119213,119215],{"className":119214,"style":8315},[642],[363,119216],{},[363,119218],{"className":119219,"style":2934},[505],[363,119221,119005],{"className":119222},[2938],[363,119224],{"className":119225,"style":2934},[505],[363,119227,119229,119232,119272,119278,119281,119284],{"className":119228},[398],[363,119230],{"className":119231,"style":20910},[402],[363,119233,119235,119238],{"className":119234},[407],[363,119236,554],{"className":119237,"style":682},[407,408],[363,119239,119241],{"className":119240},[629],[363,119242,119244,119264],{"className":119243},[633,634],[363,119245,119247,119261],{"className":119246},[638],[363,119248,119250],{"className":119249,"style":727},[642],[363,119251,119252,119255],{"style":11483},[363,119253],{"className":119254,"style":651},[650],[363,119256,119258],{"className":119257},[655,656,657,658],[363,119259,5748],{"className":119260,"style":2934},[407,408,658],[363,119262,666],{"className":119263},[665],[363,119265,119267],{"className":119266},[638],[363,119268,119270],{"className":119269,"style":8315},[642],[363,119271],{},[363,119273,119275],{"className":119274},[407],[363,119276,468],{"className":119277},[767,10021],[363,119279],{"className":119280,"style":506},[505],[363,119282,471],{"className":119283},[510],[363,119285],{"className":119286,"style":506},[505],[363,119288,119290,119293,119357,119363,119409,119412,119452,119455,119458],{"className":119289},[398],[363,119291],{"className":119292,"style":20910},[402],[363,119294,119296,119299],{"className":119295},[407],[363,119297,547],{"className":119298,"style":625},[407,408],[363,119300,119302],{"className":119301},[629],[363,119303,119305,119349],{"className":119304},[633,634],[363,119306,119308,119346],{"className":119307},[638],[363,119309,119311],{"className":119310,"style":643},[642],[363,119312,119313,119316],{"style":646},[363,119314],{"className":119315,"style":651},[650],[363,119317,119319],{"className":119318},[655,656,657,658],[363,119320,119322,119325,119328,119340,119343],{"className":119321},[407,658],[363,119323,1116],{"className":119324},[407,408,658],[363,119326],{"className":119327,"style":42713},[505,658],[363,119329,119331,119334,119337],{"className":119330},[1831,658],[363,119332,48005],{"className":119333},[658],[363,119335,48009],{"className":119336},[658],[363,119338,4505],{"className":119339,"style":4504},[658],[363,119341],{"className":119342,"style":42713},[505,658],[363,119344,1116],{"className":119345},[407,408,658],[363,119347,666],{"className":119348},[665],[363,119350,119352],{"className":119351},[638],[363,119353,119355],{"className":119354,"style":673},[642],[363,119356],{},[363,119358,119360],{"className":119359},[407],[363,119361,461],{"className":119362},[767,10021],[363,119364,119366,119369],{"className":119365},[407],[363,119367,554],{"className":119368,"style":682},[407,408],[363,119370,119372],{"className":119371},[629],[363,119373,119375,119401],{"className":119374},[633,634],[363,119376,119378,119398],{"className":119377},[638],[363,119379,119381],{"className":119380,"style":727},[642],[363,119382,119383,119386],{"style":11483},[363,119384],{"className":119385,"style":651},[650],[363,119387,119389],{"className":119388},[655,656,657,658],[363,119390,119392,119395],{"className":119391},[407,658],[363,119393,945],{"className":119394,"style":9234},[407,408,658],[363,119396,5748],{"className":119397,"style":2934},[407,408,658],[363,119399,666],{"className":119400},[665],[363,119402,119404],{"className":119403},[638],[363,119405,119407],{"className":119406,"style":8315},[642],[363,119408],{},[363,119410,558],{"className":119411},[407],[363,119413,119415,119418],{"className":119414},[407],[363,119416,554],{"className":119417,"style":682},[407,408],[363,119419,119421],{"className":119420},[629],[363,119422,119424,119444],{"className":119423},[633,634],[363,119425,119427,119441],{"className":119426},[638],[363,119428,119430],{"className":119429,"style":727},[642],[363,119431,119432,119435],{"style":11483},[363,119433],{"className":119434,"style":651},[650],[363,119436,119438],{"className":119437},[655,656,657,658],[363,119439,945],{"className":119440,"style":9234},[407,408,658],[363,119442,666],{"className":119443},[665],[363,119445,119447],{"className":119446},[638],[363,119448,119450],{"className":119449,"style":8315},[642],[363,119451],{},[363,119453],{"className":119454,"style":2934},[505],[363,119456,119005],{"className":119457},[2938],[363,119459],{"className":119460,"style":2934},[505],[363,119462,119464,119467,119507,119513],{"className":119463},[398],[363,119465],{"className":119466,"style":20910},[402],[363,119468,119470,119473],{"className":119469},[407],[363,119471,554],{"className":119472,"style":682},[407,408],[363,119474,119476],{"className":119475},[629],[363,119477,119479,119499],{"className":119478},[633,634],[363,119480,119482,119496],{"className":119481},[638],[363,119483,119485],{"className":119484,"style":727},[642],[363,119486,119487,119490],{"style":11483},[363,119488],{"className":119489,"style":651},[650],[363,119491,119493],{"className":119492},[655,656,657,658],[363,119494,5748],{"className":119495,"style":2934},[407,408,658],[363,119497,666],{"className":119498},[665],[363,119500,119502],{"className":119501},[638],[363,119503,119505],{"className":119504,"style":8315},[642],[363,119506],{},[363,119508,119510],{"className":119509},[407],[363,119511,468],{"className":119512},[767,10021],[363,119514,898],{"className":119515},[920],[11,119517,119518,119519,119547,119548,119576,119577,119635],{},"因此它是 f-散度的特例。MINE 用 Donsker–Varadhan 对偶估计它，f-MINE 则对一般 ",[363,119520,119522,119535],{"className":119521,"translate":367},[366],[363,119523,119525],{"className":119524},[371],[373,119526,119527],{"xmlns":375},[377,119528,119529,119533],{},[380,119530,119531],{},[383,119532,385],{},[387,119534,385],{"encoding":389},[363,119536,119538],{"className":119537,"ariaHidden":394},[393],[363,119539,119541,119544],{"className":119540},[398],[363,119542],{"className":119543,"style":403},[402],[363,119545,385],{"className":119546,"style":409},[407,408]," 用 4.4 节的对偶；不同 ",[363,119549,119551,119564],{"className":119550,"translate":367},[366],[363,119552,119554],{"className":119553},[371],[373,119555,119556],{"xmlns":375},[377,119557,119558,119562],{},[380,119559,119560],{},[383,119561,385],{},[387,119563,385],{"encoding":389},[363,119565,119567],{"className":119566,"ariaHidden":394},[393],[363,119568,119570,119573],{"className":119569},[398],[363,119571],{"className":119572,"style":403},[402],[363,119574,385],{"className":119575,"style":409},[407,408],"（KL、JS、",[363,119578,119580,119597],{"className":119579,"translate":367},[366],[363,119581,119583],{"className":119582},[371],[373,119584,119585],{"xmlns":375},[377,119586,119587,119595],{},[380,119588,119589],{},[7161,119590,119591,119593],{},[383,119592,37796],{},[463,119594,2810],{},[387,119596,40741],{"encoding":389},[363,119598,119600],{"className":119599,"ariaHidden":394},[393],[363,119601,119603,119606],{"className":119602},[398],[363,119604],{"className":119605,"style":40751},[402],[363,119607,119609,119612],{"className":119608},[407],[363,119610,37796],{"className":119611},[407,408],[363,119613,119615],{"className":119614},[629],[363,119616,119618],{"className":119617},[633],[363,119619,119621],{"className":119620},[638],[363,119622,119624],{"className":119623,"style":20375},[642],[363,119625,119626,119629],{"style":7212},[363,119627],{"className":119628,"style":651},[650],[363,119630,119632],{"className":119631},[655,656,657,658],[363,119633,2810],{"className":119634},[407,658],"）给出不同的「MI 下界」和不同的方差—偏差折衷。对比式学习的 InfoNCE 也是 KL 下界的一种变体。",[2658,119637,119639],{"id":119638},"_74-表示学习","7.4 表示学习",[11,119641,119642,119643,119687],{},"任何表示 ",[363,119644,119646,119666],{"className":119645,"translate":367},[366],[363,119647,119649],{"className":119648},[371],[373,119650,119651],{"xmlns":375},[377,119652,119653,119663],{},[380,119654,119655,119657,119659,119661],{},[383,119656,5739],{},[458,119658,461],{"stretchy":460},[383,119660,945],{},[458,119662,468],{"stretchy":460},[387,119664,119665],{"encoding":389},"T(X)",[363,119667,119669],{"className":119668,"ariaHidden":394},[393],[363,119670,119672,119675,119678,119681,119684],{"className":119671},[398],[363,119673],{"className":119674,"style":487},[402],[363,119676,5739],{"className":119677,"style":682},[407,408],[363,119679,461],{"className":119680},[494],[363,119682,945],{"className":119683,"style":9234},[407,408],[363,119685,468],{"className":119686},[501]," 都满足（4.5 节）",[363,119689,119691],{"className":119690,"translate":367},[528],[363,119692,119694,119774],{"className":119693,"translate":367},[366],[363,119695,119697],{"className":119696},[371],[373,119698,119699],{"xmlns":375,"display":537},[377,119700,119701,119771],{},[380,119702,119703,119709,119711,119725,119727,119741,119743,119745,119751,119753,119759,119761,119767,119769],{},[543,119704,119705,119707],{},[383,119706,547],{},[383,119708,385],{},[458,119710,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[543,119712,119713,119715],{},[383,119714,554],{},[380,119716,119717,119719,119721,119723],{},[383,119718,5739],{},[458,119720,461],{"stretchy":460},[383,119722,945],{},[458,119724,468],{"stretchy":460},[383,119726,558],{"mathvariant":557},[543,119728,119729,119731],{},[383,119730,561],{},[380,119732,119733,119735,119737,119739],{},[383,119734,5739],{},[458,119736,461],{"stretchy":460},[383,119738,945],{},[458,119740,468],{"stretchy":460},[458,119742,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,119744,10299],{},[543,119746,119747,119749],{},[383,119748,547],{},[383,119750,385],{},[458,119752,461],{"stretchy":460},[543,119754,119755,119757],{},[383,119756,554],{},[383,119758,945],{},[383,119760,558],{"mathvariant":557},[543,119762,119763,119765],{},[383,119764,561],{},[383,119766,945],{},[458,119768,468],{"stretchy":460},[458,119770,898],{"separator":394},[387,119772,119773],{"encoding":389},"D_f\\big(P_{T(X)}\\|Q_{T(X)}\\big)\n\\le D_f(P_X\\|Q_X),",[363,119775,119777,119953],{"className":119776,"ariaHidden":394},[393],[363,119778,119780,119784,119824,119830,119883,119886,119938,119944,119947,119950],{"className":119779},[398],[363,119781],{"className":119782,"style":119783},[402],"height:1.2052em;vertical-align:-0.3552em;",[363,119785,119787,119790],{"className":119786},[407],[363,119788,547],{"className":119789,"style":625},[407,408],[363,119791,119793],{"className":119792},[629],[363,119794,119796,119816],{"className":119795},[633,634],[363,119797,119799,119813],{"className":119798},[638],[363,119800,119802],{"className":119801,"style":643},[642],[363,119803,119804,119807],{"style":646},[363,119805],{"className":119806,"style":651},[650],[363,119808,119810],{"className":119809},[655,656,657,658],[363,119811,385],{"className":119812,"style":409},[407,408,658],[363,119814,666],{"className":119815},[665],[363,119817,119819],{"className":119818},[638],[363,119820,119822],{"className":119821,"style":673},[642],[363,119823],{},[363,119825,119827],{"className":119826},[407],[363,119828,461],{"className":119829},[767,10021],[363,119831,119833,119836],{"className":119832},[407],[363,119834,554],{"className":119835,"style":682},[407,408],[363,119837,119839],{"className":119838},[629],[363,119840,119842,119875],{"className":119841},[633,634],[363,119843,119845,119872],{"className":119844},[638],[363,119846,119848],{"className":119847,"style":6445},[642],[363,119849,119851,119854],{"style":119850},"top:-2.5198em;margin-left:-0.1389em;margin-right:0.05em;",[363,119852],{"className":119853,"style":651},[650],[363,119855,119857],{"className":119856},[655,656,657,658],[363,119858,119860,119863,119866,119869],{"className":119859},[407,658],[363,119861,5739],{"className":119862,"style":682},[407,408,658],[363,119864,461],{"className":119865},[494,658],[363,119867,945],{"className":119868,"style":9234},[407,408,658],[363,119870,468],{"className":119871},[501,658],[363,119873,666],{"className":119874},[665],[363,119876,119878],{"className":119877},[638],[363,119879,119881],{"className":119880,"style":6491},[642],[363,119882],{},[363,119884,558],{"className":119885},[407],[363,119887,119889,119892],{"className":119888},[407],[363,119890,561],{"className":119891},[407,408],[363,119893,119895],{"className":119894},[629],[363,119896,119898,119930],{"className":119897},[633,634],[363,119899,119901,119927],{"className":119900},[638],[363,119902,119904],{"className":119903,"style":6445},[642],[363,119905,119906,119909],{"style":75920},[363,119907],{"className":119908,"style":651},[650],[363,119910,119912],{"className":119911},[655,656,657,658],[363,119913,119915,119918,119921,119924],{"className":119914},[407,658],[363,119916,5739],{"className":119917,"style":682},[407,408,658],[363,119919,461],{"className":119920},[494,658],[363,119922,945],{"className":119923,"style":9234},[407,408,658],[363,119925,468],{"className":119926},[501,658],[363,119928,666],{"className":119929},[665],[363,119931,119933],{"className":119932},[638],[363,119934,119936],{"className":119935,"style":6491},[642],[363,119937],{},[363,119939,119941],{"className":119940},[407],[363,119942,468],{"className":119943},[767,10021],[363,119945],{"className":119946,"style":506},[505],[363,119948,10299],{"className":119949},[510],[363,119951],{"className":119952,"style":506},[505],[363,119954,119956,119959,119999,120002,120042,120045,120085,120088],{"className":119955},[398],[363,119957],{"className":119958,"style":618},[402],[363,119960,119962,119965],{"className":119961},[407],[363,119963,547],{"className":119964,"style":625},[407,408],[363,119966,119968],{"className":119967},[629],[363,119969,119971,119991],{"className":119970},[633,634],[363,119972,119974,119988],{"className":119973},[638],[363,119975,119977],{"className":119976,"style":643},[642],[363,119978,119979,119982],{"style":646},[363,119980],{"className":119981,"style":651},[650],[363,119983,119985],{"className":119984},[655,656,657,658],[363,119986,385],{"className":119987,"style":409},[407,408,658],[363,119989,666],{"className":119990},[665],[363,119992,119994],{"className":119993},[638],[363,119995,119997],{"className":119996,"style":673},[642],[363,119998],{},[363,120000,461],{"className":120001},[494],[363,120003,120005,120008],{"className":120004},[407],[363,120006,554],{"className":120007,"style":682},[407,408],[363,120009,120011],{"className":120010},[629],[363,120012,120014,120034],{"className":120013},[633,634],[363,120015,120017,120031],{"className":120016},[638],[363,120018,120020],{"className":120019,"style":727},[642],[363,120021,120022,120025],{"style":11483},[363,120023],{"className":120024,"style":651},[650],[363,120026,120028],{"className":120027},[655,656,657,658],[363,120029,945],{"className":120030,"style":9234},[407,408,658],[363,120032,666],{"className":120033},[665],[363,120035,120037],{"className":120036},[638],[363,120038,120040],{"className":120039,"style":8315},[642],[363,120041],{},[363,120043,558],{"className":120044},[407],[363,120046,120048,120051],{"className":120047},[407],[363,120049,561],{"className":120050},[407,408],[363,120052,120054],{"className":120053},[629],[363,120055,120057,120077],{"className":120056},[633,634],[363,120058,120060,120074],{"className":120059},[638],[363,120061,120063],{"className":120062,"style":727},[642],[363,120064,120065,120068],{"style":730},[363,120066],{"className":120067,"style":651},[650],[363,120069,120071],{"className":120070},[655,656,657,658],[363,120072,945],{"className":120073,"style":9234},[407,408,658],[363,120075,666],{"className":120076},[665],[363,120078,120080],{"className":120079},[638],[363,120081,120083],{"className":120082,"style":8315},[642],[363,120084],{},[363,120086,468],{"className":120087},[501],[363,120089,898],{"className":120090},[920],[11,120092,120093],{},"即「编码不会创造信息」。这为对比学习、域对齐、特征选择提供了可证伪的约束：任何声称「表示后差异更大」的方法都必然在某个环节违反了 DPI，需要解释为什么。",[2658,120095,120097],{"id":120096},"_75-域适应","7.5 域适应",[11,120099,120100,120101,120131,120132,120162],{},"在源域 ",[363,120102,120104,120118],{"className":120103,"translate":367},[366],[363,120105,120107],{"className":120106},[371],[373,120108,120109],{"xmlns":375},[377,120110,120111,120115],{},[380,120112,120113],{},[383,120114,26084],{"mathvariant":944},[387,120116,120117],{"encoding":389},"\\mathcal S",[363,120119,120121],{"className":120120,"ariaHidden":394},[393],[363,120122,120124,120127],{"className":120123},[398],[363,120125],{"className":120126,"style":1011},[402],[363,120128,26084],{"className":120129,"style":120130},[407,971],"margin-right:0.075em;"," 与目标域 ",[363,120133,120135,120149],{"className":120134,"translate":367},[366],[363,120136,120138],{"className":120137},[371],[373,120139,120140],{"xmlns":375},[377,120141,120142,120146],{},[380,120143,120144],{},[383,120145,5739],{"mathvariant":944},[387,120147,120148],{"encoding":389},"\\mathcal T",[363,120150,120152],{"className":120151,"ariaHidden":394},[393],[363,120153,120155,120158],{"className":120154},[398],[363,120156],{"className":120157,"style":1011},[402],[363,120159,5739],{"className":120160,"style":120161},[407,971],"margin-right:0.2542em;"," 上，衡量分布漂移的现代方法（DANN、ADDA）本质上用 f-散度或 IPM 对齐边缘分布；其中用 JS 的（GAN 式）对齐与用 MMD\u002FWasserstein 的对齐，区别正是 6.2 节的几何与支撑问题。",[2658,120164,120166],{"id":120165},"_76-假设检验","7.6 假设检验",[11,120168,120169],{},"f-散度是假设检验的错误指数：",[10374,120171,120172,120239],{},[7012,120173,120174,120177,120178,20313],{},[1572,120175,120176],{},"Stein 引理","：在固定第一类错误下，第二类错误的最优指数为 ",[363,120179,120181,120209],{"className":120180,"translate":367},[366],[363,120182,120184],{"className":120183},[371],[373,120185,120186],{"xmlns":375},[377,120187,120188,120206],{},[380,120189,120190,120196,120198,120200,120202,120204],{},[380,120191,120192,120194],{},[383,120193,11041],{"mathvariant":557},[383,120195,22240],{"mathvariant":557},[458,120197,461],{"stretchy":460},[383,120199,554],{},[383,120201,558],{"mathvariant":557},[383,120203,561],{},[458,120205,468],{"stretchy":460},[387,120207,120208],{"encoding":389},"\\mathrm{KL}(P\\|Q)",[363,120210,120212],{"className":120211,"ariaHidden":394},[393],[363,120213,120215,120218,120224,120227,120230,120233,120236],{"className":120214},[398],[363,120216],{"className":120217,"style":487},[402],[363,120219,120221],{"className":120220},[407],[363,120222,33010],{"className":120223},[407,33009],[363,120225,461],{"className":120226},[494],[363,120228,554],{"className":120229,"style":682},[407,408],[363,120231,558],{"className":120232},[407],[363,120234,561],{"className":120235},[407,408],[363,120237,468],{"className":120238},[501],[7012,120240,120241,9747,120244,120523],{},[1572,120242,120243],{},"Chernoff 信息",[363,120245,120247,120321],{"className":120246,"translate":367},[366],[363,120248,120250],{"className":120249},[371],[373,120251,120252],{"xmlns":375},[377,120253,120254,120318],{},[380,120255,120256,120258,120260,120262,120264,120266,120268,120270,120290,120292,120294,120296,120298,120300,120308,120310,120312,120314,120316],{},[383,120257,39641],{},[458,120259,461],{"stretchy":460},[383,120261,554],{},[458,120263,898],{"separator":394},[383,120265,561],{},[458,120267,468],{"stretchy":460},[458,120269,471],{},[543,120271,120272,120278],{},[380,120273,120274,120276],{},[383,120275,35779],{},[458,120277,4450],{},[380,120279,120280,120282,120284,120286,120288],{},[463,120281,474],{},[458,120283,7598],{},[383,120285,11686],{},[458,120287,7598],{},[463,120289,465],{},[458,120291,461],{"stretchy":460},[463,120293,465],{},[458,120295,5160],{},[383,120297,11686],{},[458,120299,468],{"stretchy":460},[7900,120301,120302,120304,120306],{},[383,120303,547],{},[383,120305,11686],{},[383,120307,1379],{},[458,120309,461],{"stretchy":460},[383,120311,554],{},[383,120313,558],{"mathvariant":557},[383,120315,561],{},[458,120317,468],{"stretchy":460},[387,120319,120320],{"encoding":389},"C(P,Q)=\\sup_{0\u003C\\lambda\u003C1}(1-\\lambda)D^{R}_{\\lambda}(P\\|Q)",[363,120322,120324,120360,120437],{"className":120323,"ariaHidden":394},[393],[363,120325,120327,120330,120333,120336,120339,120342,120345,120348,120351,120354,120357],{"className":120326},[398],[363,120328],{"className":120329,"style":487},[402],[363,120331,39641],{"className":120332,"style":11129},[407,408],[363,120334,461],{"className":120335},[494],[363,120337,554],{"className":120338,"style":682},[407,408],[363,120340,898],{"className":120341},[920],[363,120343],{"className":120344,"style":754},[505],[363,120346,561],{"className":120347},[407,408],[363,120349,468],{"className":120350},[501],[363,120352],{"className":120353,"style":506},[505],[363,120355,471],{"className":120356},[510],[363,120358],{"className":120359,"style":506},[505],[363,120361,120363,120366,120422,120425,120428,120431,120434],{"className":120362},[398],[363,120364],{"className":120365,"style":35903},[402],[363,120367,120369,120372],{"className":120368},[1831],[363,120370,35779],{"className":120371},[1831],[363,120373,120375],{"className":120374},[629],[363,120376,120378,120414],{"className":120377},[633,634],[363,120379,120381,120411],{"className":120380},[638],[363,120382,120385],{"className":120383,"style":120384},[642],"height:0.242em;",[363,120386,120387,120390],{"style":35925},[363,120388],{"className":120389,"style":651},[650],[363,120391,120393],{"className":120392},[655,656,657,658],[363,120394,120396,120399,120402,120405,120408],{"className":120395},[407,658],[363,120397,474],{"className":120398},[407,658],[363,120400,7598],{"className":120401},[510,658],[363,120403,11686],{"className":120404},[407,408,658],[363,120406,7598],{"className":120407},[510,658],[363,120409,465],{"className":120410},[407,658],[363,120412,666],{"className":120413},[665],[363,120415,120417],{"className":120416},[638],[363,120418,120420],{"className":120419,"style":35953},[642],[363,120421],{},[363,120423,461],{"className":120424},[494],[363,120426,465],{"className":120427},[407],[363,120429],{"className":120430,"style":2934},[505],[363,120432,5160],{"className":120433},[2938],[363,120435],{"className":120436,"style":2934},[505],[363,120438,120440,120444,120447,120450,120508,120511,120514,120517,120520],{"className":120439},[398],[363,120441],{"className":120442,"style":120443},[402],"height:1.1244em;vertical-align:-0.2831em;",[363,120445,11686],{"className":120446},[407,408],[363,120448,468],{"className":120449},[501],[363,120451,120453,120456],{"className":120452},[407],[363,120454,547],{"className":120455,"style":625},[407,408],[363,120457,120459],{"className":120458},[629],[363,120460,120462,120500],{"className":120461},[633,634],[363,120463,120465,120497],{"className":120464},[638],[363,120466,120468,120483],{"className":120467,"style":52432},[642],[363,120469,120471,120474],{"style":120470},"top:-2.4169em;margin-left:-0.0278em;margin-right:0.05em;",[363,120472],{"className":120473,"style":651},[650],[363,120475,120477],{"className":120476},[655,656,657,658],[363,120478,120480],{"className":120479},[407,658],[363,120481,11686],{"className":120482},[407,408,658],[363,120484,120485,120488],{"style":7212},[363,120486],{"className":120487,"style":651},[650],[363,120489,120491],{"className":120490},[655,656,657,658],[363,120492,120494],{"className":120493},[407,658],[363,120495,1379],{"className":120496,"style":49946},[407,408,658],[363,120498,666],{"className":120499},[665],[363,120501,120503],{"className":120502},[638],[363,120504,120506],{"className":120505,"style":8894},[642],[363,120507],{},[363,120509,461],{"className":120510},[494],[363,120512,554],{"className":120513,"style":682},[407,408],[363,120515,558],{"className":120516},[407],[363,120518,561],{"className":120519},[407,408],[363,120521,468],{"className":120522},[501],"，即 Rényi\u002Fα-族中的最优点；对称检验的指数由它决定。",[11,120525,120526],{},"因此 f-散度不只是「训练目标」，也是统计判决的极限性能。",[18,120528,120530],{"id":120529},"_8-差分隐私f-dp","8. 差分隐私（f-DP）",[11,120532,120533,120534,120537,120538,6841,120541,120569,120570,120611],{},"一个较新的应用是把 f-散度的语言搬到隐私保护。差分隐私（DP）要求相邻数据集的输出分布「难以区分」。Dong–Roth–Su 提出 ",[1572,120535,120536],{},"f-差分隐私（f-DP）","：用一个",[1572,120539,120540],{},"权衡函数（tradeoff function）",[363,120542,120544,120557],{"className":120543,"translate":367},[366],[363,120545,120547],{"className":120546},[371],[373,120548,120549],{"xmlns":375},[377,120550,120551,120555],{},[380,120552,120553],{},[383,120554,385],{},[387,120556,385],{"encoding":389},[363,120558,120560],{"className":120559,"ariaHidden":394},[393],[363,120561,120563,120566],{"className":120562},[398],[363,120564],{"className":120565,"style":403},[402],[363,120567,385],{"className":120568,"style":409},[407,408]," 刻画两个输出分布 ",[363,120571,120573,120590],{"className":120572,"translate":367},[366],[363,120574,120576],{"className":120575},[371],[373,120577,120578],{"xmlns":375},[377,120579,120580,120588],{},[380,120581,120582,120584,120586],{},[383,120583,554],{},[458,120585,898],{"separator":394},[383,120587,561],{},[387,120589,903],{"encoding":389},[363,120591,120593],{"className":120592,"ariaHidden":394},[393],[363,120594,120596,120599,120602,120605,120608],{"className":120595},[398],[363,120597],{"className":120598,"style":913},[402],[363,120600,554],{"className":120601,"style":682},[407,408],[363,120603,898],{"className":120604},[920],[363,120606],{"className":120607,"style":754},[505],[363,120609,561],{"className":120610},[407,408]," 上「漏报率—误报率」的权衡曲线：",[363,120613,120615],{"className":120614,"translate":367},[528],[363,120616,120618,120715],{"className":120617,"translate":367},[366],[363,120619,120621],{"className":120620},[371],[373,120622,120623],{"xmlns":375,"display":537},[377,120624,120625,120712],{},[380,120626,120627,120629,120631,120633,120635,120637,120639,120641,120643,120645,120647,120658,120660,120662,120664,120666,120668,120670,120672,120674,120676,120678,120680,120682,120684,120686,120688,120690,120692,120694,120696,120698,120700,120702,120704,120706,120708,120710],{},[383,120628,5739],{},[458,120630,461],{"stretchy":460},[383,120632,554],{},[458,120634,898],{"separator":394},[383,120636,561],{},[458,120638,468],{"stretchy":460},[458,120640,461],{"stretchy":460},[383,120642,45101],{},[458,120644,468],{"stretchy":460},[458,120646,471],{},[6363,120648,120649,120656],{},[380,120650,120651,120654],{},[383,120652,120653],{},"inf",[458,120655,4450],{},[383,120657,950],{},[458,120659,3245],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,120661,554],{},[458,120663,461],{"stretchy":460},[383,120665,950],{},[458,120667,468],{"stretchy":460},[1644,120669,4630],{},[458,120671,1362],{},[1644,120673,4630],{},[383,120675,561],{},[458,120677,461],{"stretchy":460},[383,120679,950],{},[458,120681,468],{"stretchy":460},[458,120683,7275],{},[463,120685,465],{},[458,120687,5160],{},[383,120689,45101],{},[458,120691,3255],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,120693,898],{"separator":394},[505,120695],{"width":3609},[383,120697,45101],{},[458,120699,6256],{},[458,120701,578],{"stretchy":460},[463,120703,474],{},[458,120705,898],{"separator":394},[463,120707,465],{},[458,120709,605],{"stretchy":460},[383,120711,4722],{"mathvariant":557},[387,120713,120714],{"encoding":389},"T(P,Q)(\\alpha)\n=\\inf_{A}\\big\\{P(A)\\ :\\ Q(A)\\ge1-\\alpha\\big\\},\n\\qquad \\alpha\\in[0,1] .",[363,120716,120718,120763,120858,120885,120903,120939],{"className":120717,"ariaHidden":394},[393],[363,120719,120721,120724,120727,120730,120733,120736,120739,120742,120745,120748,120751,120754,120757,120760],{"className":120720},[398],[363,120722],{"className":120723,"style":487},[402],[363,120725,5739],{"className":120726,"style":682},[407,408],[363,120728,461],{"className":120729},[494],[363,120731,554],{"className":120732,"style":682},[407,408],[363,120734,898],{"className":120735},[920],[363,120737],{"className":120738,"style":754},[505],[363,120740,561],{"className":120741},[407,408],[363,120743,468],{"className":120744},[501],[363,120746,461],{"className":120747},[494],[363,120749,45101],{"className":120750,"style":45131},[407,408],[363,120752,468],{"className":120753},[501],[363,120755],{"className":120756,"style":506},[505],[363,120758,471],{"className":120759},[510],[363,120761],{"className":120762,"style":506},[505],[363,120764,120766,120770,120822,120825,120831,120834,120837,120840,120843,120846,120849,120852,120855],{"className":120765},[398],[363,120767],{"className":120768,"style":120769},[402],"height:1.5943em;vertical-align:-0.7443em;",[363,120771,120773],{"className":120772},[1831,14063],[363,120774,120776,120813],{"className":120775},[633,634],[363,120777,120779,120810],{"className":120778},[638],[363,120780,120782,120797],{"className":120781,"style":12944},[642],[363,120783,120785,120788],{"style":120784},"top:-2.3557em;margin-left:0em;",[363,120786],{"className":120787,"style":809},[650],[363,120789,120791],{"className":120790},[655,656,657,658],[363,120792,120794],{"className":120793},[407,658],[363,120795,950],{"className":120796},[407,408,658],[363,120798,120799,120802],{"style":12210},[363,120800],{"className":120801,"style":809},[650],[363,120803,120804],{},[363,120805,120807,120808],{"className":120806},[1831],"in",[363,120809,385],{"style":95181},[363,120811,666],{"className":120812},[665],[363,120814,120816],{"className":120815},[638],[363,120817,120820],{"className":120818,"style":120819},[642],"height:0.7443em;",[363,120821],{},[363,120823],{"className":120824,"style":754},[505],[363,120826,120828],{"className":120827},[407],[363,120829,3245],{"className":120830},[767,10021],[363,120832,554],{"className":120833,"style":682},[407,408],[363,120835,461],{"className":120836},[494],[363,120838,950],{"className":120839},[407,408],[363,120841,468],{"className":120842},[501],[363,120844,4630],{"className":120845},[505],[363,120847],{"className":120848,"style":506},[505],[363,120850,1362],{"className":120851},[510],[363,120853,4630],{"className":120854},[505],[363,120856],{"className":120857,"style":506},[505],[363,120859,120861,120864,120867,120870,120873,120876,120879,120882],{"className":120860},[398],[363,120862],{"className":120863,"style":487},[402],[363,120865,561],{"className":120866},[407,408],[363,120868,461],{"className":120869},[494],[363,120871,950],{"className":120872},[407,408],[363,120874,468],{"className":120875},[501],[363,120877],{"className":120878,"style":506},[505],[363,120880,7275],{"className":120881},[510],[363,120883],{"className":120884,"style":506},[505],[363,120886,120888,120891,120894,120897,120900],{"className":120887},[398],[363,120889],{"className":120890,"style":12925},[402],[363,120892,465],{"className":120893},[407],[363,120895],{"className":120896,"style":2934},[505],[363,120898,5160],{"className":120899},[2938],[363,120901],{"className":120902,"style":2934},[505],[363,120904,120906,120909,120912,120918,120921,120924,120927,120930,120933,120936],{"className":120905},[398],[363,120907],{"className":120908,"style":20910},[402],[363,120910,45101],{"className":120911,"style":45131},[407,408],[363,120913,120915],{"className":120914},[407],[363,120916,3255],{"className":120917},[767,10021],[363,120919,898],{"className":120920},[920],[363,120922],{"className":120923,"style":3981},[505],[363,120925],{"className":120926,"style":754},[505],[363,120928,45101],{"className":120929,"style":45131},[407,408],[363,120931],{"className":120932,"style":506},[505],[363,120934,6256],{"className":120935},[510],[363,120937],{"className":120938,"style":506},[505],[363,120940,120942,120945,120948,120951,120954,120957,120960,120963],{"className":120941},[398],[363,120943],{"className":120944,"style":487},[402],[363,120946,578],{"className":120947},[494],[363,120949,474],{"className":120950},[407],[363,120952,898],{"className":120953},[920],[363,120955],{"className":120956,"style":754},[505],[363,120958,465],{"className":120959},[407],[363,120961,605],{"className":120962},[501],[363,120964,4722],{"className":120965},[407],[11,120967,120968,120969,78414,120997,121025,121026,121101,121102,121241],{},"机制 ",[363,120970,120972,120985],{"className":120971,"translate":367},[366],[363,120973,120975],{"className":120974},[371],[373,120976,120977],{"xmlns":375},[377,120978,120979,120983],{},[380,120980,120981],{},[383,120982,25914],{},[387,120984,25914],{"encoding":389},[363,120986,120988],{"className":120987,"ariaHidden":394},[393],[363,120989,120991,120994],{"className":120990},[398],[363,120992],{"className":120993,"style":1011},[402],[363,120995,25914],{"className":120996,"style":25948},[407,408],[363,120998,121000,121013],{"className":120999,"translate":367},[366],[363,121001,121003],{"className":121002},[371],[373,121004,121005],{"xmlns":375},[377,121006,121007,121011],{},[380,121008,121009],{},[383,121010,385],{},[387,121012,385],{"encoding":389},[363,121014,121016],{"className":121015,"ariaHidden":394},[393],[363,121017,121019,121022],{"className":121018},[398],[363,121020],{"className":121021,"style":403},[402],[363,121023,385],{"className":121024,"style":409},[407,408],"-DP，若对所有相邻 ",[363,121027,121029,121051],{"className":121028,"translate":367},[366],[363,121030,121032],{"className":121031},[371],[373,121033,121034],{"xmlns":375},[377,121035,121036,121048],{},[380,121037,121038,121040,121042],{},[383,121039,547],{},[458,121041,898],{"separator":394},[7161,121043,121044,121046],{},[383,121045,547],{},[458,121047,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[387,121049,121050],{"encoding":389},"D,D'",[363,121052,121054],{"className":121053,"ariaHidden":394},[393],[363,121055,121057,121060,121063,121066,121069],{"className":121056},[398],[363,121058],{"className":121059,"style":64508},[402],[363,121061,547],{"className":121062,"style":625},[407,408],[363,121064,898],{"className":121065},[920],[363,121067],{"className":121068,"style":754},[505],[363,121070,121072,121075],{"className":121071},[407],[363,121073,547],{"className":121074,"style":625},[407,408],[363,121076,121078],{"className":121077},[629],[363,121079,121081],{"className":121080},[633],[363,121082,121084],{"className":121083},[638],[363,121085,121087],{"className":121086,"style":7209},[642],[363,121088,121089,121092],{"style":7212},[363,121090],{"className":121091,"style":651},[650],[363,121093,121095],{"className":121094},[655,656,657,658],[363,121096,121098],{"className":121097},[407,658],[363,121099,7167],{"className":121100},[407,658],"，恒有 ",[363,121103,121105,121149],{"className":121104,"translate":367},[366],[363,121106,121108],{"className":121107},[371],[373,121109,121110],{"xmlns":375},[377,121111,121112,121146],{},[380,121113,121114,121116,121118,121120,121122,121124,121126,121128,121130,121132,121138,121140,121142,121144],{},[383,121115,5739],{},[458,121117,461],{"stretchy":460},[383,121119,25914],{},[458,121121,461],{"stretchy":460},[383,121123,547],{},[458,121125,468],{"stretchy":460},[458,121127,898],{"separator":394},[383,121129,25914],{},[458,121131,461],{"stretchy":460},[7161,121133,121134,121136],{},[383,121135,547],{},[458,121137,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,121139,468],{"stretchy":460},[458,121141,468],{"stretchy":460},[458,121143,7275],{},[383,121145,385],{},[387,121147,121148],{"encoding":389},"T(M(D),M(D'))\\ge f",[363,121150,121152,121232],{"className":121151,"ariaHidden":394},[393],[363,121153,121155,121158,121161,121164,121167,121170,121173,121176,121179,121182,121185,121188,121220,121223,121226,121229],{"className":121154},[398],[363,121156],{"className":121157,"style":7190},[402],[363,121159,5739],{"className":121160,"style":682},[407,408],[363,121162,461],{"className":121163},[494],[363,121165,25914],{"className":121166,"style":25948},[407,408],[363,121168,461],{"className":121169},[494],[363,121171,547],{"className":121172,"style":625},[407,408],[363,121174,468],{"className":121175},[501],[363,121177,898],{"className":121178},[920],[363,121180],{"className":121181,"style":754},[505],[363,121183,25914],{"className":121184,"style":25948},[407,408],[363,121186,461],{"className":121187},[494],[363,121189,121191,121194],{"className":121190},[407],[363,121192,547],{"className":121193,"style":625},[407,408],[363,121195,121197],{"className":121196},[629],[363,121198,121200],{"className":121199},[633],[363,121201,121203],{"className":121202},[638],[363,121204,121206],{"className":121205,"style":7209},[642],[363,121207,121208,121211],{"style":7212},[363,121209],{"className":121210,"style":651},[650],[363,121212,121214],{"className":121213},[655,656,657,658],[363,121215,121217],{"className":121216},[407,658],[363,121218,7167],{"className":121219},[407,658],[363,121221,19394],{"className":121222},[501],[363,121224],{"className":121225,"style":506},[505],[363,121227,7275],{"className":121228},[510],[363,121230],{"className":121231,"style":506},[505],[363,121233,121235,121238],{"className":121234},[398],[363,121236],{"className":121237,"style":403},[402],[363,121239,385],{"className":121240,"style":409},[407,408],"。可以证明：",[10374,121243,121244],{},[7012,121245,121246,32436,121249,121321,121322,121370,121371,121399],{},[1572,121247,121248],{},"权衡曲线与 f-散度互相决定。",[363,121250,121252,121282],{"className":121251,"translate":367},[366],[363,121253,121255],{"className":121254},[371],[373,121256,121257],{"xmlns":375},[377,121258,121259,121279],{},[380,121260,121261,121263,121265,121267,121269,121271,121273,121275,121277],{},[383,121262,5739],{},[458,121264,461],{"stretchy":460},[383,121266,554],{},[458,121268,898],{"separator":394},[383,121270,561],{},[458,121272,468],{"stretchy":460},[458,121274,461],{"stretchy":460},[383,121276,45101],{},[458,121278,468],{"stretchy":460},[387,121280,121281],{"encoding":389},"T(P,Q)(\\alpha)",[363,121283,121285],{"className":121284,"ariaHidden":394},[393],[363,121286,121288,121291,121294,121297,121300,121303,121306,121309,121312,121315,121318],{"className":121287},[398],[363,121289],{"className":121290,"style":487},[402],[363,121292,5739],{"className":121293,"style":682},[407,408],[363,121295,461],{"className":121296},[494],[363,121298,554],{"className":121299,"style":682},[407,408],[363,121301,898],{"className":121302},[920],[363,121304],{"className":121305,"style":754},[505],[363,121307,561],{"className":121308},[407,408],[363,121310,468],{"className":121311},[501],[363,121313,461],{"className":121314},[494],[363,121316,45101],{"className":121317,"style":45131},[407,408],[363,121319,468],{"className":121320},[501]," 只依赖似然比 ",[363,121323,121325,121346],{"className":121324,"translate":367},[366],[363,121326,121328],{"className":121327},[371],[373,121329,121330],{"xmlns":375},[377,121331,121332,121344],{},[380,121333,121334,121336,121338,121340,121342],{},[383,121335,592],{},[383,121337,554],{},[383,121339,1288],{"mathvariant":557},[383,121341,592],{},[383,121343,561],{},[387,121345,114988],{"encoding":389},[363,121347,121349],{"className":121348,"ariaHidden":394},[393],[363,121350,121352,121355,121358,121361,121364,121367],{"className":121351},[398],[363,121353],{"className":121354,"style":487},[402],[363,121356,592],{"className":121357},[407,408],[363,121359,554],{"className":121360,"style":682},[407,408],[363,121362,1288],{"className":121363},[407],[363,121365,592],{"className":121366},[407,408],[363,121368,561],{"className":121369},[407,408]," 的分布，因此 ",[363,121372,121374,121387],{"className":121373,"translate":367},[366],[363,121375,121377],{"className":121376},[371],[373,121378,121379],{"xmlns":375},[377,121380,121381,121385],{},[380,121382,121383],{},[383,121384,5739],{},[387,121386,5739],{"encoding":389},[363,121388,121390],{"className":121389,"ariaHidden":394},[393],[363,121391,121393,121396],{"className":121392},[398],[363,121394],{"className":121395,"style":1011},[402],[363,121397,5739],{"className":121398,"style":682},[407,408]," 与\"全体 f-散度\"携带同样的信息。对 hockey-stick 生成元族",[363,121401,121403],{"className":121402,"translate":367},[528],[363,121404,121406,121473],{"className":121405,"translate":367},[366],[363,121407,121409],{"className":121408},[371],[373,121410,121411],{"xmlns":375,"display":537},[377,121412,121413,121470],{},[380,121414,121415,121422,121424,121426,121428,121430,121432,121434,121436,121438,121440,121442,121444,121446,121448,121450,121452,121454,121456,121458,121460,121462,121464,121466,121468],{},[543,121416,121417,121419],{},[383,121418,4505],{},[383,121420,121421],{},"γ",[458,121423,461],{"stretchy":460},[383,121425,1116],{},[458,121427,468],{"stretchy":460},[458,121429,471],{},[383,121431,52734],{},[458,121433,4450],{},[458,121435,3245],{"stretchy":460},[463,121437,474],{},[458,121439,898],{"separator":394},[1644,121441,1646],{},[383,121443,1116],{},[458,121445,5160],{},[383,121447,121421],{},[458,121449,3255],{"stretchy":460},[458,121451,898],{"separator":394},[505,121453],{"width":3609},[383,121455,121421],{},[458,121457,6256],{},[458,121459,578],{"stretchy":460},[463,121461,474],{},[458,121463,898],{"separator":394},[463,121465,465],{},[458,121467,605],{"stretchy":460},[458,121469,898],{"separator":394},[387,121471,121472],{"encoding":389},"g_\\gamma(t)=\\max\\{0,\\,t-\\gamma\\},\n\\qquad \\gamma\\in[0,1],",[363,121474,121476,121541,121577,121610],{"className":121475,"ariaHidden":394},[393],[363,121477,121479,121482,121523,121526,121529,121532,121535,121538],{"className":121478},[398],[363,121480],{"className":121481,"style":618},[402],[363,121483,121485,121488],{"className":121484},[407],[363,121486,4505],{"className":121487,"style":1328},[407,408],[363,121489,121491],{"className":121490},[629],[363,121492,121494,121515],{"className":121493},[633,634],[363,121495,121497,121512],{"className":121496},[638],[363,121498,121500],{"className":121499,"style":45276},[642],[363,121501,121502,121505],{"style":19190},[363,121503],{"className":121504,"style":651},[650],[363,121506,121508],{"className":121507},[655,656,657,658],[363,121509,121421],{"className":121510,"style":121511},[407,408,658],"margin-right:0.0556em;",[363,121513,666],{"className":121514},[665],[363,121516,121518],{"className":121517},[638],[363,121519,121521],{"className":121520,"style":673},[642],[363,121522],{},[363,121524,461],{"className":121525},[494],[363,121527,1116],{"className":121528},[407,408],[363,121530,468],{"className":121531},[501],[363,121533],{"className":121534,"style":506},[505],[363,121536,471],{"className":121537},[510],[363,121539],{"className":121540,"style":506},[505],[363,121542,121544,121547,121550,121553,121556,121559,121562,121565,121568,121571,121574],{"className":121543},[398],[363,121545],{"className":121546,"style":487},[402],[363,121548,52734],{"className":121549},[1831],[363,121551,3245],{"className":121552},[494],[363,121554,474],{"className":121555},[407],[363,121557,898],{"className":121558},[920],[363,121560],{"className":121561,"style":754},[505],[363,121563],{"className":121564,"style":754},[505],[363,121566,1116],{"className":121567},[407,408],[363,121569],{"className":121570,"style":2934},[505],[363,121572,5160],{"className":121573},[2938],[363,121575],{"className":121576,"style":2934},[505],[363,121578,121580,121583,121586,121589,121592,121595,121598,121601,121604,121607],{"className":121579},[398],[363,121581],{"className":121582,"style":487},[402],[363,121584,121421],{"className":121585,"style":121511},[407,408],[363,121587,3255],{"className":121588},[501],[363,121590,898],{"className":121591},[920],[363,121593],{"className":121594,"style":3981},[505],[363,121596],{"className":121597,"style":754},[505],[363,121599,121421],{"className":121600,"style":121511},[407,408],[363,121602],{"className":121603,"style":506},[505],[363,121605,6256],{"className":121606},[510],[363,121608],{"className":121609,"style":506},[505],[363,121611,121613,121616,121619,121622,121625,121628,121631,121634],{"className":121612},[398],[363,121614],{"className":121615,"style":487},[402],[363,121617,578],{"className":121618},[494],[363,121620,474],{"className":121621},[407],[363,121623,898],{"className":121624},[920],[363,121626],{"className":121627,"style":754},[505],[363,121629,465],{"className":121630},[407],[363,121632,605],{"className":121633},[501],[363,121635,898],{"className":121636},[920],[11,121638,121639,121640,121821,121822,9014,121851,121902],{},"（Dong–Roth–Su 的 ",[363,121641,121643,121691],{"className":121642,"translate":367},[366],[363,121644,121646],{"className":121645},[371],[373,121647,121648],{"xmlns":375},[377,121649,121650,121688],{},[380,121651,121652,121658,121660,121662,121664,121666,121668,121670,121672,121674,121676,121678,121680,121682,121684,121686],{},[543,121653,121654,121656],{},[383,121655,39012],{},[383,121657,121421],{},[458,121659,461],{"stretchy":460},[383,121661,1116],{},[458,121663,468],{"stretchy":460},[458,121665,471],{},[383,121667,52734],{},[458,121669,4450],{},[458,121671,3245],{"stretchy":460},[463,121673,474],{},[458,121675,898],{"separator":394},[383,121677,1116],{},[458,121679,5160],{},[463,121681,465],{},[458,121683,2817],{},[383,121685,121421],{},[458,121687,3255],{"stretchy":460},[387,121689,121690],{"encoding":389},"h_\\gamma(t)=\\max\\{0,t-1+\\gamma\\}",[363,121692,121694,121758,121791,121809],{"className":121693,"ariaHidden":394},[393],[363,121695,121697,121700,121740,121743,121746,121749,121752,121755],{"className":121696},[398],[363,121698],{"className":121699,"style":618},[402],[363,121701,121703,121706],{"className":121702},[407],[363,121704,39012],{"className":121705},[407,408],[363,121707,121709],{"className":121708},[629],[363,121710,121712,121732],{"className":121711},[633,634],[363,121713,121715,121729],{"className":121714},[638],[363,121716,121718],{"className":121717,"style":45276},[642],[363,121719,121720,121723],{"style":730},[363,121721],{"className":121722,"style":651},[650],[363,121724,121726],{"className":121725},[655,656,657,658],[363,121727,121421],{"className":121728,"style":121511},[407,408,658],[363,121730,666],{"className":121731},[665],[363,121733,121735],{"className":121734},[638],[363,121736,121738],{"className":121737,"style":673},[642],[363,121739],{},[363,121741,461],{"className":121742},[494],[363,121744,1116],{"className":121745},[407,408],[363,121747,468],{"className":121748},[501],[363,121750],{"className":121751,"style":506},[505],[363,121753,471],{"className":121754},[510],[363,121756],{"className":121757,"style":506},[505],[363,121759,121761,121764,121767,121770,121773,121776,121779,121782,121785,121788],{"className":121760},[398],[363,121762],{"className":121763,"style":487},[402],[363,121765,52734],{"className":121766},[1831],[363,121768,3245],{"className":121769},[494],[363,121771,474],{"className":121772},[407],[363,121774,898],{"className":121775},[920],[363,121777],{"className":121778,"style":754},[505],[363,121780,1116],{"className":121781},[407,408],[363,121783],{"className":121784,"style":2934},[505],[363,121786,5160],{"className":121787},[2938],[363,121789],{"className":121790,"style":2934},[505],[363,121792,121794,121797,121800,121803,121806],{"className":121793},[398],[363,121795],{"className":121796,"style":12925},[402],[363,121798,465],{"className":121799},[407],[363,121801],{"className":121802,"style":2934},[505],[363,121804,2817],{"className":121805},[2938],[363,121807],{"className":121808,"style":2934},[505],[363,121810,121812,121815,121818],{"className":121811},[398],[363,121813],{"className":121814,"style":487},[402],[363,121816,121421],{"className":121817,"style":121511},[407,408],[363,121819,3255],{"className":121820},[501]," 就是把 ",[363,121823,121825,121839],{"className":121824,"translate":367},[366],[363,121826,121828],{"className":121827},[371],[373,121829,121830],{"xmlns":375},[377,121831,121832,121836],{},[380,121833,121834],{},[383,121835,121421],{},[387,121837,121838],{"encoding":389},"\\gamma",[363,121840,121842],{"className":121841,"ariaHidden":394},[393],[363,121843,121845,121848],{"className":121844},[398],[363,121846],{"className":121847,"style":2623},[402],[363,121849,121421],{"className":121850,"style":121511},[407,408],[363,121852,121854,121872],{"className":121853,"translate":367},[366],[363,121855,121857],{"className":121856},[371],[373,121858,121859],{"xmlns":375},[377,121860,121861,121869],{},[380,121862,121863,121865,121867],{},[463,121864,465],{},[458,121866,5160],{},[383,121868,121421],{},[387,121870,121871],{"encoding":389},"1-\\gamma",[363,121873,121875,121893],{"className":121874,"ariaHidden":394},[393],[363,121876,121878,121881,121884,121887,121890],{"className":121877},[398],[363,121879],{"className":121880,"style":12925},[402],[363,121882,465],{"className":121883},[407],[363,121885],{"className":121886,"style":2934},[505],[363,121888,5160],{"className":121889},[2938],[363,121891],{"className":121892,"style":2934},[505],[363,121894,121896,121899],{"className":121895},[398],[363,121897],{"className":121898,"style":2623},[402],[363,121900,121421],{"className":121901,"style":121511},[407,408]," 的同一族），变分表示给出干净的检验集形式：",[363,121904,121906],{"className":121905,"translate":367},[528],[363,121907,121909,121987],{"className":121908,"translate":367},[366],[363,121910,121912],{"className":121911},[371],[373,121913,121914],{"xmlns":375,"display":537},[377,121915,121916,121984],{},[380,121917,121918,121928,121930,121932,121934,121936,121938,121940,121956,121958,121960,121962,121964,121966,121968,121970,121972,121974,121976,121978,121980,121982],{},[543,121919,121920,121922],{},[383,121921,547],{},[543,121923,121924,121926],{},[383,121925,4505],{},[383,121927,121421],{},[458,121929,461],{"stretchy":460},[383,121931,554],{},[383,121933,558],{"mathvariant":557},[383,121935,561],{},[458,121937,468],{"stretchy":460},[458,121939,471],{},[6363,121941,121942,121948],{},[380,121943,121944,121946],{},[383,121945,35779],{},[458,121947,4450],{},[380,121949,121950,121952,121954],{},[383,121951,950],{},[458,121953,6256],{},[383,121955,950],{"mathvariant":944},[458,121957,3245],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,121959,554],{},[458,121961,461],{"stretchy":460},[383,121963,950],{},[458,121965,468],{"stretchy":460},[458,121967,5160],{},[383,121969,121421],{},[1644,121971,1646],{},[383,121973,561],{},[458,121975,461],{"stretchy":460},[383,121977,950],{},[458,121979,468],{"stretchy":460},[458,121981,3255],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,121983,4722],{"mathvariant":557},[387,121985,121986],{"encoding":389},"D_{g_\\gamma}(P\\|Q)\n=\\sup_{A\\in\\mathcal A}\\big\\{P(A)\n-\\gamma\\,Q(A)\\big\\}.",[363,121988,121990,122104,122193],{"className":121989,"ariaHidden":394},[393],[363,121991,121993,121997,122080,122083,122086,122089,122092,122095,122098,122101],{"className":121992},[398],[363,121994],{"className":121995,"style":121996},[402],"height:1.0973em;vertical-align:-0.3473em;",[363,121998,122000,122003],{"className":121999},[407],[363,122001,547],{"className":122002,"style":625},[407,408],[363,122004,122006],{"className":122005},[629],[363,122007,122009,122071],{"className":122008},[633,634],[363,122010,122012,122068],{"className":122011},[638],[363,122013,122015],{"className":122014,"style":45276},[642],[363,122016,122017,122020],{"style":646},[363,122018],{"className":122019,"style":651},[650],[363,122021,122023],{"className":122022},[655,656,657,658],[363,122024,122026],{"className":122025},[407,658],[363,122027,122029,122032],{"className":122028},[407,658],[363,122030,4505],{"className":122031,"style":1328},[407,408,658],[363,122033,122035],{"className":122034},[629],[363,122036,122038,122059],{"className":122037},[633,634],[363,122039,122041,122056],{"className":122040},[638],[363,122042,122044],{"className":122043,"style":74609},[642],[363,122045,122047,122050],{"style":122046},"top:-2.357em;margin-left:-0.0359em;margin-right:0.0714em;",[363,122048],{"className":122049,"style":30553},[650],[363,122051,122053],{"className":122052},[655,30557,10021,658],[363,122054,121421],{"className":122055,"style":121511},[407,408,658],[363,122057,666],{"className":122058},[665],[363,122060,122062],{"className":122061},[638],[363,122063,122066],{"className":122064,"style":122065},[642],"height:0.2819em;",[363,122067],{},[363,122069,666],{"className":122070},[665],[363,122072,122074],{"className":122073},[638],[363,122075,122078],{"className":122076,"style":122077},[642],"height:0.3473em;",[363,122079],{},[363,122081,461],{"className":122082},[494],[363,122084,554],{"className":122085,"style":682},[407,408],[363,122087,558],{"className":122088},[407],[363,122090,561],{"className":122091},[407,408],[363,122093,468],{"className":122094},[501],[363,122096],{"className":122097,"style":506},[505],[363,122099,471],{"className":122100},[510],[363,122102],{"className":122103,"style":506},[505],[363,122105,122107,122110,122163,122166,122172,122175,122178,122181,122184,122187,122190],{"className":122106},[398],[363,122108],{"className":122109,"style":36700},[402],[363,122111,122113],{"className":122112},[1831,14063],[363,122114,122116,122155],{"className":122115},[633,634],[363,122117,122119,122152],{"className":122118},[638],[363,122120,122122,122142],{"className":122121,"style":2692},[642],[363,122123,122124,122127],{"style":36715},[363,122125],{"className":122126,"style":809},[650],[363,122128,122130],{"className":122129},[655,656,657,658],[363,122131,122133,122136,122139],{"className":122132},[407,658],[363,122134,950],{"className":122135},[407,408,658],[363,122137,6256],{"className":122138},[510,658],[363,122140,950],{"className":122141},[407,971,658],[363,122143,122144,122147],{"style":12210},[363,122145],{"className":122146,"style":809},[650],[363,122148,122149],{},[363,122150,35779],{"className":122151},[1831],[363,122153,666],{"className":122154},[665],[363,122156,122158],{"className":122157},[638],[363,122159,122161],{"className":122160,"style":36753},[642],[363,122162],{},[363,122164],{"className":122165,"style":754},[505],[363,122167,122169],{"className":122168},[407],[363,122170,3245],{"className":122171},[767,10021],[363,122173,554],{"className":122174,"style":682},[407,408],[363,122176,461],{"className":122177},[494],[363,122179,950],{"className":122180},[407,408],[363,122182,468],{"className":122183},[501],[363,122185],{"className":122186,"style":2934},[505],[363,122188,5160],{"className":122189},[2938],[363,122191],{"className":122192,"style":2934},[505],[363,122194,122196,122199,122202,122205,122208,122211,122214,122217,122223],{"className":122195},[398],[363,122197],{"className":122198,"style":20910},[402],[363,122200,121421],{"className":122201,"style":121511},[407,408],[363,122203],{"className":122204,"style":754},[505],[363,122206,561],{"className":122207},[407,408],[363,122209,461],{"className":122210},[494],[363,122212,950],{"className":122213},[407,408],[363,122215,468],{"className":122216},[501],[363,122218,122220],{"className":122219},[407],[363,122221,3255],{"className":122222},[767,10021],[363,122224,4722],{"className":122225},[407],[11,122227,122228,122230,122231,122305,122306,2627,122475,122503,122504,122597],{},[1572,122229,107624],{}," 一方面，任意 ",[363,122232,122234,122256],{"className":122233,"translate":367},[366],[363,122235,122237],{"className":122236},[371],[373,122238,122239],{"xmlns":375},[377,122240,122241,122253],{},[380,122242,122243,122245,122247,122249,122251],{},[463,122244,474],{},[458,122246,10299],{},[383,122248,4505],{},[458,122250,10299],{},[463,122252,465],{},[387,122254,122255],{"encoding":389},"0\\le g\\le1",[363,122257,122259,122278,122296],{"className":122258,"ariaHidden":394},[393],[363,122260,122262,122266,122269,122272,122275],{"className":122261},[398],[363,122263],{"className":122264,"style":122265},[402],"height:0.7804em;vertical-align:-0.136em;",[363,122267,474],{"className":122268},[407],[363,122270],{"className":122271,"style":506},[505],[363,122273,10299],{"className":122274},[510],[363,122276],{"className":122277,"style":506},[505],[363,122279,122281,122284,122287,122290,122293],{"className":122280},[398],[363,122282],{"className":122283,"style":15764},[402],[363,122285,4505],{"className":122286,"style":1328},[407,408],[363,122288],{"className":122289,"style":506},[505],[363,122291,10299],{"className":122292},[510],[363,122294],{"className":122295,"style":506},[505],[363,122297,122299,122302],{"className":122298},[398],[363,122300],{"className":122301,"style":520},[402],[363,122303,465],{"className":122304},[407]," 可写为指示函数的线性组合（层叠公式），而 ",[363,122307,122309,122349],{"className":122308,"translate":367},[366],[363,122310,122312],{"className":122311},[371],[373,122313,122314],{"xmlns":375},[377,122315,122316,122346],{},[380,122317,122318,122324,122326,122328,122330,122332,122334,122340,122342,122344],{},[543,122319,122320,122322],{},[383,122321,571],{},[383,122323,554],{},[458,122325,578],{"stretchy":460},[383,122327,4505],{},[458,122329,605],{"stretchy":460},[458,122331,5160],{},[383,122333,121421],{},[543,122335,122336,122338],{},[383,122337,571],{},[383,122339,561],{},[458,122341,578],{"stretchy":460},[383,122343,4505],{},[458,122345,605],{"stretchy":460},[387,122347,122348],{"encoding":389},"E_P[g]-\\gamma E_Q[g]",[363,122350,122352,122417],{"className":122351,"ariaHidden":394},[393],[363,122353,122355,122358,122399,122402,122405,122408,122411,122414],{"className":122354},[398],[363,122356],{"className":122357,"style":487},[402],[363,122359,122361,122364],{"className":122360},[407],[363,122362,571],{"className":122363,"style":26208},[407,408],[363,122365,122367],{"className":122366},[629],[363,122368,122370,122391],{"className":122369},[633,634],[363,122371,122373,122388],{"className":122372},[638],[363,122374,122376],{"className":122375,"style":727},[642],[363,122377,122379,122382],{"style":122378},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[363,122380],{"className":122381,"style":651},[650],[363,122383,122385],{"className":122384},[655,656,657,658],[363,122386,554],{"className":122387,"style":682},[407,408,658],[363,122389,666],{"className":122390},[665],[363,122392,122394],{"className":122393},[638],[363,122395,122397],{"className":122396,"style":8315},[642],[363,122398],{},[363,122400,578],{"className":122401},[494],[363,122403,4505],{"className":122404,"style":1328},[407,408],[363,122406,605],{"className":122407},[501],[363,122409],{"className":122410,"style":2934},[505],[363,122412,5160],{"className":122413},[2938],[363,122415],{"className":122416,"style":2934},[505],[363,122418,122420,122423,122426,122466,122469,122472],{"className":122419},[398],[363,122421],{"className":122422,"style":618},[402],[363,122424,121421],{"className":122425,"style":121511},[407,408],[363,122427,122429,122432],{"className":122428},[407],[363,122430,571],{"className":122431,"style":26208},[407,408],[363,122433,122435],{"className":122434},[629],[363,122436,122438,122458],{"className":122437},[633,634],[363,122439,122441,122455],{"className":122440},[638],[363,122442,122444],{"className":122443,"style":727},[642],[363,122445,122446,122449],{"style":122378},[363,122447],{"className":122448,"style":651},[650],[363,122450,122452],{"className":122451},[655,656,657,658],[363,122453,561],{"className":122454},[407,408,658],[363,122456,666],{"className":122457},[665],[363,122459,122461],{"className":122460},[638],[363,122462,122464],{"className":122463,"style":673},[642],[363,122465],{},[363,122467,578],{"className":122468},[494],[363,122470,4505],{"className":122471,"style":1328},[407,408],[363,122473,605],{"className":122474},[501],[363,122476,122478,122491],{"className":122477,"translate":367},[366],[363,122479,122481],{"className":122480},[371],[373,122482,122483],{"xmlns":375},[377,122484,122485,122489],{},[380,122486,122487],{},[383,122488,4505],{},[387,122490,4505],{"encoding":389},[363,122492,122494],{"className":122493,"ariaHidden":394},[393],[363,122495,122497,122500],{"className":122496},[398],[363,122498],{"className":122499,"style":2623},[402],[363,122501,4505],{"className":122502,"style":1328},[407,408]," 的线性泛函，故其上确界在指示函数 ",[363,122505,122507,122529],{"className":122506,"translate":367},[366],[363,122508,122510],{"className":122509},[371],[373,122511,122512],{"xmlns":375},[377,122513,122514,122526],{},[380,122515,122516,122518,122520],{},[383,122517,4505],{},[458,122519,471],{},[543,122521,122522,122524],{},[463,122523,465],{"mathvariant":75560},[383,122525,950],{},[387,122527,122528],{"encoding":389},"g=\\mathbf1_A",[363,122530,122532,122550],{"className":122531,"ariaHidden":394},[393],[363,122533,122535,122538,122541,122544,122547],{"className":122534},[398],[363,122536],{"className":122537,"style":2623},[402],[363,122539,4505],{"className":122540,"style":1328},[407,408],[363,122542],{"className":122543,"style":506},[505],[363,122545,471],{"className":122546},[510],[363,122548],{"className":122549,"style":506},[505],[363,122551,122553,122557],{"className":122552},[398],[363,122554],{"className":122555,"style":122556},[402],"height:0.7944em;vertical-align:-0.15em;",[363,122558,122560,122563],{"className":122559},[407],[363,122561,465],{"className":122562},[407,75905],[363,122564,122566],{"className":122565},[629],[363,122567,122569,122589],{"className":122568},[633,634],[363,122570,122572,122586],{"className":122571},[638],[363,122573,122575],{"className":122574,"style":727},[642],[363,122576,122577,122580],{"style":730},[363,122578],{"className":122579,"style":651},[650],[363,122581,122583],{"className":122582},[655,656,657,658],[363,122584,950],{"className":122585},[407,408,658],[363,122587,666],{"className":122588},[665],[363,122590,122592],{"className":122591},[638],[363,122593,122595],{"className":122594,"style":8315},[642],[363,122596],{}," 上达到：",[363,122599,122601],{"className":122600,"translate":367},[528],[363,122602,122604,122706],{"className":122603,"translate":367},[366],[363,122605,122607],{"className":122606},[371],[373,122608,122609],{"xmlns":375,"display":537},[377,122610,122611,122703],{},[380,122612,122613,122633,122635,122641,122643,122645,122647,122649,122651,122657,122659,122661,122663,122665,122667,122677,122679,122681,122683,122685,122687,122689,122691,122693,122695,122697,122699,122701],{},[6363,122614,122615,122621],{},[380,122616,122617,122619],{},[383,122618,35779],{},[458,122620,4450],{},[380,122622,122623,122625,122627,122629,122631],{},[463,122624,474],{},[458,122626,10299],{},[383,122628,4505],{},[458,122630,10299],{},[463,122632,465],{},[458,122634,3245],{"stretchy":460},[543,122636,122637,122639],{},[383,122638,571],{},[383,122640,554],{},[458,122642,578],{"stretchy":460},[383,122644,4505],{},[458,122646,605],{"stretchy":460},[458,122648,5160],{},[383,122650,121421],{},[543,122652,122653,122655],{},[383,122654,571],{},[383,122656,561],{},[458,122658,578],{"stretchy":460},[383,122660,4505],{},[458,122662,605],{"stretchy":460},[458,122664,3255],{"stretchy":460},[458,122666,471],{},[6363,122668,122669,122675],{},[380,122670,122671,122673],{},[383,122672,35779],{},[458,122674,4450],{},[383,122676,950],{},[458,122678,3245],{"stretchy":460},[383,122680,554],{},[458,122682,461],{"stretchy":460},[383,122684,950],{},[458,122686,468],{"stretchy":460},[458,122688,5160],{},[383,122690,121421],{},[383,122692,561],{},[458,122694,461],{"stretchy":460},[383,122696,950],{},[458,122698,468],{"stretchy":460},[458,122700,3255],{"stretchy":460},[458,122702,898],{"separator":394},[387,122704,122705],{"encoding":389},"\\sup_{0\\le g\\le1}\\{E_P[g]-\\gamma E_Q[g]\\}\n=\\sup_{A}\\{P(A)-\\gamma Q(A)\\},",[363,122707,122709,122837,122905,122984],{"className":122708,"ariaHidden":394},[393],[363,122710,122712,122716,122776,122779,122819,122822,122825,122828,122831,122834],{"className":122711},[398],[363,122713],{"className":122714,"style":122715},[402],"height:1.7977em;vertical-align:-1.0477em;",[363,122717,122719],{"className":122718},[1831,14063],[363,122720,122722,122767],{"className":122721},[633,634],[363,122723,122725,122764],{"className":122724},[638],[363,122726,122728,122754],{"className":122727,"style":2692},[642],[363,122729,122730,122733],{"style":61269},[363,122731],{"className":122732,"style":809},[650],[363,122734,122736],{"className":122735},[655,656,657,658],[363,122737,122739,122742,122745,122748,122751],{"className":122738},[407,658],[363,122740,474],{"className":122741},[407,658],[363,122743,10299],{"className":122744},[510,658],[363,122746,4505],{"className":122747,"style":1328},[407,408,658],[363,122749,10299],{"className":122750},[510,658],[363,122752,465],{"className":122753},[407,658],[363,122755,122756,122759],{"style":12210},[363,122757],{"className":122758,"style":809},[650],[363,122760,122761],{},[363,122762,35779],{"className":122763},[1831],[363,122765,666],{"className":122766},[665],[363,122768,122770],{"className":122769},[638],[363,122771,122774],{"className":122772,"style":122773},[642],"height:1.0477em;",[363,122775],{},[363,122777,3245],{"className":122778},[494],[363,122780,122782,122785],{"className":122781},[407],[363,122783,571],{"className":122784,"style":26208},[407,408],[363,122786,122788],{"className":122787},[629],[363,122789,122791,122811],{"className":122790},[633,634],[363,122792,122794,122808],{"className":122793},[638],[363,122795,122797],{"className":122796,"style":727},[642],[363,122798,122799,122802],{"style":122378},[363,122800],{"className":122801,"style":651},[650],[363,122803,122805],{"className":122804},[655,656,657,658],[363,122806,554],{"className":122807,"style":682},[407,408,658],[363,122809,666],{"className":122810},[665],[363,122812,122814],{"className":122813},[638],[363,122815,122817],{"className":122816,"style":8315},[642],[363,122818],{},[363,122820,578],{"className":122821},[494],[363,122823,4505],{"className":122824,"style":1328},[407,408],[363,122826,605],{"className":122827},[501],[363,122829],{"className":122830,"style":2934},[505],[363,122832,5160],{"className":122833},[2938],[363,122835],{"className":122836,"style":2934},[505],[363,122838,122840,122843,122846,122886,122889,122892,122896,122899,122902],{"className":122839},[398],[363,122841],{"className":122842,"style":618},[402],[363,122844,121421],{"className":122845,"style":121511},[407,408],[363,122847,122849,122852],{"className":122848},[407],[363,122850,571],{"className":122851,"style":26208},[407,408],[363,122853,122855],{"className":122854},[629],[363,122856,122858,122878],{"className":122857},[633,634],[363,122859,122861,122875],{"className":122860},[638],[363,122862,122864],{"className":122863,"style":727},[642],[363,122865,122866,122869],{"style":122378},[363,122867],{"className":122868,"style":651},[650],[363,122870,122872],{"className":122871},[655,656,657,658],[363,122873,561],{"className":122874},[407,408,658],[363,122876,666],{"className":122877},[665],[363,122879,122881],{"className":122880},[638],[363,122882,122884],{"className":122883,"style":673},[642],[363,122885],{},[363,122887,578],{"className":122888},[494],[363,122890,4505],{"className":122891,"style":1328},[407,408],[363,122893,122895],{"className":122894},[501],"]}",[363,122897],{"className":122898,"style":506},[505],[363,122900,471],{"className":122901},[510],[363,122903],{"className":122904,"style":506},[505],[363,122906,122908,122912,122960,122963,122966,122969,122972,122975,122978,122981],{"className":122907},[398],[363,122909],{"className":122910,"style":122911},[402],"height:1.6888em;vertical-align:-0.9388em;",[363,122913,122915],{"className":122914},[1831,14063],[363,122916,122918,122951],{"className":122917},[633,634],[363,122919,122921,122948],{"className":122920},[638],[363,122922,122924,122938],{"className":122923,"style":2692},[642],[363,122925,122926,122929],{"style":36715},[363,122927],{"className":122928,"style":809},[650],[363,122930,122932],{"className":122931},[655,656,657,658],[363,122933,122935],{"className":122934},[407,658],[363,122936,950],{"className":122937},[407,408,658],[363,122939,122940,122943],{"style":12210},[363,122941],{"className":122942,"style":809},[650],[363,122944,122945],{},[363,122946,35779],{"className":122947},[1831],[363,122949,666],{"className":122950},[665],[363,122952,122954],{"className":122953},[638],[363,122955,122958],{"className":122956,"style":122957},[642],"height:0.9388em;",[363,122959],{},[363,122961,3245],{"className":122962},[494],[363,122964,554],{"className":122965,"style":682},[407,408],[363,122967,461],{"className":122968},[494],[363,122970,950],{"className":122971},[407,408],[363,122973,468],{"className":122974},[501],[363,122976],{"className":122977,"style":2934},[505],[363,122979,5160],{"className":122980},[2938],[363,122982],{"className":122983,"style":2934},[505],[363,122985,122987,122990,122993,122996,122999,123002,123005],{"className":122986},[398],[363,122988],{"className":122989,"style":487},[402],[363,122991,121421],{"className":122992,"style":121511},[407,408],[363,122994,561],{"className":122995},[407,408],[363,122997,461],{"className":122998},[494],[363,123000,950],{"className":123001},[407,408],[363,123003,61346],{"className":123004},[501],[363,123006,898],{"className":123007},[920],[11,123009,123010,123011,123184,123185,19055,123331,123446,123447,123595,123596,123882],{},"且由 ",[363,123012,123014,123056],{"className":123013,"translate":367},[366],[363,123015,123017],{"className":123016},[371],[373,123018,123019],{"xmlns":375},[377,123020,123021,123053],{},[380,123022,123023,123029,123031,123033,123035,123037,123043,123045,123047,123049,123051],{},[543,123024,123025,123027],{},[383,123026,571],{},[383,123028,554],{},[458,123030,578],{"stretchy":460},[383,123032,4505],{},[458,123034,605],{"stretchy":460},[458,123036,471],{},[543,123038,123039,123041],{},[383,123040,571],{},[383,123042,561],{},[458,123044,578],{"stretchy":460},[383,123046,4505],{},[1644,123048,1646],{},[383,123050,1116],{},[458,123052,605],{"stretchy":460},[387,123054,123055],{"encoding":389},"E_P[g]=E_Q[g\\,t]",[363,123057,123059,123123],{"className":123058,"ariaHidden":394},[393],[363,123060,123062,123065,123105,123108,123111,123114,123117,123120],{"className":123061},[398],[363,123063],{"className":123064,"style":487},[402],[363,123066,123068,123071],{"className":123067},[407],[363,123069,571],{"className":123070,"style":26208},[407,408],[363,123072,123074],{"className":123073},[629],[363,123075,123077,123097],{"className":123076},[633,634],[363,123078,123080,123094],{"className":123079},[638],[363,123081,123083],{"className":123082,"style":727},[642],[363,123084,123085,123088],{"style":122378},[363,123086],{"className":123087,"style":651},[650],[363,123089,123091],{"className":123090},[655,656,657,658],[363,123092,554],{"className":123093,"style":682},[407,408,658],[363,123095,666],{"className":123096},[665],[363,123098,123100],{"className":123099},[638],[363,123101,123103],{"className":123102,"style":8315},[642],[363,123104],{},[363,123106,578],{"className":123107},[494],[363,123109,4505],{"className":123110,"style":1328},[407,408],[363,123112,605],{"className":123113},[501],[363,123115],{"className":123116,"style":506},[505],[363,123118,471],{"className":123119},[510],[363,123121],{"className":123122,"style":506},[505],[363,123124,123126,123129,123169,123172,123175,123178,123181],{"className":123125},[398],[363,123127],{"className":123128,"style":618},[402],[363,123130,123132,123135],{"className":123131},[407],[363,123133,571],{"className":123134,"style":26208},[407,408],[363,123136,123138],{"className":123137},[629],[363,123139,123141,123161],{"className":123140},[633,634],[363,123142,123144,123158],{"className":123143},[638],[363,123145,123147],{"className":123146,"style":727},[642],[363,123148,123149,123152],{"style":122378},[363,123150],{"className":123151,"style":651},[650],[363,123153,123155],{"className":123154},[655,656,657,658],[363,123156,561],{"className":123157},[407,408,658],[363,123159,666],{"className":123160},[665],[363,123162,123164],{"className":123163},[638],[363,123165,123167],{"className":123166,"style":673},[642],[363,123168],{},[363,123170,578],{"className":123171},[494],[363,123173,4505],{"className":123174,"style":1328},[407,408],[363,123176],{"className":123177,"style":754},[505],[363,123179,1116],{"className":123180},[407,408],[363,123182,605],{"className":123183},[501],"，左端点态上确界为 ",[363,123186,123188,123224],{"className":123187,"translate":367},[366],[363,123189,123191],{"className":123190},[371],[373,123192,123193],{"xmlns":375},[377,123194,123195,123221],{},[380,123196,123197,123203,123205,123207,123209,123211,123213,123219],{},[543,123198,123199,123201],{},[383,123200,571],{},[383,123202,561],{},[458,123204,578],{"stretchy":460},[458,123206,461],{"stretchy":460},[383,123208,1116],{},[458,123210,5160],{},[383,123212,121421],{},[7161,123214,123215,123217],{},[458,123216,468],{"stretchy":460},[458,123218,2817],{},[458,123220,605],{"stretchy":460},[387,123222,123223],{"encoding":389},"E_Q[(t-\\gamma)^+]",[363,123225,123227,123289],{"className":123226,"ariaHidden":394},[393],[363,123228,123230,123233,123273,123277,123280,123283,123286],{"className":123229},[398],[363,123231],{"className":123232,"style":618},[402],[363,123234,123236,123239],{"className":123235},[407],[363,123237,571],{"className":123238,"style":26208},[407,408],[363,123240,123242],{"className":123241},[629],[363,123243,123245,123265],{"className":123244},[633,634],[363,123246,123248,123262],{"className":123247},[638],[363,123249,123251],{"className":123250,"style":727},[642],[363,123252,123253,123256],{"style":122378},[363,123254],{"className":123255,"style":651},[650],[363,123257,123259],{"className":123258},[655,656,657,658],[363,123260,561],{"className":123261},[407,408,658],[363,123263,666],{"className":123264},[665],[363,123266,123268],{"className":123267},[638],[363,123269,123271],{"className":123270,"style":673},[642],[363,123272],{},[363,123274,123276],{"className":123275},[494],"[(",[363,123278,1116],{"className":123279},[407,408],[363,123281],{"className":123282,"style":2934},[505],[363,123284,5160],{"className":123285},[2938],[363,123287],{"className":123288,"style":2934},[505],[363,123290,123292,123296,123299,123328],{"className":123291},[398],[363,123293],{"className":123294,"style":123295},[402],"height:1.0213em;vertical-align:-0.25em;",[363,123297,121421],{"className":123298,"style":121511},[407,408],[363,123300,123302,123305],{"className":123301},[501],[363,123303,468],{"className":123304},[501],[363,123306,123308],{"className":123307},[629],[363,123309,123311],{"className":123310},[633],[363,123312,123314],{"className":123313},[638],[363,123315,123317],{"className":123316,"style":21356},[642],[363,123318,123319,123322],{"style":7212},[363,123320],{"className":123321,"style":651},[650],[363,123323,123325],{"className":123324},[655,656,657,658],[363,123326,2817],{"className":123327},[2938,658],[363,123329,605],{"className":123330},[501],[363,123332,123334,123356],{"className":123333,"translate":367},[366],[363,123335,123337],{"className":123336},[371],[373,123338,123339],{"xmlns":375},[377,123340,123341,123353],{},[380,123342,123343],{},[543,123344,123345,123347],{},[383,123346,547],{},[543,123348,123349,123351],{},[383,123350,4505],{},[383,123352,121421],{},[387,123354,123355],{"encoding":389},"D_{g_\\gamma}",[363,123357,123359],{"className":123358,"ariaHidden":394},[393],[363,123360,123362,123366],{"className":123361},[398],[363,123363],{"className":123364,"style":123365},[402],"height:1.0307em;vertical-align:-0.3473em;",[363,123367,123369,123372],{"className":123368},[407],[363,123370,547],{"className":123371,"style":625},[407,408],[363,123373,123375],{"className":123374},[629],[363,123376,123378,123438],{"className":123377},[633,634],[363,123379,123381,123435],{"className":123380},[638],[363,123382,123384],{"className":123383,"style":45276},[642],[363,123385,123386,123389],{"style":646},[363,123387],{"className":123388,"style":651},[650],[363,123390,123392],{"className":123391},[655,656,657,658],[363,123393,123395],{"className":123394},[407,658],[363,123396,123398,123401],{"className":123397},[407,658],[363,123399,4505],{"className":123400,"style":1328},[407,408,658],[363,123402,123404],{"className":123403},[629],[363,123405,123407,123427],{"className":123406},[633,634],[363,123408,123410,123424],{"className":123409},[638],[363,123411,123413],{"className":123412,"style":74609},[642],[363,123414,123415,123418],{"style":122046},[363,123416],{"className":123417,"style":30553},[650],[363,123419,123421],{"className":123420},[655,30557,10021,658],[363,123422,121421],{"className":123423,"style":121511},[407,408,658],[363,123425,666],{"className":123426},[665],[363,123428,123430],{"className":123429},[638],[363,123431,123433],{"className":123432,"style":122065},[642],[363,123434],{},[363,123436,666],{"className":123437},[665],[363,123439,123441],{"className":123440},[638],[363,123442,123444],{"className":123443,"style":122077},[642],[363,123445],{},"。另一方面取 ",[363,123448,123450,123486],{"className":123449,"translate":367},[366],[363,123451,123453],{"className":123452},[371],[373,123454,123455],{"xmlns":375},[377,123456,123457,123483],{},[380,123458,123459,123465,123467],{},[7161,123460,123461,123463],{},[383,123462,4505],{},[458,123464,7920],{},[458,123466,471],{},[543,123468,123469,123471],{},[463,123470,465],{"mathvariant":75560},[380,123472,123473,123475,123477,123479,123481],{},[458,123474,3245],{"stretchy":460},[383,123476,1116],{},[458,123478,3250],{},[383,123480,121421],{},[458,123482,3255],{"stretchy":460},[387,123484,123485],{"encoding":389},"g^*=\\mathbf 1_{\\{t>\\gamma\\}}",[363,123487,123489,123533],{"className":123488,"ariaHidden":394},[393],[363,123490,123492,123495,123524,123527,123530],{"className":123491},[398],[363,123493],{"className":123494,"style":64362},[402],[363,123496,123498,123501],{"className":123497},[407],[363,123499,4505],{"className":123500,"style":1328},[407,408],[363,123502,123504],{"className":123503},[629],[363,123505,123507],{"className":123506},[633],[363,123508,123510],{"className":123509},[638],[363,123511,123513],{"className":123512,"style":8846},[642],[363,123514,123515,123518],{"style":7212},[363,123516],{"className":123517,"style":651},[650],[363,123519,123521],{"className":123520},[655,656,657,658],[363,123522,7920],{"className":123523},[2938,658],[363,123525],{"className":123526,"style":506},[505],[363,123528,471],{"className":123529},[510],[363,123531],{"className":123532,"style":506},[505],[363,123534,123536,123540],{"className":123535},[398],[363,123537],{"className":123538,"style":123539},[402],"height:0.9996em;vertical-align:-0.3552em;",[363,123541,123543,123546],{"className":123542},[407],[363,123544,465],{"className":123545},[407,75905],[363,123547,123549],{"className":123548},[629],[363,123550,123552,123587],{"className":123551},[633,634],[363,123553,123555,123584],{"className":123554},[638],[363,123556,123558],{"className":123557,"style":6445},[642],[363,123559,123560,123563],{"style":75920},[363,123561],{"className":123562,"style":651},[650],[363,123564,123566],{"className":123565},[655,656,657,658],[363,123567,123569,123572,123575,123578,123581],{"className":123568},[407,658],[363,123570,3245],{"className":123571},[494,658],[363,123573,1116],{"className":123574},[407,408,658],[363,123576,3250],{"className":123577},[510,658],[363,123579,121421],{"className":123580,"style":121511},[407,408,658],[363,123582,3255],{"className":123583},[501,658],[363,123585,666],{"className":123586},[665],[363,123588,123590],{"className":123589},[638],[363,123591,123593],{"className":123592,"style":6491},[642],[363,123594],{}," 恰有 ",[363,123597,123599,123663],{"className":123598,"translate":367},[366],[363,123600,123602],{"className":123601},[371],[373,123603,123604],{"xmlns":375},[377,123605,123606,123660],{},[380,123607,123608,123614,123616,123622,123624,123626,123628,123630,123632,123634,123636,123642,123644,123646,123648,123650,123652,123658],{},[543,123609,123610,123612],{},[383,123611,571],{},[383,123613,561],{},[458,123615,578],{"stretchy":460},[7161,123617,123618,123620],{},[383,123619,4505],{},[458,123621,7920],{},[458,123623,461],{"stretchy":460},[383,123625,1116],{},[458,123627,5160],{},[383,123629,121421],{},[458,123631,468],{"stretchy":460},[458,123633,605],{"stretchy":460},[458,123635,471],{},[543,123637,123638,123640],{},[383,123639,571],{},[383,123641,561],{},[458,123643,578],{"stretchy":460},[458,123645,461],{"stretchy":460},[383,123647,1116],{},[458,123649,5160],{},[383,123651,121421],{},[7161,123653,123654,123656],{},[458,123655,468],{"stretchy":460},[458,123657,2817],{},[458,123659,605],{"stretchy":460},[387,123661,123662],{"encoding":389},"E_Q[g^*(t-\\gamma)]=E_Q[(t-\\gamma)^+]",[363,123664,123666,123759,123780,123841],{"className":123665,"ariaHidden":394},[393],[363,123667,123669,123672,123712,123715,123744,123747,123750,123753,123756],{"className":123668},[398],[363,123670],{"className":123671,"style":618},[402],[363,123673,123675,123678],{"className":123674},[407],[363,123676,571],{"className":123677,"style":26208},[407,408],[363,123679,123681],{"className":123680},[629],[363,123682,123684,123704],{"className":123683},[633,634],[363,123685,123687,123701],{"className":123686},[638],[363,123688,123690],{"className":123689,"style":727},[642],[363,123691,123692,123695],{"style":122378},[363,123693],{"className":123694,"style":651},[650],[363,123696,123698],{"className":123697},[655,656,657,658],[363,123699,561],{"className":123700},[407,408,658],[363,123702,666],{"className":123703},[665],[363,123705,123707],{"className":123706},[638],[363,123708,123710],{"className":123709,"style":673},[642],[363,123711],{},[363,123713,578],{"className":123714},[494],[363,123716,123718,123721],{"className":123717},[407],[363,123719,4505],{"className":123720,"style":1328},[407,408],[363,123722,123724],{"className":123723},[629],[363,123725,123727],{"className":123726},[633],[363,123728,123730],{"className":123729},[638],[363,123731,123733],{"className":123732,"style":8846},[642],[363,123734,123735,123738],{"style":7212},[363,123736],{"className":123737,"style":651},[650],[363,123739,123741],{"className":123740},[655,656,657,658],[363,123742,7920],{"className":123743},[2938,658],[363,123745,461],{"className":123746},[494],[363,123748,1116],{"className":123749},[407,408],[363,123751],{"className":123752,"style":2934},[505],[363,123754,5160],{"className":123755},[2938],[363,123757],{"className":123758,"style":2934},[505],[363,123760,123762,123765,123768,123771,123774,123777],{"className":123761},[398],[363,123763],{"className":123764,"style":487},[402],[363,123766,121421],{"className":123767,"style":121511},[407,408],[363,123769,20737],{"className":123770},[501],[363,123772],{"className":123773,"style":506},[505],[363,123775,471],{"className":123776},[510],[363,123778],{"className":123779,"style":506},[505],[363,123781,123783,123786,123826,123829,123832,123835,123838],{"className":123782},[398],[363,123784],{"className":123785,"style":618},[402],[363,123787,123789,123792],{"className":123788},[407],[363,123790,571],{"className":123791,"style":26208},[407,408],[363,123793,123795],{"className":123794},[629],[363,123796,123798,123818],{"className":123797},[633,634],[363,123799,123801,123815],{"className":123800},[638],[363,123802,123804],{"className":123803,"style":727},[642],[363,123805,123806,123809],{"style":122378},[363,123807],{"className":123808,"style":651},[650],[363,123810,123812],{"className":123811},[655,656,657,658],[363,123813,561],{"className":123814},[407,408,658],[363,123816,666],{"className":123817},[665],[363,123819,123821],{"className":123820},[638],[363,123822,123824],{"className":123823,"style":673},[642],[363,123825],{},[363,123827,123276],{"className":123828},[494],[363,123830,1116],{"className":123831},[407,408],[363,123833],{"className":123834,"style":2934},[505],[363,123836,5160],{"className":123837},[2938],[363,123839],{"className":123840,"style":2934},[505],[363,123842,123844,123847,123850,123879],{"className":123843},[398],[363,123845],{"className":123846,"style":123295},[402],[363,123848,121421],{"className":123849,"style":121511},[407,408],[363,123851,123853,123856],{"className":123852},[501],[363,123854,468],{"className":123855},[501],[363,123857,123859],{"className":123858},[629],[363,123860,123862],{"className":123861},[633],[363,123863,123865],{"className":123864},[638],[363,123866,123868],{"className":123867,"style":21356},[642],[363,123869,123870,123873],{"style":7212},[363,123871],{"className":123872,"style":651},[650],[363,123874,123876],{"className":123875},[655,656,657,658],[363,123877,2817],{"className":123878},[2938,658],[363,123880,605],{"className":123881},[501],"，故等号可取。",[11,123884,123885,123886,123914,123915,123966,123967,124003,124004,16142,124107,124158,124159,124326,124327,124385,124386,124414],{},"几何解释：",[363,123887,123889,123902],{"className":123888,"translate":367},[366],[363,123890,123892],{"className":123891},[371],[373,123893,123894],{"xmlns":375},[377,123895,123896,123900],{},[380,123897,123898],{},[383,123899,121421],{},[387,123901,121838],{"encoding":389},[363,123903,123905],{"className":123904,"ariaHidden":394},[393],[363,123906,123908,123911],{"className":123907},[398],[363,123909],{"className":123910,"style":2623},[402],[363,123912,121421],{"className":123913,"style":121511},[407,408]," 扫过 ",[363,123916,123918,123939],{"className":123917,"translate":367},[366],[363,123919,123921],{"className":123920},[371],[373,123922,123923],{"xmlns":375},[377,123924,123925,123937],{},[380,123926,123927,123929,123931,123933,123935],{},[458,123928,578],{"stretchy":460},[463,123930,474],{},[458,123932,898],{"separator":394},[463,123934,465],{},[458,123936,605],{"stretchy":460},[387,123938,37161],{"encoding":389},[363,123940,123942],{"className":123941,"ariaHidden":394},[393],[363,123943,123945,123948,123951,123954,123957,123960,123963],{"className":123944},[398],[363,123946],{"className":123947,"style":487},[402],[363,123949,578],{"className":123950},[494],[363,123952,474],{"className":123953},[407],[363,123955,898],{"className":123956},[920],[363,123958],{"className":123959,"style":754},[505],[363,123961,465],{"className":123962},[407],[363,123964,605],{"className":123965},[501]," 时，右端就是权衡曲线（ROC 下边界）各条斜率为 ",[363,123968,123970,123988],{"className":123969,"translate":367},[366],[363,123971,123973],{"className":123972},[371],[373,123974,123975],{"xmlns":375},[377,123976,123977,123985],{},[380,123978,123979,123981,123983],{},[463,123980,465],{},[383,123982,1288],{"mathvariant":557},[383,123984,121421],{},[387,123986,123987],{"encoding":389},"1\u002F\\gamma",[363,123989,123991],{"className":123990,"ariaHidden":394},[393],[363,123992,123994,123997,124000],{"className":123993},[398],[363,123995],{"className":123996,"style":487},[402],[363,123998,8936],{"className":123999},[407],[363,124001,121421],{"className":124002,"style":121511},[407,408]," 的支撑线的截距——",[1572,124005,124006,124007,124035,124036,124106],{},"知道整条曲线 ",[363,124008,124010,124023],{"className":124009,"translate":367},[366],[363,124011,124013],{"className":124012},[371],[373,124014,124015],{"xmlns":375},[377,124016,124017,124021],{},[380,124018,124019],{},[383,124020,5739],{},[387,124022,5739],{"encoding":389},[363,124024,124026],{"className":124025,"ariaHidden":394},[393],[363,124027,124029,124032],{"className":124028},[398],[363,124030],{"className":124031,"style":1011},[402],[363,124033,5739],{"className":124034,"style":682},[407,408]," 就知道全部 ",[363,124037,124039,124057],{"className":124038,"translate":367},[366],[363,124040,124042],{"className":124041},[371],[373,124043,124044],{"xmlns":375},[377,124045,124046,124054],{},[380,124047,124048],{},[543,124049,124050,124052],{},[383,124051,4505],{},[383,124053,121421],{},[387,124055,124056],{"encoding":389},"g_\\gamma",[363,124058,124060],{"className":124059,"ariaHidden":394},[393],[363,124061,124063,124066],{"className":124062},[398],[363,124064],{"className":124065,"style":93305},[402],[363,124067,124069,124072],{"className":124068},[407],[363,124070,4505],{"className":124071,"style":1328},[407,408],[363,124073,124075],{"className":124074},[629],[363,124076,124078,124098],{"className":124077},[633,634],[363,124079,124081,124095],{"className":124080},[638],[363,124082,124084],{"className":124083,"style":45276},[642],[363,124085,124086,124089],{"style":19190},[363,124087],{"className":124088,"style":651},[650],[363,124090,124092],{"className":124091},[655,656,657,658],[363,124093,121421],{"className":124094,"style":121511},[407,408,658],[363,124096,666],{"className":124097},[665],[363,124099,124101],{"className":124100},[638],[363,124102,124104],{"className":124103,"style":673},[642],[363,124105],{},"-散度",[363,124108,124110,124128],{"className":124109,"translate":367},[366],[363,124111,124113],{"className":124112},[371],[373,124114,124115],{"xmlns":375},[377,124116,124117,124125],{},[380,124118,124119,124121,124123],{},[383,124120,121421],{},[458,124122,471],{},[463,124124,465],{},[387,124126,124127],{"encoding":389},"\\gamma=1",[363,124129,124131,124149],{"className":124130,"ariaHidden":394},[393],[363,124132,124134,124137,124140,124143,124146],{"className":124133},[398],[363,124135],{"className":124136,"style":2623},[402],[363,124138,121421],{"className":124139,"style":121511},[407,408],[363,124141],{"className":124142,"style":506},[505],[363,124144,471],{"className":124145},[510],[363,124147],{"className":124148,"style":506},[505],[363,124150,124152,124155],{"className":124151},[398],[363,124153],{"className":124154,"style":520},[402],[363,124156,465],{"className":124157},[407]," 时立刻给出 ",[363,124160,124162,124214],{"className":124161,"translate":367},[366],[363,124163,124165],{"className":124164},[371],[373,124166,124167],{"xmlns":375},[377,124168,124169,124211],{},[380,124170,124171,124177,124179,124189,124191,124193,124195,124197,124199,124201,124203,124205,124207,124209],{},[380,124172,124173,124175],{},[383,124174,5739],{"mathvariant":557},[383,124176,35197],{"mathvariant":557},[458,124178,471],{},[543,124180,124181,124187],{},[380,124182,124183,124185],{},[383,124184,35779],{},[458,124186,4450],{},[383,124188,950],{},[458,124190,3245],{"stretchy":460},[383,124192,554],{},[458,124194,461],{"stretchy":460},[383,124196,950],{},[458,124198,468],{"stretchy":460},[458,124200,5160],{},[383,124202,561],{},[458,124204,461],{"stretchy":460},[383,124206,950],{},[458,124208,468],{"stretchy":460},[458,124210,3255],{"stretchy":460},[387,124212,124213],{"encoding":389},"\\mathrm{TV}=\\sup_A\\{P(A)-Q(A)\\}",[363,124215,124217,124238,124308],{"className":124216,"ariaHidden":394},[393],[363,124218,124220,124223,124229,124232,124235],{"className":124219},[398],[363,124221],{"className":124222,"style":1011},[402],[363,124224,124226],{"className":124225},[407],[363,124227,87109],{"className":124228,"style":4504},[407,33009],[363,124230],{"className":124231,"style":506},[505],[363,124233,471],{"className":124234},[510],[363,124236],{"className":124237,"style":506},[505],[363,124239,124241,124244,124284,124287,124290,124293,124296,124299,124302,124305],{"className":124240},[398],[363,124242],{"className":124243,"style":487},[402],[363,124245,124247,124250],{"className":124246},[1831],[363,124248,35779],{"className":124249},[1831],[363,124251,124253],{"className":124252},[629],[363,124254,124256,124276],{"className":124255},[633,634],[363,124257,124259,124273],{"className":124258},[638],[363,124260,124262],{"className":124261,"style":35922},[642],[363,124263,124264,124267],{"style":35925},[363,124265],{"className":124266,"style":651},[650],[363,124268,124270],{"className":124269},[655,656,657,658],[363,124271,950],{"className":124272},[407,408,658],[363,124274,666],{"className":124275},[665],[363,124277,124279],{"className":124278},[638],[363,124280,124282],{"className":124281,"style":37367},[642],[363,124283],{},[363,124285,3245],{"className":124286},[494],[363,124288,554],{"className":124289,"style":682},[407,408],[363,124291,461],{"className":124292},[494],[363,124294,950],{"className":124295},[407,408],[363,124297,468],{"className":124298},[501],[363,124300],{"className":124301,"style":2934},[505],[363,124303,5160],{"className":124304},[2938],[363,124306],{"className":124307,"style":2934},[505],[363,124309,124311,124314,124317,124320,124323],{"className":124310},[398],[363,124312],{"className":124313,"style":487},[402],[363,124315,561],{"className":124316},[407,408],[363,124318,461],{"className":124319},[494],[363,124321,950],{"className":124322},[407,408],[363,124324,61346],{"className":124325},[501],"）。反过来，知道单个标量散度（如 KL 或 ",[363,124328,124330,124347],{"className":124329,"translate":367},[366],[363,124331,124333],{"className":124332},[371],[373,124334,124335],{"xmlns":375},[377,124336,124337,124345],{},[380,124338,124339],{},[7161,124340,124341,124343],{},[383,124342,37796],{},[463,124344,2810],{},[387,124346,40741],{"encoding":389},[363,124348,124350],{"className":124349,"ariaHidden":394},[393],[363,124351,124353,124356],{"className":124352},[398],[363,124354],{"className":124355,"style":40751},[402],[363,124357,124359,124362],{"className":124358},[407],[363,124360,37796],{"className":124361},[407,408],[363,124363,124365],{"className":124364},[629],[363,124366,124368],{"className":124367},[633],[363,124369,124371],{"className":124370},[638],[363,124372,124374],{"className":124373,"style":20375},[642],[363,124375,124376,124379],{"style":7212},[363,124377],{"className":124378,"style":651},[650],[363,124380,124382],{"className":124381},[655,656,657,658],[363,124383,2810],{"className":124384},[407,658],"）只对 ",[363,124387,124389,124402],{"className":124388,"translate":367},[366],[363,124390,124392],{"className":124391},[371],[373,124393,124394],{"xmlns":375},[377,124395,124396,124400],{},[380,124397,124398],{},[383,124399,5739],{},[387,124401,5739],{"encoding":389},[363,124403,124405],{"className":124404,"ariaHidden":394},[393],[363,124406,124408,124411],{"className":124407},[398],[363,124409],{"className":124410,"style":1011},[402],[363,124412,5739],{"className":124413,"style":682},[407,408]," 施加一个切向约束（4.7 节的不等式网络），信息严格更少；",[10374,124416,124417,124649],{},[7012,124418,124419,124420,20313],{},"在「小隐私预算」下，所有 f-DP 都由**高斯差分隐私（GDP）**统一逼近，其权衡函数 ",[363,124421,124423,124481],{"className":124422,"translate":367},[366],[363,124424,124426],{"className":124425},[371],[373,124427,124428],{"xmlns":375},[377,124429,124430,124478],{},[380,124431,124432,124439,124441,124443,124445,124447,124450,124452,124462,124464,124466,124468,124470,124472,124474,124476],{},[543,124433,124434,124437],{},[383,124435,124436],{},"G",[383,124438,2711],{},[458,124440,461],{"stretchy":460},[383,124442,45101],{},[458,124444,468],{"stretchy":460},[458,124446,471],{},[383,124448,124449],{"mathvariant":557},"Φ",[458,124451,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[7161,124453,124454,124456],{},[383,124455,124449],{"mathvariant":557},[380,124457,124458,124460],{},[458,124459,5160],{},[463,124461,465],{},[458,124463,461],{"stretchy":460},[463,124465,465],{},[458,124467,5160],{},[383,124469,45101],{},[458,124471,468],{"stretchy":460},[458,124473,5160],{},[383,124475,2711],{},[458,124477,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[387,124479,124480],{"encoding":389},"G_\\mu(\\alpha)=\\Phi\\big(\\Phi^{-1}(1-\\alpha)-\\mu\\big)",[363,124482,124484,124548,124613,124634],{"className":124483,"ariaHidden":394},[393],[363,124485,124487,124490,124530,124533,124536,124539,124542,124545],{"className":124486},[398],[363,124488],{"className":124489,"style":618},[402],[363,124491,124493,124496],{"className":124492},[407],[363,124494,124436],{"className":124495},[407,408],[363,124497,124499],{"className":124498},[629],[363,124500,124502,124522],{"className":124501},[633,634],[363,124503,124505,124519],{"className":124504},[638],[363,124506,124508],{"className":124507,"style":45276},[642],[363,124509,124510,124513],{"style":730},[363,124511],{"className":124512,"style":651},[650],[363,124514,124516],{"className":124515},[655,656,657,658],[363,124517,2711],{"className":124518},[407,408,658],[363,124520,666],{"className":124521},[665],[363,124523,124525],{"className":124524},[638],[363,124526,124528],{"className":124527,"style":673},[642],[363,124529],{},[363,124531,461],{"className":124532},[494],[363,124534,45101],{"className":124535,"style":45131},[407,408],[363,124537,468],{"className":124538},[501],[363,124540],{"className":124541,"style":506},[505],[363,124543,471],{"className":124544},[510],[363,124546],{"className":124547,"style":506},[505],[363,124549,124551,124554,124557,124563,124598,124601,124604,124607,124610],{"className":124550},[398],[363,124552],{"className":124553,"style":20910},[402],[363,124555,124449],{"className":124556},[407],[363,124558,124560],{"className":124559},[407],[363,124561,461],{"className":124562},[767,10021],[363,124564,124566,124569],{"className":124565},[407],[363,124567,124449],{"className":124568},[407],[363,124570,124572],{"className":124571},[629],[363,124573,124575],{"className":124574},[633],[363,124576,124578],{"className":124577},[638],[363,124579,124581],{"className":124580,"style":20375},[642],[363,124582,124583,124586],{"style":7212},[363,124584],{"className":124585,"style":651},[650],[363,124587,124589],{"className":124588},[655,656,657,658],[363,124590,124592,124595],{"className":124591},[407,658],[363,124593,5160],{"className":124594},[407,658],[363,124596,465],{"className":124597},[407,658],[363,124599,461],{"className":124600},[494],[363,124602,465],{"className":124603},[407],[363,124605],{"className":124606,"style":2934},[505],[363,124608,5160],{"className":124609},[2938],[363,124611],{"className":124612,"style":2934},[505],[363,124614,124616,124619,124622,124625,124628,124631],{"className":124615},[398],[363,124617],{"className":124618,"style":487},[402],[363,124620,45101],{"className":124621,"style":45131},[407,408],[363,124623,468],{"className":124624},[501],[363,124626],{"className":124627,"style":2934},[505],[363,124629,5160],{"className":124630},[2938],[363,124632],{"className":124633,"style":2934},[505],[363,124635,124637,124640,124643],{"className":124636},[398],[363,124638],{"className":124639,"style":20910},[402],[363,124641,2711],{"className":124642},[407,408],[363,124644,124646],{"className":124645},[407],[363,124647,468],{"className":124648},[767,10021],[7012,124650,124651,124652,124655,124656,124684],{},"权衡函数族在",[1572,124653,124654],{},"组合","（post-processing、串联）下封闭，并装备了一个与 f-散度\"散度序\"同构的偏序——这与 f-散度族的\"",[363,124657,124659,124672],{"className":124658,"translate":367},[366],[363,124660,124662],{"className":124661},[371],[373,124663,124664],{"xmlns":375},[377,124665,124666,124670],{},[380,124667,124668],{},[458,124669,7275],{},[387,124671,55836],{"encoding":389},[363,124673,124675],{"className":124674,"ariaHidden":394},[393],[363,124676,124678,124681],{"className":124677},[398],[363,124679],{"className":124680,"style":43535},[402],[363,124682,7275],{"className":124683},[510]," 比较\"在结构上完全平行。",[11,124686,124687],{},"这说明 f-散度不仅统一了信息论度量，也统一了现代隐私的定义框架：用一条凸曲线代替一个标量数字。",[18,124689,124691],{"id":124690},"_9-计算实例","9. 计算实例",[2658,124693,124695],{"id":124694},"_91-正态分布","9.1 正态分布",[11,124697,881,124698,5992,124873,10527],{},[363,124699,124701,124739],{"className":124700,"translate":367},[366],[363,124702,124704],{"className":124703},[371],[373,124705,124706],{"xmlns":375},[377,124707,124708,124736],{},[380,124709,124710,124712,124714,124716,124718,124724,124726,124734],{},[383,124711,554],{},[458,124713,471],{},[383,124715,38631],{},[458,124717,461],{"stretchy":460},[543,124719,124720,124722],{},[383,124721,2711],{},[463,124723,465],{},[458,124725,898],{"separator":394},[7900,124727,124728,124730,124732],{},[383,124729,2679],{},[463,124731,465],{},[463,124733,2810],{},[458,124735,468],{"stretchy":460},[387,124737,124738],{"encoding":389},"P=N(\\mu_1,\\sigma_1^2)",[363,124740,124742,124760],{"className":124741,"ariaHidden":394},[393],[363,124743,124745,124748,124751,124754,124757],{"className":124744},[398],[363,124746],{"className":124747,"style":1011},[402],[363,124749,554],{"className":124750,"style":682},[407,408],[363,124752],{"className":124753,"style":506},[505],[363,124755,471],{"className":124756},[510],[363,124758],{"className":124759,"style":506},[505],[363,124761,124763,124766,124769,124772,124812,124815,124818,124870],{"className":124762},[398],[363,124764],{"className":124765,"style":20350},[402],[363,124767,38631],{"className":124768,"style":25948},[407,408],[363,124770,461],{"className":124771},[494],[363,124773,124775,124778],{"className":124774},[407],[363,124776,2711],{"className":124777},[407,408],[363,124779,124781],{"className":124780},[629],[363,124782,124784,124804],{"className":124783},[633,634],[363,124785,124787,124801],{"className":124786},[638],[363,124788,124790],{"className":124789,"style":11480},[642],[363,124791,124792,124795],{"style":730},[363,124793],{"className":124794,"style":651},[650],[363,124796,124798],{"className":124797},[655,656,657,658],[363,124799,465],{"className":124800},[407,658],[363,124802,666],{"className":124803},[665],[363,124805,124807],{"className":124806},[638],[363,124808,124810],{"className":124809,"style":8315},[642],[363,124811],{},[363,124813,898],{"className":124814},[920],[363,124816],{"className":124817,"style":754},[505],[363,124819,124821,124824],{"className":124820},[407],[363,124822,2679],{"className":124823,"style":1328},[407,408],[363,124825,124827],{"className":124826},[629],[363,124828,124830,124862],{"className":124829},[633,634],[363,124831,124833,124859],{"className":124832},[638],[363,124834,124836,124848],{"className":124835,"style":20375},[642],[363,124837,124839,124842],{"style":124838},"top:-2.4519em;margin-left:-0.0359em;margin-right:0.05em;",[363,124840],{"className":124841,"style":651},[650],[363,124843,124845],{"className":124844},[655,656,657,658],[363,124846,465],{"className":124847},[407,658],[363,124849,124850,124853],{"style":7212},[363,124851],{"className":124852,"style":651},[650],[363,124854,124856],{"className":124855},[655,656,657,658],[363,124857,2810],{"className":124858},[407,658],[363,124860,666],{"className":124861},[665],[363,124863,124865],{"className":124864},[638],[363,124866,124868],{"className":124867,"style":52471},[642],[363,124869],{},[363,124871,468],{"className":124872},[501],[363,124874,124876,124914],{"className":124875,"translate":367},[366],[363,124877,124879],{"className":124878},[371],[373,124880,124881],{"xmlns":375},[377,124882,124883,124911],{},[380,124884,124885,124887,124889,124891,124893,124899,124901,124909],{},[383,124886,561],{},[458,124888,471],{},[383,124890,38631],{},[458,124892,461],{"stretchy":460},[543,124894,124895,124897],{},[383,124896,2711],{},[463,124898,2810],{},[458,124900,898],{"separator":394},[7900,124902,124903,124905,124907],{},[383,124904,2679],{},[463,124906,2810],{},[463,124908,2810],{},[458,124910,468],{"stretchy":460},[387,124912,124913],{"encoding":389},"Q=N(\\mu_2,\\sigma_2^2)",[363,124915,124917,124935],{"className":124916,"ariaHidden":394},[393],[363,124918,124920,124923,124926,124929,124932],{"className":124919},[398],[363,124921],{"className":124922,"style":913},[402],[363,124924,561],{"className":124925},[407,408],[363,124927],{"className":124928,"style":506},[505],[363,124930,471],{"className":124931},[510],[363,124933],{"className":124934,"style":506},[505],[363,124936,124938,124941,124944,124947,124987,124990,124993,125044],{"className":124937},[398],[363,124939],{"className":124940,"style":20350},[402],[363,124942,38631],{"className":124943,"style":25948},[407,408],[363,124945,461],{"className":124946},[494],[363,124948,124950,124953],{"className":124949},[407],[363,124951,2711],{"className":124952},[407,408],[363,124954,124956],{"className":124955},[629],[363,124957,124959,124979],{"className":124958},[633,634],[363,124960,124962,124976],{"className":124961},[638],[363,124963,124965],{"className":124964,"style":11480},[642],[363,124966,124967,124970],{"style":730},[363,124968],{"className":124969,"style":651},[650],[363,124971,124973],{"className":124972},[655,656,657,658],[363,124974,2810],{"className":124975},[407,658],[363,124977,666],{"className":124978},[665],[363,124980,124982],{"className":124981},[638],[363,124983,124985],{"className":124984,"style":8315},[642],[363,124986],{},[363,124988,898],{"className":124989},[920],[363,124991],{"className":124992,"style":754},[505],[363,124994,124996,124999],{"className":124995},[407],[363,124997,2679],{"className":124998,"style":1328},[407,408],[363,125000,125002],{"className":125001},[629],[363,125003,125005,125036],{"className":125004},[633,634],[363,125006,125008,125033],{"className":125007},[638],[363,125009,125011,125022],{"className":125010,"style":20375},[642],[363,125012,125013,125016],{"style":124838},[363,125014],{"className":125015,"style":651},[650],[363,125017,125019],{"className":125018},[655,656,657,658],[363,125020,2810],{"className":125021},[407,658],[363,125023,125024,125027],{"style":7212},[363,125025],{"className":125026,"style":651},[650],[363,125028,125030],{"className":125029},[655,656,657,658],[363,125031,2810],{"className":125032},[407,658],[363,125034,666],{"className":125035},[665],[363,125037,125039],{"className":125038},[638],[363,125040,125042],{"className":125041,"style":52471},[642],[363,125043],{},[363,125045,468],{"className":125046},[501],[11,125048,125049],{},[1572,125050,125051],{},"KL（经典公式）。",[363,125053,125055],{"className":125054,"translate":367},[528],[363,125056,125058,125170],{"className":125057,"translate":367},[366],[363,125059,125061],{"className":125060},[371],[373,125062,125063],{"xmlns":375,"display":537},[377,125064,125065,125167],{},[380,125066,125067,125077,125079,125081,125083,125085,125087,125089,125091,125093,125107,125109,125157,125159,125165],{},[543,125068,125069,125071],{},[383,125070,547],{},[380,125072,125073,125075],{},[383,125074,11041],{},[383,125076,22240],{},[458,125078,461],{"stretchy":460},[383,125080,554],{},[383,125082,558],{"mathvariant":557},[383,125084,561],{},[458,125086,468],{"stretchy":460},[458,125088,471],{},[383,125090,4447],{},[458,125092,4450],{},[586,125094,125095,125101],{},[543,125096,125097,125099],{},[383,125098,2679],{},[463,125100,2810],{},[543,125102,125103,125105],{},[383,125104,2679],{},[463,125106,465],{},[458,125108,2817],{},[586,125110,125111,125145],{},[380,125112,125113,125121,125123,125125,125131,125133,125139],{},[7900,125114,125115,125117,125119],{},[383,125116,2679],{},[463,125118,465],{},[463,125120,2810],{},[458,125122,2817],{},[458,125124,461],{"stretchy":460},[543,125126,125127,125129],{},[383,125128,2711],{},[463,125130,465],{},[458,125132,5160],{},[543,125134,125135,125137],{},[383,125136,2711],{},[463,125138,2810],{},[7161,125140,125141,125143],{},[458,125142,468],{"stretchy":460},[463,125144,2810],{},[380,125146,125147,125149],{},[463,125148,2810],{},[7900,125150,125151,125153,125155],{},[383,125152,2679],{},[463,125154,2810],{},[463,125156,2810],{},[458,125158,5160],{},[586,125160,125161,125163],{},[463,125162,465],{},[463,125164,2810],{},[383,125166,4722],{"mathvariant":557},[387,125168,125169],{"encoding":389},"D_{KL}(P\\|Q)=\\log\\frac{\\sigma_2}{\\sigma_1}\n+\\frac{\\sigma_1^2+(\\mu_1-\\mu_2)^2}{2\\sigma_2^2}\n-\\frac12 .",[363,125171,125173,125249,125410,125720],{"className":125172,"ariaHidden":394},[393],[363,125174,125176,125179,125225,125228,125231,125234,125237,125240,125243,125246],{"className":125175},[398],[363,125177],{"className":125178,"style":487},[402],[363,125180,125182,125185],{"className":125181},[407],[363,125183,547],{"className":125184,"style":625},[407,408],[363,125186,125188],{"className":125187},[629],[363,125189,125191,125217],{"className":125190},[633,634],[363,125192,125194,125214],{"className":125193},[638],[363,125195,125197],{"className":125196,"style":727},[642],[363,125198,125199,125202],{"style":646},[363,125200],{"className":125201,"style":651},[650],[363,125203,125205],{"className":125204},[655,656,657,658],[363,125206,125208,125211],{"className":125207},[407,658],[363,125209,11041],{"className":125210,"style":11129},[407,408,658],[363,125212,22240],{"className":125213},[407,408,658],[363,125215,666],{"className":125216},[665],[363,125218,125220],{"className":125219},[638],[363,125221,125223],{"className":125222,"style":8315},[642],[363,125224],{},[363,125226,461],{"className":125227},[494],[363,125229,554],{"className":125230,"style":682},[407,408],[363,125232,558],{"className":125233},[407],[363,125235,561],{"className":125236},[407,408],[363,125238,468],{"className":125239},[501],[363,125241],{"className":125242,"style":506},[505],[363,125244,471],{"className":125245},[510],[363,125247],{"className":125248,"style":506},[505],[363,125250,125252,125256,125261,125264,125401,125404,125407],{"className":125251},[398],[363,125253],{"className":125254,"style":125255},[402],"height:1.9436em;vertical-align:-0.836em;",[363,125257,4501,125259],{"className":125258},[1831],[363,125260,4505],{"style":4504},[363,125262],{"className":125263,"style":754},[505],[363,125265,125267,125270,125398],{"className":125266},[407],[363,125268],{"className":125269},[494,789],[363,125271,125273],{"className":125272},[586],[363,125274,125276,125389],{"className":125275},[633,634],[363,125277,125279,125386],{"className":125278},[638],[363,125280,125282,125330,125338],{"className":125281,"style":3901},[642],[363,125283,125284,125287],{"style":805},[363,125285],{"className":125286,"style":809},[650],[363,125288,125290],{"className":125289},[407],[363,125291,125293,125296],{"className":125292},[407],[363,125294,2679],{"className":125295,"style":1328},[407,408],[363,125297,125299],{"className":125298},[629],[363,125300,125302,125322],{"className":125301},[633,634],[363,125303,125305,125319],{"className":125304},[638],[363,125306,125308],{"className":125307,"style":11480},[642],[363,125309,125310,125313],{"style":19190},[363,125311],{"className":125312,"style":651},[650],[363,125314,125316],{"className":125315},[655,656,657,658],[363,125317,465],{"className":125318},[407,658],[363,125320,666],{"className":125321},[665],[363,125323,125325],{"className":125324},[638],[363,125326,125328],{"className":125327,"style":8315},[642],[363,125329],{},[363,125331,125332,125335],{"style":821},[363,125333],{"className":125334,"style":809},[650],[363,125336],{"className":125337,"style":829},[828],[363,125339,125340,125343],{"style":832},[363,125341],{"className":125342,"style":809},[650],[363,125344,125346],{"className":125345},[407],[363,125347,125349,125352],{"className":125348},[407],[363,125350,2679],{"className":125351,"style":1328},[407,408],[363,125353,125355],{"className":125354},[629],[363,125356,125358,125378],{"className":125357},[633,634],[363,125359,125361,125375],{"className":125360},[638],[363,125362,125364],{"className":125363,"style":11480},[642],[363,125365,125366,125369],{"style":19190},[363,125367],{"className":125368,"style":651},[650],[363,125370,125372],{"className":125371},[655,656,657,658],[363,125373,2810],{"className":125374},[407,658],[363,125376,666],{"className":125377},[665],[363,125379,125381],{"className":125380},[638],[363,125382,125384],{"className":125383,"style":8315},[642],[363,125385],{},[363,125387,666],{"className":125388},[665],[363,125390,125392],{"className":125391},[638],[363,125393,125396],{"className":125394,"style":125395},[642],"height:0.836em;",[363,125397],{},[363,125399],{"className":125400},[501,789],[363,125402],{"className":125403,"style":2934},[505],[363,125405,2817],{"className":125406},[2938],[363,125408],{"className":125409,"style":2934},[505],[363,125411,125413,125417,125711,125714,125717],{"className":125412},[398],[363,125414],{"className":125415,"style":125416},[402],"height:2.4434em;vertical-align:-0.9523em;",[363,125418,125420,125423,125708],{"className":125419},[407],[363,125421],{"className":125422},[494,789],[363,125424,125426],{"className":125425},[586],[363,125427,125429,125699],{"className":125428},[633,634],[363,125430,125432,125696],{"className":125431},[638],[363,125433,125435,125499,125507],{"className":125434,"style":38070},[642],[363,125436,125437,125440],{"style":805},[363,125438],{"className":125439,"style":809},[650],[363,125441,125443,125446],{"className":125442},[407],[363,125444,2810],{"className":125445},[407],[363,125447,125449,125452],{"className":125448},[407],[363,125450,2679],{"className":125451,"style":1328},[407,408],[363,125453,125455],{"className":125454},[629],[363,125456,125458,125490],{"className":125457},[633,634],[363,125459,125461,125487],{"className":125460},[638],[363,125462,125464,125476],{"className":125463,"style":97910},[642],[363,125465,125467,125470],{"style":125466},"top:-2.4337em;margin-left:-0.0359em;margin-right:0.05em;",[363,125468],{"className":125469,"style":651},[650],[363,125471,125473],{"className":125472},[655,656,657,658],[363,125474,2810],{"className":125475},[407,658],[363,125477,125478,125481],{"style":97931},[363,125479],{"className":125480,"style":651},[650],[363,125482,125484],{"className":125483},[655,656,657,658],[363,125485,2810],{"className":125486},[407,658],[363,125488,666],{"className":125489},[665],[363,125491,125493],{"className":125492},[638],[363,125494,125497],{"className":125495,"style":125496},[642],"height:0.2663em;",[363,125498],{},[363,125500,125501,125504],{"style":821},[363,125502],{"className":125503,"style":809},[650],[363,125505],{"className":125506,"style":829},[828],[363,125508,125509,125512],{"style":832},[363,125510],{"className":125511,"style":809},[650],[363,125513,125515,125566,125569,125572,125575,125578,125618,125621,125624,125627,125667],{"className":125514},[407],[363,125516,125518,125521],{"className":125517},[407],[363,125519,2679],{"className":125520,"style":1328},[407,408],[363,125522,125524],{"className":125523},[629],[363,125525,125527,125558],{"className":125526},[633,634],[363,125528,125530,125555],{"className":125529},[638],[363,125531,125533,125544],{"className":125532,"style":20375},[642],[363,125534,125535,125538],{"style":124838},[363,125536],{"className":125537,"style":651},[650],[363,125539,125541],{"className":125540},[655,656,657,658],[363,125542,465],{"className":125543},[407,658],[363,125545,125546,125549],{"style":7212},[363,125547],{"className":125548,"style":651},[650],[363,125550,125552],{"className":125551},[655,656,657,658],[363,125553,2810],{"className":125554},[407,658],[363,125556,666],{"className":125557},[665],[363,125559,125561],{"className":125560},[638],[363,125562,125564],{"className":125563,"style":52471},[642],[363,125565],{},[363,125567],{"className":125568,"style":2934},[505],[363,125570,2817],{"className":125571},[2938],[363,125573],{"className":125574,"style":2934},[505],[363,125576,461],{"className":125577},[494],[363,125579,125581,125584],{"className":125580},[407],[363,125582,2711],{"className":125583},[407,408],[363,125585,125587],{"className":125586},[629],[363,125588,125590,125610],{"className":125589},[633,634],[363,125591,125593,125607],{"className":125592},[638],[363,125594,125596],{"className":125595,"style":11480},[642],[363,125597,125598,125601],{"style":730},[363,125599],{"className":125600,"style":651},[650],[363,125602,125604],{"className":125603},[655,656,657,658],[363,125605,465],{"className":125606},[407,658],[363,125608,666],{"className":125609},[665],[363,125611,125613],{"className":125612},[638],[363,125614,125616],{"className":125615,"style":8315},[642],[363,125617],{},[363,125619],{"className":125620,"style":2934},[505],[363,125622,5160],{"className":125623},[2938],[363,125625],{"className":125626,"style":2934},[505],[363,125628,125630,125633],{"className":125629},[407],[363,125631,2711],{"className":125632},[407,408],[363,125634,125636],{"className":125635},[629],[363,125637,125639,125659],{"className":125638},[633,634],[363,125640,125642,125656],{"className":125641},[638],[363,125643,125645],{"className":125644,"style":11480},[642],[363,125646,125647,125650],{"style":730},[363,125648],{"className":125649,"style":651},[650],[363,125651,125653],{"className":125652},[655,656,657,658],[363,125654,2810],{"className":125655},[407,658],[363,125657,666],{"className":125658},[665],[363,125660,125662],{"className":125661},[638],[363,125663,125665],{"className":125664,"style":8315},[642],[363,125666],{},[363,125668,125670,125673],{"className":125669},[501],[363,125671,468],{"className":125672},[501],[363,125674,125676],{"className":125675},[629],[363,125677,125679],{"className":125678},[633],[363,125680,125682],{"className":125681},[638],[363,125683,125685],{"className":125684,"style":20375},[642],[363,125686,125687,125690],{"style":7212},[363,125688],{"className":125689,"style":651},[650],[363,125691,125693],{"className":125692},[655,656,657,658],[363,125694,2810],{"className":125695},[407,658],[363,125697,666],{"className":125698},[665],[363,125700,125702],{"className":125701},[638],[363,125703,125706],{"className":125704,"style":125705},[642],"height:0.9523em;",[363,125707],{},[363,125709],{"className":125710},[501,789],[363,125712],{"className":125713,"style":2934},[505],[363,125715,5160],{"className":125716},[2938],[363,125718],{"className":125719,"style":2934},[505],[363,125721,125723,125726,125788],{"className":125722},[398],[363,125724],{"className":125725,"style":26250},[402],[363,125727,125729,125732,125785],{"className":125728},[407],[363,125730],{"className":125731},[494,789],[363,125733,125735],{"className":125734},[586],[363,125736,125738,125777],{"className":125737},[633,634],[363,125739,125741,125774],{"className":125740},[638],[363,125742,125744,125755,125763],{"className":125743,"style":23236},[642],[363,125745,125746,125749],{"style":805},[363,125747],{"className":125748,"style":809},[650],[363,125750,125752],{"className":125751},[407],[363,125753,2810],{"className":125754},[407],[363,125756,125757,125760],{"style":821},[363,125758],{"className":125759,"style":809},[650],[363,125761],{"className":125762,"style":829},[828],[363,125764,125765,125768],{"style":832},[363,125766],{"className":125767,"style":809},[650],[363,125769,125771],{"className":125770},[407],[363,125772,465],{"className":125773},[407],[363,125775,666],{"className":125776},[665],[363,125778,125780],{"className":125779},[638],[363,125781,125783],{"className":125782,"style":4125},[642],[363,125784],{},[363,125786],{"className":125787},[501,789],[363,125789,4722],{"className":125790},[407],[11,125792,125793,126165,126166,126243],{},[1572,125794,54088,125795,125853,125854,3092,126009,1338],{},[363,125796,125798,125815],{"className":125797,"translate":367},[366],[363,125799,125801],{"className":125800},[371],[373,125802,125803],{"xmlns":375},[377,125804,125805,125813],{},[380,125806,125807],{},[7161,125808,125809,125811],{},[383,125810,37796],{},[463,125812,2810],{},[387,125814,40741],{"encoding":389},[363,125816,125818],{"className":125817,"ariaHidden":394},[393],[363,125819,125821,125824],{"className":125820},[398],[363,125822],{"className":125823,"style":40751},[402],[363,125825,125827,125830],{"className":125826},[407],[363,125828,37796],{"className":125829},[407,408],[363,125831,125833],{"className":125832},[629],[363,125834,125836],{"className":125835},[633],[363,125837,125839],{"className":125838},[638],[363,125840,125842],{"className":125841,"style":20375},[642],[363,125843,125844,125847],{"style":7212},[363,125845],{"className":125846,"style":651},[650],[363,125848,125850],{"className":125849},[655,656,657,658],[363,125851,2810],{"className":125852},[407,658],"（等方差 ",[363,125855,125857,125887],{"className":125856,"translate":367},[366],[363,125858,125860],{"className":125859},[371],[373,125861,125862],{"xmlns":375},[377,125863,125864,125884],{},[380,125865,125866,125872,125874,125880,125882],{},[543,125867,125868,125870],{},[383,125869,2679],{},[463,125871,465],{},[458,125873,471],{},[543,125875,125876,125878],{},[383,125877,2679],{},[463,125879,2810],{},[458,125881,471],{},[383,125883,2679],{},[387,125885,125886],{"encoding":389},"\\sigma_1=\\sigma_2=\\sigma",[363,125888,125890,125945,126000],{"className":125889,"ariaHidden":394},[393],[363,125891,125893,125896,125936,125939,125942],{"className":125892},[398],[363,125894],{"className":125895,"style":13721},[402],[363,125897,125899,125902],{"className":125898},[407],[363,125900,2679],{"className":125901,"style":1328},[407,408],[363,125903,125905],{"className":125904},[629],[363,125906,125908,125928],{"className":125907},[633,634],[363,125909,125911,125925],{"className":125910},[638],[363,125912,125914],{"className":125913,"style":11480},[642],[363,125915,125916,125919],{"style":19190},[363,125917],{"className":125918,"style":651},[650],[363,125920,125922],{"className":125921},[655,656,657,658],[363,125923,465],{"className":125924},[407,658],[363,125926,666],{"className":125927},[665],[363,125929,125931],{"className":125930},[638],[363,125932,125934],{"className":125933,"style":8315},[642],[363,125935],{},[363,125937],{"className":125938,"style":506},[505],[363,125940,471],{"className":125941},[510],[363,125943],{"className":125944,"style":506},[505],[363,125946,125948,125951,125991,125994,125997],{"className":125947},[398],[363,125949],{"className":125950,"style":13721},[402],[363,125952,125954,125957],{"className":125953},[407],[363,125955,2679],{"className":125956,"style":1328},[407,408],[363,125958,125960],{"className":125959},[629],[363,125961,125963,125983],{"className":125962},[633,634],[363,125964,125966,125980],{"className":125965},[638],[363,125967,125969],{"className":125968,"style":11480},[642],[363,125970,125971,125974],{"style":19190},[363,125972],{"className":125973,"style":651},[650],[363,125975,125977],{"className":125976},[655,656,657,658],[363,125978,2810],{"className":125979},[407,658],[363,125981,666],{"className":125982},[665],[363,125984,125986],{"className":125985},[638],[363,125987,125989],{"className":125988,"style":8315},[642],[363,125990],{},[363,125992],{"className":125993,"style":506},[505],[363,125995,471],{"className":125996},[510],[363,125998],{"className":125999,"style":506},[505],[363,126001,126003,126006],{"className":126002},[398],[363,126004],{"className":126005,"style":2692},[402],[363,126007,2679],{"className":126008,"style":1328},[407,408],[363,126010,126012,126043],{"className":126011,"translate":367},[366],[363,126013,126015],{"className":126014},[371],[373,126016,126017],{"xmlns":375},[377,126018,126019,126040],{},[380,126020,126021,126024,126026,126032,126034],{},[383,126022,126023],{"mathvariant":557},"Δ",[458,126025,471],{},[543,126027,126028,126030],{},[383,126029,2711],{},[463,126031,465],{},[458,126033,5160],{},[543,126035,126036,126038],{},[383,126037,2711],{},[463,126039,2810],{},[387,126041,126042],{"encoding":389},"\\Delta=\\mu_1-\\mu_2",[363,126044,126046,126064,126119],{"className":126045,"ariaHidden":394},[393],[363,126047,126049,126052,126055,126058,126061],{"className":126048},[398],[363,126050],{"className":126051,"style":1011},[402],[363,126053,126023],{"className":126054},[407],[363,126056],{"className":126057,"style":506},[505],[363,126059,471],{"className":126060},[510],[363,126062],{"className":126063,"style":506},[505],[363,126065,126067,126070,126110,126113,126116],{"className":126066},[398],[363,126068],{"className":126069,"style":40668},[402],[363,126071,126073,126076],{"className":126072},[407],[363,126074,2711],{"className":126075},[407,408],[363,126077,126079],{"className":126078},[629],[363,126080,126082,126102],{"className":126081},[633,634],[363,126083,126085,126099],{"className":126084},[638],[363,126086,126088],{"className":126087,"style":11480},[642],[363,126089,126090,126093],{"style":730},[363,126091],{"className":126092,"style":651},[650],[363,126094,126096],{"className":126095},[655,656,657,658],[363,126097,465],{"className":126098},[407,658],[363,126100,666],{"className":126101},[665],[363,126103,126105],{"className":126104},[638],[363,126106,126108],{"className":126107,"style":8315},[642],[363,126109],{},[363,126111],{"className":126112,"style":2934},[505],[363,126114,5160],{"className":126115},[2938],[363,126117],{"className":126118,"style":2934},[505],[363,126120,126122,126125],{"className":126121},[398],[363,126123],{"className":126124,"style":2623},[402],[363,126126,126128,126131],{"className":126127},[407],[363,126129,2711],{"className":126130},[407,408],[363,126132,126134],{"className":126133},[629],[363,126135,126137,126157],{"className":126136},[633,634],[363,126138,126140,126154],{"className":126139},[638],[363,126141,126143],{"className":126142,"style":11480},[642],[363,126144,126145,126148],{"style":730},[363,126146],{"className":126147,"style":651},[650],[363,126149,126151],{"className":126150},[655,656,657,658],[363,126152,2810],{"className":126153},[407,658],[363,126155,666],{"className":126156},[665],[363,126158,126160],{"className":126159},[638],[363,126161,126163],{"className":126162,"style":8315},[642],[363,126164],{}," 计算 ",[363,126167,126169,126193],{"className":126168,"translate":367},[366],[363,126170,126172],{"className":126171},[371],[373,126173,126174],{"xmlns":375},[377,126175,126176,126190],{},[380,126177,126178,126180,126186,126188],{},[458,126179,1634],{},[7161,126181,126182,126184],{},[383,126183,11],{},[463,126185,2810],{},[383,126187,1288],{"mathvariant":557},[383,126189,1291],{},[387,126191,126192],{"encoding":389},"\\int p^2\u002Fq",[363,126194,126196],{"className":126195,"ariaHidden":394},[393],[363,126197,126199,126202,126205,126208,126237,126240],{"className":126198},[398],[363,126200],{"className":126201,"style":50675},[402],[363,126203,1634],{"className":126204,"style":5964},[1831,1832,5963],[363,126206],{"className":126207,"style":754},[505],[363,126209,126211,126214],{"className":126210},[407],[363,126212,11],{"className":126213},[407,408],[363,126215,126217],{"className":126216},[629],[363,126218,126220],{"className":126219},[633],[363,126221,126223],{"className":126222},[638],[363,126224,126226],{"className":126225,"style":20375},[642],[363,126227,126228,126231],{"style":7212},[363,126229],{"className":126230,"style":651},[650],[363,126232,126234],{"className":126233},[655,656,657,658],[363,126235,2810],{"className":126236},[407,658],[363,126238,1288],{"className":126239},[407],[363,126241,1291],{"className":126242,"style":1328},[407,408],"：由配方可得",[363,126245,126247],{"className":126246,"translate":367},[528],[363,126248,126250,126311],{"className":126249,"translate":367},[366],[363,126251,126253],{"className":126252},[371],[373,126254,126255],{"xmlns":375,"display":537},[377,126256,126257,126308],{},[380,126258,126259,126261,126271,126273,126275,126277,126279,126282,126284,126286,126306],{},[458,126260,1634],{},[586,126262,126263,126269],{},[7161,126264,126265,126267],{},[383,126266,11],{},[463,126268,2810],{},[383,126270,1291],{},[1644,126272,1646],{},[383,126274,592],{},[383,126276,1121],{},[458,126278,471],{},[383,126280,126281],{},"exp",[458,126283,4450],{},[1644,126285,1651],{},[380,126287,126288,126290,126304],{},[458,126289,461],{"fence":394},[586,126291,126292,126298],{},[7161,126293,126294,126296],{},[383,126295,126023],{"mathvariant":557},[463,126297,2810],{},[7161,126299,126300,126302],{},[383,126301,2679],{},[463,126303,2810],{},[458,126305,468],{"fence":394},[458,126307,898],{"separator":394},[387,126309,126310],{"encoding":389},"\\int \\frac{p^2}{q}\\,dx\n=\\exp\\!\\left(\\frac{\\Delta^2}{\\sigma^2}\\right),",[363,126312,126314,126432],{"className":126313,"ariaHidden":394},[393],[363,126315,126317,126320,126323,126326,126414,126417,126420,126423,126426,126429],{"className":126316},[398],[363,126318],{"className":126319,"style":38045},[402],[363,126321,1634],{"className":126322,"style":1834},[1831,1832,1833],[363,126324],{"className":126325,"style":754},[505],[363,126327,126329,126332,126411],{"className":126328},[407],[363,126330],{"className":126331},[494,789],[363,126333,126335],{"className":126334},[586],[363,126336,126338,126403],{"className":126337},[633,634],[363,126339,126341,126400],{"className":126340},[638],[363,126342,126344,126355,126363],{"className":126343,"style":38070},[642],[363,126345,126346,126349],{"style":805},[363,126347],{"className":126348,"style":809},[650],[363,126350,126352],{"className":126351},[407],[363,126353,1291],{"className":126354,"style":1328},[407,408],[363,126356,126357,126360],{"style":821},[363,126358],{"className":126359,"style":809},[650],[363,126361],{"className":126362,"style":829},[828],[363,126364,126365,126368],{"style":832},[363,126366],{"className":126367,"style":809},[650],[363,126369,126371],{"className":126370},[407],[363,126372,126374,126377],{"className":126373},[407],[363,126375,11],{"className":126376},[407,408],[363,126378,126380],{"className":126379},[629],[363,126381,126383],{"className":126382},[633],[363,126384,126386],{"className":126385},[638],[363,126387,126389],{"className":126388,"style":20375},[642],[363,126390,126391,126394],{"style":7212},[363,126392],{"className":126393,"style":651},[650],[363,126395,126397],{"className":126396},[655,656,657,658],[363,126398,2810],{"className":126399},[407,658],[363,126401,666],{"className":126402},[665],[363,126404,126406],{"className":126405},[638],[363,126407,126409],{"className":126408,"style":854},[642],[363,126410],{},[363,126412],{"className":126413},[501,789],[363,126415],{"className":126416,"style":754},[505],[363,126418,592],{"className":126419},[407,408],[363,126421,1121],{"className":126422},[407,408],[363,126424],{"className":126425,"style":506},[505],[363,126427,471],{"className":126428},[510],[363,126430],{"className":126431,"style":506},[505],[363,126433,126435,126438,126441,126444,126447,126576,126579],{"className":126434},[398],[363,126436],{"className":126437,"style":87605},[402],[363,126439,126281],{"className":126440},[1831],[363,126442],{"className":126443,"style":1859},[505],[363,126445],{"className":126446,"style":754},[505],[363,126448,126450,126456,126570],{"className":126449},[758],[363,126451,126453],{"className":126452,"style":763},[494,762],[363,126454,461],{"className":126455},[767,657],[363,126457,126459,126462,126567],{"className":126458},[407],[363,126460],{"className":126461},[494,789],[363,126463,126465],{"className":126464},[586],[363,126466,126468,126559],{"className":126467},[633,634],[363,126469,126471,126556],{"className":126470},[638],[363,126472,126474,126511,126519],{"className":126473,"style":38070},[642],[363,126475,126476,126479],{"style":805},[363,126477],{"className":126478,"style":809},[650],[363,126480,126482],{"className":126481},[407],[363,126483,126485,126488],{"className":126484},[407],[363,126486,2679],{"className":126487,"style":1328},[407,408],[363,126489,126491],{"className":126490},[629],[363,126492,126494],{"className":126493},[633],[363,126495,126497],{"className":126496},[638],[363,126498,126500],{"className":126499,"style":45379},[642],[363,126501,126502,126505],{"style":45382},[363,126503],{"className":126504,"style":651},[650],[363,126506,126508],{"className":126507},[655,656,657,658],[363,126509,2810],{"className":126510},[407,658],[363,126512,126513,126516],{"style":821},[363,126514],{"className":126515,"style":809},[650],[363,126517],{"className":126518,"style":829},[828],[363,126520,126521,126524],{"style":832},[363,126522],{"className":126523,"style":809},[650],[363,126525,126527],{"className":126526},[407],[363,126528,126530,126533],{"className":126529},[407],[363,126531,126023],{"className":126532},[407],[363,126534,126536],{"className":126535},[629],[363,126537,126539],{"className":126538},[633],[363,126540,126542],{"className":126541},[638],[363,126543,126545],{"className":126544,"style":20375},[642],[363,126546,126547,126550],{"style":7212},[363,126548],{"className":126549,"style":651},[650],[363,126551,126553],{"className":126552},[655,656,657,658],[363,126554,2810],{"className":126555},[407,658],[363,126557,666],{"className":126558},[665],[363,126560,126562],{"className":126561},[638],[363,126563,126565],{"className":126564,"style":4125},[642],[363,126566],{},[363,126568],{"className":126569},[501,789],[363,126571,126573],{"className":126572,"style":763},[501,762],[363,126574,468],{"className":126575},[767,657],[363,126577],{"className":126578,"style":754},[505],[363,126580,898],{"className":126581},[920],[11,126583,48506],{},[363,126585,126587],{"className":126586,"translate":367},[528],[363,126588,126590,126698],{"className":126589,"translate":367},[366],[363,126591,126593],{"className":126592},[371],[373,126594,126595],{"xmlns":375,"display":537},[377,126596,126597,126695],{},[380,126598,126599,126605,126607,126609,126611,126613,126615,126617,126619,126639,126641,126643,126645,126647,126649,126659,126661,126663,126665,126667,126669,126671,126691,126693],{},[7161,126600,126601,126603],{},[383,126602,37796],{},[463,126604,2810],{},[458,126606,461],{"stretchy":460},[383,126608,554],{},[383,126610,558],{"mathvariant":557},[383,126612,561],{},[458,126614,468],{"stretchy":460},[458,126616,471],{},[458,126618,1634],{},[586,126620,126621,126637],{},[380,126622,126623,126625,126627,126629,126631],{},[458,126624,461],{"stretchy":460},[383,126626,11],{},[458,126628,5160],{},[383,126630,1291],{},[7161,126632,126633,126635],{},[458,126634,468],{"stretchy":460},[463,126636,2810],{},[383,126638,1291],{},[1644,126640,1646],{},[383,126642,592],{},[383,126644,1121],{},[458,126646,471],{},[458,126648,1634],{},[586,126650,126651,126657],{},[7161,126652,126653,126655],{},[383,126654,11],{},[463,126656,2810],{},[383,126658,1291],{},[458,126660,5160],{},[463,126662,465],{},[458,126664,471],{},[383,126666,126281],{},[458,126668,4450],{},[1644,126670,1651],{},[380,126672,126673,126675,126689],{},[458,126674,461],{"fence":394},[586,126676,126677,126683],{},[7161,126678,126679,126681],{},[383,126680,126023],{"mathvariant":557},[463,126682,2810],{},[7161,126684,126685,126687],{},[383,126686,2679],{},[463,126688,2810],{},[458,126690,468],{"fence":394},[458,126692,5160],{},[463,126694,49857],{},[387,126696,126697],{"encoding":389},"\\chi^2(P\\|Q)=\\int\\frac{(p-q)^2}{q}\\,dx\n=\\int\\frac{p^2}{q}-1\n=\\exp\\!\\left(\\frac{\\Delta^2}{\\sigma^2}\\right)\n-1 .",[363,126699,126701,126760,126896,127005,127023,127176],{"className":126700,"ariaHidden":394},[393],[363,126702,126704,126707,126736,126739,126742,126745,126748,126751,126754,126757],{"className":126703},[398],[363,126705],{"className":126706,"style":37598},[402],[363,126708,126710,126713],{"className":126709},[407],[363,126711,37796],{"className":126712},[407,408],[363,126714,126716],{"className":126715},[629],[363,126717,126719],{"className":126718},[633],[363,126720,126722],{"className":126721},[638],[363,126723,126725],{"className":126724,"style":20082},[642],[363,126726,126727,126730],{"style":8624},[363,126728],{"className":126729,"style":651},[650],[363,126731,126733],{"className":126732},[655,656,657,658],[363,126734,2810],{"className":126735},[407,658],[363,126737,461],{"className":126738},[494],[363,126740,554],{"className":126741,"style":682},[407,408],[363,126743,558],{"className":126744},[407],[363,126746,561],{"className":126747},[407,408],[363,126749,468],{"className":126750},[501],[363,126752],{"className":126753,"style":506},[505],[363,126755,471],{"className":126756},[510],[363,126758],{"className":126759,"style":506},[505],[363,126761,126763,126766,126769,126772,126878,126881,126884,126887,126890,126893],{"className":126762},[398],[363,126764],{"className":126765,"style":38045},[402],[363,126767,1634],{"className":126768,"style":1834},[1831,1832,1833],[363,126770],{"className":126771,"style":754},[505],[363,126773,126775,126778,126875],{"className":126774},[407],[363,126776],{"className":126777},[494,789],[363,126779,126781],{"className":126780},[586],[363,126782,126784,126867],{"className":126783},[633,634],[363,126785,126787,126864],{"className":126786},[638],[363,126788,126790,126801,126809],{"className":126789,"style":38070},[642],[363,126791,126792,126795],{"style":805},[363,126793],{"className":126794,"style":809},[650],[363,126796,126798],{"className":126797},[407],[363,126799,1291],{"className":126800,"style":1328},[407,408],[363,126802,126803,126806],{"style":821},[363,126804],{"className":126805,"style":809},[650],[363,126807],{"className":126808,"style":829},[828],[363,126810,126811,126814],{"style":832},[363,126812],{"className":126813,"style":809},[650],[363,126815,126817,126820,126823,126826,126829,126832,126835],{"className":126816},[407],[363,126818,461],{"className":126819},[494],[363,126821,11],{"className":126822},[407,408],[363,126824],{"className":126825,"style":2934},[505],[363,126827,5160],{"className":126828},[2938],[363,126830],{"className":126831,"style":2934},[505],[363,126833,1291],{"className":126834,"style":1328},[407,408],[363,126836,126838,126841],{"className":126837},[501],[363,126839,468],{"className":126840},[501],[363,126842,126844],{"className":126843},[629],[363,126845,126847],{"className":126846},[633],[363,126848,126850],{"className":126849},[638],[363,126851,126853],{"className":126852,"style":20375},[642],[363,126854,126855,126858],{"style":7212},[363,126856],{"className":126857,"style":651},[650],[363,126859,126861],{"className":126860},[655,656,657,658],[363,126862,2810],{"className":126863},[407,658],[363,126865,666],{"className":126866},[665],[363,126868,126870],{"className":126869},[638],[363,126871,126873],{"className":126872,"style":854},[642],[363,126874],{},[363,126876],{"className":126877},[501,789],[363,126879],{"className":126880,"style":754},[505],[363,126882,592],{"className":126883},[407,408],[363,126885,1121],{"className":126886},[407,408],[363,126888],{"className":126889,"style":506},[505],[363,126891,471],{"className":126892},[510],[363,126894],{"className":126895,"style":506},[505],[363,126897,126899,126902,126905,126908,126996,126999,127002],{"className":126898},[398],[363,126900],{"className":126901,"style":38045},[402],[363,126903,1634],{"className":126904,"style":1834},[1831,1832,1833],[363,126906],{"className":126907,"style":754},[505],[363,126909,126911,126914,126993],{"className":126910},[407],[363,126912],{"className":126913},[494,789],[363,126915,126917],{"className":126916},[586],[363,126918,126920,126985],{"className":126919},[633,634],[363,126921,126923,126982],{"className":126922},[638],[363,126924,126926,126937,126945],{"className":126925,"style":38070},[642],[363,126927,126928,126931],{"style":805},[363,126929],{"className":126930,"style":809},[650],[363,126932,126934],{"className":126933},[407],[363,126935,1291],{"className":126936,"style":1328},[407,408],[363,126938,126939,126942],{"style":821},[363,126940],{"className":126941,"style":809},[650],[363,126943],{"className":126944,"style":829},[828],[363,126946,126947,126950],{"style":832},[363,126948],{"className":126949,"style":809},[650],[363,126951,126953],{"className":126952},[407],[363,126954,126956,126959],{"className":126955},[407],[363,126957,11],{"className":126958},[407,408],[363,126960,126962],{"className":126961},[629],[363,126963,126965],{"className":126964},[633],[363,126966,126968],{"className":126967},[638],[363,126969,126971],{"className":126970,"style":20375},[642],[363,126972,126973,126976],{"style":7212},[363,126974],{"className":126975,"style":651},[650],[363,126977,126979],{"className":126978},[655,656,657,658],[363,126980,2810],{"className":126981},[407,658],[363,126983,666],{"className":126984},[665],[363,126986,126988],{"className":126987},[638],[363,126989,126991],{"className":126990,"style":854},[642],[363,126992],{},[363,126994],{"className":126995},[501,789],[363,126997],{"className":126998,"style":2934},[505],[363,127000,5160],{"className":127001},[2938],[363,127003],{"className":127004,"style":2934},[505],[363,127006,127008,127011,127014,127017,127020],{"className":127007},[398],[363,127009],{"className":127010,"style":520},[402],[363,127012,465],{"className":127013},[407],[363,127015],{"className":127016,"style":506},[505],[363,127018,471],{"className":127019},[510],[363,127021],{"className":127022,"style":506},[505],[363,127024,127026,127029,127032,127035,127038,127167,127170,127173],{"className":127025},[398],[363,127027],{"className":127028,"style":87605},[402],[363,127030,126281],{"className":127031},[1831],[363,127033],{"className":127034,"style":1859},[505],[363,127036],{"className":127037,"style":754},[505],[363,127039,127041,127047,127161],{"className":127040},[758],[363,127042,127044],{"className":127043,"style":763},[494,762],[363,127045,461],{"className":127046},[767,657],[363,127048,127050,127053,127158],{"className":127049},[407],[363,127051],{"className":127052},[494,789],[363,127054,127056],{"className":127055},[586],[363,127057,127059,127150],{"className":127058},[633,634],[363,127060,127062,127147],{"className":127061},[638],[363,127063,127065,127102,127110],{"className":127064,"style":38070},[642],[363,127066,127067,127070],{"style":805},[363,127068],{"className":127069,"style":809},[650],[363,127071,127073],{"className":127072},[407],[363,127074,127076,127079],{"className":127075},[407],[363,127077,2679],{"className":127078,"style":1328},[407,408],[363,127080,127082],{"className":127081},[629],[363,127083,127085],{"className":127084},[633],[363,127086,127088],{"className":127087},[638],[363,127089,127091],{"className":127090,"style":45379},[642],[363,127092,127093,127096],{"style":45382},[363,127094],{"className":127095,"style":651},[650],[363,127097,127099],{"className":127098},[655,656,657,658],[363,127100,2810],{"className":127101},[407,658],[363,127103,127104,127107],{"style":821},[363,127105],{"className":127106,"style":809},[650],[363,127108],{"className":127109,"style":829},[828],[363,127111,127112,127115],{"style":832},[363,127113],{"className":127114,"style":809},[650],[363,127116,127118],{"className":127117},[407],[363,127119,127121,127124],{"className":127120},[407],[363,127122,126023],{"className":127123},[407],[363,127125,127127],{"className":127126},[629],[363,127128,127130],{"className":127129},[633],[363,127131,127133],{"className":127132},[638],[363,127134,127136],{"className":127135,"style":20375},[642],[363,127137,127138,127141],{"style":7212},[363,127139],{"className":127140,"style":651},[650],[363,127142,127144],{"className":127143},[655,656,657,658],[363,127145,2810],{"className":127146},[407,658],[363,127148,666],{"className":127149},[665],[363,127151,127153],{"className":127152},[638],[363,127154,127156],{"className":127155,"style":4125},[642],[363,127157],{},[363,127159],{"className":127160},[501,789],[363,127162,127164],{"className":127163,"style":763},[501,762],[363,127165,468],{"className":127166},[767,657],[363,127168],{"className":127169,"style":2934},[505],[363,127171,5160],{"className":127172},[2938],[363,127174],{"className":127175,"style":2934},[505],[363,127177,127179,127182],{"className":127178},[398],[363,127180],{"className":127181,"style":520},[402],[363,127183,49857],{"className":127184},[407],[11,127186,127187,127188,127246,127247,127346],{},"这印证了「无界」：两个虽很接近但支撑重叠的正态，",[363,127189,127191,127208],{"className":127190,"translate":367},[366],[363,127192,127194],{"className":127193},[371],[373,127195,127196],{"xmlns":375},[377,127197,127198,127206],{},[380,127199,127200],{},[7161,127201,127202,127204],{},[383,127203,37796],{},[463,127205,2810],{},[387,127207,40741],{"encoding":389},[363,127209,127211],{"className":127210,"ariaHidden":394},[393],[363,127212,127214,127217],{"className":127213},[398],[363,127215],{"className":127216,"style":40751},[402],[363,127218,127220,127223],{"className":127219},[407],[363,127221,37796],{"className":127222},[407,408],[363,127224,127226],{"className":127225},[629],[363,127227,127229],{"className":127228},[633],[363,127230,127232],{"className":127231},[638],[363,127233,127235],{"className":127234,"style":20375},[642],[363,127236,127237,127240],{"style":7212},[363,127238],{"className":127239,"style":651},[650],[363,127241,127243],{"className":127242},[655,656,657,658],[363,127244,2810],{"className":127245},[407,658]," 也会随 ",[363,127248,127250,127276],{"className":127249,"translate":367},[366],[363,127251,127253],{"className":127252},[371],[373,127254,127255],{"xmlns":375},[377,127256,127257,127273],{},[380,127258,127259,127265,127267],{},[7161,127260,127261,127263],{},[383,127262,126023],{"mathvariant":557},[463,127264,2810],{},[383,127266,1288],{"mathvariant":557},[7161,127268,127269,127271],{},[383,127270,2679],{},[463,127272,2810],{},[387,127274,127275],{"encoding":389},"\\Delta^2\u002F\\sigma^2",[363,127277,127279],{"className":127278,"ariaHidden":394},[393],[363,127280,127282,127285,127314,127317],{"className":127281},[398],[363,127283],{"className":127284,"style":20350},[402],[363,127286,127288,127291],{"className":127287},[407],[363,127289,126023],{"className":127290},[407],[363,127292,127294],{"className":127293},[629],[363,127295,127297],{"className":127296},[633],[363,127298,127300],{"className":127299},[638],[363,127301,127303],{"className":127302,"style":20375},[642],[363,127304,127305,127308],{"style":7212},[363,127306],{"className":127307,"style":651},[650],[363,127309,127311],{"className":127310},[655,656,657,658],[363,127312,2810],{"className":127313},[407,658],[363,127315,1288],{"className":127316},[407],[363,127318,127320,127323],{"className":127319},[407],[363,127321,2679],{"className":127322,"style":1328},[407,408],[363,127324,127326],{"className":127325},[629],[363,127327,127329],{"className":127328},[633],[363,127330,127332],{"className":127331},[638],[363,127333,127335],{"className":127334,"style":20375},[642],[363,127336,127337,127340],{"style":7212},[363,127338],{"className":127339,"style":651},[650],[363,127341,127343],{"className":127342},[655,656,657,658],[363,127344,2810],{"className":127345},[407,658]," 指数爆炸。",[11,127348,127349,127352],{},[1572,127350,127351],{},"Hellinger²（等方差）。"," Bhattacharyya 系数",[363,127354,127356],{"className":127355,"translate":367},[528],[363,127357,127359,127433],{"className":127358,"translate":367},[366],[363,127360,127362],{"className":127361},[371],[373,127363,127364],{"xmlns":375,"display":537},[377,127365,127366,127430],{},[380,127367,127368,127370,127372,127374,127376,127378,127380,127382,127384,127386,127394,127396,127398,127400,127402,127428],{},[383,127369,39638],{},[383,127371,39641],{},[458,127373,461],{"stretchy":460},[383,127375,554],{},[458,127377,898],{"separator":394},[383,127379,561],{},[458,127381,468],{"stretchy":460},[458,127383,471],{},[458,127385,1634],{},[34686,127387,127388],{},[380,127389,127390,127392],{},[383,127391,11],{},[383,127393,1291],{},[458,127395,471],{},[383,127397,126281],{},[458,127399,4450],{},[1644,127401,1651],{},[380,127403,127404,127406,127408,127426],{},[458,127405,461],{"fence":394},[458,127407,5160],{},[586,127409,127410,127416],{},[7161,127411,127412,127414],{},[383,127413,126023],{"mathvariant":557},[463,127415,2810],{},[380,127417,127418,127420],{},[463,127419,39650],{},[7161,127421,127422,127424],{},[383,127423,2679],{},[463,127425,2810],{},[458,127427,468],{"fence":394},[458,127429,898],{"separator":394},[387,127431,127432],{"encoding":389},"BC(P,Q)=\\int\\sqrt{pq}\n=\\exp\\!\\left(-\\frac{\\Delta^2}{8\\sigma^2}\\right),",[363,127434,127436,127475,127543],{"className":127435,"ariaHidden":394},[393],[363,127437,127439,127442,127445,127448,127451,127454,127457,127460,127463,127466,127469,127472],{"className":127438},[398],[363,127440],{"className":127441,"style":487},[402],[363,127443,39638],{"className":127444,"style":39734},[407,408],[363,127446,39641],{"className":127447,"style":11129},[407,408],[363,127449,461],{"className":127450},[494],[363,127452,554],{"className":127453,"style":682},[407,408],[363,127455,898],{"className":127456},[920],[363,127458],{"className":127459,"style":754},[505],[363,127461,561],{"className":127462},[407,408],[363,127464,468],{"className":127465},[501],[363,127467],{"className":127468,"style":506},[505],[363,127470,471],{"className":127471},[510],[363,127473],{"className":127474,"style":506},[505],[363,127476,127478,127481,127484,127487,127534,127537,127540],{"className":127477},[398],[363,127479],{"className":127480,"style":6124},[402],[363,127482,1634],{"className":127483,"style":1834},[1831,1832,1833],[363,127485],{"className":127486,"style":754},[505],[363,127488,127490],{"className":127489},[407,34714],[363,127491,127493,127526],{"className":127492},[633,634],[363,127494,127496,127523],{"className":127495},[638],[363,127497,127499,127511],{"className":127498,"style":7209},[642],[363,127500,127502,127505],{"className":127501,"style":12210},[6654],[363,127503],{"className":127504,"style":809},[650],[363,127506,127508],{"className":127507,"style":34734},[407],[363,127509,41952],{"className":127510,"style":1328},[407,408],[363,127512,127513,127516],{"style":41697},[363,127514],{"className":127515,"style":809},[650],[363,127517,127519],{"className":127518,"style":34791},[34790],[6670,127520,127521],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,127522],{"d":34798},[363,127524,666],{"className":127525},[665],[363,127527,127529],{"className":127528},[638],[363,127530,127532],{"className":127531,"style":41717},[642],[363,127533],{},[363,127535],{"className":127536,"style":506},[505],[363,127538,471],{"className":127539},[510],[363,127541],{"className":127542,"style":506},[505],[363,127544,127546,127549,127552,127555,127558,127693,127696],{"className":127545},[398],[363,127547],{"className":127548,"style":87605},[402],[363,127550,126281],{"className":127551},[1831],[363,127553],{"className":127554,"style":1859},[505],[363,127556],{"className":127557,"style":754},[505],[363,127559,127561,127567,127570,127687],{"className":127560},[758],[363,127562,127564],{"className":127563,"style":763},[494,762],[363,127565,461],{"className":127566},[767,657],[363,127568,5160],{"className":127569},[407],[363,127571,127573,127576,127684],{"className":127572},[407],[363,127574],{"className":127575},[494,789],[363,127577,127579],{"className":127578},[586],[363,127580,127582,127676],{"className":127581},[633,634],[363,127583,127585,127673],{"className":127584},[638],[363,127586,127588,127628,127636],{"className":127587,"style":38070},[642],[363,127589,127590,127593],{"style":805},[363,127591],{"className":127592,"style":809},[650],[363,127594,127596,127599],{"className":127595},[407],[363,127597,39650],{"className":127598},[407],[363,127600,127602,127605],{"className":127601},[407],[363,127603,2679],{"className":127604,"style":1328},[407,408],[363,127606,127608],{"className":127607},[629],[363,127609,127611],{"className":127610},[633],[363,127612,127614],{"className":127613},[638],[363,127615,127617],{"className":127616,"style":45379},[642],[363,127618,127619,127622],{"style":45382},[363,127620],{"className":127621,"style":651},[650],[363,127623,127625],{"className":127624},[655,656,657,658],[363,127626,2810],{"className":127627},[407,658],[363,127629,127630,127633],{"style":821},[363,127631],{"className":127632,"style":809},[650],[363,127634],{"className":127635,"style":829},[828],[363,127637,127638,127641],{"style":832},[363,127639],{"className":127640,"style":809},[650],[363,127642,127644],{"className":127643},[407],[363,127645,127647,127650],{"className":127646},[407],[363,127648,126023],{"className":127649},[407],[363,127651,127653],{"className":127652},[629],[363,127654,127656],{"className":127655},[633],[363,127657,127659],{"className":127658},[638],[363,127660,127662],{"className":127661,"style":20375},[642],[363,127663,127664,127667],{"style":7212},[363,127665],{"className":127666,"style":651},[650],[363,127668,127670],{"className":127669},[655,656,657,658],[363,127671,2810],{"className":127672},[407,658],[363,127674,666],{"className":127675},[665],[363,127677,127679],{"className":127678},[638],[363,127680,127682],{"className":127681,"style":4125},[642],[363,127683],{},[363,127685],{"className":127686},[501,789],[363,127688,127690],{"className":127689,"style":763},[501,762],[363,127691,468],{"className":127692},[767,657],[363,127694],{"className":127695,"style":754},[505],[363,127697,898],{"className":127698},[920],[11,127700,92140,127701,3092,127959,128214],{},[363,127702,127704,127758],{"className":127703,"translate":367},[366],[363,127705,127707],{"className":127706},[371],[373,127708,127709],{"xmlns":375},[377,127710,127711,127755],{},[380,127712,127713,127721,127723,127725,127727],{},[7900,127714,127715,127717,127719],{},[383,127716,34231],{},[1644,127718,42484],{},[463,127720,2810],{},[458,127722,471],{},[463,127724,465],{},[458,127726,5160],{},[7161,127728,127729,127731],{},[383,127730,7914],{},[380,127732,127733,127735,127741,127743,127745,127747,127753],{},[458,127734,5160],{},[7161,127736,127737,127739],{},[383,127738,126023],{"mathvariant":557},[463,127740,2810],{},[383,127742,1288],{"mathvariant":557},[458,127744,461],{"stretchy":460},[463,127746,39650],{},[7161,127748,127749,127751],{},[383,127750,2679],{},[463,127752,2810],{},[458,127754,468],{"stretchy":460},[387,127756,127757],{"encoding":389},"H^2_{\\text{Bhattacharyya}}=1-e^{-\\Delta^2\u002F(8\\sigma^2)}",[363,127759,127761,127833,127851],{"className":127760,"ariaHidden":394},[393],[363,127762,127764,127767,127824,127827,127830],{"className":127763},[398],[363,127765],{"className":127766,"style":43232},[402],[363,127768,127770,127773],{"className":127769},[407],[363,127771,34231],{"className":127772,"style":34385},[407,408],[363,127774,127776],{"className":127775},[629],[363,127777,127779,127816],{"className":127778},[633,634],[363,127780,127782,127813],{"className":127781},[638],[363,127783,127785,127802],{"className":127784,"style":20375},[642],[363,127786,127787,127790],{"style":43256},[363,127788],{"className":127789,"style":651},[650],[363,127791,127793],{"className":127792},[655,656,657,658],[363,127794,127796],{"className":127795},[407,658],[363,127797,127799],{"className":127798},[407,4945,658],[363,127800,42484],{"className":127801},[407,658],[363,127803,127804,127807],{"style":7212},[363,127805],{"className":127806,"style":651},[650],[363,127808,127810],{"className":127809},[655,656,657,658],[363,127811,2810],{"className":127812},[407,658],[363,127814,666],{"className":127815},[665],[363,127817,127819],{"className":127818},[638],[363,127820,127822],{"className":127821,"style":43292},[642],[363,127823],{},[363,127825],{"className":127826,"style":506},[505],[363,127828,471],{"className":127829},[510],[363,127831],{"className":127832,"style":506},[505],[363,127834,127836,127839,127842,127845,127848],{"className":127835},[398],[363,127837],{"className":127838,"style":12925},[402],[363,127840,465],{"className":127841},[407],[363,127843],{"className":127844,"style":2934},[505],[363,127846,5160],{"className":127847},[2938],[363,127849],{"className":127850,"style":2934},[505],[363,127852,127854,127857],{"className":127853},[398],[363,127855],{"className":127856,"style":117628},[402],[363,127858,127860,127863],{"className":127859},[407],[363,127861,7914],{"className":127862},[407,408],[363,127864,127866],{"className":127865},[629],[363,127867,127869],{"className":127868},[633],[363,127870,127872],{"className":127871},[638],[363,127873,127875],{"className":127874,"style":117628},[642],[363,127876,127877,127880],{"style":7212},[363,127878],{"className":127879,"style":651},[650],[363,127881,127883],{"className":127882},[655,656,657,658],[363,127884,127886,127889,127918,127921,127924,127927,127956],{"className":127885},[407,658],[363,127887,5160],{"className":127888},[407,658],[363,127890,127892,127895],{"className":127891},[407,658],[363,127893,126023],{"className":127894},[407,658],[363,127896,127898],{"className":127897},[629],[363,127899,127901],{"className":127900},[633],[363,127902,127904],{"className":127903},[638],[363,127905,127907],{"className":127906,"style":38859},[642],[363,127908,127909,127912],{"style":38862},[363,127910],{"className":127911,"style":30553},[650],[363,127913,127915],{"className":127914},[655,30557,10021,658],[363,127916,2810],{"className":127917},[407,658],[363,127919,1288],{"className":127920},[407,658],[363,127922,461],{"className":127923},[494,658],[363,127925,39650],{"className":127926},[407,658],[363,127928,127930,127933],{"className":127929},[407,658],[363,127931,2679],{"className":127932,"style":1328},[407,408,658],[363,127934,127936],{"className":127935},[629],[363,127937,127939],{"className":127938},[633],[363,127940,127942],{"className":127941},[638],[363,127943,127945],{"className":127944,"style":38859},[642],[363,127946,127947,127950],{"style":38862},[363,127948],{"className":127949,"style":30553},[650],[363,127951,127953],{"className":127952},[655,30557,10021,658],[363,127954,2810],{"className":127955},[407,658],[363,127957,468],{"className":127958},[501,658],[363,127960,127962,128020],{"className":127961,"translate":367},[366],[363,127963,127965],{"className":127964},[371],[373,127966,127967],{"xmlns":375},[377,127968,127969,128017],{},[380,127970,127971,127977,127979,127981,127983,127985,127987,128015],{},[543,127972,127973,127975],{},[383,127974,547],{},[383,127976,385],{},[458,127978,471],{},[463,127980,2810],{},[458,127982,461],{"stretchy":460},[463,127984,465],{},[458,127986,5160],{},[7161,127988,127989,127991],{},[383,127990,7914],{},[380,127992,127993,127995,128001,128003,128005,128007,128013],{},[458,127994,5160],{},[7161,127996,127997,127999],{},[383,127998,126023],{"mathvariant":557},[463,128000,2810],{},[383,128002,1288],{"mathvariant":557},[458,128004,461],{"stretchy":460},[463,128006,39650],{},[7161,128008,128009,128011],{},[383,128010,2679],{},[463,128012,2810],{},[458,128014,468],{"stretchy":460},[458,128016,468],{"stretchy":460},[387,128018,128019],{"encoding":389},"D_f=2(1-e^{-\\Delta^2\u002F(8\\sigma^2)})",[363,128021,128023,128078,128102],{"className":128022,"ariaHidden":394},[393],[363,128024,128026,128029,128069,128072,128075],{"className":128025},[398],[363,128027],{"className":128028,"style":4379},[402],[363,128030,128032,128035],{"className":128031},[407],[363,128033,547],{"className":128034,"style":625},[407,408],[363,128036,128038],{"className":128037},[629],[363,128039,128041,128061],{"className":128040},[633,634],[363,128042,128044,128058],{"className":128043},[638],[363,128045,128047],{"className":128046,"style":643},[642],[363,128048,128049,128052],{"style":646},[363,128050],{"className":128051,"style":651},[650],[363,128053,128055],{"className":128054},[655,656,657,658],[363,128056,385],{"className":128057,"style":409},[407,408,658],[363,128059,666],{"className":128060},[665],[363,128062,128064],{"className":128063},[638],[363,128065,128067],{"className":128066,"style":673},[642],[363,128068],{},[363,128070],{"className":128071,"style":506},[505],[363,128073,471],{"className":128074},[510],[363,128076],{"className":128077,"style":506},[505],[363,128079,128081,128084,128087,128090,128093,128096,128099],{"className":128080},[398],[363,128082],{"className":128083,"style":487},[402],[363,128085,2810],{"className":128086},[407],[363,128088,461],{"className":128089},[494],[363,128091,465],{"className":128092},[407],[363,128094],{"className":128095,"style":2934},[505],[363,128097,5160],{"className":128098},[2938],[363,128100],{"className":128101,"style":2934},[505],[363,128103,128105,128109,128211],{"className":128104},[398],[363,128106],{"className":128107,"style":128108},[402],"height:1.2369em;vertical-align:-0.25em;",[363,128110,128112,128115],{"className":128111},[407],[363,128113,7914],{"className":128114},[407,408],[363,128116,128118],{"className":128117},[629],[363,128119,128121],{"className":128120},[633],[363,128122,128124],{"className":128123},[638],[363,128125,128127],{"className":128126,"style":117628},[642],[363,128128,128129,128132],{"style":7212},[363,128130],{"className":128131,"style":651},[650],[363,128133,128135],{"className":128134},[655,656,657,658],[363,128136,128138,128141,128170,128173,128176,128179,128208],{"className":128137},[407,658],[363,128139,5160],{"className":128140},[407,658],[363,128142,128144,128147],{"className":128143},[407,658],[363,128145,126023],{"className":128146},[407,658],[363,128148,128150],{"className":128149},[629],[363,128151,128153],{"className":128152},[633],[363,128154,128156],{"className":128155},[638],[363,128157,128159],{"className":128158,"style":38859},[642],[363,128160,128161,128164],{"style":38862},[363,128162],{"className":128163,"style":30553},[650],[363,128165,128167],{"className":128166},[655,30557,10021,658],[363,128168,2810],{"className":128169},[407,658],[363,128171,1288],{"className":128172},[407,658],[363,128174,461],{"className":128175},[494,658],[363,128177,39650],{"className":128178},[407,658],[363,128180,128182,128185],{"className":128181},[407,658],[363,128183,2679],{"className":128184,"style":1328},[407,408,658],[363,128186,128188],{"className":128187},[629],[363,128189,128191],{"className":128190},[633],[363,128192,128194],{"className":128193},[638],[363,128195,128197],{"className":128196,"style":38859},[642],[363,128198,128199,128202],{"style":38862},[363,128200],{"className":128201,"style":30553},[650],[363,128203,128205],{"className":128204},[655,30557,10021,658],[363,128206,2810],{"className":128207},[407,658],[363,128209,468],{"className":128210},[501,658],[363,128212,468],{"className":128213},[501],"（本文约定）。",[11,128216,128217,128220],{},[1572,128218,128219],{},"α-散度（等方差）。"," 由 3.6 节",[363,128222,128224],{"className":128223,"translate":367},[528],[363,128225,128227,128335],{"className":128226,"translate":367},[366],[363,128228,128230],{"className":128229},[371],[373,128231,128232],{"xmlns":375,"display":537},[377,128233,128234,128332],{},[380,128235,128236,128242,128244,128262,128264,128266,128268,128308,128310,128312,128314,128316,128318,128330],{},[543,128237,128238,128240],{},[383,128239,547],{},[383,128241,45101],{},[458,128243,471],{},[586,128245,128246,128248],{},[463,128247,465],{},[380,128249,128250,128252,128254,128256,128258,128260],{},[383,128251,45527],{},[458,128253,461],{"stretchy":460},[463,128255,465],{},[458,128257,5160],{},[383,128259,45527],{},[458,128261,468],{"stretchy":460},[458,128263,461],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[463,128265,465],{},[458,128267,5160],{},[7161,128269,128270,128272],{},[383,128271,7914],{},[380,128273,128274,128276],{},[458,128275,5160],{},[586,128277,128278,128298],{},[380,128279,128280,128282,128284,128286,128288,128290,128292],{},[383,128281,45527],{},[458,128283,461],{"stretchy":460},[463,128285,465],{},[458,128287,5160],{},[383,128289,45527],{},[458,128291,468],{"stretchy":460},[7161,128293,128294,128296],{},[383,128295,126023],{"mathvariant":557},[463,128297,2810],{},[380,128299,128300,128302],{},[463,128301,2810],{},[7161,128303,128304,128306],{},[383,128305,2679],{},[463,128307,2810],{},[458,128309,468],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[458,128311,898],{"separator":394},[505,128313],{"width":3609},[383,128315,45527],{},[458,128317,471],{},[586,128319,128320,128328],{},[380,128321,128322,128324,128326],{},[463,128323,465],{},[458,128325,2817],{},[383,128327,45101],{},[463,128329,2810],{},[458,128331,898],{"separator":394},[387,128333,128334],{"encoding":389},"D_\\alpha=\\frac{1}{a(1-a)}\n\\Big(1-\ne^{-\\frac{a(1-a)\\Delta^2}{2\\sigma^2}}\\Big),\n\\qquad a=\\frac{1+\\alpha}{2},",[363,128336,128338,128393,128500,128712],{"className":128337,"ariaHidden":394},[393],[363,128339,128341,128344,128384,128387,128390],{"className":128340},[398],[363,128342],{"className":128343,"style":16308},[402],[363,128345,128347,128350],{"className":128346},[407],[363,128348,547],{"className":128349,"style":625},[407,408],[363,128351,128353],{"className":128352},[629],[363,128354,128356,128376],{"className":128355},[633,634],[363,128357,128359,128373],{"className":128358},[638],[363,128360,128362],{"className":128361,"style":45276},[642],[363,128363,128364,128367],{"style":646},[363,128365],{"className":128366,"style":651},[650],[363,128368,128370],{"className":128369},[655,656,657,658],[363,128371,45101],{"className":128372,"style":45131},[407,408,658],[363,128374,666],{"className":128375},[665],[363,128377,128379],{"className":128378},[638],[363,128380,128382],{"className":128381,"style":8315},[642],[363,128383],{},[363,128385],{"className":128386,"style":506},[505],[363,128388,471],{"className":128389},[510],[363,128391],{"className":128392,"style":506},[505],[363,128394,128396,128399,128482,128488,128491,128494,128497],{"className":128395},[398],[363,128397],{"className":128398,"style":68916},[402],[363,128400,128402,128405,128479],{"className":128401},[407],[363,128403],{"className":128404},[494,789],[363,128406,128408],{"className":128407},[586],[363,128409,128411,128471],{"className":128410},[633,634],[363,128412,128414,128468],{"className":128413},[638],[363,128415,128417,128449,128457],{"className":128416,"style":23236},[642],[363,128418,128419,128422],{"style":805},[363,128420],{"className":128421,"style":809},[650],[363,128423,128425,128428,128431,128434,128437,128440,128443,128446],{"className":128424},[407],[363,128426,45527],{"className":128427},[407,408],[363,128429,461],{"className":128430},[494],[363,128432,465],{"className":128433},[407],[363,128435],{"className":128436,"style":2934},[505],[363,128438,5160],{"className":128439},[2938],[363,128441],{"className":128442,"style":2934},[505],[363,128444,45527],{"className":128445},[407,408],[363,128447,468],{"className":128448},[501],[363,128450,128451,128454],{"style":821},[363,128452],{"className":128453,"style":809},[650],[363,128455],{"className":128456,"style":829},[828],[363,128458,128459,128462],{"style":832},[363,128460],{"className":128461,"style":809},[650],[363,128463,128465],{"className":128464},[407],[363,128466,465],{"className":128467},[407],[363,128469,666],{"className":128470},[665],[363,128472,128474],{"className":128473},[638],[363,128475,128477],{"className":128476,"style":1948},[642],[363,128478],{},[363,128480],{"className":128481},[501,789],[363,128483,128485],{"className":128484},[407],[363,128486,461],{"className":128487},[767,4067],[363,128489,465],{"className":128490},[407],[363,128492],{"className":128493,"style":2934},[505],[363,128495,5160],{"className":128496},[2938],[363,128498],{"className":128499,"style":2934},[505],[363,128501,128503,128507,128685,128691,128694,128697,128700,128703,128706,128709],{"className":128502},[398],[363,128504],{"className":128505,"style":128506},[402],"height:1.9791em;vertical-align:-0.65em;",[363,128508,128510,128513],{"className":128509},[407],[363,128511,7914],{"className":128512},[407,408],[363,128514,128516],{"className":128515},[629],[363,128517,128519],{"className":128518},[633],[363,128520,128522],{"className":128521},[638],[363,128523,128526],{"className":128524,"style":128525},[642],"height:1.3291em;",[363,128527,128529,128532],{"style":128528},"top:-3.4534em;margin-right:0.05em;",[363,128530],{"className":128531,"style":809},[650],[363,128533,128535],{"className":128534},[655,656,657,658],[363,128536,128538,128541],{"className":128537},[407,658],[363,128539,5160],{"className":128540},[407,658],[363,128542,128544,128547,128682],{"className":128543},[407,658],[363,128545],{"className":128546},[494,789,655,30557,111670],[363,128548,128550],{"className":128549},[586],[363,128551,128553,128673],{"className":128552},[633,634],[363,128554,128556,128670],{"className":128555},[638],[363,128557,128560,128604,128612],{"className":128558,"style":128559},[642],"height:1.251em;",[363,128561,128563,128566],{"style":128562},"top:-2.5062em;",[363,128564],{"className":128565,"style":809},[650],[363,128567,128569],{"className":128568},[655,30557,10021,658],[363,128570,128572,128575],{"className":128571},[407,658],[363,128573,2810],{"className":128574},[407,658],[363,128576,128578,128581],{"className":128577},[407,658],[363,128579,2679],{"className":128580,"style":1328},[407,408,658],[363,128582,128584],{"className":128583},[629],[363,128585,128587],{"className":128586},[633],[363,128588,128590],{"className":128589},[638],[363,128591,128594],{"className":128592,"style":128593},[642],"height:0.9384em;",[363,128595,128597,128601],{"style":128596},"top:-2.9384em;margin-right:0.1em;",[363,128598],{"className":128599,"style":128600},[650],"height:2.6444em;",[363,128602,2810],{"className":128603},[407,658],[363,128605,128606,128609],{"style":111707},[363,128607],{"className":128608,"style":809},[650],[363,128610],{"className":128611,"style":111714},[828,658],[363,128613,128615,128618],{"style":128614},"top:-3.5021em;",[363,128616],{"className":128617,"style":809},[650],[363,128619,128621],{"className":128620},[655,30557,10021,658],[363,128622,128624,128627,128630,128633,128636,128639,128642],{"className":128623},[407,658],[363,128625,45527],{"className":128626},[407,408,658],[363,128628,461],{"className":128629},[494,658],[363,128631,465],{"className":128632},[407,658],[363,128634,5160],{"className":128635},[2938,658],[363,128637,45527],{"className":128638},[407,408,658],[363,128640,468],{"className":128641},[501,658],[363,128643,128645,128648],{"className":128644},[407,658],[363,128646,126023],{"className":128647},[407,658],[363,128649,128651],{"className":128650},[629],[363,128652,128654],{"className":128653},[633],[363,128655,128657],{"className":128656},[638],[363,128658,128661],{"className":128659,"style":128660},[642],"height:1.0484em;",[363,128662,128664,128667],{"style":128663},"top:-3.0484em;margin-right:0.1em;",[363,128665],{"className":128666,"style":128600},[650],[363,128668,2810],{"className":128669},[407,658],[363,128671,666],{"className":128672},[665],[363,128674,128676],{"className":128675},[638],[363,128677,128680],{"className":128678,"style":128679},[642],"height:0.4938em;",[363,128681],{},[363,128683],{"className":128684},[501,789,655,30557,111670],[363,128686,128688],{"className":128687},[407],[363,128689,468],{"className":128690},[767,4067],[363,128692,898],{"className":128693},[920],[363,128695],{"className":128696,"style":3981},[505],[363,128698],{"className":128699,"style":754},[505],[363,128701,45527],{"className":128702},[407,408],[363,128704],{"className":128705,"style":506},[505],[363,128707,471],{"className":128708},[510],[363,128710],{"className":128711,"style":506},[505],[363,128713,128715,128718,128792],{"className":128714},[398],[363,128716],{"className":128717,"style":26250},[402],[363,128719,128721,128724,128789],{"className":128720},[407],[363,128722],{"className":128723},[494,789],[363,128725,128727],{"className":128726},[586],[363,128728,128730,128781],{"className":128729},[633,634],[363,128731,128733,128778],{"className":128732},[638],[363,128734,128736,128747,128755],{"className":128735,"style":23236},[642],[363,128737,128738,128741],{"style":805},[363,128739],{"className":128740,"style":809},[650],[363,128742,128744],{"className":128743},[407],[363,128745,2810],{"className":128746},[407],[363,128748,128749,128752],{"style":821},[363,128750],{"className":128751,"style":809},[650],[363,128753],{"className":128754,"style":829},[828],[363,128756,128757,128760],{"style":832},[363,128758],{"className":128759,"style":809},[650],[363,128761,128763,128766,128769,128772,128775],{"className":128762},[407],[363,128764,465],{"className":128765},[407],[363,128767],{"className":128768,"style":2934},[505],[363,128770,2817],{"className":128771},[2938],[363,128773],{"className":128774,"style":2934},[505],[363,128776,45101],{"className":128777,"style":45131},[407,408],[363,128779,666],{"className":128780},[665],[363,128782,128784],{"className":128783},[638],[363,128785,128787],{"className":128786,"style":4125},[642],[363,128788],{},[363,128790],{"className":128791},[501,789],[363,128793,898],{"className":128794},[920],[11,128796,128797,128798,32571,128827,129007,129008,129036],{},"在小 ",[363,128799,128801,128815],{"className":128800,"translate":367},[366],[363,128802,128804],{"className":128803},[371],[373,128805,128806],{"xmlns":375},[377,128807,128808,128812],{},[380,128809,128810],{},[383,128811,126023],{"mathvariant":557},[387,128813,128814],{"encoding":389},"\\Delta",[363,128816,128818],{"className":128817,"ariaHidden":394},[393],[363,128819,128821,128824],{"className":128820},[398],[363,128822],{"className":128823,"style":1011},[402],[363,128825,126023],{"className":128826},[407],[363,128828,128830,128862],{"className":128829,"translate":367},[366],[363,128831,128833],{"className":128832},[371],[373,128834,128835],{"xmlns":375},[377,128836,128837,128859],{},[380,128838,128839,128841],{},[458,128840,33306],{},[586,128842,128843,128849],{},[7161,128844,128845,128847],{},[383,128846,126023],{"mathvariant":557},[463,128848,2810],{},[380,128850,128851,128853],{},[463,128852,2810],{},[7161,128854,128855,128857],{},[383,128856,2679],{},[463,128858,2810],{},[387,128860,128861],{"encoding":389},"\\approx\\frac{\\Delta^2}{2\\sigma^2}",[363,128863,128865,128877],{"className":128864,"ariaHidden":394},[393],[363,128866,128868,128871,128874],{"className":128867},[398],[363,128869],{"className":128870,"style":117508},[402],[363,128872,33306],{"className":128873},[510],[363,128875],{"className":128876,"style":506},[505],[363,128878,128880,128884],{"className":128879},[398],[363,128881],{"className":128882,"style":128883},[402],"height:1.3629em;vertical-align:-0.345em;",[363,128885,128887,128890,129004],{"className":128886},[407],[363,128888],{"className":128889},[494,789],[363,128891,128893],{"className":128892},[586],[363,128894,128896,128996],{"className":128895},[633,634],[363,128897,128899,128993],{"className":128898},[638],[363,128900,128902,128945,128953],{"className":128901,"style":114119},[642],[363,128903,128904,128907],{"style":2874},[363,128905],{"className":128906,"style":809},[650],[363,128908,128910],{"className":128909},[655,656,657,658],[363,128911,128913,128916],{"className":128912},[407,658],[363,128914,2810],{"className":128915},[407,658],[363,128917,128919,128922],{"className":128918},[407,658],[363,128920,2679],{"className":128921,"style":1328},[407,408,658],[363,128923,128925],{"className":128924},[629],[363,128926,128928],{"className":128927},[633],[363,128929,128931],{"className":128930},[638],[363,128932,128934],{"className":128933,"style":45806},[642],[363,128935,128936,128939],{"style":45809},[363,128937],{"className":128938,"style":30553},[650],[363,128940,128942],{"className":128941},[655,30557,10021,658],[363,128943,2810],{"className":128944},[407,658],[363,128946,128947,128950],{"style":821},[363,128948],{"className":128949,"style":809},[650],[363,128951],{"className":128952,"style":829},[828],[363,128954,128955,128958],{"style":2897},[363,128956],{"className":128957,"style":809},[650],[363,128959,128961],{"className":128960},[655,656,657,658],[363,128962,128964],{"className":128963},[407,658],[363,128965,128967,128970],{"className":128966},[407,658],[363,128968,126023],{"className":128969},[407,658],[363,128971,128973],{"className":128972},[629],[363,128974,128976],{"className":128975},[633],[363,128977,128979],{"className":128978},[638],[363,128980,128982],{"className":128981,"style":38859},[642],[363,128983,128984,128987],{"style":38862},[363,128985],{"className":128986,"style":30553},[650],[363,128988,128990],{"className":128989},[655,30557,10021,658],[363,128991,2810],{"className":128992},[407,658],[363,128994,666],{"className":128995},[665],[363,128997,128999],{"className":128998},[638],[363,129000,129002],{"className":129001,"style":2919},[642],[363,129003],{},[363,129005],{"className":129006},[501,789],"，与 4.6 节的局部展开一致（且此时与 ",[363,129009,129011,129024],{"className":129010,"translate":367},[366],[363,129012,129014],{"className":129013},[371],[373,129015,129016],{"xmlns":375},[377,129017,129018,129022],{},[380,129019,129020],{},[383,129021,45101],{},[387,129023,49437],{"encoding":389},[363,129025,129027],{"className":129026,"ariaHidden":394},[393],[363,129028,129030,129033],{"className":129029},[398],[363,129031],{"className":129032,"style":2692},[402],[363,129034,45101],{"className":129035,"style":45131},[407,408]," 无关）。",[2658,129038,129040],{"id":129039},"_92-伯努利分布","9.2 伯努利分布",[11,129042,881,129043,5992,129120,16142,129197,129284,129285,129387,129388,129416,129417,129387,129583,1338],{},[363,129044,129046,129078],{"className":129045,"translate":367},[366],[363,129047,129049],{"className":129048},[371],[373,129050,129051],{"xmlns":375},[377,129052,129053,129075],{},[380,129054,129055,129057,129059,129069,129071,129073],{},[383,129056,554],{},[458,129058,471],{},[380,129060,129061,129063,129065,129067],{},[383,129062,39638],{"mathvariant":557},[383,129064,7914],{"mathvariant":557},[383,129066,16797],{"mathvariant":557},[383,129068,82643],{"mathvariant":557},[458,129070,461],{"stretchy":460},[383,129072,11],{},[458,129074,468],{"stretchy":460},[387,129076,129077],{"encoding":389},"P=\\mathrm{Bern}(p)",[363,129079,129081,129099],{"className":129080,"ariaHidden":394},[393],[363,129082,129084,129087,129090,129093,129096],{"className":129083},[398],[363,129085],{"className":129086,"style":1011},[402],[363,129088,554],{"className":129089,"style":682},[407,408],[363,129091],{"className":129092,"style":506},[505],[363,129094,471],{"className":129095},[510],[363,129097],{"className":129098,"style":506},[505],[363,129100,129102,129105,129111,129114,129117],{"className":129101},[398],[363,129103],{"className":129104,"style":487},[402],[363,129106,129108],{"className":129107},[407],[363,129109,84655],{"className":129110},[407,33009],[363,129112,461],{"className":129113},[494],[363,129115,11],{"className":129116},[407,408],[363,129118,468],{"className":129119},[501],[363,129121,129123,129155],{"className":129122,"translate":367},[366],[363,129124,129126],{"className":129125},[371],[373,129127,129128],{"xmlns":375},[377,129129,129130,129152],{},[380,129131,129132,129134,129136,129146,129148,129150],{},[383,129133,561],{},[458,129135,471],{},[380,129137,129138,129140,129142,129144],{},[383,129139,39638],{"mathvariant":557},[383,129141,7914],{"mathvariant":557},[383,129143,16797],{"mathvariant":557},[383,129145,82643],{"mathvariant":557},[458,129147,461],{"stretchy":460},[383,129149,1291],{},[458,129151,468],{"stretchy":460},[387,129153,129154],{"encoding":389},"Q=\\mathrm{Bern}(q)",[363,129156,129158,129176],{"className":129157,"ariaHidden":394},[393],[363,129159,129161,129164,129167,129170,129173],{"className":129160},[398],[363,129162],{"className":129163,"style":913},[402],[363,129165,561],{"className":129166},[407,408],[363,129168],{"className":129169,"style":506},[505],[363,129171,471],{"className":129172},[510],[363,129174],{"className":129175,"style":506},[505],[363,129177,129179,129182,129188,129191,129194],{"className":129178},[398],[363,129180],{"className":129181,"style":487},[402],[363,129183,129185],{"className":129184},[407],[363,129186,84655],{"className":129187},[407,33009],[363,129189,461],{"className":129190},[494],[363,129192,1291],{"className":129193,"style":1328},[407,408],[363,129195,468],{"className":129196},[501],[363,129198,129200,129230],{"className":129199,"translate":367},[366],[363,129201,129203],{"className":129202},[371],[373,129204,129205],{"xmlns":375},[377,129206,129207,129227],{},[380,129208,129209,129211,129213,129215,129217,129219,129221,129223,129225],{},[383,129210,11],{},[458,129212,898],{"separator":394},[383,129214,1291],{},[458,129216,6256],{},[458,129218,461],{"stretchy":460},[463,129220,474],{},[458,129222,898],{"separator":394},[463,129224,465],{},[458,129226,468],{"stretchy":460},[387,129228,129229],{"encoding":389},"p,q\\in(0,1)",[363,129231,129233,129260],{"className":129232,"ariaHidden":394},[393],[363,129234,129236,129239,129242,129245,129248,129251,129254,129257],{"className":129235},[398],[363,129237],{"className":129238,"style":32039},[402],[363,129240,11],{"className":129241},[407,408],[363,129243,898],{"className":129244},[920],[363,129246],{"className":129247,"style":754},[505],[363,129249,1291],{"className":129250,"style":1328},[407,408],[363,129252],{"className":129253,"style":506},[505],[363,129255,6256],{"className":129256},[510],[363,129258],{"className":129259,"style":506},[505],[363,129261,129263,129266,129269,129272,129275,129278,129281],{"className":129262},[398],[363,129264],{"className":129265,"style":487},[402],[363,129267,461],{"className":129268},[494],[363,129270,474],{"className":129271},[407],[363,129273,898],{"className":129274},[920],[363,129276],{"className":129277,"style":754},[505],[363,129279,465],{"className":129280},[407],[363,129282,468],{"className":129283},[501],"），似然比取值 ",[363,129286,129288,129314],{"className":129287,"translate":367},[366],[363,129289,129291],{"className":129290},[371],[373,129292,129293],{"xmlns":375},[377,129294,129295,129311],{},[380,129296,129297,129303,129305,129307,129309],{},[543,129298,129299,129301],{},[383,129300,1116],{},[463,129302,465],{},[458,129304,471],{},[383,129306,11],{},[383,129308,1288],{"mathvariant":557},[383,129310,1291],{},[387,129312,129313],{"encoding":389},"t_1=p\u002Fq",[363,129315,129317,129372],{"className":129316,"ariaHidden":394},[393],[363,129318,129320,129323,129363,129366,129369],{"className":129319},[398],[363,129321],{"className":129322,"style":96272},[402],[363,129324,129326,129329],{"className":129325},[407],[363,129327,1116],{"className":129328},[407,408],[363,129330,129332],{"className":129331},[629],[363,129333,129335,129355],{"className":129334},[633,634],[363,129336,129338,129352],{"className":129337},[638],[363,129339,129341],{"className":129340,"style":11480},[642],[363,129342,129343,129346],{"style":730},[363,129344],{"className":129345,"style":651},[650],[363,129347,129349],{"className":129348},[655,656,657,658],[363,129350,465],{"className":129351},[407,658],[363,129353,666],{"className":129354},[665],[363,129356,129358],{"className":129357},[638],[363,129359,129361],{"className":129360,"style":8315},[642],[363,129362],{},[363,129364],{"className":129365,"style":506},[505],[363,129367,471],{"className":129368},[510],[363,129370],{"className":129371,"style":506},[505],[363,129373,129375,129378,129381,129384],{"className":129374},[398],[363,129376],{"className":129377,"style":487},[402],[363,129379,11],{"className":129380},[407,408],[363,129382,1288],{"className":129383},[407],[363,129385,1291],{"className":129386,"style":1328},[407,408],"（概率 ",[363,129389,129391,129404],{"className":129390,"translate":367},[366],[363,129392,129394],{"className":129393},[371],[373,129395,129396],{"xmlns":375},[377,129397,129398,129402],{},[380,129399,129400],{},[383,129401,1291],{},[387,129403,1291],{"encoding":389},[363,129405,129407],{"className":129406,"ariaHidden":394},[393],[363,129408,129410,129413],{"className":129409},[398],[363,129411],{"className":129412,"style":2623},[402],[363,129414,1291],{"className":129415,"style":1328},[407,408],"）与 ",[363,129418,129420,129462],{"className":129419,"translate":367},[366],[363,129421,129423],{"className":129422},[371],[373,129424,129425],{"xmlns":375},[377,129426,129427,129459],{},[380,129428,129429,129435,129437,129439,129441,129443,129445,129447,129449,129451,129453,129455,129457],{},[543,129430,129431,129433],{},[383,129432,1116],{},[463,129434,474],{},[458,129436,471],{},[458,129438,461],{"stretchy":460},[463,129440,465],{},[458,129442,5160],{},[383,129444,11],{},[458,129446,468],{"stretchy":460},[383,129448,1288],{"mathvariant":557},[458,129450,461],{"stretchy":460},[463,129452,465],{},[458,129454,5160],{},[383,129456,1291],{},[458,129458,468],{"stretchy":460},[387,129460,129461],{"encoding":389},"t_0=(1-p)\u002F(1-q)",[363,129463,129465,129520,129541,129571],{"className":129464,"ariaHidden":394},[393],[363,129466,129468,129471,129511,129514,129517],{"className":129467},[398],[363,129469],{"className":129470,"style":96272},[402],[363,129472,129474,129477],{"className":129473},[407],[363,129475,1116],{"className":129476},[407,408],[363,129478,129480],{"className":129479},[629],[363,129481,129483,129503],{"className":129482},[633,634],[363,129484,129486,129500],{"className":129485},[638],[363,129487,129489],{"className":129488,"style":11480},[642],[363,129490,129491,129494],{"style":730},[363,129492],{"className":129493,"style":651},[650],[363,129495,129497],{"className":129496},[655,656,657,658],[363,129498,474],{"className":129499},[407,658],[363,129501,666],{"className":129502},[665],[363,129504,129506],{"className":129505},[638],[363,129507,129509],{"className":129508,"style":8315},[642],[363,129510],{},[363,129512],{"className":129513,"style":506},[505],[363,129515,471],{"className":129516},[510],[363,129518],{"className":129519,"style":506},[505],[363,129521,129523,129526,129529,129532,129535,129538],{"className":129522},[398],[363,129524],{"className":129525,"style":487},[402],[363,129527,461],{"className":129528},[494],[363,129530,465],{"className":129531},[407],[363,129533],{"className":129534,"style":2934},[505],[363,129536,5160],{"className":129537},[2938],[363,129539],{"className":129540,"style":2934},[505],[363,129542,129544,129547,129550,129553,129556,129559,129562,129565,129568],{"className":129543},[398],[363,129545],{"className":129546,"style":487},[402],[363,129548,11],{"className":129549},[407,408],[363,129551,468],{"className":129552},[501],[363,129554,1288],{"className":129555},[407],[363,129557,461],{"className":129558},[494],[363,129560,465],{"className":129561},[407],[363,129563],{"className":129564,"style":2934},[505],[363,129566,5160],{"className":129567},[2938],[363,129569],{"className":129570,"style":2934},[505],[363,129572,129574,129577,129580],{"className":129573},[398],[363,129575],{"className":129576,"style":487},[402],[363,129578,1291],{"className":129579,"style":1328},[407,408],[363,129581,468],{"className":129582},[501],[363,129584,129586,129604],{"className":129585,"translate":367},[366],[363,129587,129589],{"className":129588},[371],[373,129590,129591],{"xmlns":375},[377,129592,129593,129601],{},[380,129594,129595,129597,129599],{},[463,129596,465],{},[458,129598,5160],{},[383,129600,1291],{},[387,129602,129603],{"encoding":389},"1-q",[363,129605,129607,129625],{"className":129606,"ariaHidden":394},[393],[363,129608,129610,129613,129616,129619,129622],{"className":129609},[398],[363,129611],{"className":129612,"style":12925},[402],[363,129614,465],{"className":129615},[407],[363,129617],{"className":129618,"style":2934},[505],[363,129620,5160],{"className":129621},[2938],[363,129623],{"className":129624,"style":2934},[505],[363,129626,129628,129631],{"className":129627},[398],[363,129629],{"className":129630,"style":2623},[402],[363,129632,1291],{"className":129633,"style":1328},[407,408],[363,129635,129637],{"className":129636,"translate":367},[528],[363,129638,129640,129722],{"className":129639,"translate":367},[366],[363,129641,129643],{"className":129642},[371],[373,129644,129645],{"xmlns":375,"display":537},[377,129646,129647,129719],{},[380,129648,129649,129659,129661,129663,129665,129667,129669,129671,129673,129675,129677,129683,129685,129687,129689,129691,129693,129695,129697,129699,129717],{},[543,129650,129651,129653],{},[383,129652,547],{},[380,129654,129655,129657],{},[383,129656,11041],{},[383,129658,22240],{},[458,129660,461],{"stretchy":460},[383,129662,554],{},[383,129664,558],{"mathvariant":557},[383,129666,561],{},[458,129668,468],{"stretchy":460},[458,129670,471],{},[383,129672,11],{},[383,129674,4447],{},[458,129676,4450],{},[586,129678,129679,129681],{},[383,129680,11],{},[383,129682,1291],{},[458,129684,2817],{},[458,129686,461],{"stretchy":460},[463,129688,465],{},[458,129690,5160],{},[383,129692,11],{},[458,129694,468],{"stretchy":460},[383,129696,4447],{},[458,129698,4450],{},[586,129700,129701,129709],{},[380,129702,129703,129705,129707],{},[463,129704,465],{},[458,129706,5160],{},[383,129708,11],{},[380,129710,129711,129713,129715],{},[463,129712,465],{},[458,129714,5160],{},[383,129716,1291],{},[458,129718,898],{"separator":394},[387,129720,129721],{"encoding":389},"D_{KL}(P\\|Q)=p\\log\\frac pq\n+(1-p)\\log\\frac{1-p}{1-q},",[363,129723,129725,129801,129892,129913],{"className":129724,"ariaHidden":394},[393],[363,129726,129728,129731,129777,129780,129783,129786,129789,129792,129795,129798],{"className":129727},[398],[363,129729],{"className":129730,"style":487},[402],[363,129732,129734,129737],{"className":129733},[407],[363,129735,547],{"className":129736,"style":625},[407,408],[363,129738,129740],{"className":129739},[629],[363,129741,129743,129769],{"className":129742},[633,634],[363,129744,129746,129766],{"className":129745},[638],[363,129747,129749],{"className":129748,"style":727},[642],[363,129750,129751,129754],{"style":646},[363,129752],{"className":129753,"style":651},[650],[363,129755,129757],{"className":129756},[655,656,657,658],[363,129758,129760,129763],{"className":129759},[407,658],[363,129761,11041],{"className":129762,"style":11129},[407,408,658],[363,129764,22240],{"className":129765},[407,408,658],[363,129767,666],{"className":129768},[665],[363,129770,129772],{"className":129771},[638],[363,129773,129775],{"className":129774,"style":8315},[642],[363,129776],{},[363,129778,461],{"className":129779},[494],[363,129781,554],{"className":129782,"style":682},[407,408],[363,129784,558],{"className":129785},[407],[363,129787,561],{"className":129788},[407,408],[363,129790,468],{"className":129791},[501],[363,129793],{"className":129794,"style":506},[505],[363,129796,471],{"className":129797},[510],[363,129799],{"className":129800,"style":506},[505],[363,129802,129804,129807,129810,129813,129818,129821,129883,129886,129889],{"className":129803},[398],[363,129805],{"className":129806,"style":22357},[402],[363,129808,11],{"className":129809},[407,408],[363,129811],{"className":129812,"style":754},[505],[363,129814,4501,129816],{"className":129815},[1831],[363,129817,4505],{"style":4504},[363,129819],{"className":129820,"style":754},[505],[363,129822,129824,129827,129880],{"className":129823},[407],[363,129825],{"className":129826},[494,789],[363,129828,129830],{"className":129829},[586],[363,129831,129833,129872],{"className":129832},[633,634],[363,129834,129836,129869],{"className":129835},[638],[363,129837,129839,129850,129858],{"className":129838,"style":3901},[642],[363,129840,129841,129844],{"style":805},[363,129842],{"className":129843,"style":809},[650],[363,129845,129847],{"className":129846},[407],[363,129848,1291],{"className":129849,"style":1328},[407,408],[363,129851,129852,129855],{"style":821},[363,129853],{"className":129854,"style":809},[650],[363,129856],{"className":129857,"style":829},[828],[363,129859,129860,129863],{"style":832},[363,129861],{"className":129862,"style":809},[650],[363,129864,129866],{"className":129865},[407],[363,129867,11],{"className":129868},[407,408],[363,129870,666],{"className":129871},[665],[363,129873,129875],{"className":129874},[638],[363,129876,129878],{"className":129877,"style":854},[642],[363,129879],{},[363,129881],{"className":129882},[501,789],[363,129884],{"className":129885,"style":2934},[505],[363,129887,2817],{"className":129888},[2938],[363,129890],{"className":129891,"style":2934},[505],[363,129893,129895,129898,129901,129904,129907,129910],{"className":129894},[398],[363,129896],{"className":129897,"style":487},[402],[363,129899,461],{"className":129900},[494],[363,129902,465],{"className":129903},[407],[363,129905],{"className":129906,"style":2934},[505],[363,129908,5160],{"className":129909},[2938],[363,129911],{"className":129912,"style":2934},[505],[363,129914,129916,129919,129922,129925,129928,129933,129936,130022],{"className":129915},[398],[363,129917],{"className":129918,"style":31650},[402],[363,129920,11],{"className":129921},[407,408],[363,129923,468],{"className":129924},[501],[363,129926],{"className":129927,"style":754},[505],[363,129929,4501,129931],{"className":129930},[1831],[363,129932,4505],{"style":4504},[363,129934],{"className":129935,"style":754},[505],[363,129937,129939,129942,130019],{"className":129938},[407],[363,129940],{"className":129941},[494,789],[363,129943,129945],{"className":129944},[586],[363,129946,129948,130011],{"className":129947},[633,634],[363,129949,129951,130008],{"className":129950},[638],[363,129952,129954,129977,129985],{"className":129953,"style":23236},[642],[363,129955,129956,129959],{"style":805},[363,129957],{"className":129958,"style":809},[650],[363,129960,129962,129965,129968,129971,129974],{"className":129961},[407],[363,129963,465],{"className":129964},[407],[363,129966],{"className":129967,"style":2934},[505],[363,129969,5160],{"className":129970},[2938],[363,129972],{"className":129973,"style":2934},[505],[363,129975,1291],{"className":129976,"style":1328},[407,408],[363,129978,129979,129982],{"style":821},[363,129980],{"className":129981,"style":809},[650],[363,129983],{"className":129984,"style":829},[828],[363,129986,129987,129990],{"style":832},[363,129988],{"className":129989,"style":809},[650],[363,129991,129993,129996,129999,130002,130005],{"className":129992},[407],[363,129994,465],{"className":129995},[407],[363,129997],{"className":129998,"style":2934},[505],[363,130000,5160],{"className":130001},[2938],[363,130003],{"className":130004,"style":2934},[505],[363,130006,11],{"className":130007},[407,408],[363,130009,666],{"className":130010},[665],[363,130012,130014],{"className":130013},[638],[363,130015,130017],{"className":130016,"style":854},[642],[363,130018],{},[363,130020],{"className":130021},[501,789],[363,130023,898],{"className":130024},[920],[363,130026,130028],{"className":130027,"translate":367},[528],[363,130029,130031,130131],{"className":130030,"translate":367},[366],[363,130032,130034],{"className":130033},[371],[373,130035,130036],{"xmlns":375,"display":537},[377,130037,130038,130128],{},[380,130039,130040,130050,130052,130054,130056,130058,130060,130062,130064,130066,130068,130070,130072,130074,130076,130082,130084,130086,130088,130090,130092,130094,130126],{},[543,130041,130042,130044],{},[383,130043,547],{},[380,130045,130046,130048],{},[383,130047,5739],{},[383,130049,35197],{},[458,130051,461],{"stretchy":460},[383,130053,554],{},[458,130055,898],{"separator":394},[383,130057,561],{},[458,130059,468],{"stretchy":460},[458,130061,471],{},[383,130063,5155],{"mathvariant":557},[383,130065,11],{},[458,130067,5160],{},[383,130069,1291],{},[383,130071,5155],{"mathvariant":557},[458,130073,898],{"separator":394},[505,130075],{"width":3609},[7161,130077,130078,130080],{},[383,130079,37796],{},[463,130081,2810],{},[458,130083,461],{"stretchy":460},[383,130085,554],{},[383,130087,558],{"mathvariant":557},[383,130089,561],{},[458,130091,468],{"stretchy":460},[458,130093,471],{},[586,130095,130096,130112],{},[380,130097,130098,130100,130102,130104,130106],{},[458,130099,461],{"stretchy":460},[383,130101,11],{},[458,130103,5160],{},[383,130105,1291],{},[7161,130107,130108,130110],{},[458,130109,468],{"stretchy":460},[463,130111,2810],{},[380,130113,130114,130116,130118,130120,130122,130124],{},[383,130115,1291],{},[458,130117,461],{"stretchy":460},[463,130119,465],{},[458,130121,5160],{},[383,130123,1291],{},[458,130125,468],{"stretchy":460},[458,130127,898],{"separator":394},[387,130129,130130],{"encoding":389},"D_{TV}(P,Q)=|p-q|,\\qquad\n\\chi^2(P\\|Q)=\\frac{(p-q)^2}{q(1-q)},",[363,130132,130134,130213,130234,130308],{"className":130133,"ariaHidden":394},[393],[363,130135,130137,130140,130186,130189,130192,130195,130198,130201,130204,130207,130210],{"className":130136},[398],[363,130138],{"className":130139,"style":487},[402],[363,130141,130143,130146],{"className":130142},[407],[363,130144,547],{"className":130145,"style":625},[407,408],[363,130147,130149],{"className":130148},[629],[363,130150,130152,130178],{"className":130151},[633,634],[363,130153,130155,130175],{"className":130154},[638],[363,130156,130158],{"className":130157,"style":727},[642],[363,130159,130160,130163],{"style":646},[363,130161],{"className":130162,"style":651},[650],[363,130164,130166],{"className":130165},[655,656,657,658],[363,130167,130169,130172],{"className":130168},[407,658],[363,130170,5739],{"className":130171,"style":682},[407,408,658],[363,130173,35197],{"className":130174,"style":2934},[407,408,658],[363,130176,666],{"className":130177},[665],[363,130179,130181],{"className":130180},[638],[363,130182,130184],{"className":130183,"style":8315},[642],[363,130185],{},[363,130187,461],{"className":130188},[494],[363,130190,554],{"className":130191,"style":682},[407,408],[363,130193,898],{"className":130194},[920],[363,130196],{"className":130197,"style":754},[505],[363,130199,561],{"className":130200},[407,408],[363,130202,468],{"className":130203},[501],[363,130205],{"className":130206,"style":506},[505],[363,130208,471],{"className":130209},[510],[363,130211],{"className":130212,"style":506},[505],[363,130214,130216,130219,130222,130225,130228,130231],{"className":130215},[398],[363,130217],{"className":130218,"style":487},[402],[363,130220,5155],{"className":130221},[407],[363,130223,11],{"className":130224},[407,408],[363,130226],{"className":130227,"style":2934},[505],[363,130229,5160],{"className":130230},[2938],[363,130232],{"className":130233,"style":2934},[505],[363,130235,130237,130240,130243,130246,130249,130252,130255,130284,130287,130290,130293,130296,130299,130302,130305],{"className":130236},[398],[363,130238],{"className":130239,"style":37598},[402],[363,130241,1291],{"className":130242,"style":1328},[407,408],[363,130244,5155],{"className":130245},[407],[363,130247,898],{"className":130248},[920],[363,130250],{"className":130251,"style":3981},[505],[363,130253],{"className":130254,"style":754},[505],[363,130256,130258,130261],{"className":130257},[407],[363,130259,37796],{"className":130260},[407,408],[363,130262,130264],{"className":130263},[629],[363,130265,130267],{"className":130266},[633],[363,130268,130270],{"className":130269},[638],[363,130271,130273],{"className":130272,"style":20082},[642],[363,130274,130275,130278],{"style":8624},[363,130276],{"className":130277,"style":651},[650],[363,130279,130281],{"className":130280},[655,656,657,658],[363,130282,2810],{"className":130283},[407,658],[363,130285,461],{"className":130286},[494],[363,130288,554],{"className":130289,"style":682},[407,408],[363,130291,558],{"className":130292},[407],[363,130294,561],{"className":130295},[407,408],[363,130297,468],{"className":130298},[501],[363,130300],{"className":130301,"style":506},[505],[363,130303,471],{"className":130304},[510],[363,130306],{"className":130307,"style":506},[505],[363,130309,130311,130315,130442],{"className":130310},[398],[363,130312],{"className":130313,"style":130314},[402],"height:2.4271em;vertical-align:-0.936em;",[363,130316,130318,130321,130439],{"className":130317},[407],[363,130319],{"className":130320},[494,789],[363,130322,130324],{"className":130323},[586],[363,130325,130327,130431],{"className":130326},[633,634],[363,130328,130330,130428],{"className":130329},[638],[363,130331,130333,130365,130373],{"className":130332,"style":38070},[642],[363,130334,130335,130338],{"style":805},[363,130336],{"className":130337,"style":809},[650],[363,130339,130341,130344,130347,130350,130353,130356,130359,130362],{"className":130340},[407],[363,130342,1291],{"className":130343,"style":1328},[407,408],[363,130345,461],{"className":130346},[494],[363,130348,465],{"className":130349},[407],[363,130351],{"className":130352,"style":2934},[505],[363,130354,5160],{"className":130355},[2938],[363,130357],{"className":130358,"style":2934},[505],[363,130360,1291],{"className":130361,"style":1328},[407,408],[363,130363,468],{"className":130364},[501],[363,130366,130367,130370],{"style":821},[363,130368],{"className":130369,"style":809},[650],[363,130371],{"className":130372,"style":829},[828],[363,130374,130375,130378],{"style":832},[363,130376],{"className":130377,"style":809},[650],[363,130379,130381,130384,130387,130390,130393,130396,130399],{"className":130380},[407],[363,130382,461],{"className":130383},[494],[363,130385,11],{"className":130386},[407,408],[363,130388],{"className":130389,"style":2934},[505],[363,130391,5160],{"className":130392},[2938],[363,130394],{"className":130395,"style":2934},[505],[363,130397,1291],{"className":130398,"style":1328},[407,408],[363,130400,130402,130405],{"className":130401},[501],[363,130403,468],{"className":130404},[501],[363,130406,130408],{"className":130407},[629],[363,130409,130411],{"className":130410},[633],[363,130412,130414],{"className":130413},[638],[363,130415,130417],{"className":130416,"style":20375},[642],[363,130418,130419,130422],{"style":7212},[363,130420],{"className":130421,"style":651},[650],[363,130423,130425],{"className":130424},[655,656,657,658],[363,130426,2810],{"className":130427},[407,658],[363,130429,666],{"className":130430},[665],[363,130432,130434],{"className":130433},[638],[363,130435,130437],{"className":130436,"style":1948},[642],[363,130438],{},[363,130440],{"className":130441},[501,789],[363,130443,898],{"className":130444},[920],[363,130446,130448],{"className":130447,"translate":367},[528],[363,130449,130451,130523],{"className":130450,"translate":367},[366],[363,130452,130454],{"className":130453},[371],[373,130455,130456],{"xmlns":375,"display":537},[377,130457,130458,130520],{},[380,130459,130460,130468,130470,130472,130474,130476,130478,130480,130482,130484,130492,130494,130518],{},[7900,130461,130462,130464,130466],{},[383,130463,34231],{},[1644,130465,42484],{},[463,130467,2810],{},[458,130469,461],{"stretchy":460},[383,130471,554],{},[458,130473,898],{"separator":394},[383,130475,561],{},[458,130477,468],{"stretchy":460},[458,130479,471],{},[463,130481,465],{},[458,130483,5160],{},[34686,130485,130486],{},[380,130487,130488,130490],{},[383,130489,11],{},[383,130491,1291],{},[458,130493,5160],{},[34686,130495,130496],{},[380,130497,130498,130500,130502,130504,130506,130508,130510,130512,130514,130516],{},[458,130499,461],{"stretchy":460},[463,130501,465],{},[458,130503,5160],{},[383,130505,11],{},[458,130507,468],{"stretchy":460},[458,130509,461],{"stretchy":460},[463,130511,465],{},[458,130513,5160],{},[383,130515,1291],{},[458,130517,468],{"stretchy":460},[383,130519,4722],{"mathvariant":557},[387,130521,130522],{"encoding":389},"H^2_{\\text{Bhattacharyya}}(P,Q)\n=1-\\sqrt{pq}-\\sqrt{(1-p)(1-q)} .",[363,130524,130526,130616,130634,130697],{"className":130525,"ariaHidden":394},[393],[363,130527,130529,130532,130589,130592,130595,130598,130601,130604,130607,130610,130613],{"className":130528},[398],[363,130530],{"className":130531,"style":46749},[402],[363,130533,130535,130538],{"className":130534},[407],[363,130536,34231],{"className":130537,"style":34385},[407,408],[363,130539,130541],{"className":130540},[629],[363,130542,130544,130581],{"className":130543},[633,634],[363,130545,130547,130578],{"className":130546},[638],[363,130548,130550,130567],{"className":130549,"style":20082},[642],[363,130551,130552,130555],{"style":42627},[363,130553],{"className":130554,"style":651},[650],[363,130556,130558],{"className":130557},[655,656,657,658],[363,130559,130561],{"className":130560},[407,658],[363,130562,130564],{"className":130563},[407,4945,658],[363,130565,42484],{"className":130566},[407,658],[363,130568,130569,130572],{"style":8624},[363,130570],{"className":130571,"style":651},[650],[363,130573,130575],{"className":130574},[655,656,657,658],[363,130576,2810],{"className":130577},[407,658],[363,130579,666],{"className":130580},[665],[363,130582,130584],{"className":130583},[638],[363,130585,130587],{"className":130586,"style":42663},[642],[363,130588],{},[363,130590,461],{"className":130591},[494],[363,130593,554],{"className":130594,"style":682},[407,408],[363,130596,898],{"className":130597},[920],[363,130599],{"className":130600,"style":754},[505],[363,130602,561],{"className":130603},[407,408],[363,130605,468],{"className":130606},[501],[363,130608],{"className":130609,"style":506},[505],[363,130611,471],{"className":130612},[510],[363,130614],{"className":130615,"style":506},[505],[363,130617,130619,130622,130625,130628,130631],{"className":130618},[398],[363,130620],{"className":130621,"style":12925},[402],[363,130623,465],{"className":130624},[407],[363,130626],{"className":130627,"style":2934},[505],[363,130629,5160],{"className":130630},[2938],[363,130632],{"className":130633,"style":2934},[505],[363,130635,130637,130641,130688,130691,130694],{"className":130636},[398],[363,130638],{"className":130639,"style":130640},[402],"height:1.04em;vertical-align:-0.2881em;",[363,130642,130644],{"className":130643},[407,34714],[363,130645,130647,130680],{"className":130646},[633,634],[363,130648,130650,130677],{"className":130649},[638],[363,130651,130653,130665],{"className":130652,"style":7209},[642],[363,130654,130656,130659],{"className":130655,"style":12210},[6654],[363,130657],{"className":130658,"style":809},[650],[363,130660,130662],{"className":130661,"style":34734},[407],[363,130663,41952],{"className":130664,"style":1328},[407,408],[363,130666,130667,130670],{"style":41697},[363,130668],{"className":130669,"style":809},[650],[363,130671,130673],{"className":130672,"style":34791},[34790],[6670,130674,130675],{"xmlns":6672,"width":6673,"height":34794,"viewBox":34795,"preserveAspectRatio":6676},[6678,130676],{"d":34798},[363,130678,666],{"className":130679},[665],[363,130681,130683],{"className":130682},[638],[363,130684,130686],{"className":130685,"style":41717},[642],[363,130687],{},[363,130689],{"className":130690,"style":2934},[505],[363,130692,5160],{"className":130693},[2938],[363,130695],{"className":130696,"style":2934},[505],[363,130698,130700,130704,130790],{"className":130699},[398],[363,130701],{"className":130702,"style":130703},[402],"height:1.24em;vertical-align:-0.2561em;",[363,130705,130707],{"className":130706},[407,34714],[363,130708,130710,130782],{"className":130709},[633,634],[363,130711,130713,130779],{"className":130712},[638],[363,130714,130716,130767],{"className":130715,"style":83879},[642],[363,130717,130719,130722],{"className":130718,"style":83883},[6654],[363,130720],{"className":130721,"style":15193},[650],[363,130723,130725,130728,130731,130734,130737,130740,130743,130746,130749,130752,130755,130758,130761,130764],{"className":130724,"style":41508},[407],[363,130726,461],{"className":130727},[494],[363,130729,465],{"className":130730},[407],[363,130732],{"className":130733,"style":2934},[505],[363,130735,5160],{"className":130736},[2938],[363,130738],{"className":130739,"style":2934},[505],[363,130741,11],{"className":130742},[407,408],[363,130744,468],{"className":130745},[501],[363,130747,461],{"className":130748},[494],[363,130750,465],{"className":130751},[407],[363,130753],{"className":130754,"style":2934},[505],[363,130756,5160],{"className":130757},[2938],[363,130759],{"className":130760,"style":2934},[505],[363,130762,1291],{"className":130763,"style":1328},[407,408],[363,130765,468],{"className":130766},[501],[363,130768,130769,130772],{"style":83968},[363,130770],{"className":130771,"style":15193},[650],[363,130773,130775],{"className":130774,"style":83975},[34790],[6670,130776,130777],{"xmlns":6672,"width":6673,"height":83978,"viewBox":83979,"preserveAspectRatio":6676},[6678,130778],{"d":83982},[363,130780,666],{"className":130781},[665],[363,130783,130785],{"className":130784},[638],[363,130786,130788],{"className":130787,"style":83992},[642],[363,130789],{},[363,130791,4722],{"className":130792},[407],[11,130794,130795,130796,130876,130877,4200,130905,130956,130957,131266],{},"这些是检验公式是否自洽的好练习：例如把 ",[363,130797,130799,130821],{"className":130798,"translate":367},[366],[363,130800,130802],{"className":130801},[371],[373,130803,130804],{"xmlns":375},[377,130805,130806,130818],{},[380,130807,130808],{},[543,130809,130810,130812],{},[383,130811,547],{},[380,130813,130814,130816],{},[383,130815,11041],{},[383,130817,22240],{},[387,130819,130820],{"encoding":389},"D_{KL}",[363,130822,130824],{"className":130823,"ariaHidden":394},[393],[363,130825,130827,130830],{"className":130826},[398],[363,130828],{"className":130829,"style":16308},[402],[363,130831,130833,130836],{"className":130832},[407],[363,130834,547],{"className":130835,"style":625},[407,408],[363,130837,130839],{"className":130838},[629],[363,130840,130842,130868],{"className":130841},[633,634],[363,130843,130845,130865],{"className":130844},[638],[363,130846,130848],{"className":130847,"style":727},[642],[363,130849,130850,130853],{"style":646},[363,130851],{"className":130852,"style":651},[650],[363,130854,130856],{"className":130855},[655,656,657,658],[363,130857,130859,130862],{"className":130858},[407,658],[363,130860,11041],{"className":130861,"style":11129},[407,408,658],[363,130863,22240],{"className":130864},[407,408,658],[363,130866,666],{"className":130867},[665],[363,130869,130871],{"className":130870},[638],[363,130872,130874],{"className":130873,"style":8315},[642],[363,130875],{}," 对 ",[363,130878,130880,130893],{"className":130879,"translate":367},[366],[363,130881,130883],{"className":130882},[371],[373,130884,130885],{"xmlns":375},[377,130886,130887,130891],{},[380,130888,130889],{},[383,130890,11],{},[387,130892,11],{"encoding":389},[363,130894,130896],{"className":130895,"ariaHidden":394},[393],[363,130897,130899,130902],{"className":130898},[398],[363,130900],{"className":130901,"style":2623},[402],[363,130903,11],{"className":130904},[407,408],[363,130906,130908,130926],{"className":130907,"translate":367},[366],[363,130909,130911],{"className":130910},[371],[373,130912,130913],{"xmlns":375},[377,130914,130915,130923],{},[380,130916,130917,130919,130921],{},[383,130918,11],{},[458,130920,471],{},[383,130922,1291],{},[387,130924,130925],{"encoding":389},"p=q",[363,130927,130929,130947],{"className":130928,"ariaHidden":394},[393],[363,130930,130932,130935,130938,130941,130944],{"className":130931},[398],[363,130933],{"className":130934,"style":2623},[402],[363,130936,11],{"className":130937},[407,408],[363,130939],{"className":130940,"style":506},[505],[363,130942,471],{"className":130943},[510],[363,130945],{"className":130946,"style":506},[505],[363,130948,130950,130953],{"className":130949},[398],[363,130951],{"className":130952,"style":2623},[402],[363,130954,1291],{"className":130955,"style":1328},[407,408]," 处做二阶展开，应回到 ",[363,130958,130960,131020],{"className":130959,"translate":367},[366],[363,130961,130963],{"className":130962},[371],[373,130964,130965],{"xmlns":375},[377,130966,130967,131017],{},[380,130968,130969,131003,131005,131011],{},[586,130970,130971,130987],{},[380,130972,130973,130975,130977,130979,130981],{},[458,130974,461],{"stretchy":460},[383,130976,11],{},[458,130978,5160],{},[383,130980,1291],{},[7161,130982,130983,130985],{},[458,130984,468],{"stretchy":460},[463,130986,2810],{},[380,130988,130989,130991,130993,130995,130997,130999,131001],{},[463,130990,2810],{},[383,130992,1291],{},[458,130994,461],{"stretchy":460},[463,130996,465],{},[458,130998,5160],{},[383,131000,1291],{},[458,131002,468],{"stretchy":460},[458,131004,471],{},[586,131006,131007,131009],{},[463,131008,465],{},[463,131010,2810],{},[7161,131012,131013,131015],{},[383,131014,37796],{},[463,131016,2810],{},[387,131018,131019],{"encoding":389},"\\frac{(p-q)^2}{2q(1-q)}=\\frac12\\chi^2",[363,131021,131023,131163],{"className":131022,"ariaHidden":394},[393],[363,131024,131026,131030,131154,131157,131160],{"className":131025},[398],[363,131027],{"className":131028,"style":131029},[402],"height:1.6289em;vertical-align:-0.52em;",[363,131031,131033,131036,131151],{"className":131032},[407],[363,131034],{"className":131035},[494,789],[363,131037,131039],{"className":131038},[586],[363,131040,131042,131143],{"className":131041},[633,634],[363,131043,131045,131140],{"className":131044},[638],[363,131046,131048,131080,131088],{"className":131047,"style":38795},[642],[363,131049,131050,131053],{"style":2874},[363,131051],{"className":131052,"style":809},[650],[363,131054,131056],{"className":131055},[655,656,657,658],[363,131057,131059,131062,131065,131068,131071,131074,131077],{"className":131058},[407,658],[363,131060,2810],{"className":131061},[407,658],[363,131063,1291],{"className":131064,"style":1328},[407,408,658],[363,131066,461],{"className":131067},[494,658],[363,131069,465],{"className":131070},[407,658],[363,131072,5160],{"className":131073},[2938,658],[363,131075,1291],{"className":131076,"style":1328},[407,408,658],[363,131078,468],{"className":131079},[501,658],[363,131081,131082,131085],{"style":821},[363,131083],{"className":131084,"style":809},[650],[363,131086],{"className":131087,"style":829},[828],[363,131089,131090,131093],{"style":26765},[363,131091],{"className":131092,"style":809},[650],[363,131094,131096],{"className":131095},[655,656,657,658],[363,131097,131099,131102,131105,131108,131111],{"className":131098},[407,658],[363,131100,461],{"className":131101},[494,658],[363,131103,11],{"className":131104},[407,408,658],[363,131106,5160],{"className":131107},[2938,658],[363,131109,1291],{"className":131110,"style":1328},[407,408,658],[363,131112,131114,131117],{"className":131113},[501,658],[363,131115,468],{"className":131116},[501,658],[363,131118,131120],{"className":131119},[629],[363,131121,131123],{"className":131122},[633],[363,131124,131126],{"className":131125},[638],[363,131127,131129],{"className":131128,"style":38859},[642],[363,131130,131131,131134],{"style":38862},[363,131132],{"className":131133,"style":30553},[650],[363,131135,131137],{"className":131136},[655,30557,10021,658],[363,131138,2810],{"className":131139},[407,658],[363,131141,666],{"className":131142},[665],[363,131144,131146],{"className":131145},[638],[363,131147,131149],{"className":131148,"style":45949},[642],[363,131150],{},[363,131152],{"className":131153},[501,789],[363,131155],{"className":131156,"style":506},[505],[363,131158,471],{"className":131159},[510],[363,131161],{"className":131162,"style":506},[505],[363,131164,131166,131169,131237],{"className":131165},[398],[363,131167],{"className":131168,"style":2852},[402],[363,131170,131172,131175,131234],{"className":131171},[407],[363,131173],{"className":131174},[494,789],[363,131176,131178],{"className":131177},[586],[363,131179,131181,131226],{"className":131180},[633,634],[363,131182,131184,131223],{"className":131183},[638],[363,131185,131187,131201,131209],{"className":131186,"style":2871},[642],[363,131188,131189,131192],{"style":2874},[363,131190],{"className":131191,"style":809},[650],[363,131193,131195],{"className":131194},[655,656,657,658],[363,131196,131198],{"className":131197},[407,658],[363,131199,2810],{"className":131200},[407,658],[363,131202,131203,131206],{"style":821},[363,131204],{"className":131205,"style":809},[650],[363,131207],{"className":131208,"style":829},[828],[363,131210,131211,131214],{"style":2897},[363,131212],{"className":131213,"style":809},[650],[363,131215,131217],{"className":131216},[655,656,657,658],[363,131218,131220],{"className":131219},[407,658],[363,131221,465],{"className":131222},[407,658],[363,131224,666],{"className":131225},[665],[363,131227,131229],{"className":131228},[638],[363,131230,131232],{"className":131231,"style":2919},[642],[363,131233],{},[363,131235],{"className":131236},[501,789],[363,131238,131240,131243],{"className":131239},[407],[363,131241,37796],{"className":131242},[407,408],[363,131244,131246],{"className":131245},[629],[363,131247,131249],{"className":131248},[633],[363,131250,131252],{"className":131251},[638],[363,131253,131255],{"className":131254,"style":20375},[642],[363,131256,131257,131260],{"style":7212},[363,131258],{"className":131259,"style":651},[650],[363,131261,131263],{"className":131262},[655,656,657,658],[363,131264,2810],{"className":131265},[407,658],"，与 4.6 节吻合。",[2658,131268,131270],{"id":131269},"_93-用对偶表示反推-kl","9.3 用对偶表示反推 KL",[11,131272,131273,131274,5992,131359,131500,131501,9747],{},"取 ",[363,131275,131277,131306],{"className":131276,"translate":367},[366],[363,131278,131280],{"className":131279},[371],[373,131281,131282],{"xmlns":375},[377,131283,131284,131304],{},[380,131285,131286,131288,131290,131292,131294,131296,131298,131300,131302],{},[383,131287,385],{},[458,131289,461],{"stretchy":460},[383,131291,1116],{},[458,131293,468],{"stretchy":460},[458,131295,471],{},[383,131297,1116],{},[383,131299,4447],{},[458,131301,4450],{},[383,131303,1116],{},[387,131305,4455],{"encoding":389},[363,131307,131309,131336],{"className":131308,"ariaHidden":394},[393],[363,131310,131312,131315,131318,131321,131324,131327,131330,131333],{"className":131311},[398],[363,131313],{"className":131314,"style":487},[402],[363,131316,385],{"className":131317,"style":409},[407,408],[363,131319,461],{"className":131320},[494],[363,131322,1116],{"className":131323},[407,408],[363,131325,468],{"className":131326},[501],[363,131328],{"className":131329,"style":506},[505],[363,131331,471],{"className":131332},[510],[363,131334],{"className":131335,"style":506},[505],[363,131337,131339,131342,131345,131348,131353,131356],{"className":131338},[398],[363,131340],{"className":131341,"style":403},[402],[363,131343,1116],{"className":131344},[407,408],[363,131346],{"className":131347,"style":754},[505],[363,131349,4501,131351],{"className":131350},[1831],[363,131352,4505],{"style":4504},[363,131354],{"className":131355,"style":754},[505],[363,131357,1116],{"className":131358},[407,408],[363,131360,131362,131400],{"className":131361,"translate":367},[366],[363,131363,131365],{"className":131364},[371],[373,131366,131367],{"xmlns":375},[377,131368,131369,131397],{},[380,131370,131371,131377,131379,131381,131383,131385],{},[7161,131372,131373,131375],{},[383,131374,385],{},[458,131376,7920],{},[458,131378,461],{"stretchy":460},[383,131380,40584],{},[458,131382,468],{"stretchy":460},[458,131384,471],{},[7161,131386,131387,131389],{},[383,131388,7914],{},[380,131390,131391,131393,131395],{},[383,131392,40584],{},[458,131394,5160],{},[463,131396,465],{},[387,131398,131399],{"encoding":389},"f^*(y)=e^{y-1}",[363,131401,131403,131456],{"className":131402,"ariaHidden":394},[393],[363,131404,131406,131409,131438,131441,131444,131447,131450,131453],{"className":131405},[398],[363,131407],{"className":131408,"style":487},[402],[363,131410,131412,131415],{"className":131411},[407],[363,131413,385],{"className":131414,"style":409},[407,408],[363,131416,131418],{"className":131417},[629],[363,131419,131421],{"className":131420},[633],[363,131422,131424],{"className":131423},[638],[363,131425,131427],{"className":131426,"style":8846},[642],[363,131428,131429,131432],{"style":7212},[363,131430],{"className":131431,"style":651},[650],[363,131433,131435],{"className":131434},[655,656,657,658],[363,131436,7920],{"className":131437},[2938,658],[363,131439,461],{"className":131440},[494],[363,131442,40584],{"className":131443,"style":1328},[407,408],[363,131445,468],{"className":131446},[501],[363,131448],{"className":131449,"style":506},[505],[363,131451,471],{"className":131452},[510],[363,131454],{"className":131455,"style":506},[505],[363,131457,131459,131462],{"className":131458},[398],[363,131460],{"className":131461,"style":20375},[402],[363,131463,131465,131468],{"className":131464},[407],[363,131466,7914],{"className":131467},[407,408],[363,131469,131471],{"className":131470},[629],[363,131472,131474],{"className":131473},[633],[363,131475,131477],{"className":131476},[638],[363,131478,131480],{"className":131479,"style":20375},[642],[363,131481,131482,131485],{"style":7212},[363,131483],{"className":131484,"style":651},[650],[363,131486,131488],{"className":131487},[655,656,657,658],[363,131489,131491,131494,131497],{"className":131490},[407,658],[363,131492,40584],{"className":131493,"style":1328},[407,408,658],[363,131495,5160],{"className":131496},[2938,658],[363,131498,465],{"className":131499},[407,658],"，则对任意 ",[363,131502,131504,131517],{"className":131503,"translate":367},[366],[363,131505,131507],{"className":131506},[371],[373,131508,131509],{"xmlns":375},[377,131510,131511,131515],{},[380,131512,131513],{},[383,131514,4505],{},[387,131516,4505],{"encoding":389},[363,131518,131520],{"className":131519,"ariaHidden":394},[393],[363,131521,131523,131526],{"className":131522},[398],[363,131524],{"className":131525,"style":2623},[402],[363,131527,4505],{"className":131528,"style":1328},[407,408],[363,131530,131532],{"className":131531,"translate":367},[528],[363,131533,131535,131607],{"className":131534,"translate":367},[366],[363,131536,131538],{"className":131537},[371],[373,131539,131540],{"xmlns":375,"display":537},[377,131541,131542,131604],{},[380,131543,131544,131554,131556,131558,131560,131562,131564,131566,131572,131574,131576,131578,131580,131586,131588,131600,131602],{},[543,131545,131546,131548],{},[383,131547,547],{},[380,131549,131550,131552],{},[383,131551,11041],{},[383,131553,22240],{},[458,131555,461],{"stretchy":460},[383,131557,554],{},[383,131559,558],{"mathvariant":557},[383,131561,561],{},[458,131563,468],{"stretchy":460},[458,131565,7275],{},[543,131567,131568,131570],{},[383,131569,571],{"mathvariant":570},[383,131571,554],{},[458,131573,578],{"stretchy":460},[383,131575,4505],{},[458,131577,605],{"stretchy":460},[458,131579,5160],{},[543,131581,131582,131584],{},[383,131583,571],{"mathvariant":570},[383,131585,561],{},[458,131587,578],{"stretchy":460},[7161,131589,131590,131592],{},[383,131591,7914],{},[380,131593,131594,131596,131598],{},[383,131595,4505],{},[458,131597,5160],{},[463,131599,465],{},[458,131601,605],{"stretchy":460},[458,131603,898],{"separator":394},[387,131605,131606],{"encoding":389},"D_{KL}(P\\|Q)\\ge \\mathbb E_P[g]\n-\\mathbb E_Q[e^{g-1}],",[363,131608,131610,131686,131750],{"className":131609,"ariaHidden":394},[393],[363,131611,131613,131616,131662,131665,131668,131671,131674,131677,131680,131683],{"className":131612},[398],[363,131614],{"className":131615,"style":487},[402],[363,131617,131619,131622],{"className":131618},[407],[363,131620,547],{"className":131621,"style":625},[407,408],[363,131623,131625],{"className":131624},[629],[363,131626,131628,131654],{"className":131627},[633,634],[363,131629,131631,131651],{"className":131630},[638],[363,131632,131634],{"className":131633,"style":727},[642],[363,131635,131636,131639],{"style":646},[363,131637],{"className":131638,"style":651},[650],[363,131640,131642],{"className":131641},[655,656,657,658],[363,131643,131645,131648],{"className":131644},[407,658],[363,131646,11041],{"className":131647,"style":11129},[407,408,658],[363,131649,22240],{"className":131650},[407,408,658],[363,131652,666],{"className":131653},[665],[363,131655,131657],{"className":131656},[638],[363,131658,131660],{"className":131659,"style":8315},[642],[363,131661],{},[363,131663,461],{"className":131664},[494],[363,131666,554],{"className":131667,"style":682},[407,408],[363,131669,558],{"className":131670},[407],[363,131672,561],{"className":131673},[407,408],[363,131675,468],{"className":131676},[501],[363,131678],{"className":131679,"style":506},[505],[363,131681,7275],{"className":131682},[510],[363,131684],{"className":131685,"style":506},[505],[363,131687,131689,131692,131732,131735,131738,131741,131744,131747],{"className":131688},[398],[363,131690],{"className":131691,"style":487},[402],[363,131693,131695,131698],{"className":131694},[407],[363,131696,571],{"className":131697},[407,714],[363,131699,131701],{"className":131700},[629],[363,131702,131704,131724],{"className":131703},[633,634],[363,131705,131707,131721],{"className":131706},[638],[363,131708,131710],{"className":131709,"style":727},[642],[363,131711,131712,131715],{"style":730},[363,131713],{"className":131714,"style":651},[650],[363,131716,131718],{"className":131717},[655,656,657,658],[363,131719,554],{"className":131720,"style":682},[407,408,658],[363,131722,666],{"className":131723},[665],[363,131725,131727],{"className":131726},[638],[363,131728,131730],{"className":131729,"style":8315},[642],[363,131731],{},[363,131733,578],{"className":131734},[494],[363,131736,4505],{"className":131737,"style":1328},[407,408],[363,131739,605],{"className":131740},[501],[363,131742],{"className":131743,"style":2934},[505],[363,131745,5160],{"className":131746},[2938],[363,131748],{"className":131749,"style":2934},[505],[363,131751,131753,131757,131797,131800,131838,131841],{"className":131752},[398],[363,131754],{"className":131755,"style":131756},[402],"height:1.1502em;vertical-align:-0.2861em;",[363,131758,131760,131763],{"className":131759},[407],[363,131761,571],{"className":131762},[407,714],[363,131764,131766],{"className":131765},[629],[363,131767,131769,131789],{"className":131768},[633,634],[363,131770,131772,131786],{"className":131771},[638],[363,131773,131775],{"className":131774,"style":727},[642],[363,131776,131777,131780],{"style":730},[363,131778],{"className":131779,"style":651},[650],[363,131781,131783],{"className":131782},[655,656,657,658],[363,131784,561],{"className":131785},[407,408,658],[363,131787,666],{"className":131788},[665],[363,131790,131792],{"className":131791},[638],[363,131793,131795],{"className":131794,"style":673},[642],[363,131796],{},[363,131798,578],{"className":131799},[494],[363,131801,131803,131806],{"className":131802},[407],[363,131804,7914],{"className":131805},[407,408],[363,131807,131809],{"className":131808},[629],[363,131810,131812],{"className":131811},[633],[363,131813,131815],{"className":131814},[638],[363,131816,131818],{"className":131817,"style":20082},[642],[363,131819,131820,131823],{"style":8624},[363,131821],{"className":131822,"style":651},[650],[363,131824,131826],{"className":131825},[655,656,657,658],[363,131827,131829,131832,131835],{"className":131828},[407,658],[363,131830,4505],{"className":131831,"style":1328},[407,408,658],[363,131833,5160],{"className":131834},[2938,658],[363,131836,465],{"className":131837},[407,658],[363,131839,605],{"className":131840},[501],[363,131842,898],{"className":131843},[920],[11,131845,131846,131847,131949],{},"等号在 ",[363,131848,131850,131884],{"className":131849,"translate":367},[366],[363,131851,131853],{"className":131852},[371],[373,131854,131855],{"xmlns":375},[377,131856,131857,131881],{},[380,131858,131859,131861,131863,131865,131867,131869,131871,131873,131875,131877,131879],{},[383,131860,4505],{},[458,131862,471],{},[383,131864,4447],{},[458,131866,4450],{},[458,131868,461],{"stretchy":460},[383,131870,11],{},[383,131872,1288],{"mathvariant":557},[383,131874,1291],{},[458,131876,468],{"stretchy":460},[458,131878,2817],{},[463,131880,465],{},[387,131882,131883],{"encoding":389},"g=\\log(p\u002Fq)+1",[363,131885,131887,131905,131940],{"className":131886,"ariaHidden":394},[393],[363,131888,131890,131893,131896,131899,131902],{"className":131889},[398],[363,131891],{"className":131892,"style":2623},[402],[363,131894,4505],{"className":131895,"style":1328},[407,408],[363,131897],{"className":131898,"style":506},[505],[363,131900,471],{"className":131901},[510],[363,131903],{"className":131904,"style":506},[505],[363,131906,131908,131911,131916,131919,131922,131925,131928,131931,131934,131937],{"className":131907},[398],[363,131909],{"className":131910,"style":487},[402],[363,131912,4501,131914],{"className":131913},[1831],[363,131915,4505],{"style":4504},[363,131917,461],{"className":131918},[494],[363,131920,11],{"className":131921},[407,408],[363,131923,1288],{"className":131924},[407],[363,131926,1291],{"className":131927,"style":1328},[407,408],[363,131929,468],{"className":131930},[501],[363,131932],{"className":131933,"style":2934},[505],[363,131935,2817],{"className":131936},[2938],[363,131938],{"className":131939,"style":2934},[505],[363,131941,131943,131946],{"className":131942},[398],[363,131944],{"className":131945,"style":520},[402],[363,131947,465],{"className":131948},[407]," 处取到。代回：",[363,131951,131953],{"className":131952,"translate":367},[528],[363,131954,131956,132082],{"className":131955,"translate":367},[366],[363,131957,131959],{"className":131958},[371],[373,131960,131961],{"xmlns":375,"display":537},[377,131962,131963,132079],{},[380,131964,131965,131971,131973,131975,131977,131979,131981,131983,131985,131987,131989,131991,131993,131995,132001,132003,132023,132025,132027,132037,132039,132041,132043,132045,132047,132049,132051,132053,132055,132057,132067,132069,132071,132073,132075,132077],{},[543,131966,131967,131969],{},[383,131968,571],{"mathvariant":570},[383,131970,554],{},[458,131972,578],{"stretchy":460},[383,131974,4447],{},[458,131976,4450],{},[458,131978,461],{"stretchy":460},[383,131980,11],{},[383,131982,1288],{"mathvariant":557},[383,131984,1291],{},[458,131986,468],{"stretchy":460},[458,131988,2817],{},[463,131990,465],{},[458,131992,605],{"stretchy":460},[458,131994,5160],{},[543,131996,131997,131999],{},[383,131998,571],{"mathvariant":570},[383,132000,561],{},[458,132002,578],{"stretchy":460},[7161,132004,132005,132007],{},[383,132006,7914],{},[380,132008,132009,132011,132013,132015,132017,132019,132021],{},[383,132010,4447],{},[458,132012,4450],{},[458,132014,461],{"stretchy":460},[383,132016,11],{},[383,132018,1288],{"mathvariant":557},[383,132020,1291],{},[458,132022,468],{"stretchy":460},[458,132024,605],{"stretchy":460},[458,132026,471],{},[543,132028,132029,132031],{},[383,132030,547],{},[380,132032,132033,132035],{},[383,132034,11041],{},[383,132036,22240],{},[458,132038,461],{"stretchy":460},[383,132040,554],{},[383,132042,558],{"mathvariant":557},[383,132044,561],{},[458,132046,468],{"stretchy":460},[458,132048,2817],{},[463,132050,465],{},[458,132052,5160],{},[463,132054,465],{},[458,132056,471],{},[543,132058,132059,132061],{},[383,132060,547],{},[380,132062,132063,132065],{},[383,132064,11041],{},[383,132066,22240],{},[458,132068,461],{"stretchy":460},[383,132070,554],{},[383,132072,558],{"mathvariant":557},[383,132074,561],{},[458,132076,468],{"stretchy":460},[458,132078,898],{"separator":394},[387,132080,132081],{"encoding":389},"\\mathbb E_P[\\log(p\u002Fq)+1]\n-\\mathbb E_Q[e^{\\log(p\u002Fq)}]\n=D_{KL}(P\\|Q)+1-1=D_{KL}(P\\|Q),",[363,132083,132085,132163,132184,132302,132378,132396,132414],{"className":132084,"ariaHidden":394},[393],[363,132086,132088,132091,132131,132134,132139,132142,132145,132148,132151,132154,132157,132160],{"className":132087},[398],[363,132089],{"className":132090,"style":487},[402],[363,132092,132094,132097],{"className":132093},[407],[363,132095,571],{"className":132096},[407,714],[363,132098,132100],{"className":132099},[629],[363,132101,132103,132123],{"className":132102},[633,634],[363,132104,132106,132120],{"className":132105},[638],[363,132107,132109],{"className":132108,"style":727},[642],[363,132110,132111,132114],{"style":730},[363,132112],{"className":132113,"style":651},[650],[363,132115,132117],{"className":132116},[655,656,657,658],[363,132118,554],{"className":132119,"style":682},[407,408,658],[363,132121,666],{"className":132122},[665],[363,132124,132126],{"className":132125},[638],[363,132127,132129],{"className":132128,"style":8315},[642],[363,132130],{},[363,132132,578],{"className":132133},[494],[363,132135,4501,132137],{"className":132136},[1831],[363,132138,4505],{"style":4504},[363,132140,461],{"className":132141},[494],[363,132143,11],{"className":132144},[407,408],[363,132146,1288],{"className":132147},[407],[363,132149,1291],{"className":132150,"style":1328},[407,408],[363,132152,468],{"className":132153},[501],[363,132155],{"className":132156,"style":2934},[505],[363,132158,2817],{"className":132159},[2938],[363,132161],{"className":132162,"style":2934},[505],[363,132164,132166,132169,132172,132175,132178,132181],{"className":132165},[398],[363,132167],{"className":132168,"style":487},[402],[363,132170,465],{"className":132171},[407],[363,132173,605],{"className":132174},[501],[363,132176],{"className":132177,"style":2934},[505],[363,132179,5160],{"className":132180},[2938],[363,132182],{"className":132183,"style":2934},[505],[363,132185,132187,132191,132231,132234,132290,132293,132296,132299],{"className":132186},[398],[363,132188],{"className":132189,"style":132190},[402],"height:1.2241em;vertical-align:-0.2861em;",[363,132192,132194,132197],{"className":132193},[407],[363,132195,571],{"className":132196},[407,714],[363,132198,132200],{"className":132199},[629],[363,132201,132203,132223],{"className":132202},[633,634],[363,132204,132206,132220],{"className":132205},[638],[363,132207,132209],{"className":132208,"style":727},[642],[363,132210,132211,132214],{"style":730},[363,132212],{"className":132213,"style":651},[650],[363,132215,132217],{"className":132216},[655,656,657,658],[363,132218,561],{"className":132219},[407,408,658],[363,132221,666],{"className":132222},[665],[363,132224,132226],{"className":132225},[638],[363,132227,132229],{"className":132228,"style":673},[642],[363,132230],{},[363,132232,578],{"className":132233},[494],[363,132235,132237,132240],{"className":132236},[407],[363,132238,7914],{"className":132239},[407,408],[363,132241,132243],{"className":132242},[629],[363,132244,132246],{"className":132245},[633],[363,132247,132249],{"className":132248},[638],[363,132250,132252],{"className":132251,"style":45467},[642],[363,132253,132254,132257],{"style":8624},[363,132255],{"className":132256,"style":651},[650],[363,132258,132260],{"className":132259},[655,656,657,658],[363,132261,132263,132275,132278,132281,132284,132287],{"className":132262},[407,658],[363,132264,132266,132269,132272],{"className":132265},[1831,658],[363,132267,48005],{"className":132268},[658],[363,132270,48009],{"className":132271},[658],[363,132273,4505],{"className":132274,"style":4504},[658],[363,132276,461],{"className":132277},[494,658],[363,132279,11],{"className":132280},[407,408,658],[363,132282,1288],{"className":132283},[407,658],[363,132285,1291],{"className":132286,"style":1328},[407,408,658],[363,132288,468],{"className":132289},[501,658],[363,132291,605],{"className":132292},[501],[363,132294],{"className":132295,"style":506},[505],[363,132297,471],{"className":132298},[510],[363,132300],{"className":132301,"style":506},[505],[363,132303,132305,132308,132354,132357,132360,132363,132366,132369,132372,132375],{"className":132304},[398],[363,132306],{"className":132307,"style":487},[402],[363,132309,132311,132314],{"className":132310},[407],[363,132312,547],{"className":132313,"style":625},[407,408],[363,132315,132317],{"className":132316},[629],[363,132318,132320,132346],{"className":132319},[633,634],[363,132321,132323,132343],{"className":132322},[638],[363,132324,132326],{"className":132325,"style":727},[642],[363,132327,132328,132331],{"style":646},[363,132329],{"className":132330,"style":651},[650],[363,132332,132334],{"className":132333},[655,656,657,658],[363,132335,132337,132340],{"className":132336},[407,658],[363,132338,11041],{"className":132339,"style":11129},[407,408,658],[363,132341,22240],{"className":132342},[407,408,658],[363,132344,666],{"className":132345},[665],[363,132347,132349],{"className":132348},[638],[363,132350,132352],{"className":132351,"style":8315},[642],[363,132353],{},[363,132355,461],{"className":132356},[494],[363,132358,554],{"className":132359,"style":682},[407,408],[363,132361,558],{"className":132362},[407],[363,132364,561],{"className":132365},[407,408],[363,132367,468],{"className":132368},[501],[363,132370],{"className":132371,"style":2934},[505],[363,132373,2817],{"className":132374},[2938],[363,132376],{"className":132377,"style":2934},[505],[363,132379,132381,132384,132387,132390,132393],{"className":132380},[398],[363,132382],{"className":132383,"style":12925},[402],[363,132385,465],{"className":132386},[407],[363,132388],{"className":132389,"style":2934},[505],[363,132391,5160],{"className":132392},[2938],[363,132394],{"className":132395,"style":2934},[505],[363,132397,132399,132402,132405,132408,132411],{"className":132398},[398],[363,132400],{"className":132401,"style":520},[402],[363,132403,465],{"className":132404},[407],[363,132406],{"className":132407,"style":506},[505],[363,132409,471],{"className":132410},[510],[363,132412],{"className":132413,"style":506},[505],[363,132415,132417,132420,132466,132469,132472,132475,132478,132481],{"className":132416},[398],[363,132418],{"className":132419,"style":487},[402],[363,132421,132423,132426],{"className":132422},[407],[363,132424,547],{"className":132425,"style":625},[407,408],[363,132427,132429],{"className":132428},[629],[363,132430,132432,132458],{"className":132431},[633,634],[363,132433,132435,132455],{"className":132434},[638],[363,132436,132438],{"className":132437,"style":727},[642],[363,132439,132440,132443],{"style":646},[363,132441],{"className":132442,"style":651},[650],[363,132444,132446],{"className":132445},[655,656,657,658],[363,132447,132449,132452],{"className":132448},[407,658],[363,132450,11041],{"className":132451,"style":11129},[407,408,658],[363,132453,22240],{"className":132454},[407,408,658],[363,132456,666],{"className":132457},[665],[363,132459,132461],{"className":132460},[638],[363,132462,132464],{"className":132463,"style":8315},[642],[363,132465],{},[363,132467,461],{"className":132468},[494],[363,132470,554],{"className":132471,"style":682},[407,408],[363,132473,558],{"className":132474},[407],[363,132476,561],{"className":132477},[407,408],[363,132479,468],{"className":132480},[501],[363,132482,898],{"className":132483},[920],[11,132485,132486],{},"完全自洽。这给出了一个「可验证」的对偶表示练习。",[18,132488,132490],{"id":132489},"_10-结论","10. 结论",[11,132492,132493],{},"f-散度族的故事可以浓缩成三句话：",[7009,132495,132496,132799,132965],{},[7012,132497,132498,9747,132501,3092,132706,92816,132734,10527],{},[1572,132499,132500],{},"一个模板",[363,132502,132504,132560],{"className":132503,"translate":367},[366],[363,132505,132507],{"className":132506},[371],[373,132508,132509],{"xmlns":375},[377,132510,132511,132557],{},[380,132512,132513,132519,132521,132523,132525,132527,132529,132531,132537,132539,132541,132543,132545,132547,132549,132551,132553,132555],{},[543,132514,132515,132517],{},[383,132516,547],{},[383,132518,385],{},[458,132520,461],{"stretchy":460},[383,132522,554],{},[383,132524,558],{"mathvariant":557},[383,132526,561],{},[458,132528,468],{"stretchy":460},[458,132530,471],{},[543,132532,132533,132535],{},[383,132534,571],{"mathvariant":570},[383,132536,561],{},[458,132538,578],{"stretchy":460},[383,132540,385],{},[458,132542,461],{"stretchy":460},[383,132544,592],{},[383,132546,554],{},[383,132548,1288],{"mathvariant":557},[383,132550,592],{},[383,132552,561],{},[458,132554,468],{"stretchy":460},[458,132556,605],{"stretchy":460},[387,132558,132559],{"encoding":389},"D_f(P\\|Q)=\\mathbb E_Q[f(dP\u002FdQ)]",[363,132561,132563,132633],{"className":132562,"ariaHidden":394},[393],[363,132564,132566,132569,132609,132612,132615,132618,132621,132624,132627,132630],{"className":132565},[398],[363,132567],{"className":132568,"style":618},[402],[363,132570,132572,132575],{"className":132571},[407],[363,132573,547],{"className":132574,"style":625},[407,408],[363,132576,132578],{"className":132577},[629],[363,132579,132581,132601],{"className":132580},[633,634],[363,132582,132584,132598],{"className":132583},[638],[363,132585,132587],{"className":132586,"style":643},[642],[363,132588,132589,132592],{"style":646},[363,132590],{"className":132591,"style":651},[650],[363,132593,132595],{"className":132594},[655,656,657,658],[363,132596,385],{"className":132597,"style":409},[407,408,658],[363,132599,666],{"className":132600},[665],[363,132602,132604],{"className":132603},[638],[363,132605,132607],{"className":132606,"style":673},[642],[363,132608],{},[363,132610,461],{"className":132611},[494],[363,132613,554],{"className":132614,"style":682},[407,408],[363,132616,558],{"className":132617},[407],[363,132619,561],{"className":132620},[407,408],[363,132622,468],{"className":132623},[501],[363,132625],{"className":132626,"style":506},[505],[363,132628,471],{"className":132629},[510],[363,132631],{"className":132632,"style":506},[505],[363,132634,132636,132639,132679,132682,132685,132688,132691,132694,132697,132700,132703],{"className":132635},[398],[363,132637],{"className":132638,"style":618},[402],[363,132640,132642,132645],{"className":132641},[407],[363,132643,571],{"className":132644},[407,714],[363,132646,132648],{"className":132647},[629],[363,132649,132651,132671],{"className":132650},[633,634],[363,132652,132654,132668],{"className":132653},[638],[363,132655,132657],{"className":132656,"style":727},[642],[363,132658,132659,132662],{"style":730},[363,132660],{"className":132661,"style":651},[650],[363,132663,132665],{"className":132664},[655,656,657,658],[363,132666,561],{"className":132667},[407,408,658],[363,132669,666],{"className":132670},[665],[363,132672,132674],{"className":132673},[638],[363,132675,132677],{"className":132676,"style":673},[642],[363,132678],{},[363,132680,578],{"className":132681},[494],[363,132683,385],{"className":132684,"style":409},[407,408],[363,132686,461],{"className":132687},[494],[363,132689,592],{"className":132690},[407,408],[363,132692,554],{"className":132693,"style":682},[407,408],[363,132695,1288],{"className":132696},[407],[363,132698,592],{"className":132699},[407,408],[363,132701,561],{"className":132702},[407,408],[363,132704,20737],{"className":132705},[501],[363,132707,132709,132722],{"className":132708,"translate":367},[366],[363,132710,132712],{"className":132711},[371],[373,132713,132714],{"xmlns":375},[377,132715,132716,132720],{},[380,132717,132718],{},[383,132719,385],{},[387,132721,385],{"encoding":389},[363,132723,132725],{"className":132724,"ariaHidden":394},[393],[363,132726,132728,132731],{"className":132727},[398],[363,132729],{"className":132730,"style":403},[402],[363,132732,385],{"className":132733,"style":409},[407,408],[363,132735,132737,132760],{"className":132736,"translate":367},[366],[363,132738,132740],{"className":132739},[371],[373,132741,132742],{"xmlns":375},[377,132743,132744,132758],{},[380,132745,132746,132748,132750,132752,132754,132756],{},[383,132747,385],{},[458,132749,461],{"stretchy":460},[463,132751,465],{},[458,132753,468],{"stretchy":460},[458,132755,471],{},[463,132757,474],{},[387,132759,477],{"encoding":389},[363,132761,132763,132790],{"className":132762,"ariaHidden":394},[393],[363,132764,132766,132769,132772,132775,132778,132781,132784,132787],{"className":132765},[398],[363,132767],{"className":132768,"style":487},[402],[363,132770,385],{"className":132771,"style":409},[407,408],[363,132773,461],{"className":132774},[494],[363,132776,465],{"className":132777},[407],[363,132779,468],{"className":132780},[501],[363,132782],{"className":132783,"style":506},[505],[363,132785,471],{"className":132786},[510],[363,132788],{"className":132789,"style":506},[505],[363,132791,132793,132796],{"className":132792},[398],[363,132794],{"className":132795,"style":520},[402],[363,132797,474],{"className":132798},[407],[7012,132800,132801,9747,132804,132885,132886,132964],{},[1572,132802,132803],{},"两组对偶",[363,132805,132807,132829],{"className":132806,"translate":367},[366],[363,132808,132810],{"className":132809},[371],[373,132811,132812],{"xmlns":375},[377,132813,132814,132826],{},[380,132815,132816,132818,132820],{},[383,132817,385],{},[458,132819,21706],{},[7161,132821,132822,132824],{},[383,132823,385],{},[458,132825,7920],{},[387,132827,132828],{"encoding":389},"f\\leftrightarrow f^*",[363,132830,132832,132850],{"className":132831,"ariaHidden":394},[393],[363,132833,132835,132838,132841,132844,132847],{"className":132834},[398],[363,132836],{"className":132837,"style":403},[402],[363,132839,385],{"className":132840,"style":409},[407,408],[363,132842],{"className":132843,"style":506},[505],[363,132845,21706],{"className":132846},[510],[363,132848],{"className":132849,"style":506},[505],[363,132851,132853,132856],{"className":132852},[398],[363,132854],{"className":132855,"style":403},[402],[363,132857,132859,132862],{"className":132858},[407],[363,132860,385],{"className":132861,"style":409},[407,408],[363,132863,132865],{"className":132864},[629],[363,132866,132868],{"className":132867},[633],[363,132869,132871],{"className":132870},[638],[363,132872,132874],{"className":132873,"style":8846},[642],[363,132875,132876,132879],{"style":7212},[363,132877],{"className":132878,"style":651},[650],[363,132880,132882],{"className":132881},[655,656,657,658],[363,132883,7920],{"className":132884},[2938,658]," 给出变分表示（可用于估计与对抗训练）；",[363,132887,132889,132919],{"className":132888,"translate":367},[366],[363,132890,132892],{"className":132891},[371],[373,132893,132894],{"xmlns":375},[377,132895,132896,132916],{},[380,132897,132898,132900,132902,132904,132906,132908,132910,132912,132914],{},[383,132899,385],{},[458,132901,21706],{},[383,132903,1116],{},[383,132905,385],{},[458,132907,461],{"stretchy":460},[463,132909,465],{},[383,132911,1288],{"mathvariant":557},[383,132913,1116],{},[458,132915,468],{"stretchy":460},[387,132917,132918],{"encoding":389},"f\\leftrightarrow t f(1\u002Ft)",[363,132920,132922,132940],{"className":132921,"ariaHidden":394},[393],[363,132923,132925,132928,132931,132934,132937],{"className":132924},[398],[363,132926],{"className":132927,"style":403},[402],[363,132929,385],{"className":132930,"style":409},[407,408],[363,132932],{"className":132933,"style":506},[505],[363,132935,21706],{"className":132936},[510],[363,132938],{"className":132939,"style":506},[505],[363,132941,132943,132946,132949,132952,132955,132958,132961],{"className":132942},[398],[363,132944],{"className":132945,"style":487},[402],[363,132947,1116],{"className":132948},[407,408],[363,132950,385],{"className":132951,"style":409},[407,408],[363,132953,461],{"className":132954},[494],[363,132956,8936],{"className":132957},[407],[363,132959,1116],{"className":132960},[407,408],[363,132962,468],{"className":132963},[501]," 给出方向对称性（可用于构造对称散度）。",[7012,132966,132967,132970],{},[1572,132968,132969],{},"一个不变量","：数据处理不等式，说明它是「信息量」而非「几何量」。正因如此，它与 Wasserstein\u002FMMD 在支撑分离时行为迥异。",[11,132972,132973],{},"经典文献可参考：Csiszár (1967)、Ali–Silvey (1966) 的原始定义；Liese–Vajda 的专著对 f-散度的对偶、拓扑与充分性做了系统处理；Amari 的信息几何给出 α-族与 Fisher 度量；Nowozin 等 (2016) 的 f-GAN、Belghazi 等 (2018) 的 MINE 把对偶表示变成可训练算法；Dong–Roth–Su (2022) 说明 f-散度的语言如何统一差分隐私。把这几条线索接起来，读者就能在「定义—性质—估计—应用」四个层面上自由穿梭。",{"title":330,"searchDepth":331,"depth":331,"links":132975},[132976,132983,132988,132998,133008,133015,133020,133028,133029,133034],{"id":877,"depth":331,"text":878,"children":132977},[132978,132980,132981,132982],{"id":2660,"depth":132979,"text":2661},3,{"id":5551,"depth":132979,"text":5552},{"id":5920,"depth":132979,"text":5921},{"id":7708,"depth":132979,"text":7709},{"id":9098,"depth":331,"text":132984,"children":132985},"2. 为何 fff 凸且 f(1)=0f(1)=0f(1)=0",[132986,132987],{"id":9196,"depth":132979,"text":9197},{"id":10907,"depth":132979,"text":10908},{"id":21754,"depth":331,"text":21755,"children":132989},[132990,132991,132992,132993,132994,132995,132996,132997],{"id":21816,"depth":132979,"text":21817},{"id":25895,"depth":132979,"text":25896},{"id":34856,"depth":132979,"text":34857},{"id":37495,"depth":132979,"text":37496},{"id":40784,"depth":132979,"text":40785},{"id":45083,"depth":132979,"text":45084},{"id":49722,"depth":132979,"text":49723},{"id":52836,"depth":132979,"text":52837},{"id":55259,"depth":331,"text":55260,"children":132999},[133000,133001,133002,133003,133004,133005,133006,133007],{"id":55558,"depth":132979,"text":55559},{"id":56483,"depth":132979,"text":56484},{"id":58637,"depth":132979,"text":58638},{"id":61028,"depth":132979,"text":61029},{"id":74797,"depth":132979,"text":74798},{"id":78379,"depth":132979,"text":78380},{"id":82405,"depth":132979,"text":82406},{"id":97296,"depth":132979,"text":97297},{"id":99644,"depth":331,"text":99645,"children":133009},[133010,133011,133012,133013,133014],{"id":99648,"depth":132979,"text":99649},{"id":101692,"depth":132979,"text":101693},{"id":103534,"depth":132979,"text":103535},{"id":105696,"depth":132979,"text":105697},{"id":108588,"depth":132979,"text":108589},{"id":108929,"depth":331,"text":108930,"children":133016},[133017,133018,133019],{"id":108933,"depth":132979,"text":108934},{"id":114959,"depth":132979,"text":114960},{"id":116741,"depth":132979,"text":116742},{"id":117785,"depth":331,"text":117786,"children":133021},[133022,133023,133024,133025,133026,133027],{"id":117854,"depth":132979,"text":117855},{"id":118048,"depth":132979,"text":118049},{"id":118939,"depth":132979,"text":118940},{"id":119638,"depth":132979,"text":119639},{"id":120096,"depth":132979,"text":120097},{"id":120165,"depth":132979,"text":120166},{"id":120529,"depth":331,"text":120530},{"id":124690,"depth":331,"text":124691,"children":133030},[133031,133032,133033],{"id":124694,"depth":132979,"text":124695},{"id":129039,"depth":132979,"text":129040},{"id":131269,"depth":132979,"text":131270},{"id":132489,"depth":331,"text":132490},"f-散度族是概率分布之间差异的一大类度量，它用一个凸函数 fff 来统一描述 KL 散度、JS 散度、全变差、卡方散度等许多常见散度。可以把它理解为「散度」的通用模板。",{},"\u002Fblog\u002F2026\u002F0011-about-the-f-divergence",{"title":356,"description":133035},"blog\u002F2026\u002F0011-about-the-f-divergence","f-散度族（f-divergence）用一个凸函数 f 统一刻画两个概率分布之间的差异，KL、JS、全变差、卡方、Hellinger、α-散度都是它的特例。",[133042,133043],"statistics","mathematics","2026-10-17T04:47:08+08:00","iwqHXZqjOaalRKrTl4b8l9DoWDfn8fPQY2GEv_zt_Xw",{"id":133047,"title":133048,"body":133049,"description":197565,"draft":341,"enableCodeHighlight":341,"enableCodeHightlight":341,"enableComment":342,"enableD2":341,"enableKatex":342,"extension":343,"image":330,"important":341,"location":344,"meta":197566,"navigation":342,"ogImage":344,"path":197567,"seo":197568,"stem":197569,"summary":197570,"tags":197571,"time":197573,"__hash__":197574},"blog\u002Fblog\u002F2026\u002F0007-dirichlet-distribution-and-evidential-deep-learning.md","Dirichlet 分布与证据深度学习",{"type":8,"value":133050,"toc":197525},[133051,133204,133599,133728,133801,133804,133808,133812,134746,135207,135984,135988,137482,137485,137989,138089,138696,139585,140396,140913,142057,142146,142209,142213,143430,143952,144936,145054,145318,145322,145606,146568,146623,147297,147460,147464,147468,148822,151095,151293,151640,152189,152193,152302,152599,153122,153749,154308,154428,154432,155190,155287,155959,156683,157189,157375,157379,158040,158223,158563,158644,158647,159636,161120,161503,161507,162365,162372,163111,164074,164177,164181,164219,164861,164929,165356,165951,165955,165959,165966,166931,167431,167600,167604,167610,168491,168980,169757,169760,169767,169771,170423,170826,170971,170974,170978,170984,171735,172020,172023,172870,172874,173664,173848,173879,174770,174955,175507,175575,175579,175648,175839,176412,177992,179463,179738,179981,179985,180072,180076,180083,180353,180568,180913,180916,181649,181990,182714,183479,183515,183519,183522,184250,185251,185534,185702,185706,185795,185798,186266,186406,188240,189244,189250,189694,189913,189917,189920,190156,190425,190428,190552,190563,190567,190570,192093,192100,192104,192108,192236,192686,192897,193029,193036,193039,193043,193268,193768,193842,194068,194072,194292,194408,194412,194418,194609,194645,194649,194655,194992,195477,195480,195484,196100,196103,196645,196958,197110,197113,197279,197282,197285,197409,197477,197480,197518],[11,133052,881,133053,133082,133083,133174,133175,133203],{},[363,133054,133056,133070],{"className":133055,"translate":367},[366],[363,133057,133059],{"className":133058},[371],[373,133060,133061],{"xmlns":375},[377,133062,133063,133067],{},[380,133064,133065],{},[383,133066,945],{"mathvariant":944},[387,133068,133069],{"encoding":389},"\\mathcal{X}",[363,133071,133073],{"className":133072,"ariaHidden":394},[393],[363,133074,133076,133079],{"className":133075},[398],[363,133077],{"className":133078,"style":1011},[402],[363,133080,945],{"className":133081,"style":972},[407,971]," 为输入空间，",[363,133084,133086,133117],{"className":133085,"translate":367},[366],[363,133087,133089],{"className":133088},[371],[373,133090,133091],{"xmlns":375},[377,133092,133093,133114],{},[380,133094,133095,133097,133099,133101,133103,133105,133108,133110,133112],{},[383,133096,40584],{},[458,133098,6256],{},[458,133100,3245],{"stretchy":460},[463,133102,465],{},[458,133104,898],{"separator":394},[458,133106,133107],{},"…",[458,133109,898],{"separator":394},[383,133111,11041],{},[458,133113,3255],{"stretchy":460},[387,133115,133116],{"encoding":389},"y \\in \\{1, \\dots, K\\}",[363,133118,133120,133138],{"className":133119,"ariaHidden":394},[393],[363,133121,133123,133126,133129,133132,133135],{"className":133122},[398],[363,133124],{"className":133125,"style":32039},[402],[363,133127,40584],{"className":133128,"style":1328},[407,408],[363,133130],{"className":133131,"style":506},[505],[363,133133,6256],{"className":133134},[510],[363,133136],{"className":133137,"style":506},[505],[363,133139,133141,133144,133147,133150,133153,133156,133159,133162,133165,133168,133171],{"className":133140},[398],[363,133142],{"className":133143,"style":487},[402],[363,133145,3245],{"className":133146},[494],[363,133148,465],{"className":133149},[407],[363,133151,898],{"className":133152},[920],[363,133154],{"className":133155,"style":754},[505],[363,133157,133107],{"className":133158},[758],[363,133160],{"className":133161,"style":754},[505],[363,133163,898],{"className":133164},[920],[363,133166],{"className":133167,"style":754},[505],[363,133169,11041],{"className":133170,"style":11129},[407,408],[363,133172,3255],{"className":133173},[501]," 为类别标签。一个 ",[363,133176,133178,133191],{"className":133177,"translate":367},[366],[363,133179,133181],{"className":133180},[371],[373,133182,133183],{"xmlns":375},[377,133184,133185,133189],{},[380,133186,133187],{},[383,133188,11041],{},[387,133190,11041],{"encoding":389},[363,133192,133194],{"className":133193,"ariaHidden":394},[393],[363,133195,133197,133200],{"className":133196},[398],[363,133198],{"className":133199,"style":1011},[402],[363,133201,11041],{"className":133202,"style":11129},[407,408]," 分类器的输出在数学上究竟是什么？若要求它给出「属于各类别的概率」，则输出必须落在",[363,133205,133207],{"className":133206,"translate":367},[528],[363,133208,133210,133294],{"className":133209,"translate":367},[366],[363,133211,133213],{"className":133212},[371],[373,133214,133215],{"xmlns":375,"display":537},[377,133216,133217,133291],{},[380,133218,133219,133231,133233],{},[7161,133220,133221,133223],{},[383,133222,126023],{"mathvariant":557},[380,133224,133225,133227,133229],{},[383,133226,11041],{},[458,133228,5160],{},[463,133230,465],{},[458,133232,471],{},[380,133234,133235,133237,133239,133241,133247,133249,133255,133257,133259,133261,133263,133289],{},[458,133236,3245],{"fence":394},[383,133238,11],{"mathvariant":75560},[458,133240,6256],{},[7161,133242,133243,133245],{},[383,133244,1379],{"mathvariant":570},[383,133246,11041],{},[458,133248,1362],{},[543,133250,133251,133253],{},[383,133252,11],{},[383,133254,7911],{},[458,133256,7275],{},[463,133258,474],{},[458,133260,898],{"separator":394},[1644,133262,4630],{},[1602,133264,133265,133279,133285,133287],{"scriptlevel":474,"displaystyle":460},[7900,133266,133267,133269,133277],{},[458,133268,13808],{},[380,133270,133271,133273,133275],{},[383,133272,7911],{},[458,133274,471],{},[463,133276,465],{},[383,133278,11041],{},[543,133280,133281,133283],{},[383,133282,11],{},[383,133284,7911],{},[458,133286,471],{},[463,133288,465],{},[458,133290,3255],{"fence":394},[387,133292,133293],{"encoding":389},"\\Delta^{K-1} = \\left\\{ \\mathbf{p} \\in \\mathbb{R}^K : p_k \\ge 0,\\ \\textstyle\\sum_{k=1}^K p_k = 1 \\right\\}",[363,133295,133297,133350],{"className":133296,"ariaHidden":394},[393],[363,133298,133300,133303,133341,133344,133347],{"className":133299},[398],[363,133301],{"className":133302,"style":38859},[402],[363,133304,133306,133309],{"className":133305},[407],[363,133307,126023],{"className":133308},[407],[363,133310,133312],{"className":133311},[629],[363,133313,133315],{"className":133314},[633],[363,133316,133318],{"className":133317},[638],[363,133319,133321],{"className":133320,"style":38859},[642],[363,133322,133323,133326],{"style":8624},[363,133324],{"className":133325,"style":651},[650],[363,133327,133329],{"className":133328},[655,656,657,658],[363,133330,133332,133335,133338],{"className":133331},[407,658],[363,133333,11041],{"className":133334,"style":11129},[407,408,658],[363,133336,5160],{"className":133337},[2938,658],[363,133339,465],{"className":133340},[407,658],[363,133342],{"className":133343,"style":506},[505],[363,133345,471],{"className":133346},[510],[363,133348],{"className":133349,"style":506},[505],[363,133351,133353,133356],{"className":133352},[398],[363,133354],{"className":133355,"style":68464},[402],[363,133357,133359,133365,133368,133371,133374,133377,133406,133409,133412,133415,133455,133458,133461,133464,133467,133470,133473,133476,133538,133541,133581,133584,133587,133590,133593],{"className":133358},[758],[363,133360,133362],{"className":133361,"style":763},[494,762],[363,133363,3245],{"className":133364},[767,4067],[363,133366,11],{"className":133367},[407,75905],[363,133369],{"className":133370,"style":506},[505],[363,133372,6256],{"className":133373},[510],[363,133375],{"className":133376,"style":506},[505],[363,133378,133380,133383],{"className":133379},[407],[363,133381,1379],{"className":133382},[407,714],[363,133384,133386],{"className":133385},[629],[363,133387,133389],{"className":133388},[633],[363,133390,133392],{"className":133391},[638],[363,133393,133395],{"className":133394,"style":38859},[642],[363,133396,133397,133400],{"style":8624},[363,133398],{"className":133399,"style":651},[650],[363,133401,133403],{"className":133402},[655,656,657,658],[363,133404,11041],{"className":133405,"style":11129},[407,408,658],[363,133407],{"className":133408,"style":506},[505],[363,133410,1362],{"className":133411},[510],[363,133413],{"className":133414,"style":506},[505],[363,133416,133418,133421],{"className":133417},[407],[363,133419,11],{"className":133420},[407,408],[363,133422,133424],{"className":133423},[629],[363,133425,133427,133447],{"className":133426},[633,634],[363,133428,133430,133444],{"className":133429},[638],[363,133431,133433],{"className":133432,"style":643},[642],[363,133434,133435,133438],{"style":730},[363,133436],{"className":133437,"style":651},[650],[363,133439,133441],{"className":133440},[655,656,657,658],[363,133442,7911],{"className":133443,"style":8614},[407,408,658],[363,133445,666],{"className":133446},[665],[363,133448,133450],{"className":133449},[638],[363,133451,133453],{"className":133452,"style":8315},[642],[363,133454],{},[363,133456],{"className":133457,"style":506},[505],[363,133459,7275],{"className":133460},[510],[363,133462],{"className":133463,"style":506},[505],[363,133465,474],{"className":133466},[407],[363,133468,898],{"className":133469},[920],[363,133471,4630],{"className":133472},[505],[363,133474],{"className":133475,"style":754},[505],[363,133477,133479,133482],{"className":133478},[1831],[363,133480,13808],{"className":133481,"style":40007},[1831,1832,5963],[363,133483,133485],{"className":133484},[629],[363,133486,133488,133530],{"className":133487},[633,634],[363,133489,133491,133527],{"className":133490},[638],[363,133492,133495,133515],{"className":133493,"style":133494},[642],"height:0.9812em;",[363,133496,133497,133500],{"style":40023},[363,133498],{"className":133499,"style":651},[650],[363,133501,133503],{"className":133502},[655,656,657,658],[363,133504,133506,133509,133512],{"className":133505},[407,658],[363,133507,7911],{"className":133508,"style":8614},[407,408,658],[363,133510,471],{"className":133511},[510,658],[363,133513,465],{"className":133514},[407,658],[363,133516,133518,133521],{"style":133517},"top:-3.2029em;margin-right:0.05em;",[363,133519],{"className":133520,"style":651},[650],[363,133522,133524],{"className":133523},[655,656,657,658],[363,133525,11041],{"className":133526,"style":11129},[407,408,658],[363,133528,666],{"className":133529},[665],[363,133531,133533],{"className":133532},[638],[363,133534,133536],{"className":133535,"style":40042},[642],[363,133537],{},[363,133539],{"className":133540,"style":754},[505],[363,133542,133544,133547],{"className":133543},[407],[363,133545,11],{"className":133546},[407,408],[363,133548,133550],{"className":133549},[629],[363,133551,133553,133573],{"className":133552},[633,634],[363,133554,133556,133570],{"className":133555},[638],[363,133557,133559],{"className":133558,"style":643},[642],[363,133560,133561,133564],{"style":730},[363,133562],{"className":133563,"style":651},[650],[363,133565,133567],{"className":133566},[655,656,657,658],[363,133568,7911],{"className":133569,"style":8614},[407,408,658],[363,133571,666],{"className":133572},[665],[363,133574,133576],{"className":133575},[638],[363,133577,133579],{"className":133578,"style":8315},[642],[363,133580],{},[363,133582],{"className":133583,"style":506},[505],[363,133585,471],{"className":133586},[510],[363,133588],{"className":133589,"style":506},[505],[363,133591,465],{"className":133592},[407],[363,133594,133596],{"className":133595,"style":763},[501,762],[363,133597,3255],{"className":133598},[767,4067],[11,133600,133601,133602,133605,133606,133665,133666,133727],{},"之中——",[1572,133603,133604],{},"概率单纯形","上的一个点。这是分类器输出的自然状态空间：它不是 ",[363,133607,133609,133627],{"className":133608,"translate":367},[366],[363,133610,133612],{"className":133611},[371],[373,133613,133614],{"xmlns":375},[377,133615,133616,133624],{},[380,133617,133618],{},[7161,133619,133620,133622],{},[383,133621,1379],{"mathvariant":570},[383,133623,11041],{},[387,133625,133626],{"encoding":389},"\\mathbb{R}^K",[363,133628,133630],{"className":133629,"ariaHidden":394},[393],[363,133631,133633,133636],{"className":133632},[398],[363,133634],{"className":133635,"style":52432},[402],[363,133637,133639,133642],{"className":133638},[407],[363,133640,1379],{"className":133641},[407,714],[363,133643,133645],{"className":133644},[629],[363,133646,133648],{"className":133647},[633],[363,133649,133651],{"className":133650},[638],[363,133652,133654],{"className":133653,"style":52432},[642],[363,133655,133656,133659],{"style":7212},[363,133657],{"className":133658,"style":651},[650],[363,133660,133662],{"className":133661},[655,656,657,658],[363,133663,11041],{"className":133664,"style":11129},[407,408,658],"，而是一个 ",[363,133667,133669,133691],{"className":133668,"translate":367},[366],[363,133670,133672],{"className":133671},[371],[373,133673,133674],{"xmlns":375},[377,133675,133676,133688],{},[380,133677,133678,133680,133682,133684,133686],{},[458,133679,461],{"stretchy":460},[383,133681,11041],{},[458,133683,5160],{},[463,133685,465],{},[458,133687,468],{"stretchy":460},[387,133689,133690],{"encoding":389},"(K-1)",[363,133692,133694,133715],{"className":133693,"ariaHidden":394},[393],[363,133695,133697,133700,133703,133706,133709,133712],{"className":133696},[398],[363,133698],{"className":133699,"style":487},[402],[363,133701,461],{"className":133702},[494],[363,133704,11041],{"className":133705,"style":11129},[407,408],[363,133707],{"className":133708,"style":2934},[505],[363,133710,5160],{"className":133711},[2938],[363,133713],{"className":133714,"style":2934},[505],[363,133716,133718,133721,133724],{"className":133717},[398],[363,133719],{"className":133720,"style":487},[402],[363,133722,465],{"className":133723},[407],[363,133725,468],{"className":133726},[501]," 维的紧凸集。",[11,133729,133730,133731,133734,133735,6841,133738,133768,133769,133797,133798,10527],{},"一旦承认了这一点，一个二阶问题便随即出现：分类器对自身输出的",[1572,133732,133733],{},"把握","有多大？若把输出建模为单纯形上的一个",[1572,133736,133737],{},"确定点",[363,133739,133741,133755],{"className":133740,"translate":367},[366],[363,133742,133744],{"className":133743},[371],[373,133745,133746],{"xmlns":375},[377,133747,133748,133752],{},[380,133749,133750],{},[383,133751,11],{"mathvariant":75560},[387,133753,133754],{"encoding":389},"\\mathbf{p}",[363,133756,133758],{"className":133757,"ariaHidden":394},[393],[363,133759,133761,133765],{"className":133760},[398],[363,133762],{"className":133763,"style":133764},[402],"height:0.6389em;vertical-align:-0.1944em;",[363,133766,11],{"className":133767},[407,75905],"，则这个问题在表达力上是被禁止的：单纯形内部不存在可以指代「无信息」的元素，因为每个点都是一份完整的、和为 ",[363,133770,133772,133785],{"className":133771,"translate":367},[366],[363,133773,133775],{"className":133774},[371],[373,133776,133777],{"xmlns":375},[377,133778,133779,133783],{},[380,133780,133781],{},[463,133782,465],{},[387,133784,465],{"encoding":389},[363,133786,133788],{"className":133787,"ariaHidden":394},[393],[363,133789,133791,133794],{"className":133790},[398],[363,133792],{"className":133793,"style":520},[402],[363,133795,465],{"className":133796},[407]," 的断言。要回答二阶问题，必须把输出从「单纯形上的点」提升为「单纯形上的分布」。承担这一角色的标准对象正是 ",[1572,133799,133800],{},"迪利克雷分布（Dirichlet distribution）",[11,133802,133803],{},"本文的组织如下。第一部分给出迪利克雷分布的形式化定义、生成性刻画与几何图像。第二部分展开其矩结构、重参数化、共轭更新与分裂构造，并澄清「伪计数」这一常见的直观说法在何处成立、在何处失效。第三部分经由主观逻辑（subjective logic）建立迪利克雷分布与神经网络输出之间的双射，由此引入证据深度学习（Evidential Deep Learning, EDL）。第四部分推导 EDL 的损失函数族及其理论缺陷。第五部分讨论其应用形态与边界。第六部分总结。",[18,133805,133807],{"id":133806},"一形式化","一、形式化",[2658,133809,133811],{"id":133810},"_11-概率单纯形","1.1 概率单纯形",[1340,133813,133815],{"title":133814},"定义 1.1（概率单纯形）",[11,133816,133817,133818,3092,133869,133921,133922,134449,134450,10527],{},"对整数 ",[363,133819,133821,133839],{"className":133820,"translate":367},[366],[363,133822,133824],{"className":133823},[371],[373,133825,133826],{"xmlns":375},[377,133827,133828,133836],{},[380,133829,133830,133832,133834],{},[383,133831,11041],{},[458,133833,7275],{},[463,133835,2810],{},[387,133837,133838],{"encoding":389},"K \\ge 2",[363,133840,133842,133860],{"className":133841,"ariaHidden":394},[393],[363,133843,133845,133848,133851,133854,133857],{"className":133844},[398],[363,133846],{"className":133847,"style":88701},[402],[363,133849,11041],{"className":133850,"style":11129},[407,408],[363,133852],{"className":133853,"style":506},[505],[363,133855,7275],{"className":133856},[510],[363,133858],{"className":133859,"style":506},[505],[363,133861,133863,133866],{"className":133862},[398],[363,133864],{"className":133865,"style":520},[402],[363,133867,2810],{"className":133868},[407],[363,133870,133872,133890],{"className":133871,"translate":367},[366],[363,133873,133875],{"className":133874},[371],[373,133876,133877],{"xmlns":375},[377,133878,133879,133887],{},[380,133880,133881,133883,133885],{},[383,133882,11041],{},[458,133884,5160],{},[463,133886,465],{},[387,133888,133889],{"encoding":389},"K-1",[363,133891,133893,133912],{"className":133892,"ariaHidden":394},[393],[363,133894,133896,133900,133903,133906,133909],{"className":133895},[398],[363,133897],{"className":133898,"style":133899},[402],"height:0.7667em;vertical-align:-0.0833em;",[363,133901,11041],{"className":133902,"style":11129},[407,408],[363,133904],{"className":133905,"style":2934},[505],[363,133907,5160],{"className":133908},[2938],[363,133910],{"className":133911,"style":2934},[505],[363,133913,133915,133918],{"className":133914},[398],[363,133916],{"className":133917,"style":520},[402],[363,133919,465],{"className":133920},[407]," 维标准单纯形定义为\n",[363,133923,133925,134033],{"className":133924,"translate":367},[366],[363,133926,133928],{"className":133927},[371],[373,133929,133930],{"xmlns":375},[377,133931,133932,134030],{},[380,133933,133934,133946,133948],{},[7161,133935,133936,133938],{},[383,133937,126023],{"mathvariant":557},[380,133939,133940,133942,133944],{},[383,133941,11041],{},[458,133943,5160],{},[463,133945,465],{},[458,133947,471],{},[380,133949,133950,133952,133954,133956,133958,133964,133966,133968,133970,133976,133978,133980,133986,133988,133994,133996,133998,134000,134002,134028],{},[458,133951,3245],{"fence":394},[383,133953,1121],{"mathvariant":75560},[458,133955,471],{},[458,133957,461],{"stretchy":460},[543,133959,133960,133962],{},[383,133961,1121],{},[463,133963,465],{},[458,133965,898],{"separator":394},[458,133967,133107],{},[458,133969,898],{"separator":394},[543,133971,133972,133974],{},[383,133973,1121],{},[383,133975,11041],{},[458,133977,468],{"stretchy":460},[458,133979,6256],{},[7161,133981,133982,133984],{},[383,133983,1379],{"mathvariant":570},[383,133985,11041],{},[458,133987,1362],{},[543,133989,133990,133992],{},[383,133991,1121],{},[383,133993,12310],{},[458,133995,7275],{},[463,133997,474],{},[458,133999,898],{"separator":394},[1644,134001,4630],{},[1602,134003,134004,134018,134024,134026],{"scriptlevel":474,"displaystyle":460},[7900,134005,134006,134008,134016],{},[458,134007,13808],{},[380,134009,134010,134012,134014],{},[383,134011,12310],{},[458,134013,471],{},[463,134015,465],{},[383,134017,11041],{},[543,134019,134020,134022],{},[383,134021,1121],{},[383,134023,12310],{},[458,134025,471],{},[463,134027,465],{},[458,134029,3255],{"fence":394},[387,134031,134032],{"encoding":389},"\\Delta^{K-1} = \\left\\{ \\mathbf{x} = (x_1, \\dots, x_K) \\in \\mathbb{R}^K : x_i \\ge 0,\\ \\textstyle\\sum_{i=1}^K x_i = 1 \\right\\}",[363,134034,134036,134089],{"className":134035,"ariaHidden":394},[393],[363,134037,134039,134042,134080,134083,134086],{"className":134038},[398],[363,134040],{"className":134041,"style":52432},[402],[363,134043,134045,134048],{"className":134044},[407],[363,134046,126023],{"className":134047},[407],[363,134049,134051],{"className":134050},[629],[363,134052,134054],{"className":134053},[633],[363,134055,134057],{"className":134056},[638],[363,134058,134060],{"className":134059,"style":52432},[642],[363,134061,134062,134065],{"style":7212},[363,134063],{"className":134064,"style":651},[650],[363,134066,134068],{"className":134067},[655,656,657,658],[363,134069,134071,134074,134077],{"className":134070},[407,658],[363,134072,11041],{"className":134073,"style":11129},[407,408,658],[363,134075,5160],{"className":134076},[2938,658],[363,134078,465],{"className":134079},[407,658],[363,134081],{"className":134082,"style":506},[505],[363,134084,471],{"className":134085},[510],[363,134087],{"className":134088,"style":506},[505],[363,134090,134092,134095],{"className":134091},[398],[363,134093],{"className":134094,"style":68464},[402],[363,134096,134098,134104,134107,134110,134113,134116,134119,134159,134162,134165,134168,134171,134174,134177,134217,134220,134223,134226,134229,134258,134261,134264,134267,134307,134310,134313,134316,134319,134322,134325,134328,134388,134391,134431,134434,134437,134440,134443],{"className":134097},[758],[363,134099,134101],{"className":134100,"style":763},[494,762],[363,134102,3245],{"className":134103},[767,4067],[363,134105,1121],{"className":134106},[407,75905],[363,134108],{"className":134109,"style":506},[505],[363,134111,471],{"className":134112},[510],[363,134114],{"className":134115,"style":506},[505],[363,134117,461],{"className":134118},[494],[363,134120,134122,134125],{"className":134121},[407],[363,134123,1121],{"className":134124},[407,408],[363,134126,134128],{"className":134127},[629],[363,134129,134131,134151],{"className":134130},[633,634],[363,134132,134134,134148],{"className":134133},[638],[363,134135,134137],{"className":134136,"style":11480},[642],[363,134138,134139,134142],{"style":730},[363,134140],{"className":134141,"style":651},[650],[363,134143,134145],{"className":134144},[655,656,657,658],[363,134146,465],{"className":134147},[407,658],[363,134149,666],{"className":134150},[665],[363,134152,134154],{"className":134153},[638],[363,134155,134157],{"className":134156,"style":8315},[642],[363,134158],{},[363,134160,898],{"className":134161},[920],[363,134163],{"className":134164,"style":754},[505],[363,134166,133107],{"className":134167},[758],[363,134169],{"className":134170,"style":754},[505],[363,134172,898],{"className":134173},[920],[363,134175],{"className":134176,"style":754},[505],[363,134178,134180,134183],{"className":134179},[407],[363,134181,1121],{"className":134182},[407,408],[363,134184,134186],{"className":134185},[629],[363,134187,134189,134209],{"className":134188},[633,634],[363,134190,134192,134206],{"className":134191},[638],[363,134193,134195],{"className":134194,"style":727},[642],[363,134196,134197,134200],{"style":730},[363,134198],{"className":134199,"style":651},[650],[363,134201,134203],{"className":134202},[655,656,657,658],[363,134204,11041],{"className":134205,"style":11129},[407,408,658],[363,134207,666],{"className":134208},[665],[363,134210,134212],{"className":134211},[638],[363,134213,134215],{"className":134214,"style":8315},[642],[363,134216],{},[363,134218,468],{"className":134219},[501],[363,134221],{"className":134222,"style":506},[505],[363,134224,6256],{"className":134225},[510],[363,134227],{"className":134228,"style":506},[505],[363,134230,134232,134235],{"className":134231},[407],[363,134233,1379],{"className":134234},[407,714],[363,134236,134238],{"className":134237},[629],[363,134239,134241],{"className":134240},[633],[363,134242,134244],{"className":134243},[638],[363,134245,134247],{"className":134246,"style":52432},[642],[363,134248,134249,134252],{"style":7212},[363,134250],{"className":134251,"style":651},[650],[363,134253,134255],{"className":134254},[655,656,657,658],[363,134256,11041],{"className":134257,"style":11129},[407,408,658],[363,134259],{"className":134260,"style":506},[505],[363,134262,1362],{"className":134263},[510],[363,134265],{"className":134266,"style":506},[505],[363,134268,134270,134273],{"className":134269},[407],[363,134271,1121],{"className":134272},[407,408],[363,134274,134276],{"className":134275},[629],[363,134277,134279,134299],{"className":134278},[633,634],[363,134280,134282,134296],{"className":134281},[638],[363,134283,134285],{"className":134284,"style":12529},[642],[363,134286,134287,134290],{"style":730},[363,134288],{"className":134289,"style":651},[650],[363,134291,134293],{"className":134292},[655,656,657,658],[363,134294,12310],{"className":134295},[407,408,658],[363,134297,666],{"className":134298},[665],[363,134300,134302],{"className":134301},[638],[363,134303,134305],{"className":134304,"style":8315},[642],[363,134306],{},[363,134308],{"className":134309,"style":506},[505],[363,134311,7275],{"className":134312},[510],[363,134314],{"className":134315,"style":506},[505],[363,134317,474],{"className":134318},[407],[363,134320,898],{"className":134321},[920],[363,134323,4630],{"className":134324},[505],[363,134326],{"className":134327,"style":754},[505],[363,134329,134331,134334],{"className":134330},[1831],[363,134332,13808],{"className":134333,"style":40007},[1831,1832,5963],[363,134335,134337],{"className":134336},[629],[363,134338,134340,134380],{"className":134339},[633,634],[363,134341,134343,134377],{"className":134342},[638],[363,134344,134346,134366],{"className":134345,"style":133494},[642],[363,134347,134348,134351],{"style":40023},[363,134349],{"className":134350,"style":651},[650],[363,134352,134354],{"className":134353},[655,656,657,658],[363,134355,134357,134360,134363],{"className":134356},[407,658],[363,134358,12310],{"className":134359},[407,408,658],[363,134361,471],{"className":134362},[510,658],[363,134364,465],{"className":134365},[407,658],[363,134367,134368,134371],{"style":133517},[363,134369],{"className":134370,"style":651},[650],[363,134372,134374],{"className":134373},[655,656,657,658],[363,134375,11041],{"className":134376,"style":11129},[407,408,658],[363,134378,666],{"className":134379},[665],[363,134381,134383],{"className":134382},[638],[363,134384,134386],{"className":134385,"style":40042},[642],[363,134387],{},[363,134389],{"className":134390,"style":754},[505],[363,134392,134394,134397],{"className":134393},[407],[363,134395,1121],{"className":134396},[407,408],[363,134398,134400],{"className":134399},[629],[363,134401,134403,134423],{"className":134402},[633,634],[363,134404,134406,134420],{"className":134405},[638],[363,134407,134409],{"className":134408,"style":12529},[642],[363,134410,134411,134414],{"style":730},[363,134412],{"className":134413,"style":651},[650],[363,134415,134417],{"className":134416},[655,656,657,658],[363,134418,12310],{"className":134419},[407,408,658],[363,134421,666],{"className":134422},[665],[363,134424,134426],{"className":134425},[638],[363,134427,134429],{"className":134428,"style":8315},[642],[363,134430],{},[363,134432],{"className":134433,"style":506},[505],[363,134435,471],{"className":134436},[510],[363,134438],{"className":134439,"style":506},[505],[363,134441,465],{"className":134442},[407],[363,134444,134446],{"className":134445,"style":763},[501,762],[363,134447,3255],{"className":134448},[767,4067],"\n其内部记作 ",[363,134451,134453,134524],{"className":134452,"translate":367},[366],[363,134454,134456],{"className":134455},[371],[373,134457,134458],{"xmlns":375},[377,134459,134460,134521],{},[380,134461,134462,134465,134467,134479,134481,134483,134485,134487,134499,134501,134507,134509,134511,134513,134515,134517,134519],{},[383,134463,134464],{"mathvariant":557},"int",[458,134466,4450],{},[7161,134468,134469,134471],{},[383,134470,126023],{"mathvariant":557},[380,134472,134473,134475,134477],{},[383,134474,11041],{},[458,134476,5160],{},[463,134478,465],{},[458,134480,471],{},[458,134482,3245],{"stretchy":460},[383,134484,1121],{"mathvariant":75560},[458,134486,6256],{},[7161,134488,134489,134491],{},[383,134490,126023],{"mathvariant":557},[380,134492,134493,134495,134497],{},[383,134494,11041],{},[458,134496,5160],{},[463,134498,465],{},[458,134500,1362],{},[543,134502,134503,134505],{},[383,134504,1121],{},[383,134506,12310],{},[458,134508,3250],{},[463,134510,474],{},[458,134512,898],{"separator":394},[1644,134514,4630],{},[383,134516,61947],{"mathvariant":557},[383,134518,12310],{},[458,134520,3255],{"stretchy":460},[387,134522,134523],{"encoding":389},"\\operatorname{int}\\Delta^{K-1} = \\{\\mathbf{x} \\in \\Delta^{K-1} : x_i > 0,\\ \\forall i\\}",[363,134525,134527,134589,134610,134663,134719],{"className":134526,"ariaHidden":394},[393],[363,134528,134530,134533,134539,134542,134580,134583,134586],{"className":134529},[398],[363,134531],{"className":134532,"style":52432},[402],[363,134534,134536],{"className":134535},[1831],[363,134537,134464],{"className":134538},[407,33009],[363,134540],{"className":134541,"style":754},[505],[363,134543,134545,134548],{"className":134544},[407],[363,134546,126023],{"className":134547},[407],[363,134549,134551],{"className":134550},[629],[363,134552,134554],{"className":134553},[633],[363,134555,134557],{"className":134556},[638],[363,134558,134560],{"className":134559,"style":52432},[642],[363,134561,134562,134565],{"style":7212},[363,134563],{"className":134564,"style":651},[650],[363,134566,134568],{"className":134567},[655,656,657,658],[363,134569,134571,134574,134577],{"className":134570},[407,658],[363,134572,11041],{"className":134573,"style":11129},[407,408,658],[363,134575,5160],{"className":134576},[2938,658],[363,134578,465],{"className":134579},[407,658],[363,134581],{"className":134582,"style":506},[505],[363,134584,471],{"className":134585},[510],[363,134587],{"className":134588,"style":506},[505],[363,134590,134592,134595,134598,134601,134604,134607],{"className":134591},[398],[363,134593],{"className":134594,"style":487},[402],[363,134596,3245],{"className":134597},[494],[363,134599,1121],{"className":134600},[407,75905],[363,134602],{"className":134603,"style":506},[505],[363,134605,6256],{"className":134606},[510],[363,134608],{"className":134609,"style":506},[505],[363,134611,134613,134616,134654,134657,134660],{"className":134612},[398],[363,134614],{"className":134615,"style":52432},[402],[363,134617,134619,134622],{"className":134618},[407],[363,134620,126023],{"className":134621},[407],[363,134623,134625],{"className":134624},[629],[363,134626,134628],{"className":134627},[633],[363,134629,134631],{"className":134630},[638],[363,134632,134634],{"className":134633,"style":52432},[642],[363,134635,134636,134639],{"style":7212},[363,134637],{"className":134638,"style":651},[650],[363,134640,134642],{"className":134641},[655,656,657,658],[363,134643,134645,134648,134651],{"className":134644},[407,658],[363,134646,11041],{"className":134647,"style":11129},[407,408,658],[363,134649,5160],{"className":134650},[2938,658],[363,134652,465],{"className":134653},[407,658],[363,134655],{"className":134656,"style":506},[505],[363,134658,1362],{"className":134659},[510],[363,134661],{"className":134662,"style":506},[505],[363,134664,134666,134670,134710,134713,134716],{"className":134665},[398],[363,134667],{"className":134668,"style":134669},[402],"height:0.6891em;vertical-align:-0.15em;",[363,134671,134673,134676],{"className":134672},[407],[363,134674,1121],{"className":134675},[407,408],[363,134677,134679],{"className":134678},[629],[363,134680,134682,134702],{"className":134681},[633,634],[363,134683,134685,134699],{"className":134684},[638],[363,134686,134688],{"className":134687,"style":12529},[642],[363,134689,134690,134693],{"style":730},[363,134691],{"className":134692,"style":651},[650],[363,134694,134696],{"className":134695},[655,656,657,658],[363,134697,12310],{"className":134698},[407,408,658],[363,134700,666],{"className":134701},[665],[363,134703,134705],{"className":134704},[638],[363,134706,134708],{"className":134707,"style":8315},[642],[363,134709],{},[363,134711],{"className":134712,"style":506},[505],[363,134714,3250],{"className":134715},[510],[363,134717],{"className":134718,"style":506},[505],[363,134720,134722,134725,134728,134731,134734,134737,134740,134743],{"className":134721},[398],[363,134723],{"className":134724,"style":487},[402],[363,134726,474],{"className":134727},[407],[363,134729,898],{"className":134730},[920],[363,134732,4630],{"className":134733},[505],[363,134735],{"className":134736,"style":754},[505],[363,134738,61947],{"className":134739},[407],[363,134741,12310],{"className":134742},[407,408],[363,134744,3255],{"className":134745},[501],[11,134747,134748,2627,134822,134880,134881,135021,135022,135073,135074,135125,135126,135177,135178,135206],{},[363,134749,134751,134775],{"className":134750,"translate":367},[366],[363,134752,134754],{"className":134753},[371],[373,134755,134756],{"xmlns":375},[377,134757,134758,134772],{},[380,134759,134760],{},[7161,134761,134762,134764],{},[383,134763,126023],{"mathvariant":557},[380,134765,134766,134768,134770],{},[383,134767,11041],{},[458,134769,5160],{},[463,134771,465],{},[387,134773,134774],{"encoding":389},"\\Delta^{K-1}",[363,134776,134778],{"className":134777,"ariaHidden":394},[393],[363,134779,134781,134784],{"className":134780},[398],[363,134782],{"className":134783,"style":52432},[402],[363,134785,134787,134790],{"className":134786},[407],[363,134788,126023],{"className":134789},[407],[363,134791,134793],{"className":134792},[629],[363,134794,134796],{"className":134795},[633],[363,134797,134799],{"className":134798},[638],[363,134800,134802],{"className":134801,"style":52432},[642],[363,134803,134804,134807],{"style":7212},[363,134805],{"className":134806,"style":651},[650],[363,134808,134810],{"className":134809},[655,656,657,658],[363,134811,134813,134816,134819],{"className":134812},[407,658],[363,134814,11041],{"className":134815,"style":11129},[407,408,658],[363,134817,5160],{"className":134818},[2938,658],[363,134820,465],{"className":134821},[407,658],[363,134823,134825,134842],{"className":134824,"translate":367},[366],[363,134826,134828],{"className":134827},[371],[373,134829,134830],{"xmlns":375},[377,134831,134832,134840],{},[380,134833,134834],{},[7161,134835,134836,134838],{},[383,134837,1379],{"mathvariant":570},[383,134839,11041],{},[387,134841,133626],{"encoding":389},[363,134843,134845],{"className":134844,"ariaHidden":394},[393],[363,134846,134848,134851],{"className":134847},[398],[363,134849],{"className":134850,"style":52432},[402],[363,134852,134854,134857],{"className":134853},[407],[363,134855,1379],{"className":134856},[407,714],[363,134858,134860],{"className":134859},[629],[363,134861,134863],{"className":134862},[633],[363,134864,134866],{"className":134865},[638],[363,134867,134869],{"className":134868,"style":52432},[642],[363,134870,134871,134874],{"style":7212},[363,134872],{"className":134873,"style":651},[650],[363,134875,134877],{"className":134876},[655,656,657,658],[363,134878,11041],{"className":134879,"style":11129},[407,408,658]," 中的紧凸集，其顶点为坐标向量 ",[363,134882,134884,134914],{"className":134883,"translate":367},[366],[363,134885,134887],{"className":134886},[371],[373,134888,134889],{"xmlns":375},[377,134890,134891,134911],{},[380,134892,134893,134899,134901,134903,134905],{},[543,134894,134895,134897],{},[383,134896,7914],{"mathvariant":75560},[463,134898,465],{},[458,134900,898],{"separator":394},[458,134902,133107],{},[458,134904,898],{"separator":394},[543,134906,134907,134909],{},[383,134908,7914],{"mathvariant":75560},[383,134910,11041],{},[387,134912,134913],{"encoding":389},"\\mathbf{e}_1, \\dots, \\mathbf{e}_K",[363,134915,134917],{"className":134916,"ariaHidden":394},[393],[363,134918,134920,134923,134963,134966,134969,134972,134975,134978,134981],{"className":134919},[398],[363,134921],{"className":134922,"style":133764},[402],[363,134924,134926,134929],{"className":134925},[407],[363,134927,7914],{"className":134928},[407,75905],[363,134930,134932],{"className":134931},[629],[363,134933,134935,134955],{"className":134934},[633,634],[363,134936,134938,134952],{"className":134937},[638],[363,134939,134941],{"className":134940,"style":11480},[642],[363,134942,134943,134946],{"style":730},[363,134944],{"className":134945,"style":651},[650],[363,134947,134949],{"className":134948},[655,656,657,658],[363,134950,465],{"className":134951},[407,658],[363,134953,666],{"className":134954},[665],[363,134956,134958],{"className":134957},[638],[363,134959,134961],{"className":134960,"style":8315},[642],[363,134962],{},[363,134964,898],{"className":134965},[920],[363,134967],{"className":134968,"style":754},[505],[363,134970,133107],{"className":134971},[758],[363,134973],{"className":134974,"style":754},[505],[363,134976,898],{"className":134977},[920],[363,134979],{"className":134980,"style":754},[505],[363,134982,134984,134987],{"className":134983},[407],[363,134985,7914],{"className":134986},[407,75905],[363,134988,134990],{"className":134989},[629],[363,134991,134993,135013],{"className":134992},[633,634],[363,134994,134996,135010],{"className":134995},[638],[363,134997,134999],{"className":134998,"style":727},[642],[363,135000,135001,135004],{"style":730},[363,135002],{"className":135003,"style":651},[650],[363,135005,135007],{"className":135006},[655,656,657,658],[363,135008,11041],{"className":135009,"style":11129},[407,408,658],[363,135011,666],{"className":135012},[665],[363,135014,135016],{"className":135015},[638],[363,135017,135019],{"className":135018,"style":8315},[642],[363,135020],{},"。低维特例给出了全部几何直观：",[363,135023,135025,135043],{"className":135024,"translate":367},[366],[363,135026,135028],{"className":135027},[371],[373,135029,135030],{"xmlns":375},[377,135031,135032,135040],{},[380,135033,135034,135036,135038],{},[383,135035,11041],{},[458,135037,471],{},[463,135039,2810],{},[387,135041,135042],{"encoding":389},"K = 2",[363,135044,135046,135064],{"className":135045,"ariaHidden":394},[393],[363,135047,135049,135052,135055,135058,135061],{"className":135048},[398],[363,135050],{"className":135051,"style":1011},[402],[363,135053,11041],{"className":135054,"style":11129},[407,408],[363,135056],{"className":135057,"style":506},[505],[363,135059,471],{"className":135060},[510],[363,135062],{"className":135063,"style":506},[505],[363,135065,135067,135070],{"className":135066},[398],[363,135068],{"className":135069,"style":520},[402],[363,135071,2810],{"className":135072},[407]," 时它是一维线段，",[363,135075,135077,135095],{"className":135076,"translate":367},[366],[363,135078,135080],{"className":135079},[371],[373,135081,135082],{"xmlns":375},[377,135083,135084,135092],{},[380,135085,135086,135088,135090],{},[383,135087,11041],{},[458,135089,471],{},[463,135091,41082],{},[387,135093,135094],{"encoding":389},"K = 3",[363,135096,135098,135116],{"className":135097,"ariaHidden":394},[393],[363,135099,135101,135104,135107,135110,135113],{"className":135100},[398],[363,135102],{"className":135103,"style":1011},[402],[363,135105,11041],{"className":135106,"style":11129},[407,408],[363,135108],{"className":135109,"style":506},[505],[363,135111,471],{"className":135112},[510],[363,135114],{"className":135115,"style":506},[505],[363,135117,135119,135122],{"className":135118},[398],[363,135120],{"className":135121,"style":520},[402],[363,135123,41082],{"className":135124},[407]," 时是二维三角形，",[363,135127,135129,135147],{"className":135128,"translate":367},[366],[363,135130,135132],{"className":135131},[371],[373,135133,135134],{"xmlns":375},[377,135135,135136,135144],{},[380,135137,135138,135140,135142],{},[383,135139,11041],{},[458,135141,471],{},[463,135143,39336],{},[387,135145,135146],{"encoding":389},"K = 4",[363,135148,135150,135168],{"className":135149,"ariaHidden":394},[393],[363,135151,135153,135156,135159,135162,135165],{"className":135152},[398],[363,135154],{"className":135155,"style":1011},[402],[363,135157,11041],{"className":135158,"style":11129},[407,408],[363,135160],{"className":135161,"style":506},[505],[363,135163,471],{"className":135164},[510],[363,135166],{"className":135167,"style":506},[505],[363,135169,135171,135174],{"className":135170},[398],[363,135172],{"className":135173,"style":520},[402],[363,135175,39336],{"className":135176},[407]," 时是三维四面体。它与 ",[363,135179,135181,135194],{"className":135180,"translate":367},[366],[363,135182,135184],{"className":135183},[371],[373,135185,135186],{"xmlns":375},[377,135187,135188,135192],{},[380,135189,135190],{},[383,135191,11041],{},[387,135193,11041],{"encoding":389},[363,135195,135197],{"className":135196,"ariaHidden":394},[393],[363,135198,135200,135203],{"className":135199},[398],[363,135201],{"className":135202,"style":1011},[402],[363,135204,11041],{"className":135205,"style":11129},[407,408]," 个取值上的离散概率分布全体一一对应，因此「分类器的输出」与「单纯形上的点」是同一件事的两种说法。",[11,135208,135209,135210,135367,135368,135590,135591,135621,135622,135682,135683,135836,135837,135910,135911,135983],{},"本文采用如下测度约定：以 ",[363,135211,135213,135249],{"className":135212,"translate":367},[366],[363,135214,135216],{"className":135215},[371],[373,135217,135218],{"xmlns":375},[377,135219,135220,135246],{},[380,135221,135222,135228,135230,135232,135234],{},[543,135223,135224,135226],{},[383,135225,1121],{},[463,135227,465],{},[458,135229,898],{"separator":394},[458,135231,133107],{},[458,135233,898],{"separator":394},[543,135235,135236,135238],{},[383,135237,1121],{},[380,135239,135240,135242,135244],{},[383,135241,11041],{},[458,135243,5160],{},[463,135245,465],{},[387,135247,135248],{"encoding":389},"x_1, \\dots, x_{K-1}",[363,135250,135252],{"className":135251,"ariaHidden":394},[393],[363,135253,135255,135259,135299,135302,135305,135308,135311,135314,135317],{"className":135254},[398],[363,135256],{"className":135257,"style":135258},[402],"height:0.6389em;vertical-align:-0.2083em;",[363,135260,135262,135265],{"className":135261},[407],[363,135263,1121],{"className":135264},[407,408],[363,135266,135268],{"className":135267},[629],[363,135269,135271,135291],{"className":135270},[633,634],[363,135272,135274,135288],{"className":135273},[638],[363,135275,135277],{"className":135276,"style":11480},[642],[363,135278,135279,135282],{"style":730},[363,135280],{"className":135281,"style":651},[650],[363,135283,135285],{"className":135284},[655,656,657,658],[363,135286,465],{"className":135287},[407,658],[363,135289,666],{"className":135290},[665],[363,135292,135294],{"className":135293},[638],[363,135295,135297],{"className":135296,"style":8315},[642],[363,135298],{},[363,135300,898],{"className":135301},[920],[363,135303],{"className":135304,"style":754},[505],[363,135306,133107],{"className":135307},[758],[363,135309],{"className":135310,"style":754},[505],[363,135312,898],{"className":135313},[920],[363,135315],{"className":135316,"style":754},[505],[363,135318,135320,135323],{"className":135319},[407],[363,135321,1121],{"className":135322},[407,408],[363,135324,135326],{"className":135325},[629],[363,135327,135329,135358],{"className":135328},[633,634],[363,135330,135332,135355],{"className":135331},[638],[363,135333,135335],{"className":135334,"style":727},[642],[363,135336,135337,135340],{"style":730},[363,135338],{"className":135339,"style":651},[650],[363,135341,135343],{"className":135342},[655,656,657,658],[363,135344,135346,135349,135352],{"className":135345},[407,658],[363,135347,11041],{"className":135348,"style":11129},[407,408,658],[363,135350,5160],{"className":135351},[2938,658],[363,135353,465],{"className":135354},[407,658],[363,135356,666],{"className":135357},[665],[363,135359,135361],{"className":135360},[638],[363,135362,135365],{"className":135363,"style":135364},[642],"height:0.2083em;",[363,135366],{}," 为自由坐标、",[363,135369,135371,135413],{"className":135370,"translate":367},[366],[363,135372,135374],{"className":135373},[371],[373,135375,135376],{"xmlns":375},[377,135377,135378,135410],{},[380,135379,135380,135386,135388,135390,135392,135404],{},[543,135381,135382,135384],{},[383,135383,1121],{},[383,135385,11041],{},[458,135387,471],{},[463,135389,465],{},[458,135391,5160],{},[543,135393,135394,135396],{},[458,135395,13808],{},[380,135397,135398,135400,135402],{},[383,135399,12310],{},[458,135401,7598],{},[383,135403,11041],{},[543,135405,135406,135408],{},[383,135407,1121],{},[383,135409,12310],{},[387,135411,135412],{"encoding":389},"x_K = 1 - \\sum_{i\u003CK} x_i",[363,135414,135416,135471,135489],{"className":135415,"ariaHidden":394},[393],[363,135417,135419,135422,135462,135465,135468],{"className":135418},[398],[363,135420],{"className":135421,"style":13721},[402],[363,135423,135425,135428],{"className":135424},[407],[363,135426,1121],{"className":135427},[407,408],[363,135429,135431],{"className":135430},[629],[363,135432,135434,135454],{"className":135433},[633,634],[363,135435,135437,135451],{"className":135436},[638],[363,135438,135440],{"className":135439,"style":727},[642],[363,135441,135442,135445],{"style":730},[363,135443],{"className":135444,"style":651},[650],[363,135446,135448],{"className":135447},[655,656,657,658],[363,135449,11041],{"className":135450,"style":11129},[407,408,658],[363,135452,666],{"className":135453},[665],[363,135455,135457],{"className":135456},[638],[363,135458,135460],{"className":135459,"style":8315},[642],[363,135461],{},[363,135463],{"className":135464,"style":506},[505],[363,135466,471],{"className":135467},[510],[363,135469],{"className":135470,"style":506},[505],[363,135472,135474,135477,135480,135483,135486],{"className":135473},[398],[363,135475],{"className":135476,"style":12925},[402],[363,135478,465],{"className":135479},[407],[363,135481],{"className":135482,"style":2934},[505],[363,135484,5160],{"className":135485},[2938],[363,135487],{"className":135488,"style":2934},[505],[363,135490,135492,135496,135547,135550],{"className":135491},[398],[363,135493],{"className":135494,"style":135495},[402],"height:1.0771em;vertical-align:-0.3271em;",[363,135497,135499,135502],{"className":135498},[1831],[363,135500,13808],{"className":135501,"style":40007},[1831,1832,5963],[363,135503,135505],{"className":135504},[629],[363,135506,135508,135538],{"className":135507},[633,634],[363,135509,135511,135535],{"className":135510},[638],[363,135512,135515],{"className":135513,"style":135514},[642],"height:0.1786em;",[363,135516,135517,135520],{"style":40023},[363,135518],{"className":135519,"style":651},[650],[363,135521,135523],{"className":135522},[655,656,657,658],[363,135524,135526,135529,135532],{"className":135525},[407,658],[363,135527,12310],{"className":135528},[407,408,658],[363,135530,7598],{"className":135531},[510,658],[363,135533,11041],{"className":135534,"style":11129},[407,408,658],[363,135536,666],{"className":135537},[665],[363,135539,135541],{"className":135540},[638],[363,135542,135545],{"className":135543,"style":135544},[642],"height:0.3271em;",[363,135546],{},[363,135548],{"className":135549,"style":754},[505],[363,135551,135553,135556],{"className":135552},[407],[363,135554,1121],{"className":135555},[407,408],[363,135557,135559],{"className":135558},[629],[363,135560,135562,135582],{"className":135561},[633,634],[363,135563,135565,135579],{"className":135564},[638],[363,135566,135568],{"className":135567,"style":12529},[642],[363,135569,135570,135573],{"style":730},[363,135571],{"className":135572,"style":651},[650],[363,135574,135576],{"className":135575},[655,656,657,658],[363,135577,12310],{"className":135578},[407,408,658],[363,135580,666],{"className":135581},[665],[363,135583,135585],{"className":135584},[638],[363,135586,135588],{"className":135587,"style":8315},[642],[363,135589],{},"，并以 ",[363,135592,135594,135608],{"className":135593,"translate":367},[366],[363,135595,135597],{"className":135596},[371],[373,135598,135599],{"xmlns":375},[377,135600,135601,135605],{},[380,135602,135603],{},[383,135604,1121],{"mathvariant":75560},[387,135606,135607],{"encoding":389},"\\mathbf{x}",[363,135609,135611],{"className":135610,"ariaHidden":394},[393],[363,135612,135614,135618],{"className":135613},[398],[363,135615],{"className":135616,"style":135617},[402],"height:0.4444em;",[363,135619,1121],{"className":135620},[407,75905]," 上的 ",[363,135623,135625,135646],{"className":135624,"translate":367},[366],[363,135626,135628],{"className":135627},[371],[373,135629,135630],{"xmlns":375},[377,135631,135632,135644],{},[380,135633,135634,135636,135638,135640,135642],{},[458,135635,461],{"stretchy":460},[383,135637,11041],{},[458,135639,5160],{},[463,135641,465],{},[458,135643,468],{"stretchy":460},[387,135645,133690],{"encoding":389},[363,135647,135649,135670],{"className":135648,"ariaHidden":394},[393],[363,135650,135652,135655,135658,135661,135664,135667],{"className":135651},[398],[363,135653],{"className":135654,"style":487},[402],[363,135656,461],{"className":135657},[494],[363,135659,11041],{"className":135660,"style":11129},[407,408],[363,135662],{"className":135663,"style":2934},[505],[363,135665,5160],{"className":135666},[2938],[363,135668],{"className":135669,"style":2934},[505],[363,135671,135673,135676,135679],{"className":135672},[398],[363,135674],{"className":135675,"style":487},[402],[363,135677,465],{"className":135678},[407],[363,135680,468],{"className":135681},[501]," 维 Lebesgue 测度 ",[363,135684,135686,135722],{"className":135685,"translate":367},[366],[363,135687,135689],{"className":135688},[371],[373,135690,135691],{"xmlns":375},[377,135692,135693,135719],{},[380,135694,135695,135697,135703,135705,135707],{},[383,135696,592],{"mathvariant":557},[543,135698,135699,135701],{},[383,135700,1121],{},[463,135702,465],{},[458,135704,87471],{},[383,135706,592],{"mathvariant":557},[543,135708,135709,135711],{},[383,135710,1121],{},[380,135712,135713,135715,135717],{},[383,135714,11041],{},[458,135716,5160],{},[463,135718,465],{},[387,135720,135721],{"encoding":389},"\\mathrm{d}x_1 \\cdots \\mathrm{d}x_{K-1}",[363,135723,135725],{"className":135724,"ariaHidden":394},[393],[363,135726,135728,135732,135735,135775,135778,135781,135784,135787],{"className":135727},[398],[363,135729],{"className":135730,"style":135731},[402],"height:0.9028em;vertical-align:-0.2083em;",[363,135733,592],{"className":135734},[407,33009],[363,135736,135738,135741],{"className":135737},[407],[363,135739,1121],{"className":135740},[407,408],[363,135742,135744],{"className":135743},[629],[363,135745,135747,135767],{"className":135746},[633,634],[363,135748,135750,135764],{"className":135749},[638],[363,135751,135753],{"className":135752,"style":11480},[642],[363,135754,135755,135758],{"style":730},[363,135756],{"className":135757,"style":651},[650],[363,135759,135761],{"className":135760},[655,656,657,658],[363,135762,465],{"className":135763},[407,658],[363,135765,666],{"className":135766},[665],[363,135768,135770],{"className":135769},[638],[363,135771,135773],{"className":135772,"style":8315},[642],[363,135774],{},[363,135776],{"className":135777,"style":754},[505],[363,135779,87471],{"className":135780},[758],[363,135782],{"className":135783,"style":754},[505],[363,135785,592],{"className":135786},[407,33009],[363,135788,135790,135793],{"className":135789},[407],[363,135791,1121],{"className":135792},[407,408],[363,135794,135796],{"className":135795},[629],[363,135797,135799,135828],{"className":135798},[633,634],[363,135800,135802,135825],{"className":135801},[638],[363,135803,135805],{"className":135804,"style":727},[642],[363,135806,135807,135810],{"style":730},[363,135808],{"className":135809,"style":651},[650],[363,135811,135813],{"className":135812},[655,656,657,658],[363,135814,135816,135819,135822],{"className":135815},[407,658],[363,135817,11041],{"className":135818,"style":11129},[407,408,658],[363,135820,5160],{"className":135821},[2938,658],[363,135823,465],{"className":135824},[407,658],[363,135826,666],{"className":135827},[665],[363,135829,135831],{"className":135830},[638],[363,135832,135834],{"className":135833,"style":135364},[642],[363,135835],{}," 为参考测度。在该约定下 ",[363,135838,135840,135863],{"className":135839,"translate":367},[366],[363,135841,135843],{"className":135842},[371],[373,135844,135845],{"xmlns":375},[377,135846,135847,135861],{},[380,135848,135849],{},[7161,135850,135851,135853],{},[383,135852,126023],{"mathvariant":557},[380,135854,135855,135857,135859],{},[383,135856,11041],{},[458,135858,5160],{},[463,135860,465],{},[387,135862,134774],{"encoding":389},[363,135864,135866],{"className":135865,"ariaHidden":394},[393],[363,135867,135869,135872],{"className":135868},[398],[363,135870],{"className":135871,"style":52432},[402],[363,135873,135875,135878],{"className":135874},[407],[363,135876,126023],{"className":135877},[407],[363,135879,135881],{"className":135880},[629],[363,135882,135884],{"className":135883},[633],[363,135885,135887],{"className":135886},[638],[363,135888,135890],{"className":135889,"style":52432},[642],[363,135891,135892,135895],{"style":7212},[363,135893],{"className":135894,"style":651},[650],[363,135896,135898],{"className":135897},[655,656,657,658],[363,135899,135901,135904,135907],{"className":135900},[407,658],[363,135902,11041],{"className":135903,"style":11129},[407,408,658],[363,135905,5160],{"className":135906},[2938,658],[363,135908,465],{"className":135909},[407,658]," 的体积为 ",[363,135912,135914,135943],{"className":135913,"translate":367},[366],[363,135915,135917],{"className":135916},[371],[373,135918,135919],{"xmlns":375},[377,135920,135921,135940],{},[380,135922,135923,135925,135927,135929,135931,135933,135935,135937],{},[463,135924,465],{},[383,135926,1288],{"mathvariant":557},[458,135928,461],{"stretchy":460},[383,135930,11041],{},[458,135932,5160],{},[463,135934,465],{},[458,135936,468],{"stretchy":460},[458,135938,135939],{"stretchy":460},"!",[387,135941,135942],{"encoding":389},"1\u002F(K-1)!",[363,135944,135946,135970],{"className":135945,"ariaHidden":394},[393],[363,135947,135949,135952,135955,135958,135961,135964,135967],{"className":135948},[398],[363,135950],{"className":135951,"style":487},[402],[363,135953,8936],{"className":135954},[407],[363,135956,461],{"className":135957},[494],[363,135959,11041],{"className":135960,"style":11129},[407,408],[363,135962],{"className":135963,"style":2934},[505],[363,135965,5160],{"className":135966},[2938],[363,135968],{"className":135969,"style":2934},[505],[363,135971,135973,135976,135979],{"className":135972},[398],[363,135974],{"className":135975,"style":487},[402],[363,135977,465],{"className":135978},[407],[363,135980,135982],{"className":135981},[501],")!","，这一点在后文讨论熵时会重新出现。",[2658,135985,135987],{"id":135986},"_12-形式化定义","1.2 形式化定义",[1340,135989,135991],{"title":135990},"定义 1.2（Dirichlet 分布）",[11,135992,135993,135994,11748,136264,136475,136476,136504,136505,136592,136593,136981,136982,137010,137011,137046,137047,137125,137126,137129],{},"设参数向量 ",[363,135995,135997,136050],{"className":135996,"translate":367},[366],[363,135998,136000],{"className":135999},[371],[373,136001,136002],{"xmlns":375},[377,136003,136004,136047],{},[380,136005,136006,136009,136011,136013,136019,136021,136023,136025,136031,136033,136035],{},[383,136007,45101],{"mathvariant":136008},"bold-italic",[458,136010,471],{},[458,136012,461],{"stretchy":460},[543,136014,136015,136017],{},[383,136016,45101],{},[463,136018,465],{},[458,136020,898],{"separator":394},[458,136022,133107],{},[458,136024,898],{"separator":394},[543,136026,136027,136029],{},[383,136028,45101],{},[383,136030,11041],{},[458,136032,468],{"stretchy":460},[458,136034,6256],{},[7900,136036,136037,136039,136045],{},[383,136038,1379],{"mathvariant":570},[380,136040,136041,136043],{},[458,136042,3250],{},[463,136044,474],{},[383,136046,11041],{},[387,136048,136049],{"encoding":389},"\\boldsymbol{\\alpha} = (\\alpha_1, \\dots, \\alpha_K) \\in \\mathbb{R}_{>0}^K",[363,136051,136053,136078,136198],{"className":136052,"ariaHidden":394},[393],[363,136054,136056,136059,136069,136072,136075],{"className":136055},[398],[363,136057],{"className":136058,"style":135617},[402],[363,136060,136062],{"className":136061},[407],[363,136063,136065],{"className":136064},[407],[363,136066,45101],{"className":136067},[407,136068],"boldsymbol",[363,136070],{"className":136071,"style":506},[505],[363,136073,471],{"className":136074},[510],[363,136076],{"className":136077,"style":506},[505],[363,136079,136081,136084,136087,136128,136131,136134,136137,136140,136143,136146,136186,136189,136192,136195],{"className":136080},[398],[363,136082],{"className":136083,"style":487},[402],[363,136085,461],{"className":136086},[494],[363,136088,136090,136093],{"className":136089},[407],[363,136091,45101],{"className":136092,"style":45131},[407,408],[363,136094,136096],{"className":136095},[629],[363,136097,136099,136120],{"className":136098},[633,634],[363,136100,136102,136117],{"className":136101},[638],[363,136103,136105],{"className":136104,"style":11480},[642],[363,136106,136108,136111],{"style":136107},"top:-2.55em;margin-left:-0.0037em;margin-right:0.05em;",[363,136109],{"className":136110,"style":651},[650],[363,136112,136114],{"className":136113},[655,656,657,658],[363,136115,465],{"className":136116},[407,658],[363,136118,666],{"className":136119},[665],[363,136121,136123],{"className":136122},[638],[363,136124,136126],{"className":136125,"style":8315},[642],[363,136127],{},[363,136129,898],{"className":136130},[920],[363,136132],{"className":136133,"style":754},[505],[363,136135,133107],{"className":136136},[758],[363,136138],{"className":136139,"style":754},[505],[363,136141,898],{"className":136142},[920],[363,136144],{"className":136145,"style":754},[505],[363,136147,136149,136152],{"className":136148},[407],[363,136150,45101],{"className":136151,"style":45131},[407,408],[363,136153,136155],{"className":136154},[629],[363,136156,136158,136178],{"className":136157},[633,634],[363,136159,136161,136175],{"className":136160},[638],[363,136162,136164],{"className":136163,"style":727},[642],[363,136165,136166,136169],{"style":136107},[363,136167],{"className":136168,"style":651},[650],[363,136170,136172],{"className":136171},[655,656,657,658],[363,136173,11041],{"className":136174,"style":11129},[407,408,658],[363,136176,666],{"className":136177},[665],[363,136179,136181],{"className":136180},[638],[363,136182,136184],{"className":136183,"style":8315},[642],[363,136185],{},[363,136187,468],{"className":136188},[501],[363,136190],{"className":136191,"style":506},[505],[363,136193,6256],{"className":136194},[510],[363,136196],{"className":136197,"style":506},[505],[363,136199,136201,136205],{"className":136200},[398],[363,136202],{"className":136203,"style":136204},[402],"height:1.1168em;vertical-align:-0.2755em;",[363,136206,136208,136211],{"className":136207},[407],[363,136209,1379],{"className":136210},[407,714],[363,136212,136214],{"className":136213},[629],[363,136215,136217,136255],{"className":136216},[633,634],[363,136218,136220,136252],{"className":136219},[638],[363,136221,136223,136241],{"className":136222,"style":52432},[642],[363,136224,136226,136229],{"style":136225},"top:-2.4519em;margin-left:0em;margin-right:0.05em;",[363,136227],{"className":136228,"style":651},[650],[363,136230,136232],{"className":136231},[655,656,657,658],[363,136233,136235,136238],{"className":136234},[407,658],[363,136236,3250],{"className":136237},[510,658],[363,136239,474],{"className":136240},[407,658],[363,136242,136243,136246],{"style":7212},[363,136244],{"className":136245,"style":651},[650],[363,136247,136249],{"className":136248},[655,656,657,658],[363,136250,11041],{"className":136251,"style":11129},[407,408,658],[363,136253,666],{"className":136254},[665],[363,136256,136258],{"className":136257},[638],[363,136259,136262],{"className":136260,"style":136261},[642],"height:0.2755em;",[363,136263],{},[363,136265,136267,136307],{"className":136266,"translate":367},[366],[363,136268,136270],{"className":136269},[371],[373,136271,136272],{"xmlns":375},[377,136273,136274,136304],{},[380,136275,136276,136282,136284,136298],{},[543,136277,136278,136280],{},[383,136279,45101],{},[463,136281,474],{},[458,136283,471],{},[7900,136285,136286,136288,136296],{},[458,136287,13808],{},[380,136289,136290,136292,136294],{},[383,136291,12310],{},[458,136293,471],{},[463,136295,465],{},[383,136297,11041],{},[543,136299,136300,136302],{},[383,136301,45101],{},[383,136303,12310],{},[387,136305,136306],{"encoding":389},"\\alpha_0 = \\sum_{i=1}^K \\alpha_i",[363,136308,136310,136365],{"className":136309,"ariaHidden":394},[393],[363,136311,136313,136316,136356,136359,136362],{"className":136312},[398],[363,136314],{"className":136315,"style":13721},[402],[363,136317,136319,136322],{"className":136318},[407],[363,136320,45101],{"className":136321,"style":45131},[407,408],[363,136323,136325],{"className":136324},[629],[363,136326,136328,136348],{"className":136327},[633,634],[363,136329,136331,136345],{"className":136330},[638],[363,136332,136334],{"className":136333,"style":11480},[642],[363,136335,136336,136339],{"style":136107},[363,136337],{"className":136338,"style":651},[650],[363,136340,136342],{"className":136341},[655,656,657,658],[363,136343,474],{"className":136344},[407,658],[363,136346,666],{"className":136347},[665],[363,136349,136351],{"className":136350},[638],[363,136352,136354],{"className":136353,"style":8315},[642],[363,136355],{},[363,136357],{"className":136358,"style":506},[505],[363,136360,471],{"className":136361},[510],[363,136363],{"className":136364,"style":506},[505],[363,136366,136368,136372,136432,136435],{"className":136367},[398],[363,136369],{"className":136370,"style":136371},[402],"height:1.2809em;vertical-align:-0.2997em;",[363,136373,136375,136378],{"className":136374},[1831],[363,136376,13808],{"className":136377,"style":40007},[1831,1832,5963],[363,136379,136381],{"className":136380},[629],[363,136382,136384,136424],{"className":136383},[633,634],[363,136385,136387,136421],{"className":136386},[638],[363,136388,136390,136410],{"className":136389,"style":133494},[642],[363,136391,136392,136395],{"style":40023},[363,136393],{"className":136394,"style":651},[650],[363,136396,136398],{"className":136397},[655,656,657,658],[363,136399,136401,136404,136407],{"className":136400},[407,658],[363,136402,12310],{"className":136403},[407,408,658],[363,136405,471],{"className":136406},[510,658],[363,136408,465],{"className":136409},[407,658],[363,136411,136412,136415],{"style":133517},[363,136413],{"className":136414,"style":651},[650],[363,136416,136418],{"className":136417},[655,656,657,658],[363,136419,11041],{"className":136420,"style":11129},[407,408,658],[363,136422,666],{"className":136423},[665],[363,136425,136427],{"className":136426},[638],[363,136428,136430],{"className":136429,"style":40042},[642],[363,136431],{},[363,136433],{"className":136434,"style":754},[505],[363,136436,136438,136441],{"className":136437},[407],[363,136439,45101],{"className":136440,"style":45131},[407,408],[363,136442,136444],{"className":136443},[629],[363,136445,136447,136467],{"className":136446},[633,634],[363,136448,136450,136464],{"className":136449},[638],[363,136451,136453],{"className":136452,"style":12529},[642],[363,136454,136455,136458],{"style":136107},[363,136456],{"className":136457,"style":651},[650],[363,136459,136461],{"className":136460},[655,656,657,658],[363,136462,12310],{"className":136463},[407,408,658],[363,136465,666],{"className":136466},[665],[363,136468,136470],{"className":136469},[638],[363,136471,136473],{"className":136472,"style":8315},[642],[363,136474],{},"。若随机向量 ",[363,136477,136479,136492],{"className":136478,"translate":367},[366],[363,136480,136482],{"className":136481},[371],[373,136483,136484],{"xmlns":375},[377,136485,136486,136490],{},[380,136487,136488],{},[383,136489,1121],{"mathvariant":75560},[387,136491,135607],{"encoding":389},[363,136493,136495],{"className":136494,"ariaHidden":394},[393],[363,136496,136498,136501],{"className":136497},[398],[363,136499],{"className":136500,"style":135617},[402],[363,136502,1121],{"className":136503},[407,75905]," 取值于 ",[363,136506,136508,136536],{"className":136507,"translate":367},[366],[363,136509,136511],{"className":136510},[371],[373,136512,136513],{"xmlns":375},[377,136514,136515,136533],{},[380,136516,136517,136519,136521],{},[383,136518,134464],{"mathvariant":557},[458,136520,4450],{},[7161,136522,136523,136525],{},[383,136524,126023],{"mathvariant":557},[380,136526,136527,136529,136531],{},[383,136528,11041],{},[458,136530,5160],{},[463,136532,465],{},[387,136534,136535],{"encoding":389},"\\operatorname{int}\\Delta^{K-1}",[363,136537,136539],{"className":136538,"ariaHidden":394},[393],[363,136540,136542,136545,136551,136554],{"className":136541},[398],[363,136543],{"className":136544,"style":52432},[402],[363,136546,136548],{"className":136547},[1831],[363,136549,134464],{"className":136550},[407,33009],[363,136552],{"className":136553,"style":754},[505],[363,136555,136557,136560],{"className":136556},[407],[363,136558,126023],{"className":136559},[407],[363,136561,136563],{"className":136562},[629],[363,136564,136566],{"className":136565},[633],[363,136567,136569],{"className":136568},[638],[363,136570,136572],{"className":136571,"style":52432},[642],[363,136573,136574,136577],{"style":7212},[363,136575],{"className":136576,"style":651},[650],[363,136578,136580],{"className":136579},[655,656,657,658],[363,136581,136583,136586,136589],{"className":136582},[407,658],[363,136584,11041],{"className":136585,"style":11129},[407,408,658],[363,136587,5160],{"className":136588},[2938,658],[363,136590,465],{"className":136591},[407,658],"，且关于上述参考测度的密度为\n",[363,136594,136596,136669],{"className":136595,"translate":367},[366],[363,136597,136599],{"className":136598},[371],[373,136600,136601],{"xmlns":375},[377,136602,136603,136666],{},[380,136604,136605,136607,136609,136611,136613,136615,136617,136619,136633,136648],{},[383,136606,385],{},[458,136608,461],{"stretchy":460},[383,136610,1121],{"mathvariant":75560},[458,136612,5155],{},[383,136614,45101],{"mathvariant":136008},[458,136616,468],{"stretchy":460},[458,136618,471],{},[586,136620,136621,136623],{},[463,136622,465],{},[380,136624,136625,136627,136629,136631],{},[383,136626,39638],{},[458,136628,461],{"stretchy":460},[383,136630,45101],{"mathvariant":136008},[458,136632,468],{"stretchy":460},[7900,136634,136635,136638,136646],{},[458,136636,136637],{},"∏",[380,136639,136640,136642,136644],{},[383,136641,12310],{},[458,136643,471],{},[463,136645,465],{},[383,136647,11041],{},[7900,136649,136650,136652,136654],{},[383,136651,1121],{},[383,136653,12310],{},[380,136655,136656,136662,136664],{},[543,136657,136658,136660],{},[383,136659,45101],{},[383,136661,12310],{},[458,136663,5160],{},[463,136665,465],{},[387,136667,136668],{"encoding":389},"f(\\mathbf{x} \\mid \\boldsymbol{\\alpha}) = \\frac{1}{B(\\boldsymbol{\\alpha})} \\prod_{i=1}^K x_i^{\\alpha_i - 1}",[363,136670,136672,136696,136723],{"className":136671,"ariaHidden":394},[393],[363,136673,136675,136678,136681,136684,136687,136690,136693],{"className":136674},[398],[363,136676],{"className":136677,"style":487},[402],[363,136679,385],{"className":136680,"style":409},[407,408],[363,136682,461],{"className":136683},[494],[363,136685,1121],{"className":136686},[407,75905],[363,136688],{"className":136689,"style":506},[505],[363,136691,5155],{"className":136692},[510],[363,136694],{"className":136695,"style":506},[505],[363,136697,136699,136702,136711,136714,136717,136720],{"className":136698},[398],[363,136700],{"className":136701,"style":487},[402],[363,136703,136705],{"className":136704},[407],[363,136706,136708],{"className":136707},[407],[363,136709,45101],{"className":136710},[407,136068],[363,136712,468],{"className":136713},[501],[363,136715],{"className":136716,"style":506},[505],[363,136718,471],{"className":136719},[510],[363,136721],{"className":136722,"style":506},[505],[363,136724,136726,136730,136813,136816,136876,136879],{"className":136725},[398],[363,136727],{"className":136728,"style":136729},[402],"height:1.5012em;vertical-align:-0.52em;",[363,136731,136733,136736,136810],{"className":136732},[407],[363,136734],{"className":136735},[494,789],[363,136737,136739],{"className":136738},[586],[363,136740,136742,136802],{"className":136741},[633,634],[363,136743,136745,136799],{"className":136744},[638],[363,136746,136748,136777,136785],{"className":136747,"style":2871},[642],[363,136749,136750,136753],{"style":2874},[363,136751],{"className":136752,"style":809},[650],[363,136754,136756],{"className":136755},[655,656,657,658],[363,136757,136759,136762,136765,136774],{"className":136758},[407,658],[363,136760,39638],{"className":136761,"style":39734},[407,408,658],[363,136763,461],{"className":136764},[494,658],[363,136766,136768],{"className":136767},[407,658],[363,136769,136771],{"className":136770},[407,658],[363,136772,45101],{"className":136773},[407,136068,658],[363,136775,468],{"className":136776},[501,658],[363,136778,136779,136782],{"style":821},[363,136780],{"className":136781,"style":809},[650],[363,136783],{"className":136784,"style":829},[828],[363,136786,136787,136790],{"style":2897},[363,136788],{"className":136789,"style":809},[650],[363,136791,136793],{"className":136792},[655,656,657,658],[363,136794,136796],{"className":136795},[407,658],[363,136797,465],{"className":136798},[407,658],[363,136800,666],{"className":136801},[665],[363,136803,136805],{"className":136804},[638],[363,136806,136808],{"className":136807,"style":45949},[642],[363,136809],{},[363,136811],{"className":136812},[501,789],[363,136814],{"className":136815,"style":754},[505],[363,136817,136819,136822],{"className":136818},[1831],[363,136820,136637],{"className":136821,"style":40007},[1831,1832,5963],[363,136823,136825],{"className":136824},[629],[363,136826,136828,136868],{"className":136827},[633,634],[363,136829,136831,136865],{"className":136830},[638],[363,136832,136834,136854],{"className":136833,"style":133494},[642],[363,136835,136836,136839],{"style":40023},[363,136837],{"className":136838,"style":651},[650],[363,136840,136842],{"className":136841},[655,656,657,658],[363,136843,136845,136848,136851],{"className":136844},[407,658],[363,136846,12310],{"className":136847},[407,408,658],[363,136849,471],{"className":136850},[510,658],[363,136852,465],{"className":136853},[407,658],[363,136855,136856,136859],{"style":133517},[363,136857],{"className":136858,"style":651},[650],[363,136860,136862],{"className":136861},[655,656,657,658],[363,136863,11041],{"className":136864,"style":11129},[407,408,658],[363,136866,666],{"className":136867},[665],[363,136869,136871],{"className":136870},[638],[363,136872,136874],{"className":136873,"style":40042},[642],[363,136875],{},[363,136877],{"className":136878,"style":754},[505],[363,136880,136882,136885],{"className":136881},[407],[363,136883,1121],{"className":136884},[407,408],[363,136886,136888],{"className":136887},[629],[363,136889,136891,136972],{"className":136890},[633,634],[363,136892,136894,136969],{"className":136893},[638],[363,136895,136898,136910],{"className":136896,"style":136897},[642],"height:0.896em;",[363,136899,136901,136904],{"style":136900},"top:-2.4231em;margin-left:0em;margin-right:0.05em;",[363,136902],{"className":136903,"style":651},[650],[363,136905,136907],{"className":136906},[655,656,657,658],[363,136908,12310],{"className":136909},[407,408,658],[363,136911,136913,136916],{"style":136912},"top:-3.1449em;margin-right:0.05em;",[363,136914],{"className":136915,"style":651},[650],[363,136917,136919],{"className":136918},[655,656,657,658],[363,136920,136922,136963,136966],{"className":136921},[407,658],[363,136923,136925,136928],{"className":136924},[407,658],[363,136926,45101],{"className":136927,"style":45131},[407,408,658],[363,136929,136931],{"className":136930},[629],[363,136932,136934,136955],{"className":136933},[633,634],[363,136935,136937,136952],{"className":136936},[638],[363,136938,136940],{"className":136939,"style":40095},[642],[363,136941,136943,136946],{"style":136942},"top:-2.357em;margin-left:-0.0037em;margin-right:0.0714em;",[363,136944],{"className":136945,"style":30553},[650],[363,136947,136949],{"className":136948},[655,30557,10021,658],[363,136950,12310],{"className":136951},[407,408,658],[363,136953,666],{"className":136954},[665],[363,136956,136958],{"className":136957},[638],[363,136959,136961],{"className":136960,"style":40117},[642],[363,136962],{},[363,136964,5160],{"className":136965},[2938,658],[363,136967,465],{"className":136968},[407,658],[363,136970,666],{"className":136971},[665],[363,136973,136975],{"className":136974},[638],[363,136976,136979],{"className":136977,"style":136978},[642],"height:0.2769em;",[363,136980],{},"\n则称 ",[363,136983,136985,136998],{"className":136984,"translate":367},[366],[363,136986,136988],{"className":136987},[371],[373,136989,136990],{"xmlns":375},[377,136991,136992,136996],{},[380,136993,136994],{},[383,136995,1121],{"mathvariant":75560},[387,136997,135607],{"encoding":389},[363,136999,137001],{"className":137000,"ariaHidden":394},[393],[363,137002,137004,137007],{"className":137003},[398],[363,137005],{"className":137006,"style":135617},[402],[363,137008,1121],{"className":137009},[407,75905]," 服从参数为 ",[363,137012,137014,137028],{"className":137013,"translate":367},[366],[363,137015,137017],{"className":137016},[371],[373,137018,137019],{"xmlns":375},[377,137020,137021,137025],{},[380,137022,137023],{},[383,137024,45101],{"mathvariant":136008},[387,137026,137027],{"encoding":389},"\\boldsymbol{\\alpha}",[363,137029,137031],{"className":137030,"ariaHidden":394},[393],[363,137032,137034,137037],{"className":137033},[398],[363,137035],{"className":137036,"style":135617},[402],[363,137038,137040],{"className":137039},[407],[363,137041,137043],{"className":137042},[407],[363,137044,45101],{"className":137045},[407,136068]," 的迪利克雷分布，记作 ",[363,137048,137050,137077],{"className":137049,"translate":367},[366],[363,137051,137053],{"className":137052},[371],[373,137054,137055],{"xmlns":375},[377,137056,137057,137074],{},[380,137058,137059,137061,137063,137066,137068,137070,137072],{},[383,137060,1121],{"mathvariant":75560},[458,137062,9216],{},[383,137064,137065],{"mathvariant":557},"Dir",[458,137067,4450],{},[458,137069,461],{"stretchy":460},[383,137071,45101],{"mathvariant":136008},[458,137073,468],{"stretchy":460},[387,137075,137076],{"encoding":389},"\\mathbf{x} \\sim \\operatorname{Dir}(\\boldsymbol{\\alpha})",[363,137078,137080,137098],{"className":137079,"ariaHidden":394},[393],[363,137081,137083,137086,137089,137092,137095],{"className":137082},[398],[363,137084],{"className":137085,"style":135617},[402],[363,137087,1121],{"className":137088},[407,75905],[363,137090],{"className":137091,"style":506},[505],[363,137093,9216],{"className":137094},[510],[363,137096],{"className":137097,"style":506},[505],[363,137099,137101,137104,137110,137113,137122],{"className":137100},[398],[363,137102],{"className":137103,"style":487},[402],[363,137105,137107],{"className":137106},[1831],[363,137108,137065],{"className":137109},[407,33009],[363,137111,461],{"className":137112},[494],[363,137114,137116],{"className":137115},[407],[363,137117,137119],{"className":137118},[407],[363,137120,45101],{"className":137121},[407,136068],[363,137123,468],{"className":137124},[501],"。其中归一化常数为",[1572,137127,137128],{},"多元 Beta 函数",[363,137130,137132,137201],{"className":137131,"translate":367},[366],[363,137133,137135],{"className":137134},[371],[373,137136,137137],{"xmlns":375},[377,137138,137139,137198],{},[380,137140,137141,137143,137145,137147,137149,137151],{},[383,137142,39638],{},[458,137144,461],{"stretchy":460},[383,137146,45101],{"mathvariant":136008},[458,137148,468],{"stretchy":460},[458,137150,471],{},[586,137152,137153,137182],{},[380,137154,137155,137169,137172,137174,137180],{},[7900,137156,137157,137159,137167],{},[458,137158,136637],{},[380,137160,137161,137163,137165],{},[383,137162,12310],{},[458,137164,471],{},[463,137166,465],{},[383,137168,11041],{},[383,137170,137171],{"mathvariant":557},"Γ",[458,137173,461],{"stretchy":460},[543,137175,137176,137178],{},[383,137177,45101],{},[383,137179,12310],{},[458,137181,468],{"stretchy":460},[380,137183,137184,137186],{},[383,137185,137171],{"mathvariant":557},[380,137187,137188,137190,137196],{},[458,137189,461],{"fence":394},[543,137191,137192,137194],{},[383,137193,45101],{},[463,137195,474],{},[458,137197,468],{"fence":394},[387,137199,137200],{"encoding":389},"B(\\boldsymbol{\\alpha}) = \\frac{\\prod_{i=1}^K \\Gamma(\\alpha_i)}{\\Gamma\\left(\\alpha_0\\right)}",[363,137202,137204,137237],{"className":137203,"ariaHidden":394},[393],[363,137205,137207,137210,137213,137216,137225,137228,137231,137234],{"className":137206},[398],[363,137208],{"className":137209,"style":487},[402],[363,137211,39638],{"className":137212,"style":39734},[407,408],[363,137214,461],{"className":137215},[494],[363,137217,137219],{"className":137218},[407],[363,137220,137222],{"className":137221},[407],[363,137223,45101],{"className":137224},[407,136068],[363,137226,468],{"className":137227},[501],[363,137229],{"className":137230,"style":506},[505],[363,137232,471],{"className":137233},[510],[363,137235],{"className":137236,"style":506},[505],[363,137238,137240,137244],{"className":137239},[398],[363,137241],{"className":137242,"style":137243},[402],"height:1.6984em;vertical-align:-0.52em;",[363,137245,137247,137250,137479],{"className":137246},[407],[363,137248],{"className":137249},[494,789],[363,137251,137253],{"className":137252},[586],[363,137254,137256,137471],{"className":137255},[633,634],[363,137257,137259,137468],{"className":137258},[638],[363,137260,137263,137333,137341],{"className":137261,"style":137262},[642],"height:1.1784em;",[363,137264,137265,137268],{"style":2874},[363,137266],{"className":137267,"style":809},[650],[363,137269,137271],{"className":137270},[655,656,657,658],[363,137272,137274,137277],{"className":137273},[407,658],[363,137275,137171],{"className":137276},[407,658],[363,137278,137280,137286,137327],{"className":137279},[758,658],[363,137281,137283],{"className":137282,"style":763},[494,658,762],[363,137284,461],{"className":137285},[658],[363,137287,137289,137292],{"className":137288},[407,658],[363,137290,45101],{"className":137291,"style":45131},[407,408,658],[363,137293,137295],{"className":137294},[629],[363,137296,137298,137319],{"className":137297},[633,634],[363,137299,137301,137316],{"className":137300},[638],[363,137302,137305],{"className":137303,"style":137304},[642],"height:0.3173em;",[363,137306,137307,137310],{"style":136942},[363,137308],{"className":137309,"style":30553},[650],[363,137311,137313],{"className":137312},[655,30557,10021,658],[363,137314,474],{"className":137315},[407,658],[363,137317,666],{"className":137318},[665],[363,137320,137322],{"className":137321},[638],[363,137323,137325],{"className":137324,"style":40117},[642],[363,137326],{},[363,137328,137330],{"className":137329,"style":763},[501,658,762],[363,137331,468],{"className":137332},[658],[363,137334,137335,137338],{"style":821},[363,137336],{"className":137337,"style":809},[650],[363,137339],{"className":137340,"style":829},[828],[363,137342,137344,137347],{"style":137343},"top:-3.535em;",[363,137345],{"className":137346,"style":809},[650],[363,137348,137350],{"className":137349},[655,656,657,658],[363,137351,137353,137416,137419,137422,137425,137465],{"className":137352},[407,658],[363,137354,137356,137359],{"className":137355},[1831,658],[363,137357,136637],{"className":137358,"style":40007},[1831,1832,5963,658],[363,137360,137362],{"className":137361},[629],[363,137363,137365,137407],{"className":137364},[633,634],[363,137366,137368,137404],{"className":137367},[638],[363,137369,137372,137393],{"className":137370,"style":137371},[642],"height:0.9191em;",[363,137373,137375,137378],{"style":137374},"top:-2.1786em;margin-left:0em;margin-right:0.0714em;",[363,137376],{"className":137377,"style":30553},[650],[363,137379,137381],{"className":137380},[655,30557,10021,658],[363,137382,137384,137387,137390],{"className":137383},[407,658],[363,137385,12310],{"className":137386},[407,408,658],[363,137388,471],{"className":137389},[510,658],[363,137391,465],{"className":137392},[407,658],[363,137394,137395,137398],{"style":38862},[363,137396],{"className":137397,"style":30553},[650],[363,137399,137401],{"className":137400},[655,30557,10021,658],[363,137402,11041],{"className":137403,"style":11129},[407,408,658],[363,137405,666],{"className":137406},[665],[363,137408,137410],{"className":137409},[638],[363,137411,137414],{"className":137412,"style":137413},[642],"height:0.3214em;",[363,137415],{},[363,137417],{"className":137418,"style":42713},[505,658],[363,137420,137171],{"className":137421},[407,658],[363,137423,461],{"className":137424},[494,658],[363,137426,137428,137431],{"className":137427},[407,658],[363,137429,45101],{"className":137430,"style":45131},[407,408,658],[363,137432,137434],{"className":137433},[629],[363,137435,137437,137457],{"className":137436},[633,634],[363,137438,137440,137454],{"className":137439},[638],[363,137441,137443],{"className":137442,"style":40095},[642],[363,137444,137445,137448],{"style":136942},[363,137446],{"className":137447,"style":30553},[650],[363,137449,137451],{"className":137450},[655,30557,10021,658],[363,137452,12310],{"className":137453},[407,408,658],[363,137455,666],{"className":137456},[665],[363,137458,137460],{"className":137459},[638],[363,137461,137463],{"className":137462,"style":40117},[642],[363,137464],{},[363,137466,468],{"className":137467},[501,658],[363,137469,666],{"className":137470},[665],[363,137472,137474],{"className":137473},[638],[363,137475,137477],{"className":137476,"style":45949},[642],[363,137478],{},[363,137480],{"className":137481},[501,789],[11,137483,137484],{},"该定义之所以合法，依赖于下述恒等式。它是整个理论的算术基础，值得单独给出证明。",[1340,137486,137488],{"title":137487},"命题 1.3（归一化恒等式）",[11,137489,137490,137491,137612,137613],{},"对任意 ",[363,137492,137494,137522],{"className":137493,"translate":367},[366],[363,137495,137497],{"className":137496},[371],[373,137498,137499],{"xmlns":375},[377,137500,137501,137519],{},[380,137502,137503,137505,137507],{},[383,137504,45101],{"mathvariant":136008},[458,137506,6256],{},[7900,137508,137509,137511,137517],{},[383,137510,1379],{"mathvariant":570},[380,137512,137513,137515],{},[458,137514,3250],{},[463,137516,474],{},[383,137518,11041],{},[387,137520,137521],{"encoding":389},"\\boldsymbol{\\alpha} \\in \\mathbb{R}_{>0}^K",[363,137523,137525,137549],{"className":137524,"ariaHidden":394},[393],[363,137526,137528,137531,137540,137543,137546],{"className":137527},[398],[363,137529],{"className":137530,"style":6271},[402],[363,137532,137534],{"className":137533},[407],[363,137535,137537],{"className":137536},[407],[363,137538,45101],{"className":137539},[407,136068],[363,137541],{"className":137542,"style":506},[505],[363,137544,6256],{"className":137545},[510],[363,137547],{"className":137548,"style":506},[505],[363,137550,137552,137555],{"className":137551},[398],[363,137553],{"className":137554,"style":136204},[402],[363,137556,137558,137561],{"className":137557},[407],[363,137559,1379],{"className":137560},[407,714],[363,137562,137564],{"className":137563},[629],[363,137565,137567,137604],{"className":137566},[633,634],[363,137568,137570,137601],{"className":137569},[638],[363,137571,137573,137590],{"className":137572,"style":52432},[642],[363,137574,137575,137578],{"style":136225},[363,137576],{"className":137577,"style":651},[650],[363,137579,137581],{"className":137580},[655,656,657,658],[363,137582,137584,137587],{"className":137583},[407,658],[363,137585,3250],{"className":137586},[510,658],[363,137588,474],{"className":137589},[407,658],[363,137591,137592,137595],{"style":7212},[363,137593],{"className":137594,"style":651},[650],[363,137596,137598],{"className":137597},[655,656,657,658],[363,137599,11041],{"className":137600,"style":11129},[407,408,658],[363,137602,666],{"className":137603},[665],[363,137605,137607],{"className":137606},[638],[363,137608,137610],{"className":137609,"style":136261},[642],[363,137611],{},"，\n",[363,137614,137616,137692],{"className":137615,"translate":367},[366],[363,137617,137619],{"className":137618},[371],[373,137620,137621],{"xmlns":375},[377,137622,137623,137689],{},[380,137624,137625,137641,137655,137673,137675,137677,137679,137681,137683,137685,137687],{},[543,137626,137627,137629],{},[458,137628,1634],{},[7161,137630,137631,137633],{},[383,137632,126023],{"mathvariant":557},[380,137634,137635,137637,137639],{},[383,137636,11041],{},[458,137638,5160],{},[463,137640,465],{},[7900,137642,137643,137645,137653],{},[458,137644,136637],{},[380,137646,137647,137649,137651],{},[383,137648,12310],{},[458,137650,471],{},[463,137652,465],{},[383,137654,11041],{},[7900,137656,137657,137659,137661],{},[383,137658,1121],{},[383,137660,12310],{},[380,137662,137663,137669,137671],{},[543,137664,137665,137667],{},[383,137666,45101],{},[383,137668,12310],{},[458,137670,5160],{},[463,137672,465],{},[1644,137674,1646],{},[383,137676,592],{"mathvariant":557},[383,137678,1121],{"mathvariant":75560},[458,137680,471],{},[383,137682,39638],{},[458,137684,461],{"stretchy":460},[383,137686,45101],{"mathvariant":136008},[458,137688,468],{"stretchy":460},[387,137690,137691],{"encoding":389},"\\int_{\\Delta^{K-1}} \\prod_{i=1}^K x_i^{\\alpha_i - 1} \\,\\mathrm{d}\\mathbf{x} = B(\\boldsymbol{\\alpha})",[363,137693,137695,137965],{"className":137694,"ariaHidden":394},[393],[363,137696,137698,137702,137784,137787,137847,137850,137947,137950,137953,137956,137959,137962],{"className":137697},[398],[363,137699],{"className":137700,"style":137701},[402],"height:1.3371em;vertical-align:-0.3558em;",[363,137703,137705,137708],{"className":137704},[1831],[363,137706,1634],{"className":137707,"style":5964},[1831,1832,5963],[363,137709,137711],{"className":137710},[629],[363,137712,137714,137775],{"className":137713},[633,634],[363,137715,137717,137772],{"className":137716},[638],[363,137718,137721],{"className":137719,"style":137720},[642],"height:0.186em;",[363,137722,137724,137727],{"style":137723},"top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;",[363,137725],{"className":137726,"style":651},[650],[363,137728,137730],{"className":137729},[655,656,657,658],[363,137731,137733],{"className":137732},[407,658],[363,137734,137736,137739],{"className":137735},[407,658],[363,137737,126023],{"className":137738},[407,658],[363,137740,137742],{"className":137741},[629],[363,137743,137745],{"className":137744},[633],[363,137746,137748],{"className":137747},[638],[363,137749,137752],{"className":137750,"style":137751},[642],"height:0.7741em;",[363,137753,137754,137757],{"style":45809},[363,137755],{"className":137756,"style":30553},[650],[363,137758,137760],{"className":137759},[655,30557,10021,658],[363,137761,137763,137766,137769],{"className":137762},[407,658],[363,137764,11041],{"className":137765,"style":11129},[407,408,658],[363,137767,5160],{"className":137768},[2938,658],[363,137770,465],{"className":137771},[407,658],[363,137773,666],{"className":137774},[665],[363,137776,137778],{"className":137777},[638],[363,137779,137782],{"className":137780,"style":137781},[642],"height:0.3558em;",[363,137783],{},[363,137785],{"className":137786,"style":754},[505],[363,137788,137790,137793],{"className":137789},[1831],[363,137791,136637],{"className":137792,"style":40007},[1831,1832,5963],[363,137794,137796],{"className":137795},[629],[363,137797,137799,137839],{"className":137798},[633,634],[363,137800,137802,137836],{"className":137801},[638],[363,137803,137805,137825],{"className":137804,"style":133494},[642],[363,137806,137807,137810],{"style":40023},[363,137808],{"className":137809,"style":651},[650],[363,137811,137813],{"className":137812},[655,656,657,658],[363,137814,137816,137819,137822],{"className":137815},[407,658],[363,137817,12310],{"className":137818},[407,408,658],[363,137820,471],{"className":137821},[510,658],[363,137823,465],{"className":137824},[407,658],[363,137826,137827,137830],{"style":133517},[363,137828],{"className":137829,"style":651},[650],[363,137831,137833],{"className":137832},[655,656,657,658],[363,137834,11041],{"className":137835,"style":11129},[407,408,658],[363,137837,666],{"className":137838},[665],[363,137840,137842],{"className":137841},[638],[363,137843,137845],{"className":137844,"style":40042},[642],[363,137846],{},[363,137848],{"className":137849,"style":754},[505],[363,137851,137853,137856],{"className":137852},[407],[363,137854,1121],{"className":137855},[407,408],[363,137857,137859],{"className":137858},[629],[363,137860,137862,137939],{"className":137861},[633,634],[363,137863,137865,137936],{"className":137864},[638],[363,137866,137868,137879],{"className":137867,"style":136897},[642],[363,137869,137870,137873],{"style":136900},[363,137871],{"className":137872,"style":651},[650],[363,137874,137876],{"className":137875},[655,656,657,658],[363,137877,12310],{"className":137878},[407,408,658],[363,137880,137881,137884],{"style":136912},[363,137882],{"className":137883,"style":651},[650],[363,137885,137887],{"className":137886},[655,656,657,658],[363,137888,137890,137930,137933],{"className":137889},[407,658],[363,137891,137893,137896],{"className":137892},[407,658],[363,137894,45101],{"className":137895,"style":45131},[407,408,658],[363,137897,137899],{"className":137898},[629],[363,137900,137902,137922],{"className":137901},[633,634],[363,137903,137905,137919],{"className":137904},[638],[363,137906,137908],{"className":137907,"style":40095},[642],[363,137909,137910,137913],{"style":136942},[363,137911],{"className":137912,"style":30553},[650],[363,137914,137916],{"className":137915},[655,30557,10021,658],[363,137917,12310],{"className":137918},[407,408,658],[363,137920,666],{"className":137921},[665],[363,137923,137925],{"className":137924},[638],[363,137926,137928],{"className":137927,"style":40117},[642],[363,137929],{},[363,137931,5160],{"className":137932},[2938,658],[363,137934,465],{"className":137935},[407,658],[363,137937,666],{"className":137938},[665],[363,137940,137942],{"className":137941},[638],[363,137943,137945],{"className":137944,"style":136978},[642],[363,137946],{},[363,137948],{"className":137949,"style":754},[505],[363,137951,592],{"className":137952},[407,33009],[363,137954,1121],{"className":137955},[407,75905],[363,137957],{"className":137958,"style":506},[505],[363,137960,471],{"className":137961},[510],[363,137963],{"className":137964,"style":506},[505],[363,137966,137968,137971,137974,137977,137986],{"className":137967},[398],[363,137969],{"className":137970,"style":487},[402],[363,137972,39638],{"className":137973,"style":39734},[407,408],[363,137975,461],{"className":137976},[494],[363,137978,137980],{"className":137979},[407],[363,137981,137983],{"className":137982},[407],[363,137984,45101],{"className":137985},[407,136068],[363,137987,468],{"className":137988},[501],[11,137990,137991,137994,137995,138088],{},[1572,137992,137993],{},"证明"," 考虑 ",[363,137996,137998,138022],{"className":137997,"translate":367},[366],[363,137999,138001],{"className":138000},[371],[373,138002,138003],{"xmlns":375},[377,138004,138005,138019],{},[380,138006,138007],{},[7900,138008,138009,138011,138017],{},[383,138010,1379],{"mathvariant":570},[380,138012,138013,138015],{},[458,138014,3250],{},[463,138016,474],{},[383,138018,11041],{},[387,138020,138021],{"encoding":389},"\\mathbb{R}_{>0}^K",[363,138023,138025],{"className":138024,"ariaHidden":394},[393],[363,138026,138028,138031],{"className":138027},[398],[363,138029],{"className":138030,"style":136204},[402],[363,138032,138034,138037],{"className":138033},[407],[363,138035,1379],{"className":138036},[407,714],[363,138038,138040],{"className":138039},[629],[363,138041,138043,138080],{"className":138042},[633,634],[363,138044,138046,138077],{"className":138045},[638],[363,138047,138049,138066],{"className":138048,"style":52432},[642],[363,138050,138051,138054],{"style":136225},[363,138052],{"className":138053,"style":651},[650],[363,138055,138057],{"className":138056},[655,656,657,658],[363,138058,138060,138063],{"className":138059},[407,658],[363,138061,3250],{"className":138062},[510,658],[363,138064,474],{"className":138065},[407,658],[363,138067,138068,138071],{"style":7212},[363,138069],{"className":138070,"style":651},[650],[363,138072,138074],{"className":138073},[655,656,657,658],[363,138075,11041],{"className":138076,"style":11129},[407,408,658],[363,138078,666],{"className":138079},[665],[363,138081,138083],{"className":138082},[638],[363,138084,138086],{"className":138085,"style":136261},[642],[363,138087],{}," 上的 Gamma 积分之积：",[363,138090,138092],{"className":138091,"translate":367},[528],[363,138093,138095,138203],{"className":138094,"translate":367},[366],[363,138096,138098],{"className":138097},[371],[373,138099,138100],{"xmlns":375,"display":537},[377,138101,138102,138200],{},[380,138103,138104,138118,138120,138122,138128,138130,138132,138148,138162,138180,138194,138196,138198],{},[48667,138105,138106,138108,138116],{},[458,138107,136637],{},[380,138109,138110,138112,138114],{},[383,138111,12310],{},[458,138113,471],{},[463,138115,465],{},[383,138117,11041],{},[383,138119,137171],{"mathvariant":557},[458,138121,461],{"stretchy":460},[543,138123,138124,138126],{},[383,138125,45101],{},[383,138127,12310],{},[458,138129,468],{"stretchy":460},[458,138131,471],{},[543,138133,138134,138136],{},[458,138135,1634],{},[7900,138137,138138,138140,138146],{},[383,138139,1379],{"mathvariant":570},[380,138141,138142,138144],{},[458,138143,3250],{},[463,138145,474],{},[383,138147,11041],{},[48667,138149,138150,138152,138160],{},[458,138151,136637],{},[380,138153,138154,138156,138158],{},[383,138155,12310],{},[458,138157,471],{},[463,138159,465],{},[383,138161,11041],{},[7900,138163,138164,138166,138168],{},[383,138165,1116],{},[383,138167,12310],{},[380,138169,138170,138176,138178],{},[543,138171,138172,138174],{},[383,138173,45101],{},[383,138175,12310],{},[458,138177,5160],{},[463,138179,465],{},[7161,138181,138182,138184],{},[383,138183,7914],{},[380,138185,138186,138188],{},[458,138187,5160],{},[543,138189,138190,138192],{},[383,138191,1116],{},[383,138193,12310],{},[1644,138195,1646],{},[383,138197,592],{"mathvariant":557},[383,138199,1116],{"mathvariant":75560},[387,138201,138202],{"encoding":389},"\\prod_{i=1}^K \\Gamma(\\alpha_i) = \\int_{\\mathbb{R}_{>0}^K} \\prod_{i=1}^K t_i^{\\alpha_i - 1} e^{-t_i} \\,\\mathrm{d}\\mathbf{t}",[363,138204,138206,138339],{"className":138205,"ariaHidden":394},[393],[363,138207,138209,138213,138278,138281,138284,138287,138327,138330,138333,138336],{"className":138208},[398],[363,138210],{"className":138211,"style":138212},[402],"height:3.106em;vertical-align:-1.2777em;",[363,138214,138216],{"className":138215},[1831,14063],[363,138217,138219,138270],{"className":138218},[633,634],[363,138220,138222,138267],{"className":138221},[638],[363,138223,138226,138246,138256],{"className":138224,"style":138225},[642],"height:1.8283em;",[363,138227,138228,138231],{"style":14076},[363,138229],{"className":138230,"style":14080},[650],[363,138232,138234],{"className":138233},[655,656,657,658],[363,138235,138237,138240,138243],{"className":138236},[407,658],[363,138238,12310],{"className":138239},[407,408,658],[363,138241,471],{"className":138242},[510,658],[363,138244,465],{"className":138245},[407,658],[363,138247,138248,138251],{"style":14089},[363,138249],{"className":138250,"style":14080},[650],[363,138252,138253],{},[363,138254,136637],{"className":138255},[1831,1832,1833],[363,138257,138258,138261],{"style":100671},[363,138259],{"className":138260,"style":14080},[650],[363,138262,138264],{"className":138263},[655,656,657,658],[363,138265,11041],{"className":138266,"style":11129},[407,408,658],[363,138268,666],{"className":138269},[665],[363,138271,138273],{"className":138272},[638],[363,138274,138276],{"className":138275,"style":14107},[642],[363,138277],{},[363,138279],{"className":138280,"style":754},[505],[363,138282,137171],{"className":138283},[407],[363,138285,461],{"className":138286},[494],[363,138288,138290,138293],{"className":138289},[407],[363,138291,45101],{"className":138292,"style":45131},[407,408],[363,138294,138296],{"className":138295},[629],[363,138297,138299,138319],{"className":138298},[633,634],[363,138300,138302,138316],{"className":138301},[638],[363,138303,138305],{"className":138304,"style":12529},[642],[363,138306,138307,138310],{"style":136107},[363,138308],{"className":138309,"style":651},[650],[363,138311,138313],{"className":138312},[655,656,657,658],[363,138314,12310],{"className":138315},[407,408,658],[363,138317,666],{"className":138318},[665],[363,138320,138322],{"className":138321},[638],[363,138323,138325],{"className":138324,"style":8315},[642],[363,138326],{},[363,138328,468],{"className":138329},[501],[363,138331],{"className":138332,"style":506},[505],[363,138334,471],{"className":138335},[510],[363,138337],{"className":138338,"style":506},[505],[363,138340,138342,138345,138447,138450,138514,138517,138614,138687,138690,138693],{"className":138341},[398],[363,138343],{"className":138344,"style":138212},[402],[363,138346,138348,138351],{"className":138347},[1831],[363,138349,1634],{"className":138350,"style":1834},[1831,1832,1833],[363,138352,138354],{"className":138353},[629],[363,138355,138357,138438],{"className":138356},[633,634],[363,138358,138360,138435],{"className":138359},[638],[363,138361,138364],{"className":138362,"style":138363},[642],"height:-0.3289em;",[363,138365,138366,138369],{"style":3825},[363,138367],{"className":138368,"style":651},[650],[363,138370,138372],{"className":138371},[655,656,657,658],[363,138373,138375],{"className":138374},[407,658],[363,138376,138378,138381],{"className":138377},[407,658],[363,138379,1379],{"className":138380},[407,714,658],[363,138382,138384],{"className":138383},[629],[363,138385,138387,138426],{"className":138386},[633,634],[363,138388,138390,138423],{"className":138389},[638],[363,138391,138394,138412],{"className":138392,"style":138393},[642],"height:0.8329em;",[363,138395,138397,138400],{"style":138396},"top:-2.1885em;margin-left:0em;margin-right:0.0714em;",[363,138398],{"className":138399,"style":30553},[650],[363,138401,138403],{"className":138402},[655,30557,10021,658],[363,138404,138406,138409],{"className":138405},[407,658],[363,138407,3250],{"className":138408},[510,658],[363,138410,474],{"className":138411},[407,658],[363,138413,138414,138417],{"style":59260},[363,138415],{"className":138416,"style":30553},[650],[363,138418,138420],{"className":138419},[655,30557,10021,658],[363,138421,11041],{"className":138422,"style":11129},[407,408,658],[363,138424,666],{"className":138425},[665],[363,138427,138429],{"className":138428},[638],[363,138430,138433],{"className":138431,"style":138432},[642],"height:0.3394em;",[363,138434],{},[363,138436,666],{"className":138437},[665],[363,138439,138441],{"className":138440},[638],[363,138442,138445],{"className":138443,"style":138444},[642],"height:1.1496em;",[363,138446],{},[363,138448],{"className":138449,"style":754},[505],[363,138451,138453],{"className":138452},[1831,14063],[363,138454,138456,138506],{"className":138455},[633,634],[363,138457,138459,138503],{"className":138458},[638],[363,138460,138462,138482,138492],{"className":138461,"style":138225},[642],[363,138463,138464,138467],{"style":14076},[363,138465],{"className":138466,"style":14080},[650],[363,138468,138470],{"className":138469},[655,656,657,658],[363,138471,138473,138476,138479],{"className":138472},[407,658],[363,138474,12310],{"className":138475},[407,408,658],[363,138477,471],{"className":138478},[510,658],[363,138480,465],{"className":138481},[407,658],[363,138483,138484,138487],{"style":14089},[363,138485],{"className":138486,"style":14080},[650],[363,138488,138489],{},[363,138490,136637],{"className":138491},[1831,1832,1833],[363,138493,138494,138497],{"style":100671},[363,138495],{"className":138496,"style":14080},[650],[363,138498,138500],{"className":138499},[655,656,657,658],[363,138501,11041],{"className":138502,"style":11129},[407,408,658],[363,138504,666],{"className":138505},[665],[363,138507,138509],{"className":138508},[638],[363,138510,138512],{"className":138511,"style":14107},[642],[363,138513],{},[363,138515],{"className":138516,"style":754},[505],[363,138518,138520,138523],{"className":138519},[407],[363,138521,1116],{"className":138522},[407,408],[363,138524,138526],{"className":138525},[629],[363,138527,138529,138606],{"className":138528},[633,634],[363,138530,138532,138603],{"className":138531},[638],[363,138533,138535,138546],{"className":138534,"style":136897},[642],[363,138536,138537,138540],{"style":136900},[363,138538],{"className":138539,"style":651},[650],[363,138541,138543],{"className":138542},[655,656,657,658],[363,138544,12310],{"className":138545},[407,408,658],[363,138547,138548,138551],{"style":136912},[363,138549],{"className":138550,"style":651},[650],[363,138552,138554],{"className":138553},[655,656,657,658],[363,138555,138557,138597,138600],{"className":138556},[407,658],[363,138558,138560,138563],{"className":138559},[407,658],[363,138561,45101],{"className":138562,"style":45131},[407,408,658],[363,138564,138566],{"className":138565},[629],[363,138567,138569,138589],{"className":138568},[633,634],[363,138570,138572,138586],{"className":138571},[638],[363,138573,138575],{"className":138574,"style":40095},[642],[363,138576,138577,138580],{"style":136942},[363,138578],{"className":138579,"style":30553},[650],[363,138581,138583],{"className":138582},[655,30557,10021,658],[363,138584,12310],{"className":138585},[407,408,658],[363,138587,666],{"className":138588},[665],[363,138590,138592],{"className":138591},[638],[363,138593,138595],{"className":138594,"style":40117},[642],[363,138596],{},[363,138598,5160],{"className":138599},[2938,658],[363,138601,465],{"className":138602},[407,658],[363,138604,666],{"className":138605},[665],[363,138607,138609],{"className":138608},[638],[363,138610,138612],{"className":138611,"style":136978},[642],[363,138613],{},[363,138615,138617,138620],{"className":138616},[407],[363,138618,7914],{"className":138619},[407,408],[363,138621,138623],{"className":138622},[629],[363,138624,138626],{"className":138625},[633],[363,138627,138629],{"className":138628},[638],[363,138630,138633],{"className":138631,"style":138632},[642],"height:0.8436em;",[363,138634,138635,138638],{"style":8624},[363,138636],{"className":138637,"style":651},[650],[363,138639,138641],{"className":138640},[655,656,657,658],[363,138642,138644,138647],{"className":138643},[407,658],[363,138645,5160],{"className":138646},[407,658],[363,138648,138650,138653],{"className":138649},[407,658],[363,138651,1116],{"className":138652},[407,408,658],[363,138654,138656],{"className":138655},[629],[363,138657,138659,138679],{"className":138658},[633,634],[363,138660,138662,138676],{"className":138661},[638],[363,138663,138665],{"className":138664,"style":40095},[642],[363,138666,138667,138670],{"style":74612},[363,138668],{"className":138669,"style":30553},[650],[363,138671,138673],{"className":138672},[655,30557,10021,658],[363,138674,12310],{"className":138675},[407,408,658],[363,138677,666],{"className":138678},[665],[363,138680,138682],{"className":138681},[638],[363,138683,138685],{"className":138684,"style":40117},[642],[363,138686],{},[363,138688],{"className":138689,"style":754},[505],[363,138691,592],{"className":138692},[407,33009],[363,138694,1116],{"className":138695},[407,75905],[11,138697,138698,138699,87128,138842,5992,139006,139102,139103,139223,139224,139274,139275,139584],{},"作变量替换 ",[363,138700,138702,138732],{"className":138701,"translate":367},[366],[363,138703,138705],{"className":138704},[371],[373,138706,138707],{"xmlns":375},[377,138708,138709,138729],{},[380,138710,138711,138717,138719,138721,138723],{},[543,138712,138713,138715],{},[383,138714,1116],{},[383,138716,12310],{},[458,138718,471],{},[383,138720,7908],{},[1644,138722,1646],{},[543,138724,138725,138727],{},[383,138726,1121],{},[383,138728,12310],{},[387,138730,138731],{"encoding":389},"t_i = s\\, x_i",[363,138733,138735,138790],{"className":138734,"ariaHidden":394},[393],[363,138736,138738,138741,138781,138784,138787],{"className":138737},[398],[363,138739],{"className":138740,"style":96272},[402],[363,138742,138744,138747],{"className":138743},[407],[363,138745,1116],{"className":138746},[407,408],[363,138748,138750],{"className":138749},[629],[363,138751,138753,138773],{"className":138752},[633,634],[363,138754,138756,138770],{"className":138755},[638],[363,138757,138759],{"className":138758,"style":12529},[642],[363,138760,138761,138764],{"style":730},[363,138762],{"className":138763,"style":651},[650],[363,138765,138767],{"className":138766},[655,656,657,658],[363,138768,12310],{"className":138769},[407,408,658],[363,138771,666],{"className":138772},[665],[363,138774,138776],{"className":138775},[638],[363,138777,138779],{"className":138778,"style":8315},[642],[363,138780],{},[363,138782],{"className":138783,"style":506},[505],[363,138785,471],{"className":138786},[510],[363,138788],{"className":138789,"style":506},[505],[363,138791,138793,138796,138799,138802],{"className":138792},[398],[363,138794],{"className":138795,"style":13721},[402],[363,138797,7908],{"className":138798},[407,408],[363,138800],{"className":138801,"style":754},[505],[363,138803,138805,138808],{"className":138804},[407],[363,138806,1121],{"className":138807},[407,408],[363,138809,138811],{"className":138810},[629],[363,138812,138814,138834],{"className":138813},[633,634],[363,138815,138817,138831],{"className":138816},[638],[363,138818,138820],{"className":138819,"style":12529},[642],[363,138821,138822,138825],{"style":730},[363,138823],{"className":138824,"style":651},[650],[363,138826,138828],{"className":138827},[655,656,657,658],[363,138829,12310],{"className":138830},[407,408,658],[363,138832,666],{"className":138833},[665],[363,138835,138837],{"className":138836},[638],[363,138838,138840],{"className":138839,"style":8315},[642],[363,138841],{},[363,138843,138845,138877],{"className":138844,"translate":367},[366],[363,138846,138848],{"className":138847},[371],[373,138849,138850],{"xmlns":375},[377,138851,138852,138874],{},[380,138853,138854,138856,138858,138864,138870,138872],{},[383,138855,7908],{},[458,138857,471],{},[543,138859,138860,138862],{},[458,138861,13808],{},[383,138863,12310],{},[543,138865,138866,138868],{},[383,138867,1116],{},[383,138869,12310],{},[458,138871,3250],{},[463,138873,474],{},[387,138875,138876],{"encoding":389},"s = \\sum_i t_i > 0",[363,138878,138880,138898,138997],{"className":138879,"ariaHidden":394},[393],[363,138881,138883,138886,138889,138892,138895],{"className":138882},[398],[363,138884],{"className":138885,"style":2692},[402],[363,138887,7908],{"className":138888},[407,408],[363,138890],{"className":138891,"style":506},[505],[363,138893,471],{"className":138894},[510],[363,138896],{"className":138897,"style":506},[505],[363,138899,138901,138905,138945,138948,138988,138991,138994],{"className":138900},[398],[363,138902],{"className":138903,"style":138904},[402],"height:1.0497em;vertical-align:-0.2997em;",[363,138906,138908,138911],{"className":138907},[1831],[363,138909,13808],{"className":138910,"style":40007},[1831,1832,5963],[363,138912,138914],{"className":138913},[629],[363,138915,138917,138937],{"className":138916},[633,634],[363,138918,138920,138934],{"className":138919},[638],[363,138921,138923],{"className":138922,"style":40020},[642],[363,138924,138925,138928],{"style":40023},[363,138926],{"className":138927,"style":651},[650],[363,138929,138931],{"className":138930},[655,656,657,658],[363,138932,12310],{"className":138933},[407,408,658],[363,138935,666],{"className":138936},[665],[363,138938,138940],{"className":138939},[638],[363,138941,138943],{"className":138942,"style":40042},[642],[363,138944],{},[363,138946],{"className":138947,"style":754},[505],[363,138949,138951,138954],{"className":138950},[407],[363,138952,1116],{"className":138953},[407,408],[363,138955,138957],{"className":138956},[629],[363,138958,138960,138980],{"className":138959},[633,634],[363,138961,138963,138977],{"className":138962},[638],[363,138964,138966],{"className":138965,"style":12529},[642],[363,138967,138968,138971],{"style":730},[363,138969],{"className":138970,"style":651},[650],[363,138972,138974],{"className":138973},[655,656,657,658],[363,138975,12310],{"className":138976},[407,408,658],[363,138978,666],{"className":138979},[665],[363,138981,138983],{"className":138982},[638],[363,138984,138986],{"className":138985,"style":8315},[642],[363,138987],{},[363,138989],{"className":138990,"style":506},[505],[363,138992,3250],{"className":138993},[510],[363,138995],{"className":138996,"style":506},[505],[363,138998,139000,139003],{"className":138999},[398],[363,139001],{"className":139002,"style":520},[402],[363,139004,474],{"className":139005},[407],[363,139007,139009,139037],{"className":139008,"translate":367},[366],[363,139010,139012],{"className":139011},[371],[373,139013,139014],{"xmlns":375},[377,139015,139016,139034],{},[380,139017,139018,139020,139022],{},[383,139019,1121],{"mathvariant":75560},[458,139021,6256],{},[7161,139023,139024,139026],{},[383,139025,126023],{"mathvariant":557},[380,139027,139028,139030,139032],{},[383,139029,11041],{},[458,139031,5160],{},[463,139033,465],{},[387,139035,139036],{"encoding":389},"\\mathbf{x} \\in \\Delta^{K-1}",[363,139038,139040,139058],{"className":139039,"ariaHidden":394},[393],[363,139041,139043,139046,139049,139052,139055],{"className":139042},[398],[363,139044],{"className":139045,"style":6271},[402],[363,139047,1121],{"className":139048},[407,75905],[363,139050],{"className":139051,"style":506},[505],[363,139053,6256],{"className":139054},[510],[363,139056],{"className":139057,"style":506},[505],[363,139059,139061,139064],{"className":139060},[398],[363,139062],{"className":139063,"style":52432},[402],[363,139065,139067,139070],{"className":139066},[407],[363,139068,126023],{"className":139069},[407],[363,139071,139073],{"className":139072},[629],[363,139074,139076],{"className":139075},[633],[363,139077,139079],{"className":139078},[638],[363,139080,139082],{"className":139081,"style":52432},[642],[363,139083,139084,139087],{"style":7212},[363,139085],{"className":139086,"style":651},[650],[363,139088,139090],{"className":139089},[655,656,657,658],[363,139091,139093,139096,139099],{"className":139092},[407,658],[363,139094,11041],{"className":139095,"style":11129},[407,408,658],[363,139097,5160],{"className":139098},[2938,658],[363,139100,465],{"className":139101},[407,658],"。该替换的 Jacobi 行列式绝对值为 ",[363,139104,139106,139143],{"className":139105,"translate":367},[366],[363,139107,139109],{"className":139108},[371],[373,139110,139111],{"xmlns":375},[377,139112,139113,139140],{},[380,139114,139115,139117,139120,139122,139124,139126,139128],{},[383,139116,5155],{"mathvariant":557},[383,139118,139119],{},"det",[458,139121,4450],{},[383,139123,24090],{},[383,139125,5155],{"mathvariant":557},[458,139127,471],{},[7161,139129,139130,139132],{},[383,139131,7908],{},[380,139133,139134,139136,139138],{},[383,139135,11041],{},[458,139137,5160],{},[463,139139,465],{},[387,139141,139142],{"encoding":389},"|\\det J| = s^{K-1}",[363,139144,139146,139179],{"className":139145,"ariaHidden":394},[393],[363,139147,139149,139152,139155,139158,139161,139164,139167,139170,139173,139176],{"className":139148},[398],[363,139150],{"className":139151,"style":487},[402],[363,139153,5155],{"className":139154},[407],[363,139156],{"className":139157,"style":754},[505],[363,139159,139119],{"className":139160},[1831],[363,139162],{"className":139163,"style":754},[505],[363,139165,24090],{"className":139166,"style":24500},[407,408],[363,139168,5155],{"className":139169},[407],[363,139171],{"className":139172,"style":506},[505],[363,139174,471],{"className":139175},[510],[363,139177],{"className":139178,"style":506},[505],[363,139180,139182,139185],{"className":139181},[398],[363,139183],{"className":139184,"style":52432},[402],[363,139186,139188,139191],{"className":139187},[407],[363,139189,7908],{"className":139190},[407,408],[363,139192,139194],{"className":139193},[629],[363,139195,139197],{"className":139196},[633],[363,139198,139200],{"className":139199},[638],[363,139201,139203],{"className":139202,"style":52432},[642],[363,139204,139205,139208],{"style":7212},[363,139206],{"className":139207,"style":651},[650],[363,139209,139211],{"className":139210},[655,656,657,658],[363,139212,139214,139217,139220],{"className":139213},[407,658],[363,139215,11041],{"className":139216,"style":11129},[407,408,658],[363,139218,5160],{"className":139219},[2938,658],[363,139221,465],{"className":139222},[407,658],"（可由 ",[363,139225,139227,139244],{"className":139226,"translate":367},[366],[363,139228,139230],{"className":139229},[371],[373,139231,139232],{"xmlns":375},[377,139233,139234,139242],{},[380,139235,139236,139238,139240],{},[383,139237,11041],{},[458,139239,471],{},[463,139241,2810],{},[387,139243,135042],{"encoding":389},[363,139245,139247,139265],{"className":139246,"ariaHidden":394},[393],[363,139248,139250,139253,139256,139259,139262],{"className":139249},[398],[363,139251],{"className":139252,"style":1011},[402],[363,139254,11041],{"className":139255,"style":11129},[407,408],[363,139257],{"className":139258,"style":506},[505],[363,139260,471],{"className":139261},[510],[363,139263],{"className":139264,"style":506},[505],[363,139266,139268,139271],{"className":139267},[398],[363,139269],{"className":139270,"style":520},[402],[363,139272,2810],{"className":139273},[407]," 时的 ",[363,139276,139278,139350],{"className":139277,"translate":367},[366],[363,139279,139281],{"className":139280},[371],[373,139282,139283],{"xmlns":375},[377,139284,139285,139347],{},[380,139286,139287,139289,139291,139341,139343,139345],{},[383,139288,139119],{},[458,139290,4450],{},[380,139292,139293,139295,139339],{},[458,139294,461],{"fence":394},[1590,139296,139299,139317],{"rowspacing":139297,"columnalign":139298,"columnspacing":4662},"0.16em","center center",[1596,139300,139301,139311],{},[1599,139302,139303],{},[1602,139304,139305],{"scriptlevel":474,"displaystyle":460},[543,139306,139307,139309],{},[383,139308,1121],{},[463,139310,465],{},[1599,139312,139313],{},[1602,139314,139315],{"scriptlevel":474,"displaystyle":460},[383,139316,7908],{},[1596,139318,139319,139329],{},[1599,139320,139321],{},[1602,139322,139323],{"scriptlevel":474,"displaystyle":460},[543,139324,139325,139327],{},[383,139326,1121],{},[463,139328,2810],{},[1599,139330,139331],{},[1602,139332,139333],{"scriptlevel":474,"displaystyle":460},[380,139334,139335,139337],{},[458,139336,5160],{},[383,139338,7908],{},[458,139340,468],{"fence":394},[458,139342,471],{},[458,139344,5160],{},[383,139346,7908],{},[387,139348,139349],{"encoding":389},"\\det\\begin{pmatrix} x_1 & s \\\\ x_2 & -s\\end{pmatrix} = -s",[363,139351,139353,139572],{"className":139352,"ariaHidden":394},[393],[363,139354,139356,139359,139362,139365,139563,139566,139569],{"className":139355},[398],[363,139357],{"className":139358,"style":707},[402],[363,139360,139119],{"className":139361},[1831],[363,139363],{"className":139364,"style":754},[505],[363,139366,139368,139374,139557],{"className":139367},[758],[363,139369,139371],{"className":139370,"style":763},[494,762],[363,139372,461],{"className":139373},[767,657],[363,139375,139377],{"className":139376},[407],[363,139378,139380,139502,139506,139509],{"className":139379},[1590],[363,139381,139384],{"className":139382},[139383],"col-align-c",[363,139385,139387,139494],{"className":139386},[633,634],[363,139388,139390,139491],{"className":139389},[638],[363,139391,139393,139442],{"className":139392,"style":1717},[642],[363,139394,139396,139399],{"style":139395},"top:-3.61em;",[363,139397],{"className":139398,"style":809},[650],[363,139400,139402],{"className":139401},[407],[363,139403,139405,139408],{"className":139404},[407],[363,139406,1121],{"className":139407},[407,408],[363,139409,139411],{"className":139410},[629],[363,139412,139414,139434],{"className":139413},[633,634],[363,139415,139417,139431],{"className":139416},[638],[363,139418,139420],{"className":139419,"style":11480},[642],[363,139421,139422,139425],{"style":730},[363,139423],{"className":139424,"style":651},[650],[363,139426,139428],{"className":139427},[655,656,657,658],[363,139429,465],{"className":139430},[407,658],[363,139432,666],{"className":139433},[665],[363,139435,139437],{"className":139436},[638],[363,139438,139440],{"className":139439,"style":8315},[642],[363,139441],{},[363,139443,139445,139448],{"style":139444},"top:-2.41em;",[363,139446],{"className":139447,"style":809},[650],[363,139449,139451],{"className":139450},[407],[363,139452,139454,139457],{"className":139453},[407],[363,139455,1121],{"className":139456},[407,408],[363,139458,139460],{"className":139459},[629],[363,139461,139463,139483],{"className":139462},[633,634],[363,139464,139466,139480],{"className":139465},[638],[363,139467,139469],{"className":139468,"style":11480},[642],[363,139470,139471,139474],{"style":730},[363,139472],{"className":139473,"style":651},[650],[363,139475,139477],{"className":139476},[655,656,657,658],[363,139478,2810],{"className":139479},[407,658],[363,139481,666],{"className":139482},[665],[363,139484,139486],{"className":139485},[638],[363,139487,139489],{"className":139488,"style":8315},[642],[363,139490],{},[363,139492,666],{"className":139493},[665],[363,139495,139497],{"className":139496},[638],[363,139498,139500],{"className":139499,"style":1792},[642],[363,139501],{},[363,139503],{"className":139504,"style":139505},[4968],"width:0.5em;",[363,139507],{"className":139508,"style":139505},[4968],[363,139510,139512],{"className":139511},[139383],[363,139513,139515,139549],{"className":139514},[633,634],[363,139516,139518,139546],{"className":139517},[638],[363,139519,139521,139532],{"className":139520,"style":1717},[642],[363,139522,139523,139526],{"style":139395},[363,139524],{"className":139525,"style":809},[650],[363,139527,139529],{"className":139528},[407],[363,139530,7908],{"className":139531},[407,408],[363,139533,139534,139537],{"style":139444},[363,139535],{"className":139536,"style":809},[650],[363,139538,139540,139543],{"className":139539},[407],[363,139541,5160],{"className":139542},[407],[363,139544,7908],{"className":139545},[407,408],[363,139547,666],{"className":139548},[665],[363,139550,139552],{"className":139551},[638],[363,139553,139555],{"className":139554,"style":1792},[642],[363,139556],{},[363,139558,139560],{"className":139559,"style":763},[501,762],[363,139561,468],{"className":139562},[767,657],[363,139564],{"className":139565,"style":506},[505],[363,139567,471],{"className":139568},[510],[363,139570],{"className":139571,"style":506},[505],[363,139573,139575,139578,139581],{"className":139574},[398],[363,139576],{"className":139577,"style":4598},[402],[363,139579,5160],{"className":139580},[407],[363,139582,7908],{"className":139583},[407,408]," 归纳验证）。代入得",[363,139586,139588],{"className":139587,"translate":367},[528],[363,139589,139591,139745],{"className":139590,"translate":367},[366],[363,139592,139594],{"className":139593},[371],[373,139595,139596],{"xmlns":375,"display":537},[377,139597,139598,139742],{},[380,139599,139600,139614,139616,139618,139624,139626,139628,139636,139638,139640,139656,139668,139682,139684,139686,139692,139708,139730,139732,139734,139736,139738,139740],{},[48667,139601,139602,139604,139612],{},[458,139603,136637],{},[380,139605,139606,139608,139610],{},[383,139607,12310],{},[458,139609,471],{},[463,139611,465],{},[383,139613,11041],{},[383,139615,137171],{"mathvariant":557},[458,139617,461],{"stretchy":460},[543,139619,139620,139622],{},[383,139621,45101],{},[383,139623,12310],{},[458,139625,468],{"stretchy":460},[458,139627,471],{},[7900,139629,139630,139632,139634],{},[458,139631,1634],{},[463,139633,474],{},[383,139635,1371],{"mathvariant":557},[1644,139637,1651],{},[1644,139639,1651],{},[543,139641,139642,139644],{},[458,139643,1634],{},[7161,139645,139646,139648],{},[383,139647,126023],{"mathvariant":557},[380,139649,139650,139652,139654],{},[383,139651,11041],{},[458,139653,5160],{},[463,139655,465],{},[7161,139657,139658,139660],{},[383,139659,7908],{},[380,139661,139662,139664,139666],{},[383,139663,11041],{},[458,139665,5160],{},[463,139667,465],{},[48667,139669,139670,139672,139680],{},[458,139671,136637],{},[380,139673,139674,139676,139678],{},[383,139675,12310],{},[458,139677,471],{},[463,139679,465],{},[383,139681,11041],{},[458,139683,461],{"stretchy":460},[383,139685,7908],{},[543,139687,139688,139690],{},[383,139689,1121],{},[383,139691,12310],{},[7161,139693,139694,139696],{},[458,139695,468],{"stretchy":460},[380,139697,139698,139704,139706],{},[543,139699,139700,139702],{},[383,139701,45101],{},[383,139703,12310],{},[458,139705,5160],{},[463,139707,465],{},[7161,139709,139710,139712],{},[383,139711,7914],{},[380,139713,139714,139716,139718,139724],{},[458,139715,5160],{},[383,139717,7908],{},[6363,139719,139720,139722],{},[458,139721,13808],{},[383,139723,12310],{},[543,139725,139726,139728],{},[383,139727,1121],{},[383,139729,12310],{},[1644,139731,1646],{},[383,139733,592],{"mathvariant":557},[383,139735,1121],{"mathvariant":75560},[1644,139737,1646],{},[383,139739,592],{"mathvariant":557},[383,139741,7908],{},[387,139743,139744],{"encoding":389},"\\prod_{i=1}^K \\Gamma(\\alpha_i) = \\int_0^\\infty \\!\\!\\int_{\\Delta^{K-1}} s^{K-1} \\prod_{i=1}^K (s x_i)^{\\alpha_i - 1} e^{-s \\sum_i x_i} \\,\\mathrm{d}\\mathbf{x} \\,\\mathrm{d}s",[363,139746,139748,139879],{"className":139747,"ariaHidden":394},[393],[363,139749,139751,139754,139818,139821,139824,139827,139867,139870,139873,139876],{"className":139750},[398],[363,139752],{"className":139753,"style":138212},[402],[363,139755,139757],{"className":139756},[1831,14063],[363,139758,139760,139810],{"className":139759},[633,634],[363,139761,139763,139807],{"className":139762},[638],[363,139764,139766,139786,139796],{"className":139765,"style":138225},[642],[363,139767,139768,139771],{"style":14076},[363,139769],{"className":139770,"style":14080},[650],[363,139772,139774],{"className":139773},[655,656,657,658],[363,139775,139777,139780,139783],{"className":139776},[407,658],[363,139778,12310],{"className":139779},[407,408,658],[363,139781,471],{"className":139782},[510,658],[363,139784,465],{"className":139785},[407,658],[363,139787,139788,139791],{"style":14089},[363,139789],{"className":139790,"style":14080},[650],[363,139792,139793],{},[363,139794,136637],{"className":139795},[1831,1832,1833],[363,139797,139798,139801],{"style":100671},[363,139799],{"className":139800,"style":14080},[650],[363,139802,139804],{"className":139803},[655,656,657,658],[363,139805,11041],{"className":139806,"style":11129},[407,408,658],[363,139808,666],{"className":139809},[665],[363,139811,139813],{"className":139812},[638],[363,139814,139816],{"className":139815,"style":14107},[642],[363,139817],{},[363,139819],{"className":139820,"style":754},[505],[363,139822,137171],{"className":139823},[407],[363,139825,461],{"className":139826},[494],[363,139828,139830,139833],{"className":139829},[407],[363,139831,45101],{"className":139832,"style":45131},[407,408],[363,139834,139836],{"className":139835},[629],[363,139837,139839,139859],{"className":139838},[633,634],[363,139840,139842,139856],{"className":139841},[638],[363,139843,139845],{"className":139844,"style":12529},[642],[363,139846,139847,139850],{"style":136107},[363,139848],{"className":139849,"style":651},[650],[363,139851,139853],{"className":139852},[655,656,657,658],[363,139854,12310],{"className":139855},[407,408,658],[363,139857,666],{"className":139858},[665],[363,139860,139862],{"className":139861},[638],[363,139863,139865],{"className":139864,"style":8315},[642],[363,139866],{},[363,139868,468],{"className":139869},[501],[363,139871],{"className":139872,"style":506},[505],[363,139874,471],{"className":139875},[510],[363,139877],{"className":139878,"style":506},[505],[363,139880,139882,139885,139939,139942,139945,139948,140027,140030,140068,140071,140135,140138,140141,140181,140256,140378,140381,140384,140387,140390,140393],{"className":139881},[398],[363,139883],{"className":139884,"style":138212},[402],[363,139886,139888,139891],{"className":139887},[1831],[363,139889,1634],{"className":139890,"style":1834},[1831,1832,1833],[363,139892,139894],{"className":139893},[629],[363,139895,139897,139930],{"className":139896},[633,634],[363,139898,139900,139927],{"className":139899},[638],[363,139901,139904,139915],{"className":139902,"style":139903},[642],"height:1.4143em;",[363,139905,139906,139909],{"style":3825},[363,139907],{"className":139908,"style":651},[650],[363,139910,139912],{"className":139911},[655,656,657,658],[363,139913,474],{"className":139914},[407,658],[363,139916,139918,139921],{"style":139917},"top:-3.8129em;margin-right:0.05em;",[363,139919],{"className":139920,"style":651},[650],[363,139922,139924],{"className":139923},[655,656,657,658],[363,139925,1371],{"className":139926},[407,658],[363,139928,666],{"className":139929},[665],[363,139931,139933],{"className":139932},[638],[363,139934,139937],{"className":139935,"style":139936},[642],"height:0.9119em;",[363,139938],{},[363,139940],{"className":139941,"style":1859},[505],[363,139943],{"className":139944,"style":1859},[505],[363,139946],{"className":139947,"style":754},[505],[363,139949,139951,139954],{"className":139950},[1831],[363,139952,1634],{"className":139953,"style":1834},[1831,1832,1833],[363,139955,139957],{"className":139956},[629],[363,139958,139960,140019],{"className":139959},[633,634],[363,139961,139963,140016],{"className":139962},[638],[363,139964,139967],{"className":139965,"style":139966},[642],"height:-0.3701em;",[363,139968,139969,139972],{"style":3825},[363,139970],{"className":139971,"style":651},[650],[363,139973,139975],{"className":139974},[655,656,657,658],[363,139976,139978],{"className":139977},[407,658],[363,139979,139981,139984],{"className":139980},[407,658],[363,139982,126023],{"className":139983},[407,658],[363,139985,139987],{"className":139986},[629],[363,139988,139990],{"className":139989},[633],[363,139991,139993],{"className":139992},[638],[363,139994,139996],{"className":139995,"style":137751},[642],[363,139997,139998,140001],{"style":45809},[363,139999],{"className":140000,"style":30553},[650],[363,140002,140004],{"className":140003},[655,30557,10021,658],[363,140005,140007,140010,140013],{"className":140006},[407,658],[363,140008,11041],{"className":140009,"style":11129},[407,408,658],[363,140011,5160],{"className":140012},[2938,658],[363,140014,465],{"className":140015},[407,658],[363,140017,666],{"className":140018},[665],[363,140020,140022],{"className":140021},[638],[363,140023,140025],{"className":140024,"style":139936},[642],[363,140026],{},[363,140028],{"className":140029,"style":754},[505],[363,140031,140033,140036],{"className":140032},[407],[363,140034,7908],{"className":140035},[407,408],[363,140037,140039],{"className":140038},[629],[363,140040,140042],{"className":140041},[633],[363,140043,140045],{"className":140044},[638],[363,140046,140048],{"className":140047,"style":38859},[642],[363,140049,140050,140053],{"style":8624},[363,140051],{"className":140052,"style":651},[650],[363,140054,140056],{"className":140055},[655,656,657,658],[363,140057,140059,140062,140065],{"className":140058},[407,658],[363,140060,11041],{"className":140061,"style":11129},[407,408,658],[363,140063,5160],{"className":140064},[2938,658],[363,140066,465],{"className":140067},[407,658],[363,140069],{"className":140070,"style":754},[505],[363,140072,140074],{"className":140073},[1831,14063],[363,140075,140077,140127],{"className":140076},[633,634],[363,140078,140080,140124],{"className":140079},[638],[363,140081,140083,140103,140113],{"className":140082,"style":138225},[642],[363,140084,140085,140088],{"style":14076},[363,140086],{"className":140087,"style":14080},[650],[363,140089,140091],{"className":140090},[655,656,657,658],[363,140092,140094,140097,140100],{"className":140093},[407,658],[363,140095,12310],{"className":140096},[407,408,658],[363,140098,471],{"className":140099},[510,658],[363,140101,465],{"className":140102},[407,658],[363,140104,140105,140108],{"style":14089},[363,140106],{"className":140107,"style":14080},[650],[363,140109,140110],{},[363,140111,136637],{"className":140112},[1831,1832,1833],[363,140114,140115,140118],{"style":100671},[363,140116],{"className":140117,"style":14080},[650],[363,140119,140121],{"className":140120},[655,656,657,658],[363,140122,11041],{"className":140123,"style":11129},[407,408,658],[363,140125,666],{"className":140126},[665],[363,140128,140130],{"className":140129},[638],[363,140131,140133],{"className":140132,"style":14107},[642],[363,140134],{},[363,140136,461],{"className":140137},[494],[363,140139,7908],{"className":140140},[407,408],[363,140142,140144,140147],{"className":140143},[407],[363,140145,1121],{"className":140146},[407,408],[363,140148,140150],{"className":140149},[629],[363,140151,140153,140173],{"className":140152},[633,634],[363,140154,140156,140170],{"className":140155},[638],[363,140157,140159],{"className":140158,"style":12529},[642],[363,140160,140161,140164],{"style":730},[363,140162],{"className":140163,"style":651},[650],[363,140165,140167],{"className":140166},[655,656,657,658],[363,140168,12310],{"className":140169},[407,408,658],[363,140171,666],{"className":140172},[665],[363,140174,140176],{"className":140175},[638],[363,140177,140179],{"className":140178,"style":8315},[642],[363,140180],{},[363,140182,140184,140187],{"className":140183},[501],[363,140185,468],{"className":140186},[501],[363,140188,140190],{"className":140189},[629],[363,140191,140193],{"className":140192},[633],[363,140194,140196],{"className":140195},[638],[363,140197,140199],{"className":140198,"style":20082},[642],[363,140200,140201,140204],{"style":8624},[363,140202],{"className":140203,"style":651},[650],[363,140205,140207],{"className":140206},[655,656,657,658],[363,140208,140210,140250,140253],{"className":140209},[407,658],[363,140211,140213,140216],{"className":140212},[407,658],[363,140214,45101],{"className":140215,"style":45131},[407,408,658],[363,140217,140219],{"className":140218},[629],[363,140220,140222,140242],{"className":140221},[633,634],[363,140223,140225,140239],{"className":140224},[638],[363,140226,140228],{"className":140227,"style":40095},[642],[363,140229,140230,140233],{"style":136942},[363,140231],{"className":140232,"style":30553},[650],[363,140234,140236],{"className":140235},[655,30557,10021,658],[363,140237,12310],{"className":140238},[407,408,658],[363,140240,666],{"className":140241},[665],[363,140243,140245],{"className":140244},[638],[363,140246,140248],{"className":140247,"style":40117},[642],[363,140249],{},[363,140251,5160],{"className":140252},[2938,658],[363,140254,465],{"className":140255},[407,658],[363,140257,140259,140262],{"className":140258},[407],[363,140260,7914],{"className":140261},[407,408],[363,140263,140265],{"className":140264},[629],[363,140266,140268],{"className":140267},[633],[363,140269,140271],{"className":140270},[638],[363,140272,140274],{"className":140273,"style":45467},[642],[363,140275,140276,140279],{"style":8624},[363,140277],{"className":140278,"style":651},[650],[363,140280,140282],{"className":140281},[655,656,657,658],[363,140283,140285,140288,140291,140294,140335,140338],{"className":140284},[407,658],[363,140286,5160],{"className":140287},[407,658],[363,140289,7908],{"className":140290},[407,408,658],[363,140292],{"className":140293,"style":42713},[505,658],[363,140295,140297,140300],{"className":140296},[1831,658],[363,140298,13808],{"className":140299,"style":40007},[1831,1832,5963,658],[363,140301,140303],{"className":140302},[629],[363,140304,140306,140327],{"className":140305},[633,634],[363,140307,140309,140324],{"className":140308},[638],[363,140310,140313],{"className":140311,"style":140312},[642],"height:0.1496em;",[363,140314,140315,140318],{"style":137374},[363,140316],{"className":140317,"style":30553},[650],[363,140319,140321],{"className":140320},[655,30557,10021,658],[363,140322,12310],{"className":140323},[407,408,658],[363,140325,666],{"className":140326},[665],[363,140328,140330],{"className":140329},[638],[363,140331,140333],{"className":140332,"style":137413},[642],[363,140334],{},[363,140336],{"className":140337,"style":42713},[505,658],[363,140339,140341,140344],{"className":140340},[407,658],[363,140342,1121],{"className":140343},[407,408,658],[363,140345,140347],{"className":140346},[629],[363,140348,140350,140370],{"className":140349},[633,634],[363,140351,140353,140367],{"className":140352},[638],[363,140354,140356],{"className":140355,"style":40095},[642],[363,140357,140358,140361],{"style":74612},[363,140359],{"className":140360,"style":30553},[650],[363,140362,140364],{"className":140363},[655,30557,10021,658],[363,140365,12310],{"className":140366},[407,408,658],[363,140368,666],{"className":140369},[665],[363,140371,140373],{"className":140372},[638],[363,140374,140376],{"className":140375,"style":40117},[642],[363,140377],{},[363,140379],{"className":140380,"style":754},[505],[363,140382,592],{"className":140383},[407,33009],[363,140385,1121],{"className":140386},[407,75905],[363,140388],{"className":140389,"style":754},[505],[363,140391,592],{"className":140392},[407,33009],[363,140394,7908],{"className":140395},[407,408],[11,140397,140398,140399,140540,140541,140569,140570,140813,140814,140883,140884,140912],{},"利用约束 ",[363,140400,140402,140430],{"className":140401,"translate":367},[366],[363,140403,140405],{"className":140404},[371],[373,140406,140407],{"xmlns":375},[377,140408,140409,140427],{},[380,140410,140411,140417,140423,140425],{},[543,140412,140413,140415],{},[458,140414,13808],{},[383,140416,12310],{},[543,140418,140419,140421],{},[383,140420,1121],{},[383,140422,12310],{},[458,140424,471],{},[463,140426,465],{},[387,140428,140429],{"encoding":389},"\\sum_i x_i = 1",[363,140431,140433,140531],{"className":140432,"ariaHidden":394},[393],[363,140434,140436,140439,140479,140482,140522,140525,140528],{"className":140435},[398],[363,140437],{"className":140438,"style":138904},[402],[363,140440,140442,140445],{"className":140441},[1831],[363,140443,13808],{"className":140444,"style":40007},[1831,1832,5963],[363,140446,140448],{"className":140447},[629],[363,140449,140451,140471],{"className":140450},[633,634],[363,140452,140454,140468],{"className":140453},[638],[363,140455,140457],{"className":140456,"style":40020},[642],[363,140458,140459,140462],{"style":40023},[363,140460],{"className":140461,"style":651},[650],[363,140463,140465],{"className":140464},[655,656,657,658],[363,140466,12310],{"className":140467},[407,408,658],[363,140469,666],{"className":140470},[665],[363,140472,140474],{"className":140473},[638],[363,140475,140477],{"className":140476,"style":40042},[642],[363,140478],{},[363,140480],{"className":140481,"style":754},[505],[363,140483,140485,140488],{"className":140484},[407],[363,140486,1121],{"className":140487},[407,408],[363,140489,140491],{"className":140490},[629],[363,140492,140494,140514],{"className":140493},[633,634],[363,140495,140497,140511],{"className":140496},[638],[363,140498,140500],{"className":140499,"style":12529},[642],[363,140501,140502,140505],{"style":730},[363,140503],{"className":140504,"style":651},[650],[363,140506,140508],{"className":140507},[655,656,657,658],[363,140509,12310],{"className":140510},[407,408,658],[363,140512,666],{"className":140513},[665],[363,140515,140517],{"className":140516},[638],[363,140518,140520],{"className":140519,"style":8315},[642],[363,140521],{},[363,140523],{"className":140524,"style":506},[505],[363,140526,471],{"className":140527},[510],[363,140529],{"className":140530,"style":506},[505],[363,140532,140534,140537],{"className":140533},[398],[363,140535],{"className":140536,"style":520},[402],[363,140538,465],{"className":140539},[407],"，被积函数中的 ",[363,140542,140544,140557],{"className":140543,"translate":367},[366],[363,140545,140547],{"className":140546},[371],[373,140548,140549],{"xmlns":375},[377,140550,140551,140555],{},[380,140552,140553],{},[383,140554,7908],{},[387,140556,7908],{"encoding":389},[363,140558,140560],{"className":140559,"ariaHidden":394},[393],[363,140561,140563,140566],{"className":140562},[398],[363,140564],{"className":140565,"style":2692},[402],[363,140567,7908],{"className":140568},[407,408]," 因子合并为 ",[363,140571,140573,140627],{"className":140572,"translate":367},[366],[363,140574,140576],{"className":140575},[371],[373,140577,140578],{"xmlns":375},[377,140579,140580,140624],{},[380,140581,140582,140606,140608],{},[7161,140583,140584,140586],{},[383,140585,7908],{},[380,140587,140588,140590,140592,140594,140596,140602,140604],{},[383,140589,11041],{},[458,140591,5160],{},[463,140593,465],{},[458,140595,2817],{},[543,140597,140598,140600],{},[383,140599,45101],{},[463,140601,474],{},[458,140603,5160],{},[383,140605,11041],{},[458,140607,471],{},[7161,140609,140610,140612],{},[383,140611,7908],{},[380,140613,140614,140620,140622],{},[543,140615,140616,140618],{},[383,140617,45101],{},[463,140619,474],{},[458,140621,5160],{},[463,140623,465],{},[387,140625,140626],{"encoding":389},"s^{K - 1 + \\alpha_0 - K} = s^{\\alpha_0 - 1}",[363,140628,140630,140732],{"className":140629,"ariaHidden":394},[393],[363,140631,140633,140636,140723,140726,140729],{"className":140632},[398],[363,140634],{"className":140635,"style":52432},[402],[363,140637,140639,140642],{"className":140638},[407],[363,140640,7908],{"className":140641},[407,408],[363,140643,140645],{"className":140644},[629],[363,140646,140648],{"className":140647},[633],[363,140649,140651],{"className":140650},[638],[363,140652,140654],{"className":140653,"style":52432},[642],[363,140655,140656,140659],{"style":7212},[363,140657],{"className":140658,"style":651},[650],[363,140660,140662],{"className":140661},[655,656,657,658],[363,140663,140665,140668,140671,140674,140677,140717,140720],{"className":140664},[407,658],[363,140666,11041],{"className":140667,"style":11129},[407,408,658],[363,140669,5160],{"className":140670},[2938,658],[363,140672,465],{"className":140673},[407,658],[363,140675,2817],{"className":140676},[2938,658],[363,140678,140680,140683],{"className":140679},[407,658],[363,140681,45101],{"className":140682,"style":45131},[407,408,658],[363,140684,140686],{"className":140685},[629],[363,140687,140689,140709],{"className":140688},[633,634],[363,140690,140692,140706],{"className":140691},[638],[363,140693,140695],{"className":140694,"style":137304},[642],[363,140696,140697,140700],{"style":136942},[363,140698],{"className":140699,"style":30553},[650],[363,140701,140703],{"className":140702},[655,30557,10021,658],[363,140704,474],{"className":140705},[407,658],[363,140707,666],{"className":140708},[665],[363,140710,140712],{"className":140711},[638],[363,140713,140715],{"className":140714,"style":40117},[642],[363,140716],{},[363,140718,5160],{"className":140719},[2938,658],[363,140721,11041],{"className":140722,"style":11129},[407,408,658],[363,140724],{"className":140725,"style":506},[505],[363,140727,471],{"className":140728},[510],[363,140730],{"className":140731,"style":506},[505],[363,140733,140735,140738],{"className":140734},[398],[363,140736],{"className":140737,"style":20375},[402],[363,140739,140741,140744],{"className":140740},[407],[363,140742,7908],{"className":140743},[407,408],[363,140745,140747],{"className":140746},[629],[363,140748,140750],{"className":140749},[633],[363,140751,140753],{"className":140752},[638],[363,140754,140756],{"className":140755,"style":20375},[642],[363,140757,140758,140761],{"style":7212},[363,140759],{"className":140760,"style":651},[650],[363,140762,140764],{"className":140763},[655,656,657,658],[363,140765,140767,140807,140810],{"className":140766},[407,658],[363,140768,140770,140773],{"className":140769},[407,658],[363,140771,45101],{"className":140772,"style":45131},[407,408,658],[363,140774,140776],{"className":140775},[629],[363,140777,140779,140799],{"className":140778},[633,634],[363,140780,140782,140796],{"className":140781},[638],[363,140783,140785],{"className":140784,"style":137304},[642],[363,140786,140787,140790],{"style":136942},[363,140788],{"className":140789,"style":30553},[650],[363,140791,140793],{"className":140792},[655,30557,10021,658],[363,140794,474],{"className":140795},[407,658],[363,140797,666],{"className":140798},[665],[363,140800,140802],{"className":140801},[638],[363,140803,140805],{"className":140804,"style":40117},[642],[363,140806],{},[363,140808,5160],{"className":140809},[2938,658],[363,140811,465],{"className":140812},[407,658],"，指数因子合并为 ",[363,140815,140817,140839],{"className":140816,"translate":367},[366],[363,140818,140820],{"className":140819},[371],[373,140821,140822],{"xmlns":375},[377,140823,140824,140836],{},[380,140825,140826],{},[7161,140827,140828,140830],{},[383,140829,7914],{},[380,140831,140832,140834],{},[458,140833,5160],{},[383,140835,7908],{},[387,140837,140838],{"encoding":389},"e^{-s}",[363,140840,140842],{"className":140841,"ariaHidden":394},[393],[363,140843,140845,140848],{"className":140844},[398],[363,140846],{"className":140847,"style":21356},[402],[363,140849,140851,140854],{"className":140850},[407],[363,140852,7914],{"className":140853},[407,408],[363,140855,140857],{"className":140856},[629],[363,140858,140860],{"className":140859},[633],[363,140861,140863],{"className":140862},[638],[363,140864,140866],{"className":140865,"style":21356},[642],[363,140867,140868,140871],{"style":7212},[363,140869],{"className":140870,"style":651},[650],[363,140872,140874],{"className":140873},[655,656,657,658],[363,140875,140877,140880],{"className":140876},[407,658],[363,140878,5160],{"className":140879},[407,658],[363,140881,7908],{"className":140882},[407,408,658],"，二者均与 ",[363,140885,140887,140900],{"className":140886,"translate":367},[366],[363,140888,140890],{"className":140889},[371],[373,140891,140892],{"xmlns":375},[377,140893,140894,140898],{},[380,140895,140896],{},[383,140897,1121],{"mathvariant":75560},[387,140899,135607],{"encoding":389},[363,140901,140903],{"className":140902,"ariaHidden":394},[393],[363,140904,140906,140909],{"className":140905},[398],[363,140907],{"className":140908,"style":135617},[402],[363,140910,1121],{"className":140911},[407,75905]," 解耦：",[363,140914,140916],{"className":140915,"translate":367},[528],[363,140917,140919,141135],{"className":140918,"translate":367},[366],[363,140920,140922],{"className":140921},[371],[373,140923,140924],{"xmlns":375,"display":537},[377,140925,140926,141132],{},[380,140927,140928,140942,140944,140946,140952,140954,140956,141002,141062,141064,141066,141068,141070,141076,141078,141094,141108,141126,141128,141130],{},[48667,140929,140930,140932,140940],{},[458,140931,136637],{},[380,140933,140934,140936,140938],{},[383,140935,12310],{},[458,140937,471],{},[463,140939,465],{},[383,140941,11041],{},[383,140943,137171],{"mathvariant":557},[458,140945,461],{"stretchy":460},[543,140947,140948,140950],{},[383,140949,45101],{},[383,140951,12310],{},[458,140953,468],{"stretchy":460},[458,140955,471],{},[380,140957,140958,140960,140968,140984,140994,140996,140998,141000],{},[458,140959,461],{"fence":394},[7900,140961,140962,140964,140966],{},[458,140963,1634],{},[463,140965,474],{},[383,140967,1371],{"mathvariant":557},[7161,140969,140970,140972],{},[383,140971,7908],{},[380,140973,140974,140980,140982],{},[543,140975,140976,140978],{},[383,140977,45101],{},[463,140979,474],{},[458,140981,5160],{},[463,140983,465],{},[7161,140985,140986,140988],{},[383,140987,7914],{},[380,140989,140990,140992],{},[458,140991,5160],{},[383,140993,7908],{},[1644,140995,1646],{},[383,140997,592],{"mathvariant":557},[383,140999,7908],{},[458,141001,468],{"fence":394},[380,141003,141004,141006,141022,141036,141054,141056,141058,141060],{},[458,141005,461],{"fence":394},[543,141007,141008,141010],{},[458,141009,1634],{},[7161,141011,141012,141014],{},[383,141013,126023],{"mathvariant":557},[380,141015,141016,141018,141020],{},[383,141017,11041],{},[458,141019,5160],{},[463,141021,465],{},[48667,141023,141024,141026,141034],{},[458,141025,136637],{},[380,141027,141028,141030,141032],{},[383,141029,12310],{},[458,141031,471],{},[463,141033,465],{},[383,141035,11041],{},[7900,141037,141038,141040,141042],{},[383,141039,1121],{},[383,141041,12310],{},[380,141043,141044,141050,141052],{},[543,141045,141046,141048],{},[383,141047,45101],{},[383,141049,12310],{},[458,141051,5160],{},[463,141053,465],{},[1644,141055,1646],{},[383,141057,592],{"mathvariant":557},[383,141059,1121],{"mathvariant":75560},[458,141061,468],{"fence":394},[458,141063,471],{},[505,141065],{"linebreak":24035},[383,141067,137171],{"mathvariant":557},[458,141069,461],{"stretchy":460},[543,141071,141072,141074],{},[383,141073,45101],{},[463,141075,474],{},[458,141077,468],{"stretchy":460},[543,141079,141080,141082],{},[458,141081,1634],{},[7161,141083,141084,141086],{},[383,141085,126023],{"mathvariant":557},[380,141087,141088,141090,141092],{},[383,141089,11041],{},[458,141091,5160],{},[463,141093,465],{},[48667,141095,141096,141098,141106],{},[458,141097,136637],{},[380,141099,141100,141102,141104],{},[383,141101,12310],{},[458,141103,471],{},[463,141105,465],{},[383,141107,11041],{},[7900,141109,141110,141112,141114],{},[383,141111,1121],{},[383,141113,12310],{},[380,141115,141116,141122,141124],{},[543,141117,141118,141120],{},[383,141119,45101],{},[383,141121,12310],{},[458,141123,5160],{},[463,141125,465],{},[1644,141127,1646],{},[383,141129,592],{"mathvariant":557},[383,141131,1121],{"mathvariant":75560},[387,141133,141134],{"encoding":389},"\\prod_{i=1}^K \\Gamma(\\alpha_i) = \\left(\\int_0^\\infty s^{\\alpha_0 - 1} e^{-s} \\,\\mathrm{d}s\\right) \\left(\\int_{\\Delta^{K-1}} \\prod_{i=1}^K x_i^{\\alpha_i - 1} \\,\\mathrm{d}\\mathbf{x}\\right) = \\\\ \\Gamma(\\alpha_0) \\int_{\\Delta^{K-1}} \\prod_{i=1}^K x_i^{\\alpha_i - 1} \\,\\mathrm{d}\\mathbf{x}",[363,141136,141138,141269,141742,141745],{"className":141137,"ariaHidden":394},[393],[363,141139,141141,141144,141208,141211,141214,141217,141257,141260,141263,141266],{"className":141140},[398],[363,141142],{"className":141143,"style":138212},[402],[363,141145,141147],{"className":141146},[1831,14063],[363,141148,141150,141200],{"className":141149},[633,634],[363,141151,141153,141197],{"className":141152},[638],[363,141154,141156,141176,141186],{"className":141155,"style":138225},[642],[363,141157,141158,141161],{"style":14076},[363,141159],{"className":141160,"style":14080},[650],[363,141162,141164],{"className":141163},[655,656,657,658],[363,141165,141167,141170,141173],{"className":141166},[407,658],[363,141168,12310],{"className":141169},[407,408,658],[363,141171,471],{"className":141172},[510,658],[363,141174,465],{"className":141175},[407,658],[363,141177,141178,141181],{"style":14089},[363,141179],{"className":141180,"style":14080},[650],[363,141182,141183],{},[363,141184,136637],{"className":141185},[1831,1832,1833],[363,141187,141188,141191],{"style":100671},[363,141189],{"className":141190,"style":14080},[650],[363,141192,141194],{"className":141193},[655,656,657,658],[363,141195,11041],{"className":141196,"style":11129},[407,408,658],[363,141198,666],{"className":141199},[665],[363,141201,141203],{"className":141202},[638],[363,141204,141206],{"className":141205,"style":14107},[642],[363,141207],{},[363,141209],{"className":141210,"style":754},[505],[363,141212,137171],{"className":141213},[407],[363,141215,461],{"className":141216},[494],[363,141218,141220,141223],{"className":141219},[407],[363,141221,45101],{"className":141222,"style":45131},[407,408],[363,141224,141226],{"className":141225},[629],[363,141227,141229,141249],{"className":141228},[633,634],[363,141230,141232,141246],{"className":141231},[638],[363,141233,141235],{"className":141234,"style":12529},[642],[363,141236,141237,141240],{"style":136107},[363,141238],{"className":141239,"style":651},[650],[363,141241,141243],{"className":141242},[655,656,657,658],[363,141244,12310],{"className":141245},[407,408,658],[363,141247,666],{"className":141248},[665],[363,141250,141252],{"className":141251},[638],[363,141253,141255],{"className":141254,"style":8315},[642],[363,141256],{},[363,141258,468],{"className":141259},[501],[363,141261],{"className":141262,"style":506},[505],[363,141264,471],{"className":141265},[510],[363,141267],{"className":141268,"style":506},[505],[363,141270,141272,141275,141464,141467,141736,141739],{"className":141271},[398],[363,141273],{"className":141274,"style":138212},[402],[363,141276,141278,141284,141335,141338,141413,141449,141452,141455,141458],{"className":141277},[758],[363,141279,141281],{"className":141280,"style":763},[494,762],[363,141282,461],{"className":141283},[767,657],[363,141285,141287,141290],{"className":141286},[1831],[363,141288,1634],{"className":141289,"style":1834},[1831,1832,1833],[363,141291,141293],{"className":141292},[629],[363,141294,141296,141327],{"className":141295},[633,634],[363,141297,141299,141324],{"className":141298},[638],[363,141300,141302,141313],{"className":141301,"style":139903},[642],[363,141303,141304,141307],{"style":3825},[363,141305],{"className":141306,"style":651},[650],[363,141308,141310],{"className":141309},[655,656,657,658],[363,141311,474],{"className":141312},[407,658],[363,141314,141315,141318],{"style":139917},[363,141316],{"className":141317,"style":651},[650],[363,141319,141321],{"className":141320},[655,656,657,658],[363,141322,1371],{"className":141323},[407,658],[363,141325,666],{"className":141326},[665],[363,141328,141330],{"className":141329},[638],[363,141331,141333],{"className":141332,"style":139936},[642],[363,141334],{},[363,141336],{"className":141337,"style":754},[505],[363,141339,141341,141344],{"className":141340},[407],[363,141342,7908],{"className":141343},[407,408],[363,141345,141347],{"className":141346},[629],[363,141348,141350],{"className":141349},[633],[363,141351,141353],{"className":141352},[638],[363,141354,141356],{"className":141355,"style":20082},[642],[363,141357,141358,141361],{"style":8624},[363,141359],{"className":141360,"style":651},[650],[363,141362,141364],{"className":141363},[655,656,657,658],[363,141365,141367,141407,141410],{"className":141366},[407,658],[363,141368,141370,141373],{"className":141369},[407,658],[363,141371,45101],{"className":141372,"style":45131},[407,408,658],[363,141374,141376],{"className":141375},[629],[363,141377,141379,141399],{"className":141378},[633,634],[363,141380,141382,141396],{"className":141381},[638],[363,141383,141385],{"className":141384,"style":137304},[642],[363,141386,141387,141390],{"style":136942},[363,141388],{"className":141389,"style":30553},[650],[363,141391,141393],{"className":141392},[655,30557,10021,658],[363,141394,474],{"className":141395},[407,658],[363,141397,666],{"className":141398},[665],[363,141400,141402],{"className":141401},[638],[363,141403,141405],{"className":141404,"style":40117},[642],[363,141406],{},[363,141408,5160],{"className":141409},[2938,658],[363,141411,465],{"className":141412},[407,658],[363,141414,141416,141419],{"className":141415},[407],[363,141417,7914],{"className":141418},[407,408],[363,141420,141422],{"className":141421},[629],[363,141423,141425],{"className":141424},[633],[363,141426,141428],{"className":141427},[638],[363,141429,141432],{"className":141430,"style":141431},[642],"height:0.8213em;",[363,141433,141434,141437],{"style":8624},[363,141435],{"className":141436,"style":651},[650],[363,141438,141440],{"className":141439},[655,656,657,658],[363,141441,141443,141446],{"className":141442},[407,658],[363,141444,5160],{"className":141445},[407,658],[363,141447,7908],{"className":141448},[407,408,658],[363,141450],{"className":141451,"style":754},[505],[363,141453,592],{"className":141454},[407,33009],[363,141456,7908],{"className":141457},[407,408],[363,141459,141461],{"className":141460,"style":763},[501,762],[363,141462,468],{"className":141463},[767,657],[363,141465],{"className":141466,"style":754},[505],[363,141468,141470,141476,141554,141557,141621,141624,141721,141724,141727,141730],{"className":141469},[758],[363,141471,141473],{"className":141472,"style":763},[494,762],[363,141474,461],{"className":141475},[767,4894],[363,141477,141479,141482],{"className":141478},[1831],[363,141480,1634],{"className":141481,"style":1834},[1831,1832,1833],[363,141483,141485],{"className":141484},[629],[363,141486,141488,141546],{"className":141487},[633,634],[363,141489,141491,141543],{"className":141490},[638],[363,141492,141494],{"className":141493,"style":139966},[642],[363,141495,141496,141499],{"style":3825},[363,141497],{"className":141498,"style":651},[650],[363,141500,141502],{"className":141501},[655,656,657,658],[363,141503,141505],{"className":141504},[407,658],[363,141506,141508,141511],{"className":141507},[407,658],[363,141509,126023],{"className":141510},[407,658],[363,141512,141514],{"className":141513},[629],[363,141515,141517],{"className":141516},[633],[363,141518,141520],{"className":141519},[638],[363,141521,141523],{"className":141522,"style":137751},[642],[363,141524,141525,141528],{"style":45809},[363,141526],{"className":141527,"style":30553},[650],[363,141529,141531],{"className":141530},[655,30557,10021,658],[363,141532,141534,141537,141540],{"className":141533},[407,658],[363,141535,11041],{"className":141536,"style":11129},[407,408,658],[363,141538,5160],{"className":141539},[2938,658],[363,141541,465],{"className":141542},[407,658],[363,141544,666],{"className":141545},[665],[363,141547,141549],{"className":141548},[638],[363,141550,141552],{"className":141551,"style":139936},[642],[363,141553],{},[363,141555],{"className":141556,"style":754},[505],[363,141558,141560],{"className":141559},[1831,14063],[363,141561,141563,141613],{"className":141562},[633,634],[363,141564,141566,141610],{"className":141565},[638],[363,141567,141569,141589,141599],{"className":141568,"style":138225},[642],[363,141570,141571,141574],{"style":14076},[363,141572],{"className":141573,"style":14080},[650],[363,141575,141577],{"className":141576},[655,656,657,658],[363,141578,141580,141583,141586],{"className":141579},[407,658],[363,141581,12310],{"className":141582},[407,408,658],[363,141584,471],{"className":141585},[510,658],[363,141587,465],{"className":141588},[407,658],[363,141590,141591,141594],{"style":14089},[363,141592],{"className":141593,"style":14080},[650],[363,141595,141596],{},[363,141597,136637],{"className":141598},[1831,1832,1833],[363,141600,141601,141604],{"style":100671},[363,141602],{"className":141603,"style":14080},[650],[363,141605,141607],{"className":141606},[655,656,657,658],[363,141608,11041],{"className":141609,"style":11129},[407,408,658],[363,141611,666],{"className":141612},[665],[363,141614,141616],{"className":141615},[638],[363,141617,141619],{"className":141618,"style":14107},[642],[363,141620],{},[363,141622],{"className":141623,"style":754},[505],[363,141625,141627,141630],{"className":141626},[407],[363,141628,1121],{"className":141629},[407,408],[363,141631,141633],{"className":141632},[629],[363,141634,141636,141713],{"className":141635},[633,634],[363,141637,141639,141710],{"className":141638},[638],[363,141640,141642,141653],{"className":141641,"style":136897},[642],[363,141643,141644,141647],{"style":136900},[363,141645],{"className":141646,"style":651},[650],[363,141648,141650],{"className":141649},[655,656,657,658],[363,141651,12310],{"className":141652},[407,408,658],[363,141654,141655,141658],{"style":136912},[363,141656],{"className":141657,"style":651},[650],[363,141659,141661],{"className":141660},[655,656,657,658],[363,141662,141664,141704,141707],{"className":141663},[407,658],[363,141665,141667,141670],{"className":141666},[407,658],[363,141668,45101],{"className":141669,"style":45131},[407,408,658],[363,141671,141673],{"className":141672},[629],[363,141674,141676,141696],{"className":141675},[633,634],[363,141677,141679,141693],{"className":141678},[638],[363,141680,141682],{"className":141681,"style":40095},[642],[363,141683,141684,141687],{"style":136942},[363,141685],{"className":141686,"style":30553},[650],[363,141688,141690],{"className":141689},[655,30557,10021,658],[363,141691,12310],{"className":141692},[407,408,658],[363,141694,666],{"className":141695},[665],[363,141697,141699],{"className":141698},[638],[363,141700,141702],{"className":141701,"style":40117},[642],[363,141703],{},[363,141705,5160],{"className":141706},[2938,658],[363,141708,465],{"className":141709},[407,658],[363,141711,666],{"className":141712},[665],[363,141714,141716],{"className":141715},[638],[363,141717,141719],{"className":141718,"style":136978},[642],[363,141720],{},[363,141722],{"className":141723,"style":754},[505],[363,141725,592],{"className":141726},[407,33009],[363,141728,1121],{"className":141729},[407,75905],[363,141731,141733],{"className":141732,"style":763},[501,762],[363,141734,468],{"className":141735},[767,4894],[363,141737],{"className":141738,"style":506},[505],[363,141740,471],{"className":141741},[510],[363,141743],{"className":141744},[505,24035],[363,141746,141748,141751,141754,141757,141797,141800,141803,141881,141884,141948,141951,142048,142051,142054],{"className":141747},[398],[363,141749],{"className":141750,"style":138212},[402],[363,141752,137171],{"className":141753},[407],[363,141755,461],{"className":141756},[494],[363,141758,141760,141763],{"className":141759},[407],[363,141761,45101],{"className":141762,"style":45131},[407,408],[363,141764,141766],{"className":141765},[629],[363,141767,141769,141789],{"className":141768},[633,634],[363,141770,141772,141786],{"className":141771},[638],[363,141773,141775],{"className":141774,"style":11480},[642],[363,141776,141777,141780],{"style":136107},[363,141778],{"className":141779,"style":651},[650],[363,141781,141783],{"className":141782},[655,656,657,658],[363,141784,474],{"className":141785},[407,658],[363,141787,666],{"className":141788},[665],[363,141790,141792],{"className":141791},[638],[363,141793,141795],{"className":141794,"style":8315},[642],[363,141796],{},[363,141798,468],{"className":141799},[501],[363,141801],{"className":141802,"style":754},[505],[363,141804,141806,141809],{"className":141805},[1831],[363,141807,1634],{"className":141808,"style":1834},[1831,1832,1833],[363,141810,141812],{"className":141811},[629],[363,141813,141815,141873],{"className":141814},[633,634],[363,141816,141818,141870],{"className":141817},[638],[363,141819,141821],{"className":141820,"style":139966},[642],[363,141822,141823,141826],{"style":3825},[363,141824],{"className":141825,"style":651},[650],[363,141827,141829],{"className":141828},[655,656,657,658],[363,141830,141832],{"className":141831},[407,658],[363,141833,141835,141838],{"className":141834},[407,658],[363,141836,126023],{"className":141837},[407,658],[363,141839,141841],{"className":141840},[629],[363,141842,141844],{"className":141843},[633],[363,141845,141847],{"className":141846},[638],[363,141848,141850],{"className":141849,"style":137751},[642],[363,141851,141852,141855],{"style":45809},[363,141853],{"className":141854,"style":30553},[650],[363,141856,141858],{"className":141857},[655,30557,10021,658],[363,141859,141861,141864,141867],{"className":141860},[407,658],[363,141862,11041],{"className":141863,"style":11129},[407,408,658],[363,141865,5160],{"className":141866},[2938,658],[363,141868,465],{"className":141869},[407,658],[363,141871,666],{"className":141872},[665],[363,141874,141876],{"className":141875},[638],[363,141877,141879],{"className":141878,"style":139936},[642],[363,141880],{},[363,141882],{"className":141883,"style":754},[505],[363,141885,141887],{"className":141886},[1831,14063],[363,141888,141890,141940],{"className":141889},[633,634],[363,141891,141893,141937],{"className":141892},[638],[363,141894,141896,141916,141926],{"className":141895,"style":138225},[642],[363,141897,141898,141901],{"style":14076},[363,141899],{"className":141900,"style":14080},[650],[363,141902,141904],{"className":141903},[655,656,657,658],[363,141905,141907,141910,141913],{"className":141906},[407,658],[363,141908,12310],{"className":141909},[407,408,658],[363,141911,471],{"className":141912},[510,658],[363,141914,465],{"className":141915},[407,658],[363,141917,141918,141921],{"style":14089},[363,141919],{"className":141920,"style":14080},[650],[363,141922,141923],{},[363,141924,136637],{"className":141925},[1831,1832,1833],[363,141927,141928,141931],{"style":100671},[363,141929],{"className":141930,"style":14080},[650],[363,141932,141934],{"className":141933},[655,656,657,658],[363,141935,11041],{"className":141936,"style":11129},[407,408,658],[363,141938,666],{"className":141939},[665],[363,141941,141943],{"className":141942},[638],[363,141944,141946],{"className":141945,"style":14107},[642],[363,141947],{},[363,141949],{"className":141950,"style":754},[505],[363,141952,141954,141957],{"className":141953},[407],[363,141955,1121],{"className":141956},[407,408],[363,141958,141960],{"className":141959},[629],[363,141961,141963,142040],{"className":141962},[633,634],[363,141964,141966,142037],{"className":141965},[638],[363,141967,141969,141980],{"className":141968,"style":136897},[642],[363,141970,141971,141974],{"style":136900},[363,141972],{"className":141973,"style":651},[650],[363,141975,141977],{"className":141976},[655,656,657,658],[363,141978,12310],{"className":141979},[407,408,658],[363,141981,141982,141985],{"style":136912},[363,141983],{"className":141984,"style":651},[650],[363,141986,141988],{"className":141987},[655,656,657,658],[363,141989,141991,142031,142034],{"className":141990},[407,658],[363,141992,141994,141997],{"className":141993},[407,658],[363,141995,45101],{"className":141996,"style":45131},[407,408,658],[363,141998,142000],{"className":141999},[629],[363,142001,142003,142023],{"className":142002},[633,634],[363,142004,142006,142020],{"className":142005},[638],[363,142007,142009],{"className":142008,"style":40095},[642],[363,142010,142011,142014],{"style":136942},[363,142012],{"className":142013,"style":30553},[650],[363,142015,142017],{"className":142016},[655,30557,10021,658],[363,142018,12310],{"className":142019},[407,408,658],[363,142021,666],{"className":142022},[665],[363,142024,142026],{"className":142025},[638],[363,142027,142029],{"className":142028,"style":40117},[642],[363,142030],{},[363,142032,5160],{"className":142033},[2938,658],[363,142035,465],{"className":142036},[407,658],[363,142038,666],{"className":142039},[665],[363,142041,142043],{"className":142042},[638],[363,142044,142046],{"className":142045,"style":136978},[642],[363,142047],{},[363,142049],{"className":142050,"style":754},[505],[363,142052,592],{"className":142053},[407,33009],[363,142055,1121],{"className":142056},[407,75905],[11,142058,142059,142060,142145],{},"两端除以 ",[363,142061,142063,142087],{"className":142062,"translate":367},[366],[363,142064,142066],{"className":142065},[371],[373,142067,142068],{"xmlns":375},[377,142069,142070,142084],{},[380,142071,142072,142074,142076,142082],{},[383,142073,137171],{"mathvariant":557},[458,142075,461],{"stretchy":460},[543,142077,142078,142080],{},[383,142079,45101],{},[463,142081,474],{},[458,142083,468],{"stretchy":460},[387,142085,142086],{"encoding":389},"\\Gamma(\\alpha_0)",[363,142088,142090],{"className":142089,"ariaHidden":394},[393],[363,142091,142093,142096,142099,142102,142142],{"className":142092},[398],[363,142094],{"className":142095,"style":487},[402],[363,142097,137171],{"className":142098},[407],[363,142100,461],{"className":142101},[494],[363,142103,142105,142108],{"className":142104},[407],[363,142106,45101],{"className":142107,"style":45131},[407,408],[363,142109,142111],{"className":142110},[629],[363,142112,142114,142134],{"className":142113},[633,634],[363,142115,142117,142131],{"className":142116},[638],[363,142118,142120],{"className":142119,"style":11480},[642],[363,142121,142122,142125],{"style":136107},[363,142123],{"className":142124,"style":651},[650],[363,142126,142128],{"className":142127},[655,656,657,658],[363,142129,474],{"className":142130},[407,658],[363,142132,666],{"className":142133},[665],[363,142135,142137],{"className":142136},[638],[363,142138,142140],{"className":142139,"style":8315},[642],[363,142141],{},[363,142143,468],{"className":142144},[501]," 即得结论。",[11,142147,142148,142149,2756,142177,34172,142205,142208],{},"命题 1.3 的证明过程本身包含了比结论更多的信息：",[363,142150,142152,142165],{"className":142151,"translate":367},[366],[363,142153,142155],{"className":142154},[371],[373,142156,142157],{"xmlns":375},[377,142158,142159,142163],{},[380,142160,142161],{},[383,142162,7908],{},[387,142164,7908],{"encoding":389},[363,142166,142168],{"className":142167,"ariaHidden":394},[393],[363,142169,142171,142174],{"className":142170},[398],[363,142172],{"className":142173,"style":2692},[402],[363,142175,7908],{"className":142176},[407,408],[363,142178,142180,142193],{"className":142179,"translate":367},[366],[363,142181,142183],{"className":142182},[371],[373,142184,142185],{"xmlns":375},[377,142186,142187,142191],{},[380,142188,142189],{},[383,142190,1121],{"mathvariant":75560},[387,142192,135607],{"encoding":389},[363,142194,142196],{"className":142195,"ariaHidden":394},[393],[363,142197,142199,142202],{"className":142198},[398],[363,142200],{"className":142201,"style":135617},[402],[363,142203,1121],{"className":142204},[407,75905],[1572,142206,142207],{},"完全可分离性","。下一小节的生成性刻画正是对这一可分离性的直接读解。",[2658,142210,142212],{"id":142211},"_13-生成性刻画gamma-商表示","1.3 生成性刻画：Gamma 商表示",[1340,142214,142216],{"title":142215},"命题 1.4（Gamma 商表示）",[11,142217,881,142218,142359,142360,142527,142528,142598,142599,142627,142628,143151,143152,23877,143228,87128,143305,10527],{},[363,142219,142221,142251],{"className":142220,"translate":367},[366],[363,142222,142224],{"className":142223},[371],[373,142225,142226],{"xmlns":375},[377,142227,142228,142248],{},[380,142229,142230,142236,142238,142240,142242],{},[543,142231,142232,142234],{},[383,142233,121421],{},[463,142235,465],{},[458,142237,898],{"separator":394},[458,142239,133107],{},[458,142241,898],{"separator":394},[543,142243,142244,142246],{},[383,142245,121421],{},[383,142247,11041],{},[387,142249,142250],{"encoding":389},"\\gamma_1, \\dots, \\gamma_K",[363,142252,142254],{"className":142253,"ariaHidden":394},[393],[363,142255,142257,142260,142301,142304,142307,142310,142313,142316,142319],{"className":142256},[398],[363,142258],{"className":142259,"style":2623},[402],[363,142261,142263,142266],{"className":142262},[407],[363,142264,121421],{"className":142265,"style":121511},[407,408],[363,142267,142269],{"className":142268},[629],[363,142270,142272,142293],{"className":142271},[633,634],[363,142273,142275,142290],{"className":142274},[638],[363,142276,142278],{"className":142277,"style":11480},[642],[363,142279,142281,142284],{"style":142280},"top:-2.55em;margin-left:-0.0556em;margin-right:0.05em;",[363,142282],{"className":142283,"style":651},[650],[363,142285,142287],{"className":142286},[655,656,657,658],[363,142288,465],{"className":142289},[407,658],[363,142291,666],{"className":142292},[665],[363,142294,142296],{"className":142295},[638],[363,142297,142299],{"className":142298,"style":8315},[642],[363,142300],{},[363,142302,898],{"className":142303},[920],[363,142305],{"className":142306,"style":754},[505],[363,142308,133107],{"className":142309},[758],[363,142311],{"className":142312,"style":754},[505],[363,142314,898],{"className":142315},[920],[363,142317],{"className":142318,"style":754},[505],[363,142320,142322,142325],{"className":142321},[407],[363,142323,121421],{"className":142324,"style":121511},[407,408],[363,142326,142328],{"className":142327},[629],[363,142329,142331,142351],{"className":142330},[633,634],[363,142332,142334,142348],{"className":142333},[638],[363,142335,142337],{"className":142336,"style":727},[642],[363,142338,142339,142342],{"style":142280},[363,142340],{"className":142341,"style":651},[650],[363,142343,142345],{"className":142344},[655,656,657,658],[363,142346,11041],{"className":142347,"style":11129},[407,408,658],[363,142349,666],{"className":142350},[665],[363,142352,142354],{"className":142353},[638],[363,142355,142357],{"className":142356,"style":8315},[642],[363,142358],{}," 相互独立且 ",[363,142361,142363,142402],{"className":142362,"translate":367},[366],[363,142364,142366],{"className":142365},[371],[373,142367,142368],{"xmlns":375},[377,142369,142370,142399],{},[380,142371,142372,142378,142380,142383,142385,142387,142393,142395,142397],{},[543,142373,142374,142376],{},[383,142375,121421],{},[383,142377,12310],{},[458,142379,9216],{},[383,142381,142382],{"mathvariant":557},"Gamma",[458,142384,4450],{},[458,142386,461],{"stretchy":460},[543,142388,142389,142391],{},[383,142390,45101],{},[383,142392,12310],{},[458,142394,898],{"separator":394},[463,142396,465],{},[458,142398,468],{"stretchy":460},[387,142400,142401],{"encoding":389},"\\gamma_i \\sim \\operatorname{Gamma}(\\alpha_i, 1)",[363,142403,142405,142460],{"className":142404,"ariaHidden":394},[393],[363,142406,142408,142411,142451,142454,142457],{"className":142407},[398],[363,142409],{"className":142410,"style":2623},[402],[363,142412,142414,142417],{"className":142413},[407],[363,142415,121421],{"className":142416,"style":121511},[407,408],[363,142418,142420],{"className":142419},[629],[363,142421,142423,142443],{"className":142422},[633,634],[363,142424,142426,142440],{"className":142425},[638],[363,142427,142429],{"className":142428,"style":12529},[642],[363,142430,142431,142434],{"style":142280},[363,142432],{"className":142433,"style":651},[650],[363,142435,142437],{"className":142436},[655,656,657,658],[363,142438,12310],{"className":142439},[407,408,658],[363,142441,666],{"className":142442},[665],[363,142444,142446],{"className":142445},[638],[363,142447,142449],{"className":142448,"style":8315},[642],[363,142450],{},[363,142452],{"className":142453,"style":506},[505],[363,142455,9216],{"className":142456},[510],[363,142458],{"className":142459,"style":506},[505],[363,142461,142463,142466,142472,142475,142515,142518,142521,142524],{"className":142462},[398],[363,142464],{"className":142465,"style":487},[402],[363,142467,142469],{"className":142468},[1831],[363,142470,142382],{"className":142471},[407,33009],[363,142473,461],{"className":142474},[494],[363,142476,142478,142481],{"className":142477},[407],[363,142479,45101],{"className":142480,"style":45131},[407,408],[363,142482,142484],{"className":142483},[629],[363,142485,142487,142507],{"className":142486},[633,634],[363,142488,142490,142504],{"className":142489},[638],[363,142491,142493],{"className":142492,"style":12529},[642],[363,142494,142495,142498],{"style":136107},[363,142496],{"className":142497,"style":651},[650],[363,142499,142501],{"className":142500},[655,656,657,658],[363,142502,12310],{"className":142503},[407,408,658],[363,142505,666],{"className":142506},[665],[363,142508,142510],{"className":142509},[638],[363,142511,142513],{"className":142512,"style":8315},[642],[363,142514],{},[363,142516,898],{"className":142517},[920],[363,142519],{"className":142520,"style":754},[505],[363,142522,465],{"className":142523},[407],[363,142525,468],{"className":142526},[501],"（形状 ",[363,142529,142531,142549],{"className":142530,"translate":367},[366],[363,142532,142534],{"className":142533},[371],[373,142535,142536],{"xmlns":375},[377,142537,142538,142546],{},[380,142539,142540],{},[543,142541,142542,142544],{},[383,142543,45101],{},[383,142545,12310],{},[387,142547,142548],{"encoding":389},"\\alpha_i",[363,142550,142552],{"className":142551,"ariaHidden":394},[393],[363,142553,142555,142558],{"className":142554},[398],[363,142556],{"className":142557,"style":13721},[402],[363,142559,142561,142564],{"className":142560},[407],[363,142562,45101],{"className":142563,"style":45131},[407,408],[363,142565,142567],{"className":142566},[629],[363,142568,142570,142590],{"className":142569},[633,634],[363,142571,142573,142587],{"className":142572},[638],[363,142574,142576],{"className":142575,"style":12529},[642],[363,142577,142578,142581],{"style":136107},[363,142579],{"className":142580,"style":651},[650],[363,142582,142584],{"className":142583},[655,656,657,658],[363,142585,12310],{"className":142586},[407,408,658],[363,142588,666],{"className":142589},[665],[363,142591,142593],{"className":142592},[638],[363,142594,142596],{"className":142595,"style":8315},[642],[363,142597],{},"、率 ",[363,142600,142602,142615],{"className":142601,"translate":367},[366],[363,142603,142605],{"className":142604},[371],[373,142606,142607],{"xmlns":375},[377,142608,142609,142613],{},[380,142610,142611],{},[463,142612,465],{},[387,142614,465],{"encoding":389},[363,142616,142618],{"className":142617,"ariaHidden":394},[393],[363,142619,142621,142624],{"className":142620},[398],[363,142622],{"className":142623,"style":520},[402],[363,142625,465],{"className":142626},[407],"）。令\n",[363,142629,142631,142719],{"className":142630,"translate":367},[366],[363,142632,142634],{"className":142633},[371],[373,142635,142636],{"xmlns":375},[377,142637,142638,142716],{},[380,142639,142640,142642,142644,142658,142664,142666,142668,142674,142676,142686,142688,142690,142692,142694,142696,142702,142704,142706,142708,142714],{},[383,142641,7908],{},[458,142643,471],{},[7900,142645,142646,142648,142656],{},[458,142647,13808],{},[380,142649,142650,142652,142654],{},[383,142651,12310],{},[458,142653,471],{},[463,142655,465],{},[383,142657,11041],{},[543,142659,142660,142662],{},[383,142661,121421],{},[383,142663,12310],{},[458,142665,898],{"separator":394},[505,142667],{"width":3609},[543,142669,142670,142672],{},[383,142671,1121],{},[383,142673,12310],{},[458,142675,471],{},[586,142677,142678,142684],{},[543,142679,142680,142682],{},[383,142681,121421],{},[383,142683,12310],{},[383,142685,7908],{},[458,142687,898],{"separator":394},[505,142689],{"width":3609},[383,142691,1121],{"mathvariant":75560},[458,142693,471],{},[458,142695,461],{"stretchy":460},[543,142697,142698,142700],{},[383,142699,1121],{},[463,142701,465],{},[458,142703,898],{"separator":394},[458,142705,133107],{},[458,142707,898],{"separator":394},[543,142709,142710,142712],{},[383,142711,1121],{},[383,142713,11041],{},[458,142715,468],{"stretchy":460},[387,142717,142718],{"encoding":389},"s = \\sum_{i=1}^K \\gamma_i, \\qquad x_i = \\frac{\\gamma_i}{s}, \\qquad \\mathbf{x} = (x_1, \\dots, x_K)",[363,142720,142722,142740,142907,143041],{"className":142721,"ariaHidden":394},[393],[363,142723,142725,142728,142731,142734,142737],{"className":142724},[398],[363,142726],{"className":142727,"style":2692},[402],[363,142729,7908],{"className":142730},[407,408],[363,142732],{"className":142733,"style":506},[505],[363,142735,471],{"className":142736},[510],[363,142738],{"className":142739,"style":506},[505],[363,142741,142743,142746,142806,142809,142849,142852,142855,142858,142898,142901,142904],{"className":142742},[398],[363,142744],{"className":142745,"style":136371},[402],[363,142747,142749,142752],{"className":142748},[1831],[363,142750,13808],{"className":142751,"style":40007},[1831,1832,5963],[363,142753,142755],{"className":142754},[629],[363,142756,142758,142798],{"className":142757},[633,634],[363,142759,142761,142795],{"className":142760},[638],[363,142762,142764,142784],{"className":142763,"style":133494},[642],[363,142765,142766,142769],{"style":40023},[363,142767],{"className":142768,"style":651},[650],[363,142770,142772],{"className":142771},[655,656,657,658],[363,142773,142775,142778,142781],{"className":142774},[407,658],[363,142776,12310],{"className":142777},[407,408,658],[363,142779,471],{"className":142780},[510,658],[363,142782,465],{"className":142783},[407,658],[363,142785,142786,142789],{"style":133517},[363,142787],{"className":142788,"style":651},[650],[363,142790,142792],{"className":142791},[655,656,657,658],[363,142793,11041],{"className":142794,"style":11129},[407,408,658],[363,142796,666],{"className":142797},[665],[363,142799,142801],{"className":142800},[638],[363,142802,142804],{"className":142803,"style":40042},[642],[363,142805],{},[363,142807],{"className":142808,"style":754},[505],[363,142810,142812,142815],{"className":142811},[407],[363,142813,121421],{"className":142814,"style":121511},[407,408],[363,142816,142818],{"className":142817},[629],[363,142819,142821,142841],{"className":142820},[633,634],[363,142822,142824,142838],{"className":142823},[638],[363,142825,142827],{"className":142826,"style":12529},[642],[363,142828,142829,142832],{"style":142280},[363,142830],{"className":142831,"style":651},[650],[363,142833,142835],{"className":142834},[655,656,657,658],[363,142836,12310],{"className":142837},[407,408,658],[363,142839,666],{"className":142840},[665],[363,142842,142844],{"className":142843},[638],[363,142845,142847],{"className":142846,"style":8315},[642],[363,142848],{},[363,142850,898],{"className":142851},[920],[363,142853],{"className":142854,"style":3981},[505],[363,142856],{"className":142857,"style":754},[505],[363,142859,142861,142864],{"className":142860},[407],[363,142862,1121],{"className":142863},[407,408],[363,142865,142867],{"className":142866},[629],[363,142868,142870,142890],{"className":142869},[633,634],[363,142871,142873,142887],{"className":142872},[638],[363,142874,142876],{"className":142875,"style":12529},[642],[363,142877,142878,142881],{"style":730},[363,142879],{"className":142880,"style":651},[650],[363,142882,142884],{"className":142883},[655,656,657,658],[363,142885,12310],{"className":142886},[407,408,658],[363,142888,666],{"className":142889},[665],[363,142891,142893],{"className":142892},[638],[363,142894,142896],{"className":142895,"style":8315},[642],[363,142897],{},[363,142899],{"className":142900,"style":506},[505],[363,142902,471],{"className":142903},[510],[363,142905],{"className":142906,"style":506},[505],[363,142908,142910,142914,143020,143023,143026,143029,143032,143035,143038],{"className":142909},[398],[363,142911],{"className":142912,"style":142913},[402],"height:1.0925em;vertical-align:-0.345em;",[363,142915,142917,142920,143017],{"className":142916},[407],[363,142918],{"className":142919},[494,789],[363,142921,142923],{"className":142922},[586],[363,142924,142926,143009],{"className":142925},[633,634],[363,142927,142929,143006],{"className":142928},[638],[363,142930,142932,142946,142954],{"className":142931,"style":3450},[642],[363,142933,142934,142937],{"style":2874},[363,142935],{"className":142936,"style":809},[650],[363,142938,142940],{"className":142939},[655,656,657,658],[363,142941,142943],{"className":142942},[407,658],[363,142944,7908],{"className":142945},[407,408,658],[363,142947,142948,142951],{"style":821},[363,142949],{"className":142950,"style":809},[650],[363,142952],{"className":142953,"style":829},[828],[363,142955,142956,142959],{"style":3200},[363,142957],{"className":142958,"style":809},[650],[363,142960,142962],{"className":142961},[655,656,657,658],[363,142963,142965],{"className":142964},[407,658],[363,142966,142968,142971],{"className":142967},[407,658],[363,142969,121421],{"className":142970,"style":121511},[407,408,658],[363,142972,142974],{"className":142973},[629],[363,142975,142977,142998],{"className":142976},[633,634],[363,142978,142980,142995],{"className":142979},[638],[363,142981,142983],{"className":142982,"style":40095},[642],[363,142984,142986,142989],{"style":142985},"top:-2.357em;margin-left:-0.0556em;margin-right:0.0714em;",[363,142987],{"className":142988,"style":30553},[650],[363,142990,142992],{"className":142991},[655,30557,10021,658],[363,142993,12310],{"className":142994},[407,408,658],[363,142996,666],{"className":142997},[665],[363,142999,143001],{"className":143000},[638],[363,143002,143004],{"className":143003,"style":40117},[642],[363,143005],{},[363,143007,666],{"className":143008},[665],[363,143010,143012],{"className":143011},[638],[363,143013,143015],{"className":143014,"style":2919},[642],[363,143016],{},[363,143018],{"className":143019},[501,789],[363,143021,898],{"className":143022},[920],[363,143024],{"className":143025,"style":3981},[505],[363,143027],{"className":143028,"style":754},[505],[363,143030,1121],{"className":143031},[407,75905],[363,143033],{"className":143034,"style":506},[505],[363,143036,471],{"className":143037},[510],[363,143039],{"className":143040,"style":506},[505],[363,143042,143044,143047,143050,143090,143093,143096,143099,143102,143105,143108,143148],{"className":143043},[398],[363,143045],{"className":143046,"style":487},[402],[363,143048,461],{"className":143049},[494],[363,143051,143053,143056],{"className":143052},[407],[363,143054,1121],{"className":143055},[407,408],[363,143057,143059],{"className":143058},[629],[363,143060,143062,143082],{"className":143061},[633,634],[363,143063,143065,143079],{"className":143064},[638],[363,143066,143068],{"className":143067,"style":11480},[642],[363,143069,143070,143073],{"style":730},[363,143071],{"className":143072,"style":651},[650],[363,143074,143076],{"className":143075},[655,656,657,658],[363,143077,465],{"className":143078},[407,658],[363,143080,666],{"className":143081},[665],[363,143083,143085],{"className":143084},[638],[363,143086,143088],{"className":143087,"style":8315},[642],[363,143089],{},[363,143091,898],{"className":143092},[920],[363,143094],{"className":143095,"style":754},[505],[363,143097,133107],{"className":143098},[758],[363,143100],{"className":143101,"style":754},[505],[363,143103,898],{"className":143104},[920],[363,143106],{"className":143107,"style":754},[505],[363,143109,143111,143114],{"className":143110},[407],[363,143112,1121],{"className":143113},[407,408],[363,143115,143117],{"className":143116},[629],[363,143118,143120,143140],{"className":143119},[633,634],[363,143121,143123,143137],{"className":143122},[638],[363,143124,143126],{"className":143125,"style":727},[642],[363,143127,143128,143131],{"style":730},[363,143129],{"className":143130,"style":651},[650],[363,143132,143134],{"className":143133},[655,656,657,658],[363,143135,11041],{"className":143136,"style":11129},[407,408,658],[363,143138,666],{"className":143139},[665],[363,143141,143143],{"className":143142},[638],[363,143144,143146],{"className":143145,"style":8315},[642],[363,143147],{},[363,143149,468],{"className":143150},[501],"\n则 ",[363,143153,143155,143180],{"className":143154,"translate":367},[366],[363,143156,143158],{"className":143157},[371],[373,143159,143160],{"xmlns":375},[377,143161,143162,143178],{},[380,143163,143164,143166,143168,143170,143172,143174,143176],{},[383,143165,1121],{"mathvariant":75560},[458,143167,9216],{},[383,143169,137065],{"mathvariant":557},[458,143171,4450],{},[458,143173,461],{"stretchy":460},[383,143175,45101],{"mathvariant":136008},[458,143177,468],{"stretchy":460},[387,143179,137076],{"encoding":389},[363,143181,143183,143201],{"className":143182,"ariaHidden":394},[393],[363,143184,143186,143189,143192,143195,143198],{"className":143185},[398],[363,143187],{"className":143188,"style":135617},[402],[363,143190,1121],{"className":143191},[407,75905],[363,143193],{"className":143194,"style":506},[505],[363,143196,9216],{"className":143197},[510],[363,143199],{"className":143200,"style":506},[505],[363,143202,143204,143207,143213,143216,143225],{"className":143203},[398],[363,143205],{"className":143206,"style":487},[402],[363,143208,143210],{"className":143209},[1831],[363,143211,137065],{"className":143212},[407,33009],[363,143214,461],{"className":143215},[494],[363,143217,143219],{"className":143218},[407],[363,143220,143222],{"className":143221},[407],[363,143223,45101],{"className":143224},[407,136068],[363,143226,468],{"className":143227},[501],[363,143229,143231,143257],{"className":143230,"translate":367},[366],[363,143232,143234],{"className":143233},[371],[373,143235,143236],{"xmlns":375},[377,143237,143238,143254],{},[380,143239,143240,143242,143244,143246,143248,143250,143252],{},[383,143241,1121],{"mathvariant":75560},[458,143243,33894],{},[1644,143245,1651],{},[1644,143247,1651],{},[1644,143249,1651],{},[458,143251,33894],{},[383,143253,7908],{},[387,143255,143256],{"encoding":389},"\\mathbf{x} \\perp\\!\\!\\!\\perp s",[363,143258,143260,143284,143296],{"className":143259,"ariaHidden":394},[393],[363,143261,143263,143266,143269,143272,143275,143278,143281],{"className":143262},[398],[363,143264],{"className":143265,"style":12944},[402],[363,143267,1121],{"className":143268},[407,75905],[363,143270],{"className":143271,"style":506},[505],[363,143273,33894],{"className":143274},[510],[363,143276],{"className":143277,"style":1859},[505],[363,143279],{"className":143280,"style":1859},[505],[363,143282],{"className":143283,"style":1859},[505],[363,143285,143287,143290,143293],{"className":143286},[398],[363,143288],{"className":143289,"style":12944},[402],[363,143291,33894],{"className":143292},[510],[363,143294],{"className":143295,"style":506},[505],[363,143297,143299,143302],{"className":143298},[398],[363,143300],{"className":143301,"style":2692},[402],[363,143303,7908],{"className":143304},[407,408],[363,143306,143308,143342],{"className":143307,"translate":367},[366],[363,143309,143311],{"className":143310},[371],[373,143312,143313],{"xmlns":375},[377,143314,143315,143339],{},[380,143316,143317,143319,143321,143323,143325,143327,143333,143335,143337],{},[383,143318,7908],{},[458,143320,9216],{},[383,143322,142382],{"mathvariant":557},[458,143324,4450],{},[458,143326,461],{"stretchy":460},[543,143328,143329,143331],{},[383,143330,45101],{},[463,143332,474],{},[458,143334,898],{"separator":394},[463,143336,465],{},[458,143338,468],{"stretchy":460},[387,143340,143341],{"encoding":389},"s \\sim \\operatorname{Gamma}(\\alpha_0, 1)",[363,143343,143345,143363],{"className":143344,"ariaHidden":394},[393],[363,143346,143348,143351,143354,143357,143360],{"className":143347},[398],[363,143349],{"className":143350,"style":2692},[402],[363,143352,7908],{"className":143353},[407,408],[363,143355],{"className":143356,"style":506},[505],[363,143358,9216],{"className":143359},[510],[363,143361],{"className":143362,"style":506},[505],[363,143364,143366,143369,143375,143378,143418,143421,143424,143427],{"className":143365},[398],[363,143367],{"className":143368,"style":487},[402],[363,143370,143372],{"className":143371},[1831],[363,143373,142382],{"className":143374},[407,33009],[363,143376,461],{"className":143377},[494],[363,143379,143381,143384],{"className":143380},[407],[363,143382,45101],{"className":143383,"style":45131},[407,408],[363,143385,143387],{"className":143386},[629],[363,143388,143390,143410],{"className":143389},[633,634],[363,143391,143393,143407],{"className":143392},[638],[363,143394,143396],{"className":143395,"style":11480},[642],[363,143397,143398,143401],{"style":136107},[363,143399],{"className":143400,"style":651},[650],[363,143402,143404],{"className":143403},[655,656,657,658],[363,143405,474],{"className":143406},[407,658],[363,143408,666],{"className":143409},[665],[363,143411,143413],{"className":143412},[638],[363,143414,143416],{"className":143415,"style":8315},[642],[363,143417],{},[363,143419,898],{"className":143420},[920],[363,143422],{"className":143423,"style":754},[505],[363,143425,465],{"className":143426},[407],[363,143428,468],{"className":143429},[501],[11,143431,143432,143434,143435,143471,143472,143812,143813,143951],{},[1572,143433,137993],{}," 由独立性，",[363,143436,143438,143452],{"className":143437,"translate":367},[366],[363,143439,143441],{"className":143440},[371],[373,143442,143443],{"xmlns":375},[377,143444,143445,143449],{},[380,143446,143447],{},[383,143448,121421],{"mathvariant":136008},[387,143450,143451],{"encoding":389},"\\boldsymbol{\\gamma}",[363,143453,143455],{"className":143454,"ariaHidden":394},[393],[363,143456,143458,143461],{"className":143457},[398],[363,143459],{"className":143460,"style":133764},[402],[363,143462,143464],{"className":143463},[407],[363,143465,143467],{"className":143466},[407],[363,143468,121421],{"className":143469,"style":143470},[407,136068],"margin-right:0.0639em;"," 的联合密度为 ",[363,143473,143475,143539],{"className":143474,"translate":367},[366],[363,143476,143478],{"className":143477},[371],[373,143479,143480],{"xmlns":375},[377,143481,143482,143536],{},[380,143483,143484,143490,143508,143522,143524,143526,143528,143534],{},[543,143485,143486,143488],{},[458,143487,136637],{},[383,143489,12310],{},[7900,143491,143492,143494,143496],{},[383,143493,121421],{},[383,143495,12310],{},[380,143497,143498,143504,143506],{},[543,143499,143500,143502],{},[383,143501,45101],{},[383,143503,12310],{},[458,143505,5160],{},[463,143507,465],{},[7161,143509,143510,143512],{},[383,143511,7914],{},[380,143513,143514,143516],{},[458,143515,5160],{},[543,143517,143518,143520],{},[383,143519,121421],{},[383,143521,12310],{},[383,143523,1288],{"mathvariant":557},[383,143525,137171],{"mathvariant":557},[458,143527,461],{"stretchy":460},[543,143529,143530,143532],{},[383,143531,45101],{},[383,143533,12310],{},[458,143535,468],{"stretchy":460},[387,143537,143538],{"encoding":389},"\\prod_i \\gamma_i^{\\alpha_i - 1} e^{-\\gamma_i} \u002F \\Gamma(\\alpha_i)",[363,143540,143542],{"className":143541,"ariaHidden":394},[393],[363,143543,143545,143549,143589,143592,143690,143762,143766,143769,143809],{"className":143544},[398],[363,143546],{"className":143547,"style":143548},[402],"height:1.1957em;vertical-align:-0.2997em;",[363,143550,143552,143555],{"className":143551},[1831],[363,143553,136637],{"className":143554,"style":40007},[1831,1832,5963],[363,143556,143558],{"className":143557},[629],[363,143559,143561,143581],{"className":143560},[633,634],[363,143562,143564,143578],{"className":143563},[638],[363,143565,143567],{"className":143566,"style":40020},[642],[363,143568,143569,143572],{"style":40023},[363,143570],{"className":143571,"style":651},[650],[363,143573,143575],{"className":143574},[655,656,657,658],[363,143576,12310],{"className":143577},[407,408,658],[363,143579,666],{"className":143580},[665],[363,143582,143584],{"className":143583},[638],[363,143585,143587],{"className":143586,"style":40042},[642],[363,143588],{},[363,143590],{"className":143591,"style":754},[505],[363,143593,143595,143598],{"className":143594},[407],[363,143596,121421],{"className":143597,"style":121511},[407,408],[363,143599,143601],{"className":143600},[629],[363,143602,143604,143682],{"className":143603},[633,634],[363,143605,143607,143679],{"className":143606},[638],[363,143608,143610,143622],{"className":143609,"style":136897},[642],[363,143611,143613,143616],{"style":143612},"top:-2.4231em;margin-left:-0.0556em;margin-right:0.05em;",[363,143614],{"className":143615,"style":651},[650],[363,143617,143619],{"className":143618},[655,656,657,658],[363,143620,12310],{"className":143621},[407,408,658],[363,143623,143624,143627],{"style":136912},[363,143625],{"className":143626,"style":651},[650],[363,143628,143630],{"className":143629},[655,656,657,658],[363,143631,143633,143673,143676],{"className":143632},[407,658],[363,143634,143636,143639],{"className":143635},[407,658],[363,143637,45101],{"className":143638,"style":45131},[407,408,658],[363,143640,143642],{"className":143641},[629],[363,143643,143645,143665],{"className":143644},[633,634],[363,143646,143648,143662],{"className":143647},[638],[363,143649,143651],{"className":143650,"style":40095},[642],[363,143652,143653,143656],{"style":136942},[363,143654],{"className":143655,"style":30553},[650],[363,143657,143659],{"className":143658},[655,30557,10021,658],[363,143660,12310],{"className":143661},[407,408,658],[363,143663,666],{"className":143664},[665],[363,143666,143668],{"className":143667},[638],[363,143669,143671],{"className":143670,"style":40117},[642],[363,143672],{},[363,143674,5160],{"className":143675},[2938,658],[363,143677,465],{"className":143678},[407,658],[363,143680,666],{"className":143681},[665],[363,143683,143685],{"className":143684},[638],[363,143686,143688],{"className":143687,"style":136978},[642],[363,143689],{},[363,143691,143693,143696],{"className":143692},[407],[363,143694,7914],{"className":143695},[407,408],[363,143697,143699],{"className":143698},[629],[363,143700,143702],{"className":143701},[633],[363,143703,143705],{"className":143704},[638],[363,143706,143708],{"className":143707,"style":21356},[642],[363,143709,143710,143713],{"style":7212},[363,143711],{"className":143712,"style":651},[650],[363,143714,143716],{"className":143715},[655,656,657,658],[363,143717,143719,143722],{"className":143718},[407,658],[363,143720,5160],{"className":143721},[407,658],[363,143723,143725,143728],{"className":143724},[407,658],[363,143726,121421],{"className":143727,"style":121511},[407,408,658],[363,143729,143731],{"className":143730},[629],[363,143732,143734,143754],{"className":143733},[633,634],[363,143735,143737,143751],{"className":143736},[638],[363,143738,143740],{"className":143739,"style":40095},[642],[363,143741,143742,143745],{"style":142985},[363,143743],{"className":143744,"style":30553},[650],[363,143746,143748],{"className":143747},[655,30557,10021,658],[363,143749,12310],{"className":143750},[407,408,658],[363,143752,666],{"className":143753},[665],[363,143755,143757],{"className":143756},[638],[363,143758,143760],{"className":143759,"style":40117},[642],[363,143761],{},[363,143763,143765],{"className":143764},[407],"\u002FΓ",[363,143767,461],{"className":143768},[494],[363,143770,143772,143775],{"className":143771},[407],[363,143773,45101],{"className":143774,"style":45131},[407,408],[363,143776,143778],{"className":143777},[629],[363,143779,143781,143801],{"className":143780},[633,634],[363,143782,143784,143798],{"className":143783},[638],[363,143785,143787],{"className":143786,"style":12529},[642],[363,143788,143789,143792],{"style":136107},[363,143790],{"className":143791,"style":651},[650],[363,143793,143795],{"className":143794},[655,656,657,658],[363,143796,12310],{"className":143797},[407,408,658],[363,143799,666],{"className":143800},[665],[363,143802,143804],{"className":143803},[638],[363,143805,143807],{"className":143806,"style":8315},[642],[363,143808],{},[363,143810,468],{"className":143811},[501],"。施行与命题 1.3 相同的替换 ",[363,143814,143816,143844],{"className":143815,"translate":367},[366],[363,143817,143819],{"className":143818},[371],[373,143820,143821],{"xmlns":375},[377,143822,143823,143841],{},[380,143824,143825,143831,143833,143835],{},[543,143826,143827,143829],{},[383,143828,121421],{},[383,143830,12310],{},[458,143832,471],{},[383,143834,7908],{},[543,143836,143837,143839],{},[383,143838,1121],{},[383,143840,12310],{},[387,143842,143843],{"encoding":389},"\\gamma_i = s x_i",[363,143845,143847,143902],{"className":143846,"ariaHidden":394},[393],[363,143848,143850,143853,143893,143896,143899],{"className":143849},[398],[363,143851],{"className":143852,"style":2623},[402],[363,143854,143856,143859],{"className":143855},[407],[363,143857,121421],{"className":143858,"style":121511},[407,408],[363,143860,143862],{"className":143861},[629],[363,143863,143865,143885],{"className":143864},[633,634],[363,143866,143868,143882],{"className":143867},[638],[363,143869,143871],{"className":143870,"style":12529},[642],[363,143872,143873,143876],{"style":142280},[363,143874],{"className":143875,"style":651},[650],[363,143877,143879],{"className":143878},[655,656,657,658],[363,143880,12310],{"className":143881},[407,408,658],[363,143883,666],{"className":143884},[665],[363,143886,143888],{"className":143887},[638],[363,143889,143891],{"className":143890,"style":8315},[642],[363,143892],{},[363,143894],{"className":143895,"style":506},[505],[363,143897,471],{"className":143898},[510],[363,143900],{"className":143901,"style":506},[505],[363,143903,143905,143908,143911],{"className":143904},[398],[363,143906],{"className":143907,"style":13721},[402],[363,143909,7908],{"className":143910},[407,408],[363,143912,143914,143917],{"className":143913},[407],[363,143915,1121],{"className":143916},[407,408],[363,143918,143920],{"className":143919},[629],[363,143921,143923,143943],{"className":143922},[633,634],[363,143924,143926,143940],{"className":143925},[638],[363,143927,143929],{"className":143928,"style":12529},[642],[363,143930,143931,143934],{"style":730},[363,143932],{"className":143933,"style":651},[650],[363,143935,143937],{"className":143936},[655,656,657,658],[363,143938,12310],{"className":143939},[407,408,658],[363,143941,666],{"className":143942},[665],[363,143944,143946],{"className":143945},[638],[363,143947,143949],{"className":143948,"style":8315},[642],[363,143950],{},"，联合密度变换为",[363,143953,143955],{"className":143954,"translate":367},[528],[363,143956,143958,144146],{"className":143957,"translate":367},[366],[363,143959,143961],{"className":143960},[371],[373,143962,143963],{"xmlns":375,"display":537},[377,143964,143965,144143],{},[380,143966,143967,143969,143971,143973,143975,143977,143979,143981,144025,144027,144103,144105,144107,144109,144111,144113,144115,144121,144123,144125,144127,144129,144131,144133,144135,144137,144139,144141],{},[383,143968,11],{},[458,143970,461],{"stretchy":460},[383,143972,7908],{},[458,143974,898],{"separator":394},[383,143976,1121],{"mathvariant":75560},[458,143978,468],{"stretchy":460},[458,143980,471],{},[586,143982,143983,144011],{},[380,143984,143985,144001],{},[7161,143986,143987,143989],{},[383,143988,7908],{},[380,143990,143991,143997,143999],{},[543,143992,143993,143995],{},[383,143994,45101],{},[463,143996,474],{},[458,143998,5160],{},[463,144000,465],{},[7161,144002,144003,144005],{},[383,144004,7914],{},[380,144006,144007,144009],{},[458,144008,5160],{},[383,144010,7908],{},[380,144012,144013,144015,144017,144023],{},[383,144014,137171],{"mathvariant":557},[458,144016,461],{"stretchy":460},[543,144018,144019,144021],{},[383,144020,45101],{},[463,144022,474],{},[458,144024,468],{"stretchy":460},[458,144026,3646],{},[586,144028,144029,144075],{},[380,144030,144031,144033,144035,144041,144043,144057],{},[383,144032,137171],{"mathvariant":557},[458,144034,461],{"stretchy":460},[543,144036,144037,144039],{},[383,144038,45101],{},[463,144040,474],{},[458,144042,468],{"stretchy":460},[48667,144044,144045,144047,144055],{},[458,144046,136637],{},[380,144048,144049,144051,144053],{},[383,144050,12310],{},[458,144052,471],{},[463,144054,465],{},[383,144056,11041],{},[7900,144058,144059,144061,144063],{},[383,144060,1121],{},[383,144062,12310],{},[380,144064,144065,144071,144073],{},[543,144066,144067,144069],{},[383,144068,45101],{},[383,144070,12310],{},[458,144072,5160],{},[463,144074,465],{},[380,144076,144077,144091,144093,144095,144101],{},[48667,144078,144079,144081,144089],{},[458,144080,136637],{},[380,144082,144083,144085,144087],{},[383,144084,12310],{},[458,144086,471],{},[463,144088,465],{},[383,144090,11041],{},[383,144092,137171],{"mathvariant":557},[458,144094,461],{"stretchy":460},[543,144096,144097,144099],{},[383,144098,45101],{},[383,144100,12310],{},[458,144102,468],{"stretchy":460},[458,144104,471],{},[383,144106,142382],{"mathvariant":557},[458,144108,4450],{},[458,144110,461],{"stretchy":460},[383,144112,7908],{},[458,144114,34222],{"separator":394},[543,144116,144117,144119],{},[383,144118,45101],{},[463,144120,474],{},[458,144122,898],{"separator":394},[463,144124,465],{},[458,144126,468],{"stretchy":460},[458,144128,3646],{},[383,144130,137065],{"mathvariant":557},[458,144132,4450],{},[458,144134,461],{"stretchy":460},[383,144136,1121],{"mathvariant":75560},[458,144138,34222],{"separator":394},[383,144140,45101],{"mathvariant":136008},[458,144142,468],{"stretchy":460},[387,144144,144145],{"encoding":389},"p(s, \\mathbf{x}) = \\frac{s^{\\alpha_0 - 1} e^{-s}}{\\Gamma(\\alpha_0)} \\cdot \\frac{\\Gamma(\\alpha_0) \\prod_{i=1}^K x_i^{\\alpha_i - 1}}{\\prod_{i=1}^K \\Gamma(\\alpha_i)}\n= \\operatorname{Gamma}(s; \\alpha_0, 1) \\cdot \\operatorname{Dir}(\\mathbf{x}; \\boldsymbol{\\alpha})",[363,144147,144149,144185,144415,144815,144900],{"className":144148,"ariaHidden":394},[393],[363,144150,144152,144155,144158,144161,144164,144167,144170,144173,144176,144179,144182],{"className":144151},[398],[363,144153],{"className":144154,"style":487},[402],[363,144156,11],{"className":144157},[407,408],[363,144159,461],{"className":144160},[494],[363,144162,7908],{"className":144163},[407,408],[363,144165,898],{"className":144166},[920],[363,144168],{"className":144169,"style":754},[505],[363,144171,1121],{"className":144172},[407,75905],[363,144174,468],{"className":144175},[501],[363,144177],{"className":144178,"style":506},[505],[363,144180,471],{"className":144181},[510],[363,144183],{"className":144184,"style":506},[505],[363,144186,144188,144191,144406,144409,144412],{"className":144187},[398],[363,144189],{"className":144190,"style":130314},[402],[363,144192,144194,144197,144403],{"className":144193},[407],[363,144195],{"className":144196},[494,789],[363,144198,144200],{"className":144199},[586],[363,144201,144203,144395],{"className":144202},[633,634],[363,144204,144206,144392],{"className":144205},[638],[363,144207,144209,144266,144274],{"className":144208,"style":38070},[642],[363,144210,144211,144214],{"style":805},[363,144212],{"className":144213,"style":809},[650],[363,144215,144217,144220,144223,144263],{"className":144216},[407],[363,144218,137171],{"className":144219},[407],[363,144221,461],{"className":144222},[494],[363,144224,144226,144229],{"className":144225},[407],[363,144227,45101],{"className":144228,"style":45131},[407,408],[363,144230,144232],{"className":144231},[629],[363,144233,144235,144255],{"className":144234},[633,634],[363,144236,144238,144252],{"className":144237},[638],[363,144239,144241],{"className":144240,"style":11480},[642],[363,144242,144243,144246],{"style":136107},[363,144244],{"className":144245,"style":651},[650],[363,144247,144249],{"className":144248},[655,656,657,658],[363,144250,474],{"className":144251},[407,658],[363,144253,666],{"className":144254},[665],[363,144256,144258],{"className":144257},[638],[363,144259,144261],{"className":144260,"style":8315},[642],[363,144262],{},[363,144264,468],{"className":144265},[501],[363,144267,144268,144271],{"style":821},[363,144269],{"className":144270,"style":809},[650],[363,144272],{"className":144273,"style":829},[828],[363,144275,144276,144279],{"style":832},[363,144277],{"className":144278,"style":809},[650],[363,144280,144282,144357],{"className":144281},[407],[363,144283,144285,144288],{"className":144284},[407],[363,144286,7908],{"className":144287},[407,408],[363,144289,144291],{"className":144290},[629],[363,144292,144294],{"className":144293},[633],[363,144295,144297],{"className":144296},[638],[363,144298,144300],{"className":144299,"style":20375},[642],[363,144301,144302,144305],{"style":7212},[363,144303],{"className":144304,"style":651},[650],[363,144306,144308],{"className":144307},[655,656,657,658],[363,144309,144311,144351,144354],{"className":144310},[407,658],[363,144312,144314,144317],{"className":144313},[407,658],[363,144315,45101],{"className":144316,"style":45131},[407,408,658],[363,144318,144320],{"className":144319},[629],[363,144321,144323,144343],{"className":144322},[633,634],[363,144324,144326,144340],{"className":144325},[638],[363,144327,144329],{"className":144328,"style":137304},[642],[363,144330,144331,144334],{"style":136942},[363,144332],{"className":144333,"style":30553},[650],[363,144335,144337],{"className":144336},[655,30557,10021,658],[363,144338,474],{"className":144339},[407,658],[363,144341,666],{"className":144342},[665],[363,144344,144346],{"className":144345},[638],[363,144347,144349],{"className":144348,"style":40117},[642],[363,144350],{},[363,144352,5160],{"className":144353},[2938,658],[363,144355,465],{"className":144356},[407,658],[363,144358,144360,144363],{"className":144359},[407],[363,144361,7914],{"className":144362},[407,408],[363,144364,144366],{"className":144365},[629],[363,144367,144369],{"className":144368},[633],[363,144370,144372],{"className":144371},[638],[363,144373,144375],{"className":144374,"style":21356},[642],[363,144376,144377,144380],{"style":7212},[363,144378],{"className":144379,"style":651},[650],[363,144381,144383],{"className":144382},[655,656,657,658],[363,144384,144386,144389],{"className":144385},[407,658],[363,144387,5160],{"className":144388},[407,658],[363,144390,7908],{"className":144391},[407,408,658],[363,144393,666],{"className":144394},[665],[363,144396,144398],{"className":144397},[638],[363,144399,144401],{"className":144400,"style":1948},[642],[363,144402],{},[363,144404],{"className":144405},[501,789],[363,144407],{"className":144408,"style":2934},[505],[363,144410,3646],{"className":144411},[2938],[363,144413],{"className":144414,"style":2934},[505],[363,144416,144418,144422,144806,144809,144812],{"className":144417},[398],[363,144419],{"className":144420,"style":144421},[402],"height:2.8419em;vertical-align:-1.1709em;",[363,144423,144425,144428,144803],{"className":144424},[407],[363,144426],{"className":144427},[494,789],[363,144429,144431],{"className":144430},[586],[363,144432,144434,144794],{"className":144433},[633,634],[363,144435,144437,144791],{"className":144436},[638],[363,144438,144441,144562,144570],{"className":144439,"style":144440},[642],"height:1.6709em;",[363,144442,144444,144447],{"style":144443},"top:-2.1288em;",[363,144445],{"className":144446,"style":809},[650],[363,144448,144450,144510,144513,144516,144519,144559],{"className":144449},[407],[363,144451,144453,144456],{"className":144452},[1831],[363,144454,136637],{"className":144455,"style":40007},[1831,1832,5963],[363,144457,144459],{"className":144458},[629],[363,144460,144462,144502],{"className":144461},[633,634],[363,144463,144465,144499],{"className":144464},[638],[363,144466,144468,144488],{"className":144467,"style":133494},[642],[363,144469,144470,144473],{"style":40023},[363,144471],{"className":144472,"style":651},[650],[363,144474,144476],{"className":144475},[655,656,657,658],[363,144477,144479,144482,144485],{"className":144478},[407,658],[363,144480,12310],{"className":144481},[407,408,658],[363,144483,471],{"className":144484},[510,658],[363,144486,465],{"className":144487},[407,658],[363,144489,144490,144493],{"style":133517},[363,144491],{"className":144492,"style":651},[650],[363,144494,144496],{"className":144495},[655,656,657,658],[363,144497,11041],{"className":144498,"style":11129},[407,408,658],[363,144500,666],{"className":144501},[665],[363,144503,144505],{"className":144504},[638],[363,144506,144508],{"className":144507,"style":40042},[642],[363,144509],{},[363,144511],{"className":144512,"style":754},[505],[363,144514,137171],{"className":144515},[407],[363,144517,461],{"className":144518},[494],[363,144520,144522,144525],{"className":144521},[407],[363,144523,45101],{"className":144524,"style":45131},[407,408],[363,144526,144528],{"className":144527},[629],[363,144529,144531,144551],{"className":144530},[633,634],[363,144532,144534,144548],{"className":144533},[638],[363,144535,144537],{"className":144536,"style":12529},[642],[363,144538,144539,144542],{"style":136107},[363,144540],{"className":144541,"style":651},[650],[363,144543,144545],{"className":144544},[655,656,657,658],[363,144546,12310],{"className":144547},[407,408,658],[363,144549,666],{"className":144550},[665],[363,144552,144554],{"className":144553},[638],[363,144555,144557],{"className":144556,"style":8315},[642],[363,144558],{},[363,144560,468],{"className":144561},[501],[363,144563,144564,144567],{"style":821},[363,144565],{"className":144566,"style":809},[650],[363,144568],{"className":144569,"style":829},[828],[363,144571,144573,144576],{"style":144572},"top:-3.6897em;",[363,144574],{"className":144575,"style":809},[650],[363,144577,144579,144582,144585,144625,144628,144631,144691,144694],{"className":144578},[407],[363,144580,137171],{"className":144581},[407],[363,144583,461],{"className":144584},[494],[363,144586,144588,144591],{"className":144587},[407],[363,144589,45101],{"className":144590,"style":45131},[407,408],[363,144592,144594],{"className":144593},[629],[363,144595,144597,144617],{"className":144596},[633,634],[363,144598,144600,144614],{"className":144599},[638],[363,144601,144603],{"className":144602,"style":11480},[642],[363,144604,144605,144608],{"style":136107},[363,144606],{"className":144607,"style":651},[650],[363,144609,144611],{"className":144610},[655,656,657,658],[363,144612,474],{"className":144613},[407,658],[363,144615,666],{"className":144616},[665],[363,144618,144620],{"className":144619},[638],[363,144621,144623],{"className":144622,"style":8315},[642],[363,144624],{},[363,144626,468],{"className":144627},[501],[363,144629],{"className":144630,"style":754},[505],[363,144632,144634,144637],{"className":144633},[1831],[363,144635,136637],{"className":144636,"style":40007},[1831,1832,5963],[363,144638,144640],{"className":144639},[629],[363,144641,144643,144683],{"className":144642},[633,634],[363,144644,144646,144680],{"className":144645},[638],[363,144647,144649,144669],{"className":144648,"style":133494},[642],[363,144650,144651,144654],{"style":40023},[363,144652],{"className":144653,"style":651},[650],[363,144655,144657],{"className":144656},[655,656,657,658],[363,144658,144660,144663,144666],{"className":144659},[407,658],[363,144661,12310],{"className":144662},[407,408,658],[363,144664,471],{"className":144665},[510,658],[363,144667,465],{"className":144668},[407,658],[363,144670,144671,144674],{"style":133517},[363,144672],{"className":144673,"style":651},[650],[363,144675,144677],{"className":144676},[655,656,657,658],[363,144678,11041],{"className":144679,"style":11129},[407,408,658],[363,144681,666],{"className":144682},[665],[363,144684,144686],{"className":144685},[638],[363,144687,144689],{"className":144688,"style":40042},[642],[363,144690],{},[363,144692],{"className":144693,"style":754},[505],[363,144695,144697,144700],{"className":144696},[407],[363,144698,1121],{"className":144699},[407,408],[363,144701,144703],{"className":144702},[629],[363,144704,144706,144783],{"className":144705},[633,634],[363,144707,144709,144780],{"className":144708},[638],[363,144710,144712,144723],{"className":144711,"style":136897},[642],[363,144713,144714,144717],{"style":136900},[363,144715],{"className":144716,"style":651},[650],[363,144718,144720],{"className":144719},[655,656,657,658],[363,144721,12310],{"className":144722},[407,408,658],[363,144724,144725,144728],{"style":136912},[363,144726],{"className":144727,"style":651},[650],[363,144729,144731],{"className":144730},[655,656,657,658],[363,144732,144734,144774,144777],{"className":144733},[407,658],[363,144735,144737,144740],{"className":144736},[407,658],[363,144738,45101],{"className":144739,"style":45131},[407,408,658],[363,144741,144743],{"className":144742},[629],[363,144744,144746,144766],{"className":144745},[633,634],[363,144747,144749,144763],{"className":144748},[638],[363,144750,144752],{"className":144751,"style":40095},[642],[363,144753,144754,144757],{"style":136942},[363,144755],{"className":144756,"style":30553},[650],[363,144758,144760],{"className":144759},[655,30557,10021,658],[363,144761,12310],{"className":144762},[407,408,658],[363,144764,666],{"className":144765},[665],[363,144767,144769],{"className":144768},[638],[363,144770,144772],{"className":144771,"style":40117},[642],[363,144773],{},[363,144775,5160],{"className":144776},[2938,658],[363,144778,465],{"className":144779},[407,658],[363,144781,666],{"className":144782},[665],[363,144784,144786],{"className":144785},[638],[363,144787,144789],{"className":144788,"style":136978},[642],[363,144790],{},[363,144792,666],{"className":144793},[665],[363,144795,144797],{"className":144796},[638],[363,144798,144801],{"className":144799,"style":144800},[642],"height:1.1709em;",[363,144802],{},[363,144804],{"className":144805},[501,789],[363,144807],{"className":144808,"style":506},[505],[363,144810,471],{"className":144811},[510],[363,144813],{"className":144814,"style":506},[505],[363,144816,144818,144821,144827,144830,144833,144836,144839,144879,144882,144885,144888,144891,144894,144897],{"className":144817},[398],[363,144819],{"className":144820,"style":487},[402],[363,144822,144824],{"className":144823},[1831],[363,144825,142382],{"className":144826},[407,33009],[363,144828,461],{"className":144829},[494],[363,144831,7908],{"className":144832},[407,408],[363,144834,34222],{"className":144835},[920],[363,144837],{"className":144838,"style":754},[505],[363,144840,144842,144845],{"className":144841},[407],[363,144843,45101],{"className":144844,"style":45131},[407,408],[363,144846,144848],{"className":144847},[629],[363,144849,144851,144871],{"className":144850},[633,634],[363,144852,144854,144868],{"className":144853},[638],[363,144855,144857],{"className":144856,"style":11480},[642],[363,144858,144859,144862],{"style":136107},[363,144860],{"className":144861,"style":651},[650],[363,144863,144865],{"className":144864},[655,656,657,658],[363,144866,474],{"className":144867},[407,658],[363,144869,666],{"className":144870},[665],[363,144872,144874],{"className":144873},[638],[363,144875,144877],{"className":144876,"style":8315},[642],[363,144878],{},[363,144880,898],{"className":144881},[920],[363,144883],{"className":144884,"style":754},[505],[363,144886,465],{"className":144887},[407],[363,144889,468],{"className":144890},[501],[363,144892],{"className":144893,"style":2934},[505],[363,144895,3646],{"className":144896},[2938],[363,144898],{"className":144899,"style":2934},[505],[363,144901,144903,144906,144912,144915,144918,144921,144924,144933],{"className":144902},[398],[363,144904],{"className":144905,"style":487},[402],[363,144907,144909],{"className":144908},[1831],[363,144910,137065],{"className":144911},[407,33009],[363,144913,461],{"className":144914},[494],[363,144916,1121],{"className":144917},[407,75905],[363,144919,34222],{"className":144920},[920],[363,144922],{"className":144923,"style":754},[505],[363,144925,144927],{"className":144926},[407],[363,144928,144930],{"className":144929},[407],[363,144931,45101],{"className":144932},[407,136068],[363,144934,468],{"className":144935},[501],[11,144937,144938,144939,144967,144968,144996,144997,2756,145025,145053],{},"右侧分解为仅含 ",[363,144940,144942,144955],{"className":144941,"translate":367},[366],[363,144943,144945],{"className":144944},[371],[373,144946,144947],{"xmlns":375},[377,144948,144949,144953],{},[380,144950,144951],{},[383,144952,7908],{},[387,144954,7908],{"encoding":389},[363,144956,144958],{"className":144957,"ariaHidden":394},[393],[363,144959,144961,144964],{"className":144960},[398],[363,144962],{"className":144963,"style":2692},[402],[363,144965,7908],{"className":144966},[407,408]," 与仅含 ",[363,144969,144971,144984],{"className":144970,"translate":367},[366],[363,144972,144974],{"className":144973},[371],[373,144975,144976],{"xmlns":375},[377,144977,144978,144982],{},[380,144979,144980],{},[383,144981,1121],{"mathvariant":75560},[387,144983,135607],{"encoding":389},[363,144985,144987],{"className":144986,"ariaHidden":394},[393],[363,144988,144990,144993],{"className":144989},[398],[363,144991],{"className":144992,"style":135617},[402],[363,144994,1121],{"className":144995},[407,75905]," 的两个因子的乘积，故 ",[363,144998,145000,145013],{"className":144999,"translate":367},[366],[363,145001,145003],{"className":145002},[371],[373,145004,145005],{"xmlns":375},[377,145006,145007,145011],{},[380,145008,145009],{},[383,145010,7908],{},[387,145012,7908],{"encoding":389},[363,145014,145016],{"className":145015,"ariaHidden":394},[393],[363,145017,145019,145022],{"className":145018},[398],[363,145020],{"className":145021,"style":2692},[402],[363,145023,7908],{"className":145024},[407,408],[363,145026,145028,145041],{"className":145027,"translate":367},[366],[363,145029,145031],{"className":145030},[371],[373,145032,145033],{"xmlns":375},[377,145034,145035,145039],{},[380,145036,145037],{},[383,145038,1121],{"mathvariant":75560},[387,145040,135607],{"encoding":389},[363,145042,145044],{"className":145043,"ariaHidden":394},[393],[363,145045,145047,145050],{"className":145046},[398],[363,145048],{"className":145049,"style":135617},[402],[363,145051,1121],{"className":145052},[407,75905]," 独立，且各自的边缘分布如命题所述。",[11,145055,145056,145057,145101,145102,145130,145131,145313,145314,145317],{},"命题 1.4 给出了三条即时的推论。其一，它提供了一个 ",[363,145058,145060,145080],{"className":145059,"translate":367},[366],[363,145061,145063],{"className":145062},[371],[373,145064,145065],{"xmlns":375},[377,145066,145067,145077],{},[380,145068,145069,145071,145073,145075],{},[383,145070,19568],{},[458,145072,461],{"stretchy":460},[383,145074,11041],{},[458,145076,468],{"stretchy":460},[387,145078,145079],{"encoding":389},"O(K)",[363,145081,145083],{"className":145082,"ariaHidden":394},[393],[363,145084,145086,145089,145092,145095,145098],{"className":145085},[398],[363,145087],{"className":145088,"style":487},[402],[363,145090,19568],{"className":145091,"style":625},[407,408],[363,145093,461],{"className":145094},[494],[363,145096,11041],{"className":145097,"style":11129},[407,408],[363,145099,468],{"className":145100},[501]," 的精确采样算法：独立抽取 ",[363,145103,145105,145118],{"className":145104,"translate":367},[366],[363,145106,145108],{"className":145107},[371],[373,145109,145110],{"xmlns":375},[377,145111,145112,145116],{},[380,145113,145114],{},[383,145115,11041],{},[387,145117,11041],{"encoding":389},[363,145119,145121],{"className":145120,"ariaHidden":394},[393],[363,145122,145124,145127],{"className":145123},[398],[363,145125],{"className":145126,"style":1011},[402],[363,145128,11041],{"className":145129,"style":11129},[407,408]," 个 Gamma 变量再归一化，无需拒绝采样或逆变换。其二，它说明参数 ",[363,145132,145134,145166],{"className":145133,"translate":367},[366],[363,145135,145137],{"className":145136},[371],[373,145138,145139],{"xmlns":375},[377,145140,145141,145163],{},[380,145142,145143,145149,145151,145157],{},[543,145144,145145,145147],{},[383,145146,45101],{},[463,145148,474],{},[458,145150,471],{},[543,145152,145153,145155],{},[458,145154,13808],{},[383,145156,12310],{},[543,145158,145159,145161],{},[383,145160,45101],{},[383,145162,12310],{},[387,145164,145165],{"encoding":389},"\\alpha_0 = \\sum_i \\alpha_i",[363,145167,145169,145224],{"className":145168,"ariaHidden":394},[393],[363,145170,145172,145175,145215,145218,145221],{"className":145171},[398],[363,145173],{"className":145174,"style":13721},[402],[363,145176,145178,145181],{"className":145177},[407],[363,145179,45101],{"className":145180,"style":45131},[407,408],[363,145182,145184],{"className":145183},[629],[363,145185,145187,145207],{"className":145186},[633,634],[363,145188,145190,145204],{"className":145189},[638],[363,145191,145193],{"className":145192,"style":11480},[642],[363,145194,145195,145198],{"style":136107},[363,145196],{"className":145197,"style":651},[650],[363,145199,145201],{"className":145200},[655,656,657,658],[363,145202,474],{"className":145203},[407,658],[363,145205,666],{"className":145206},[665],[363,145208,145210],{"className":145209},[638],[363,145211,145213],{"className":145212,"style":8315},[642],[363,145214],{},[363,145216],{"className":145217,"style":506},[505],[363,145219,471],{"className":145220},[510],[363,145222],{"className":145223,"style":506},[505],[363,145225,145227,145230,145270,145273],{"className":145226},[398],[363,145228],{"className":145229,"style":138904},[402],[363,145231,145233,145236],{"className":145232},[1831],[363,145234,13808],{"className":145235,"style":40007},[1831,1832,5963],[363,145237,145239],{"className":145238},[629],[363,145240,145242,145262],{"className":145241},[633,634],[363,145243,145245,145259],{"className":145244},[638],[363,145246,145248],{"className":145247,"style":40020},[642],[363,145249,145250,145253],{"style":40023},[363,145251],{"className":145252,"style":651},[650],[363,145254,145256],{"className":145255},[655,656,657,658],[363,145257,12310],{"className":145258},[407,408,658],[363,145260,666],{"className":145261},[665],[363,145263,145265],{"className":145264},[638],[363,145266,145268],{"className":145267,"style":40042},[642],[363,145269],{},[363,145271],{"className":145272,"style":754},[505],[363,145274,145276,145279],{"className":145275},[407],[363,145277,45101],{"className":145278,"style":45131},[407,408],[363,145280,145282],{"className":145281},[629],[363,145283,145285,145305],{"className":145284},[633,634],[363,145286,145288,145302],{"className":145287},[638],[363,145289,145291],{"className":145290,"style":12529},[642],[363,145292,145293,145296],{"style":136107},[363,145294],{"className":145295,"style":651},[650],[363,145297,145299],{"className":145298},[655,656,657,658],[363,145300,12310],{"className":145301},[407,408,658],[363,145303,666],{"className":145304},[665],[363,145306,145308],{"className":145307},[638],[363,145309,145311],{"className":145310,"style":8315},[642],[363,145312],{}," 在概率意义上是",[1572,145315,145316],{},"先于归一化的总质量","，这一角色将在 2.2 节被重新参数化为一个精度参数。其三，它把迪利克雷分布与 Gamma 分布、进而与 Poisson 过程联系起来，这正是 2.5 节分裂构造的来源。",[2658,145319,145321],{"id":145320},"_14-与-beta-分布多项分布的关系","1.4 与 Beta 分布、多项分布的关系",[11,145323,145324,31165,145327,145377,145378,145534,145535,145605],{},[1572,145325,145326],{},"退化到 Beta 分布。",[363,145328,145330,145347],{"className":145329,"translate":367},[366],[363,145331,145333],{"className":145332},[371],[373,145334,145335],{"xmlns":375},[377,145336,145337,145345],{},[380,145338,145339,145341,145343],{},[383,145340,11041],{},[458,145342,471],{},[463,145344,2810],{},[387,145346,135042],{"encoding":389},[363,145348,145350,145368],{"className":145349,"ariaHidden":394},[393],[363,145351,145353,145356,145359,145362,145365],{"className":145352},[398],[363,145354],{"className":145355,"style":1011},[402],[363,145357,11041],{"className":145358,"style":11129},[407,408],[363,145360],{"className":145361,"style":506},[505],[363,145363,471],{"className":145364},[510],[363,145366],{"className":145367,"style":506},[505],[363,145369,145371,145374],{"className":145370},[398],[363,145372],{"className":145373,"style":520},[402],[363,145375,2810],{"className":145376},[407]," 时，约束 ",[363,145379,145381,145411],{"className":145380,"translate":367},[366],[363,145382,145384],{"className":145383},[371],[373,145385,145386],{"xmlns":375},[377,145387,145388,145408],{},[380,145389,145390,145396,145398,145404,145406],{},[543,145391,145392,145394],{},[383,145393,1121],{},[463,145395,465],{},[458,145397,2817],{},[543,145399,145400,145402],{},[383,145401,1121],{},[463,145403,2810],{},[458,145405,471],{},[463,145407,465],{},[387,145409,145410],{"encoding":389},"x_1 + x_2 = 1",[363,145412,145414,145470,145525],{"className":145413,"ariaHidden":394},[393],[363,145415,145417,145421,145461,145464,145467],{"className":145416},[398],[363,145418],{"className":145419,"style":145420},[402],"height:0.7333em;vertical-align:-0.15em;",[363,145422,145424,145427],{"className":145423},[407],[363,145425,1121],{"className":145426},[407,408],[363,145428,145430],{"className":145429},[629],[363,145431,145433,145453],{"className":145432},[633,634],[363,145434,145436,145450],{"className":145435},[638],[363,145437,145439],{"className":145438,"style":11480},[642],[363,145440,145441,145444],{"style":730},[363,145442],{"className":145443,"style":651},[650],[363,145445,145447],{"className":145446},[655,656,657,658],[363,145448,465],{"className":145449},[407,658],[363,145451,666],{"className":145452},[665],[363,145454,145456],{"className":145455},[638],[363,145457,145459],{"className":145458,"style":8315},[642],[363,145460],{},[363,145462],{"className":145463,"style":2934},[505],[363,145465,2817],{"className":145466},[2938],[363,145468],{"className":145469,"style":2934},[505],[363,145471,145473,145476,145516,145519,145522],{"className":145472},[398],[363,145474],{"className":145475,"style":13721},[402],[363,145477,145479,145482],{"className":145478},[407],[363,145480,1121],{"className":145481},[407,408],[363,145483,145485],{"className":145484},[629],[363,145486,145488,145508],{"className":145487},[633,634],[363,145489,145491,145505],{"className":145490},[638],[363,145492,145494],{"className":145493,"style":11480},[642],[363,145495,145496,145499],{"style":730},[363,145497],{"className":145498,"style":651},[650],[363,145500,145502],{"className":145501},[655,656,657,658],[363,145503,2810],{"className":145504},[407,658],[363,145506,666],{"className":145507},[665],[363,145509,145511],{"className":145510},[638],[363,145512,145514],{"className":145513,"style":8315},[642],[363,145515],{},[363,145517],{"className":145518,"style":506},[505],[363,145520,471],{"className":145521},[510],[363,145523],{"className":145524,"style":506},[505],[363,145526,145528,145531],{"className":145527},[398],[363,145529],{"className":145530,"style":520},[402],[363,145532,465],{"className":145533},[407]," 使分布由单一变量 ",[363,145536,145538,145556],{"className":145537,"translate":367},[366],[363,145539,145541],{"className":145540},[371],[373,145542,145543],{"xmlns":375},[377,145544,145545,145553],{},[380,145546,145547],{},[543,145548,145549,145551],{},[383,145550,1121],{},[463,145552,465],{},[387,145554,145555],{"encoding":389},"x_1",[363,145557,145559],{"className":145558,"ariaHidden":394},[393],[363,145560,145562,145565],{"className":145561},[398],[363,145563],{"className":145564,"style":13721},[402],[363,145566,145568,145571],{"className":145567},[407],[363,145569,1121],{"className":145570},[407,408],[363,145572,145574],{"className":145573},[629],[363,145575,145577,145597],{"className":145576},[633,634],[363,145578,145580,145594],{"className":145579},[638],[363,145581,145583],{"className":145582,"style":11480},[642],[363,145584,145585,145588],{"style":730},[363,145586],{"className":145587,"style":651},[650],[363,145589,145591],{"className":145590},[655,656,657,658],[363,145592,465],{"className":145593},[407,658],[363,145595,666],{"className":145596},[665],[363,145598,145600],{"className":145599},[638],[363,145601,145603],{"className":145602,"style":8315},[642],[363,145604],{}," 完全决定，密度退化为",[363,145607,145609],{"className":145608,"translate":367},[528],[363,145610,145612,145781],{"className":145611,"translate":367},[366],[363,145613,145615],{"className":145614},[371],[373,145616,145617],{"xmlns":375,"display":537},[377,145618,145619,145778],{},[380,145620,145621,145623,145625,145631,145633,145639,145641,145647,145649,145651,145723,145725,145727,145729,145731,145733,145735,145737,145743,145745,145751,145753,145755,145758,145760,145762,145768,145770,145776],{},[383,145622,385],{},[458,145624,461],{"stretchy":460},[543,145626,145627,145629],{},[383,145628,1121],{},[463,145630,465],{},[458,145632,5155],{},[543,145634,145635,145637],{},[383,145636,45101],{},[463,145638,465],{},[458,145640,898],{"separator":394},[543,145642,145643,145645],{},[383,145644,45101],{},[463,145646,2810],{},[458,145648,468],{"stretchy":460},[458,145650,471],{},[586,145652,145653,145701],{},[380,145654,145655,145673,145675,145677,145679,145685],{},[7900,145656,145657,145659,145661],{},[383,145658,1121],{},[463,145660,465],{},[380,145662,145663,145669,145671],{},[543,145664,145665,145667],{},[383,145666,45101],{},[463,145668,465],{},[458,145670,5160],{},[463,145672,465],{},[458,145674,461],{"stretchy":460},[463,145676,465],{},[458,145678,5160],{},[543,145680,145681,145683],{},[383,145682,1121],{},[463,145684,465],{},[7161,145686,145687,145689],{},[458,145688,468],{"stretchy":460},[380,145690,145691,145697,145699],{},[543,145692,145693,145695],{},[383,145694,45101],{},[463,145696,2810],{},[458,145698,5160],{},[463,145700,465],{},[380,145702,145703,145705,145707,145713,145715,145721],{},[383,145704,39638],{},[458,145706,461],{"stretchy":460},[543,145708,145709,145711],{},[383,145710,45101],{},[463,145712,465],{},[458,145714,898],{"separator":394},[543,145716,145717,145719],{},[383,145718,45101],{},[463,145720,2810],{},[458,145722,468],{"stretchy":460},[458,145724,898],{"separator":394},[505,145726],{"width":3609},[1644,145728,87982],{},[505,145730],{"width":3609},[383,145732,137065],{"mathvariant":557},[458,145734,4450],{},[458,145736,461],{"stretchy":460},[543,145738,145739,145741],{},[383,145740,45101],{},[463,145742,465],{},[458,145744,898],{"separator":394},[543,145746,145747,145749],{},[383,145748,45101],{},[463,145750,2810],{},[458,145752,468],{"stretchy":460},[458,145754,94874],{},[383,145756,145757],{"mathvariant":557},"Beta",[458,145759,4450],{},[458,145761,461],{"stretchy":460},[543,145763,145764,145766],{},[383,145765,45101],{},[463,145767,465],{},[458,145769,898],{"separator":394},[543,145771,145772,145774],{},[383,145773,45101],{},[463,145775,2810],{},[458,145777,468],{"stretchy":460},[387,145779,145780],{"encoding":389},"f(x_1 \\mid \\alpha_1, \\alpha_2) = \\frac{x_1^{\\alpha_1 - 1}(1 - x_1)^{\\alpha_2 - 1}}{B(\\alpha_1, \\alpha_2)},\n\\qquad \\text{即} \\qquad \\operatorname{Dir}(\\alpha_1, \\alpha_2) \\equiv \\operatorname{Beta}(\\alpha_1, \\alpha_2)",[363,145782,145784,145845,145949,146464],{"className":145783,"ariaHidden":394},[393],[363,145785,145787,145790,145793,145796,145836,145839,145842],{"className":145786},[398],[363,145788],{"className":145789,"style":487},[402],[363,145791,385],{"className":145792,"style":409},[407,408],[363,145794,461],{"className":145795},[494],[363,145797,145799,145802],{"className":145798},[407],[363,145800,1121],{"className":145801},[407,408],[363,145803,145805],{"className":145804},[629],[363,145806,145808,145828],{"className":145807},[633,634],[363,145809,145811,145825],{"className":145810},[638],[363,145812,145814],{"className":145813,"style":11480},[642],[363,145815,145816,145819],{"style":730},[363,145817],{"className":145818,"style":651},[650],[363,145820,145822],{"className":145821},[655,656,657,658],[363,145823,465],{"className":145824},[407,658],[363,145826,666],{"className":145827},[665],[363,145829,145831],{"className":145830},[638],[363,145832,145834],{"className":145833,"style":8315},[642],[363,145835],{},[363,145837],{"className":145838,"style":506},[505],[363,145840,5155],{"className":145841},[510],[363,145843],{"className":145844,"style":506},[505],[363,145846,145848,145851,145891,145894,145897,145937,145940,145943,145946],{"className":145847},[398],[363,145849],{"className":145850,"style":487},[402],[363,145852,145854,145857],{"className":145853},[407],[363,145855,45101],{"className":145856,"style":45131},[407,408],[363,145858,145860],{"className":145859},[629],[363,145861,145863,145883],{"className":145862},[633,634],[363,145864,145866,145880],{"className":145865},[638],[363,145867,145869],{"className":145868,"style":11480},[642],[363,145870,145871,145874],{"style":136107},[363,145872],{"className":145873,"style":651},[650],[363,145875,145877],{"className":145876},[655,656,657,658],[363,145878,465],{"className":145879},[407,658],[363,145881,666],{"className":145882},[665],[363,145884,145886],{"className":145885},[638],[363,145887,145889],{"className":145888,"style":8315},[642],[363,145890],{},[363,145892,898],{"className":145893},[920],[363,145895],{"className":145896,"style":754},[505],[363,145898,145900,145903],{"className":145899},[407],[363,145901,45101],{"className":145902,"style":45131},[407,408],[363,145904,145906],{"className":145905},[629],[363,145907,145909,145929],{"className":145908},[633,634],[363,145910,145912,145926],{"className":145911},[638],[363,145913,145915],{"className":145914,"style":11480},[642],[363,145916,145917,145920],{"style":136107},[363,145918],{"className":145919,"style":651},[650],[363,145921,145923],{"className":145922},[655,656,657,658],[363,145924,2810],{"className":145925},[407,658],[363,145927,666],{"className":145928},[665],[363,145930,145932],{"className":145931},[638],[363,145933,145935],{"className":145934,"style":8315},[642],[363,145936],{},[363,145938,468],{"className":145939},[501],[363,145941],{"className":145942,"style":506},[505],[363,145944,471],{"className":145945},[510],[363,145947],{"className":145948,"style":506},[505],[363,145950,145952,145956,146336,146339,146342,146345,146351,146354,146357,146363,146366,146406,146409,146412,146452,146455,146458,146461],{"className":145951},[398],[363,145953],{"className":145954,"style":145955},[402],"height:2.509em;vertical-align:-0.936em;",[363,145957,145959,145962,146333],{"className":145958},[407],[363,145960],{"className":145961},[494,789],[363,145963,145965],{"className":145964},[586],[363,145966,145968,146325],{"className":145967},[633,634],[363,145969,145971,146322],{"className":145970},[638],[363,145972,145975,146078,146086],{"className":145973,"style":145974},[642],"height:1.573em;",[363,145976,145977,145980],{"style":805},[363,145978],{"className":145979,"style":809},[650],[363,145981,145983,145986,145989,146029,146032,146035,146075],{"className":145982},[407],[363,145984,39638],{"className":145985,"style":39734},[407,408],[363,145987,461],{"className":145988},[494],[363,145990,145992,145995],{"className":145991},[407],[363,145993,45101],{"className":145994,"style":45131},[407,408],[363,145996,145998],{"className":145997},[629],[363,145999,146001,146021],{"className":146000},[633,634],[363,146002,146004,146018],{"className":146003},[638],[363,146005,146007],{"className":146006,"style":11480},[642],[363,146008,146009,146012],{"style":136107},[363,146010],{"className":146011,"style":651},[650],[363,146013,146015],{"className":146014},[655,656,657,658],[363,146016,465],{"className":146017},[407,658],[363,146019,666],{"className":146020},[665],[363,146022,146024],{"className":146023},[638],[363,146025,146027],{"className":146026,"style":8315},[642],[363,146028],{},[363,146030,898],{"className":146031},[920],[363,146033],{"className":146034,"style":754},[505],[363,146036,146038,146041],{"className":146037},[407],[363,146039,45101],{"className":146040,"style":45131},[407,408],[363,146042,146044],{"className":146043},[629],[363,146045,146047,146067],{"className":146046},[633,634],[363,146048,146050,146064],{"className":146049},[638],[363,146051,146053],{"className":146052,"style":11480},[642],[363,146054,146055,146058],{"style":136107},[363,146056],{"className":146057,"style":651},[650],[363,146059,146061],{"className":146060},[655,656,657,658],[363,146062,2810],{"className":146063},[407,658],[363,146065,666],{"className":146066},[665],[363,146068,146070],{"className":146069},[638],[363,146071,146073],{"className":146072,"style":8315},[642],[363,146074],{},[363,146076,468],{"className":146077},[501],[363,146079,146080,146083],{"style":821},[363,146081],{"className":146082,"style":809},[650],[363,146084],{"className":146085,"style":829},[828],[363,146087,146088,146091],{"style":832},[363,146089],{"className":146090,"style":809},[650],[363,146092,146094,146192,146195,146198,146201,146204,146207,146247],{"className":146093},[407],[363,146095,146097,146100],{"className":146096},[407],[363,146098,1121],{"className":146099},[407,408],[363,146101,146103],{"className":146102},[629],[363,146104,146106,146184],{"className":146105},[633,634],[363,146107,146109,146181],{"className":146108},[638],[363,146110,146112,146124],{"className":146111,"style":136897},[642],[363,146113,146115,146118],{"style":146114},"top:-2.4337em;margin-left:0em;margin-right:0.05em;",[363,146116],{"className":146117,"style":651},[650],[363,146119,146121],{"className":146120},[655,656,657,658],[363,146122,465],{"className":146123},[407,658],[363,146125,146126,146129],{"style":136912},[363,146127],{"className":146128,"style":651},[650],[363,146130,146132],{"className":146131},[655,656,657,658],[363,146133,146135,146175,146178],{"className":146134},[407,658],[363,146136,146138,146141],{"className":146137},[407,658],[363,146139,45101],{"className":146140,"style":45131},[407,408,658],[363,146142,146144],{"className":146143},[629],[363,146145,146147,146167],{"className":146146},[633,634],[363,146148,146150,146164],{"className":146149},[638],[363,146151,146153],{"className":146152,"style":137304},[642],[363,146154,146155,146158],{"style":136942},[363,146156],{"className":146157,"style":30553},[650],[363,146159,146161],{"className":146160},[655,30557,10021,658],[363,146162,465],{"className":146163},[407,658],[363,146165,666],{"className":146166},[665],[363,146168,146170],{"className":146169},[638],[363,146171,146173],{"className":146172,"style":40117},[642],[363,146174],{},[363,146176,5160],{"className":146177},[2938,658],[363,146179,465],{"className":146180},[407,658],[363,146182,666],{"className":146183},[665],[363,146185,146187],{"className":146186},[638],[363,146188,146190],{"className":146189,"style":125496},[642],[363,146191],{},[363,146193,461],{"className":146194},[494],[363,146196,465],{"className":146197},[407],[363,146199],{"className":146200,"style":2934},[505],[363,146202,5160],{"className":146203},[2938],[363,146205],{"className":146206,"style":2934},[505],[363,146208,146210,146213],{"className":146209},[407],[363,146211,1121],{"className":146212},[407,408],[363,146214,146216],{"className":146215},[629],[363,146217,146219,146239],{"className":146218},[633,634],[363,146220,146222,146236],{"className":146221},[638],[363,146223,146225],{"className":146224,"style":11480},[642],[363,146226,146227,146230],{"style":730},[363,146228],{"className":146229,"style":651},[650],[363,146231,146233],{"className":146232},[655,656,657,658],[363,146234,465],{"className":146235},[407,658],[363,146237,666],{"className":146238},[665],[363,146240,146242],{"className":146241},[638],[363,146243,146245],{"className":146244,"style":8315},[642],[363,146246],{},[363,146248,146250,146253],{"className":146249},[501],[363,146251,468],{"className":146252},[501],[363,146254,146256],{"className":146255},[629],[363,146257,146259],{"className":146258},[633],[363,146260,146262],{"className":146261},[638],[363,146263,146265],{"className":146264,"style":20375},[642],[363,146266,146267,146270],{"style":7212},[363,146268],{"className":146269,"style":651},[650],[363,146271,146273],{"className":146272},[655,656,657,658],[363,146274,146276,146316,146319],{"className":146275},[407,658],[363,146277,146279,146282],{"className":146278},[407,658],[363,146280,45101],{"className":146281,"style":45131},[407,408,658],[363,146283,146285],{"className":146284},[629],[363,146286,146288,146308],{"className":146287},[633,634],[363,146289,146291,146305],{"className":146290},[638],[363,146292,146294],{"className":146293,"style":137304},[642],[363,146295,146296,146299],{"style":136942},[363,146297],{"className":146298,"style":30553},[650],[363,146300,146302],{"className":146301},[655,30557,10021,658],[363,146303,2810],{"className":146304},[407,658],[363,146306,666],{"className":146307},[665],[363,146309,146311],{"className":146310},[638],[363,146312,146314],{"className":146313,"style":40117},[642],[363,146315],{},[363,146317,5160],{"className":146318},[2938,658],[363,146320,465],{"className":146321},[407,658],[363,146323,666],{"className":146324},[665],[363,146326,146328],{"className":146327},[638],[363,146329,146331],{"className":146330,"style":1948},[642],[363,146332],{},[363,146334],{"className":146335},[501,789],[363,146337,898],{"className":146338},[920],[363,146340],{"className":146341,"style":3981},[505],[363,146343],{"className":146344,"style":754},[505],[363,146346,146348],{"className":146347},[407,4945],[363,146349,87982],{"className":146350},[407,4949],[363,146352],{"className":146353,"style":3981},[505],[363,146355],{"className":146356,"style":754},[505],[363,146358,146360],{"className":146359},[1831],[363,146361,137065],{"className":146362},[407,33009],[363,146364,461],{"className":146365},[494],[363,146367,146369,146372],{"className":146368},[407],[363,146370,45101],{"className":146371,"style":45131},[407,408],[363,146373,146375],{"className":146374},[629],[363,146376,146378,146398],{"className":146377},[633,634],[363,146379,146381,146395],{"className":146380},[638],[363,146382,146384],{"className":146383,"style":11480},[642],[363,146385,146386,146389],{"style":136107},[363,146387],{"className":146388,"style":651},[650],[363,146390,146392],{"className":146391},[655,656,657,658],[363,146393,465],{"className":146394},[407,658],[363,146396,666],{"className":146397},[665],[363,146399,146401],{"className":146400},[638],[363,146402,146404],{"className":146403,"style":8315},[642],[363,146405],{},[363,146407,898],{"className":146408},[920],[363,146410],{"className":146411,"style":754},[505],[363,146413,146415,146418],{"className":146414},[407],[363,146416,45101],{"className":146417,"style":45131},[407,408],[363,146419,146421],{"className":146420},[629],[363,146422,146424,146444],{"className":146423},[633,634],[363,146425,146427,146441],{"className":146426},[638],[363,146428,146430],{"className":146429,"style":11480},[642],[363,146431,146432,146435],{"style":136107},[363,146433],{"className":146434,"style":651},[650],[363,146436,146438],{"className":146437},[655,656,657,658],[363,146439,2810],{"className":146440},[407,658],[363,146442,666],{"className":146443},[665],[363,146445,146447],{"className":146446},[638],[363,146448,146450],{"className":146449,"style":8315},[642],[363,146451],{},[363,146453,468],{"className":146454},[501],[363,146456],{"className":146457,"style":506},[505],[363,146459,94874],{"className":146460},[510],[363,146462],{"className":146463,"style":506},[505],[363,146465,146467,146470,146476,146479,146519,146522,146525,146565],{"className":146466},[398],[363,146468],{"className":146469,"style":487},[402],[363,146471,146473],{"className":146472},[1831],[363,146474,145757],{"className":146475},[407,33009],[363,146477,461],{"className":146478},[494],[363,146480,146482,146485],{"className":146481},[407],[363,146483,45101],{"className":146484,"style":45131},[407,408],[363,146486,146488],{"className":146487},[629],[363,146489,146491,146511],{"className":146490},[633,634],[363,146492,146494,146508],{"className":146493},[638],[363,146495,146497],{"className":146496,"style":11480},[642],[363,146498,146499,146502],{"style":136107},[363,146500],{"className":146501,"style":651},[650],[363,146503,146505],{"className":146504},[655,656,657,658],[363,146506,465],{"className":146507},[407,658],[363,146509,666],{"className":146510},[665],[363,146512,146514],{"className":146513},[638],[363,146515,146517],{"className":146516,"style":8315},[642],[363,146518],{},[363,146520,898],{"className":146521},[920],[363,146523],{"className":146524,"style":754},[505],[363,146526,146528,146531],{"className":146527},[407],[363,146529,45101],{"className":146530,"style":45131},[407,408],[363,146532,146534],{"className":146533},[629],[363,146535,146537,146557],{"className":146536},[633,634],[363,146538,146540,146554],{"className":146539},[638],[363,146541,146543],{"className":146542,"style":11480},[642],[363,146544,146545,146548],{"style":136107},[363,146546],{"className":146547,"style":651},[650],[363,146549,146551],{"className":146550},[655,656,657,658],[363,146552,2810],{"className":146553},[407,658],[363,146555,666],{"className":146556},[665],[363,146558,146560],{"className":146559},[638],[363,146561,146563],{"className":146562,"style":8315},[642],[363,146564],{},[363,146566,468],{"className":146567},[501],[11,146569,146570,146571,146622],{},"故迪利克雷分布是 Beta 分布在维度上的推广。下文所有关于迪利克雷分布的陈述，在 ",[363,146572,146574,146592],{"className":146573,"translate":367},[366],[363,146575,146577],{"className":146576},[371],[373,146578,146579],{"xmlns":375},[377,146580,146581,146589],{},[380,146582,146583,146585,146587],{},[383,146584,11041],{},[458,146586,471],{},[463,146588,2810],{},[387,146590,146591],{"encoding":389},"K=2",[363,146593,146595,146613],{"className":146594,"ariaHidden":394},[393],[363,146596,146598,146601,146604,146607,146610],{"className":146597},[398],[363,146599],{"className":146600,"style":1011},[402],[363,146602,11041],{"className":146603,"style":11129},[407,408],[363,146605],{"className":146606,"style":506},[505],[363,146608,471],{"className":146609},[510],[363,146611],{"className":146612,"style":506},[505],[363,146614,146616,146619],{"className":146615},[398],[363,146617],{"className":146618,"style":520},[402],[363,146620,2810],{"className":146621},[407]," 时都应退化为 Beta 分布的相应陈述，这构成了检验公式正确性的一个廉价判据。",[11,146624,146625,146628,146629,146699,146700,146907,146908,147061,147062,43112,147227,147296],{},[1572,146626,146627],{},"边缘分布仍为 Beta。"," 更一般地，任意单个分量 ",[363,146630,146632,146650],{"className":146631,"translate":367},[366],[363,146633,146635],{"className":146634},[371],[373,146636,146637],{"xmlns":375},[377,146638,146639,146647],{},[380,146640,146641],{},[543,146642,146643,146645],{},[383,146644,1121],{},[383,146646,12310],{},[387,146648,146649],{"encoding":389},"x_i",[363,146651,146653],{"className":146652,"ariaHidden":394},[393],[363,146654,146656,146659],{"className":146655},[398],[363,146657],{"className":146658,"style":13721},[402],[363,146660,146662,146665],{"className":146661},[407],[363,146663,1121],{"className":146664},[407,408],[363,146666,146668],{"className":146667},[629],[363,146669,146671,146691],{"className":146670},[633,634],[363,146672,146674,146688],{"className":146673},[638],[363,146675,146677],{"className":146676,"style":12529},[642],[363,146678,146679,146682],{"style":730},[363,146680],{"className":146681,"style":651},[650],[363,146683,146685],{"className":146684},[655,656,657,658],[363,146686,12310],{"className":146687},[407,408,658],[363,146689,666],{"className":146690},[665],[363,146692,146694],{"className":146693},[638],[363,146695,146697],{"className":146696,"style":8315},[642],[363,146698],{}," 的边缘分布是 ",[363,146701,146703,146745],{"className":146702,"translate":367},[366],[363,146704,146706],{"className":146705},[371],[373,146707,146708],{"xmlns":375},[377,146709,146710,146742],{},[380,146711,146712,146714,146716,146718,146724,146726,146732,146734,146740],{},[383,146713,145757],{"mathvariant":557},[458,146715,4450],{},[458,146717,461],{"stretchy":460},[543,146719,146720,146722],{},[383,146721,45101],{},[383,146723,12310],{},[458,146725,898],{"separator":394},[543,146727,146728,146730],{},[383,146729,45101],{},[463,146731,474],{},[458,146733,5160],{},[543,146735,146736,146738],{},[383,146737,45101],{},[383,146739,12310],{},[458,146741,468],{"stretchy":460},[387,146743,146744],{"encoding":389},"\\operatorname{Beta}(\\alpha_i, \\alpha_0 - \\alpha_i)",[363,146746,146748,146858],{"className":146747,"ariaHidden":394},[393],[363,146749,146751,146754,146760,146763,146803,146806,146809,146849,146852,146855],{"className":146750},[398],[363,146752],{"className":146753,"style":487},[402],[363,146755,146757],{"className":146756},[1831],[363,146758,145757],{"className":146759},[407,33009],[363,146761,461],{"className":146762},[494],[363,146764,146766,146769],{"className":146765},[407],[363,146767,45101],{"className":146768,"style":45131},[407,408],[363,146770,146772],{"className":146771},[629],[363,146773,146775,146795],{"className":146774},[633,634],[363,146776,146778,146792],{"className":146777},[638],[363,146779,146781],{"className":146780,"style":12529},[642],[363,146782,146783,146786],{"style":136107},[363,146784],{"className":146785,"style":651},[650],[363,146787,146789],{"className":146788},[655,656,657,658],[363,146790,12310],{"className":146791},[407,408,658],[363,146793,666],{"className":146794},[665],[363,146796,146798],{"className":146797},[638],[363,146799,146801],{"className":146800,"style":8315},[642],[363,146802],{},[363,146804,898],{"className":146805},[920],[363,146807],{"className":146808,"style":754},[505],[363,146810,146812,146815],{"className":146811},[407],[363,146813,45101],{"className":146814,"style":45131},[407,408],[363,146816,146818],{"className":146817},[629],[363,146819,146821,146841],{"className":146820},[633,634],[363,146822,146824,146838],{"className":146823},[638],[363,146825,146827],{"className":146826,"style":11480},[642],[363,146828,146829,146832],{"style":136107},[363,146830],{"className":146831,"style":651},[650],[363,146833,146835],{"className":146834},[655,656,657,658],[363,146836,474],{"className":146837},[407,658],[363,146839,666],{"className":146840},[665],[363,146842,146844],{"className":146843},[638],[363,146845,146847],{"className":146846,"style":8315},[642],[363,146848],{},[363,146850],{"className":146851,"style":2934},[505],[363,146853,5160],{"className":146854},[2938],[363,146856],{"className":146857,"style":2934},[505],[363,146859,146861,146864,146904],{"className":146860},[398],[363,146862],{"className":146863,"style":487},[402],[363,146865,146867,146870],{"className":146866},[407],[363,146868,45101],{"className":146869,"style":45131},[407,408],[363,146871,146873],{"className":146872},[629],[363,146874,146876,146896],{"className":146875},[633,634],[363,146877,146879,146893],{"className":146878},[638],[363,146880,146882],{"className":146881,"style":12529},[642],[363,146883,146884,146887],{"style":136107},[363,146885],{"className":146886,"style":651},[650],[363,146888,146890],{"className":146889},[655,656,657,658],[363,146891,12310],{"className":146892},[407,408,658],[363,146894,666],{"className":146895},[665],[363,146897,146899],{"className":146898},[638],[363,146900,146902],{"className":146901,"style":8315},[642],[363,146903],{},[363,146905,468],{"className":146906},[501],"。这一点可由命题 1.4 直接看出：",[363,146909,146911,146945],{"className":146910,"translate":367},[366],[363,146912,146914],{"className":146913},[371],[373,146915,146916],{"xmlns":375},[377,146917,146918,146942],{},[380,146919,146920,146926,146928,146934,146936,146938,146940],{},[543,146921,146922,146924],{},[383,146923,1121],{},[383,146925,12310],{},[458,146927,471],{},[543,146929,146930,146932],{},[383,146931,121421],{},[383,146933,12310],{},[383,146935,1288],{"mathvariant":557},[458,146937,461],{"stretchy":460},[383,146939,7908],{},[458,146941,468],{"stretchy":460},[387,146943,146944],{"encoding":389},"x_i = \\gamma_i \u002F (s)",[363,146946,146948,147003],{"className":146947,"ariaHidden":394},[393],[363,146949,146951,146954,146994,146997,147000],{"className":146950},[398],[363,146952],{"className":146953,"style":13721},[402],[363,146955,146957,146960],{"className":146956},[407],[363,146958,1121],{"className":146959},[407,408],[363,146961,146963],{"className":146962},[629],[363,146964,146966,146986],{"className":146965},[633,634],[363,146967,146969,146983],{"className":146968},[638],[363,146970,146972],{"className":146971,"style":12529},[642],[363,146973,146974,146977],{"style":730},[363,146975],{"className":146976,"style":651},[650],[363,146978,146980],{"className":146979},[655,656,657,658],[363,146981,12310],{"className":146982},[407,408,658],[363,146984,666],{"className":146985},[665],[363,146987,146989],{"className":146988},[638],[363,146990,146992],{"className":146991,"style":8315},[642],[363,146993],{},[363,146995],{"className":146996,"style":506},[505],[363,146998,471],{"className":146999},[510],[363,147001],{"className":147002,"style":506},[505],[363,147004,147006,147009,147049,147052,147055,147058],{"className":147005},[398],[363,147007],{"className":147008,"style":487},[402],[363,147010,147012,147015],{"className":147011},[407],[363,147013,121421],{"className":147014,"style":121511},[407,408],[363,147016,147018],{"className":147017},[629],[363,147019,147021,147041],{"className":147020},[633,634],[363,147022,147024,147038],{"className":147023},[638],[363,147025,147027],{"className":147026,"style":12529},[642],[363,147028,147029,147032],{"style":142280},[363,147030],{"className":147031,"style":651},[650],[363,147033,147035],{"className":147034},[655,656,657,658],[363,147036,12310],{"className":147037},[407,408,658],[363,147039,666],{"className":147040},[665],[363,147042,147044],{"className":147043},[638],[363,147045,147047],{"className":147046,"style":8315},[642],[363,147048],{},[363,147050,1288],{"className":147051},[407],[363,147053,461],{"className":147054},[494],[363,147056,7908],{"className":147057},[407,408],[363,147059,468],{"className":147060},[501],"，而 ",[363,147063,147065,147099],{"className":147064,"translate":367},[366],[363,147066,147068],{"className":147067},[371],[373,147069,147070],{"xmlns":375},[377,147071,147072,147096],{},[380,147073,147074,147080,147082,147084,147086,147088,147094],{},[543,147075,147076,147078],{},[383,147077,121421],{},[383,147079,12310],{},[458,147081,33894],{},[458,147083,461],{"stretchy":460},[383,147085,7908],{},[458,147087,5160],{},[543,147089,147090,147092],{},[383,147091,121421],{},[383,147093,12310],{},[458,147095,468],{"stretchy":460},[387,147097,147098],{"encoding":389},"\\gamma_i \\perp (s - \\gamma_i)",[363,147100,147102,147157,147178],{"className":147101,"ariaHidden":394},[393],[363,147103,147105,147108,147148,147151,147154],{"className":147104},[398],[363,147106],{"className":147107,"style":403},[402],[363,147109,147111,147114],{"className":147110},[407],[363,147112,121421],{"className":147113,"style":121511},[407,408],[363,147115,147117],{"className":147116},[629],[363,147118,147120,147140],{"className":147119},[633,634],[363,147121,147123,147137],{"className":147122},[638],[363,147124,147126],{"className":147125,"style":12529},[642],[363,147127,147128,147131],{"style":142280},[363,147129],{"className":147130,"style":651},[650],[363,147132,147134],{"className":147133},[655,656,657,658],[363,147135,12310],{"className":147136},[407,408,658],[363,147138,666],{"className":147139},[665],[363,147141,147143],{"className":147142},[638],[363,147144,147146],{"className":147145,"style":8315},[642],[363,147147],{},[363,147149],{"className":147150,"style":506},[505],[363,147152,33894],{"className":147153},[510],[363,147155],{"className":147156,"style":506},[505],[363,147158,147160,147163,147166,147169,147172,147175],{"className":147159},[398],[363,147161],{"className":147162,"style":487},[402],[363,147164,461],{"className":147165},[494],[363,147167,7908],{"className":147168},[407,408],[363,147170],{"className":147171,"style":2934},[505],[363,147173,5160],{"className":147174},[2938],[363,147176],{"className":147177,"style":2934},[505],[363,147179,147181,147184,147224],{"className":147180},[398],[363,147182],{"className":147183,"style":487},[402],[363,147185,147187,147190],{"className":147186},[407],[363,147188,121421],{"className":147189,"style":121511},[407,408],[363,147191,147193],{"className":147192},[629],[363,147194,147196,147216],{"className":147195},[633,634],[363,147197,147199,147213],{"className":147198},[638],[363,147200,147202],{"className":147201,"style":12529},[642],[363,147203,147204,147207],{"style":142280},[363,147205],{"className":147206,"style":651},[650],[363,147208,147210],{"className":147209},[655,656,657,658],[363,147211,12310],{"className":147212},[407,408,658],[363,147214,666],{"className":147215},[665],[363,147217,147219],{"className":147218},[638],[363,147220,147222],{"className":147221,"style":8315},[642],[363,147223],{},[363,147225,468],{"className":147226},[501],[363,147228,147230,147247],{"className":147229,"translate":367},[366],[363,147231,147233],{"className":147232},[371],[373,147234,147235],{"xmlns":375},[377,147236,147237,147245],{},[380,147238,147239],{},[543,147240,147241,147243],{},[383,147242,1121],{},[383,147244,12310],{},[387,147246,146649],{"encoding":389},[363,147248,147250],{"className":147249,"ariaHidden":394},[393],[363,147251,147253,147256],{"className":147252},[398],[363,147254],{"className":147255,"style":13721},[402],[363,147257,147259,147262],{"className":147258},[407],[363,147260,1121],{"className":147261},[407,408],[363,147263,147265],{"className":147264},[629],[363,147266,147268,147288],{"className":147267},[633,634],[363,147269,147271,147285],{"className":147270},[638],[363,147272,147274],{"className":147273,"style":12529},[642],[363,147275,147276,147279],{"style":730},[363,147277],{"className":147278,"style":651},[650],[363,147280,147282],{"className":147281},[655,656,657,658],[363,147283,12310],{"className":147284},[407,408,658],[363,147286,666],{"className":147287},[665],[363,147289,147291],{"className":147290},[638],[363,147292,147294],{"className":147293,"style":8315},[642],[363,147295],{}," 是相互独立的两个 Gamma 变量之比，其分布为 Beta。",[11,147298,147299,147302,147303,147306,147307,147341,147342,147371,147372,10527,147457],{},[1572,147300,147301],{},"与多项分布的共轭关系。"," 迪利克雷分布之所以在贝叶斯统计中占据中心位置，在于它是多项分布（等价地，分类分布）的",[1572,147304,147305],{},"共轭先验","。其确切含义与算术后果见 2.4 节。此处只指出其直觉：若先验以「伪计数」",[363,147308,147310,147323],{"className":147309,"translate":367},[366],[363,147311,147313],{"className":147312},[371],[373,147314,147315],{"xmlns":375},[377,147316,147317,147321],{},[380,147318,147319],{},[383,147320,45101],{"mathvariant":136008},[387,147322,137027],{"encoding":389},[363,147324,147326],{"className":147325,"ariaHidden":394},[393],[363,147327,147329,147332],{"className":147328},[398],[363,147330],{"className":147331,"style":135617},[402],[363,147333,147335],{"className":147334},[407],[363,147336,147338],{"className":147337},[407],[363,147339,45101],{"className":147340},[407,136068]," 描述对各类别出现次数的初始信念，则观测到计数 ",[363,147343,147345,147359],{"className":147344,"translate":367},[366],[363,147346,147348],{"className":147347},[371],[373,147349,147350],{"xmlns":375},[377,147351,147352,147356],{},[380,147353,147354],{},[383,147355,82643],{"mathvariant":75560},[387,147357,147358],{"encoding":389},"\\mathbf{n}",[363,147360,147362],{"className":147361,"ariaHidden":394},[393],[363,147363,147365,147368],{"className":147364},[398],[363,147366],{"className":147367,"style":135617},[402],[363,147369,82643],{"className":147370},[407,75905]," 后，信念的更新只是 ",[363,147373,147375,147397],{"className":147374,"translate":367},[366],[363,147376,147378],{"className":147377},[371],[373,147379,147380],{"xmlns":375},[377,147381,147382,147394],{},[380,147383,147384,147386,147388,147390,147392],{},[383,147385,45101],{"mathvariant":136008},[458,147387,9031],{},[383,147389,45101],{"mathvariant":136008},[458,147391,2817],{},[383,147393,82643],{"mathvariant":75560},[387,147395,147396],{"encoding":389},"\\boldsymbol{\\alpha} \\mapsto \\boldsymbol{\\alpha} + \\mathbf{n}",[363,147398,147400,147424,147448],{"className":147399,"ariaHidden":394},[393],[363,147401,147403,147406,147415,147418,147421],{"className":147402},[398],[363,147404],{"className":147405,"style":84306},[402],[363,147407,147409],{"className":147408},[407],[363,147410,147412],{"className":147411},[407],[363,147413,45101],{"className":147414},[407,136068],[363,147416],{"className":147417,"style":506},[505],[363,147419,9031],{"className":147420},[510],[363,147422],{"className":147423,"style":506},[505],[363,147425,147427,147430,147439,147442,147445],{"className":147426},[398],[363,147428],{"className":147429,"style":4598},[402],[363,147431,147433],{"className":147432},[407],[363,147434,147436],{"className":147435},[407],[363,147437,45101],{"className":147438},[407,136068],[363,147440],{"className":147441,"style":2934},[505],[363,147443,2817],{"className":147444},[2938],[363,147446],{"className":147447,"style":2934},[505],[363,147449,147451,147454],{"className":147450},[398],[363,147452],{"className":147453,"style":135617},[402],[363,147455,82643],{"className":147456},[407,75905],[1572,147458,147459],{},"贝叶斯更新的全部计算复杂度，在这个共轭对中退化为一次向量加法。",[18,147461,147463],{"id":147462},"二解析性质","二、解析性质",[2658,147465,147467],{"id":147466},"_21-矩结构","2.1 矩结构",[1340,147469,147471],{"title":147470},"命题 2.1（期望、方差与协方差）",[11,147472,881,147473,147549,147550,147593],{},[363,147474,147476,147501],{"className":147475,"translate":367},[366],[363,147477,147479],{"className":147478},[371],[373,147480,147481],{"xmlns":375},[377,147482,147483,147499],{},[380,147484,147485,147487,147489,147491,147493,147495,147497],{},[383,147486,1121],{"mathvariant":75560},[458,147488,9216],{},[383,147490,137065],{"mathvariant":557},[458,147492,4450],{},[458,147494,461],{"stretchy":460},[383,147496,45101],{"mathvariant":136008},[458,147498,468],{"stretchy":460},[387,147500,137076],{"encoding":389},[363,147502,147504,147522],{"className":147503,"ariaHidden":394},[393],[363,147505,147507,147510,147513,147516,147519],{"className":147506},[398],[363,147508],{"className":147509,"style":135617},[402],[363,147511,1121],{"className":147512},[407,75905],[363,147514],{"className":147515,"style":506},[505],[363,147517,9216],{"className":147518},[510],[363,147520],{"className":147521,"style":506},[505],[363,147523,147525,147528,147534,147537,147546],{"className":147524},[398],[363,147526],{"className":147527,"style":487},[402],[363,147529,147531],{"className":147530},[1831],[363,147532,137065],{"className":147533},[407,33009],[363,147535,461],{"className":147536},[494],[363,147538,147540],{"className":147539},[407],[363,147541,147543],{"className":147542},[407],[363,147544,45101],{"className":147545},[407,136068],[363,147547,468],{"className":147548},[501],"。则对任意 ",[363,147551,147553,147571],{"className":147552,"translate":367},[366],[363,147554,147556],{"className":147555},[371],[373,147557,147558],{"xmlns":375},[377,147559,147560,147568],{},[380,147561,147562,147564,147566],{},[383,147563,12310],{},[458,147565,898],{"separator":394},[383,147567,100360],{},[387,147569,147570],{"encoding":389},"i, j",[363,147572,147574],{"className":147573,"ariaHidden":394},[393],[363,147575,147577,147581,147584,147587,147590],{"className":147576},[398],[363,147578],{"className":147579,"style":147580},[402],"height:0.854em;vertical-align:-0.1944em;",[363,147582,12310],{"className":147583},[407,408],[363,147585,898],{"className":147586},[920],[363,147588],{"className":147589,"style":754},[505],[363,147591,100360],{"className":147592,"style":100888},[407,408],[363,147594,147596,147792],{"className":147595,"translate":367},[366],[363,147597,147599],{"className":147598},[371],[373,147600,147601],{"xmlns":375},[377,147602,147603,147789],{},[380,147604,147605,147607,147609,147615,147617,147619,147633,147635,147637,147640,147642,147644,147650,147652,147654,147706,147708,147710,147713,147715,147717,147723,147725,147731,147733,147735,147777,147779,147781,147783,147785,147787],{},[383,147606,571],{"mathvariant":570},[458,147608,578],{"stretchy":460},[543,147610,147611,147613],{},[383,147612,1121],{},[383,147614,12310],{},[458,147616,605],{"stretchy":460},[458,147618,471],{},[586,147620,147621,147627],{},[543,147622,147623,147625],{},[383,147624,45101],{},[383,147626,12310],{},[543,147628,147629,147631],{},[383,147630,45101],{},[463,147632,474],{},[458,147634,898],{"separator":394},[505,147636],{"width":3609},[383,147638,147639],{"mathvariant":557},"Var",[458,147641,4450],{},[458,147643,461],{"stretchy":460},[543,147645,147646,147648],{},[383,147647,1121],{},[383,147649,12310],{},[458,147651,468],{"stretchy":460},[458,147653,471],{},[586,147655,147656,147682],{},[380,147657,147658,147664,147666,147672,147674,147680],{},[543,147659,147660,147662],{},[383,147661,45101],{},[383,147663,12310],{},[458,147665,461],{"stretchy":460},[543,147667,147668,147670],{},[383,147669,45101],{},[463,147671,474],{},[458,147673,5160],{},[543,147675,147676,147678],{},[383,147677,45101],{},[383,147679,12310],{},[458,147681,468],{"stretchy":460},[380,147683,147684,147692,147694,147700,147702,147704],{},[7900,147685,147686,147688,147690],{},[383,147687,45101],{},[463,147689,474],{},[463,147691,2810],{},[458,147693,461],{"stretchy":460},[543,147695,147696,147698],{},[383,147697,45101],{},[463,147699,474],{},[458,147701,2817],{},[463,147703,465],{},[458,147705,468],{"stretchy":460},[458,147707,898],{"separator":394},[505,147709],{"width":3609},[383,147711,147712],{"mathvariant":557},"Cov",[458,147714,4450],{},[458,147716,461],{"stretchy":460},[543,147718,147719,147721],{},[383,147720,1121],{},[383,147722,12310],{},[458,147724,898],{"separator":394},[543,147726,147727,147729],{},[383,147728,1121],{},[383,147730,100360],{},[458,147732,468],{"stretchy":460},[458,147734,471],{},[586,147736,147737,147753],{},[380,147738,147739,147741,147747],{},[458,147740,5160],{},[543,147742,147743,147745],{},[383,147744,45101],{},[383,147746,12310],{},[543,147748,147749,147751],{},[383,147750,45101],{},[383,147752,100360],{},[380,147754,147755,147763,147765,147771,147773,147775],{},[7900,147756,147757,147759,147761],{},[383,147758,45101],{},[463,147760,474],{},[463,147762,2810],{},[458,147764,461],{"stretchy":460},[543,147766,147767,147769],{},[383,147768,45101],{},[463,147770,474],{},[458,147772,2817],{},[463,147774,465],{},[458,147776,468],{"stretchy":460},[505,147778],{"width":4662},[458,147780,461],{"stretchy":460},[383,147782,12310],{},[458,147784,49854],{"mathvariant":557},[383,147786,100360],{},[458,147788,468],{"stretchy":460},[387,147790,147791],{"encoding":389},"\\mathbb{E}[x_i] = \\frac{\\alpha_i}{\\alpha_0}, \\qquad \\operatorname{Var}(x_i) = \\frac{\\alpha_i(\\alpha_0 - \\alpha_i)}{\\alpha_0^2(\\alpha_0 + 1)}, \\qquad \\operatorname{Cov}(x_i, x_j) = \\frac{-\\alpha_i \\alpha_j}{\\alpha_0^2(\\alpha_0 + 1)} \\quad (i \\ne j)",[363,147793,147795,147859,148080,148502,148810],{"className":147794,"ariaHidden":394},[393],[363,147796,147798,147801,147804,147807,147847,147850,147853,147856],{"className":147797},[398],[363,147799],{"className":147800,"style":487},[402],[363,147802,571],{"className":147803},[407,714],[363,147805,578],{"className":147806},[494],[363,147808,147810,147813],{"className":147809},[407],[363,147811,1121],{"className":147812},[407,408],[363,147814,147816],{"className":147815},[629],[363,147817,147819,147839],{"className":147818},[633,634],[363,147820,147822,147836],{"className":147821},[638],[363,147823,147825],{"className":147824,"style":12529},[642],[363,147826,147827,147830],{"style":730},[363,147828],{"className":147829,"style":651},[650],[363,147831,147833],{"className":147832},[655,656,657,658],[363,147834,12310],{"className":147835},[407,408,658],[363,147837,666],{"className":147838},[665],[363,147840,147842],{"className":147841},[638],[363,147843,147845],{"className":147844,"style":8315},[642],[363,147846],{},[363,147848,605],{"className":147849},[501],[363,147851],{"className":147852,"style":506},[505],[363,147854,471],{"className":147855},[510],[363,147857],{"className":147858,"style":506},[505],[363,147860,147862,147866,148010,148013,148016,148019,148025,148028,148068,148071,148074,148077],{"className":147861},[398],[363,147863],{"className":147864,"style":147865},[402],"height:1.1951em;vertical-align:-0.4451em;",[363,147867,147869,147872,148007],{"className":147868},[407],[363,147870],{"className":147871},[494,789],[363,147873,147875],{"className":147874},[586],[363,147876,147878,147999],{"className":147877},[633,634],[363,147879,147881,147996],{"className":147880},[638],[363,147882,147885,147936,147944],{"className":147883,"style":147884},[642],"height:0.7115em;",[363,147886,147887,147890],{"style":2874},[363,147888],{"className":147889,"style":809},[650],[363,147891,147893],{"className":147892},[655,656,657,658],[363,147894,147896],{"className":147895},[407,658],[363,147897,147899,147902],{"className":147898},[407,658],[363,147900,45101],{"className":147901,"style":45131},[407,408,658],[363,147903,147905],{"className":147904},[629],[363,147906,147908,147928],{"className":147907},[633,634],[363,147909,147911,147925],{"className":147910},[638],[363,147912,147914],{"className":147913,"style":137304},[642],[363,147915,147916,147919],{"style":136942},[363,147917],{"className":147918,"style":30553},[650],[363,147920,147922],{"className":147921},[655,30557,10021,658],[363,147923,474],{"className":147924},[407,658],[363,147926,666],{"className":147927},[665],[363,147929,147931],{"className":147930},[638],[363,147932,147934],{"className":147933,"style":40117},[642],[363,147935],{},[363,147937,147938,147941],{"style":821},[363,147939],{"className":147940,"style":809},[650],[363,147942],{"className":147943,"style":829},[828],[363,147945,147947,147950],{"style":147946},"top:-3.4101em;",[363,147948],{"className":147949,"style":809},[650],[363,147951,147953],{"className":147952},[655,656,657,658],[363,147954,147956],{"className":147955},[407,658],[363,147957,147959,147962],{"className":147958},[407,658],[363,147960,45101],{"className":147961,"style":45131},[407,408,658],[363,147963,147965],{"className":147964},[629],[363,147966,147968,147988],{"className":147967},[633,634],[363,147969,147971,147985],{"className":147970},[638],[363,147972,147974],{"className":147973,"style":40095},[642],[363,147975,147976,147979],{"style":136942},[363,147977],{"className":147978,"style":30553},[650],[363,147980,147982],{"className":147981},[655,30557,10021,658],[363,147983,12310],{"className":147984},[407,408,658],[363,147986,666],{"className":147987},[665],[363,147989,147991],{"className":147990},[638],[363,147992,147994],{"className":147993,"style":40117},[642],[363,147995],{},[363,147997,666],{"className":147998},[665],[363,148000,148002],{"className":148001},[638],[363,148003,148005],{"className":148004,"style":40264},[642],[363,148006],{},[363,148008],{"className":148009},[501,789],[363,148011,898],{"className":148012},[920],[363,148014],{"className":148015,"style":3981},[505],[363,148017],{"className":148018,"style":754},[505],[363,148020,148022],{"className":148021},[1831],[363,148023,147639],{"className":148024},[407,33009],[363,148026,461],{"className":148027},[494],[363,148029,148031,148034],{"className":148030},[407],[363,148032,1121],{"className":148033},[407,408],[363,148035,148037],{"className":148036},[629],[363,148038,148040,148060],{"className":148039},[633,634],[363,148041,148043,148057],{"className":148042},[638],[363,148044,148046],{"className":148045,"style":12529},[642],[363,148047,148048,148051],{"style":730},[363,148049],{"className":148050,"style":651},[650],[363,148052,148054],{"className":148053},[655,656,657,658],[363,148055,12310],{"className":148056},[407,408,658],[363,148058,666],{"className":148059},[665],[363,148061,148063],{"className":148062},[638],[363,148064,148066],{"className":148065,"style":8315},[642],[363,148067],{},[363,148069,468],{"className":148070},[501],[363,148072],{"className":148073,"style":506},[505],[363,148075,471],{"className":148076},[510],[363,148078],{"className":148079,"style":506},[505],[363,148081,148083,148087,148386,148389,148392,148395,148401,148404,148444,148447,148450,148490,148493,148496,148499],{"className":148082},[398],[363,148084],{"className":148085,"style":148086},[402],"height:1.6016em;vertical-align:-0.5916em;",[363,148088,148090,148093,148383],{"className":148089},[407],[363,148091],{"className":148092},[494,789],[363,148094,148096],{"className":148095},[586],[363,148097,148099,148374],{"className":148098},[633,634],[363,148100,148102,148371],{"className":148101},[638],[363,148103,148105,148223,148231],{"className":148104,"style":26740},[642],[363,148106,148108,148111],{"style":148107},"top:-2.6264em;",[363,148109],{"className":148110,"style":809},[650],[363,148112,148114],{"className":148113},[655,656,657,658],[363,148115,148117,148171,148174,148214,148217,148220],{"className":148116},[407,658],[363,148118,148120,148123],{"className":148119},[407,658],[363,148121,45101],{"className":148122,"style":45131},[407,408,658],[363,148124,148126],{"className":148125},[629],[363,148127,148129,148162],{"className":148128},[633,634],[363,148130,148132,148159],{"className":148131},[638],[363,148133,148136,148148],{"className":148134,"style":148135},[642],"height:0.8051em;",[363,148137,148139,148142],{"style":148138},"top:-2.1885em;margin-left:-0.0037em;margin-right:0.0714em;",[363,148140],{"className":148141,"style":30553},[650],[363,148143,148145],{"className":148144},[655,30557,10021,658],[363,148146,474],{"className":148147},[407,658],[363,148149,148150,148153],{"style":59260},[363,148151],{"className":148152,"style":30553},[650],[363,148154,148156],{"className":148155},[655,30557,10021,658],[363,148157,2810],{"className":148158},[407,658],[363,148160,666],{"className":148161},[665],[363,148163,148165],{"className":148164},[638],[363,148166,148169],{"className":148167,"style":148168},[642],"height:0.3115em;",[363,148170],{},[363,148172,461],{"className":148173},[494,658],[363,148175,148177,148180],{"className":148176},[407,658],[363,148178,45101],{"className":148179,"style":45131},[407,408,658],[363,148181,148183],{"className":148182},[629],[363,148184,148186,148206],{"className":148185},[633,634],[363,148187,148189,148203],{"className":148188},[638],[363,148190,148192],{"className":148191,"style":137304},[642],[363,148193,148194,148197],{"style":136942},[363,148195],{"className":148196,"style":30553},[650],[363,148198,148200],{"className":148199},[655,30557,10021,658],[363,148201,474],{"className":148202},[407,658],[363,148204,666],{"className":148205},[665],[363,148207,148209],{"className":148208},[638],[363,148210,148212],{"className":148211,"style":40117},[642],[363,148213],{},[363,148215,2817],{"className":148216},[2938,658],[363,148218,465],{"className":148219},[407,658],[363,148221,468],{"className":148222},[501,658],[363,148224,148225,148228],{"style":821},[363,148226],{"className":148227,"style":809},[650],[363,148229],{"className":148230,"style":829},[828],[363,148232,148233,148236],{"style":26765},[363,148234],{"className":148235,"style":809},[650],[363,148237,148239],{"className":148238},[655,656,657,658],[363,148240,148242,148282,148285,148325,148328,148368],{"className":148241},[407,658],[363,148243,148245,148248],{"className":148244},[407,658],[363,148246,45101],{"className":148247,"style":45131},[407,408,658],[363,148249,148251],{"className":148250},[629],[363,148252,148254,148274],{"className":148253},[633,634],[363,148255,148257,148271],{"className":148256},[638],[363,148258,148260],{"className":148259,"style":40095},[642],[363,148261,148262,148265],{"style":136942},[363,148263],{"className":148264,"style":30553},[650],[363,148266,148268],{"className":148267},[655,30557,10021,658],[363,148269,12310],{"className":148270},[407,408,658],[363,148272,666],{"className":148273},[665],[363,148275,148277],{"className":148276},[638],[363,148278,148280],{"className":148279,"style":40117},[642],[363,148281],{},[363,148283,461],{"className":148284},[494,658],[363,148286,148288,148291],{"className":148287},[407,658],[363,148289,45101],{"className":148290,"style":45131},[407,408,658],[363,148292,148294],{"className":148293},[629],[363,148295,148297,148317],{"className":148296},[633,634],[363,148298,148300,148314],{"className":148299},[638],[363,148301,148303],{"className":148302,"style":137304},[642],[363,148304,148305,148308],{"style":136942},[363,148306],{"className":148307,"style":30553},[650],[363,148309,148311],{"className":148310},[655,30557,10021,658],[363,148312,474],{"className":148313},[407,658],[363,148315,666],{"className":148316},[665],[363,148318,148320],{"className":148319},[638],[363,148321,148323],{"className":148322,"style":40117},[642],[363,148324],{},[363,148326,5160],{"className":148327},[2938,658],[363,148329,148331,148334],{"className":148330},[407,658],[363,148332,45101],{"className":148333,"style":45131},[407,408,658],[363,148335,148337],{"className":148336},[629],[363,148338,148340,148360],{"className":148339},[633,634],[363,148341,148343,148357],{"className":148342},[638],[363,148344,148346],{"className":148345,"style":40095},[642],[363,148347,148348,148351],{"style":136942},[363,148349],{"className":148350,"style":30553},[650],[363,148352,148354],{"className":148353},[655,30557,10021,658],[363,148355,12310],{"className":148356},[407,408,658],[363,148358,666],{"className":148359},[665],[363,148361,148363],{"className":148362},[638],[363,148364,148366],{"className":148365,"style":40117},[642],[363,148367],{},[363,148369,468],{"className":148370},[501,658],[363,148372,666],{"className":148373},[665],[363,148375,148377],{"className":148376},[638],[363,148378,148381],{"className":148379,"style":148380},[642],"height:0.5916em;",[363,148382],{},[363,148384],{"className":148385},[501,789],[363,148387,898],{"className":148388},[920],[363,148390],{"className":148391,"style":3981},[505],[363,148393],{"className":148394,"style":754},[505],[363,148396,148398],{"className":148397},[1831],[363,148399,147712],{"className":148400,"style":4504},[407,33009],[363,148402,461],{"className":148403},[494],[363,148405,148407,148410],{"className":148406},[407],[363,148408,1121],{"className":148409},[407,408],[363,148411,148413],{"className":148412},[629],[363,148414,148416,148436],{"className":148415},[633,634],[363,148417,148419,148433],{"className":148418},[638],[363,148420,148422],{"className":148421,"style":12529},[642],[363,148423,148424,148427],{"style":730},[363,148425],{"className":148426,"style":651},[650],[363,148428,148430],{"className":148429},[655,656,657,658],[363,148431,12310],{"className":148432},[407,408,658],[363,148434,666],{"className":148435},[665],[363,148437,148439],{"className":148438},[638],[363,148440,148442],{"className":148441,"style":8315},[642],[363,148443],{},[363,148445,898],{"className":148446},[920],[363,148448],{"className":148449,"style":754},[505],[363,148451,148453,148456],{"className":148452},[407],[363,148454,1121],{"className":148455},[407,408],[363,148457,148459],{"className":148458},[629],[363,148460,148462,148482],{"className":148461},[633,634],[363,148463,148465,148479],{"className":148464},[638],[363,148466,148468],{"className":148467,"style":12529},[642],[363,148469,148470,148473],{"style":730},[363,148471],{"className":148472,"style":651},[650],[363,148474,148476],{"className":148475},[655,656,657,658],[363,148477,100360],{"className":148478,"style":100888},[407,408,658],[363,148480,666],{"className":148481},[665],[363,148483,148485],{"className":148484},[638],[363,148486,148488],{"className":148487,"style":673},[642],[363,148489],{},[363,148491,468],{"className":148492},[501],[363,148494],{"className":148495,"style":506},[505],[363,148497,471],{"className":148498},[510],[363,148500],{"className":148501,"style":506},[505],[363,148503,148505,148509,148759,148762,148765,148768,148771,148807],{"className":148504},[398],[363,148506],{"className":148507,"style":148508},[402],"height:1.5073em;vertical-align:-0.5916em;",[363,148510,148512,148515,148756],{"className":148511},[407],[363,148513],{"className":148514},[494,789],[363,148516,148518],{"className":148517},[586],[363,148519,148521,148748],{"className":148520},[633,634],[363,148522,148524,148745],{"className":148523},[638],[363,148525,148528,148642,148650],{"className":148526,"style":148527},[642],"height:0.9157em;",[363,148529,148530,148533],{"style":148107},[363,148531],{"className":148532,"style":809},[650],[363,148534,148536],{"className":148535},[655,656,657,658],[363,148537,148539,148590,148593,148633,148636,148639],{"className":148538},[407,658],[363,148540,148542,148545],{"className":148541},[407,658],[363,148543,45101],{"className":148544,"style":45131},[407,408,658],[363,148546,148548],{"className":148547},[629],[363,148549,148551,148582],{"className":148550},[633,634],[363,148552,148554,148579],{"className":148553},[638],[363,148555,148557,148568],{"className":148556,"style":148135},[642],[363,148558,148559,148562],{"style":148138},[363,148560],{"className":148561,"style":30553},[650],[363,148563,148565],{"className":148564},[655,30557,10021,658],[363,148566,474],{"className":148567},[407,658],[363,148569,148570,148573],{"style":59260},[363,148571],{"className":148572,"style":30553},[650],[363,148574,148576],{"className":148575},[655,30557,10021,658],[363,148577,2810],{"className":148578},[407,658],[363,148580,666],{"className":148581},[665],[363,148583,148585],{"className":148584},[638],[363,148586,148588],{"className":148587,"style":148168},[642],[363,148589],{},[363,148591,461],{"className":148592},[494,658],[363,148594,148596,148599],{"className":148595},[407,658],[363,148597,45101],{"className":148598,"style":45131},[407,408,658],[363,148600,148602],{"className":148601},[629],[363,148603,148605,148625],{"className":148604},[633,634],[363,148606,148608,148622],{"className":148607},[638],[363,148609,148611],{"className":148610,"style":137304},[642],[363,148612,148613,148616],{"style":136942},[363,148614],{"className":148615,"style":30553},[650],[363,148617,148619],{"className":148618},[655,30557,10021,658],[363,148620,474],{"className":148621},[407,658],[363,148623,666],{"className":148624},[665],[363,148626,148628],{"className":148627},[638],[363,148629,148631],{"className":148630,"style":40117},[642],[363,148632],{},[363,148634,2817],{"className":148635},[2938,658],[363,148637,465],{"className":148638},[407,658],[363,148640,468],{"className":148641},[501,658],[363,148643,148644,148647],{"style":821},[363,148645],{"className":148646,"style":809},[650],[363,148648],{"className":148649,"style":829},[828],[363,148651,148653,148656],{"style":148652},"top:-3.5073em;",[363,148654],{"className":148655,"style":809},[650],[363,148657,148659],{"className":148658},[655,656,657,658],[363,148660,148662,148665,148705],{"className":148661},[407,658],[363,148663,5160],{"className":148664},[407,658],[363,148666,148668,148671],{"className":148667},[407,658],[363,148669,45101],{"className":148670,"style":45131},[407,408,658],[363,148672,148674],{"className":148673},[629],[363,148675,148677,148697],{"className":148676},[633,634],[363,148678,148680,148694],{"className":148679},[638],[363,148681,148683],{"className":148682,"style":40095},[642],[363,148684,148685,148688],{"style":136942},[363,148686],{"className":148687,"style":30553},[650],[363,148689,148691],{"className":148690},[655,30557,10021,658],[363,148692,12310],{"className":148693},[407,408,658],[363,148695,666],{"className":148696},[665],[363,148698,148700],{"className":148699},[638],[363,148701,148703],{"className":148702,"style":40117},[642],[363,148704],{},[363,148706,148708,148711],{"className":148707},[407,658],[363,148709,45101],{"className":148710,"style":45131},[407,408,658],[363,148712,148714],{"className":148713},[629],[363,148715,148717,148737],{"className":148716},[633,634],[363,148718,148720,148734],{"className":148719},[638],[363,148721,148723],{"className":148722,"style":40095},[642],[363,148724,148725,148728],{"style":136942},[363,148726],{"className":148727,"style":30553},[650],[363,148729,148731],{"className":148730},[655,30557,10021,658],[363,148732,100360],{"className":148733,"style":100888},[407,408,658],[363,148735,666],{"className":148736},[665],[363,148738,148740],{"className":148739},[638],[363,148741,148743],{"className":148742,"style":122065},[642],[363,148744],{},[363,148746,666],{"className":148747},[665],[363,148749,148751],{"className":148750},[638],[363,148752,148754],{"className":148753,"style":148380},[642],[363,148755],{},[363,148757],{"className":148758},[501,789],[363,148760],{"className":148761,"style":88315},[505],[363,148763,461],{"className":148764},[494],[363,148766,12310],{"className":148767},[407,408],[363,148769],{"className":148770,"style":506},[505],[363,148772,148774,148801,148804],{"className":148773},[510],[363,148775,148777],{"className":148776},[510],[363,148778,148780],{"className":148779},[407,4747],[363,148781,148783],{"className":148782},[4751],[363,148784,148786,148789,148798],{"className":148785},[4755],[363,148787],{"className":148788,"style":403},[402],[363,148790,148792],{"className":148791},[4762],[363,148793,148795],{"className":148794},[407],[363,148796,4769],{"className":148797},[510],[363,148799],{"className":148800},[4773],[363,148802],{"className":148803},[505,4777],[363,148805,471],{"className":148806},[510],[363,148808],{"className":148809,"style":506},[505],[363,148811,148813,148816,148819],{"className":148812},[398],[363,148814],{"className":148815,"style":487},[402],[363,148817,100360],{"className":148818,"style":100888},[407,408],[363,148820,468],{"className":148821},[501],[11,148823,148824,148826,148827,7147,148970,43112,149062,149454,149455,149558,149559,2756,149712,149868,149869,23692,150167,150260,150261,2756,150672,151094],{},[1572,148825,137993],{}," 由命题 1.4，",[363,148828,148830,148860],{"className":148829,"translate":367},[366],[363,148831,148833],{"className":148832},[371],[373,148834,148835],{"xmlns":375},[377,148836,148837,148857],{},[380,148838,148839,148845,148847,148853,148855],{},[543,148840,148841,148843],{},[383,148842,1121],{},[383,148844,12310],{},[458,148846,471],{},[543,148848,148849,148851],{},[383,148850,121421],{},[383,148852,12310],{},[383,148854,1288],{"mathvariant":557},[383,148856,7908],{},[387,148858,148859],{"encoding":389},"x_i = \\gamma_i \u002F s",[363,148861,148863,148918],{"className":148862,"ariaHidden":394},[393],[363,148864,148866,148869,148909,148912,148915],{"className":148865},[398],[363,148867],{"className":148868,"style":13721},[402],[363,148870,148872,148875],{"className":148871},[407],[363,148873,1121],{"className":148874},[407,408],[363,148876,148878],{"className":148877},[629],[363,148879,148881,148901],{"className":148880},[633,634],[363,148882,148884,148898],{"className":148883},[638],[363,148885,148887],{"className":148886,"style":12529},[642],[363,148888,148889,148892],{"style":730},[363,148890],{"className":148891,"style":651},[650],[363,148893,148895],{"className":148894},[655,656,657,658],[363,148896,12310],{"className":148897},[407,408,658],[363,148899,666],{"className":148900},[665],[363,148902,148904],{"className":148903},[638],[363,148905,148907],{"className":148906,"style":8315},[642],[363,148908],{},[363,148910],{"className":148911,"style":506},[505],[363,148913,471],{"className":148914},[510],[363,148916],{"className":148917,"style":506},[505],[363,148919,148921,148924,148964,148967],{"className":148920},[398],[363,148922],{"className":148923,"style":487},[402],[363,148925,148927,148930],{"className":148926},[407],[363,148928,121421],{"className":148929,"style":121511},[407,408],[363,148931,148933],{"className":148932},[629],[363,148934,148936,148956],{"className":148935},[633,634],[363,148937,148939,148953],{"className":148938},[638],[363,148940,148942],{"className":148941,"style":12529},[642],[363,148943,148944,148947],{"style":142280},[363,148945],{"className":148946,"style":651},[650],[363,148948,148950],{"className":148949},[655,656,657,658],[363,148951,12310],{"className":148952},[407,408,658],[363,148954,666],{"className":148955},[665],[363,148957,148959],{"className":148958},[638],[363,148960,148962],{"className":148961,"style":8315},[642],[363,148963],{},[363,148965,1288],{"className":148966},[407],[363,148968,7908],{"className":148969},[407,408],[363,148971,148973,148995],{"className":148972,"translate":367},[366],[363,148974,148976],{"className":148975},[371],[373,148977,148978],{"xmlns":375},[377,148979,148980,148992],{},[380,148981,148982,148988,148990],{},[543,148983,148984,148986],{},[383,148985,121421],{},[383,148987,12310],{},[458,148989,33894],{},[383,148991,7908],{},[387,148993,148994],{"encoding":389},"\\gamma_i \\perp s",[363,148996,148998,149053],{"className":148997,"ariaHidden":394},[393],[363,148999,149001,149004,149044,149047,149050],{"className":149000},[398],[363,149002],{"className":149003,"style":403},[402],[363,149005,149007,149010],{"className":149006},[407],[363,149008,121421],{"className":149009,"style":121511},[407,408],[363,149011,149013],{"className":149012},[629],[363,149014,149016,149036],{"className":149015},[633,634],[363,149017,149019,149033],{"className":149018},[638],[363,149020,149022],{"className":149021,"style":12529},[642],[363,149023,149024,149027],{"style":142280},[363,149025],{"className":149026,"style":651},[650],[363,149028,149030],{"className":149029},[655,656,657,658],[363,149031,12310],{"className":149032},[407,408,658],[363,149034,666],{"className":149035},[665],[363,149037,149039],{"className":149038},[638],[363,149040,149042],{"className":149041,"style":8315},[642],[363,149043],{},[363,149045],{"className":149046,"style":506},[505],[363,149048,33894],{"className":149049},[510],[363,149051],{"className":149052,"style":506},[505],[363,149054,149056,149059],{"className":149055},[398],[363,149057],{"className":149058,"style":2692},[402],[363,149060,7908],{"className":149061},[407,408],[363,149063,149065,149137],{"className":149064,"translate":367},[366],[363,149066,149068],{"className":149067},[371],[373,149069,149070],{"xmlns":375},[377,149071,149072,149134],{},[380,149073,149074,149076,149078,149084,149086,149088,149090,149092,149098,149100,149102,149104,149106,149108,149110,149112,149114,149116,149122,149124],{},[383,149075,571],{"mathvariant":570},[458,149077,578],{"stretchy":460},[543,149079,149080,149082],{},[383,149081,1121],{},[383,149083,12310],{},[458,149085,605],{"stretchy":460},[458,149087,471],{},[383,149089,571],{"mathvariant":570},[458,149091,578],{"stretchy":460},[543,149093,149094,149096],{},[383,149095,121421],{},[383,149097,12310],{},[458,149099,605],{"stretchy":460},[1644,149101,1646],{},[383,149103,571],{"mathvariant":570},[458,149105,578],{"stretchy":460},[463,149107,465],{},[383,149109,1288],{"mathvariant":557},[383,149111,7908],{},[458,149113,605],{"stretchy":460},[458,149115,471],{},[543,149117,149118,149120],{},[383,149119,45101],{},[383,149121,12310],{},[458,149123,3646],{},[586,149125,149126,149128],{},[463,149127,465],{},[543,149129,149130,149132],{},[383,149131,45101],{},[463,149133,474],{},[387,149135,149136],{"encoding":389},"\\mathbb{E}[x_i] = \\mathbb{E}[\\gamma_i]\\,\\mathbb{E}[1\u002Fs] = \\alpha_i \\cdot \\frac{1}{\\alpha_0}",[363,149138,149140,149204,149286,149342],{"className":149139,"ariaHidden":394},[393],[363,149141,149143,149146,149149,149152,149192,149195,149198,149201],{"className":149142},[398],[363,149144],{"className":149145,"style":487},[402],[363,149147,571],{"className":149148},[407,714],[363,149150,578],{"className":149151},[494],[363,149153,149155,149158],{"className":149154},[407],[363,149156,1121],{"className":149157},[407,408],[363,149159,149161],{"className":149160},[629],[363,149162,149164,149184],{"className":149163},[633,634],[363,149165,149167,149181],{"className":149166},[638],[363,149168,149170],{"className":149169,"style":12529},[642],[363,149171,149172,149175],{"style":730},[363,149173],{"className":149174,"style":651},[650],[363,149176,149178],{"className":149177},[655,656,657,658],[363,149179,12310],{"className":149180},[407,408,658],[363,149182,666],{"className":149183},[665],[363,149185,149187],{"className":149186},[638],[363,149188,149190],{"className":149189,"style":8315},[642],[363,149191],{},[363,149193,605],{"className":149194},[501],[363,149196],{"className":149197,"style":506},[505],[363,149199,471],{"className":149200},[510],[363,149202],{"className":149203,"style":506},[505],[363,149205,149207,149210,149213,149216,149256,149259,149262,149265,149268,149271,149274,149277,149280,149283],{"className":149206},[398],[363,149208],{"className":149209,"style":487},[402],[363,149211,571],{"className":149212},[407,714],[363,149214,578],{"className":149215},[494],[363,149217,149219,149222],{"className":149218},[407],[363,149220,121421],{"className":149221,"style":121511},[407,408],[363,149223,149225],{"className":149224},[629],[363,149226,149228,149248],{"className":149227},[633,634],[363,149229,149231,149245],{"className":149230},[638],[363,149232,149234],{"className":149233,"style":12529},[642],[363,149235,149236,149239],{"style":142280},[363,149237],{"className":149238,"style":651},[650],[363,149240,149242],{"className":149241},[655,656,657,658],[363,149243,12310],{"className":149244},[407,408,658],[363,149246,666],{"className":149247},[665],[363,149249,149251],{"className":149250},[638],[363,149252,149254],{"className":149253,"style":8315},[642],[363,149255],{},[363,149257,605],{"className":149258},[501],[363,149260],{"className":149261,"style":754},[505],[363,149263,571],{"className":149264},[407,714],[363,149266,578],{"className":149267},[494],[363,149269,8936],{"className":149270},[407],[363,149272,7908],{"className":149273},[407,408],[363,149275,605],{"className":149276},[501],[363,149278],{"className":149279,"style":506},[505],[363,149281,471],{"className":149282},[510],[363,149284],{"className":149285,"style":506},[505],[363,149287,149289,149293,149333,149336,149339],{"className":149288},[398],[363,149290],{"className":149291,"style":149292},[402],"height:0.5945em;vertical-align:-0.15em;",[363,149294,149296,149299],{"className":149295},[407],[363,149297,45101],{"className":149298,"style":45131},[407,408],[363,149300,149302],{"className":149301},[629],[363,149303,149305,149325],{"className":149304},[633,634],[363,149306,149308,149322],{"className":149307},[638],[363,149309,149311],{"className":149310,"style":12529},[642],[363,149312,149313,149316],{"style":136107},[363,149314],{"className":149315,"style":651},[650],[363,149317,149319],{"className":149318},[655,656,657,658],[363,149320,12310],{"className":149321},[407,408,658],[363,149323,666],{"className":149324},[665],[363,149326,149328],{"className":149327},[638],[363,149329,149331],{"className":149330,"style":8315},[642],[363,149332],{},[363,149334],{"className":149335,"style":2934},[505],[363,149337,3646],{"className":149338},[2938],[363,149340],{"className":149341,"style":2934},[505],[363,149343,149345,149349],{"className":149344},[398],[363,149346],{"className":149347,"style":149348},[402],"height:1.2902em;vertical-align:-0.4451em;",[363,149350,149352,149355,149451],{"className":149351},[407],[363,149353],{"className":149354},[494,789],[363,149356,149358],{"className":149357},[586],[363,149359,149361,149443],{"className":149360},[633,634],[363,149362,149364,149440],{"className":149363},[638],[363,149365,149367,149418,149426],{"className":149366,"style":2871},[642],[363,149368,149369,149372],{"style":2874},[363,149370],{"className":149371,"style":809},[650],[363,149373,149375],{"className":149374},[655,656,657,658],[363,149376,149378],{"className":149377},[407,658],[363,149379,149381,149384],{"className":149380},[407,658],[363,149382,45101],{"className":149383,"style":45131},[407,408,658],[363,149385,149387],{"className":149386},[629],[363,149388,149390,149410],{"className":149389},[633,634],[363,149391,149393,149407],{"className":149392},[638],[363,149394,149396],{"className":149395,"style":137304},[642],[363,149397,149398,149401],{"style":136942},[363,149399],{"className":149400,"style":30553},[650],[363,149402,149404],{"className":149403},[655,30557,10021,658],[363,149405,474],{"className":149406},[407,658],[363,149408,666],{"className":149409},[665],[363,149411,149413],{"className":149412},[638],[363,149414,149416],{"className":149415,"style":40117},[642],[363,149417],{},[363,149419,149420,149423],{"style":821},[363,149421],{"className":149422,"style":809},[650],[363,149424],{"className":149425,"style":829},[828],[363,149427,149428,149431],{"style":2897},[363,149429],{"className":149430,"style":809},[650],[363,149432,149434],{"className":149433},[655,656,657,658],[363,149435,149437],{"className":149436},[407,658],[363,149438,465],{"className":149439},[407,658],[363,149441,666],{"className":149442},[665],[363,149444,149446],{"className":149445},[638],[363,149447,149449],{"className":149448,"style":40264},[642],[363,149450],{},[363,149452],{"className":149453},[501,789],"，末一步用到 ",[363,149456,149458,149488],{"className":149457,"translate":367},[366],[363,149459,149461],{"className":149460},[371],[373,149462,149463],{"xmlns":375},[377,149464,149465,149485],{},[380,149466,149467,149469,149471,149473,149479,149481,149483],{},[383,149468,142382],{"mathvariant":557},[458,149470,4450],{},[458,149472,461],{"stretchy":460},[543,149474,149475,149477],{},[383,149476,45101],{},[463,149478,474],{},[458,149480,898],{"separator":394},[463,149482,465],{},[458,149484,468],{"stretchy":460},[387,149486,149487],{"encoding":389},"\\operatorname{Gamma}(\\alpha_0,1)",[363,149489,149491],{"className":149490,"ariaHidden":394},[393],[363,149492,149494,149497,149503,149506,149546,149549,149552,149555],{"className":149493},[398],[363,149495],{"className":149496,"style":487},[402],[363,149498,149500],{"className":149499},[1831],[363,149501,142382],{"className":149502},[407,33009],[363,149504,461],{"className":149505},[494],[363,149507,149509,149512],{"className":149508},[407],[363,149510,45101],{"className":149511,"style":45131},[407,408],[363,149513,149515],{"className":149514},[629],[363,149516,149518,149538],{"className":149517},[633,634],[363,149519,149521,149535],{"className":149520},[638],[363,149522,149524],{"className":149523,"style":11480},[642],[363,149525,149526,149529],{"style":136107},[363,149527],{"className":149528,"style":651},[650],[363,149530,149532],{"className":149531},[655,656,657,658],[363,149533,474],{"className":149534},[407,658],[363,149536,666],{"className":149537},[665],[363,149539,149541],{"className":149540},[638],[363,149542,149544],{"className":149543,"style":8315},[642],[363,149545],{},[363,149547,898],{"className":149548},[920],[363,149550],{"className":149551,"style":754},[505],[363,149553,465],{"className":149554},[407],[363,149556,468],{"className":149557},[501]," 的倒数的期望 ",[363,149560,149562,149606],{"className":149561,"translate":367},[366],[363,149563,149565],{"className":149564},[371],[373,149566,149567],{"xmlns":375},[377,149568,149569,149603],{},[380,149570,149571,149573,149575,149577,149579,149581,149583,149585,149587,149589,149591,149597,149599,149601],{},[383,149572,571],{"mathvariant":570},[458,149574,578],{"stretchy":460},[463,149576,465],{},[383,149578,1288],{"mathvariant":557},[383,149580,7908],{},[458,149582,605],{"stretchy":460},[458,149584,471],{},[463,149586,465],{},[383,149588,1288],{"mathvariant":557},[458,149590,461],{"stretchy":460},[543,149592,149593,149595],{},[383,149594,45101],{},[463,149596,474],{},[458,149598,5160],{},[463,149600,465],{},[458,149602,468],{"stretchy":460},[387,149604,149605],{"encoding":389},"\\mathbb{E}[1\u002Fs] = 1\u002F(\\alpha_0 - 1)",[363,149607,149609,149639,149700],{"className":149608,"ariaHidden":394},[393],[363,149610,149612,149615,149618,149621,149624,149627,149630,149633,149636],{"className":149611},[398],[363,149613],{"className":149614,"style":487},[402],[363,149616,571],{"className":149617},[407,714],[363,149619,578],{"className":149620},[494],[363,149622,8936],{"className":149623},[407],[363,149625,7908],{"className":149626},[407,408],[363,149628,605],{"className":149629},[501],[363,149631],{"className":149632,"style":506},[505],[363,149634,471],{"className":149635},[510],[363,149637],{"className":149638,"style":506},[505],[363,149640,149642,149645,149648,149651,149691,149694,149697],{"className":149641},[398],[363,149643],{"className":149644,"style":487},[402],[363,149646,8936],{"className":149647},[407],[363,149649,461],{"className":149650},[494],[363,149652,149654,149657],{"className":149653},[407],[363,149655,45101],{"className":149656,"style":45131},[407,408],[363,149658,149660],{"className":149659},[629],[363,149661,149663,149683],{"className":149662},[633,634],[363,149664,149666,149680],{"className":149665},[638],[363,149667,149669],{"className":149668,"style":11480},[642],[363,149670,149671,149674],{"style":136107},[363,149672],{"className":149673,"style":651},[650],[363,149675,149677],{"className":149676},[655,656,657,658],[363,149678,474],{"className":149679},[407,658],[363,149681,666],{"className":149682},[665],[363,149684,149686],{"className":149685},[638],[363,149687,149689],{"className":149688,"style":8315},[642],[363,149690],{},[363,149692],{"className":149693,"style":2934},[505],[363,149695,5160],{"className":149696},[2938],[363,149698],{"className":149699,"style":2934},[505],[363,149701,149703,149706,149709],{"className":149702},[398],[363,149704],{"className":149705,"style":487},[402],[363,149707,465],{"className":149708},[407],[363,149710,468],{"className":149711},[501],[363,149713,149715,149745],{"className":149714,"translate":367},[366],[363,149716,149718],{"className":149717},[371],[373,149719,149720],{"xmlns":375},[377,149721,149722,149742],{},[380,149723,149724,149730,149732,149738,149740],{},[543,149725,149726,149728],{},[383,149727,45101],{},[463,149729,474],{},[458,149731,9031],{},[543,149733,149734,149736],{},[383,149735,45101],{},[463,149737,474],{},[458,149739,5160],{},[463,149741,465],{},[387,149743,149744],{"encoding":389},"\\alpha_0 \\mapsto \\alpha_0 - 1",[363,149746,149748,149804,149859],{"className":149747,"ariaHidden":394},[393],[363,149749,149751,149755,149795,149798,149801],{"className":149750},[398],[363,149752],{"className":149753,"style":149754},[402],"height:0.661em;vertical-align:-0.15em;",[363,149756,149758,149761],{"className":149757},[407],[363,149759,45101],{"className":149760,"style":45131},[407,408],[363,149762,149764],{"className":149763},[629],[363,149765,149767,149787],{"className":149766},[633,634],[363,149768,149770,149784],{"className":149769},[638],[363,149771,149773],{"className":149772,"style":11480},[642],[363,149774,149775,149778],{"style":136107},[363,149776],{"className":149777,"style":651},[650],[363,149779,149781],{"className":149780},[655,656,657,658],[363,149782,474],{"className":149783},[407,658],[363,149785,666],{"className":149786},[665],[363,149788,149790],{"className":149789},[638],[363,149791,149793],{"className":149792,"style":8315},[642],[363,149794],{},[363,149796],{"className":149797,"style":506},[505],[363,149799,9031],{"className":149800},[510],[363,149802],{"className":149803,"style":506},[505],[363,149805,149807,149810,149850,149853,149856],{"className":149806},[398],[363,149808],{"className":149809,"style":145420},[402],[363,149811,149813,149816],{"className":149812},[407],[363,149814,45101],{"className":149815,"style":45131},[407,408],[363,149817,149819],{"className":149818},[629],[363,149820,149822,149842],{"className":149821},[633,634],[363,149823,149825,149839],{"className":149824},[638],[363,149826,149828],{"className":149827,"style":11480},[642],[363,149829,149830,149833],{"style":136107},[363,149831],{"className":149832,"style":651},[650],[363,149834,149836],{"className":149835},[655,656,657,658],[363,149837,474],{"className":149838},[407,658],[363,149840,666],{"className":149841},[665],[363,149843,149845],{"className":149844},[638],[363,149846,149848],{"className":149847,"style":8315},[642],[363,149849],{},[363,149851],{"className":149852,"style":2934},[505],[363,149854,5160],{"className":149855},[2938],[363,149857],{"className":149858,"style":2934},[505],[363,149860,149862,149865],{"className":149861},[398],[363,149863],{"className":149864,"style":520},[402],[363,149866,465],{"className":149867},[407]," 的平移技巧，或直接由命题 1.3 的矩恒等式 ",[363,149870,149872,149932],{"className":149871,"translate":367},[366],[363,149873,149875],{"className":149874},[371],[373,149876,149877],{"xmlns":375},[377,149878,149879,149929],{},[380,149880,149881,149883,149885,149891,149903,149905,149907,149909,149911,149913,149915,149917,149919,149921,149923,149925,149927],{},[383,149882,571],{"mathvariant":570},[458,149884,578],{"stretchy":460},[543,149886,149887,149889],{},[458,149888,136637],{},[383,149890,12310],{},[7900,149892,149893,149895,149897],{},[383,149894,1121],{},[383,149896,12310],{},[543,149898,149899,149901],{},[383,149900,84464],{},[383,149902,12310],{},[458,149904,605],{"stretchy":460},[458,149906,471],{},[383,149908,39638],{},[458,149910,461],{"stretchy":460},[383,149912,45101],{"mathvariant":136008},[458,149914,2817],{},[383,149916,84464],{"mathvariant":136008},[458,149918,468],{"stretchy":460},[383,149920,1288],{"mathvariant":557},[383,149922,39638],{},[458,149924,461],{"stretchy":460},[383,149926,45101],{"mathvariant":136008},[458,149928,468],{"stretchy":460},[387,149930,149931],{"encoding":389},"\\mathbb{E}[\\prod_i x_i^{\\beta_i}] = B(\\boldsymbol{\\alpha} + \\boldsymbol{\\beta})\u002FB(\\boldsymbol{\\alpha})",[363,149933,149935,150097,150127],{"className":149934,"ariaHidden":394},[393],[363,149936,149938,149942,149945,149948,149988,149991,150085,150088,150091,150094],{"className":149937},[398],[363,149939],{"className":149940,"style":149941},[402],"height:1.2667em;vertical-align:-0.2997em;",[363,149943,571],{"className":149944},[407,714],[363,149946,578],{"className":149947},[494],[363,149949,149951,149954],{"className":149950},[1831],[363,149952,136637],{"className":149953,"style":40007},[1831,1832,5963],[363,149955,149957],{"className":149956},[629],[363,149958,149960,149980],{"className":149959},[633,634],[363,149961,149963,149977],{"className":149962},[638],[363,149964,149966],{"className":149965,"style":40020},[642],[363,149967,149968,149971],{"style":40023},[363,149969],{"className":149970,"style":651},[650],[363,149972,149974],{"className":149973},[655,656,657,658],[363,149975,12310],{"className":149976},[407,408,658],[363,149978,666],{"className":149979},[665],[363,149981,149983],{"className":149982},[638],[363,149984,149986],{"className":149985,"style":40042},[642],[363,149987],{},[363,149989],{"className":149990,"style":754},[505],[363,149992,149994,149997],{"className":149993},[407],[363,149995,1121],{"className":149996},[407,408],[363,149998,150000],{"className":149999},[629],[363,150001,150003,150077],{"className":150002},[633,634],[363,150004,150006,150074],{"className":150005},[638],[363,150007,150010,150021],{"className":150008,"style":150009},[642],"height:0.967em;",[363,150011,150012,150015],{"style":136900},[363,150013],{"className":150014,"style":651},[650],[363,150016,150018],{"className":150017},[655,656,657,658],[363,150019,12310],{"className":150020},[407,408,658],[363,150022,150024,150027],{"style":150023},"top:-3.1809em;margin-right:0.05em;",[363,150025],{"className":150026,"style":651},[650],[363,150028,150030],{"className":150029},[655,656,657,658],[363,150031,150033],{"className":150032},[407,658],[363,150034,150036,150039],{"className":150035},[407,658],[363,150037,84464],{"className":150038,"style":84686},[407,408,658],[363,150040,150042],{"className":150041},[629],[363,150043,150045,150066],{"className":150044},[633,634],[363,150046,150048,150063],{"className":150047},[638],[363,150049,150051],{"className":150050,"style":40095},[642],[363,150052,150054,150057],{"style":150053},"top:-2.357em;margin-left:-0.0528em;margin-right:0.0714em;",[363,150055],{"className":150056,"style":30553},[650],[363,150058,150060],{"className":150059},[655,30557,10021,658],[363,150061,12310],{"className":150062},[407,408,658],[363,150064,666],{"className":150065},[665],[363,150067,150069],{"className":150068},[638],[363,150070,150072],{"className":150071,"style":40117},[642],[363,150073],{},[363,150075,666],{"className":150076},[665],[363,150078,150080],{"className":150079},[638],[363,150081,150083],{"className":150082,"style":136978},[642],[363,150084],{},[363,150086,605],{"className":150087},[501],[363,150089],{"className":150090,"style":506},[505],[363,150092,471],{"className":150093},[510],[363,150095],{"className":150096,"style":506},[505],[363,150098,150100,150103,150106,150109,150118,150121,150124],{"className":150099},[398],[363,150101],{"className":150102,"style":487},[402],[363,150104,39638],{"className":150105,"style":39734},[407,408],[363,150107,461],{"className":150108},[494],[363,150110,150112],{"className":150111},[407],[363,150113,150115],{"className":150114},[407],[363,150116,45101],{"className":150117},[407,136068],[363,150119],{"className":150120,"style":2934},[505],[363,150122,2817],{"className":150123},[2938],[363,150125],{"className":150126,"style":2934},[505],[363,150128,150130,150133,150143,150146,150149,150152,150155,150164],{"className":150129},[398],[363,150131],{"className":150132,"style":487},[402],[363,150134,150136],{"className":150135},[407],[363,150137,150139],{"className":150138},[407],[363,150140,84464],{"className":150141,"style":150142},[407,136068],"margin-right:0.034em;",[363,150144,468],{"className":150145},[501],[363,150147,1288],{"className":150148},[407],[363,150150,39638],{"className":150151,"style":39734},[407,408],[363,150153,461],{"className":150154},[494],[363,150156,150158],{"className":150157},[407],[363,150159,150161],{"className":150160},[407],[363,150162,45101],{"className":150163},[407,136068],[363,150165,468],{"className":150166},[501],[363,150168,150170,150192],{"className":150169,"translate":367},[366],[363,150171,150173],{"className":150172},[371],[373,150174,150175],{"xmlns":375},[377,150176,150177,150189],{},[380,150178,150179,150185,150187],{},[543,150180,150181,150183],{},[383,150182,84464],{},[383,150184,12310],{},[458,150186,471],{},[463,150188,465],{},[387,150190,150191],{"encoding":389},"\\beta_i = 1",[363,150193,150195,150251],{"className":150194,"ariaHidden":394},[393],[363,150196,150198,150201,150242,150245,150248],{"className":150197},[398],[363,150199],{"className":150200,"style":403},[402],[363,150202,150204,150207],{"className":150203},[407],[363,150205,84464],{"className":150206,"style":84686},[407,408],[363,150208,150210],{"className":150209},[629],[363,150211,150213,150234],{"className":150212},[633,634],[363,150214,150216,150231],{"className":150215},[638],[363,150217,150219],{"className":150218,"style":12529},[642],[363,150220,150222,150225],{"style":150221},"top:-2.55em;margin-left:-0.0528em;margin-right:0.05em;",[363,150223],{"className":150224,"style":651},[650],[363,150226,150228],{"className":150227},[655,656,657,658],[363,150229,12310],{"className":150230},[407,408,658],[363,150232,666],{"className":150233},[665],[363,150235,150237],{"className":150236},[638],[363,150238,150240],{"className":150239,"style":8315},[642],[363,150241],{},[363,150243],{"className":150244,"style":506},[505],[363,150246,471],{"className":150247},[510],[363,150249],{"className":150250,"style":506},[505],[363,150252,150254,150257],{"className":150253},[398],[363,150255],{"className":150256,"style":520},[402],[363,150258,465],{"className":150259},[407]," 得到。二阶矩由 ",[363,150262,150264,150338],{"className":150263,"translate":367},[366],[363,150265,150267],{"className":150266},[371],[373,150268,150269],{"xmlns":375},[377,150270,150271,150335],{},[380,150272,150273,150275,150277,150285,150287,150289],{},[383,150274,571],{"mathvariant":570},[458,150276,578],{"stretchy":460},[7900,150278,150279,150281,150283],{},[383,150280,1121],{},[383,150282,12310],{},[463,150284,2810],{},[458,150286,605],{"stretchy":460},[458,150288,471],{},[586,150290,150291,150313],{},[380,150292,150293,150299,150301,150307,150309,150311],{},[543,150294,150295,150297],{},[383,150296,45101],{},[383,150298,12310],{},[458,150300,461],{"stretchy":460},[543,150302,150303,150305],{},[383,150304,45101],{},[383,150306,12310],{},[458,150308,2817],{},[463,150310,465],{},[458,150312,468],{"stretchy":460},[380,150314,150315,150321,150323,150329,150331,150333],{},[543,150316,150317,150319],{},[383,150318,45101],{},[463,150320,474],{},[458,150322,461],{"stretchy":460},[543,150324,150325,150327],{},[383,150326,45101],{},[463,150328,474],{},[458,150330,2817],{},[463,150332,465],{},[458,150334,468],{"stretchy":460},[387,150336,150337],{"encoding":389},"\\mathbb{E}[x_i^2] = \\frac{\\alpha_i(\\alpha_i+1)}{\\alpha_0(\\alpha_0+1)}",[363,150339,150341,150419],{"className":150340,"ariaHidden":394},[393],[363,150342,150344,150348,150351,150354,150407,150410,150413,150416],{"className":150343},[398],[363,150345],{"className":150346,"style":150347},[402],"height:1.0728em;vertical-align:-0.2587em;",[363,150349,571],{"className":150350},[407,714],[363,150352,578],{"className":150353},[494],[363,150355,150357,150360],{"className":150356},[407],[363,150358,1121],{"className":150359},[407,408],[363,150361,150363],{"className":150362},[629],[363,150364,150366,150398],{"className":150365},[633,634],[363,150367,150369,150395],{"className":150368},[638],[363,150370,150372,150384],{"className":150371,"style":20375},[642],[363,150373,150375,150378],{"style":150374},"top:-2.4413em;margin-left:0em;margin-right:0.05em;",[363,150376],{"className":150377,"style":651},[650],[363,150379,150381],{"className":150380},[655,656,657,658],[363,150382,12310],{"className":150383},[407,408,658],[363,150385,150386,150389],{"style":7212},[363,150387],{"className":150388,"style":651},[650],[363,150390,150392],{"className":150391},[655,656,657,658],[363,150393,2810],{"className":150394},[407,658],[363,150396,666],{"className":150397},[665],[363,150399,150401],{"className":150400},[638],[363,150402,150405],{"className":150403,"style":150404},[642],"height:0.2587em;",[363,150406],{},[363,150408,605],{"className":150409},[501],[363,150411],{"className":150412,"style":506},[505],[363,150414,471],{"className":150415},[510],[363,150417],{"className":150418,"style":506},[505],[363,150420,150422,150426],{"className":150421},[398],[363,150423],{"className":150424,"style":150425},[402],"height:1.53em;vertical-align:-0.52em;",[363,150427,150429,150432,150669],{"className":150428},[407],[363,150430],{"className":150431},[494,789],[363,150433,150435],{"className":150434},[586],[363,150436,150438,150661],{"className":150437},[633,634],[363,150439,150441,150658],{"className":150440},[638],[363,150442,150444,150547,150555],{"className":150443,"style":26740},[642],[363,150445,150446,150449],{"style":2874},[363,150447],{"className":150448,"style":809},[650],[363,150450,150452],{"className":150451},[655,656,657,658],[363,150453,150455,150495,150498,150538,150541,150544],{"className":150454},[407,658],[363,150456,150458,150461],{"className":150457},[407,658],[363,150459,45101],{"className":150460,"style":45131},[407,408,658],[363,150462,150464],{"className":150463},[629],[363,150465,150467,150487],{"className":150466},[633,634],[363,150468,150470,150484],{"className":150469},[638],[363,150471,150473],{"className":150472,"style":137304},[642],[363,150474,150475,150478],{"style":136942},[363,150476],{"className":150477,"style":30553},[650],[363,150479,150481],{"className":150480},[655,30557,10021,658],[363,150482,474],{"className":150483},[407,658],[363,150485,666],{"className":150486},[665],[363,150488,150490],{"className":150489},[638],[363,150491,150493],{"className":150492,"style":40117},[642],[363,150494],{},[363,150496,461],{"className":150497},[494,658],[363,150499,150501,150504],{"className":150500},[407,658],[363,150502,45101],{"className":150503,"style":45131},[407,408,658],[363,150505,150507],{"className":150506},[629],[363,150508,150510,150530],{"className":150509},[633,634],[363,150511,150513,150527],{"className":150512},[638],[363,150514,150516],{"className":150515,"style":137304},[642],[363,150517,150518,150521],{"style":136942},[363,150519],{"className":150520,"style":30553},[650],[363,150522,150524],{"className":150523},[655,30557,10021,658],[363,150525,474],{"className":150526},[407,658],[363,150528,666],{"className":150529},[665],[363,150531,150533],{"className":150532},[638],[363,150534,150536],{"className":150535,"style":40117},[642],[363,150537],{},[363,150539,2817],{"className":150540},[2938,658],[363,150542,465],{"className":150543},[407,658],[363,150545,468],{"className":150546},[501,658],[363,150548,150549,150552],{"style":821},[363,150550],{"className":150551,"style":809},[650],[363,150553],{"className":150554,"style":829},[828],[363,150556,150557,150560],{"style":26765},[363,150558],{"className":150559,"style":809},[650],[363,150561,150563],{"className":150562},[655,656,657,658],[363,150564,150566,150606,150609,150649,150652,150655],{"className":150565},[407,658],[363,150567,150569,150572],{"className":150568},[407,658],[363,150570,45101],{"className":150571,"style":45131},[407,408,658],[363,150573,150575],{"className":150574},[629],[363,150576,150578,150598],{"className":150577},[633,634],[363,150579,150581,150595],{"className":150580},[638],[363,150582,150584],{"className":150583,"style":40095},[642],[363,150585,150586,150589],{"style":136942},[363,150587],{"className":150588,"style":30553},[650],[363,150590,150592],{"className":150591},[655,30557,10021,658],[363,150593,12310],{"className":150594},[407,408,658],[363,150596,666],{"className":150597},[665],[363,150599,150601],{"className":150600},[638],[363,150602,150604],{"className":150603,"style":40117},[642],[363,150605],{},[363,150607,461],{"className":150608},[494,658],[363,150610,150612,150615],{"className":150611},[407,658],[363,150613,45101],{"className":150614,"style":45131},[407,408,658],[363,150616,150618],{"className":150617},[629],[363,150619,150621,150641],{"className":150620},[633,634],[363,150622,150624,150638],{"className":150623},[638],[363,150625,150627],{"className":150626,"style":40095},[642],[363,150628,150629,150632],{"style":136942},[363,150630],{"className":150631,"style":30553},[650],[363,150633,150635],{"className":150634},[655,30557,10021,658],[363,150636,12310],{"className":150637},[407,408,658],[363,150639,666],{"className":150640},[665],[363,150642,150644],{"className":150643},[638],[363,150645,150647],{"className":150646,"style":40117},[642],[363,150648],{},[363,150650,2817],{"className":150651},[2938,658],[363,150653,465],{"className":150654},[407,658],[363,150656,468],{"className":150657},[501,658],[363,150659,666],{"className":150660},[665],[363,150662,150664],{"className":150663},[638],[363,150665,150667],{"className":150666,"style":45949},[642],[363,150668],{},[363,150670],{"className":150671},[501,789],[363,150673,150675,150745],{"className":150674,"translate":367},[366],[363,150676,150678],{"className":150677},[371],[373,150679,150680],{"xmlns":375},[377,150681,150682,150742],{},[380,150683,150684,150686,150688,150694,150700,150702,150704],{},[383,150685,571],{"mathvariant":570},[458,150687,578],{"stretchy":460},[543,150689,150690,150692],{},[383,150691,1121],{},[383,150693,12310],{},[543,150695,150696,150698],{},[383,150697,1121],{},[383,150699,100360],{},[458,150701,605],{"stretchy":460},[458,150703,471],{},[586,150705,150706,150720],{},[380,150707,150708,150714],{},[543,150709,150710,150712],{},[383,150711,45101],{},[383,150713,12310],{},[543,150715,150716,150718],{},[383,150717,45101],{},[383,150719,100360],{},[380,150721,150722,150728,150730,150736,150738,150740],{},[543,150723,150724,150726],{},[383,150725,45101],{},[463,150727,474],{},[458,150729,461],{"stretchy":460},[543,150731,150732,150734],{},[383,150733,45101],{},[463,150735,474],{},[458,150737,2817],{},[463,150739,465],{},[458,150741,468],{"stretchy":460},[387,150743,150744],{"encoding":389},"\\mathbb{E}[x_i x_j] = \\frac{\\alpha_i \\alpha_j}{\\alpha_0(\\alpha_0+1)}",[363,150746,150748,150852],{"className":150747,"ariaHidden":394},[393],[363,150749,150751,150754,150757,150760,150800,150840,150843,150846,150849],{"className":150750},[398],[363,150752],{"className":150753,"style":618},[402],[363,150755,571],{"className":150756},[407,714],[363,150758,578],{"className":150759},[494],[363,150761,150763,150766],{"className":150762},[407],[363,150764,1121],{"className":150765},[407,408],[363,150767,150769],{"className":150768},[629],[363,150770,150772,150792],{"className":150771},[633,634],[363,150773,150775,150789],{"className":150774},[638],[363,150776,150778],{"className":150777,"style":12529},[642],[363,150779,150780,150783],{"style":730},[363,150781],{"className":150782,"style":651},[650],[363,150784,150786],{"className":150785},[655,656,657,658],[363,150787,12310],{"className":150788},[407,408,658],[363,150790,666],{"className":150791},[665],[363,150793,150795],{"className":150794},[638],[363,150796,150798],{"className":150797,"style":8315},[642],[363,150799],{},[363,150801,150803,150806],{"className":150802},[407],[363,150804,1121],{"className":150805},[407,408],[363,150807,150809],{"className":150808},[629],[363,150810,150812,150832],{"className":150811},[633,634],[363,150813,150815,150829],{"className":150814},[638],[363,150816,150818],{"className":150817,"style":12529},[642],[363,150819,150820,150823],{"style":730},[363,150821],{"className":150822,"style":651},[650],[363,150824,150826],{"className":150825},[655,656,657,658],[363,150827,100360],{"className":150828,"style":100888},[407,408,658],[363,150830,666],{"className":150831},[665],[363,150833,150835],{"className":150834},[638],[363,150836,150838],{"className":150837,"style":673},[642],[363,150839],{},[363,150841,605],{"className":150842},[501],[363,150844],{"className":150845,"style":506},[505],[363,150847,471],{"className":150848},[510],[363,150850],{"className":150851,"style":506},[505],[363,150853,150855,150859],{"className":150854},[398],[363,150856],{"className":150857,"style":150858},[402],"height:1.3287em;vertical-align:-0.52em;",[363,150860,150862,150865,151091],{"className":150861},[407],[363,150863],{"className":150864},[494,789],[363,150866,150868],{"className":150867},[586],[363,150869,150871,151083],{"className":150870},[633,634],[363,150872,150874,151080],{"className":150873},[638],[363,150875,150878,150981,150989],{"className":150876,"style":150877},[642],"height:0.8087em;",[363,150879,150880,150883],{"style":2874},[363,150881],{"className":150882,"style":809},[650],[363,150884,150886],{"className":150885},[655,656,657,658],[363,150887,150889,150929,150932,150972,150975,150978],{"className":150888},[407,658],[363,150890,150892,150895],{"className":150891},[407,658],[363,150893,45101],{"className":150894,"style":45131},[407,408,658],[363,150896,150898],{"className":150897},[629],[363,150899,150901,150921],{"className":150900},[633,634],[363,150902,150904,150918],{"className":150903},[638],[363,150905,150907],{"className":150906,"style":137304},[642],[363,150908,150909,150912],{"style":136942},[363,150910],{"className":150911,"style":30553},[650],[363,150913,150915],{"className":150914},[655,30557,10021,658],[363,150916,474],{"className":150917},[407,658],[363,150919,666],{"className":150920},[665],[363,150922,150924],{"className":150923},[638],[363,150925,150927],{"className":150926,"style":40117},[642],[363,150928],{},[363,150930,461],{"className":150931},[494,658],[363,150933,150935,150938],{"className":150934},[407,658],[363,150936,45101],{"className":150937,"style":45131},[407,408,658],[363,150939,150941],{"className":150940},[629],[363,150942,150944,150964],{"className":150943},[633,634],[363,150945,150947,150961],{"className":150946},[638],[363,150948,150950],{"className":150949,"style":137304},[642],[363,150951,150952,150955],{"style":136942},[363,150953],{"className":150954,"style":30553},[650],[363,150956,150958],{"className":150957},[655,30557,10021,658],[363,150959,474],{"className":150960},[407,658],[363,150962,666],{"className":150963},[665],[363,150965,150967],{"className":150966},[638],[363,150968,150970],{"className":150969,"style":40117},[642],[363,150971],{},[363,150973,2817],{"className":150974},[2938,658],[363,150976,465],{"className":150977},[407,658],[363,150979,468],{"className":150980},[501,658],[363,150982,150983,150986],{"style":821},[363,150984],{"className":150985,"style":809},[650],[363,150987],{"className":150988,"style":829},[828],[363,150990,150991,150994],{"style":148652},[363,150992],{"className":150993,"style":809},[650],[363,150995,150997],{"className":150996},[655,656,657,658],[363,150998,151000,151040],{"className":150999},[407,658],[363,151001,151003,151006],{"className":151002},[407,658],[363,151004,45101],{"className":151005,"style":45131},[407,408,658],[363,151007,151009],{"className":151008},[629],[363,151010,151012,151032],{"className":151011},[633,634],[363,151013,151015,151029],{"className":151014},[638],[363,151016,151018],{"className":151017,"style":40095},[642],[363,151019,151020,151023],{"style":136942},[363,151021],{"className":151022,"style":30553},[650],[363,151024,151026],{"className":151025},[655,30557,10021,658],[363,151027,12310],{"className":151028},[407,408,658],[363,151030,666],{"className":151031},[665],[363,151033,151035],{"className":151034},[638],[363,151036,151038],{"className":151037,"style":40117},[642],[363,151039],{},[363,151041,151043,151046],{"className":151042},[407,658],[363,151044,45101],{"className":151045,"style":45131},[407,408,658],[363,151047,151049],{"className":151048},[629],[363,151050,151052,151072],{"className":151051},[633,634],[363,151053,151055,151069],{"className":151054},[638],[363,151056,151058],{"className":151057,"style":40095},[642],[363,151059,151060,151063],{"style":136942},[363,151061],{"className":151062,"style":30553},[650],[363,151064,151066],{"className":151065},[655,30557,10021,658],[363,151067,100360],{"className":151068,"style":100888},[407,408,658],[363,151070,666],{"className":151071},[665],[363,151073,151075],{"className":151074},[638],[363,151076,151078],{"className":151077,"style":122065},[642],[363,151079],{},[363,151081,666],{"className":151082},[665],[363,151084,151086],{"className":151085},[638],[363,151087,151089],{"className":151088,"style":45949},[642],[363,151090],{},[363,151092],{"className":151093},[501,789]," 相减即得。",[11,151096,151097,151098,151292],{},"上述结果可写成更紧凑的矩阵形式。记 ",[363,151099,151101,151145],{"className":151100,"translate":367},[366],[363,151102,151104],{"className":151103},[371],[373,151105,151106],{"xmlns":375},[377,151107,151108,151142],{},[380,151109,151110,151112,151114,151116,151118,151124,151126,151128,151130],{},[383,151111,2711],{"mathvariant":136008},[458,151113,471],{},[383,151115,45101],{"mathvariant":136008},[383,151117,1288],{"mathvariant":557},[543,151119,151120,151122],{},[383,151121,45101],{},[463,151123,474],{},[458,151125,6256],{},[383,151127,134464],{"mathvariant":557},[458,151129,4450],{},[7161,151131,151132,151134],{},[383,151133,126023],{"mathvariant":557},[380,151135,151136,151138,151140],{},[383,151137,11041],{},[458,151139,5160],{},[463,151141,465],{},[387,151143,151144],{"encoding":389},"\\boldsymbol{\\mu} = \\boldsymbol{\\alpha}\u002F\\alpha_0 \\in \\operatorname{int}\\Delta^{K-1}",[363,151146,151148,151172,151239],{"className":151147,"ariaHidden":394},[393],[363,151149,151151,151154,151163,151166,151169],{"className":151150},[398],[363,151152],{"className":151153,"style":133764},[402],[363,151155,151157],{"className":151156},[407],[363,151158,151160],{"className":151159},[407],[363,151161,2711],{"className":151162},[407,136068],[363,151164],{"className":151165,"style":506},[505],[363,151167,471],{"className":151168},[510],[363,151170],{"className":151171,"style":506},[505],[363,151173,151175,151178,151187,151190,151230,151233,151236],{"className":151174},[398],[363,151176],{"className":151177,"style":487},[402],[363,151179,151181],{"className":151180},[407],[363,151182,151184],{"className":151183},[407],[363,151185,45101],{"className":151186},[407,136068],[363,151188,1288],{"className":151189},[407],[363,151191,151193,151196],{"className":151192},[407],[363,151194,45101],{"className":151195,"style":45131},[407,408],[363,151197,151199],{"className":151198},[629],[363,151200,151202,151222],{"className":151201},[633,634],[363,151203,151205,151219],{"className":151204},[638],[363,151206,151208],{"className":151207,"style":11480},[642],[363,151209,151210,151213],{"style":136107},[363,151211],{"className":151212,"style":651},[650],[363,151214,151216],{"className":151215},[655,656,657,658],[363,151217,474],{"className":151218},[407,658],[363,151220,666],{"className":151221},[665],[363,151223,151225],{"className":151224},[638],[363,151226,151228],{"className":151227,"style":8315},[642],[363,151229],{},[363,151231],{"className":151232,"style":506},[505],[363,151234,6256],{"className":151235},[510],[363,151237],{"className":151238,"style":506},[505],[363,151240,151242,151245,151251,151254],{"className":151241},[398],[363,151243],{"className":151244,"style":52432},[402],[363,151246,151248],{"className":151247},[1831],[363,151249,134464],{"className":151250},[407,33009],[363,151252],{"className":151253,"style":754},[505],[363,151255,151257,151260],{"className":151256},[407],[363,151258,126023],{"className":151259},[407],[363,151261,151263],{"className":151262},[629],[363,151264,151266],{"className":151265},[633],[363,151267,151269],{"className":151268},[638],[363,151270,151272],{"className":151271,"style":52432},[642],[363,151273,151274,151277],{"style":7212},[363,151275],{"className":151276,"style":651},[650],[363,151278,151280],{"className":151279},[655,656,657,658],[363,151281,151283,151286,151289],{"className":151282},[407,658],[363,151284,11041],{"className":151285,"style":11129},[407,408,658],[363,151287,5160],{"className":151288},[2938,658],[363,151290,465],{"className":151291},[407,658]," 为均值向量，则",[363,151294,151296],{"className":151295,"translate":367},[528],[363,151297,151299,151372],{"className":151298,"translate":367},[366],[363,151300,151302],{"className":151301},[371],[373,151303,151304],{"xmlns":375,"display":537},[377,151305,151306,151369],{},[380,151307,151308,151311,151313,151315,151317,151319,151321,151323,151325,151341],{},[383,151309,151310],{"mathvariant":75560},"Σ",[458,151312,471],{},[383,151314,147712],{"mathvariant":557},[458,151316,4450],{},[458,151318,461],{"stretchy":460},[383,151320,1121],{"mathvariant":75560},[458,151322,468],{"stretchy":460},[458,151324,471],{},[586,151326,151327,151329],{},[463,151328,465],{},[380,151330,151331,151337,151339],{},[543,151332,151333,151335],{},[383,151334,45101],{},[463,151336,474],{},[458,151338,2817],{},[463,151340,465],{},[380,151342,151343,151345,151348,151350,151352,151354,151356,151358,151360,151367],{},[458,151344,461],{"fence":394},[383,151346,151347],{"mathvariant":557},"diag",[458,151349,4450],{},[458,151351,461],{"stretchy":460},[383,151353,2711],{"mathvariant":136008},[458,151355,468],{"stretchy":460},[458,151357,5160],{},[383,151359,2711],{"mathvariant":136008},[7161,151361,151362,151364],{},[383,151363,2711],{"mathvariant":136008},[383,151365,151366],{"mathvariant":557},"⊤",[458,151368,468],{"fence":394},[387,151370,151371],{"encoding":389},"\\boldsymbol{\\Sigma} = \\operatorname{Cov}(\\mathbf{x}) = \\frac{1}{\\alpha_0 + 1}\\left(\\operatorname{diag}(\\boldsymbol{\\mu}) - \\boldsymbol{\\mu}\\boldsymbol{\\mu}^\\top\\right)",[363,151373,151375,151400,151430],{"className":151374,"ariaHidden":394},[393],[363,151376,151378,151382,151391,151394,151397],{"className":151377},[398],[363,151379],{"className":151380,"style":151381},[402],"height:0.6861em;",[363,151383,151385],{"className":151384},[407],[363,151386,151388],{"className":151387},[407],[363,151389,151310],{"className":151390},[407,75905],[363,151392],{"className":151393,"style":506},[505],[363,151395,471],{"className":151396},[510],[363,151398],{"className":151399,"style":506},[505],[363,151401,151403,151406,151412,151415,151418,151421,151424,151427],{"className":151402},[398],[363,151404],{"className":151405,"style":487},[402],[363,151407,151409],{"className":151408},[1831],[363,151410,147712],{"className":151411,"style":4504},[407,33009],[363,151413,461],{"className":151414},[494],[363,151416,1121],{"className":151417},[407,75905],[363,151419,468],{"className":151420},[501],[363,151422],{"className":151423,"style":506},[505],[363,151425,471],{"className":151426},[510],[363,151428],{"className":151429,"style":506},[505],[363,151431,151433,151437,151548,151551],{"className":151432},[398],[363,151434],{"className":151435,"style":151436},[402],"height:2.1574em;vertical-align:-0.836em;",[363,151438,151440,151443,151545],{"className":151439},[407],[363,151441],{"className":151442},[494,789],[363,151444,151446],{"className":151445},[586],[363,151447,151449,151537],{"className":151448},[633,634],[363,151450,151452,151534],{"className":151451},[638],[363,151453,151455,151515,151523],{"className":151454,"style":23236},[642],[363,151456,151457,151460],{"style":805},[363,151458],{"className":151459,"style":809},[650],[363,151461,151463,151503,151506,151509,151512],{"className":151462},[407],[363,151464,151466,151469],{"className":151465},[407],[363,151467,45101],{"className":151468,"style":45131},[407,408],[363,151470,151472],{"className":151471},[629],[363,151473,151475,151495],{"className":151474},[633,634],[363,151476,151478,151492],{"className":151477},[638],[363,151479,151481],{"className":151480,"style":11480},[642],[363,151482,151483,151486],{"style":136107},[363,151484],{"className":151485,"style":651},[650],[363,151487,151489],{"className":151488},[655,656,657,658],[363,151490,474],{"className":151491},[407,658],[363,151493,666],{"className":151494},[665],[363,151496,151498],{"className":151497},[638],[363,151499,151501],{"className":151500,"style":8315},[642],[363,151502],{},[363,151504],{"className":151505,"style":2934},[505],[363,151507,2817],{"className":151508},[2938],[363,151510],{"className":151511,"style":2934},[505],[363,151513,465],{"className":151514},[407],[363,151516,151517,151520],{"style":821},[363,151518],{"className":151519,"style":809},[650],[363,151521],{"className":151522,"style":829},[828],[363,151524,151525,151528],{"style":832},[363,151526],{"className":151527,"style":809},[650],[363,151529,151531],{"className":151530},[407],[363,151532,465],{"className":151533},[407],[363,151535,666],{"className":151536},[665],[363,151538,151540],{"className":151539},[638],[363,151541,151543],{"className":151542,"style":125395},[642],[363,151544],{},[363,151546],{"className":151547},[501,789],[363,151549],{"className":151550,"style":754},[505],[363,151552,151554,151560,151566,151569,151578,151581,151584,151587,151590,151599,151634],{"className":151553},[758],[363,151555,151557],{"className":151556,"style":763},[494,762],[363,151558,461],{"className":151559},[767,10021],[363,151561,151563],{"className":151562},[1831],[363,151564,151347],{"className":151565,"style":4504},[407,33009],[363,151567,461],{"className":151568},[494],[363,151570,151572],{"className":151571},[407],[363,151573,151575],{"className":151574},[407],[363,151576,2711],{"className":151577},[407,136068],[363,151579,468],{"className":151580},[501],[363,151582],{"className":151583,"style":2934},[505],[363,151585,5160],{"className":151586},[2938],[363,151588],{"className":151589,"style":2934},[505],[363,151591,151593],{"className":151592},[407],[363,151594,151596],{"className":151595},[407],[363,151597,2711],{"className":151598},[407,136068],[363,151600,151602,151611],{"className":151601},[407],[363,151603,151605],{"className":151604},[407],[363,151606,151608],{"className":151607},[407],[363,151609,2711],{"className":151610},[407,136068],[363,151612,151614],{"className":151613},[629],[363,151615,151617],{"className":151616},[633],[363,151618,151620],{"className":151619},[638],[363,151621,151623],{"className":151622,"style":48211},[642],[363,151624,151625,151628],{"style":8624},[363,151626],{"className":151627,"style":651},[650],[363,151629,151631],{"className":151630},[655,656,657,658],[363,151632,151366],{"className":151633},[407,658],[363,151635,151637],{"className":151636,"style":763},[501,762],[363,151638,468],{"className":151639},[767,10021],[11,151641,151642,151643,151693,151694,3092,151791,151826,151827,151856,151857,151917,151918,152159,152160,152188],{},"这一形式揭示了两个结构性事实。第一，协方差矩阵的秩为 ",[363,151644,151646,151663],{"className":151645,"translate":367},[366],[363,151647,151649],{"className":151648},[371],[373,151650,151651],{"xmlns":375},[377,151652,151653,151661],{},[380,151654,151655,151657,151659],{},[383,151656,11041],{},[458,151658,5160],{},[463,151660,465],{},[387,151662,133889],{"encoding":389},[363,151664,151666,151684],{"className":151665,"ariaHidden":394},[393],[363,151667,151669,151672,151675,151678,151681],{"className":151668},[398],[363,151670],{"className":151671,"style":133899},[402],[363,151673,11041],{"className":151674,"style":11129},[407,408],[363,151676],{"className":151677,"style":2934},[505],[363,151679,5160],{"className":151680},[2938],[363,151682],{"className":151683,"style":2934},[505],[363,151685,151687,151690],{"className":151686},[398],[363,151688],{"className":151689,"style":520},[402],[363,151691,465],{"className":151692},[407],"：由于 ",[363,151695,151697,151723],{"className":151696,"translate":367},[366],[363,151698,151700],{"className":151699},[371],[373,151701,151702],{"xmlns":375},[377,151703,151704,151720],{},[380,151705,151706,151712,151714,151716,151718],{},[7161,151707,151708,151710],{},[463,151709,465],{"mathvariant":75560},[383,151711,151366],{"mathvariant":557},[383,151713,151310],{"mathvariant":75560},[463,151715,465],{"mathvariant":75560},[458,151717,471],{},[463,151719,474],{},[387,151721,151722],{"encoding":389},"\\mathbf{1}^\\top \\boldsymbol{\\Sigma} \\mathbf{1} = 0",[363,151724,151726,151782],{"className":151725,"ariaHidden":394},[393],[363,151727,151729,151732,151761,151770,151773,151776,151779],{"className":151728},[398],[363,151730],{"className":151731,"style":47901},[402],[363,151733,151735,151738],{"className":151734},[407],[363,151736,465],{"className":151737},[407,75905],[363,151739,151741],{"className":151740},[629],[363,151742,151744],{"className":151743},[633],[363,151745,151747],{"className":151746},[638],[363,151748,151750],{"className":151749,"style":47901},[642],[363,151751,151752,151755],{"style":7212},[363,151753],{"className":151754,"style":651},[650],[363,151756,151758],{"className":151757},[655,656,657,658],[363,151759,151366],{"className":151760},[407,658],[363,151762,151764],{"className":151763},[407],[363,151765,151767],{"className":151766},[407],[363,151768,151310],{"className":151769},[407,75905],[363,151771,465],{"className":151772},[407,75905],[363,151774],{"className":151775,"style":506},[505],[363,151777,471],{"className":151778},[510],[363,151780],{"className":151781,"style":506},[505],[363,151783,151785,151788],{"className":151784},[398],[363,151786],{"className":151787,"style":520},[402],[363,151789,474],{"className":151790},[407],[363,151792,151794,151808],{"className":151793,"translate":367},[366],[363,151795,151797],{"className":151796},[371],[373,151798,151799],{"xmlns":375},[377,151800,151801,151805],{},[380,151802,151803],{},[383,151804,151310],{"mathvariant":75560},[387,151806,151807],{"encoding":389},"\\boldsymbol{\\Sigma}",[363,151809,151811],{"className":151810,"ariaHidden":394},[393],[363,151812,151814,151817],{"className":151813},[398],[363,151815],{"className":151816,"style":151381},[402],[363,151818,151820],{"className":151819},[407],[363,151821,151823],{"className":151822},[407],[363,151824,151310],{"className":151825},[407,75905]," 必然奇异，其零空间由 ",[363,151828,151830,151844],{"className":151829,"translate":367},[366],[363,151831,151833],{"className":151832},[371],[373,151834,151835],{"xmlns":375},[377,151836,151837,151841],{},[380,151838,151839],{},[463,151840,465],{"mathvariant":75560},[387,151842,151843],{"encoding":389},"\\mathbf{1}",[363,151845,151847],{"className":151846,"ariaHidden":394},[393],[363,151848,151850,151853],{"className":151849},[398],[363,151851],{"className":151852,"style":520},[402],[363,151854,465],{"className":151855},[407,75905]," 张成——这正是「分布在 ",[363,151858,151860,151881],{"className":151859,"translate":367},[366],[363,151861,151863],{"className":151862},[371],[373,151864,151865],{"xmlns":375},[377,151866,151867,151879],{},[380,151868,151869,151871,151873,151875,151877],{},[458,151870,461],{"stretchy":460},[383,151872,11041],{},[458,151874,5160],{},[463,151876,465],{},[458,151878,468],{"stretchy":460},[387,151880,133690],{"encoding":389},[363,151882,151884,151905],{"className":151883,"ariaHidden":394},[393],[363,151885,151887,151890,151893,151896,151899,151902],{"className":151886},[398],[363,151888],{"className":151889,"style":487},[402],[363,151891,461],{"className":151892},[494],[363,151894,11041],{"className":151895,"style":11129},[407,408],[363,151897],{"className":151898,"style":2934},[505],[363,151900,5160],{"className":151901},[2938],[363,151903],{"className":151904,"style":2934},[505],[363,151906,151908,151911,151914],{"className":151907},[398],[363,151909],{"className":151910,"style":487},[402],[363,151912,465],{"className":151913},[407],[363,151915,468],{"className":151916},[501]," 维对象上」的代数痕迹。第二，全部协方差为负：",[363,151919,151921,151971],{"className":151920,"translate":367},[366],[363,151922,151924],{"className":151923},[371],[373,151925,151926],{"xmlns":375},[377,151927,151928,151968],{},[380,151929,151930,151932,151934,151936,151942,151944,151950,151952,151954,151956,151958,151960,151962,151964,151966],{},[383,151931,147712],{"mathvariant":557},[458,151933,4450],{},[458,151935,461],{"stretchy":460},[543,151937,151938,151940],{},[383,151939,1121],{},[383,151941,12310],{},[458,151943,898],{"separator":394},[543,151945,151946,151948],{},[383,151947,1121],{},[383,151949,100360],{},[458,151951,468],{"stretchy":460},[458,151953,7598],{},[463,151955,474],{},[1644,151957,4630],{},[458,151959,461],{"stretchy":460},[383,151961,12310],{},[458,151963,49854],{"mathvariant":557},[383,151965,100360],{},[458,151967,468],{"stretchy":460},[387,151969,151970],{"encoding":389},"\\operatorname{Cov}(x_i, x_j) \u003C 0\\ (i \\ne j)",[363,151972,151974,152087,152147],{"className":151973,"ariaHidden":394},[393],[363,151975,151977,151980,151986,151989,152029,152032,152035,152075,152078,152081,152084],{"className":151976},[398],[363,151978],{"className":151979,"style":618},[402],[363,151981,151983],{"className":151982},[1831],[363,151984,147712],{"className":151985,"style":4504},[407,33009],[363,151987,461],{"className":151988},[494],[363,151990,151992,151995],{"className":151991},[407],[363,151993,1121],{"className":151994},[407,408],[363,151996,151998],{"className":151997},[629],[363,151999,152001,152021],{"className":152000},[633,634],[363,152002,152004,152018],{"className":152003},[638],[363,152005,152007],{"className":152006,"style":12529},[642],[363,152008,152009,152012],{"style":730},[363,152010],{"className":152011,"style":651},[650],[363,152013,152015],{"className":152014},[655,656,657,658],[363,152016,12310],{"className":152017},[407,408,658],[363,152019,666],{"className":152020},[665],[363,152022,152024],{"className":152023},[638],[363,152025,152027],{"className":152026,"style":8315},[642],[363,152028],{},[363,152030,898],{"className":152031},[920],[363,152033],{"className":152034,"style":754},[505],[363,152036,152038,152041],{"className":152037},[407],[363,152039,1121],{"className":152040},[407,408],[363,152042,152044],{"className":152043},[629],[363,152045,152047,152067],{"className":152046},[633,634],[363,152048,152050,152064],{"className":152049},[638],[363,152051,152053],{"className":152052,"style":12529},[642],[363,152054,152055,152058],{"style":730},[363,152056],{"className":152057,"style":651},[650],[363,152059,152061],{"className":152060},[655,656,657,658],[363,152062,100360],{"className":152063,"style":100888},[407,408,658],[363,152065,666],{"className":152066},[665],[363,152068,152070],{"className":152069},[638],[363,152071,152073],{"className":152072,"style":673},[642],[363,152074],{},[363,152076,468],{"className":152077},[501],[363,152079],{"className":152080,"style":506},[505],[363,152082,7598],{"className":152083},[510],[363,152085],{"className":152086,"style":506},[505],[363,152088,152090,152093,152096,152099,152102,152105,152108,152144],{"className":152089},[398],[363,152091],{"className":152092,"style":487},[402],[363,152094,474],{"className":152095},[407],[363,152097,4630],{"className":152098},[505],[363,152100,461],{"className":152101},[494],[363,152103,12310],{"className":152104},[407,408],[363,152106],{"className":152107,"style":506},[505],[363,152109,152111,152138,152141],{"className":152110},[510],[363,152112,152114],{"className":152113},[510],[363,152115,152117],{"className":152116},[407,4747],[363,152118,152120],{"className":152119},[4751],[363,152121,152123,152126,152135],{"className":152122},[4755],[363,152124],{"className":152125,"style":403},[402],[363,152127,152129],{"className":152128},[4762],[363,152130,152132],{"className":152131},[407],[363,152133,4769],{"className":152134},[510],[363,152136],{"className":152137},[4773],[363,152139],{"className":152140},[505,4777],[363,152142,471],{"className":152143},[510],[363,152145],{"className":152146,"style":506},[505],[363,152148,152150,152153,152156],{"className":152149},[398],[363,152151],{"className":152152,"style":487},[402],[363,152154,100360],{"className":152155,"style":100888},[407,408],[363,152157,468],{"className":152158},[501],"，因为分量之间必须通过和为 ",[363,152161,152163,152176],{"className":152162,"translate":367},[366],[363,152164,152166],{"className":152165},[371],[373,152167,152168],{"xmlns":375},[377,152169,152170,152174],{},[380,152171,152172],{},[463,152173,465],{},[387,152175,465],{"encoding":389},[363,152177,152179],{"className":152178,"ariaHidden":394},[393],[363,152180,152182,152185],{"className":152181},[398],[363,152183],{"className":152184,"style":520},[402],[363,152186,465],{"className":152187},[407]," 的约束相互竞争，任何一个分量的增加都以其他分量的期望减少为代价。",[2658,152190,152192],{"id":152191},"_22-均值精度重参数化","2.2 均值—精度重参数化",[11,152194,152195,152196,2756,152231,152301],{},"命题 2.1 中的 ",[363,152197,152199,152213],{"className":152198,"translate":367},[366],[363,152200,152202],{"className":152201},[371],[373,152203,152204],{"xmlns":375},[377,152205,152206,152210],{},[380,152207,152208],{},[383,152209,2711],{"mathvariant":136008},[387,152211,152212],{"encoding":389},"\\boldsymbol{\\mu}",[363,152214,152216],{"className":152215,"ariaHidden":394},[393],[363,152217,152219,152222],{"className":152218},[398],[363,152220],{"className":152221,"style":133764},[402],[363,152223,152225],{"className":152224},[407],[363,152226,152228],{"className":152227},[407],[363,152229,2711],{"className":152230},[407,136068],[363,152232,152234,152252],{"className":152233,"translate":367},[366],[363,152235,152237],{"className":152236},[371],[373,152238,152239],{"xmlns":375},[377,152240,152241,152249],{},[380,152242,152243],{},[543,152244,152245,152247],{},[383,152246,45101],{},[463,152248,474],{},[387,152250,152251],{"encoding":389},"\\alpha_0",[363,152253,152255],{"className":152254,"ariaHidden":394},[393],[363,152256,152258,152261],{"className":152257},[398],[363,152259],{"className":152260,"style":13721},[402],[363,152262,152264,152267],{"className":152263},[407],[363,152265,45101],{"className":152266,"style":45131},[407,408],[363,152268,152270],{"className":152269},[629],[363,152271,152273,152293],{"className":152272},[633,634],[363,152274,152276,152290],{"className":152275},[638],[363,152277,152279],{"className":152278,"style":11480},[642],[363,152280,152281,152284],{"style":136107},[363,152282],{"className":152283,"style":651},[650],[363,152285,152287],{"className":152286},[655,656,657,658],[363,152288,474],{"className":152289},[407,658],[363,152291,666],{"className":152292},[665],[363,152294,152296],{"className":152295},[638],[363,152297,152299],{"className":152298,"style":8315},[642],[363,152300],{}," 是两个正交的自由度：前者决定「概率质量落在何处」，后者决定「分布在该处聚集得多紧」。据此引入重参数化",[363,152303,152305],{"className":152304,"translate":367},[528],[363,152306,152308,152370],{"className":152307,"translate":367},[366],[363,152309,152311],{"className":152310},[371],[373,152312,152313],{"xmlns":375,"display":537},[377,152314,152315,152367],{},[380,152316,152317,152319,152321,152327,152329,152331,152333,152339,152341,152343,152345,152347,152349,152351,152353,152355],{},[383,152318,45101],{"mathvariant":136008},[458,152320,471],{},[543,152322,152323,152325],{},[383,152324,45101],{},[463,152326,474],{},[383,152328,2711],{"mathvariant":136008},[458,152330,898],{"separator":394},[505,152332],{"width":3609},[543,152334,152335,152337],{},[383,152336,45101],{},[463,152338,474],{},[458,152340,3250],{},[463,152342,474],{},[458,152344,898],{"separator":394},[1644,152346,4630],{},[383,152348,2711],{"mathvariant":136008},[458,152350,6256],{},[383,152352,134464],{"mathvariant":557},[458,152354,4450],{},[7161,152356,152357,152359],{},[383,152358,126023],{"mathvariant":557},[380,152360,152361,152363,152365],{},[383,152362,11041],{},[458,152364,5160],{},[463,152366,465],{},[387,152368,152369],{"encoding":389},"\\boldsymbol{\\alpha} = \\alpha_0 \\boldsymbol{\\mu}, \\qquad \\alpha_0 > 0,\\ \\boldsymbol{\\mu} \\in \\operatorname{int}\\Delta^{K-1}",[363,152371,152373,152397,152510,152546],{"className":152372,"ariaHidden":394},[393],[363,152374,152376,152379,152388,152391,152394],{"className":152375},[398],[363,152377],{"className":152378,"style":135617},[402],[363,152380,152382],{"className":152381},[407],[363,152383,152385],{"className":152384},[407],[363,152386,45101],{"className":152387},[407,136068],[363,152389],{"className":152390,"style":506},[505],[363,152392,471],{"className":152393},[510],[363,152395],{"className":152396,"style":506},[505],[363,152398,152400,152403,152443,152452,152455,152458,152461,152501,152504,152507],{"className":152399},[398],[363,152401],{"className":152402,"style":32039},[402],[363,152404,152406,152409],{"className":152405},[407],[363,152407,45101],{"className":152408,"style":45131},[407,408],[363,152410,152412],{"className":152411},[629],[363,152413,152415,152435],{"className":152414},[633,634],[363,152416,152418,152432],{"className":152417},[638],[363,152419,152421],{"className":152420,"style":11480},[642],[363,152422,152423,152426],{"style":136107},[363,152424],{"className":152425,"style":651},[650],[363,152427,152429],{"className":152428},[655,656,657,658],[363,152430,474],{"className":152431},[407,658],[363,152433,666],{"className":152434},[665],[363,152436,152438],{"className":152437},[638],[363,152439,152441],{"className":152440,"style":8315},[642],[363,152442],{},[363,152444,152446],{"className":152445},[407],[363,152447,152449],{"className":152448},[407],[363,152450,2711],{"className":152451},[407,136068],[363,152453,898],{"className":152454},[920],[363,152456],{"className":152457,"style":3981},[505],[363,152459],{"className":152460,"style":754},[505],[363,152462,152464,152467],{"className":152463},[407],[363,152465,45101],{"className":152466,"style":45131},[407,408],[363,152468,152470],{"className":152469},[629],[363,152471,152473,152493],{"className":152472},[633,634],[363,152474,152476,152490],{"className":152475},[638],[363,152477,152479],{"className":152478,"style":11480},[642],[363,152480,152481,152484],{"style":136107},[363,152482],{"className":152483,"style":651},[650],[363,152485,152487],{"className":152486},[655,656,657,658],[363,152488,474],{"className":152489},[407,658],[363,152491,666],{"className":152492},[665],[363,152494,152496],{"className":152495},[638],[363,152497,152499],{"className":152498,"style":8315},[642],[363,152500],{},[363,152502],{"className":152503,"style":506},[505],[363,152505,3250],{"className":152506},[510],[363,152508],{"className":152509,"style":506},[505],[363,152511,152513,152516,152519,152522,152525,152528,152537,152540,152543],{"className":152512},[398],[363,152514],{"className":152515,"style":9705},[402],[363,152517,474],{"className":152518},[407],[363,152520,898],{"className":152521},[920],[363,152523,4630],{"className":152524},[505],[363,152526],{"className":152527,"style":754},[505],[363,152529,152531],{"className":152530},[407],[363,152532,152534],{"className":152533},[407],[363,152535,2711],{"className":152536},[407,136068],[363,152538],{"className":152539,"style":506},[505],[363,152541,6256],{"className":152542},[510],[363,152544],{"className":152545,"style":506},[505],[363,152547,152549,152552,152558,152561],{"className":152548},[398],[363,152550],{"className":152551,"style":38859},[402],[363,152553,152555],{"className":152554},[1831],[363,152556,134464],{"className":152557},[407,33009],[363,152559],{"className":152560,"style":754},[505],[363,152562,152564,152567],{"className":152563},[407],[363,152565,126023],{"className":152566},[407],[363,152568,152570],{"className":152569},[629],[363,152571,152573],{"className":152572},[633],[363,152574,152576],{"className":152575},[638],[363,152577,152579],{"className":152578,"style":38859},[642],[363,152580,152581,152584],{"style":8624},[363,152582],{"className":152583,"style":651},[650],[363,152585,152587],{"className":152586},[655,656,657,658],[363,152588,152590,152593,152596],{"className":152589},[407,658],[363,152591,11041],{"className":152592,"style":11129},[407,408,658],[363,152594,5160],{"className":152595},[2938,658],[363,152597,465],{"className":152598},[407,658],[11,152600,152601,152602,16142,152605,152655,152656,152659,152660,3092,152943,153051,153052,153121],{},"它把参数空间分解为一个",[1572,152603,152604],{},"方向",[363,152606,152608,152625],{"className":152607,"translate":367},[366],[363,152609,152611],{"className":152610},[371],[373,152612,152613],{"xmlns":375},[377,152614,152615,152623],{},[380,152616,152617,152619,152621],{},[383,152618,11041],{},[458,152620,5160],{},[463,152622,465],{},[387,152624,133889],{"encoding":389},[363,152626,152628,152646],{"className":152627,"ariaHidden":394},[393],[363,152629,152631,152634,152637,152640,152643],{"className":152630},[398],[363,152632],{"className":152633,"style":133899},[402],[363,152635,11041],{"className":152636,"style":11129},[407,408],[363,152638],{"className":152639,"style":2934},[505],[363,152641,5160],{"className":152642},[2938],[363,152644],{"className":152645,"style":2934},[505],[363,152647,152649,152652],{"className":152648},[398],[363,152650],{"className":152651,"style":520},[402],[363,152653,465],{"className":152654},[407]," 维单纯形）与一个",[1572,152657,152658],{},"尺度","（正实数）。在此参数化下，协方差为 ",[363,152661,152663,152715],{"className":152662,"translate":367},[366],[363,152664,152666],{"className":152665},[371],[373,152667,152668],{"xmlns":375},[377,152669,152670,152712],{},[380,152671,152672,152674,152676,152692,152694,152696,152698,152700,152702,152704,152710],{},[383,152673,151310],{"mathvariant":75560},[458,152675,471],{},[586,152677,152678,152680],{},[463,152679,465],{},[380,152681,152682,152688,152690],{},[543,152683,152684,152686],{},[383,152685,45101],{},[463,152687,474],{},[458,152689,2817],{},[463,152691,465],{},[458,152693,461],{"stretchy":460},[383,152695,151347],{"mathvariant":557},[458,152697,4450],{},[383,152699,2711],{"mathvariant":136008},[458,152701,5160],{},[383,152703,2711],{"mathvariant":136008},[7161,152705,152706,152708],{},[383,152707,2711],{"mathvariant":136008},[383,152709,151366],{"mathvariant":557},[458,152711,468],{"stretchy":460},[387,152713,152714],{"encoding":389},"\\boldsymbol{\\Sigma} = \\frac{1}{\\alpha_0+1}(\\operatorname{diag}\\boldsymbol{\\mu} - \\boldsymbol{\\mu}\\boldsymbol{\\mu}^\\top)",[363,152716,152718,152742,152889],{"className":152717,"ariaHidden":394},[393],[363,152719,152721,152724,152733,152736,152739],{"className":152720},[398],[363,152722],{"className":152723,"style":151381},[402],[363,152725,152727],{"className":152726},[407],[363,152728,152730],{"className":152729},[407],[363,152731,151310],{"className":152732},[407,75905],[363,152734],{"className":152735,"style":506},[505],[363,152737,471],{"className":152738},[510],[363,152740],{"className":152741,"style":506},[505],[363,152743,152745,152748,152859,152862,152868,152871,152880,152883,152886],{"className":152744},[398],[363,152746],{"className":152747,"style":149348},[402],[363,152749,152751,152754,152856],{"className":152750},[407],[363,152752],{"className":152753},[494,789],[363,152755,152757],{"className":152756},[586],[363,152758,152760,152848],{"className":152759},[633,634],[363,152761,152763,152845],{"className":152762},[638],[363,152764,152766,152823,152831],{"className":152765,"style":2871},[642],[363,152767,152768,152771],{"style":2874},[363,152769],{"className":152770,"style":809},[650],[363,152772,152774],{"className":152773},[655,656,657,658],[363,152775,152777,152817,152820],{"className":152776},[407,658],[363,152778,152780,152783],{"className":152779},[407,658],[363,152781,45101],{"className":152782,"style":45131},[407,408,658],[363,152784,152786],{"className":152785},[629],[363,152787,152789,152809],{"className":152788},[633,634],[363,152790,152792,152806],{"className":152791},[638],[363,152793,152795],{"className":152794,"style":137304},[642],[363,152796,152797,152800],{"style":136942},[363,152798],{"className":152799,"style":30553},[650],[363,152801,152803],{"className":152802},[655,30557,10021,658],[363,152804,474],{"className":152805},[407,658],[363,152807,666],{"className":152808},[665],[363,152810,152812],{"className":152811},[638],[363,152813,152815],{"className":152814,"style":40117},[642],[363,152816],{},[363,152818,2817],{"className":152819},[2938,658],[363,152821,465],{"className":152822},[407,658],[363,152824,152825,152828],{"style":821},[363,152826],{"className":152827,"style":809},[650],[363,152829],{"className":152830,"style":829},[828],[363,152832,152833,152836],{"style":2897},[363,152834],{"className":152835,"style":809},[650],[363,152837,152839],{"className":152838},[655,656,657,658],[363,152840,152842],{"className":152841},[407,658],[363,152843,465],{"className":152844},[407,658],[363,152846,666],{"className":152847},[665],[363,152849,152851],{"className":152850},[638],[363,152852,152854],{"className":152853,"style":40264},[642],[363,152855],{},[363,152857],{"className":152858},[501,789],[363,152860,461],{"className":152861},[494],[363,152863,152865],{"className":152864},[1831],[363,152866,151347],{"className":152867,"style":4504},[407,33009],[363,152869],{"className":152870,"style":754},[505],[363,152872,152874],{"className":152873},[407],[363,152875,152877],{"className":152876},[407],[363,152878,2711],{"className":152879},[407,136068],[363,152881],{"className":152882,"style":2934},[505],[363,152884,5160],{"className":152885},[2938],[363,152887],{"className":152888,"style":2934},[505],[363,152890,152892,152896,152905,152940],{"className":152891},[398],[363,152893],{"className":152894,"style":152895},[402],"height:1.0991em;vertical-align:-0.25em;",[363,152897,152899],{"className":152898},[407],[363,152900,152902],{"className":152901},[407],[363,152903,2711],{"className":152904},[407,136068],[363,152906,152908,152917],{"className":152907},[407],[363,152909,152911],{"className":152910},[407],[363,152912,152914],{"className":152913},[407],[363,152915,2711],{"className":152916},[407,136068],[363,152918,152920],{"className":152919},[629],[363,152921,152923],{"className":152922},[633],[363,152924,152926],{"className":152925},[638],[363,152927,152929],{"className":152928,"style":47901},[642],[363,152930,152931,152934],{"style":7212},[363,152932],{"className":152933,"style":651},[650],[363,152935,152937],{"className":152936},[655,656,657,658],[363,152938,151366],{"className":152939},[407,658],[363,152941,468],{"className":152942},[501],[1572,152944,152945,152946,152980,152981,153050],{},"与 ",[363,152947,152949,152962],{"className":152948,"translate":367},[366],[363,152950,152952],{"className":152951},[371],[373,152953,152954],{"xmlns":375},[377,152955,152956,152960],{},[380,152957,152958],{},[383,152959,2711],{"mathvariant":136008},[387,152961,152212],{"encoding":389},[363,152963,152965],{"className":152964,"ariaHidden":394},[393],[363,152966,152968,152971],{"className":152967},[398],[363,152969],{"className":152970,"style":133764},[402],[363,152972,152974],{"className":152973},[407],[363,152975,152977],{"className":152976},[407],[363,152978,2711],{"className":152979},[407,136068]," 的取值无关、只随 ",[363,152982,152984,153001],{"className":152983,"translate":367},[366],[363,152985,152987],{"className":152986},[371],[373,152988,152989],{"xmlns":375},[377,152990,152991,152999],{},[380,152992,152993],{},[543,152994,152995,152997],{},[383,152996,45101],{},[463,152998,474],{},[387,153000,152251],{"encoding":389},[363,153002,153004],{"className":153003,"ariaHidden":394},[393],[363,153005,153007,153010],{"className":153006},[398],[363,153008],{"className":153009,"style":13721},[402],[363,153011,153013,153016],{"className":153012},[407],[363,153014,45101],{"className":153015,"style":45131},[407,408],[363,153017,153019],{"className":153018},[629],[363,153020,153022,153042],{"className":153021},[633,634],[363,153023,153025,153039],{"className":153024},[638],[363,153026,153028],{"className":153027,"style":11480},[642],[363,153029,153030,153033],{"style":136107},[363,153031],{"className":153032,"style":651},[650],[363,153034,153036],{"className":153035},[655,656,657,658],[363,153037,474],{"className":153038},[407,658],[363,153040,666],{"className":153041},[665],[363,153043,153045],{"className":153044},[638],[363,153046,153048],{"className":153047,"style":8315},[642],[363,153049],{}," 单调收缩","。因此 ",[363,153053,153055,153072],{"className":153054,"translate":367},[366],[363,153056,153058],{"className":153057},[371],[373,153059,153060],{"xmlns":375},[377,153061,153062,153070],{},[380,153063,153064],{},[543,153065,153066,153068],{},[383,153067,45101],{},[463,153069,474],{},[387,153071,152251],{"encoding":389},[363,153073,153075],{"className":153074,"ariaHidden":394},[393],[363,153076,153078,153081],{"className":153077},[398],[363,153079],{"className":153080,"style":13721},[402],[363,153082,153084,153087],{"className":153083},[407],[363,153085,45101],{"className":153086,"style":45131},[407,408],[363,153088,153090],{"className":153089},[629],[363,153091,153093,153113],{"className":153092},[633,634],[363,153094,153096,153110],{"className":153095},[638],[363,153097,153099],{"className":153098,"style":11480},[642],[363,153100,153101,153104],{"style":136107},[363,153102],{"className":153103,"style":651},[650],[363,153105,153107],{"className":153106},[655,656,657,658],[363,153108,474],{"className":153109},[407,658],[363,153111,666],{"className":153112},[665],[363,153114,153116],{"className":153115},[638],[363,153117,153119],{"className":153118,"style":8315},[642],[363,153120],{}," 是一个纯粹的集中度（或称精度、强度）参数：",[1340,153123,153125],{"title":153124},"命题 2.2（集中性极限）",[11,153126,153127,153128,21303,153243,153438,153439,10649,153531,153632,153633,153667,153668,10527],{},"固定 ",[363,153129,153131,153163],{"className":153130,"translate":367},[366],[363,153132,153134],{"className":153133},[371],[373,153135,153136],{"xmlns":375},[377,153137,153138,153160],{},[380,153139,153140,153142,153144,153146,153148],{},[383,153141,2711],{"mathvariant":136008},[458,153143,6256],{},[383,153145,134464],{"mathvariant":557},[458,153147,4450],{},[7161,153149,153150,153152],{},[383,153151,126023],{"mathvariant":557},[380,153153,153154,153156,153158],{},[383,153155,11041],{},[458,153157,5160],{},[463,153159,465],{},[387,153161,153162],{"encoding":389},"\\boldsymbol{\\mu} \\in \\operatorname{int}\\Delta^{K-1}",[363,153164,153166,153190],{"className":153165,"ariaHidden":394},[393],[363,153167,153169,153172,153181,153184,153187],{"className":153168},[398],[363,153170],{"className":153171,"style":32039},[402],[363,153173,153175],{"className":153174},[407],[363,153176,153178],{"className":153177},[407],[363,153179,2711],{"className":153180},[407,136068],[363,153182],{"className":153183,"style":506},[505],[363,153185,6256],{"className":153186},[510],[363,153188],{"className":153189,"style":506},[505],[363,153191,153193,153196,153202,153205],{"className":153192},[398],[363,153194],{"className":153195,"style":52432},[402],[363,153197,153199],{"className":153198},[1831],[363,153200,134464],{"className":153201},[407,33009],[363,153203],{"className":153204,"style":754},[505],[363,153206,153208,153211],{"className":153207},[407],[363,153209,126023],{"className":153210},[407],[363,153212,153214],{"className":153213},[629],[363,153215,153217],{"className":153216},[633],[363,153218,153220],{"className":153219},[638],[363,153221,153223],{"className":153222,"style":52432},[642],[363,153224,153225,153228],{"style":7212},[363,153226],{"className":153227,"style":651},[650],[363,153229,153231],{"className":153230},[655,656,657,658],[363,153232,153234,153237,153240],{"className":153233},[407,658],[363,153235,11041],{"className":153236,"style":11129},[407,408,658],[363,153238,5160],{"className":153239},[2938,658],[363,153241,465],{"className":153242},[407,658],[363,153244,153246,153284],{"className":153245,"translate":367},[366],[363,153247,153249],{"className":153248},[371],[373,153250,153251],{"xmlns":375},[377,153252,153253,153281],{},[380,153254,153255,153271,153273,153279],{},[7161,153256,153257,153259],{},[383,153258,45101],{"mathvariant":136008},[380,153260,153261,153263,153269],{},[458,153262,461],{"stretchy":460},[543,153264,153265,153267],{},[383,153266,45101],{},[463,153268,474],{},[458,153270,468],{"stretchy":460},[458,153272,471],{},[543,153274,153275,153277],{},[383,153276,45101],{},[463,153278,474],{},[383,153280,2711],{"mathvariant":136008},[387,153282,153283],{"encoding":389},"\\boldsymbol{\\alpha}^{(\\alpha_0)} = \\alpha_0 \\boldsymbol{\\mu}",[363,153285,153287,153383],{"className":153286,"ariaHidden":394},[393],[363,153288,153290,153293,153374,153377,153380],{"className":153289},[398],[363,153291],{"className":153292,"style":55128},[402],[363,153294,153296,153305],{"className":153295},[407],[363,153297,153299],{"className":153298},[407],[363,153300,153302],{"className":153301},[407],[363,153303,45101],{"className":153304},[407,136068],[363,153306,153308],{"className":153307},[629],[363,153309,153311],{"className":153310},[633],[363,153312,153314],{"className":153313},[638],[363,153315,153317],{"className":153316,"style":55128},[642],[363,153318,153319,153322],{"style":7212},[363,153320],{"className":153321,"style":651},[650],[363,153323,153325],{"className":153324},[655,656,657,658],[363,153326,153328,153331,153371],{"className":153327},[407,658],[363,153329,461],{"className":153330},[494,658],[363,153332,153334,153337],{"className":153333},[407,658],[363,153335,45101],{"className":153336,"style":45131},[407,408,658],[363,153338,153340],{"className":153339},[629],[363,153341,153343,153363],{"className":153342},[633,634],[363,153344,153346,153360],{"className":153345},[638],[363,153347,153349],{"className":153348,"style":137304},[642],[363,153350,153351,153354],{"style":136942},[363,153352],{"className":153353,"style":30553},[650],[363,153355,153357],{"className":153356},[655,30557,10021,658],[363,153358,474],{"className":153359},[407,658],[363,153361,666],{"className":153362},[665],[363,153364,153366],{"className":153365},[638],[363,153367,153369],{"className":153368,"style":40117},[642],[363,153370],{},[363,153372,468],{"className":153373},[501,658],[363,153375],{"className":153376,"style":506},[505],[363,153378,471],{"className":153379},[510],[363,153381],{"className":153382,"style":506},[505],[363,153384,153386,153389,153429],{"className":153385},[398],[363,153387],{"className":153388,"style":133764},[402],[363,153390,153392,153395],{"className":153391},[407],[363,153393,45101],{"className":153394,"style":45131},[407,408],[363,153396,153398],{"className":153397},[629],[363,153399,153401,153421],{"className":153400},[633,634],[363,153402,153404,153418],{"className":153403},[638],[363,153405,153407],{"className":153406,"style":11480},[642],[363,153408,153409,153412],{"style":136107},[363,153410],{"className":153411,"style":651},[650],[363,153413,153415],{"className":153414},[655,656,657,658],[363,153416,474],{"className":153417},[407,658],[363,153419,666],{"className":153420},[665],[363,153422,153424],{"className":153423},[638],[363,153425,153427],{"className":153426,"style":8315},[642],[363,153428],{},[363,153430,153432],{"className":153431},[407],[363,153433,153435],{"className":153434},[407],[363,153436,2711],{"className":153437},[407,136068],"。则当 ",[363,153440,153442,153464],{"className":153441,"translate":367},[366],[363,153443,153445],{"className":153444},[371],[373,153446,153447],{"xmlns":375},[377,153448,153449,153461],{},[380,153450,153451,153457,153459],{},[543,153452,153453,153455],{},[383,153454,45101],{},[463,153456,474],{},[458,153458,1376],{},[383,153460,1371],{"mathvariant":557},[387,153462,153463],{"encoding":389},"\\alpha_0 \\to \\infty",[363,153465,153467,153522],{"className":153466,"ariaHidden":394},[393],[363,153468,153470,153473,153513,153516,153519],{"className":153469},[398],[363,153471],{"className":153472,"style":13721},[402],[363,153474,153476,153479],{"className":153475},[407],[363,153477,45101],{"className":153478,"style":45131},[407,408],[363,153480,153482],{"className":153481},[629],[363,153483,153485,153505],{"className":153484},[633,634],[363,153486,153488,153502],{"className":153487},[638],[363,153489,153491],{"className":153490,"style":11480},[642],[363,153492,153493,153496],{"style":136107},[363,153494],{"className":153495,"style":651},[650],[363,153497,153499],{"className":153498},[655,656,657,658],[363,153500,474],{"className":153501},[407,658],[363,153503,666],{"className":153504},[665],[363,153506,153508],{"className":153507},[638],[363,153509,153511],{"className":153510,"style":8315},[642],[363,153512],{},[363,153514],{"className":153515,"style":506},[505],[363,153517,1376],{"className":153518},[510],[363,153520],{"className":153521,"style":506},[505],[363,153523,153525,153528],{"className":153524},[398],[363,153526],{"className":153527,"style":2692},[402],[363,153529,1371],{"className":153530},[407],[363,153532,153534,153562],{"className":153533,"translate":367},[366],[363,153535,153537],{"className":153536},[371],[373,153538,153539],{"xmlns":375},[377,153540,153541,153559],{},[380,153542,153543,153545,153547,153549,153555,153557],{},[383,153544,137065],{"mathvariant":557},[458,153546,4450],{},[458,153548,461],{"stretchy":460},[543,153550,153551,153553],{},[383,153552,45101],{},[463,153554,474],{},[383,153556,2711],{"mathvariant":136008},[458,153558,468],{"stretchy":460},[387,153560,153561],{"encoding":389},"\\operatorname{Dir}(\\alpha_0 \\boldsymbol{\\mu})",[363,153563,153565],{"className":153564,"ariaHidden":394},[393],[363,153566,153568,153571,153577,153580,153620,153629],{"className":153567},[398],[363,153569],{"className":153570,"style":487},[402],[363,153572,153574],{"className":153573},[1831],[363,153575,137065],{"className":153576},[407,33009],[363,153578,461],{"className":153579},[494],[363,153581,153583,153586],{"className":153582},[407],[363,153584,45101],{"className":153585,"style":45131},[407,408],[363,153587,153589],{"className":153588},[629],[363,153590,153592,153612],{"className":153591},[633,634],[363,153593,153595,153609],{"className":153594},[638],[363,153596,153598],{"className":153597,"style":11480},[642],[363,153599,153600,153603],{"style":136107},[363,153601],{"className":153602,"style":651},[650],[363,153604,153606],{"className":153605},[655,656,657,658],[363,153607,474],{"className":153608},[407,658],[363,153610,666],{"className":153611},[665],[363,153613,153615],{"className":153614},[638],[363,153616,153618],{"className":153617,"style":8315},[642],[363,153619],{},[363,153621,153623],{"className":153622},[407],[363,153624,153626],{"className":153625},[407],[363,153627,2711],{"className":153628},[407,136068],[363,153630,468],{"className":153631},[501]," 弱收敛于位于 ",[363,153634,153636,153649],{"className":153635,"translate":367},[366],[363,153637,153639],{"className":153638},[371],[373,153640,153641],{"xmlns":375},[377,153642,153643,153647],{},[380,153644,153645],{},[383,153646,2711],{"mathvariant":136008},[387,153648,152212],{"encoding":389},[363,153650,153652],{"className":153651,"ariaHidden":394},[393],[363,153653,153655,153658],{"className":153654},[398],[363,153656],{"className":153657,"style":133764},[402],[363,153659,153661],{"className":153660},[407],[363,153662,153664],{"className":153663},[407],[363,153665,2711],{"className":153666},[407,136068]," 的退化测度 ",[363,153669,153671,153689],{"className":153670,"translate":367},[366],[363,153672,153674],{"className":153673},[371],[373,153675,153676],{"xmlns":375},[377,153677,153678,153686],{},[380,153679,153680],{},[543,153681,153682,153684],{},[383,153683,16059],{},[383,153685,2711],{"mathvariant":136008},[387,153687,153688],{"encoding":389},"\\delta_{\\boldsymbol{\\mu}}",[363,153690,153692],{"className":153691,"ariaHidden":394},[393],[363,153693,153695,153699],{"className":153694},[398],[363,153696],{"className":153697,"style":153698},[402],"height:0.9805em;vertical-align:-0.2861em;",[363,153700,153702,153705],{"className":153701},[407],[363,153703,16059],{"className":153704,"style":16108},[407,408],[363,153706,153708],{"className":153707},[629],[363,153709,153711,153741],{"className":153710},[633,634],[363,153712,153714,153738],{"className":153713},[638],[363,153715,153718],{"className":153716,"style":153717},[642],"height:0.1611em;",[363,153719,153720,153723],{"style":95090},[363,153721],{"className":153722,"style":651},[650],[363,153724,153726],{"className":153725},[655,656,657,658],[363,153727,153729],{"className":153728},[407,658],[363,153730,153732],{"className":153731},[407,658],[363,153733,153735],{"className":153734},[407,658],[363,153736,2711],{"className":153737},[407,136068,658],[363,153739,666],{"className":153740},[665],[363,153742,153744],{"className":153743},[638],[363,153745,153747],{"className":153746,"style":673},[642],[363,153748],{},[11,153750,153751,153753,153754,7147,153826,153968,153969,154020,154021,154228,154229,10527],{},[1572,153752,137993],{}," 由命题 2.1，",[363,153755,153757,153781],{"className":153756,"translate":367},[366],[363,153758,153760],{"className":153759},[371],[373,153761,153762],{"xmlns":375},[377,153763,153764,153778],{},[380,153765,153766,153768,153770,153772,153774,153776],{},[383,153767,571],{"mathvariant":570},[458,153769,578],{"stretchy":460},[383,153771,1121],{"mathvariant":75560},[458,153773,605],{"stretchy":460},[458,153775,471],{},[383,153777,2711],{"mathvariant":136008},[387,153779,153780],{"encoding":389},"\\mathbb{E}[\\mathbf{x}] = \\boldsymbol{\\mu}",[363,153782,153784,153811],{"className":153783,"ariaHidden":394},[393],[363,153785,153787,153790,153793,153796,153799,153802,153805,153808],{"className":153786},[398],[363,153788],{"className":153789,"style":487},[402],[363,153791,571],{"className":153792},[407,714],[363,153794,578],{"className":153795},[494],[363,153797,1121],{"className":153798},[407,75905],[363,153800,605],{"className":153801},[501],[363,153803],{"className":153804,"style":506},[505],[363,153806,471],{"className":153807},[510],[363,153809],{"className":153810,"style":506},[505],[363,153812,153814,153817],{"className":153813},[398],[363,153815],{"className":153816,"style":133764},[402],[363,153818,153820],{"className":153819},[407],[363,153821,153823],{"className":153822},[407],[363,153824,2711],{"className":153825},[407,136068],[363,153827,153829,153865],{"className":153828,"translate":367},[366],[363,153830,153832],{"className":153831},[371],[373,153833,153834],{"xmlns":375},[377,153835,153836,153862],{},[380,153837,153838,153840,153842,153844,153846,153848,153850,153856,153858,153860],{},[383,153839,151310],{"mathvariant":75560},[458,153841,471],{},[383,153843,19568],{},[458,153845,461],{"stretchy":460},[463,153847,465],{},[383,153849,1288],{"mathvariant":557},[543,153851,153852,153854],{},[383,153853,45101],{},[463,153855,474],{},[458,153857,468],{"stretchy":460},[458,153859,1376],{},[463,153861,474],{"mathvariant":75560},[387,153863,153864],{"encoding":389},"\\boldsymbol{\\Sigma} = O(1\u002F\\alpha_0) \\to \\mathbf{0}",[363,153866,153868,153892,153959],{"className":153867,"ariaHidden":394},[393],[363,153869,153871,153874,153883,153886,153889],{"className":153870},[398],[363,153872],{"className":153873,"style":151381},[402],[363,153875,153877],{"className":153876},[407],[363,153878,153880],{"className":153879},[407],[363,153881,151310],{"className":153882},[407,75905],[363,153884],{"className":153885,"style":506},[505],[363,153887,471],{"className":153888},[510],[363,153890],{"className":153891,"style":506},[505],[363,153893,153895,153898,153901,153904,153907,153947,153950,153953,153956],{"className":153894},[398],[363,153896],{"className":153897,"style":487},[402],[363,153899,19568],{"className":153900,"style":625},[407,408],[363,153902,461],{"className":153903},[494],[363,153905,8936],{"className":153906},[407],[363,153908,153910,153913],{"className":153909},[407],[363,153911,45101],{"className":153912,"style":45131},[407,408],[363,153914,153916],{"className":153915},[629],[363,153917,153919,153939],{"className":153918},[633,634],[363,153920,153922,153936],{"className":153921},[638],[363,153923,153925],{"className":153924,"style":11480},[642],[363,153926,153927,153930],{"style":136107},[363,153928],{"className":153929,"style":651},[650],[363,153931,153933],{"className":153932},[655,656,657,658],[363,153934,474],{"className":153935},[407,658],[363,153937,666],{"className":153938},[665],[363,153940,153942],{"className":153941},[638],[363,153943,153945],{"className":153944,"style":8315},[642],[363,153946],{},[363,153948,468],{"className":153949},[501],[363,153951],{"className":153952,"style":506},[505],[363,153954,1376],{"className":153955},[510],[363,153957],{"className":153958,"style":506},[505],[363,153960,153962,153965],{"className":153961},[398],[363,153963],{"className":153964,"style":520},[402],[363,153966,474],{"className":153967},[407,75905],"。对任意 ",[363,153970,153972,153990],{"className":153971,"translate":367},[366],[363,153973,153975],{"className":153974},[371],[373,153976,153977],{"xmlns":375},[377,153978,153979,153987],{},[380,153980,153981,153983,153985],{},[383,153982,39009],{},[458,153984,3250],{},[463,153986,474],{},[387,153988,153989],{"encoding":389},"\\varepsilon > 0",[363,153991,153993,154011],{"className":153992,"ariaHidden":394},[393],[363,153994,153996,153999,154002,154005,154008],{"className":153995},[398],[363,153997],{"className":153998,"style":6271},[402],[363,154000,39009],{"className":154001},[407,408],[363,154003],{"className":154004,"style":506},[505],[363,154006,3250],{"className":154007},[510],[363,154009],{"className":154010,"style":506},[505],[363,154012,154014,154017],{"className":154013},[398],[363,154015],{"className":154016,"style":520},[402],[363,154018,474],{"className":154019},[407],"，由 Chebyshev 不等式 ",[363,154022,154024,154076],{"className":154023,"translate":367},[366],[363,154025,154027],{"className":154026},[371],[373,154028,154029],{"xmlns":375},[377,154030,154031,154073],{},[380,154032,154033,154035,154037,154039,154041,154043,154045,154047,154049,154051,154053,154055,154057,154059,154061,154063,154069,154071],{},[383,154034,554],{"mathvariant":570},[458,154036,461],{"stretchy":460},[383,154038,558],{"mathvariant":557},[383,154040,1121],{"mathvariant":75560},[458,154042,5160],{},[383,154044,2711],{"mathvariant":136008},[383,154046,558],{"mathvariant":557},[458,154048,3250],{},[383,154050,39009],{},[458,154052,468],{"stretchy":460},[458,154054,10299],{},[383,154056,52845],{"mathvariant":557},[458,154058,4450],{},[383,154060,151310],{"mathvariant":75560},[383,154062,1288],{"mathvariant":557},[7161,154064,154065,154067],{},[383,154066,39009],{},[463,154068,2810],{},[458,154070,1376],{},[463,154072,474],{},[387,154074,154075],{"encoding":389},"\\mathbb{P}(\\|\\mathbf{x} - \\boldsymbol{\\mu}\\| > \\varepsilon) \\le \\operatorname{tr}\\boldsymbol{\\Sigma}\u002F\\varepsilon^2 \\to 0",[363,154077,154079,154106,154133,154154,154219],{"className":154078,"ariaHidden":394},[393],[363,154080,154082,154085,154088,154091,154094,154097,154100,154103],{"className":154081},[398],[363,154083],{"className":154084,"style":487},[402],[363,154086,554],{"className":154087},[407,714],[363,154089,461],{"className":154090},[494],[363,154092,558],{"className":154093},[407],[363,154095,1121],{"className":154096},[407,75905],[363,154098],{"className":154099,"style":2934},[505],[363,154101,5160],{"className":154102},[2938],[363,154104],{"className":154105,"style":2934},[505],[363,154107,154109,154112,154121,154124,154127,154130],{"className":154108},[398],[363,154110],{"className":154111,"style":487},[402],[363,154113,154115],{"className":154114},[407],[363,154116,154118],{"className":154117},[407],[363,154119,2711],{"className":154120},[407,136068],[363,154122,558],{"className":154123},[407],[363,154125],{"className":154126,"style":506},[505],[363,154128,3250],{"className":154129},[510],[363,154131],{"className":154132,"style":506},[505],[363,154134,154136,154139,154142,154145,154148,154151],{"className":154135},[398],[363,154137],{"className":154138,"style":487},[402],[363,154140,39009],{"className":154141},[407,408],[363,154143,468],{"className":154144},[501],[363,154146],{"className":154147,"style":506},[505],[363,154149,10299],{"className":154150},[510],[363,154152],{"className":154153,"style":506},[505],[363,154155,154157,154160,154166,154169,154178,154181,154210,154213,154216],{"className":154156},[398],[363,154158],{"className":154159,"style":20350},[402],[363,154161,154163],{"className":154162},[1831],[363,154164,52845],{"className":154165},[407,33009],[363,154167],{"className":154168,"style":754},[505],[363,154170,154172],{"className":154171},[407],[363,154173,154175],{"className":154174},[407],[363,154176,151310],{"className":154177},[407,75905],[363,154179,1288],{"className":154180},[407],[363,154182,154184,154187],{"className":154183},[407],[363,154185,39009],{"className":154186},[407,408],[363,154188,154190],{"className":154189},[629],[363,154191,154193],{"className":154192},[633],[363,154194,154196],{"className":154195},[638],[363,154197,154199],{"className":154198,"style":20375},[642],[363,154200,154201,154204],{"style":7212},[363,154202],{"className":154203,"style":651},[650],[363,154205,154207],{"className":154206},[655,656,657,658],[363,154208,2810],{"className":154209},[407,658],[363,154211],{"className":154212,"style":506},[505],[363,154214,1376],{"className":154215},[510],[363,154217],{"className":154218,"style":506},[505],[363,154220,154222,154225],{"className":154221},[398],[363,154223],{"className":154224,"style":520},[402],[363,154226,474],{"className":154227},[407],"，故依概率收敛，进而弱收敛于 ",[363,154230,154232,154250],{"className":154231,"translate":367},[366],[363,154233,154235],{"className":154234},[371],[373,154236,154237],{"xmlns":375},[377,154238,154239,154247],{},[380,154240,154241],{},[543,154242,154243,154245],{},[383,154244,16059],{},[383,154246,2711],{"mathvariant":136008},[387,154248,154249],{"encoding":389},"\\delta_{\\boldsymbol\\mu}",[363,154251,154253],{"className":154252,"ariaHidden":394},[393],[363,154254,154256,154259],{"className":154255},[398],[363,154257],{"className":154258,"style":153698},[402],[363,154260,154262,154265],{"className":154261},[407],[363,154263,16059],{"className":154264,"style":16108},[407,408],[363,154266,154268],{"className":154267},[629],[363,154269,154271,154300],{"className":154270},[633,634],[363,154272,154274,154297],{"className":154273},[638],[363,154275,154277],{"className":154276,"style":153717},[642],[363,154278,154279,154282],{"style":95090},[363,154280],{"className":154281,"style":651},[650],[363,154283,154285],{"className":154284},[655,656,657,658],[363,154286,154288],{"className":154287},[407,658],[363,154289,154291],{"className":154290},[407,658],[363,154292,154294],{"className":154293},[407,658],[363,154295,2711],{"className":154296},[407,136068,658],[363,154298,666],{"className":154299},[665],[363,154301,154303],{"className":154302},[638],[363,154304,154306],{"className":154305,"style":673},[642],[363,154307],{},[11,154309,154310,154311,154427],{},"这一命题给出了本文后续所有「不确定性」语汇的几何基础：",[1572,154312,154313,154314,154391,154392,154426],{},"迪利克雷分布的「模糊程度」等于 ",[363,154315,154317,154339],{"className":154316,"translate":367},[366],[363,154318,154320],{"className":154319},[371],[373,154321,154322],{"xmlns":375},[377,154323,154324,154336],{},[380,154325,154326,154328,154330],{},[463,154327,465],{},[383,154329,1288],{"mathvariant":557},[543,154331,154332,154334],{},[383,154333,45101],{},[463,154335,474],{},[387,154337,154338],{"encoding":389},"1\u002F\\alpha_0",[363,154340,154342],{"className":154341,"ariaHidden":394},[393],[363,154343,154345,154348,154351],{"className":154344},[398],[363,154346],{"className":154347,"style":487},[402],[363,154349,8936],{"className":154350},[407],[363,154352,154354,154357],{"className":154353},[407],[363,154355,45101],{"className":154356,"style":45131},[407,408],[363,154358,154360],{"className":154359},[629],[363,154361,154363,154383],{"className":154362},[633,634],[363,154364,154366,154380],{"className":154365},[638],[363,154367,154369],{"className":154368,"style":11480},[642],[363,154370,154371,154374],{"style":136107},[363,154372],{"className":154373,"style":651},[650],[363,154375,154377],{"className":154376},[655,656,657,658],[363,154378,474],{"className":154379},[407,658],[363,154381,666],{"className":154382},[665],[363,154384,154386],{"className":154385},[638],[363,154387,154389],{"className":154388,"style":8315},[642],[363,154390],{}," 的量级，而它的「中心」由 ",[363,154393,154395,154408],{"className":154394,"translate":367},[366],[363,154396,154398],{"className":154397},[371],[373,154399,154400],{"xmlns":375},[377,154401,154402,154406],{},[380,154403,154404],{},[383,154405,2711],{"mathvariant":136008},[387,154407,152212],{"encoding":389},[363,154409,154411],{"className":154410,"ariaHidden":394},[393],[363,154412,154414,154417],{"className":154413},[398],[363,154415],{"className":154416,"style":133764},[402],[363,154418,154420],{"className":154419},[407],[363,154421,154423],{"className":154422},[407],[363,154424,2711],{"className":154425},[407,136068]," 给出。"," 两者在同一族分布中被参数化为彼此独立的量——这正是证据深度学习能够把「预测什么」与「有多确定」分离开来的数学根据。",[2658,154429,154431],{"id":154430},"_23-众数与熵","2.3 众数与熵",[1340,154433,154435],{"title":154434},"命题 2.3（众数）",[11,154436,56490,154437,154529,154530,11283,154559,4200,154631,154704,154705],{},[363,154438,154440,154462],{"className":154439,"translate":367},[366],[363,154441,154443],{"className":154442},[371],[373,154444,154445],{"xmlns":375},[377,154446,154447,154459],{},[380,154448,154449,154455,154457],{},[543,154450,154451,154453],{},[383,154452,45101],{},[383,154454,12310],{},[458,154456,3250],{},[463,154458,465],{},[387,154460,154461],{"encoding":389},"\\alpha_i > 1",[363,154463,154465,154520],{"className":154464,"ariaHidden":394},[393],[363,154466,154468,154471,154511,154514,154517],{"className":154467},[398],[363,154469],{"className":154470,"style":134669},[402],[363,154472,154474,154477],{"className":154473},[407],[363,154475,45101],{"className":154476,"style":45131},[407,408],[363,154478,154480],{"className":154479},[629],[363,154481,154483,154503],{"className":154482},[633,634],[363,154484,154486,154500],{"className":154485},[638],[363,154487,154489],{"className":154488,"style":12529},[642],[363,154490,154491,154494],{"style":136107},[363,154492],{"className":154493,"style":651},[650],[363,154495,154497],{"className":154496},[655,656,657,658],[363,154498,12310],{"className":154499},[407,408,658],[363,154501,666],{"className":154502},[665],[363,154504,154506],{"className":154505},[638],[363,154507,154509],{"className":154508,"style":8315},[642],[363,154510],{},[363,154512],{"className":154513,"style":506},[505],[363,154515,3250],{"className":154516},[510],[363,154518],{"className":154519,"style":506},[505],[363,154521,154523,154526],{"className":154522},[398],[363,154524],{"className":154525,"style":520},[402],[363,154527,465],{"className":154528},[407]," 对一切 ",[363,154531,154533,154546],{"className":154532,"translate":367},[366],[363,154534,154536],{"className":154535},[371],[373,154537,154538],{"xmlns":375},[377,154539,154540,154544],{},[380,154541,154542],{},[383,154543,12310],{},[387,154545,12310],{"encoding":389},[363,154547,154549],{"className":154548,"ariaHidden":394},[393],[363,154550,154552,154556],{"className":154551},[398],[363,154553],{"className":154554,"style":154555},[402],"height:0.6595em;",[363,154557,12310],{"className":154558},[407,408],[363,154560,154562,154586],{"className":154561,"translate":367},[366],[363,154563,154565],{"className":154564},[371],[373,154566,154567],{"xmlns":375},[377,154568,154569,154583],{},[380,154570,154571,154573,154575,154577,154579,154581],{},[383,154572,385],{},[458,154574,461],{"stretchy":460},[383,154576,1121],{"mathvariant":75560},[458,154578,5155],{},[383,154580,45101],{"mathvariant":136008},[458,154582,468],{"stretchy":460},[387,154584,154585],{"encoding":389},"f(\\mathbf{x} \\mid \\boldsymbol{\\alpha})",[363,154587,154589,154613],{"className":154588,"ariaHidden":394},[393],[363,154590,154592,154595,154598,154601,154604,154607,154610],{"className":154591},[398],[363,154593],{"className":154594,"style":487},[402],[363,154596,385],{"className":154597,"style":409},[407,408],[363,154599,461],{"className":154600},[494],[363,154602,1121],{"className":154603},[407,75905],[363,154605],{"className":154606,"style":506},[505],[363,154608,5155],{"className":154609},[510],[363,154611],{"className":154612,"style":506},[505],[363,154614,154616,154619,154628],{"className":154615},[398],[363,154617],{"className":154618,"style":487},[402],[363,154620,154622],{"className":154621},[407],[363,154623,154625],{"className":154624},[407],[363,154626,45101],{"className":154627},[407,136068],[363,154629,468],{"className":154630},[501],[363,154632,154634,154657],{"className":154633,"translate":367},[366],[363,154635,154637],{"className":154636},[371],[373,154638,154639],{"xmlns":375},[377,154640,154641,154655],{},[380,154642,154643],{},[7161,154644,154645,154647],{},[383,154646,126023],{"mathvariant":557},[380,154648,154649,154651,154653],{},[383,154650,11041],{},[458,154652,5160],{},[463,154654,465],{},[387,154656,134774],{"encoding":389},[363,154658,154660],{"className":154659,"ariaHidden":394},[393],[363,154661,154663,154666],{"className":154662},[398],[363,154664],{"className":154665,"style":52432},[402],[363,154667,154669,154672],{"className":154668},[407],[363,154670,126023],{"className":154671},[407],[363,154673,154675],{"className":154674},[629],[363,154676,154678],{"className":154677},[633],[363,154679,154681],{"className":154680},[638],[363,154682,154684],{"className":154683,"style":52432},[642],[363,154685,154686,154689],{"style":7212},[363,154687],{"className":154688,"style":651},[650],[363,154690,154692],{"className":154691},[655,656,657,658],[363,154693,154695,154698,154701],{"className":154694},[407,658],[363,154696,11041],{"className":154697,"style":11129},[407,408,658],[363,154699,5160],{"className":154700},[2938,658],[363,154702,465],{"className":154703},[407,658]," 的内部有唯一众数\n",[363,154706,154708,154792],{"className":154707,"translate":367},[366],[363,154709,154711],{"className":154710},[371],[373,154712,154713],{"xmlns":375},[377,154714,154715,154789],{},[380,154716,154717,154723,154725],{},[7161,154718,154719,154721],{},[383,154720,1121],{"mathvariant":75560},[458,154722,76305],{},[458,154724,471],{},[380,154726,154727,154729,154755,154757,154759,154761,154787],{},[458,154728,461],{"fence":394},[586,154730,154731,154743],{},[380,154732,154733,154739,154741],{},[543,154734,154735,154737],{},[383,154736,45101],{},[463,154738,465],{},[458,154740,5160],{},[463,154742,465],{},[380,154744,154745,154751,154753],{},[543,154746,154747,154749],{},[383,154748,45101],{},[463,154750,474],{},[458,154752,5160],{},[383,154754,11041],{},[458,154756,898],{"separator":394},[458,154758,133107],{},[458,154760,898],{"separator":394},[586,154762,154763,154775],{},[380,154764,154765,154771,154773],{},[543,154766,154767,154769],{},[383,154768,45101],{},[383,154770,11041],{},[458,154772,5160],{},[463,154774,465],{},[380,154776,154777,154783,154785],{},[543,154778,154779,154781],{},[383,154780,45101],{},[463,154782,474],{},[458,154784,5160],{},[383,154786,11041],{},[458,154788,468],{"fence":394},[387,154790,154791],{"encoding":389},"\\mathbf{x}^\\star = \\left( \\frac{\\alpha_1 - 1}{\\alpha_0 - K}, \\dots, \\frac{\\alpha_K - 1}{\\alpha_0 - K} \\right)",[363,154793,154795,154839],{"className":154794,"ariaHidden":394},[393],[363,154796,154798,154801,154830,154833,154836],{"className":154797},[398],[363,154799],{"className":154800,"style":8846},[402],[363,154802,154804,154807],{"className":154803},[407],[363,154805,1121],{"className":154806},[407,75905],[363,154808,154810],{"className":154809},[629],[363,154811,154813],{"className":154812},[633],[363,154814,154816],{"className":154815},[638],[363,154817,154819],{"className":154818,"style":8846},[642],[363,154820,154821,154824],{"style":7212},[363,154822],{"className":154823,"style":651},[650],[363,154825,154827],{"className":154826},[655,656,657,658],[363,154828,76305],{"className":154829},[2938,658],[363,154831],{"className":154832,"style":506},[505],[363,154834,471],{"className":154835},[510],[363,154837],{"className":154838,"style":506},[505],[363,154840,154842,154845],{"className":154841},[398],[363,154843],{"className":154844,"style":68464},[402],[363,154846,154848,154854,155009,155012,155015,155018,155021,155024,155027,155184],{"className":154847},[758],[363,154849,154851],{"className":154850,"style":763},[494,762],[363,154852,461],{"className":154853},[767,4067],[363,154855,154857,154860,155006],{"className":154856},[407],[363,154858],{"className":154859},[494,789],[363,154861,154863],{"className":154862},[586],[363,154864,154866,154998],{"className":154865},[633,634],[363,154867,154869,154995],{"className":154868},[638],[363,154870,154873,154930,154938],{"className":154871,"style":154872},[642],"height:0.8612em;",[363,154874,154875,154878],{"style":2874},[363,154876],{"className":154877,"style":809},[650],[363,154879,154881],{"className":154880},[655,656,657,658],[363,154882,154884,154924,154927],{"className":154883},[407,658],[363,154885,154887,154890],{"className":154886},[407,658],[363,154888,45101],{"className":154889,"style":45131},[407,408,658],[363,154891,154893],{"className":154892},[629],[363,154894,154896,154916],{"className":154895},[633,634],[363,154897,154899,154913],{"className":154898},[638],[363,154900,154902],{"className":154901,"style":137304},[642],[363,154903,154904,154907],{"style":136942},[363,154905],{"className":154906,"style":30553},[650],[363,154908,154910],{"className":154909},[655,30557,10021,658],[363,154911,474],{"className":154912},[407,658],[363,154914,666],{"className":154915},[665],[363,154917,154919],{"className":154918},[638],[363,154920,154922],{"className":154921,"style":40117},[642],[363,154923],{},[363,154925,5160],{"className":154926},[2938,658],[363,154928,11041],{"className":154929,"style":11129},[407,408,658],[363,154931,154932,154935],{"style":821},[363,154933],{"className":154934,"style":809},[650],[363,154936],{"className":154937,"style":829},[828],[363,154939,154940,154943],{"style":147946},[363,154941],{"className":154942,"style":809},[650],[363,154944,154946],{"className":154945},[655,656,657,658],[363,154947,154949,154989,154992],{"className":154948},[407,658],[363,154950,154952,154955],{"className":154951},[407,658],[363,154953,45101],{"className":154954,"style":45131},[407,408,658],[363,154956,154958],{"className":154957},[629],[363,154959,154961,154981],{"className":154960},[633,634],[363,154962,154964,154978],{"className":154963},[638],[363,154965,154967],{"className":154966,"style":137304},[642],[363,154968,154969,154972],{"style":136942},[363,154970],{"className":154971,"style":30553},[650],[363,154973,154975],{"className":154974},[655,30557,10021,658],[363,154976,465],{"className":154977},[407,658],[363,154979,666],{"className":154980},[665],[363,154982,154984],{"className":154983},[638],[363,154985,154987],{"className":154986,"style":40117},[642],[363,154988],{},[363,154990,5160],{"className":154991},[2938,658],[363,154993,465],{"className":154994},[407,658],[363,154996,666],{"className":154997},[665],[363,154999,155001],{"className":155000},[638],[363,155002,155004],{"className":155003,"style":40264},[642],[363,155005],{},[363,155007],{"className":155008},[501,789],[363,155010,898],{"className":155011},[920],[363,155013],{"className":155014,"style":754},[505],[363,155016,133107],{"className":155017},[758],[363,155019],{"className":155020,"style":754},[505],[363,155022,898],{"className":155023},[920],[363,155025],{"className":155026,"style":754},[505],[363,155028,155030,155033,155181],{"className":155029},[407],[363,155031],{"className":155032},[494,789],[363,155034,155036],{"className":155035},[586],[363,155037,155039,155173],{"className":155038},[633,634],[363,155040,155042,155170],{"className":155041},[638],[363,155043,155046,155103,155111],{"className":155044,"style":155045},[642],"height:0.8614em;",[363,155047,155048,155051],{"style":2874},[363,155049],{"className":155050,"style":809},[650],[363,155052,155054],{"className":155053},[655,656,657,658],[363,155055,155057,155097,155100],{"className":155056},[407,658],[363,155058,155060,155063],{"className":155059},[407,658],[363,155061,45101],{"className":155062,"style":45131},[407,408,658],[363,155064,155066],{"className":155065},[629],[363,155067,155069,155089],{"className":155068},[633,634],[363,155070,155072,155086],{"className":155071},[638],[363,155073,155075],{"className":155074,"style":137304},[642],[363,155076,155077,155080],{"style":136942},[363,155078],{"className":155079,"style":30553},[650],[363,155081,155083],{"className":155082},[655,30557,10021,658],[363,155084,474],{"className":155085},[407,658],[363,155087,666],{"className":155088},[665],[363,155090,155092],{"className":155091},[638],[363,155093,155095],{"className":155094,"style":40117},[642],[363,155096],{},[363,155098,5160],{"className":155099},[2938,658],[363,155101,11041],{"className":155102,"style":11129},[407,408,658],[363,155104,155105,155108],{"style":821},[363,155106],{"className":155107,"style":809},[650],[363,155109],{"className":155110,"style":829},[828],[363,155112,155114,155117],{"style":155113},"top:-3.4103em;",[363,155115],{"className":155116,"style":809},[650],[363,155118,155120],{"className":155119},[655,656,657,658],[363,155121,155123,155164,155167],{"className":155122},[407,658],[363,155124,155126,155129],{"className":155125},[407,658],[363,155127,45101],{"className":155128,"style":45131},[407,408,658],[363,155130,155132],{"className":155131},[629],[363,155133,155135,155156],{"className":155134},[633,634],[363,155136,155138,155153],{"className":155137},[638],[363,155139,155141],{"className":155140,"style":6445},[642],[363,155142,155144,155147],{"style":155143},"top:-2.3567em;margin-left:-0.0037em;margin-right:0.0714em;",[363,155145],{"className":155146,"style":30553},[650],[363,155148,155150],{"className":155149},[655,30557,10021,658],[363,155151,11041],{"className":155152,"style":11129},[407,408,658],[363,155154,666],{"className":155155},[665],[363,155157,155159],{"className":155158},[638],[363,155160,155162],{"className":155161,"style":30576},[642],[363,155163],{},[363,155165,5160],{"className":155166},[2938,658],[363,155168,465],{"className":155169},[407,658],[363,155171,666],{"className":155172},[665],[363,155174,155176],{"className":155175},[638],[363,155177,155179],{"className":155178,"style":40264},[642],[363,155180],{},[363,155182],{"className":155183},[501,789],[363,155185,155187],{"className":155186,"style":763},[501,762],[363,155188,468],{"className":155189},[767,4067],[11,155191,155192,155193,155286],{},"当某个 ",[363,155194,155196,155218],{"className":155195,"translate":367},[366],[363,155197,155199],{"className":155198},[371],[373,155200,155201],{"xmlns":375},[377,155202,155203,155215],{},[380,155204,155205,155211,155213],{},[543,155206,155207,155209],{},[383,155208,45101],{},[383,155210,12310],{},[458,155212,10299],{},[463,155214,465],{},[387,155216,155217],{"encoding":389},"\\alpha_i \\le 1",[363,155219,155221,155277],{"className":155220,"ariaHidden":394},[393],[363,155222,155224,155228,155268,155271,155274],{"className":155223},[398],[363,155225],{"className":155226,"style":155227},[402],"height:0.786em;vertical-align:-0.15em;",[363,155229,155231,155234],{"className":155230},[407],[363,155232,45101],{"className":155233,"style":45131},[407,408],[363,155235,155237],{"className":155236},[629],[363,155238,155240,155260],{"className":155239},[633,634],[363,155241,155243,155257],{"className":155242},[638],[363,155244,155246],{"className":155245,"style":12529},[642],[363,155247,155248,155251],{"style":136107},[363,155249],{"className":155250,"style":651},[650],[363,155252,155254],{"className":155253},[655,656,657,658],[363,155255,12310],{"className":155256},[407,408,658],[363,155258,666],{"className":155259},[665],[363,155261,155263],{"className":155262},[638],[363,155264,155266],{"className":155265,"style":8315},[642],[363,155267],{},[363,155269],{"className":155270,"style":506},[505],[363,155272,10299],{"className":155273},[510],[363,155275],{"className":155276,"style":506},[505],[363,155278,155280,155283],{"className":155279},[398],[363,155281],{"className":155282,"style":520},[402],[363,155284,465],{"className":155285},[407]," 时密度在对应边界面上无界，众数退化到边界，此时分布呈现 2.6 节所述的稀疏形态。",[1340,155288,155290],{"title":155289},"命题 2.4（微分熵）",[11,155291,155292,155293,155369,155370,155866,155867,155958],{},"在 1.1 节的测度约定下，",[363,155294,155296,155321],{"className":155295,"translate":367},[366],[363,155297,155299],{"className":155298},[371],[373,155300,155301],{"xmlns":375},[377,155302,155303,155319],{},[380,155304,155305,155307,155309,155311,155313,155315,155317],{},[383,155306,1121],{"mathvariant":75560},[458,155308,9216],{},[383,155310,137065],{"mathvariant":557},[458,155312,4450],{},[458,155314,461],{"stretchy":460},[383,155316,45101],{"mathvariant":136008},[458,155318,468],{"stretchy":460},[387,155320,137076],{"encoding":389},[363,155322,155324,155342],{"className":155323,"ariaHidden":394},[393],[363,155325,155327,155330,155333,155336,155339],{"className":155326},[398],[363,155328],{"className":155329,"style":135617},[402],[363,155331,1121],{"className":155332},[407,75905],[363,155334],{"className":155335,"style":506},[505],[363,155337,9216],{"className":155338},[510],[363,155340],{"className":155341,"style":506},[505],[363,155343,155345,155348,155354,155357,155366],{"className":155344},[398],[363,155346],{"className":155347,"style":487},[402],[363,155349,155351],{"className":155350},[1831],[363,155352,137065],{"className":155353},[407,33009],[363,155355,461],{"className":155356},[494],[363,155358,155360],{"className":155359},[407],[363,155361,155363],{"className":155362},[407],[363,155364,45101],{"className":155365},[407,136068],[363,155367,468],{"className":155368},[501]," 的微分熵为\n",[363,155371,155373,155482],{"className":155372,"translate":367},[366],[363,155374,155376],{"className":155375},[371],[373,155377,155378],{"xmlns":375},[377,155379,155380,155479],{},[380,155381,155382,155384,155386,155388,155390,155392,155394,155396,155398,155400,155402,155404,155406,155408,155414,155416,155418,155420,155422,155425,155427,155433,155435,155437,155451,155453,155459,155461,155463,155465,155467,155469,155471,155477],{},[383,155383,34231],{},[458,155385,461],{"stretchy":460},[383,155387,1121],{"mathvariant":75560},[458,155389,468],{"stretchy":460},[458,155391,471],{},[383,155393,4447],{},[458,155395,4450],{},[383,155397,39638],{},[458,155399,461],{"stretchy":460},[383,155401,45101],{"mathvariant":136008},[458,155403,468],{"stretchy":460},[458,155405,2817],{},[458,155407,461],{"stretchy":460},[543,155409,155410,155412],{},[383,155411,45101],{},[463,155413,474],{},[458,155415,5160],{},[383,155417,11041],{},[458,155419,468],{"stretchy":460},[1644,155421,1646],{},[383,155423,155424],{},"ψ",[458,155426,461],{"stretchy":460},[543,155428,155429,155431],{},[383,155430,45101],{},[463,155432,474],{},[458,155434,468],{"stretchy":460},[458,155436,5160],{},[7900,155438,155439,155441,155449],{},[458,155440,13808],{},[380,155442,155443,155445,155447],{},[383,155444,12310],{},[458,155446,471],{},[463,155448,465],{},[383,155450,11041],{},[458,155452,461],{"stretchy":460},[543,155454,155455,155457],{},[383,155456,45101],{},[383,155458,12310],{},[458,155460,5160],{},[463,155462,465],{},[458,155464,468],{"stretchy":460},[1644,155466,1646],{},[383,155468,155424],{},[458,155470,461],{"stretchy":460},[543,155472,155473,155475],{},[383,155474,45101],{},[383,155476,12310],{},[458,155478,468],{"stretchy":460},[387,155480,155481],{"encoding":389},"H(\\mathbf{x}) = \\log B(\\boldsymbol{\\alpha}) + (\\alpha_0 - K)\\,\\psi(\\alpha_0) - \\sum_{i=1}^K (\\alpha_i - 1)\\,\\psi(\\alpha_i)",[363,155483,155485,155512,155553,155611,155684,155802],{"className":155484,"ariaHidden":394},[393],[363,155486,155488,155491,155494,155497,155500,155503,155506,155509],{"className":155487},[398],[363,155489],{"className":155490,"style":487},[402],[363,155492,34231],{"className":155493,"style":34385},[407,408],[363,155495,461],{"className":155496},[494],[363,155498,1121],{"className":155499},[407,75905],[363,155501,468],{"className":155502},[501],[363,155504],{"className":155505,"style":506},[505],[363,155507,471],{"className":155508},[510],[363,155510],{"className":155511,"style":506},[505],[363,155513,155515,155518,155523,155526,155529,155532,155541,155544,155547,155550],{"className":155514},[398],[363,155516],{"className":155517,"style":487},[402],[363,155519,4501,155521],{"className":155520},[1831],[363,155522,4505],{"style":4504},[363,155524],{"className":155525,"style":754},[505],[363,155527,39638],{"className":155528,"style":39734},[407,408],[363,155530,461],{"className":155531},[494],[363,155533,155535],{"className":155534},[407],[363,155536,155538],{"className":155537},[407],[363,155539,45101],{"className":155540},[407,136068],[363,155542,468],{"className":155543},[501],[363,155545],{"className":155546,"style":2934},[505],[363,155548,2817],{"className":155549},[2938],[363,155551],{"className":155552,"style":2934},[505],[363,155554,155556,155559,155562,155602,155605,155608],{"className":155555},[398],[363,155557],{"className":155558,"style":487},[402],[363,155560,461],{"className":155561},[494],[363,155563,155565,155568],{"className":155564},[407],[363,155566,45101],{"className":155567,"style":45131},[407,408],[363,155569,155571],{"className":155570},[629],[363,155572,155574,155594],{"className":155573},[633,634],[363,155575,155577,155591],{"className":155576},[638],[363,155578,155580],{"className":155579,"style":11480},[642],[363,155581,155582,155585],{"style":136107},[363,155583],{"className":155584,"style":651},[650],[363,155586,155588],{"className":155587},[655,656,657,658],[363,155589,474],{"className":155590},[407,658],[363,155592,666],{"className":155593},[665],[363,155595,155597],{"className":155596},[638],[363,155598,155600],{"className":155599,"style":8315},[642],[363,155601],{},[363,155603],{"className":155604,"style":2934},[505],[363,155606,5160],{"className":155607},[2938],[363,155609],{"className":155610,"style":2934},[505],[363,155612,155614,155617,155620,155623,155626,155629,155632,155672,155675,155678,155681],{"className":155613},[398],[363,155615],{"className":155616,"style":487},[402],[363,155618,11041],{"className":155619,"style":11129},[407,408],[363,155621,468],{"className":155622},[501],[363,155624],{"className":155625,"style":754},[505],[363,155627,155424],{"className":155628,"style":1328},[407,408],[363,155630,461],{"className":155631},[494],[363,155633,155635,155638],{"className":155634},[407],[363,155636,45101],{"className":155637,"style":45131},[407,408],[363,155639,155641],{"className":155640},[629],[363,155642,155644,155664],{"className":155643},[633,634],[363,155645,155647,155661],{"className":155646},[638],[363,155648,155650],{"className":155649,"style":11480},[642],[363,155651,155652,155655],{"style":136107},[363,155653],{"className":155654,"style":651},[650],[363,155656,155658],{"className":155657},[655,656,657,658],[363,155659,474],{"className":155660},[407,658],[363,155662,666],{"className":155663},[665],[363,155665,155667],{"className":155666},[638],[363,155668,155670],{"className":155669,"style":8315},[642],[363,155671],{},[363,155673,468],{"className":155674},[501],[363,155676],{"className":155677,"style":2934},[505],[363,155679,5160],{"className":155680},[2938],[363,155682],{"className":155683,"style":2934},[505],[363,155685,155687,155690,155750,155753,155793,155796,155799],{"className":155686},[398],[363,155688],{"className":155689,"style":136371},[402],[363,155691,155693,155696],{"className":155692},[1831],[363,155694,13808],{"className":155695,"style":40007},[1831,1832,5963],[363,155697,155699],{"className":155698},[629],[363,155700,155702,155742],{"className":155701},[633,634],[363,155703,155705,155739],{"className":155704},[638],[363,155706,155708,155728],{"className":155707,"style":133494},[642],[363,155709,155710,155713],{"style":40023},[363,155711],{"className":155712,"style":651},[650],[363,155714,155716],{"className":155715},[655,656,657,658],[363,155717,155719,155722,155725],{"className":155718},[407,658],[363,155720,12310],{"className":155721},[407,408,658],[363,155723,471],{"className":155724},[510,658],[363,155726,465],{"className":155727},[407,658],[363,155729,155730,155733],{"style":133517},[363,155731],{"className":155732,"style":651},[650],[363,155734,155736],{"className":155735},[655,656,657,658],[363,155737,11041],{"className":155738,"style":11129},[407,408,658],[363,155740,666],{"className":155741},[665],[363,155743,155745],{"className":155744},[638],[363,155746,155748],{"className":155747,"style":40042},[642],[363,155749],{},[363,155751,461],{"className":155752},[494],[363,155754,155756,155759],{"className":155755},[407],[363,155757,45101],{"className":155758,"style":45131},[407,408],[363,155760,155762],{"className":155761},[629],[363,155763,155765,155785],{"className":155764},[633,634],[363,155766,155768,155782],{"className":155767},[638],[363,155769,155771],{"className":155770,"style":12529},[642],[363,155772,155773,155776],{"style":136107},[363,155774],{"className":155775,"style":651},[650],[363,155777,155779],{"className":155778},[655,656,657,658],[363,155780,12310],{"className":155781},[407,408,658],[363,155783,666],{"className":155784},[665],[363,155786,155788],{"className":155787},[638],[363,155789,155791],{"className":155790,"style":8315},[642],[363,155792],{},[363,155794],{"className":155795,"style":2934},[505],[363,155797,5160],{"className":155798},[2938],[363,155800],{"className":155801,"style":2934},[505],[363,155803,155805,155808,155811,155814,155817,155820,155823,155863],{"className":155804},[398],[363,155806],{"className":155807,"style":487},[402],[363,155809,465],{"className":155810},[407],[363,155812,468],{"className":155813},[501],[363,155815],{"className":155816,"style":754},[505],[363,155818,155424],{"className":155819,"style":1328},[407,408],[363,155821,461],{"className":155822},[494],[363,155824,155826,155829],{"className":155825},[407],[363,155827,45101],{"className":155828,"style":45131},[407,408],[363,155830,155832],{"className":155831},[629],[363,155833,155835,155855],{"className":155834},[633,634],[363,155836,155838,155852],{"className":155837},[638],[363,155839,155841],{"className":155840,"style":12529},[642],[363,155842,155843,155846],{"style":136107},[363,155844],{"className":155845,"style":651},[650],[363,155847,155849],{"className":155848},[655,656,657,658],[363,155850,12310],{"className":155851},[407,408,658],[363,155853,666],{"className":155854},[665],[363,155856,155858],{"className":155857},[638],[363,155859,155861],{"className":155860,"style":8315},[642],[363,155862],{},[363,155864,468],{"className":155865},[501],"\n其中 ",[363,155868,155870,155896],{"className":155869,"translate":367},[366],[363,155871,155873],{"className":155872},[371],[373,155874,155875],{"xmlns":375},[377,155876,155877,155893],{},[380,155878,155879,155881,155883,155889,155891],{},[383,155880,155424],{},[458,155882,471],{},[7161,155884,155885,155887],{},[383,155886,137171],{"mathvariant":557},[458,155888,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[383,155890,1288],{"mathvariant":557},[383,155892,137171],{"mathvariant":557},[387,155894,155895],{"encoding":389},"\\psi = \\Gamma'\u002F\\Gamma",[363,155897,155899,155917],{"className":155898,"ariaHidden":394},[393],[363,155900,155902,155905,155908,155911,155914],{"className":155901},[398],[363,155903],{"className":155904,"style":403},[402],[363,155906,155424],{"className":155907,"style":1328},[407,408],[363,155909],{"className":155910,"style":506},[505],[363,155912,471],{"className":155913},[510],[363,155915],{"className":155916,"style":506},[505],[363,155918,155920,155923,155955],{"className":155919},[398],[363,155921],{"className":155922,"style":7190},[402],[363,155924,155926,155929],{"className":155925},[407],[363,155927,137171],{"className":155928},[407],[363,155930,155932],{"className":155931},[629],[363,155933,155935],{"className":155934},[633],[363,155936,155938],{"className":155937},[638],[363,155939,155941],{"className":155940,"style":7209},[642],[363,155942,155943,155946],{"style":7212},[363,155944],{"className":155945,"style":651},[650],[363,155947,155949],{"className":155948},[655,656,657,658],[363,155950,155952],{"className":155951},[407,658],[363,155953,7167],{"className":155954},[407,658],[363,155956,143765],{"className":155957},[407]," 为 digamma 函数。",[11,155960,155961,155963,155964,156051,156052,2756,156358,156611,156612,156682],{},[1572,155962,137993],{}," 直接计算 ",[363,155965,155967,155995],{"className":155966,"translate":367},[366],[363,155968,155970],{"className":155969},[371],[373,155971,155972],{"xmlns":375},[377,155973,155974,155992],{},[380,155975,155976,155978,155980,155982,155984,155986,155988,155990],{},[383,155977,34231],{},[458,155979,471],{},[458,155981,5160],{},[458,155983,1634],{},[383,155985,385],{},[383,155987,4447],{},[458,155989,4450],{},[383,155991,385],{},[387,155993,155994],{"encoding":389},"H = -\\int f \\log f",[363,155996,155998,156016],{"className":155997,"ariaHidden":394},[393],[363,155999,156001,156004,156007,156010,156013],{"className":156000},[398],[363,156002],{"className":156003,"style":1011},[402],[363,156005,34231],{"className":156006,"style":34385},[407,408],[363,156008],{"className":156009,"style":506},[505],[363,156011,471],{"className":156012},[510],[363,156014],{"className":156015,"style":506},[505],[363,156017,156019,156022,156025,156028,156031,156034,156037,156040,156045,156048],{"className":156018},[398],[363,156020],{"className":156021,"style":5959},[402],[363,156023,5160],{"className":156024},[407],[363,156026],{"className":156027,"style":754},[505],[363,156029,1634],{"className":156030,"style":5964},[1831,1832,5963],[363,156032],{"className":156033,"style":754},[505],[363,156035,385],{"className":156036,"style":409},[407,408],[363,156038],{"className":156039,"style":754},[505],[363,156041,4501,156043],{"className":156042},[1831],[363,156044,4505],{"style":4504},[363,156046],{"className":156047,"style":754},[505],[363,156049,385],{"className":156050,"style":409},[407,408],"，代入 ",[363,156053,156055,156121],{"className":156054,"translate":367},[366],[363,156056,156058],{"className":156057},[371],[373,156059,156060],{"xmlns":375},[377,156061,156062,156118],{},[380,156063,156064,156066,156068,156070,156072,156074,156076,156078,156080,156082,156084,156086,156088,156094,156096,156102,156104,156106,156108,156110,156112],{},[458,156065,5160],{},[383,156067,4447],{},[458,156069,4450],{},[383,156071,385],{},[458,156073,471],{},[383,156075,4447],{},[458,156077,4450],{},[383,156079,39638],{},[458,156081,461],{"stretchy":460},[383,156083,45101],{"mathvariant":136008},[458,156085,468],{"stretchy":460},[458,156087,5160],{},[543,156089,156090,156092],{},[458,156091,13808],{},[383,156093,12310],{},[458,156095,461],{"stretchy":460},[543,156097,156098,156100],{},[383,156099,45101],{},[383,156101,12310],{},[458,156103,5160],{},[463,156105,465],{},[458,156107,468],{"stretchy":460},[383,156109,4447],{},[458,156111,4450],{},[543,156113,156114,156116],{},[383,156115,1121],{},[383,156117,12310],{},[387,156119,156120],{"encoding":389},"-\\log f = \\log B(\\boldsymbol{\\alpha}) - \\sum_i (\\alpha_i - 1)\\log x_i",[363,156122,156124,156156,156197,156295],{"className":156123,"ariaHidden":394},[393],[363,156125,156127,156130,156133,156136,156141,156144,156147,156150,156153],{"className":156126},[398],[363,156128],{"className":156129,"style":403},[402],[363,156131,5160],{"className":156132},[407],[363,156134],{"className":156135,"style":754},[505],[363,156137,4501,156139],{"className":156138},[1831],[363,156140,4505],{"style":4504},[363,156142],{"className":156143,"style":754},[505],[363,156145,385],{"className":156146,"style":409},[407,408],[363,156148],{"className":156149,"style":506},[505],[363,156151,471],{"className":156152},[510],[363,156154],{"className":156155,"style":506},[505],[363,156157,156159,156162,156167,156170,156173,156176,156185,156188,156191,156194],{"className":156158},[398],[363,156160],{"className":156161,"style":487},[402],[363,156163,4501,156165],{"className":156164},[1831],[363,156166,4505],{"style":4504},[363,156168],{"className":156169,"style":754},[505],[363,156171,39638],{"className":156172,"style":39734},[407,408],[363,156174,461],{"className":156175},[494],[363,156177,156179],{"className":156178},[407],[363,156180,156182],{"className":156181},[407],[363,156183,45101],{"className":156184},[407,136068],[363,156186,468],{"className":156187},[501],[363,156189],{"className":156190,"style":2934},[505],[363,156192,5160],{"className":156193},[2938],[363,156195],{"className":156196,"style":2934},[505],[363,156198,156200,156203,156243,156246,156286,156289,156292],{"className":156199},[398],[363,156201],{"className":156202,"style":138904},[402],[363,156204,156206,156209],{"className":156205},[1831],[363,156207,13808],{"className":156208,"style":40007},[1831,1832,5963],[363,156210,156212],{"className":156211},[629],[363,156213,156215,156235],{"className":156214},[633,634],[363,156216,156218,156232],{"className":156217},[638],[363,156219,156221],{"className":156220,"style":40020},[642],[363,156222,156223,156226],{"style":40023},[363,156224],{"className":156225,"style":651},[650],[363,156227,156229],{"className":156228},[655,656,657,658],[363,156230,12310],{"className":156231},[407,408,658],[363,156233,666],{"className":156234},[665],[363,156236,156238],{"className":156237},[638],[363,156239,156241],{"className":156240,"style":40042},[642],[363,156242],{},[363,156244,461],{"className":156245},[494],[363,156247,156249,156252],{"className":156248},[407],[363,156250,45101],{"className":156251,"style":45131},[407,408],[363,156253,156255],{"className":156254},[629],[363,156256,156258,156278],{"className":156257},[633,634],[363,156259,156261,156275],{"className":156260},[638],[363,156262,156264],{"className":156263,"style":12529},[642],[363,156265,156266,156269],{"style":136107},[363,156267],{"className":156268,"style":651},[650],[363,156270,156272],{"className":156271},[655,656,657,658],[363,156273,12310],{"className":156274},[407,408,658],[363,156276,666],{"className":156277},[665],[363,156279,156281],{"className":156280},[638],[363,156282,156284],{"className":156283,"style":8315},[642],[363,156285],{},[363,156287],{"className":156288,"style":2934},[505],[363,156290,5160],{"className":156291},[2938],[363,156293],{"className":156294,"style":2934},[505],[363,156296,156298,156301,156304,156307,156310,156315,156318],{"className":156297},[398],[363,156299],{"className":156300,"style":487},[402],[363,156302,465],{"className":156303},[407],[363,156305,468],{"className":156306},[501],[363,156308],{"className":156309,"style":754},[505],[363,156311,4501,156313],{"className":156312},[1831],[363,156314,4505],{"style":4504},[363,156316],{"className":156317,"style":754},[505],[363,156319,156321,156324],{"className":156320},[407],[363,156322,1121],{"className":156323},[407,408],[363,156325,156327],{"className":156326},[629],[363,156328,156330,156350],{"className":156329},[633,634],[363,156331,156333,156347],{"className":156332},[638],[363,156334,156336],{"className":156335,"style":12529},[642],[363,156337,156338,156341],{"style":730},[363,156339],{"className":156340,"style":651},[650],[363,156342,156344],{"className":156343},[655,656,657,658],[363,156345,12310],{"className":156346},[407,408,658],[363,156348,666],{"className":156349},[665],[363,156351,156353],{"className":156352},[638],[363,156354,156356],{"className":156355,"style":8315},[642],[363,156357],{},[363,156359,156361,156417],{"className":156360,"translate":367},[366],[363,156362,156364],{"className":156363},[371],[373,156365,156366],{"xmlns":375},[377,156367,156368,156414],{},[380,156369,156370,156372,156374,156376,156378,156384,156386,156388,156390,156392,156398,156400,156402,156404,156406,156412],{},[383,156371,571],{"mathvariant":570},[458,156373,578],{"stretchy":460},[383,156375,4447],{},[458,156377,4450],{},[543,156379,156380,156382],{},[383,156381,1121],{},[383,156383,12310],{},[458,156385,605],{"stretchy":460},[458,156387,471],{},[383,156389,155424],{},[458,156391,461],{"stretchy":460},[543,156393,156394,156396],{},[383,156395,45101],{},[383,156397,12310],{},[458,156399,468],{"stretchy":460},[458,156401,5160],{},[383,156403,155424],{},[458,156405,461],{"stretchy":460},[543,156407,156408,156410],{},[383,156409,45101],{},[463,156411,474],{},[458,156413,468],{"stretchy":460},[387,156415,156416],{"encoding":389},"\\mathbb{E}[\\log x_i] = \\psi(\\alpha_i) - \\psi(\\alpha_0)",[363,156418,156420,156492,156556],{"className":156419,"ariaHidden":394},[393],[363,156421,156423,156426,156429,156432,156437,156440,156480,156483,156486,156489],{"className":156422},[398],[363,156424],{"className":156425,"style":487},[402],[363,156427,571],{"className":156428},[407,714],[363,156430,578],{"className":156431},[494],[363,156433,4501,156435],{"className":156434},[1831],[363,156436,4505],{"style":4504},[363,156438],{"className":156439,"style":754},[505],[363,156441,156443,156446],{"className":156442},[407],[363,156444,1121],{"className":156445},[407,408],[363,156447,156449],{"className":156448},[629],[363,156450,156452,156472],{"className":156451},[633,634],[363,156453,156455,156469],{"className":156454},[638],[363,156456,156458],{"className":156457,"style":12529},[642],[363,156459,156460,156463],{"style":730},[363,156461],{"className":156462,"style":651},[650],[363,156464,156466],{"className":156465},[655,656,657,658],[363,156467,12310],{"className":156468},[407,408,658],[363,156470,666],{"className":156471},[665],[363,156473,156475],{"className":156474},[638],[363,156476,156478],{"className":156477,"style":8315},[642],[363,156479],{},[363,156481,605],{"className":156482},[501],[363,156484],{"className":156485,"style":506},[505],[363,156487,471],{"className":156488},[510],[363,156490],{"className":156491,"style":506},[505],[363,156493,156495,156498,156501,156504,156544,156547,156550,156553],{"className":156494},[398],[363,156496],{"className":156497,"style":487},[402],[363,156499,155424],{"className":156500,"style":1328},[407,408],[363,156502,461],{"className":156503},[494],[363,156505,156507,156510],{"className":156506},[407],[363,156508,45101],{"className":156509,"style":45131},[407,408],[363,156511,156513],{"className":156512},[629],[363,156514,156516,156536],{"className":156515},[633,634],[363,156517,156519,156533],{"className":156518},[638],[363,156520,156522],{"className":156521,"style":12529},[642],[363,156523,156524,156527],{"style":136107},[363,156525],{"className":156526,"style":651},[650],[363,156528,156530],{"className":156529},[655,656,657,658],[363,156531,12310],{"className":156532},[407,408,658],[363,156534,666],{"className":156535},[665],[363,156537,156539],{"className":156538},[638],[363,156540,156542],{"className":156541,"style":8315},[642],[363,156543],{},[363,156545,468],{"className":156546},[501],[363,156548],{"className":156549,"style":2934},[505],[363,156551,5160],{"className":156552},[2938],[363,156554],{"className":156555,"style":2934},[505],[363,156557,156559,156562,156565,156568,156608],{"className":156558},[398],[363,156560],{"className":156561,"style":487},[402],[363,156563,155424],{"className":156564,"style":1328},[407,408],[363,156566,461],{"className":156567},[494],[363,156569,156571,156574],{"className":156570},[407],[363,156572,45101],{"className":156573,"style":45131},[407,408],[363,156575,156577],{"className":156576},[629],[363,156578,156580,156600],{"className":156579},[633,634],[363,156581,156583,156597],{"className":156582},[638],[363,156584,156586],{"className":156585,"style":11480},[642],[363,156587,156588,156591],{"style":136107},[363,156589],{"className":156590,"style":651},[650],[363,156592,156594],{"className":156593},[655,656,657,658],[363,156595,474],{"className":156596},[407,658],[363,156598,666],{"className":156599},[665],[363,156601,156603],{"className":156602},[638],[363,156604,156606],{"className":156605,"style":8315},[642],[363,156607],{},[363,156609,468],{"className":156610},[501],"（由命题 1.3 的矩恒等式对 ",[363,156613,156615,156633],{"className":156614,"translate":367},[366],[363,156616,156618],{"className":156617},[371],[373,156619,156620],{"xmlns":375},[377,156621,156622,156630],{},[380,156623,156624],{},[543,156625,156626,156628],{},[383,156627,84464],{},[383,156629,12310],{},[387,156631,156632],{"encoding":389},"\\beta_i",[363,156634,156636],{"className":156635,"ariaHidden":394},[393],[363,156637,156639,156642],{"className":156638},[398],[363,156640],{"className":156641,"style":403},[402],[363,156643,156645,156648],{"className":156644},[407],[363,156646,84464],{"className":156647,"style":84686},[407,408],[363,156649,156651],{"className":156650},[629],[363,156652,156654,156674],{"className":156653},[633,634],[363,156655,156657,156671],{"className":156656},[638],[363,156658,156660],{"className":156659,"style":12529},[642],[363,156661,156662,156665],{"style":150221},[363,156663],{"className":156664,"style":651},[650],[363,156666,156668],{"className":156667},[655,656,657,658],[363,156669,12310],{"className":156670},[407,408,658],[363,156672,666],{"className":156673},[665],[363,156675,156677],{"className":156676},[638],[363,156678,156680],{"className":156679,"style":8315},[642],[363,156681],{}," 求导得到），整理即得。",[11,156684,156685,156686,156748,156749,4200,156777,156828,156829,156966,156967,157059,157060,157110,157111,157114,157115,157188],{},"在对称情形 ",[363,156687,156689,156709],{"className":156688,"translate":367},[366],[363,156690,156692],{"className":156691},[371],[373,156693,156694],{"xmlns":375},[377,156695,156696,156706],{},[380,156697,156698,156700,156702,156704],{},[383,156699,45101],{"mathvariant":136008},[458,156701,471],{},[383,156703,45101],{},[463,156705,465],{"mathvariant":75560},[387,156707,156708],{"encoding":389},"\\boldsymbol{\\alpha} = \\alpha \\mathbf{1}",[363,156710,156712,156736],{"className":156711,"ariaHidden":394},[393],[363,156713,156715,156718,156727,156730,156733],{"className":156714},[398],[363,156716],{"className":156717,"style":135617},[402],[363,156719,156721],{"className":156720},[407],[363,156722,156724],{"className":156723},[407],[363,156725,45101],{"className":156726},[407,136068],[363,156728],{"className":156729,"style":506},[505],[363,156731,471],{"className":156732},[510],[363,156734],{"className":156735,"style":506},[505],[363,156737,156739,156742,156745],{"className":156738},[398],[363,156740],{"className":156741,"style":520},[402],[363,156743,45101],{"className":156744,"style":45131},[407,408],[363,156746,465],{"className":156747},[407,75905]," 下，",[363,156750,156752,156765],{"className":156751,"translate":367},[366],[363,156753,156755],{"className":156754},[371],[373,156756,156757],{"xmlns":375},[377,156758,156759,156763],{},[380,156760,156761],{},[383,156762,34231],{},[387,156764,34231],{"encoding":389},[363,156766,156768],{"className":156767,"ariaHidden":394},[393],[363,156769,156771,156774],{"className":156770},[398],[363,156772],{"className":156773,"style":1011},[402],[363,156775,34231],{"className":156776,"style":34385},[407,408],[363,156778,156780,156798],{"className":156779,"translate":367},[366],[363,156781,156783],{"className":156782},[371],[373,156784,156785],{"xmlns":375},[377,156786,156787,156795],{},[380,156788,156789,156791,156793],{},[383,156790,45101],{},[458,156792,471],{},[463,156794,465],{},[387,156796,156797],{"encoding":389},"\\alpha = 1",[363,156799,156801,156819],{"className":156800,"ariaHidden":394},[393],[363,156802,156804,156807,156810,156813,156816],{"className":156803},[398],[363,156805],{"className":156806,"style":2692},[402],[363,156808,45101],{"className":156809,"style":45131},[407,408],[363,156811],{"className":156812,"style":506},[505],[363,156814,471],{"className":156815},[510],[363,156817],{"className":156818,"style":506},[505],[363,156820,156822,156825],{"className":156821},[398],[363,156823],{"className":156824,"style":520},[402],[363,156826,465],{"className":156827},[407]," 处取最大值 ",[363,156830,156832,156878],{"className":156831,"translate":367},[366],[363,156833,156835],{"className":156834},[371],[373,156836,156837],{"xmlns":375},[377,156838,156839,156875],{},[380,156840,156841,156843,156845,156847,156849,156851,156853,156855,156857,156859,156861,156863,156865,156867,156869,156871,156873],{},[458,156842,5160],{},[383,156844,4447],{},[458,156846,4450],{},[383,156848,137171],{"mathvariant":557},[458,156850,461],{"stretchy":460},[383,156852,11041],{},[458,156854,468],{"stretchy":460},[458,156856,471],{},[458,156858,5160],{},[383,156860,4447],{},[458,156862,4450],{},[458,156864,461],{"stretchy":460},[383,156866,11041],{},[458,156868,5160],{},[463,156870,465],{},[458,156872,468],{"stretchy":460},[458,156874,135939],{"stretchy":460},[387,156876,156877],{"encoding":389},"-\\log \\Gamma(K) = -\\log (K-1)!",[363,156879,156881,156922,156954],{"className":156880,"ariaHidden":394},[393],[363,156882,156884,156887,156890,156893,156898,156901,156904,156907,156910,156913,156916,156919],{"className":156883},[398],[363,156885],{"className":156886,"style":487},[402],[363,156888,5160],{"className":156889},[407],[363,156891],{"className":156892,"style":754},[505],[363,156894,4501,156896],{"className":156895},[1831],[363,156897,4505],{"style":4504},[363,156899],{"className":156900,"style":754},[505],[363,156902,137171],{"className":156903},[407],[363,156905,461],{"className":156906},[494],[363,156908,11041],{"className":156909,"style":11129},[407,408],[363,156911,468],{"className":156912},[501],[363,156914],{"className":156915,"style":506},[505],[363,156917,471],{"className":156918},[510],[363,156920],{"className":156921,"style":506},[505],[363,156923,156925,156928,156931,156934,156939,156942,156945,156948,156951],{"className":156924},[398],[363,156926],{"className":156927,"style":487},[402],[363,156929,5160],{"className":156930},[407],[363,156932],{"className":156933,"style":754},[505],[363,156935,4501,156937],{"className":156936},[1831],[363,156938,4505],{"style":4504},[363,156940,461],{"className":156941},[494],[363,156943,11041],{"className":156944,"style":11129},[407,408],[363,156946],{"className":156947,"style":2934},[505],[363,156949,5160],{"className":156950},[2938],[363,156952],{"className":156953,"style":2934},[505],[363,156955,156957,156960,156963],{"className":156956},[398],[363,156958],{"className":156959,"style":487},[402],[363,156961,465],{"className":156962},[407],[363,156964,135982],{"className":156965},[501],"。该值为负，并不矛盾：它是相对于体积为 ",[363,156968,156970,157002],{"className":156969,"translate":367},[366],[363,156971,156973],{"className":156972},[371],[373,156974,156975],{"xmlns":375},[377,156976,156977,156999],{},[380,156978,156979,156981,156983,156985,156987,156989,156991,156993,156995,156997],{},[463,156980,465],{},[383,156982,1288],{"mathvariant":557},[458,156984,461],{"stretchy":460},[383,156986,11041],{},[458,156988,5160],{},[463,156990,465],{},[458,156992,468],{"stretchy":460},[458,156994,135939],{"stretchy":460},[458,156996,7598],{},[463,156998,465],{},[387,157000,157001],{"encoding":389},"1\u002F(K-1)! \u003C 1",[363,157003,157005,157029,157050],{"className":157004,"ariaHidden":394},[393],[363,157006,157008,157011,157014,157017,157020,157023,157026],{"className":157007},[398],[363,157009],{"className":157010,"style":487},[402],[363,157012,8936],{"className":157013},[407],[363,157015,461],{"className":157016},[494],[363,157018,11041],{"className":157019,"style":11129},[407,408],[363,157021],{"className":157022,"style":2934},[505],[363,157024,5160],{"className":157025},[2938],[363,157027],{"className":157028,"style":2934},[505],[363,157030,157032,157035,157038,157041,157044,157047],{"className":157031},[398],[363,157033],{"className":157034,"style":487},[402],[363,157036,465],{"className":157037},[407],[363,157039,135982],{"className":157040},[501],[363,157042],{"className":157043,"style":506},[505],[363,157045,7598],{"className":157046},[510],[363,157048],{"className":157049,"style":506},[505],[363,157051,157053,157056],{"className":157052},[398],[363,157054],{"className":157055,"style":520},[402],[363,157057,465],{"className":157058},[407]," 的支撑集而言的。",[363,157061,157063,157080],{"className":157062,"translate":367},[366],[363,157064,157066],{"className":157065},[371],[373,157067,157068],{"xmlns":375},[377,157069,157070,157078],{},[380,157071,157072,157074,157076],{},[383,157073,45101],{},[458,157075,471],{},[463,157077,465],{},[387,157079,156797],{"encoding":389},[363,157081,157083,157101],{"className":157082,"ariaHidden":394},[393],[363,157084,157086,157089,157092,157095,157098],{"className":157085},[398],[363,157087],{"className":157088,"style":2692},[402],[363,157090,45101],{"className":157091,"style":45131},[407,408],[363,157093],{"className":157094,"style":506},[505],[363,157096,471],{"className":157097},[510],[363,157099],{"className":157100,"style":506},[505],[363,157102,157104,157107],{"className":157103},[398],[363,157105],{"className":157106,"style":520},[402],[363,157108,465],{"className":157109},[407]," 对应单纯形上的",[1572,157112,157113],{},"均匀分布","——一个在其支撑集上平坦、却因支撑集体积小于一而具有负微分熵的密度。一般地，由于 ",[363,157116,157118,157141],{"className":157117,"translate":367},[366],[363,157119,157121],{"className":157120},[371],[373,157122,157123],{"xmlns":375},[377,157124,157125,157139],{},[380,157126,157127],{},[7161,157128,157129,157131],{},[383,157130,126023],{"mathvariant":557},[380,157132,157133,157135,157137],{},[383,157134,11041],{},[458,157136,5160],{},[463,157138,465],{},[387,157140,134774],{"encoding":389},[363,157142,157144],{"className":157143,"ariaHidden":394},[393],[363,157145,157147,157150],{"className":157146},[398],[363,157148],{"className":157149,"style":52432},[402],[363,157151,157153,157156],{"className":157152},[407],[363,157154,126023],{"className":157155},[407],[363,157157,157159],{"className":157158},[629],[363,157160,157162],{"className":157161},[633],[363,157163,157165],{"className":157164},[638],[363,157166,157168],{"className":157167,"style":52432},[642],[363,157169,157170,157173],{"style":7212},[363,157171],{"className":157172,"style":651},[650],[363,157174,157176],{"className":157175},[655,656,657,658],[363,157177,157179,157182,157185],{"className":157178},[407,658],[363,157180,11041],{"className":157181,"style":11129},[407,408,658],[363,157183,5160],{"className":157184},[2938,658],[363,157186,465],{"className":157187},[407,658]," 紧且测度有限，均匀分布是最大熵分布，故",[363,157190,157192],{"className":157191,"translate":367},[528],[363,157193,157195,157250],{"className":157194,"translate":367},[366],[363,157196,157198],{"className":157197},[371],[373,157199,157200],{"xmlns":375,"display":537},[377,157201,157202,157247],{},[380,157203,157204,157206,157208,157210,157212,157214,157216,157218,157220,157222,157224,157226,157228,157230,157232,157235,157237,157239,157241,157243,157245],{},[383,157205,34231],{},[458,157207,461],{"stretchy":460},[383,157209,1121],{"mathvariant":75560},[458,157211,468],{"stretchy":460},[458,157213,10299],{},[458,157215,5160],{},[383,157217,4447],{},[458,157219,4450],{},[383,157221,137171],{"mathvariant":557},[458,157223,461],{"stretchy":460},[383,157225,11041],{},[458,157227,468],{"stretchy":460},[458,157229,898],{"separator":394},[505,157231],{"width":3609},[1644,157233,157234],{},"等号成立",[1644,157236,16251],{},[458,157238,96402],{},[1644,157240,16251],{},[383,157242,45101],{"mathvariant":136008},[458,157244,471],{},[463,157246,465],{"mathvariant":75560},[387,157248,157249],{"encoding":389},"H(\\mathbf{x}) \\le -\\log \\Gamma(K), \\qquad \\text{等号成立} \\iff \\boldsymbol{\\alpha} = \\mathbf{1}",[363,157251,157253,157280,157342,157366],{"className":157252,"ariaHidden":394},[393],[363,157254,157256,157259,157262,157265,157268,157271,157274,157277],{"className":157255},[398],[363,157257],{"className":157258,"style":487},[402],[363,157260,34231],{"className":157261,"style":34385},[407,408],[363,157263,461],{"className":157264},[494],[363,157266,1121],{"className":157267},[407,75905],[363,157269,468],{"className":157270},[501],[363,157272],{"className":157273,"style":506},[505],[363,157275,10299],{"className":157276},[510],[363,157278],{"className":157279,"style":506},[505],[363,157281,157283,157286,157289,157292,157297,157300,157303,157306,157309,157312,157315,157318,157321,157327,157330,157333,157336,157339],{"className":157282},[398],[363,157284],{"className":157285,"style":487},[402],[363,157287,5160],{"className":157288},[407],[363,157290],{"className":157291,"style":754},[505],[363,157293,4501,157295],{"className":157294},[1831],[363,157296,4505],{"style":4504},[363,157298],{"className":157299,"style":754},[505],[363,157301,137171],{"className":157302},[407],[363,157304,461],{"className":157305},[494],[363,157307,11041],{"className":157308,"style":11129},[407,408],[363,157310,468],{"className":157311},[501],[363,157313,898],{"className":157314},[920],[363,157316],{"className":157317,"style":3981},[505],[363,157319],{"className":157320,"style":754},[505],[363,157322,157324],{"className":157323},[407,4945],[363,157325,157234],{"className":157326},[407,4949],[363,157328],{"className":157329,"style":506},[505],[363,157331],{"className":157332,"style":506},[505],[363,157334,96402],{"className":157335},[510],[363,157337],{"className":157338,"style":506},[505],[363,157340],{"className":157341,"style":506},[505],[363,157343,157345,157348,157357,157360,157363],{"className":157344},[398],[363,157346],{"className":157347,"style":135617},[402],[363,157349,157351],{"className":157350},[407],[363,157352,157354],{"className":157353},[407],[363,157355,45101],{"className":157356},[407,136068],[363,157358],{"className":157359,"style":506},[505],[363,157361,471],{"className":157362},[510],[363,157364],{"className":157365,"style":506},[505],[363,157367,157369,157372],{"className":157368},[398],[363,157370],{"className":157371,"style":520},[402],[363,157373,465],{"className":157374},[407,75905],[2658,157376,157378],{"id":157377},"_24-共轭性与贝叶斯更新","2.4 共轭性与贝叶斯更新",[1340,157380,157382],{"title":157381},"命题 2.5（Dirichlet–Multinomial 共轭）",[11,157383,157384,157385,157470,157471,157506,157507,16142,157679,3092,157771,157912,157913],{},"设先验 ",[363,157386,157388,157415],{"className":157387,"translate":367},[366],[363,157389,157391],{"className":157390},[371],[373,157392,157393],{"xmlns":375},[377,157394,157395,157412],{},[380,157396,157397,157400,157402,157404,157406,157408,157410],{},[383,157398,157399],{"mathvariant":136008},"π",[458,157401,9216],{},[383,157403,137065],{"mathvariant":557},[458,157405,4450],{},[458,157407,461],{"stretchy":460},[383,157409,45101],{"mathvariant":136008},[458,157411,468],{"stretchy":460},[387,157413,157414],{"encoding":389},"\\boldsymbol{\\pi} \\sim \\operatorname{Dir}(\\boldsymbol{\\alpha})",[363,157416,157418,157443],{"className":157417,"ariaHidden":394},[393],[363,157419,157421,157424,157434,157437,157440],{"className":157420},[398],[363,157422],{"className":157423,"style":135617},[402],[363,157425,157427],{"className":157426},[407],[363,157428,157430],{"className":157429},[407],[363,157431,157399],{"className":157432,"style":157433},[407,136068],"margin-right:0.037em;",[363,157435],{"className":157436,"style":506},[505],[363,157438,9216],{"className":157439},[510],[363,157441],{"className":157442,"style":506},[505],[363,157444,157446,157449,157455,157458,157467],{"className":157445},[398],[363,157447],{"className":157448,"style":487},[402],[363,157450,157452],{"className":157451},[1831],[363,157453,137065],{"className":157454},[407,33009],[363,157456,461],{"className":157457},[494],[363,157459,157461],{"className":157460},[407],[363,157462,157464],{"className":157463},[407],[363,157465,45101],{"className":157466},[407,136068],[363,157468,468],{"className":157469},[501],"，给定 ",[363,157472,157474,157488],{"className":157473,"translate":367},[366],[363,157475,157477],{"className":157476},[371],[373,157478,157479],{"xmlns":375},[377,157480,157481,157485],{},[380,157482,157483],{},[383,157484,157399],{"mathvariant":136008},[387,157486,157487],{"encoding":389},"\\boldsymbol{\\pi}",[363,157489,157491],{"className":157490,"ariaHidden":394},[393],[363,157492,157494,157497],{"className":157493},[398],[363,157495],{"className":157496,"style":135617},[402],[363,157498,157500],{"className":157499},[407],[363,157501,157503],{"className":157502},[407],[363,157504,157399],{"className":157505,"style":157433},[407,136068]," 观测到计数向量 ",[363,157508,157510,157548],{"className":157509,"translate":367},[366],[363,157511,157513],{"className":157512},[371],[373,157514,157515],{"xmlns":375},[377,157516,157517,157545],{},[380,157518,157519,157521,157523,157525,157531,157533,157535,157537,157543],{},[383,157520,82643],{"mathvariant":75560},[458,157522,471],{},[458,157524,461],{"stretchy":460},[543,157526,157527,157529],{},[383,157528,82643],{},[463,157530,465],{},[458,157532,898],{"separator":394},[458,157534,133107],{},[458,157536,898],{"separator":394},[543,157538,157539,157541],{},[383,157540,82643],{},[383,157542,11041],{},[458,157544,468],{"stretchy":460},[387,157546,157547],{"encoding":389},"\\mathbf{n} = (n_1, \\dots, n_K)",[363,157549,157551,157569],{"className":157550,"ariaHidden":394},[393],[363,157552,157554,157557,157560,157563,157566],{"className":157553},[398],[363,157555],{"className":157556,"style":135617},[402],[363,157558,82643],{"className":157559},[407,75905],[363,157561],{"className":157562,"style":506},[505],[363,157564,471],{"className":157565},[510],[363,157567],{"className":157568,"style":506},[505],[363,157570,157572,157575,157578,157618,157621,157624,157627,157630,157633,157636,157676],{"className":157571},[398],[363,157573],{"className":157574,"style":487},[402],[363,157576,461],{"className":157577},[494],[363,157579,157581,157584],{"className":157580},[407],[363,157582,82643],{"className":157583},[407,408],[363,157585,157587],{"className":157586},[629],[363,157588,157590,157610],{"className":157589},[633,634],[363,157591,157593,157607],{"className":157592},[638],[363,157594,157596],{"className":157595,"style":11480},[642],[363,157597,157598,157601],{"style":730},[363,157599],{"className":157600,"style":651},[650],[363,157602,157604],{"className":157603},[655,656,657,658],[363,157605,465],{"className":157606},[407,658],[363,157608,666],{"className":157609},[665],[363,157611,157613],{"className":157612},[638],[363,157614,157616],{"className":157615,"style":8315},[642],[363,157617],{},[363,157619,898],{"className":157620},[920],[363,157622],{"className":157623,"style":754},[505],[363,157625,133107],{"className":157626},[758],[363,157628],{"className":157629,"style":754},[505],[363,157631,898],{"className":157632},[920],[363,157634],{"className":157635,"style":754},[505],[363,157637,157639,157642],{"className":157638},[407],[363,157640,82643],{"className":157641},[407,408],[363,157643,157645],{"className":157644},[629],[363,157646,157648,157668],{"className":157647},[633,634],[363,157649,157651,157665],{"className":157650},[638],[363,157652,157654],{"className":157653,"style":727},[642],[363,157655,157656,157659],{"style":730},[363,157657],{"className":157658,"style":651},[650],[363,157660,157662],{"className":157661},[655,656,657,658],[363,157663,11041],{"className":157664,"style":11129},[407,408,658],[363,157666,666],{"className":157667},[665],[363,157669,157671],{"className":157670},[638],[363,157672,157674],{"className":157673,"style":8315},[642],[363,157675],{},[363,157677,468],{"className":157678},[501],[363,157680,157682,157704],{"className":157681,"translate":367},[366],[363,157683,157685],{"className":157684},[371],[373,157686,157687],{"xmlns":375},[377,157688,157689,157701],{},[380,157690,157691,157697,157699],{},[543,157692,157693,157695],{},[383,157694,82643],{},[383,157696,12310],{},[458,157698,6256],{},[383,157700,38631],{"mathvariant":570},[387,157702,157703],{"encoding":389},"n_i \\in \\mathbb{N}",[363,157705,157707,157762],{"className":157706,"ariaHidden":394},[393],[363,157708,157710,157713,157753,157756,157759],{"className":157709},[398],[363,157711],{"className":157712,"style":134669},[402],[363,157714,157716,157719],{"className":157715},[407],[363,157717,82643],{"className":157718},[407,408],[363,157720,157722],{"className":157721},[629],[363,157723,157725,157745],{"className":157724},[633,634],[363,157726,157728,157742],{"className":157727},[638],[363,157729,157731],{"className":157730,"style":12529},[642],[363,157732,157733,157736],{"style":730},[363,157734],{"className":157735,"style":651},[650],[363,157737,157739],{"className":157738},[655,656,657,658],[363,157740,12310],{"className":157741},[407,408,658],[363,157743,666],{"className":157744},[665],[363,157746,157748],{"className":157747},[638],[363,157749,157751],{"className":157750,"style":8315},[642],[363,157752],{},[363,157754],{"className":157755,"style":506},[505],[363,157757,6256],{"className":157758},[510],[363,157760],{"className":157761,"style":506},[505],[363,157763,157765,157768],{"className":157764},[398],[363,157766],{"className":157767,"style":1443},[402],[363,157769,38631],{"className":157770},[407,714],[363,157772,157774,157802],{"className":157773,"translate":367},[366],[363,157775,157777],{"className":157776},[371],[373,157778,157779],{"xmlns":375},[377,157780,157781,157799],{},[380,157782,157783,157785,157787,157793],{},[383,157784,38631],{},[458,157786,471],{},[543,157788,157789,157791],{},[458,157790,13808],{},[383,157792,12310],{},[543,157794,157795,157797],{},[383,157796,82643],{},[383,157798,12310],{},[387,157800,157801],{"encoding":389},"N = \\sum_i n_i",[363,157803,157805,157823],{"className":157804,"ariaHidden":394},[393],[363,157806,157808,157811,157814,157817,157820],{"className":157807},[398],[363,157809],{"className":157810,"style":1011},[402],[363,157812,38631],{"className":157813,"style":25948},[407,408],[363,157815],{"className":157816,"style":506},[505],[363,157818,471],{"className":157819},[510],[363,157821],{"className":157822,"style":506},[505],[363,157824,157826,157829,157869,157872],{"className":157825},[398],[363,157827],{"className":157828,"style":138904},[402],[363,157830,157832,157835],{"className":157831},[1831],[363,157833,13808],{"className":157834,"style":40007},[1831,1832,5963],[363,157836,157838],{"className":157837},[629],[363,157839,157841,157861],{"className":157840},[633,634],[363,157842,157844,157858],{"className":157843},[638],[363,157845,157847],{"className":157846,"style":40020},[642],[363,157848,157849,157852],{"style":40023},[363,157850],{"className":157851,"style":651},[650],[363,157853,157855],{"className":157854},[655,656,657,658],[363,157856,12310],{"className":157857},[407,408,658],[363,157859,666],{"className":157860},[665],[363,157862,157864],{"className":157863},[638],[363,157865,157867],{"className":157866,"style":40042},[642],[363,157868],{},[363,157870],{"className":157871,"style":754},[505],[363,157873,157875,157878],{"className":157874},[407],[363,157876,82643],{"className":157877},[407,408],[363,157879,157881],{"className":157880},[629],[363,157882,157884,157904],{"className":157883},[633,634],[363,157885,157887,157901],{"className":157886},[638],[363,157888,157890],{"className":157889,"style":12529},[642],[363,157891,157892,157895],{"style":730},[363,157893],{"className":157894,"style":651},[650],[363,157896,157898],{"className":157897},[655,656,657,658],[363,157899,12310],{"className":157900},[407,408,658],[363,157902,666],{"className":157903},[665],[363,157905,157907],{"className":157906},[638],[363,157908,157910],{"className":157909,"style":8315},[642],[363,157911],{},"），则后验为\n",[363,157914,157916,157950],{"className":157915,"translate":367},[366],[363,157917,157919],{"className":157918},[371],[373,157920,157921],{"xmlns":375},[377,157922,157923,157947],{},[380,157924,157925,157927,157929,157931,157933,157935,157937,157939,157941,157943,157945],{},[383,157926,157399],{"mathvariant":136008},[458,157928,5155],{},[383,157930,82643],{"mathvariant":75560},[458,157932,9216],{},[383,157934,137065],{"mathvariant":557},[458,157936,4450],{},[458,157938,461],{"stretchy":460},[383,157940,45101],{"mathvariant":136008},[458,157942,2817],{},[383,157944,82643],{"mathvariant":75560},[458,157946,468],{"stretchy":460},[387,157948,157949],{"encoding":389},"\\boldsymbol{\\pi} \\mid \\mathbf{n} \\sim \\operatorname{Dir}(\\boldsymbol{\\alpha} + \\mathbf{n})",[363,157951,157953,157977,157995,158028],{"className":157952,"ariaHidden":394},[393],[363,157954,157956,157959,157968,157971,157974],{"className":157955},[398],[363,157957],{"className":157958,"style":487},[402],[363,157960,157962],{"className":157961},[407],[363,157963,157965],{"className":157964},[407],[363,157966,157399],{"className":157967,"style":157433},[407,136068],[363,157969],{"className":157970,"style":506},[505],[363,157972,5155],{"className":157973},[510],[363,157975],{"className":157976,"style":506},[505],[363,157978,157980,157983,157986,157989,157992],{"className":157979},[398],[363,157981],{"className":157982,"style":135617},[402],[363,157984,82643],{"className":157985},[407,75905],[363,157987],{"className":157988,"style":506},[505],[363,157990,9216],{"className":157991},[510],[363,157993],{"className":157994,"style":506},[505],[363,157996,157998,158001,158007,158010,158019,158022,158025],{"className":157997},[398],[363,157999],{"className":158000,"style":487},[402],[363,158002,158004],{"className":158003},[1831],[363,158005,137065],{"className":158006},[407,33009],[363,158008,461],{"className":158009},[494],[363,158011,158013],{"className":158012},[407],[363,158014,158016],{"className":158015},[407],[363,158017,45101],{"className":158018},[407,136068],[363,158020],{"className":158021,"style":2934},[505],[363,158023,2817],{"className":158024},[2938],[363,158026],{"className":158027,"style":2934},[505],[363,158029,158031,158034,158037],{"className":158030},[398],[363,158032],{"className":158033,"style":487},[402],[363,158035,82643],{"className":158036},[407,75905],[363,158038,468],{"className":158039},[501],[11,158041,158042,158044,158045,158222],{},[1572,158043,137993],{}," 多项似然正比于 ",[363,158046,158048,158078],{"className":158047,"translate":367},[366],[363,158049,158051],{"className":158050},[371],[373,158052,158053],{"xmlns":375},[377,158054,158055,158075],{},[380,158056,158057,158063],{},[543,158058,158059,158061],{},[458,158060,136637],{},[383,158062,12310],{},[7900,158064,158065,158067,158069],{},[383,158066,157399],{},[383,158068,12310],{},[543,158070,158071,158073],{},[383,158072,82643],{},[383,158074,12310],{},[387,158076,158077],{"encoding":389},"\\prod_i \\pi_i^{n_i}",[363,158079,158081],{"className":158080,"ariaHidden":394},[393],[363,158082,158084,158087,158127,158130],{"className":158083},[398],[363,158085],{"className":158086,"style":138904},[402],[363,158088,158090,158093],{"className":158089},[1831],[363,158091,136637],{"className":158092,"style":40007},[1831,1832,5963],[363,158094,158096],{"className":158095},[629],[363,158097,158099,158119],{"className":158098},[633,634],[363,158100,158102,158116],{"className":158101},[638],[363,158103,158105],{"className":158104,"style":40020},[642],[363,158106,158107,158110],{"style":40023},[363,158108],{"className":158109,"style":651},[650],[363,158111,158113],{"className":158112},[655,656,657,658],[363,158114,12310],{"className":158115},[407,408,658],[363,158117,666],{"className":158118},[665],[363,158120,158122],{"className":158121},[638],[363,158123,158125],{"className":158124,"style":40042},[642],[363,158126],{},[363,158128],{"className":158129,"style":754},[505],[363,158131,158133,158136],{"className":158132},[407],[363,158134,157399],{"className":158135,"style":1328},[407,408],[363,158137,158139],{"className":158138},[629],[363,158140,158142,158214],{"className":158141},[633,634],[363,158143,158145,158211],{"className":158144},[638],[363,158146,158148,158160],{"className":158147,"style":45806},[642],[363,158149,158151,158154],{"style":158150},"top:-2.4231em;margin-left:-0.0359em;margin-right:0.05em;",[363,158152],{"className":158153,"style":651},[650],[363,158155,158157],{"className":158156},[655,656,657,658],[363,158158,12310],{"className":158159},[407,408,658],[363,158161,158162,158165],{"style":136912},[363,158163],{"className":158164,"style":651},[650],[363,158166,158168],{"className":158167},[655,656,657,658],[363,158169,158171],{"className":158170},[407,658],[363,158172,158174,158177],{"className":158173},[407,658],[363,158175,82643],{"className":158176},[407,408,658],[363,158178,158180],{"className":158179},[629],[363,158181,158183,158203],{"className":158182},[633,634],[363,158184,158186,158200],{"className":158185},[638],[363,158187,158189],{"className":158188,"style":40095},[642],[363,158190,158191,158194],{"style":74612},[363,158192],{"className":158193,"style":30553},[650],[363,158195,158197],{"className":158196},[655,30557,10021,658],[363,158198,12310],{"className":158199},[407,408,658],[363,158201,666],{"className":158202},[665],[363,158204,158206],{"className":158205},[638],[363,158207,158209],{"className":158208,"style":40117},[642],[363,158210],{},[363,158212,666],{"className":158213},[665],[363,158215,158217],{"className":158216},[638],[363,158218,158220],{"className":158219,"style":136978},[642],[363,158221],{},"，与先验密度相乘得",[363,158224,158226],{"className":158225,"translate":367},[528],[363,158227,158229,158296],{"className":158228,"translate":367},[366],[363,158230,158232],{"className":158231},[371],[373,158233,158234],{"xmlns":375,"display":537},[377,158235,158236,158293],{},[380,158237,158238,158240,158242,158244,158246,158248,158250,158253,158267],{},[383,158239,11],{},[458,158241,461],{"stretchy":460},[383,158243,157399],{"mathvariant":136008},[458,158245,5155],{},[383,158247,82643],{"mathvariant":75560},[458,158249,468],{"stretchy":460},[458,158251,158252],{},"∝",[48667,158254,158255,158257,158265],{},[458,158256,136637],{},[380,158258,158259,158261,158263],{},[383,158260,12310],{},[458,158262,471],{},[463,158264,465],{},[383,158266,11041],{},[7900,158268,158269,158271,158273],{},[383,158270,157399],{},[383,158272,12310],{},[380,158274,158275,158281,158283,158289,158291],{},[543,158276,158277,158279],{},[383,158278,45101],{},[383,158280,12310],{},[458,158282,2817],{},[543,158284,158285,158287],{},[383,158286,82643],{},[383,158288,12310],{},[458,158290,5160],{},[463,158292,465],{},[387,158294,158295],{"encoding":389},"p(\\boldsymbol{\\pi} \\mid \\mathbf{n}) \\propto \\prod_{i=1}^K \\pi_i^{\\alpha_i + n_i - 1}",[363,158297,158299,158329,158350],{"className":158298,"ariaHidden":394},[393],[363,158300,158302,158305,158308,158311,158320,158323,158326],{"className":158301},[398],[363,158303],{"className":158304,"style":487},[402],[363,158306,11],{"className":158307},[407,408],[363,158309,461],{"className":158310},[494],[363,158312,158314],{"className":158313},[407],[363,158315,158317],{"className":158316},[407],[363,158318,157399],{"className":158319,"style":157433},[407,136068],[363,158321],{"className":158322,"style":506},[505],[363,158324,5155],{"className":158325},[510],[363,158327],{"className":158328,"style":506},[505],[363,158330,158332,158335,158338,158341,158344,158347],{"className":158331},[398],[363,158333],{"className":158334,"style":487},[402],[363,158336,82643],{"className":158337},[407,75905],[363,158339,468],{"className":158340},[501],[363,158342],{"className":158343,"style":506},[505],[363,158345,158252],{"className":158346},[510],[363,158348],{"className":158349,"style":506},[505],[363,158351,158353,158356,158420,158423],{"className":158352},[398],[363,158354],{"className":158355,"style":138212},[402],[363,158357,158359],{"className":158358},[1831,14063],[363,158360,158362,158412],{"className":158361},[633,634],[363,158363,158365,158409],{"className":158364},[638],[363,158366,158368,158388,158398],{"className":158367,"style":138225},[642],[363,158369,158370,158373],{"style":14076},[363,158371],{"className":158372,"style":14080},[650],[363,158374,158376],{"className":158375},[655,656,657,658],[363,158377,158379,158382,158385],{"className":158378},[407,658],[363,158380,12310],{"className":158381},[407,408,658],[363,158383,471],{"className":158384},[510,658],[363,158386,465],{"className":158387},[407,658],[363,158389,158390,158393],{"style":14089},[363,158391],{"className":158392,"style":14080},[650],[363,158394,158395],{},[363,158396,136637],{"className":158397},[1831,1832,1833],[363,158399,158400,158403],{"style":100671},[363,158401],{"className":158402,"style":14080},[650],[363,158404,158406],{"className":158405},[655,656,657,658],[363,158407,11041],{"className":158408,"style":11129},[407,408,658],[363,158410,666],{"className":158411},[665],[363,158413,158415],{"className":158414},[638],[363,158416,158418],{"className":158417,"style":14107},[642],[363,158419],{},[363,158421],{"className":158422,"style":754},[505],[363,158424,158426,158429],{"className":158425},[407],[363,158427,157399],{"className":158428,"style":1328},[407,408],[363,158430,158432],{"className":158431},[629],[363,158433,158435,158555],{"className":158434},[633,634],[363,158436,158438,158552],{"className":158437},[638],[363,158439,158441,158452],{"className":158440,"style":136897},[642],[363,158442,158443,158446],{"style":158150},[363,158444],{"className":158445,"style":651},[650],[363,158447,158449],{"className":158448},[655,656,657,658],[363,158450,12310],{"className":158451},[407,408,658],[363,158453,158454,158457],{"style":136912},[363,158455],{"className":158456,"style":651},[650],[363,158458,158460],{"className":158459},[655,656,657,658],[363,158461,158463,158503,158506,158546,158549],{"className":158462},[407,658],[363,158464,158466,158469],{"className":158465},[407,658],[363,158467,45101],{"className":158468,"style":45131},[407,408,658],[363,158470,158472],{"className":158471},[629],[363,158473,158475,158495],{"className":158474},[633,634],[363,158476,158478,158492],{"className":158477},[638],[363,158479,158481],{"className":158480,"style":40095},[642],[363,158482,158483,158486],{"style":136942},[363,158484],{"className":158485,"style":30553},[650],[363,158487,158489],{"className":158488},[655,30557,10021,658],[363,158490,12310],{"className":158491},[407,408,658],[363,158493,666],{"className":158494},[665],[363,158496,158498],{"className":158497},[638],[363,158499,158501],{"className":158500,"style":40117},[642],[363,158502],{},[363,158504,2817],{"className":158505},[2938,658],[363,158507,158509,158512],{"className":158508},[407,658],[363,158510,82643],{"className":158511},[407,408,658],[363,158513,158515],{"className":158514},[629],[363,158516,158518,158538],{"className":158517},[633,634],[363,158519,158521,158535],{"className":158520},[638],[363,158522,158524],{"className":158523,"style":40095},[642],[363,158525,158526,158529],{"style":74612},[363,158527],{"className":158528,"style":30553},[650],[363,158530,158532],{"className":158531},[655,30557,10021,658],[363,158533,12310],{"className":158534},[407,408,658],[363,158536,666],{"className":158537},[665],[363,158539,158541],{"className":158540},[638],[363,158542,158544],{"className":158543,"style":40117},[642],[363,158545],{},[363,158547,5160],{"className":158548},[2938,658],[363,158550,465],{"className":158551},[407,658],[363,158553,666],{"className":158554},[665],[363,158556,158558],{"className":158557},[638],[363,158559,158561],{"className":158560,"style":136978},[642],[363,158562],{},[11,158564,158565,158566,158643],{},"该核与 ",[363,158567,158569,158595],{"className":158568,"translate":367},[366],[363,158570,158572],{"className":158571},[371],[373,158573,158574],{"xmlns":375},[377,158575,158576,158592],{},[380,158577,158578,158580,158582,158584,158586,158588,158590],{},[383,158579,137065],{"mathvariant":557},[458,158581,4450],{},[458,158583,461],{"stretchy":460},[383,158585,45101],{"mathvariant":136008},[458,158587,2817],{},[383,158589,82643],{"mathvariant":75560},[458,158591,468],{"stretchy":460},[387,158593,158594],{"encoding":389},"\\operatorname{Dir}(\\boldsymbol{\\alpha} + \\mathbf{n})",[363,158596,158598,158631],{"className":158597,"ariaHidden":394},[393],[363,158599,158601,158604,158610,158613,158622,158625,158628],{"className":158600},[398],[363,158602],{"className":158603,"style":487},[402],[363,158605,158607],{"className":158606},[1831],[363,158608,137065],{"className":158609},[407,33009],[363,158611,461],{"className":158612},[494],[363,158614,158616],{"className":158615},[407],[363,158617,158619],{"className":158618},[407],[363,158620,45101],{"className":158621},[407,136068],[363,158623],{"className":158624,"style":2934},[505],[363,158626,2817],{"className":158627},[2938],[363,158629],{"className":158630,"style":2934},[505],[363,158632,158634,158637,158640],{"className":158633},[398],[363,158635],{"className":158636,"style":487},[402],[363,158638,82643],{"className":158639},[407,75905],[363,158641,468],{"className":158642},[501]," 的核成比例，归一化即得。",[11,158645,158646],{},"由共轭性可立即导出两个推论，它们在应用中的地位不低于命题本身。",[1340,158648,158650],{"title":158649},"推论 2.6（Dirichlet–Multinomial 分布）",[11,158651,158652,158653,158681,158682],{},"计数向量 ",[363,158654,158656,158669],{"className":158655,"translate":367},[366],[363,158657,158659],{"className":158658},[371],[373,158660,158661],{"xmlns":375},[377,158662,158663,158667],{},[380,158664,158665],{},[383,158666,82643],{"mathvariant":75560},[387,158668,147358],{"encoding":389},[363,158670,158672],{"className":158671,"ariaHidden":394},[393],[363,158673,158675,158678],{"className":158674},[398],[363,158676],{"className":158677,"style":135617},[402],[363,158679,82643],{"className":158680},[407,75905]," 的边缘似然为\n",[363,158683,158685,158851],{"className":158684,"translate":367},[366],[363,158686,158688],{"className":158687},[371],[373,158689,158690],{"xmlns":375},[377,158691,158692,158848],{},[380,158693,158694,158696,158698,158700,158702,158704,158706,158708,158732,158734,158760,158762,158796,158810],{},[383,158695,11],{},[458,158697,461],{"stretchy":460},[383,158699,82643],{"mathvariant":75560},[458,158701,5155],{},[383,158703,45101],{"mathvariant":136008},[458,158705,468],{"stretchy":460},[458,158707,471],{},[586,158709,158710,158716],{},[380,158711,158712,158714],{},[383,158713,38631],{},[458,158715,135939],{"stretchy":460},[380,158717,158718,158724,158730],{},[543,158719,158720,158722],{},[458,158721,136637],{},[383,158723,12310],{},[543,158725,158726,158728],{},[383,158727,82643],{},[383,158729,12310],{},[458,158731,135939],{"stretchy":460},[458,158733,3646],{},[586,158735,158736,158750],{},[380,158737,158738,158740,158742,158744,158746,158748],{},[383,158739,39638],{},[458,158741,461],{"stretchy":460},[383,158743,45101],{"mathvariant":136008},[458,158745,2817],{},[383,158747,82643],{"mathvariant":75560},[458,158749,468],{"stretchy":460},[380,158751,158752,158754,158756,158758],{},[383,158753,39638],{},[458,158755,461],{"stretchy":460},[383,158757,45101],{"mathvariant":136008},[458,158759,468],{"stretchy":460},[458,158761,471],{},[586,158763,158764,158778],{},[380,158765,158766,158768,158770,158776],{},[383,158767,137171],{"mathvariant":557},[458,158769,461],{"stretchy":460},[543,158771,158772,158774],{},[383,158773,45101],{},[463,158775,474],{},[458,158777,468],{"stretchy":460},[380,158779,158780,158782,158784,158790,158792,158794],{},[383,158781,137171],{"mathvariant":557},[458,158783,461],{"stretchy":460},[543,158785,158786,158788],{},[383,158787,45101],{},[463,158789,474],{},[458,158791,2817],{},[383,158793,38631],{},[458,158795,468],{"stretchy":460},[7900,158797,158798,158800,158808],{},[458,158799,136637],{},[380,158801,158802,158804,158806],{},[383,158803,12310],{},[458,158805,471],{},[463,158807,465],{},[383,158809,11041],{},[586,158811,158812,158834],{},[380,158813,158814,158816,158818,158824,158826,158832],{},[383,158815,137171],{"mathvariant":557},[458,158817,461],{"stretchy":460},[543,158819,158820,158822],{},[383,158821,45101],{},[383,158823,12310],{},[458,158825,2817],{},[543,158827,158828,158830],{},[383,158829,82643],{},[383,158831,12310],{},[458,158833,468],{"stretchy":460},[380,158835,158836,158838,158840,158846],{},[383,158837,137171],{"mathvariant":557},[458,158839,461],{"stretchy":460},[543,158841,158842,158844],{},[383,158843,45101],{},[383,158845,12310],{},[458,158847,468],{"stretchy":460},[387,158849,158850],{"encoding":389},"p(\\mathbf{n} \\mid \\boldsymbol{\\alpha}) = \\frac{N!}{\\prod_i n_i!} \\cdot \\frac{B(\\boldsymbol{\\alpha} + \\mathbf{n})}{B(\\boldsymbol{\\alpha})} = \\frac{\\Gamma(\\alpha_0)}{\\Gamma(\\alpha_0 + N)} \\prod_{i=1}^K \\frac{\\Gamma(\\alpha_i + n_i)}{\\Gamma(\\alpha_i)}",[363,158852,158854,158878,158905,159076,159195],{"className":158853,"ariaHidden":394},[393],[363,158855,158857,158860,158863,158866,158869,158872,158875],{"className":158856},[398],[363,158858],{"className":158859,"style":487},[402],[363,158861,11],{"className":158862},[407,408],[363,158864,461],{"className":158865},[494],[363,158867,82643],{"className":158868},[407,75905],[363,158870],{"className":158871,"style":506},[505],[363,158873,5155],{"className":158874},[510],[363,158876],{"className":158877,"style":506},[505],[363,158879,158881,158884,158893,158896,158899,158902],{"className":158880},[398],[363,158882],{"className":158883,"style":487},[402],[363,158885,158887],{"className":158886},[407],[363,158888,158890],{"className":158889},[407],[363,158891,45101],{"className":158892},[407,136068],[363,158894,468],{"className":158895},[501],[363,158897],{"className":158898,"style":506},[505],[363,158900,471],{"className":158901},[510],[363,158903],{"className":158904,"style":506},[505],[363,158906,158908,158912,159067,159070,159073],{"className":158907},[398],[363,158909],{"className":158910,"style":158911},[402],"height:1.4501em;vertical-align:-0.57em;",[363,158913,158915,158918,159064],{"className":158914},[407],[363,158916],{"className":158917},[494,789],[363,158919,158921],{"className":158920},[586],[363,158922,158924,159055],{"className":158923},[633,634],[363,158925,158927,159052],{"className":158926},[638],[363,158928,158930,159027,159035],{"className":158929,"style":3034},[642],[363,158931,158932,158935],{"style":2874},[363,158933],{"className":158934,"style":809},[650],[363,158936,158938],{"className":158937},[655,656,657,658],[363,158939,158941,158981,158984,159024],{"className":158940},[407,658],[363,158942,158944,158947],{"className":158943},[1831,658],[363,158945,136637],{"className":158946,"style":40007},[1831,1832,5963,658],[363,158948,158950],{"className":158949},[629],[363,158951,158953,158973],{"className":158952},[633,634],[363,158954,158956,158970],{"className":158955},[638],[363,158957,158959],{"className":158958,"style":140312},[642],[363,158960,158961,158964],{"style":137374},[363,158962],{"className":158963,"style":30553},[650],[363,158965,158967],{"className":158966},[655,30557,10021,658],[363,158968,12310],{"className":158969},[407,408,658],[363,158971,666],{"className":158972},[665],[363,158974,158976],{"className":158975},[638],[363,158977,158979],{"className":158978,"style":137413},[642],[363,158980],{},[363,158982],{"className":158983,"style":42713},[505,658],[363,158985,158987,158990],{"className":158986},[407,658],[363,158988,82643],{"className":158989},[407,408,658],[363,158991,158993],{"className":158992},[629],[363,158994,158996,159016],{"className":158995},[633,634],[363,158997,158999,159013],{"className":158998},[638],[363,159000,159002],{"className":159001,"style":40095},[642],[363,159003,159004,159007],{"style":74612},[363,159005],{"className":159006,"style":30553},[650],[363,159008,159010],{"className":159009},[655,30557,10021,658],[363,159011,12310],{"className":159012},[407,408,658],[363,159014,666],{"className":159015},[665],[363,159017,159019],{"className":159018},[638],[363,159020,159022],{"className":159021,"style":40117},[642],[363,159023],{},[363,159025,135939],{"className":159026},[501,658],[363,159028,159029,159032],{"style":821},[363,159030],{"className":159031,"style":809},[650],[363,159033],{"className":159034,"style":829},[828],[363,159036,159037,159040],{"style":2897},[363,159038],{"className":159039,"style":809},[650],[363,159041,159043],{"className":159042},[655,656,657,658],[363,159044,159046,159049],{"className":159045},[407,658],[363,159047,38631],{"className":159048,"style":25948},[407,408,658],[363,159050,135939],{"className":159051},[501,658],[363,159053,666],{"className":159054},[665],[363,159056,159058],{"className":159057},[638],[363,159059,159062],{"className":159060,"style":159061},[642],"height:0.57em;",[363,159063],{},[363,159065],{"className":159066},[501,789],[363,159068],{"className":159069,"style":2934},[505],[363,159071,3646],{"className":159072},[2938],[363,159074],{"className":159075,"style":2934},[505],[363,159077,159079,159082,159186,159189,159192],{"className":159078},[398],[363,159080],{"className":159081,"style":150425},[402],[363,159083,159085,159088,159183],{"className":159084},[407],[363,159086],{"className":159087},[494,789],[363,159089,159091],{"className":159090},[586],[363,159092,159094,159175],{"className":159093},[633,634],[363,159095,159097,159172],{"className":159096},[638],[363,159098,159100,159129,159137],{"className":159099,"style":26740},[642],[363,159101,159102,159105],{"style":2874},[363,159103],{"className":159104,"style":809},[650],[363,159106,159108],{"className":159107},[655,656,657,658],[363,159109,159111,159114,159117,159126],{"className":159110},[407,658],[363,159112,39638],{"className":159113,"style":39734},[407,408,658],[363,159115,461],{"className":159116},[494,658],[363,159118,159120],{"className":159119},[407,658],[363,159121,159123],{"className":159122},[407,658],[363,159124,45101],{"className":159125},[407,136068,658],[363,159127,468],{"className":159128},[501,658],[363,159130,159131,159134],{"style":821},[363,159132],{"className":159133,"style":809},[650],[363,159135],{"className":159136,"style":829},[828],[363,159138,159139,159142],{"style":26765},[363,159140],{"className":159141,"style":809},[650],[363,159143,159145],{"className":159144},[655,656,657,658],[363,159146,159148,159151,159154,159163,159166,159169],{"className":159147},[407,658],[363,159149,39638],{"className":159150,"style":39734},[407,408,658],[363,159152,461],{"className":159153},[494,658],[363,159155,159157],{"className":159156},[407,658],[363,159158,159160],{"className":159159},[407,658],[363,159161,45101],{"className":159162},[407,136068,658],[363,159164,2817],{"className":159165},[2938,658],[363,159167,82643],{"className":159168},[407,75905,658],[363,159170,468],{"className":159171},[501,658],[363,159173,666],{"className":159174},[665],[363,159176,159178],{"className":159177},[638],[363,159179,159181],{"className":159180,"style":45949},[642],[363,159182],{},[363,159184],{"className":159185},[501,789],[363,159187],{"className":159188,"style":506},[505],[363,159190,471],{"className":159191},[510],[363,159193],{"className":159194,"style":506},[505],[363,159196,159198,159201,159367,159370,159430,159433],{"className":159197},[398],[363,159199],{"className":159200,"style":150425},[402],[363,159202,159204,159207,159364],{"className":159203},[407],[363,159205],{"className":159206},[494,789],[363,159208,159210],{"className":159209},[586],[363,159211,159213,159356],{"className":159212},[633,634],[363,159214,159216,159353],{"className":159215},[638],[363,159217,159219,159285,159293],{"className":159218,"style":26740},[642],[363,159220,159221,159224],{"style":2874},[363,159222],{"className":159223,"style":809},[650],[363,159225,159227],{"className":159226},[655,656,657,658],[363,159228,159230,159233,159236,159276,159279,159282],{"className":159229},[407,658],[363,159231,137171],{"className":159232},[407,658],[363,159234,461],{"className":159235},[494,658],[363,159237,159239,159242],{"className":159238},[407,658],[363,159240,45101],{"className":159241,"style":45131},[407,408,658],[363,159243,159245],{"className":159244},[629],[363,159246,159248,159268],{"className":159247},[633,634],[363,159249,159251,159265],{"className":159250},[638],[363,159252,159254],{"className":159253,"style":137304},[642],[363,159255,159256,159259],{"style":136942},[363,159257],{"className":159258,"style":30553},[650],[363,159260,159262],{"className":159261},[655,30557,10021,658],[363,159263,474],{"className":159264},[407,658],[363,159266,666],{"className":159267},[665],[363,159269,159271],{"className":159270},[638],[363,159272,159274],{"className":159273,"style":40117},[642],[363,159275],{},[363,159277,2817],{"className":159278},[2938,658],[363,159280,38631],{"className":159281,"style":25948},[407,408,658],[363,159283,468],{"className":159284},[501,658],[363,159286,159287,159290],{"style":821},[363,159288],{"className":159289,"style":809},[650],[363,159291],{"className":159292,"style":829},[828],[363,159294,159295,159298],{"style":26765},[363,159296],{"className":159297,"style":809},[650],[363,159299,159301],{"className":159300},[655,656,657,658],[363,159302,159304,159307,159310,159350],{"className":159303},[407,658],[363,159305,137171],{"className":159306},[407,658],[363,159308,461],{"className":159309},[494,658],[363,159311,159313,159316],{"className":159312},[407,658],[363,159314,45101],{"className":159315,"style":45131},[407,408,658],[363,159317,159319],{"className":159318},[629],[363,159320,159322,159342],{"className":159321},[633,634],[363,159323,159325,159339],{"className":159324},[638],[363,159326,159328],{"className":159327,"style":137304},[642],[363,159329,159330,159333],{"style":136942},[363,159331],{"className":159332,"style":30553},[650],[363,159334,159336],{"className":159335},[655,30557,10021,658],[363,159337,474],{"className":159338},[407,658],[363,159340,666],{"className":159341},[665],[363,159343,159345],{"className":159344},[638],[363,159346,159348],{"className":159347,"style":40117},[642],[363,159349],{},[363,159351,468],{"className":159352},[501,658],[363,159354,666],{"className":159355},[665],[363,159357,159359],{"className":159358},[638],[363,159360,159362],{"className":159361,"style":45949},[642],[363,159363],{},[363,159365],{"className":159366},[501,789],[363,159368],{"className":159369,"style":754},[505],[363,159371,159373,159376],{"className":159372},[1831],[363,159374,136637],{"className":159375,"style":40007},[1831,1832,5963],[363,159377,159379],{"className":159378},[629],[363,159380,159382,159422],{"className":159381},[633,634],[363,159383,159385,159419],{"className":159384},[638],[363,159386,159388,159408],{"className":159387,"style":133494},[642],[363,159389,159390,159393],{"style":40023},[363,159391],{"className":159392,"style":651},[650],[363,159394,159396],{"className":159395},[655,656,657,658],[363,159397,159399,159402,159405],{"className":159398},[407,658],[363,159400,12310],{"className":159401},[407,408,658],[363,159403,471],{"className":159404},[510,658],[363,159406,465],{"className":159407},[407,658],[363,159409,159410,159413],{"style":133517},[363,159411],{"className":159412,"style":651},[650],[363,159414,159416],{"className":159415},[655,656,657,658],[363,159417,11041],{"className":159418,"style":11129},[407,408,658],[363,159420,666],{"className":159421},[665],[363,159423,159425],{"className":159424},[638],[363,159426,159428],{"className":159427,"style":40042},[642],[363,159429],{},[363,159431],{"className":159432,"style":754},[505],[363,159434,159436,159439,159633],{"className":159435},[407],[363,159437],{"className":159438},[494,789],[363,159440,159442],{"className":159441},[586],[363,159443,159445,159625],{"className":159444},[633,634],[363,159446,159448,159622],{"className":159447},[638],[363,159449,159451,159511,159519],{"className":159450,"style":26740},[642],[363,159452,159453,159456],{"style":2874},[363,159454],{"className":159455,"style":809},[650],[363,159457,159459],{"className":159458},[655,656,657,658],[363,159460,159462,159465,159468,159508],{"className":159461},[407,658],[363,159463,137171],{"className":159464},[407,658],[363,159466,461],{"className":159467},[494,658],[363,159469,159471,159474],{"className":159470},[407,658],[363,159472,45101],{"className":159473,"style":45131},[407,408,658],[363,159475,159477],{"className":159476},[629],[363,159478,159480,159500],{"className":159479},[633,634],[363,159481,159483,159497],{"className":159482},[638],[363,159484,159486],{"className":159485,"style":40095},[642],[363,159487,159488,159491],{"style":136942},[363,159489],{"className":159490,"style":30553},[650],[363,159492,159494],{"className":159493},[655,30557,10021,658],[363,159495,12310],{"className":159496},[407,408,658],[363,159498,666],{"className":159499},[665],[363,159501,159503],{"className":159502},[638],[363,159504,159506],{"className":159505,"style":40117},[642],[363,159507],{},[363,159509,468],{"className":159510},[501,658],[363,159512,159513,159516],{"style":821},[363,159514],{"className":159515,"style":809},[650],[363,159517],{"className":159518,"style":829},[828],[363,159520,159521,159524],{"style":26765},[363,159522],{"className":159523,"style":809},[650],[363,159525,159527],{"className":159526},[655,656,657,658],[363,159528,159530,159533,159536,159576,159579,159619],{"className":159529},[407,658],[363,159531,137171],{"className":159532},[407,658],[363,159534,461],{"className":159535},[494,658],[363,159537,159539,159542],{"className":159538},[407,658],[363,159540,45101],{"className":159541,"style":45131},[407,408,658],[363,159543,159545],{"className":159544},[629],[363,159546,159548,159568],{"className":159547},[633,634],[363,159549,159551,159565],{"className":159550},[638],[363,159552,159554],{"className":159553,"style":40095},[642],[363,159555,159556,159559],{"style":136942},[363,159557],{"className":159558,"style":30553},[650],[363,159560,159562],{"className":159561},[655,30557,10021,658],[363,159563,12310],{"className":159564},[407,408,658],[363,159566,666],{"className":159567},[665],[363,159569,159571],{"className":159570},[638],[363,159572,159574],{"className":159573,"style":40117},[642],[363,159575],{},[363,159577,2817],{"className":159578},[2938,658],[363,159580,159582,159585],{"className":159581},[407,658],[363,159583,82643],{"className":159584},[407,408,658],[363,159586,159588],{"className":159587},[629],[363,159589,159591,159611],{"className":159590},[633,634],[363,159592,159594,159608],{"className":159593},[638],[363,159595,159597],{"className":159596,"style":40095},[642],[363,159598,159599,159602],{"style":74612},[363,159600],{"className":159601,"style":30553},[650],[363,159603,159605],{"className":159604},[655,30557,10021,658],[363,159606,12310],{"className":159607},[407,408,658],[363,159609,666],{"className":159610},[665],[363,159612,159614],{"className":159613},[638],[363,159615,159617],{"className":159616,"style":40117},[642],[363,159618],{},[363,159620,468],{"className":159621},[501,658],[363,159623,666],{"className":159624},[665],[363,159626,159628],{"className":159627},[638],[363,159629,159631],{"className":159630,"style":45949},[642],[363,159632],{},[363,159634],{"className":159635},[501,789],[1340,159637,159639],{"title":159638},"推论 2.7（后验预测与收缩）",[11,159640,159641,159642,160020,160021,160128,160129,160132,160133],{},"对未见样本，\n",[363,159643,159645,159710],{"className":159644,"translate":367},[366],[363,159646,159648],{"className":159647},[371],[373,159649,159650],{"xmlns":375},[377,159651,159652,159707],{},[380,159653,159654,159656,159658,159665,159667,159669,159671,159673,159675,159677],{},[383,159655,554],{"mathvariant":570},[458,159657,461],{"stretchy":460},[543,159659,159660,159662],{},[383,159661,40584],{},[1644,159663,159664],{},"new",[458,159666,471],{},[383,159668,7911],{},[458,159670,5155],{},[383,159672,82643],{"mathvariant":75560},[458,159674,468],{"stretchy":460},[458,159676,471],{},[586,159678,159679,159695],{},[380,159680,159681,159687,159689],{},[543,159682,159683,159685],{},[383,159684,45101],{},[383,159686,7911],{},[458,159688,2817],{},[543,159690,159691,159693],{},[383,159692,82643],{},[383,159694,7911],{},[380,159696,159697,159703,159705],{},[543,159698,159699,159701],{},[383,159700,45101],{},[463,159702,474],{},[458,159704,2817],{},[383,159706,38631],{},[387,159708,159709],{"encoding":389},"\\mathbb{P}(y_{\\text{new}} = k \\mid \\mathbf{n}) = \\frac{\\alpha_k + n_k}{\\alpha_0 + N}",[363,159711,159713,159780,159798,159819],{"className":159712,"ariaHidden":394},[393],[363,159714,159716,159719,159722,159725,159771,159774,159777],{"className":159715},[398],[363,159717],{"className":159718,"style":487},[402],[363,159720,554],{"className":159721},[407,714],[363,159723,461],{"className":159724},[494],[363,159726,159728,159731],{"className":159727},[407],[363,159729,40584],{"className":159730,"style":1328},[407,408],[363,159732,159734],{"className":159733},[629],[363,159735,159737,159763],{"className":159736},[633,634],[363,159738,159740,159760],{"className":159739},[638],[363,159741,159743],{"className":159742,"style":45276},[642],[363,159744,159745,159748],{"style":19190},[363,159746],{"className":159747,"style":651},[650],[363,159749,159751],{"className":159750},[655,656,657,658],[363,159752,159754],{"className":159753},[407,658],[363,159755,159757],{"className":159756},[407,4945,658],[363,159758,159664],{"className":159759},[407,658],[363,159761,666],{"className":159762},[665],[363,159764,159766],{"className":159765},[638],[363,159767,159769],{"className":159768,"style":8315},[642],[363,159770],{},[363,159772],{"className":159773,"style":506},[505],[363,159775,471],{"className":159776},[510],[363,159778],{"className":159779,"style":506},[505],[363,159781,159783,159786,159789,159792,159795],{"className":159782},[398],[363,159784],{"className":159785,"style":487},[402],[363,159787,7911],{"className":159788,"style":8614},[407,408],[363,159790],{"className":159791,"style":506},[505],[363,159793,5155],{"className":159794},[510],[363,159796],{"className":159797,"style":506},[505],[363,159799,159801,159804,159807,159810,159813,159816],{"className":159800},[398],[363,159802],{"className":159803,"style":487},[402],[363,159805,82643],{"className":159806},[407,75905],[363,159808,468],{"className":159809},[501],[363,159811],{"className":159812,"style":506},[505],[363,159814,471],{"className":159815},[510],[363,159817],{"className":159818,"style":506},[505],[363,159820,159822,159826],{"className":159821},[398],[363,159823],{"className":159824,"style":159825},[402],"height:1.2693em;vertical-align:-0.4451em;",[363,159827,159829,159832,160017],{"className":159828},[407],[363,159830],{"className":159831},[494,789],[363,159833,159835],{"className":159834},[586],[363,159836,159838,160009],{"className":159837},[633,634],[363,159839,159841,160006],{"className":159840},[638],[363,159842,159845,159902,159910],{"className":159843,"style":159844},[642],"height:0.8242em;",[363,159846,159847,159850],{"style":2874},[363,159848],{"className":159849,"style":809},[650],[363,159851,159853],{"className":159852},[655,656,657,658],[363,159854,159856,159896,159899],{"className":159855},[407,658],[363,159857,159859,159862],{"className":159858},[407,658],[363,159860,45101],{"className":159861,"style":45131},[407,408,658],[363,159863,159865],{"className":159864},[629],[363,159866,159868,159888],{"className":159867},[633,634],[363,159869,159871,159885],{"className":159870},[638],[363,159872,159874],{"className":159873,"style":137304},[642],[363,159875,159876,159879],{"style":136942},[363,159877],{"className":159878,"style":30553},[650],[363,159880,159882],{"className":159881},[655,30557,10021,658],[363,159883,474],{"className":159884},[407,658],[363,159886,666],{"className":159887},[665],[363,159889,159891],{"className":159890},[638],[363,159892,159894],{"className":159893,"style":40117},[642],[363,159895],{},[363,159897,2817],{"className":159898},[2938,658],[363,159900,38631],{"className":159901,"style":25948},[407,408,658],[363,159903,159904,159907],{"style":821},[363,159905],{"className":159906,"style":809},[650],[363,159908],{"className":159909,"style":829},[828],[363,159911,159913,159916],{"style":159912},"top:-3.4159em;",[363,159914],{"className":159915,"style":809},[650],[363,159917,159919],{"className":159918},[655,656,657,658],[363,159920,159922,159963,159966],{"className":159921},[407,658],[363,159923,159925,159928],{"className":159924},[407,658],[363,159926,45101],{"className":159927,"style":45131},[407,408,658],[363,159929,159931],{"className":159930},[629],[363,159932,159934,159955],{"className":159933},[633,634],[363,159935,159937,159952],{"className":159936},[638],[363,159938,159940],{"className":159939,"style":6445},[642],[363,159941,159943,159946],{"style":159942},"top:-2.3488em;margin-left:-0.0037em;margin-right:0.0714em;",[363,159944],{"className":159945,"style":30553},[650],[363,159947,159949],{"className":159948},[655,30557,10021,658],[363,159950,7911],{"className":159951,"style":8614},[407,408,658],[363,159953,666],{"className":159954},[665],[363,159956,159958],{"className":159957},[638],[363,159959,159961],{"className":159960,"style":101583},[642],[363,159962],{},[363,159964,2817],{"className":159965},[2938,658],[363,159967,159969,159972],{"className":159968},[407,658],[363,159970,82643],{"className":159971},[407,408,658],[363,159973,159975],{"className":159974},[629],[363,159976,159978,159998],{"className":159977},[633,634],[363,159979,159981,159995],{"className":159980},[638],[363,159982,159984],{"className":159983,"style":6445},[642],[363,159985,159986,159989],{"style":101564},[363,159987],{"className":159988,"style":30553},[650],[363,159990,159992],{"className":159991},[655,30557,10021,658],[363,159993,7911],{"className":159994,"style":8614},[407,408,658],[363,159996,666],{"className":159997},[665],[363,159999,160001],{"className":160000},[638],[363,160002,160004],{"className":160003,"style":101583},[642],[363,160005],{},[363,160007,666],{"className":160008},[665],[363,160010,160012],{"className":160011},[638],[363,160013,160015],{"className":160014,"style":40264},[642],[363,160016],{},[363,160018],{"className":160019},[501,789],"\n而 ",[363,160022,160024,160052],{"className":160023,"translate":367},[366],[363,160025,160027],{"className":160026},[371],[373,160028,160029],{"xmlns":375},[377,160030,160031,160049],{},[380,160032,160033,160035,160037,160043,160045,160047],{},[383,160034,571],{"mathvariant":570},[458,160036,578],{"stretchy":460},[543,160038,160039,160041],{},[383,160040,157399],{},[383,160042,7911],{},[458,160044,5155],{},[383,160046,82643],{"mathvariant":75560},[458,160048,605],{"stretchy":460},[387,160050,160051],{"encoding":389},"\\mathbb{E}[\\pi_k \\mid \\mathbf{n}]",[363,160053,160055,160116],{"className":160054,"ariaHidden":394},[393],[363,160056,160058,160061,160064,160067,160107,160110,160113],{"className":160057},[398],[363,160059],{"className":160060,"style":487},[402],[363,160062,571],{"className":160063},[407,714],[363,160065,578],{"className":160066},[494],[363,160068,160070,160073],{"className":160069},[407],[363,160071,157399],{"className":160072,"style":1328},[407,408],[363,160074,160076],{"className":160075},[629],[363,160077,160079,160099],{"className":160078},[633,634],[363,160080,160082,160096],{"className":160081},[638],[363,160083,160085],{"className":160084,"style":643},[642],[363,160086,160087,160090],{"style":19190},[363,160088],{"className":160089,"style":651},[650],[363,160091,160093],{"className":160092},[655,656,657,658],[363,160094,7911],{"className":160095,"style":8614},[407,408,658],[363,160097,666],{"className":160098},[665],[363,160100,160102],{"className":160101},[638],[363,160103,160105],{"className":160104,"style":8315},[642],[363,160106],{},[363,160108],{"className":160109,"style":506},[505],[363,160111,5155],{"className":160112},[510],[363,160114],{"className":160115,"style":506},[505],[363,160117,160119,160122,160125],{"className":160118},[398],[363,160120],{"className":160121,"style":487},[402],[363,160123,82643],{"className":160124},[407,75905],[363,160126,605],{"className":160127},[501]," 是",[1572,160130,160131],{},"先验均值与经验频率的凸组合","：\n",[363,160134,160136,160250],{"className":160135,"translate":367},[366],[363,160137,160139],{"className":160138},[371],[373,160140,160141],{"xmlns":375},[377,160142,160143,160247],{},[380,160144,160145,160147,160149,160155,160157,160159,160161,160163,160192,160194,160208,160210,160235,160237],{},[383,160146,571],{"mathvariant":570},[458,160148,578],{"stretchy":460},[543,160150,160151,160153],{},[383,160152,157399],{},[383,160154,7911],{},[458,160156,5155],{},[383,160158,82643],{"mathvariant":75560},[458,160160,605],{"stretchy":460},[458,160162,471],{},[6363,160164,160165,160189],{},[6363,160166,160167,160187],{},[586,160168,160169,160175],{},[543,160170,160171,160173],{},[383,160172,45101],{},[463,160174,474],{},[380,160176,160177,160183,160185],{},[543,160178,160179,160181],{},[383,160180,45101],{},[463,160182,474],{},[458,160184,2817],{},[383,160186,38631],{},[458,160188,6387],{"stretchy":394},[1644,160190,160191],{},"收缩权重",[458,160193,3646],{},[586,160195,160196,160202],{},[543,160197,160198,160200],{},[383,160199,45101],{},[383,160201,7911],{},[543,160203,160204,160206],{},[383,160205,45101],{},[463,160207,474],{},[458,160209,2817],{},[6363,160211,160212,160232],{},[6363,160213,160214,160230],{},[586,160215,160216,160218],{},[383,160217,38631],{},[380,160219,160220,160226,160228],{},[543,160221,160222,160224],{},[383,160223,45101],{},[463,160225,474],{},[458,160227,2817],{},[383,160229,38631],{},[458,160231,6387],{"stretchy":394},[1644,160233,160234],{},"数据权重",[458,160236,3646],{},[586,160238,160239,160245],{},[543,160240,160241,160243],{},[383,160242,82643],{},[383,160244,7911],{},[383,160246,38631],{},[387,160248,160249],{"encoding":389},"\\mathbb{E}[\\pi_k \\mid \\mathbf{n}] = \\underbrace{\\frac{\\alpha_0}{\\alpha_0 + N}}_{\\text{收缩权重}} \\cdot \\frac{\\alpha_k}{\\alpha_0} + \\underbrace{\\frac{N}{\\alpha_0 + N}}_{\\text{数据权重}} \\cdot \\frac{n_k}{N}",[363,160251,160253,160314,160335,160611,160770,161008],{"className":160252,"ariaHidden":394},[393],[363,160254,160256,160259,160262,160265,160305,160308,160311],{"className":160255},[398],[363,160257],{"className":160258,"style":487},[402],[363,160260,571],{"className":160261},[407,714],[363,160263,578],{"className":160264},[494],[363,160266,160268,160271],{"className":160267},[407],[363,160269,157399],{"className":160270,"style":1328},[407,408],[363,160272,160274],{"className":160273},[629],[363,160275,160277,160297],{"className":160276},[633,634],[363,160278,160280,160294],{"className":160279},[638],[363,160281,160283],{"className":160282,"style":643},[642],[363,160284,160285,160288],{"style":19190},[363,160286],{"className":160287,"style":651},[650],[363,160289,160291],{"className":160290},[655,656,657,658],[363,160292,7911],{"className":160293,"style":8614},[407,408,658],[363,160295,666],{"className":160296},[665],[363,160298,160300],{"className":160299},[638],[363,160301,160303],{"className":160302,"style":8315},[642],[363,160304],{},[363,160306],{"className":160307,"style":506},[505],[363,160309,5155],{"className":160310},[510],[363,160312],{"className":160313,"style":506},[505],[363,160315,160317,160320,160323,160326,160329,160332],{"className":160316},[398],[363,160318],{"className":160319,"style":487},[402],[363,160321,82643],{"className":160322},[407,75905],[363,160324,605],{"className":160325},[501],[363,160327],{"className":160328,"style":506},[505],[363,160330,471],{"className":160331},[510],[363,160333],{"className":160334,"style":506},[505],[363,160336,160338,160342,160602,160605,160608],{"className":160337},[398],[363,160339],{"className":160340,"style":160341},[402],"height:3.2699em;vertical-align:-2.1623em;",[363,160343,160345],{"className":160344},[758,6363],[363,160346,160348,160593],{"className":160347},[633,634],[363,160349,160351,160590],{"className":160350},[638],[363,160352,160354,160373],{"className":160353,"style":3901},[642],[363,160355,160357,160361],{"style":160356},"top:-0.9452em;",[363,160358],{"className":160359,"style":160360},[650],"height:3.1076em;",[363,160362,160364],{"className":160363},[655,656,657,658],[363,160365,160367],{"className":160366},[407,658],[363,160368,160370],{"className":160369},[407,4945,658],[363,160371,160191],{"className":160372},[407,4949,658],[363,160374,160376,160379],{"style":160375},"top:-3.1076em;",[363,160377],{"className":160378,"style":160360},[650],[363,160380,160382],{"className":160381},[758,6363],[363,160383,160385,160581],{"className":160384},[633,634],[363,160386,160388,160578],{"className":160387},[638],[363,160389,160391,160422],{"className":160390,"style":3901},[642],[363,160392,160395,160398],{"className":160393,"style":160394},[6654],"top:-1.6236em;",[363,160396],{"className":160397,"style":160360},[650],[363,160399,160401,160408,160415],{"className":160400,"style":6663},[6662],[363,160402,160404],{"className":160403,"style":6668},[6667],[6670,160405,160406],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6676},[6678,160407],{"d":6680},[363,160409,160411],{"className":160410,"style":6668},[6684],[6670,160412,160413],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6687},[6678,160414],{"d":6690},[363,160416,160418],{"className":160417,"style":6668},[6694],[6670,160419,160420],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6697},[6678,160421],{"d":6700},[363,160423,160424,160427],{"style":160375},[363,160425],{"className":160426,"style":160360},[650],[363,160428,160430],{"className":160429},[407],[363,160431,160433,160436,160575],{"className":160432},[407],[363,160434],{"className":160435},[494,789],[363,160437,160439],{"className":160438},[586],[363,160440,160442,160567],{"className":160441},[633,634],[363,160443,160445,160564],{"className":160444},[638],[363,160446,160448,160508,160516],{"className":160447,"style":3901},[642],[363,160449,160450,160453],{"style":805},[363,160451],{"className":160452,"style":809},[650],[363,160454,160456,160496,160499,160502,160505],{"className":160455},[407],[363,160457,160459,160462],{"className":160458},[407],[363,160460,45101],{"className":160461,"style":45131},[407,408],[363,160463,160465],{"className":160464},[629],[363,160466,160468,160488],{"className":160467},[633,634],[363,160469,160471,160485],{"className":160470},[638],[363,160472,160474],{"className":160473,"style":11480},[642],[363,160475,160476,160479],{"style":136107},[363,160477],{"className":160478,"style":651},[650],[363,160480,160482],{"className":160481},[655,656,657,658],[363,160483,474],{"className":160484},[407,658],[363,160486,666],{"className":160487},[665],[363,160489,160491],{"className":160490},[638],[363,160492,160494],{"className":160493,"style":8315},[642],[363,160495],{},[363,160497],{"className":160498,"style":2934},[505],[363,160500,2817],{"className":160501},[2938],[363,160503],{"className":160504,"style":2934},[505],[363,160506,38631],{"className":160507,"style":25948},[407,408],[363,160509,160510,160513],{"style":821},[363,160511],{"className":160512,"style":809},[650],[363,160514],{"className":160515,"style":829},[828],[363,160517,160518,160521],{"style":832},[363,160519],{"className":160520,"style":809},[650],[363,160522,160524],{"className":160523},[407],[363,160525,160527,160530],{"className":160526},[407],[363,160528,45101],{"className":160529,"style":45131},[407,408],[363,160531,160533],{"className":160532},[629],[363,160534,160536,160556],{"className":160535},[633,634],[363,160537,160539,160553],{"className":160538},[638],[363,160540,160542],{"className":160541,"style":11480},[642],[363,160543,160544,160547],{"style":136107},[363,160545],{"className":160546,"style":651},[650],[363,160548,160550],{"className":160549},[655,656,657,658],[363,160551,474],{"className":160552},[407,658],[363,160554,666],{"className":160555},[665],[363,160557,160559],{"className":160558},[638],[363,160560,160562],{"className":160561,"style":8315},[642],[363,160563],{},[363,160565,666],{"className":160566},[665],[363,160568,160570],{"className":160569},[638],[363,160571,160573],{"className":160572,"style":125395},[642],[363,160574],{},[363,160576],{"className":160577},[501,789],[363,160579,666],{"className":160580},[665],[363,160582,160584],{"className":160583},[638],[363,160585,160588],{"className":160586,"style":160587},[642],"height:1.484em;",[363,160589],{},[363,160591,666],{"className":160592},[665],[363,160594,160596],{"className":160595},[638],[363,160597,160600],{"className":160598,"style":160599},[642],"height:2.1623em;",[363,160601],{},[363,160603],{"className":160604,"style":2934},[505],[363,160606,3646],{"className":160607},[2938],[363,160609],{"className":160610,"style":2934},[505],[363,160612,160614,160618,160761,160764,160767],{"className":160613},[398],[363,160615],{"className":160616,"style":160617},[402],"height:1.1624em;vertical-align:-0.4451em;",[363,160619,160621,160624,160758],{"className":160620},[407],[363,160622],{"className":160623},[494,789],[363,160625,160627],{"className":160626},[586],[363,160628,160630,160750],{"className":160629},[633,634],[363,160631,160633,160747],{"className":160632},[638],[363,160634,160637,160688,160696],{"className":160635,"style":160636},[642],"height:0.7173em;",[363,160638,160639,160642],{"style":2874},[363,160640],{"className":160641,"style":809},[650],[363,160643,160645],{"className":160644},[655,656,657,658],[363,160646,160648],{"className":160647},[407,658],[363,160649,160651,160654],{"className":160650},[407,658],[363,160652,45101],{"className":160653,"style":45131},[407,408,658],[363,160655,160657],{"className":160656},[629],[363,160658,160660,160680],{"className":160659},[633,634],[363,160661,160663,160677],{"className":160662},[638],[363,160664,160666],{"className":160665,"style":137304},[642],[363,160667,160668,160671],{"style":136942},[363,160669],{"className":160670,"style":30553},[650],[363,160672,160674],{"className":160673},[655,30557,10021,658],[363,160675,474],{"className":160676},[407,658],[363,160678,666],{"className":160679},[665],[363,160681,160683],{"className":160682},[638],[363,160684,160686],{"className":160685,"style":40117},[642],[363,160687],{},[363,160689,160690,160693],{"style":821},[363,160691],{"className":160692,"style":809},[650],[363,160694],{"className":160695,"style":829},[828],[363,160697,160698,160701],{"style":159912},[363,160699],{"className":160700,"style":809},[650],[363,160702,160704],{"className":160703},[655,656,657,658],[363,160705,160707],{"className":160706},[407,658],[363,160708,160710,160713],{"className":160709},[407,658],[363,160711,45101],{"className":160712,"style":45131},[407,408,658],[363,160714,160716],{"className":160715},[629],[363,160717,160719,160739],{"className":160718},[633,634],[363,160720,160722,160736],{"className":160721},[638],[363,160723,160725],{"className":160724,"style":6445},[642],[363,160726,160727,160730],{"style":159942},[363,160728],{"className":160729,"style":30553},[650],[363,160731,160733],{"className":160732},[655,30557,10021,658],[363,160734,7911],{"className":160735,"style":8614},[407,408,658],[363,160737,666],{"className":160738},[665],[363,160740,160742],{"className":160741},[638],[363,160743,160745],{"className":160744,"style":101583},[642],[363,160746],{},[363,160748,666],{"className":160749},[665],[363,160751,160753],{"className":160752},[638],[363,160754,160756],{"className":160755,"style":40264},[642],[363,160757],{},[363,160759],{"className":160760},[501,789],[363,160762],{"className":160763,"style":2934},[505],[363,160765,2817],{"className":160766},[2938],[363,160768],{"className":160769,"style":2934},[505],[363,160771,160773,160777,160999,161002,161005],{"className":160772},[398],[363,160774],{"className":160775,"style":160776},[402],"height:3.5227em;vertical-align:-2.1623em;",[363,160778,160780],{"className":160779},[758,6363],[363,160781,160783,160991],{"className":160782},[633,634],[363,160784,160786,160988],{"className":160785},[638],[363,160787,160790,160809],{"className":160788,"style":160789},[642],"height:1.3603em;",[363,160791,160793,160797],{"style":160792},"top:-1.198em;",[363,160794],{"className":160795,"style":160796},[650],"height:3.3603em;",[363,160798,160800],{"className":160799},[655,656,657,658],[363,160801,160803],{"className":160802},[407,658],[363,160804,160806],{"className":160805},[407,4945,658],[363,160807,160234],{"className":160808},[407,4949,658],[363,160810,160812,160815],{"style":160811},"top:-3.3603em;",[363,160813],{"className":160814,"style":160796},[650],[363,160816,160818],{"className":160817},[758,6363],[363,160819,160821,160980],{"className":160820},[633,634],[363,160822,160824,160977],{"className":160823},[638],[363,160825,160827,160858],{"className":160826,"style":160789},[642],[363,160828,160831,160834],{"className":160829,"style":160830},[6654],"top:-1.8763em;",[363,160832],{"className":160833,"style":160796},[650],[363,160835,160837,160844,160851],{"className":160836,"style":6663},[6662],[363,160838,160840],{"className":160839,"style":6668},[6667],[6670,160841,160842],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6676},[6678,160843],{"d":6680},[363,160845,160847],{"className":160846,"style":6668},[6684],[6670,160848,160849],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6687},[6678,160850],{"d":6690},[363,160852,160854],{"className":160853,"style":6668},[6694],[6670,160855,160856],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6697},[6678,160857],{"d":6700},[363,160859,160860,160863],{"style":160811},[363,160861],{"className":160862,"style":160796},[650],[363,160864,160866],{"className":160865},[407],[363,160867,160869,160872,160974],{"className":160868},[407],[363,160870],{"className":160871},[494,789],[363,160873,160875],{"className":160874},[586],[363,160876,160878,160966],{"className":160877},[633,634],[363,160879,160881,160963],{"className":160880},[638],[363,160882,160884,160944,160952],{"className":160883,"style":160789},[642],[363,160885,160886,160889],{"style":805},[363,160887],{"className":160888,"style":809},[650],[363,160890,160892,160932,160935,160938,160941],{"className":160891},[407],[363,160893,160895,160898],{"className":160894},[407],[363,160896,45101],{"className":160897,"style":45131},[407,408],[363,160899,160901],{"className":160900},[629],[363,160902,160904,160924],{"className":160903},[633,634],[363,160905,160907,160921],{"className":160906},[638],[363,160908,160910],{"className":160909,"style":11480},[642],[363,160911,160912,160915],{"style":136107},[363,160913],{"className":160914,"style":651},[650],[363,160916,160918],{"className":160917},[655,656,657,658],[363,160919,474],{"className":160920},[407,658],[363,160922,666],{"className":160923},[665],[363,160925,160927],{"className":160926},[638],[363,160928,160930],{"className":160929,"style":8315},[642],[363,160931],{},[363,160933],{"className":160934,"style":2934},[505],[363,160936,2817],{"className":160937},[2938],[363,160939],{"className":160940,"style":2934},[505],[363,160942,38631],{"className":160943,"style":25948},[407,408],[363,160945,160946,160949],{"style":821},[363,160947],{"className":160948,"style":809},[650],[363,160950],{"className":160951,"style":829},[828],[363,160953,160954,160957],{"style":832},[363,160955],{"className":160956,"style":809},[650],[363,160958,160960],{"className":160959},[407],[363,160961,38631],{"className":160962,"style":25948},[407,408],[363,160964,666],{"className":160965},[665],[363,160967,160969],{"className":160968},[638],[363,160970,160972],{"className":160971,"style":125395},[642],[363,160973],{},[363,160975],{"className":160976},[501,789],[363,160978,666],{"className":160979},[665],[363,160981,160983],{"className":160982},[638],[363,160984,160986],{"className":160985,"style":160587},[642],[363,160987],{},[363,160989,666],{"className":160990},[665],[363,160992,160994],{"className":160993},[638],[363,160995,160997],{"className":160996,"style":160599},[642],[363,160998],{},[363,161000],{"className":161001,"style":2934},[505],[363,161003,3646],{"className":161004},[2938],[363,161006],{"className":161007,"style":2934},[505],[363,161009,161011,161015],{"className":161010},[398],[363,161012],{"className":161013,"style":161014},[402],"height:1.0623em;vertical-align:-0.345em;",[363,161016,161018,161021,161117],{"className":161017},[407],[363,161019],{"className":161020},[494,789],[363,161022,161024],{"className":161023},[586],[363,161025,161027,161109],{"className":161026},[633,634],[363,161028,161030,161106],{"className":161029},[638],[363,161031,161033,161047,161055],{"className":161032,"style":160636},[642],[363,161034,161035,161038],{"style":2874},[363,161036],{"className":161037,"style":809},[650],[363,161039,161041],{"className":161040},[655,656,657,658],[363,161042,161044],{"className":161043},[407,658],[363,161045,38631],{"className":161046,"style":25948},[407,408,658],[363,161048,161049,161052],{"style":821},[363,161050],{"className":161051,"style":809},[650],[363,161053],{"className":161054,"style":829},[828],[363,161056,161057,161060],{"style":159912},[363,161058],{"className":161059,"style":809},[650],[363,161061,161063],{"className":161062},[655,656,657,658],[363,161064,161066],{"className":161065},[407,658],[363,161067,161069,161072],{"className":161068},[407,658],[363,161070,82643],{"className":161071},[407,408,658],[363,161073,161075],{"className":161074},[629],[363,161076,161078,161098],{"className":161077},[633,634],[363,161079,161081,161095],{"className":161080},[638],[363,161082,161084],{"className":161083,"style":6445},[642],[363,161085,161086,161089],{"style":101564},[363,161087],{"className":161088,"style":30553},[650],[363,161090,161092],{"className":161091},[655,30557,10021,658],[363,161093,7911],{"className":161094,"style":8614},[407,408,658],[363,161096,666],{"className":161097},[665],[363,161099,161101],{"className":161100},[638],[363,161102,161104],{"className":161103,"style":101583},[642],[363,161105],{},[363,161107,666],{"className":161108},[665],[363,161110,161112],{"className":161111},[638],[363,161113,161115],{"className":161114,"style":2919},[642],[363,161116],{},[363,161118],{"className":161119},[501,789],[11,161121,161122,161123,23692,161225,161317,161318,161409,161410,161502],{},"推论 2.7 用一句话概括了加法平滑的全部含义：",[1572,161124,161125,161126,161195,161196,161224],{},"先验强度的倒数 ",[363,161127,161129,161146],{"className":161128,"translate":367},[366],[363,161130,161132],{"className":161131},[371],[373,161133,161134],{"xmlns":375},[377,161135,161136,161144],{},[380,161137,161138],{},[543,161139,161140,161142],{},[383,161141,45101],{},[463,161143,474],{},[387,161145,152251],{"encoding":389},[363,161147,161149],{"className":161148,"ariaHidden":394},[393],[363,161150,161152,161155],{"className":161151},[398],[363,161153],{"className":161154,"style":13721},[402],[363,161156,161158,161161],{"className":161157},[407],[363,161159,45101],{"className":161160,"style":45131},[407,408],[363,161162,161164],{"className":161163},[629],[363,161165,161167,161187],{"className":161166},[633,634],[363,161168,161170,161184],{"className":161169},[638],[363,161171,161173],{"className":161172,"style":11480},[642],[363,161174,161175,161178],{"style":136107},[363,161176],{"className":161177,"style":651},[650],[363,161179,161181],{"className":161180},[655,656,657,658],[363,161182,474],{"className":161183},[407,658],[363,161185,666],{"className":161186},[665],[363,161188,161190],{"className":161189},[638],[363,161191,161193],{"className":161192,"style":8315},[642],[363,161194],{}," 相对于样本量 ",[363,161197,161199,161212],{"className":161198,"translate":367},[366],[363,161200,161202],{"className":161201},[371],[373,161203,161204],{"xmlns":375},[377,161205,161206,161210],{},[380,161207,161208],{},[383,161209,38631],{},[387,161211,38631],{"encoding":389},[363,161213,161215],{"className":161214,"ariaHidden":394},[393],[363,161216,161218,161221],{"className":161217},[398],[363,161219],{"className":161220,"style":1011},[402],[363,161222,38631],{"className":161223,"style":25948},[407,408]," 的大小，就是数据与先验的信任分配比例。",[363,161226,161228,161250],{"className":161227,"translate":367},[366],[363,161229,161231],{"className":161230},[371],[373,161232,161233],{"xmlns":375},[377,161234,161235,161247],{},[380,161236,161237,161243,161245],{},[543,161238,161239,161241],{},[383,161240,45101],{},[383,161242,12310],{},[458,161244,471],{},[463,161246,465],{},[387,161248,161249],{"encoding":389},"\\alpha_i = 1",[363,161251,161253,161308],{"className":161252,"ariaHidden":394},[393],[363,161254,161256,161259,161299,161302,161305],{"className":161255},[398],[363,161257],{"className":161258,"style":13721},[402],[363,161260,161262,161265],{"className":161261},[407],[363,161263,45101],{"className":161264,"style":45131},[407,408],[363,161266,161268],{"className":161267},[629],[363,161269,161271,161291],{"className":161270},[633,634],[363,161272,161274,161288],{"className":161273},[638],[363,161275,161277],{"className":161276,"style":12529},[642],[363,161278,161279,161282],{"style":136107},[363,161280],{"className":161281,"style":651},[650],[363,161283,161285],{"className":161284},[655,656,657,658],[363,161286,12310],{"className":161287},[407,408,658],[363,161289,666],{"className":161290},[665],[363,161292,161294],{"className":161293},[638],[363,161295,161297],{"className":161296,"style":8315},[642],[363,161298],{},[363,161300],{"className":161301,"style":506},[505],[363,161303,471],{"className":161304},[510],[363,161306],{"className":161307,"style":506},[505],[363,161309,161311,161314],{"className":161310},[398],[363,161312],{"className":161313,"style":520},[402],[363,161315,465],{"className":161316},[407]," 得 Laplace 平滑，取 ",[363,161319,161321,161342],{"className":161320,"translate":367},[366],[363,161322,161324],{"className":161323},[371],[373,161325,161326],{"xmlns":375},[377,161327,161328,161340],{},[380,161329,161330,161336,161338],{},[543,161331,161332,161334],{},[383,161333,45101],{},[383,161335,12310],{},[458,161337,3250],{},[463,161339,465],{},[387,161341,154461],{"encoding":389},[363,161343,161345,161400],{"className":161344,"ariaHidden":394},[393],[363,161346,161348,161351,161391,161394,161397],{"className":161347},[398],[363,161349],{"className":161350,"style":134669},[402],[363,161352,161354,161357],{"className":161353},[407],[363,161355,45101],{"className":161356,"style":45131},[407,408],[363,161358,161360],{"className":161359},[629],[363,161361,161363,161383],{"className":161362},[633,634],[363,161364,161366,161380],{"className":161365},[638],[363,161367,161369],{"className":161368,"style":12529},[642],[363,161370,161371,161374],{"style":136107},[363,161372],{"className":161373,"style":651},[650],[363,161375,161377],{"className":161376},[655,656,657,658],[363,161378,12310],{"className":161379},[407,408,658],[363,161381,666],{"className":161382},[665],[363,161384,161386],{"className":161385},[638],[363,161387,161389],{"className":161388,"style":8315},[642],[363,161390],{},[363,161392],{"className":161393,"style":506},[505],[363,161395,3250],{"className":161396},[510],[363,161398],{"className":161399,"style":506},[505],[363,161401,161403,161406],{"className":161402},[398],[363,161404],{"className":161405,"style":520},[402],[363,161407,465],{"className":161408},[407]," 得 Lidstone 平滑，取 ",[363,161411,161413,161435],{"className":161412,"translate":367},[366],[363,161414,161416],{"className":161415},[371],[373,161417,161418],{"xmlns":375},[377,161419,161420,161432],{},[380,161421,161422,161428,161430],{},[543,161423,161424,161426],{},[383,161425,45101],{},[383,161427,12310],{},[458,161429,1376],{},[463,161431,474],{},[387,161433,161434],{"encoding":389},"\\alpha_i \\to 0",[363,161436,161438,161493],{"className":161437,"ariaHidden":394},[393],[363,161439,161441,161444,161484,161487,161490],{"className":161440},[398],[363,161442],{"className":161443,"style":13721},[402],[363,161445,161447,161450],{"className":161446},[407],[363,161448,45101],{"className":161449,"style":45131},[407,408],[363,161451,161453],{"className":161452},[629],[363,161454,161456,161476],{"className":161455},[633,634],[363,161457,161459,161473],{"className":161458},[638],[363,161460,161462],{"className":161461,"style":12529},[642],[363,161463,161464,161467],{"style":136107},[363,161465],{"className":161466,"style":651},[650],[363,161468,161470],{"className":161469},[655,656,657,658],[363,161471,12310],{"className":161472},[407,408,658],[363,161474,666],{"className":161475},[665],[363,161477,161479],{"className":161478},[638],[363,161480,161482],{"className":161481,"style":8315},[642],[363,161483],{},[363,161485],{"className":161486,"style":506},[505],[363,161488,1376],{"className":161489},[510],[363,161491],{"className":161492,"style":506},[505],[363,161494,161496,161499],{"className":161495},[398],[363,161497],{"className":161498,"style":520},[402],[363,161500,474],{"className":161501},[407]," 得最大似然估计——这三个统计实践中彼此孤立出现的技巧，在此被识别为同一族参数的不同取值。",[2658,161504,161506],{"id":161505},"_25-聚合性中立性与分裂构造","2.5 聚合性、中立性与分裂构造",[1340,161508,161510],{"title":161509},"命题 2.8（聚合性）",[11,161511,881,161512,3092,161588,2627,161739,161807,161808,1513,162049,87128,162127,10527],{},[363,161513,161515,161540],{"className":161514,"translate":367},[366],[363,161516,161518],{"className":161517},[371],[373,161519,161520],{"xmlns":375},[377,161521,161522,161538],{},[380,161523,161524,161526,161528,161530,161532,161534,161536],{},[383,161525,1121],{"mathvariant":75560},[458,161527,9216],{},[383,161529,137065],{"mathvariant":557},[458,161531,4450],{},[458,161533,461],{"stretchy":460},[383,161535,45101],{"mathvariant":136008},[458,161537,468],{"stretchy":460},[387,161539,137076],{"encoding":389},[363,161541,161543,161561],{"className":161542,"ariaHidden":394},[393],[363,161544,161546,161549,161552,161555,161558],{"className":161545},[398],[363,161547],{"className":161548,"style":135617},[402],[363,161550,1121],{"className":161551},[407,75905],[363,161553],{"className":161554,"style":506},[505],[363,161556,9216],{"className":161557},[510],[363,161559],{"className":161560,"style":506},[505],[363,161562,161564,161567,161573,161576,161585],{"className":161563},[398],[363,161565],{"className":161566,"style":487},[402],[363,161568,161570],{"className":161569},[1831],[363,161571,137065],{"className":161572},[407,33009],[363,161574,461],{"className":161575},[494],[363,161577,161579],{"className":161578},[407],[363,161580,161582],{"className":161581},[407],[363,161583,45101],{"className":161584},[407,136068],[363,161586,468],{"className":161587},[501],[363,161589,161591,161625],{"className":161590,"translate":367},[366],[363,161592,161594],{"className":161593},[371],[373,161595,161596],{"xmlns":375},[377,161597,161598,161622],{},[380,161599,161600,161602,161608,161610,161612,161614,161620],{},[458,161601,3245],{"stretchy":460},[543,161603,161604,161606],{},[383,161605,34215],{},[463,161607,465],{},[458,161609,898],{"separator":394},[458,161611,133107],{},[458,161613,898],{"separator":394},[543,161615,161616,161618],{},[383,161617,34215],{},[383,161619,25914],{},[458,161621,3255],{"stretchy":460},[387,161623,161624],{"encoding":389},"\\{I_1, \\dots, I_M\\}",[363,161626,161628],{"className":161627,"ariaHidden":394},[393],[363,161629,161631,161634,161637,161678,161681,161684,161687,161690,161693,161696,161736],{"className":161630},[398],[363,161632],{"className":161633,"style":487},[402],[363,161635,3245],{"className":161636},[494],[363,161638,161640,161643],{"className":161639},[407],[363,161641,34215],{"className":161642,"style":9234},[407,408],[363,161644,161646],{"className":161645},[629],[363,161647,161649,161670],{"className":161648},[633,634],[363,161650,161652,161667],{"className":161651},[638],[363,161653,161655],{"className":161654,"style":11480},[642],[363,161656,161658,161661],{"style":161657},"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;",[363,161659],{"className":161660,"style":651},[650],[363,161662,161664],{"className":161663},[655,656,657,658],[363,161665,465],{"className":161666},[407,658],[363,161668,666],{"className":161669},[665],[363,161671,161673],{"className":161672},[638],[363,161674,161676],{"className":161675,"style":8315},[642],[363,161677],{},[363,161679,898],{"className":161680},[920],[363,161682],{"className":161683,"style":754},[505],[363,161685,133107],{"className":161686},[758],[363,161688],{"className":161689,"style":754},[505],[363,161691,898],{"className":161692},[920],[363,161694],{"className":161695,"style":754},[505],[363,161697,161699,161702],{"className":161698},[407],[363,161700,34215],{"className":161701,"style":9234},[407,408],[363,161703,161705],{"className":161704},[629],[363,161706,161708,161728],{"className":161707},[633,634],[363,161709,161711,161725],{"className":161710},[638],[363,161712,161714],{"className":161713,"style":727},[642],[363,161715,161716,161719],{"style":161657},[363,161717],{"className":161718,"style":651},[650],[363,161720,161722],{"className":161721},[655,656,657,658],[363,161723,25914],{"className":161724,"style":25948},[407,408,658],[363,161726,666],{"className":161727},[665],[363,161729,161731],{"className":161730},[638],[363,161732,161734],{"className":161733,"style":8315},[642],[363,161735],{},[363,161737,3255],{"className":161738},[501],[363,161740,161742,161768],{"className":161741,"translate":367},[366],[363,161743,161745],{"className":161744},[371],[373,161746,161747],{"xmlns":375},[377,161748,161749,161765],{},[380,161750,161751,161753,161755,161757,161759,161761,161763],{},[458,161752,3245],{"stretchy":460},[463,161754,465],{},[458,161756,898],{"separator":394},[458,161758,133107],{},[458,161760,898],{"separator":394},[383,161762,11041],{},[458,161764,3255],{"stretchy":460},[387,161766,161767],{"encoding":389},"\\{1, \\dots, K\\}",[363,161769,161771],{"className":161770,"ariaHidden":394},[393],[363,161772,161774,161777,161780,161783,161786,161789,161792,161795,161798,161801,161804],{"className":161773},[398],[363,161775],{"className":161776,"style":487},[402],[363,161778,3245],{"className":161779},[494],[363,161781,465],{"className":161782},[407],[363,161784,898],{"className":161785},[920],[363,161787],{"className":161788,"style":754},[505],[363,161790,133107],{"className":161791},[758],[363,161793],{"className":161794,"style":754},[505],[363,161796,898],{"className":161797},[920],[363,161799],{"className":161800,"style":754},[505],[363,161802,11041],{"className":161803,"style":11129},[407,408],[363,161805,3255],{"className":161806},[501]," 的一个划分。令 ",[363,161809,161811,161853],{"className":161810,"translate":367},[366],[363,161812,161814],{"className":161813},[371],[373,161815,161816],{"xmlns":375},[377,161817,161818,161850],{},[380,161819,161820,161826,161828,161844],{},[543,161821,161822,161824],{},[383,161823,40584],{},[383,161825,26670],{},[458,161827,471],{},[543,161829,161830,161832],{},[458,161831,13808],{},[380,161833,161834,161836,161838],{},[383,161835,12310],{},[458,161837,6256],{},[543,161839,161840,161842],{},[383,161841,34215],{},[383,161843,26670],{},[543,161845,161846,161848],{},[383,161847,1121],{},[383,161849,12310],{},[387,161851,161852],{"encoding":389},"y_m = \\sum_{i \\in I_m} x_i",[363,161854,161856,161911],{"className":161855,"ariaHidden":394},[393],[363,161857,161859,161862,161902,161905,161908],{"className":161858},[398],[363,161860],{"className":161861,"style":2623},[402],[363,161863,161865,161868],{"className":161864},[407],[363,161866,40584],{"className":161867,"style":1328},[407,408],[363,161869,161871],{"className":161870},[629],[363,161872,161874,161894],{"className":161873},[633,634],[363,161875,161877,161891],{"className":161876},[638],[363,161878,161880],{"className":161879,"style":45276},[642],[363,161881,161882,161885],{"style":19190},[363,161883],{"className":161884,"style":651},[650],[363,161886,161888],{"className":161887},[655,656,657,658],[363,161889,26670],{"className":161890},[407,408,658],[363,161892,666],{"className":161893},[665],[363,161895,161897],{"className":161896},[638],[363,161898,161900],{"className":161899,"style":8315},[642],[363,161901],{},[363,161903],{"className":161904,"style":506},[505],[363,161906,471],{"className":161907},[510],[363,161909],{"className":161910,"style":506},[505],[363,161912,161914,161918,162006,162009],{"className":161913},[398],[363,161915],{"className":161916,"style":161917},[402],"height:1.1498em;vertical-align:-0.3998em;",[363,161919,161921,161924],{"className":161920},[1831],[363,161922,13808],{"className":161923,"style":40007},[1831,1832,5963],[363,161925,161927],{"className":161926},[629],[363,161928,161930,161997],{"className":161929},[633,634],[363,161931,161933,161994],{"className":161932},[638],[363,161934,161936],{"className":161935,"style":135514},[642],[363,161937,161938,161941],{"style":40023},[363,161939],{"className":161940,"style":651},[650],[363,161942,161944],{"className":161943},[655,656,657,658],[363,161945,161947,161950,161953],{"className":161946},[407,658],[363,161948,12310],{"className":161949},[407,408,658],[363,161951,6256],{"className":161952},[510,658],[363,161954,161956,161959],{"className":161955},[407,658],[363,161957,34215],{"className":161958,"style":9234},[407,408,658],[363,161960,161962],{"className":161961},[629],[363,161963,161965,161986],{"className":161964},[633,634],[363,161966,161968,161983],{"className":161967},[638],[363,161969,161971],{"className":161970,"style":74609},[642],[363,161972,161974,161977],{"style":161973},"top:-2.357em;margin-left:-0.0785em;margin-right:0.0714em;",[363,161975],{"className":161976,"style":30553},[650],[363,161978,161980],{"className":161979},[655,30557,10021,658],[363,161981,26670],{"className":161982},[407,408,658],[363,161984,666],{"className":161985},[665],[363,161987,161989],{"className":161988},[638],[363,161990,161992],{"className":161991,"style":40117},[642],[363,161993],{},[363,161995,666],{"className":161996},[665],[363,161998,162000],{"className":161999},[638],[363,162001,162004],{"className":162002,"style":162003},[642],"height:0.3998em;",[363,162005],{},[363,162007],{"className":162008,"style":754},[505],[363,162010,162012,162015],{"className":162011},[407],[363,162013,1121],{"className":162014},[407,408],[363,162016,162018],{"className":162017},[629],[363,162019,162021,162041],{"className":162020},[633,634],[363,162022,162024,162038],{"className":162023},[638],[363,162025,162027],{"className":162026,"style":12529},[642],[363,162028,162029,162032],{"style":730},[363,162030],{"className":162031,"style":651},[650],[363,162033,162035],{"className":162034},[655,656,657,658],[363,162036,12310],{"className":162037},[407,408,658],[363,162039,666],{"className":162040},[665],[363,162042,162044],{"className":162043},[638],[363,162045,162047],{"className":162046,"style":8315},[642],[363,162048],{},[363,162050,162052,162078],{"className":162051,"translate":367},[366],[363,162053,162055],{"className":162054},[371],[373,162056,162057],{"xmlns":375},[377,162058,162059,162075],{},[380,162060,162061,162063,162065,162067,162069,162071,162073],{},[383,162062,40584],{"mathvariant":75560},[458,162064,9216],{},[383,162066,137065],{"mathvariant":557},[458,162068,4450],{},[458,162070,461],{"stretchy":460},[383,162072,84464],{"mathvariant":136008},[458,162074,468],{"stretchy":460},[387,162076,162077],{"encoding":389},"\\mathbf{y} \\sim \\operatorname{Dir}(\\boldsymbol{\\beta})",[363,162079,162081,162100],{"className":162080,"ariaHidden":394},[393],[363,162082,162084,162087,162091,162094,162097],{"className":162083},[398],[363,162085],{"className":162086,"style":133764},[402],[363,162088,40584],{"className":162089,"style":162090},[407,75905],"margin-right:0.016em;",[363,162092],{"className":162093,"style":506},[505],[363,162095,9216],{"className":162096},[510],[363,162098],{"className":162099,"style":506},[505],[363,162101,162103,162106,162112,162115,162124],{"className":162102},[398],[363,162104],{"className":162105,"style":487},[402],[363,162107,162109],{"className":162108},[1831],[363,162110,137065],{"className":162111},[407,33009],[363,162113,461],{"className":162114},[494],[363,162116,162118],{"className":162117},[407],[363,162119,162121],{"className":162120},[407],[363,162122,84464],{"className":162123,"style":150142},[407,136068],[363,162125,468],{"className":162126},[501],[363,162128,162130,162172],{"className":162129,"translate":367},[366],[363,162131,162133],{"className":162132},[371],[373,162134,162135],{"xmlns":375},[377,162136,162137,162169],{},[380,162138,162139,162145,162147,162163],{},[543,162140,162141,162143],{},[383,162142,84464],{},[383,162144,26670],{},[458,162146,471],{},[543,162148,162149,162151],{},[458,162150,13808],{},[380,162152,162153,162155,162157],{},[383,162154,12310],{},[458,162156,6256],{},[543,162158,162159,162161],{},[383,162160,34215],{},[383,162162,26670],{},[543,162164,162165,162167],{},[383,162166,45101],{},[383,162168,12310],{},[387,162170,162171],{"encoding":389},"\\beta_m = \\sum_{i \\in I_m} \\alpha_i",[363,162173,162175,162230],{"className":162174,"ariaHidden":394},[393],[363,162176,162178,162181,162221,162224,162227],{"className":162177},[398],[363,162179],{"className":162180,"style":403},[402],[363,162182,162184,162187],{"className":162183},[407],[363,162185,84464],{"className":162186,"style":84686},[407,408],[363,162188,162190],{"className":162189},[629],[363,162191,162193,162213],{"className":162192},[633,634],[363,162194,162196,162210],{"className":162195},[638],[363,162197,162199],{"className":162198,"style":45276},[642],[363,162200,162201,162204],{"style":150221},[363,162202],{"className":162203,"style":651},[650],[363,162205,162207],{"className":162206},[655,656,657,658],[363,162208,26670],{"className":162209},[407,408,658],[363,162211,666],{"className":162212},[665],[363,162214,162216],{"className":162215},[638],[363,162217,162219],{"className":162218,"style":8315},[642],[363,162220],{},[363,162222],{"className":162223,"style":506},[505],[363,162225,471],{"className":162226},[510],[363,162228],{"className":162229,"style":506},[505],[363,162231,162233,162236,162322,162325],{"className":162232},[398],[363,162234],{"className":162235,"style":161917},[402],[363,162237,162239,162242],{"className":162238},[1831],[363,162240,13808],{"className":162241,"style":40007},[1831,1832,5963],[363,162243,162245],{"className":162244},[629],[363,162246,162248,162314],{"className":162247},[633,634],[363,162249,162251,162311],{"className":162250},[638],[363,162252,162254],{"className":162253,"style":135514},[642],[363,162255,162256,162259],{"style":40023},[363,162257],{"className":162258,"style":651},[650],[363,162260,162262],{"className":162261},[655,656,657,658],[363,162263,162265,162268,162271],{"className":162264},[407,658],[363,162266,12310],{"className":162267},[407,408,658],[363,162269,6256],{"className":162270},[510,658],[363,162272,162274,162277],{"className":162273},[407,658],[363,162275,34215],{"className":162276,"style":9234},[407,408,658],[363,162278,162280],{"className":162279},[629],[363,162281,162283,162303],{"className":162282},[633,634],[363,162284,162286,162300],{"className":162285},[638],[363,162287,162289],{"className":162288,"style":74609},[642],[363,162290,162291,162294],{"style":161973},[363,162292],{"className":162293,"style":30553},[650],[363,162295,162297],{"className":162296},[655,30557,10021,658],[363,162298,26670],{"className":162299},[407,408,658],[363,162301,666],{"className":162302},[665],[363,162304,162306],{"className":162305},[638],[363,162307,162309],{"className":162308,"style":40117},[642],[363,162310],{},[363,162312,666],{"className":162313},[665],[363,162315,162317],{"className":162316},[638],[363,162318,162320],{"className":162319,"style":162003},[642],[363,162321],{},[363,162323],{"className":162324,"style":754},[505],[363,162326,162328,162331],{"className":162327},[407],[363,162329,45101],{"className":162330,"style":45131},[407,408],[363,162332,162334],{"className":162333},[629],[363,162335,162337,162357],{"className":162336},[633,634],[363,162338,162340,162354],{"className":162339},[638],[363,162341,162343],{"className":162342,"style":12529},[642],[363,162344,162345,162348],{"style":136107},[363,162346],{"className":162347,"style":651},[650],[363,162349,162351],{"className":162350},[655,656,657,658],[363,162352,12310],{"className":162353},[407,408,658],[363,162355,666],{"className":162356},[665],[363,162358,162360],{"className":162359},[638],[363,162361,162363],{"className":162362,"style":8315},[642],[363,162364],{},[11,162366,162367,162368,162371],{},"聚合性说明迪利克雷族在",[1572,162369,162370],{},"粗化","（coarsening）下封闭：把若干类别合并，得到的仍是同一族的成员，参数按分量求和。这一性质在层级分类、LDA 中主题的合并、以及 3.5 节中「由多项分布边缘化得到分类预测」的推导中都扮演关键角色。",[11,162373,162374,162375,162378,162379,3092,162407,162477,162478,162732,162733,162839,162840,163110],{},"由聚合性可导出",[1572,162376,162377],{},"中立性（neutrality）","：对任意 ",[363,162380,162382,162395],{"className":162381,"translate":367},[366],[363,162383,162385],{"className":162384},[371],[373,162386,162387],{"xmlns":375},[377,162388,162389,162393],{},[380,162390,162391],{},[383,162392,7911],{},[387,162394,7911],{"encoding":389},[363,162396,162398],{"className":162397,"ariaHidden":394},[393],[363,162399,162401,162404],{"className":162400},[398],[363,162402],{"className":162403,"style":12944},[402],[363,162405,7911],{"className":162406,"style":8614},[407,408],[363,162408,162410,162428],{"className":162409,"translate":367},[366],[363,162411,162413],{"className":162412},[371],[373,162414,162415],{"xmlns":375},[377,162416,162417,162425],{},[380,162418,162419],{},[543,162420,162421,162423],{},[383,162422,1121],{},[383,162424,7911],{},[387,162426,162427],{"encoding":389},"x_k",[363,162429,162431],{"className":162430,"ariaHidden":394},[393],[363,162432,162434,162437],{"className":162433},[398],[363,162435],{"className":162436,"style":13721},[402],[363,162438,162440,162443],{"className":162439},[407],[363,162441,1121],{"className":162442},[407,408],[363,162444,162446],{"className":162445},[629],[363,162447,162449,162469],{"className":162448},[633,634],[363,162450,162452,162466],{"className":162451},[638],[363,162453,162455],{"className":162454,"style":643},[642],[363,162456,162457,162460],{"style":730},[363,162458],{"className":162459,"style":651},[650],[363,162461,162463],{"className":162462},[655,656,657,658],[363,162464,7911],{"className":162465,"style":8614},[407,408,658],[363,162467,666],{"className":162468},[665],[363,162470,162472],{"className":162471},[638],[363,162473,162475],{"className":162474,"style":8315},[642],[363,162476],{}," 与其余分量的归一化版本 ",[363,162479,162481,162531],{"className":162480,"translate":367},[366],[363,162482,162484],{"className":162483},[371],[373,162485,162486],{"xmlns":375},[377,162487,162488,162528],{},[380,162489,162490],{},[543,162491,162492,162520],{},[380,162493,162494,162496,162502,162504,162506,162508,162510,162516,162518],{},[458,162495,461],{"fence":394},[543,162497,162498,162500],{},[383,162499,1121],{},[383,162501,12310],{},[383,162503,1288],{"mathvariant":557},[458,162505,461],{"stretchy":460},[463,162507,465],{},[458,162509,5160],{},[543,162511,162512,162514],{},[383,162513,1121],{},[383,162515,7911],{},[458,162517,468],{"stretchy":460},[458,162519,468],{"fence":394},[380,162521,162522,162524,162526],{},[383,162523,12310],{},[458,162525,49854],{"mathvariant":557},[383,162527,7911],{},[387,162529,162530],{"encoding":389},"\\left(x_i\u002F(1-x_k)\\right)_{i \\ne k}",[363,162532,162534],{"className":162533,"ariaHidden":394},[393],[363,162535,162537,162541],{"className":162536},[398],[363,162538],{"className":162539,"style":162540},[402],"height:1.1858em;vertical-align:-0.4358em;",[363,162542,162544,162654],{"className":162543},[758],[363,162545,162547,162550,162590,162593,162596,162599,162602,162605,162608,162648,162651],{"className":162546},[758],[363,162548,461],{"className":162549,"style":763},[494,762],[363,162551,162553,162556],{"className":162552},[407],[363,162554,1121],{"className":162555},[407,408],[363,162557,162559],{"className":162558},[629],[363,162560,162562,162582],{"className":162561},[633,634],[363,162563,162565,162579],{"className":162564},[638],[363,162566,162568],{"className":162567,"style":12529},[642],[363,162569,162570,162573],{"style":730},[363,162571],{"className":162572,"style":651},[650],[363,162574,162576],{"className":162575},[655,656,657,658],[363,162577,12310],{"className":162578},[407,408,658],[363,162580,666],{"className":162581},[665],[363,162583,162585],{"className":162584},[638],[363,162586,162588],{"className":162587,"style":8315},[642],[363,162589],{},[363,162591,1288],{"className":162592},[407],[363,162594,461],{"className":162595},[494],[363,162597,465],{"className":162598},[407],[363,162600],{"className":162601,"style":2934},[505],[363,162603,5160],{"className":162604},[2938],[363,162606],{"className":162607,"style":2934},[505],[363,162609,162611,162614],{"className":162610},[407],[363,162612,1121],{"className":162613},[407,408],[363,162615,162617],{"className":162616},[629],[363,162618,162620,162640],{"className":162619},[633,634],[363,162621,162623,162637],{"className":162622},[638],[363,162624,162626],{"className":162625,"style":643},[642],[363,162627,162628,162631],{"style":730},[363,162629],{"className":162630,"style":651},[650],[363,162632,162634],{"className":162633},[655,656,657,658],[363,162635,7911],{"className":162636,"style":8614},[407,408,658],[363,162638,666],{"className":162639},[665],[363,162641,162643],{"className":162642},[638],[363,162644,162646],{"className":162645,"style":8315},[642],[363,162647],{},[363,162649,468],{"className":162650},[501],[363,162652,468],{"className":162653,"style":763},[501,762],[363,162655,162657],{"className":162656},[629],[363,162658,162660,162723],{"className":162659},[633,634],[363,162661,162663,162720],{"className":162662},[638],[363,162664,162666],{"className":162665,"style":67358},[642],[363,162667,162669,162672],{"style":162668},"top:-2.4003em;margin-right:0.05em;",[363,162670],{"className":162671,"style":651},[650],[363,162673,162675],{"className":162674},[655,656,657,658],[363,162676,162678,162681,162717],{"className":162677},[407,658],[363,162679,12310],{"className":162680},[407,408,658],[363,162682,162684,162711,162714],{"className":162683},[510,658],[363,162685,162687],{"className":162686},[510,658],[363,162688,162690],{"className":162689},[407,4747,658],[363,162691,162693],{"className":162692},[4751,658],[363,162694,162696,162699,162708],{"className":162695},[4755,658],[363,162697],{"className":162698,"style":403},[402],[363,162700,162702],{"className":162701},[4762],[363,162703,162705],{"className":162704},[407,658],[363,162706,4769],{"className":162707},[510,658],[363,162709],{"className":162710},[4773],[363,162712],{"className":162713},[505,4777,658],[363,162715,471],{"className":162716},[510,658],[363,162718,7911],{"className":162719,"style":8614},[407,408,658],[363,162721,666],{"className":162722},[665],[363,162724,162726],{"className":162725},[638],[363,162727,162730],{"className":162728,"style":162729},[642],"height:0.4358em;",[363,162731],{}," 相互独立，且后者服从 ",[363,162734,162736,162766],{"className":162735,"translate":367},[366],[363,162737,162739],{"className":162738},[371],[373,162740,162741],{"xmlns":375},[377,162742,162743,162763],{},[380,162744,162745,162747,162749,162751,162761],{},[383,162746,137065],{"mathvariant":557},[458,162748,4450],{},[458,162750,461],{"stretchy":460},[543,162752,162753,162755],{},[383,162754,45101],{"mathvariant":136008},[380,162756,162757,162759],{},[458,162758,5160],{},[383,162760,7911],{},[458,162762,468],{"stretchy":460},[387,162764,162765],{"encoding":389},"\\operatorname{Dir}(\\boldsymbol{\\alpha}_{-k})",[363,162767,162769],{"className":162768,"ariaHidden":394},[393],[363,162770,162772,162775,162781,162784,162836],{"className":162771},[398],[363,162773],{"className":162774,"style":487},[402],[363,162776,162778],{"className":162777},[1831],[363,162779,137065],{"className":162780},[407,33009],[363,162782,461],{"className":162783},[494],[363,162785,162787,162796],{"className":162786},[407],[363,162788,162790],{"className":162789},[407],[363,162791,162793],{"className":162792},[407],[363,162794,45101],{"className":162795},[407,136068],[363,162797,162799],{"className":162798},[629],[363,162800,162802,162828],{"className":162801},[633,634],[363,162803,162805,162825],{"className":162804},[638],[363,162806,162808],{"className":162807,"style":643},[642],[363,162809,162810,162813],{"style":52793},[363,162811],{"className":162812,"style":651},[650],[363,162814,162816],{"className":162815},[655,656,657,658],[363,162817,162819,162822],{"className":162818},[407,658],[363,162820,5160],{"className":162821},[407,658],[363,162823,7911],{"className":162824,"style":8614},[407,408,658],[363,162826,666],{"className":162827},[665],[363,162829,162831],{"className":162830},[638],[363,162832,162834],{"className":162833,"style":135364},[642],[363,162835],{},[363,162837,468],{"className":162838},[501]," 而 ",[363,162841,162843,162893],{"className":162842,"translate":367},[366],[363,162844,162846],{"className":162845},[371],[373,162847,162848],{"xmlns":375},[377,162849,162850,162890],{},[380,162851,162852,162858,162860,162862,162864,162866,162872,162874,162880,162882,162888],{},[543,162853,162854,162856],{},[383,162855,1121],{},[383,162857,7911],{},[458,162859,9216],{},[383,162861,145757],{"mathvariant":557},[458,162863,4450],{},[458,162865,461],{"stretchy":460},[543,162867,162868,162870],{},[383,162869,45101],{},[383,162871,7911],{},[458,162873,898],{"separator":394},[543,162875,162876,162878],{},[383,162877,45101],{},[463,162879,474],{},[458,162881,5160],{},[543,162883,162884,162886],{},[383,162885,45101],{},[383,162887,7911],{},[458,162889,468],{"stretchy":460},[387,162891,162892],{"encoding":389},"x_k \\sim \\operatorname{Beta}(\\alpha_k, \\alpha_0 - \\alpha_k)",[363,162894,162896,162951,163061],{"className":162895,"ariaHidden":394},[393],[363,162897,162899,162902,162942,162945,162948],{"className":162898},[398],[363,162900],{"className":162901,"style":13721},[402],[363,162903,162905,162908],{"className":162904},[407],[363,162906,1121],{"className":162907},[407,408],[363,162909,162911],{"className":162910},[629],[363,162912,162914,162934],{"className":162913},[633,634],[363,162915,162917,162931],{"className":162916},[638],[363,162918,162920],{"className":162919,"style":643},[642],[363,162921,162922,162925],{"style":730},[363,162923],{"className":162924,"style":651},[650],[363,162926,162928],{"className":162927},[655,656,657,658],[363,162929,7911],{"className":162930,"style":8614},[407,408,658],[363,162932,666],{"className":162933},[665],[363,162935,162937],{"className":162936},[638],[363,162938,162940],{"className":162939,"style":8315},[642],[363,162941],{},[363,162943],{"className":162944,"style":506},[505],[363,162946,9216],{"className":162947},[510],[363,162949],{"className":162950,"style":506},[505],[363,162952,162954,162957,162963,162966,163006,163009,163012,163052,163055,163058],{"className":162953},[398],[363,162955],{"className":162956,"style":487},[402],[363,162958,162960],{"className":162959},[1831],[363,162961,145757],{"className":162962},[407,33009],[363,162964,461],{"className":162965},[494],[363,162967,162969,162972],{"className":162968},[407],[363,162970,45101],{"className":162971,"style":45131},[407,408],[363,162973,162975],{"className":162974},[629],[363,162976,162978,162998],{"className":162977},[633,634],[363,162979,162981,162995],{"className":162980},[638],[363,162982,162984],{"className":162983,"style":643},[642],[363,162985,162986,162989],{"style":136107},[363,162987],{"className":162988,"style":651},[650],[363,162990,162992],{"className":162991},[655,656,657,658],[363,162993,7911],{"className":162994,"style":8614},[407,408,658],[363,162996,666],{"className":162997},[665],[363,162999,163001],{"className":163000},[638],[363,163002,163004],{"className":163003,"style":8315},[642],[363,163005],{},[363,163007,898],{"className":163008},[920],[363,163010],{"className":163011,"style":754},[505],[363,163013,163015,163018],{"className":163014},[407],[363,163016,45101],{"className":163017,"style":45131},[407,408],[363,163019,163021],{"className":163020},[629],[363,163022,163024,163044],{"className":163023},[633,634],[363,163025,163027,163041],{"className":163026},[638],[363,163028,163030],{"className":163029,"style":11480},[642],[363,163031,163032,163035],{"style":136107},[363,163033],{"className":163034,"style":651},[650],[363,163036,163038],{"className":163037},[655,656,657,658],[363,163039,474],{"className":163040},[407,658],[363,163042,666],{"className":163043},[665],[363,163045,163047],{"className":163046},[638],[363,163048,163050],{"className":163049,"style":8315},[642],[363,163051],{},[363,163053],{"className":163054,"style":2934},[505],[363,163056,5160],{"className":163057},[2938],[363,163059],{"className":163060,"style":2934},[505],[363,163062,163064,163067,163107],{"className":163063},[398],[363,163065],{"className":163066,"style":487},[402],[363,163068,163070,163073],{"className":163069},[407],[363,163071,45101],{"className":163072,"style":45131},[407,408],[363,163074,163076],{"className":163075},[629],[363,163077,163079,163099],{"className":163078},[633,634],[363,163080,163082,163096],{"className":163081},[638],[363,163083,163085],{"className":163084,"style":643},[642],[363,163086,163087,163090],{"style":136107},[363,163088],{"className":163089,"style":651},[650],[363,163091,163093],{"className":163092},[655,656,657,658],[363,163094,7911],{"className":163095,"style":8614},[407,408,658],[363,163097,666],{"className":163098},[665],[363,163100,163102],{"className":163101},[638],[363,163103,163105],{"className":163104,"style":8315},[642],[363,163106],{},[363,163108,468],{"className":163109},[501],"。反复施用中立性，得到如下构造性表示：",[1340,163112,163114],{"title":163113},"命题 2.9（stick-breaking 表示）",[11,163115,881,163116,163407,163408,143151,163876,10527],{},[363,163117,163119,163178],{"className":163118,"translate":367},[366],[363,163120,163122],{"className":163121},[371],[373,163123,163124],{"xmlns":375},[377,163125,163126,163175],{},[380,163127,163128,163135,163137,163139,163141,163143],{},[543,163129,163130,163133],{},[383,163131,163132],{},"v",[383,163134,7911],{},[458,163136,9216],{},[383,163138,145757],{"mathvariant":557},[458,163140,4450],{},[1644,163142,1651],{},[380,163144,163145,163147,163153,163155,163167,163173],{},[458,163146,461],{"fence":394},[543,163148,163149,163151],{},[383,163150,45101],{},[383,163152,7911],{},[458,163154,898],{"separator":394},[543,163156,163157,163159],{},[458,163158,13808],{},[380,163160,163161,163163,163165],{},[383,163162,100360],{},[458,163164,3250],{},[383,163166,7911],{},[543,163168,163169,163171],{},[383,163170,45101],{},[383,163172,100360],{},[458,163174,468],{"fence":394},[387,163176,163177],{"encoding":389},"v_k \\sim \\operatorname{Beta}\\!\\left(\\alpha_k, \\sum_{j>k} \\alpha_j\\right)",[363,163179,163181,163236],{"className":163180,"ariaHidden":394},[393],[363,163182,163184,163187,163227,163230,163233],{"className":163183},[398],[363,163185],{"className":163186,"style":13721},[402],[363,163188,163190,163193],{"className":163189},[407],[363,163191,163132],{"className":163192,"style":1328},[407,408],[363,163194,163196],{"className":163195},[629],[363,163197,163199,163219],{"className":163198},[633,634],[363,163200,163202,163216],{"className":163201},[638],[363,163203,163205],{"className":163204,"style":643},[642],[363,163206,163207,163210],{"style":19190},[363,163208],{"className":163209,"style":651},[650],[363,163211,163213],{"className":163212},[655,656,657,658],[363,163214,7911],{"className":163215,"style":8614},[407,408,658],[363,163217,666],{"className":163218},[665],[363,163220,163222],{"className":163221},[638],[363,163223,163225],{"className":163224,"style":8315},[642],[363,163226],{},[363,163228],{"className":163229,"style":506},[505],[363,163231,9216],{"className":163232},[510],[363,163234],{"className":163235,"style":506},[505],[363,163237,163239,163242,163248,163251,163254],{"className":163238},[398],[363,163240],{"className":163241,"style":68464},[402],[363,163243,163245],{"className":163244},[1831],[363,163246,145757],{"className":163247},[407,33009],[363,163249],{"className":163250,"style":1859},[505],[363,163252],{"className":163253,"style":754},[505],[363,163255,163257,163263,163303,163306,163309,163358,163361,163401],{"className":163256},[758],[363,163258,163260],{"className":163259,"style":763},[494,762],[363,163261,461],{"className":163262},[767,4067],[363,163264,163266,163269],{"className":163265},[407],[363,163267,45101],{"className":163268,"style":45131},[407,408],[363,163270,163272],{"className":163271},[629],[363,163273,163275,163295],{"className":163274},[633,634],[363,163276,163278,163292],{"className":163277},[638],[363,163279,163281],{"className":163280,"style":643},[642],[363,163282,163283,163286],{"style":136107},[363,163284],{"className":163285,"style":651},[650],[363,163287,163289],{"className":163288},[655,656,657,658],[363,163290,7911],{"className":163291,"style":8614},[407,408,658],[363,163293,666],{"className":163294},[665],[363,163296,163298],{"className":163297},[638],[363,163299,163301],{"className":163300,"style":8315},[642],[363,163302],{},[363,163304,898],{"className":163305},[920],[363,163307],{"className":163308,"style":754},[505],[363,163310,163312,163315],{"className":163311},[1831],[363,163313,13808],{"className":163314,"style":40007},[1831,1832,5963],[363,163316,163318],{"className":163317},[629],[363,163319,163321,163350],{"className":163320},[633,634],[363,163322,163324,163347],{"className":163323},[638],[363,163325,163327],{"className":163326,"style":67358},[642],[363,163328,163329,163332],{"style":40023},[363,163330],{"className":163331,"style":651},[650],[363,163333,163335],{"className":163334},[655,656,657,658],[363,163336,163338,163341,163344],{"className":163337},[407,658],[363,163339,100360],{"className":163340,"style":100888},[407,408,658],[363,163342,3250],{"className":163343},[510,658],[363,163345,7911],{"className":163346,"style":8614},[407,408,658],[363,163348,666],{"className":163349},[665],[363,163351,163353],{"className":163352},[638],[363,163354,163356],{"className":163355,"style":162729},[642],[363,163357],{},[363,163359],{"className":163360,"style":754},[505],[363,163362,163364,163367],{"className":163363},[407],[363,163365,45101],{"className":163366,"style":45131},[407,408],[363,163368,163370],{"className":163369},[629],[363,163371,163373,163393],{"className":163372},[633,634],[363,163374,163376,163390],{"className":163375},[638],[363,163377,163379],{"className":163378,"style":12529},[642],[363,163380,163381,163384],{"style":136107},[363,163382],{"className":163383,"style":651},[650],[363,163385,163387],{"className":163386},[655,656,657,658],[363,163388,100360],{"className":163389,"style":100888},[407,408,658],[363,163391,666],{"className":163392},[665],[363,163394,163396],{"className":163395},[638],[363,163397,163399],{"className":163398,"style":673},[642],[363,163400],{},[363,163402,163404],{"className":163403,"style":763},[501,762],[363,163405,468],{"className":163406},[767,4067]," 相互独立。令\n",[363,163409,163411,163501],{"className":163410,"translate":367},[366],[363,163412,163414],{"className":163413},[371],[373,163415,163416],{"xmlns":375},[377,163417,163418,163498],{},[380,163419,163420,163426,163428,163434,163436,163438,163444,163446,163452,163464,163466,163468,163470,163476,163478,163480,163482,163484,163486,163488,163490,163492,163494,163496],{},[543,163421,163422,163424],{},[383,163423,1121],{},[463,163425,465],{},[458,163427,471],{},[543,163429,163430,163432],{},[383,163431,163132],{},[463,163433,465],{},[458,163435,898],{"separator":394},[505,163437],{"width":3609},[543,163439,163440,163442],{},[383,163441,1121],{},[383,163443,7911],{},[458,163445,471],{},[543,163447,163448,163450],{},[383,163449,163132],{},[383,163451,7911],{},[543,163453,163454,163456],{},[458,163455,136637],{},[380,163457,163458,163460,163462],{},[383,163459,100360],{},[458,163461,7598],{},[383,163463,7911],{},[458,163465,461],{"stretchy":460},[463,163467,465],{},[458,163469,5160],{},[543,163471,163472,163474],{},[383,163473,163132],{},[383,163475,100360],{},[458,163477,468],{"stretchy":460},[505,163479],{"width":4662},[458,163481,461],{"stretchy":460},[383,163483,7911],{},[458,163485,471],{},[463,163487,2810],{},[458,163489,898],{"separator":394},[458,163491,133107],{},[458,163493,898],{"separator":394},[383,163495,11041],{},[458,163497,468],{"stretchy":460},[387,163499,163500],{"encoding":389},"x_1 = v_1, \\qquad x_k = v_k \\prod_{j \u003C k}(1 - v_j) \\quad (k = 2, \\dots, K)",[363,163502,163504,163559,163663,163776,163843],{"className":163503,"ariaHidden":394},[393],[363,163505,163507,163510,163550,163553,163556],{"className":163506},[398],[363,163508],{"className":163509,"style":13721},[402],[363,163511,163513,163516],{"className":163512},[407],[363,163514,1121],{"className":163515},[407,408],[363,163517,163519],{"className":163518},[629],[363,163520,163522,163542],{"className":163521},[633,634],[363,163523,163525,163539],{"className":163524},[638],[363,163526,163528],{"className":163527,"style":11480},[642],[363,163529,163530,163533],{"style":730},[363,163531],{"className":163532,"style":651},[650],[363,163534,163536],{"className":163535},[655,656,657,658],[363,163537,465],{"className":163538},[407,658],[363,163540,666],{"className":163541},[665],[363,163543,163545],{"className":163544},[638],[363,163546,163548],{"className":163547,"style":8315},[642],[363,163549],{},[363,163551],{"className":163552,"style":506},[505],[363,163554,471],{"className":163555},[510],[363,163557],{"className":163558,"style":506},[505],[363,163560,163562,163565,163605,163608,163611,163614,163654,163657,163660],{"className":163561},[398],[363,163563],{"className":163564,"style":2623},[402],[363,163566,163568,163571],{"className":163567},[407],[363,163569,163132],{"className":163570,"style":1328},[407,408],[363,163572,163574],{"className":163573},[629],[363,163575,163577,163597],{"className":163576},[633,634],[363,163578,163580,163594],{"className":163579},[638],[363,163581,163583],{"className":163582,"style":11480},[642],[363,163584,163585,163588],{"style":19190},[363,163586],{"className":163587,"style":651},[650],[363,163589,163591],{"className":163590},[655,656,657,658],[363,163592,465],{"className":163593},[407,658],[363,163595,666],{"className":163596},[665],[363,163598,163600],{"className":163599},[638],[363,163601,163603],{"className":163602,"style":8315},[642],[363,163604],{},[363,163606,898],{"className":163607},[920],[363,163609],{"className":163610,"style":3981},[505],[363,163612],{"className":163613,"style":754},[505],[363,163615,163617,163620],{"className":163616},[407],[363,163618,1121],{"className":163619},[407,408],[363,163621,163623],{"className":163622},[629],[363,163624,163626,163646],{"className":163625},[633,634],[363,163627,163629,163643],{"className":163628},[638],[363,163630,163632],{"className":163631,"style":643},[642],[363,163633,163634,163637],{"style":730},[363,163635],{"className":163636,"style":651},[650],[363,163638,163640],{"className":163639},[655,656,657,658],[363,163641,7911],{"className":163642,"style":8614},[407,408,658],[363,163644,666],{"className":163645},[665],[363,163647,163649],{"className":163648},[638],[363,163650,163652],{"className":163651,"style":8315},[642],[363,163653],{},[363,163655],{"className":163656,"style":506},[505],[363,163658,471],{"className":163659},[510],[363,163661],{"className":163662,"style":506},[505],[363,163664,163666,163669,163709,163712,163761,163764,163767,163770,163773],{"className":163665},[398],[363,163667],{"className":163668,"style":162540},[402],[363,163670,163672,163675],{"className":163671},[407],[363,163673,163132],{"className":163674,"style":1328},[407,408],[363,163676,163678],{"className":163677},[629],[363,163679,163681,163701],{"className":163680},[633,634],[363,163682,163684,163698],{"className":163683},[638],[363,163685,163687],{"className":163686,"style":643},[642],[363,163688,163689,163692],{"style":19190},[363,163690],{"className":163691,"style":651},[650],[363,163693,163695],{"className":163694},[655,656,657,658],[363,163696,7911],{"className":163697,"style":8614},[407,408,658],[363,163699,666],{"className":163700},[665],[363,163702,163704],{"className":163703},[638],[363,163705,163707],{"className":163706,"style":8315},[642],[363,163708],{},[363,163710],{"className":163711,"style":754},[505],[363,163713,163715,163718],{"className":163714},[1831],[363,163716,136637],{"className":163717,"style":40007},[1831,1832,5963],[363,163719,163721],{"className":163720},[629],[363,163722,163724,163753],{"className":163723},[633,634],[363,163725,163727,163750],{"className":163726},[638],[363,163728,163730],{"className":163729,"style":67358},[642],[363,163731,163732,163735],{"style":40023},[363,163733],{"className":163734,"style":651},[650],[363,163736,163738],{"className":163737},[655,656,657,658],[363,163739,163741,163744,163747],{"className":163740},[407,658],[363,163742,100360],{"className":163743,"style":100888},[407,408,658],[363,163745,7598],{"className":163746},[510,658],[363,163748,7911],{"className":163749,"style":8614},[407,408,658],[363,163751,666],{"className":163752},[665],[363,163754,163756],{"className":163755},[638],[363,163757,163759],{"className":163758,"style":162729},[642],[363,163760],{},[363,163762,461],{"className":163763},[494],[363,163765,465],{"className":163766},[407],[363,163768],{"className":163769,"style":2934},[505],[363,163771,5160],{"className":163772},[2938],[363,163774],{"className":163775,"style":2934},[505],[363,163777,163779,163782,163822,163825,163828,163831,163834,163837,163840],{"className":163778},[398],[363,163780],{"className":163781,"style":618},[402],[363,163783,163785,163788],{"className":163784},[407],[363,163786,163132],{"className":163787,"style":1328},[407,408],[363,163789,163791],{"className":163790},[629],[363,163792,163794,163814],{"className":163793},[633,634],[363,163795,163797,163811],{"className":163796},[638],[363,163798,163800],{"className":163799,"style":12529},[642],[363,163801,163802,163805],{"style":19190},[363,163803],{"className":163804,"style":651},[650],[363,163806,163808],{"className":163807},[655,656,657,658],[363,163809,100360],{"className":163810,"style":100888},[407,408,658],[363,163812,666],{"className":163813},[665],[363,163815,163817],{"className":163816},[638],[363,163818,163820],{"className":163819,"style":673},[642],[363,163821],{},[363,163823,468],{"className":163824},[501],[363,163826],{"className":163827,"style":88315},[505],[363,163829,461],{"className":163830},[494],[363,163832,7911],{"className":163833,"style":8614},[407,408],[363,163835],{"className":163836,"style":506},[505],[363,163838,471],{"className":163839},[510],[363,163841],{"className":163842,"style":506},[505],[363,163844,163846,163849,163852,163855,163858,163861,163864,163867,163870,163873],{"className":163845},[398],[363,163847],{"className":163848,"style":487},[402],[363,163850,2810],{"className":163851},[407],[363,163853,898],{"className":163854},[920],[363,163856],{"className":163857,"style":754},[505],[363,163859,133107],{"className":163860},[758],[363,163862],{"className":163863,"style":754},[505],[363,163865,898],{"className":163866},[920],[363,163868],{"className":163869,"style":754},[505],[363,163871,11041],{"className":163872,"style":11129},[407,408],[363,163874,468],{"className":163875},[501],[363,163877,163879,163925],{"className":163878,"translate":367},[366],[363,163880,163882],{"className":163881},[371],[373,163883,163884],{"xmlns":375},[377,163885,163886,163922],{},[380,163887,163888,163890,163896,163898,163900,163902,163908,163910,163912,163914,163916,163918,163920],{},[458,163889,461],{"stretchy":460},[543,163891,163892,163894],{},[383,163893,1121],{},[463,163895,465],{},[458,163897,898],{"separator":394},[458,163899,133107],{},[458,163901,898],{"separator":394},[543,163903,163904,163906],{},[383,163905,1121],{},[383,163907,11041],{},[458,163909,468],{"stretchy":460},[458,163911,9216],{},[383,163913,137065],{"mathvariant":557},[458,163915,4450],{},[458,163917,461],{"stretchy":460},[383,163919,45101],{"mathvariant":136008},[458,163921,468],{"stretchy":460},[387,163923,163924],{"encoding":389},"(x_1, \\dots, x_K) \\sim \\operatorname{Dir}(\\boldsymbol{\\alpha})",[363,163926,163928,164047],{"className":163927,"ariaHidden":394},[393],[363,163929,163931,163934,163937,163977,163980,163983,163986,163989,163992,163995,164035,164038,164041,164044],{"className":163930},[398],[363,163932],{"className":163933,"style":487},[402],[363,163935,461],{"className":163936},[494],[363,163938,163940,163943],{"className":163939},[407],[363,163941,1121],{"className":163942},[407,408],[363,163944,163946],{"className":163945},[629],[363,163947,163949,163969],{"className":163948},[633,634],[363,163950,163952,163966],{"className":163951},[638],[363,163953,163955],{"className":163954,"style":11480},[642],[363,163956,163957,163960],{"style":730},[363,163958],{"className":163959,"style":651},[650],[363,163961,163963],{"className":163962},[655,656,657,658],[363,163964,465],{"className":163965},[407,658],[363,163967,666],{"className":163968},[665],[363,163970,163972],{"className":163971},[638],[363,163973,163975],{"className":163974,"style":8315},[642],[363,163976],{},[363,163978,898],{"className":163979},[920],[363,163981],{"className":163982,"style":754},[505],[363,163984,133107],{"className":163985},[758],[363,163987],{"className":163988,"style":754},[505],[363,163990,898],{"className":163991},[920],[363,163993],{"className":163994,"style":754},[505],[363,163996,163998,164001],{"className":163997},[407],[363,163999,1121],{"className":164000},[407,408],[363,164002,164004],{"className":164003},[629],[363,164005,164007,164027],{"className":164006},[633,634],[363,164008,164010,164024],{"className":164009},[638],[363,164011,164013],{"className":164012,"style":727},[642],[363,164014,164015,164018],{"style":730},[363,164016],{"className":164017,"style":651},[650],[363,164019,164021],{"className":164020},[655,656,657,658],[363,164022,11041],{"className":164023,"style":11129},[407,408,658],[363,164025,666],{"className":164026},[665],[363,164028,164030],{"className":164029},[638],[363,164031,164033],{"className":164032,"style":8315},[642],[363,164034],{},[363,164036,468],{"className":164037},[501],[363,164039],{"className":164040,"style":506},[505],[363,164042,9216],{"className":164043},[510],[363,164045],{"className":164046,"style":506},[505],[363,164048,164050,164053,164059,164062,164071],{"className":164049},[398],[363,164051],{"className":164052,"style":487},[402],[363,164054,164056],{"className":164055},[1831],[363,164057,137065],{"className":164058},[407,33009],[363,164060,461],{"className":164061},[494],[363,164063,164065],{"className":164064},[407],[363,164066,164068],{"className":164067},[407],[363,164069,45101],{"className":164070},[407,136068],[363,164072,468],{"className":164073},[501],[11,164075,164076,164077,164105,164106,164176],{},"命题 2.9 是 Sethuraman 式的「折断木棍」构造在有限维的情形：从长度为 ",[363,164078,164080,164093],{"className":164079,"translate":367},[366],[363,164081,164083],{"className":164082},[371],[373,164084,164085],{"xmlns":375},[377,164086,164087,164091],{},[380,164088,164089],{},[463,164090,465],{},[387,164092,465],{"encoding":389},[363,164094,164096],{"className":164095,"ariaHidden":394},[393],[363,164097,164099,164102],{"className":164098},[398],[363,164100],{"className":164101,"style":520},[402],[363,164103,465],{"className":164104},[407]," 的木棍中依次折断出比例 ",[363,164107,164109,164127],{"className":164108,"translate":367},[366],[363,164110,164112],{"className":164111},[371],[373,164113,164114],{"xmlns":375},[377,164115,164116,164124],{},[380,164117,164118],{},[543,164119,164120,164122],{},[383,164121,163132],{},[383,164123,7911],{},[387,164125,164126],{"encoding":389},"v_k",[363,164128,164130],{"className":164129,"ariaHidden":394},[393],[363,164131,164133,164136],{"className":164132},[398],[363,164134],{"className":164135,"style":13721},[402],[363,164137,164139,164142],{"className":164138},[407],[363,164140,163132],{"className":164141,"style":1328},[407,408],[363,164143,164145],{"className":164144},[629],[363,164146,164148,164168],{"className":164147},[633,634],[363,164149,164151,164165],{"className":164150},[638],[363,164152,164154],{"className":164153,"style":643},[642],[363,164155,164156,164159],{"style":19190},[363,164157],{"className":164158,"style":651},[650],[363,164160,164162],{"className":164161},[655,656,657,658],[363,164163,7911],{"className":164164,"style":8614},[407,408,658],[363,164166,666],{"className":164167},[665],[363,164169,164171],{"className":164170},[638],[363,164172,164174],{"className":164173,"style":8315},[642],[363,164175],{}," 的一段。它在无穷维极限下给出 Dirichlet 过程，因而把本文的有限维话题与贝叶斯非参数方法连接起来。",[2658,164178,164180],{"id":164179},"_26-参数的直观伪计数及其边界","2.6 参数的直观：伪计数及其边界",[11,164182,164183,164184,164218],{},"综合 2.1 至 2.5 节，可以把形状参数 ",[363,164185,164187,164200],{"className":164186,"translate":367},[366],[363,164188,164190],{"className":164189},[371],[373,164191,164192],{"xmlns":375},[377,164193,164194,164198],{},[380,164195,164196],{},[383,164197,45101],{"mathvariant":136008},[387,164199,137027],{"encoding":389},[363,164201,164203],{"className":164202,"ariaHidden":394},[393],[363,164204,164206,164209],{"className":164205},[398],[363,164207],{"className":164208,"style":135617},[402],[363,164210,164212],{"className":164211},[407],[363,164213,164215],{"className":164214},[407],[363,164216,45101],{"className":164217},[407,136068]," 的语义概括为三点：",[7009,164220,164221,164332,164507],{},[7012,164222,164223,164261,164262,164331],{},[1572,164224,164225,164226,164260],{},"在共轭更新中，",[363,164227,164229,164242],{"className":164228,"translate":367},[366],[363,164230,164232],{"className":164231},[371],[373,164233,164234],{"xmlns":375},[377,164235,164236,164240],{},[380,164237,164238],{},[383,164239,45101],{"mathvariant":136008},[387,164241,137027],{"encoding":389},[363,164243,164245],{"className":164244,"ariaHidden":394},[393],[363,164246,164248,164251],{"className":164247},[398],[363,164249],{"className":164250,"style":135617},[402],[363,164252,164254],{"className":164253},[407],[363,164255,164257],{"className":164256},[407],[363,164258,45101],{"className":164259},[407,136068]," 起先验样本计数的角色","（命题 2.5），其总强度 ",[363,164263,164265,164282],{"className":164264,"translate":367},[366],[363,164266,164268],{"className":164267},[371],[373,164269,164270],{"xmlns":375},[377,164271,164272,164280],{},[380,164273,164274],{},[543,164275,164276,164278],{},[383,164277,45101],{},[463,164279,474],{},[387,164281,152251],{"encoding":389},[363,164283,164285],{"className":164284,"ariaHidden":394},[393],[363,164286,164288,164291],{"className":164287},[398],[363,164289],{"className":164290,"style":13721},[402],[363,164292,164294,164297],{"className":164293},[407],[363,164295,45101],{"className":164296,"style":45131},[407,408],[363,164298,164300],{"className":164299},[629],[363,164301,164303,164323],{"className":164302},[633,634],[363,164304,164306,164320],{"className":164305},[638],[363,164307,164309],{"className":164308,"style":11480},[642],[363,164310,164311,164314],{"style":136107},[363,164312],{"className":164313,"style":651},[650],[363,164315,164317],{"className":164316},[655,656,657,658],[363,164318,474],{"className":164319},[407,658],[363,164321,666],{"className":164322},[665],[363,164324,164326],{"className":164325},[638],[363,164327,164329],{"className":164328,"style":8315},[642],[363,164330],{}," 是「先验等价样本量」（推论 2.7）。",[7012,164333,164334,164471,164472,164506],{},[1572,164335,164336,164337,164365,164366,164400,164401,164470],{},"在几何上，",[363,164338,164340,164353],{"className":164339,"translate":367},[366],[363,164341,164343],{"className":164342},[371],[373,164344,164345],{"xmlns":375},[377,164346,164347,164351],{},[380,164348,164349],{},[383,164350,45101],{},[387,164352,49437],{"encoding":389},[363,164354,164356],{"className":164355,"ariaHidden":394},[393],[363,164357,164359,164362],{"className":164358},[398],[363,164360],{"className":164361,"style":2692},[402],[363,164363,45101],{"className":164364,"style":45131},[407,408]," 由方向 ",[363,164367,164369,164382],{"className":164368,"translate":367},[366],[363,164370,164372],{"className":164371},[371],[373,164373,164374],{"xmlns":375},[377,164375,164376,164380],{},[380,164377,164378],{},[383,164379,2711],{"mathvariant":136008},[387,164381,152212],{"encoding":389},[363,164383,164385],{"className":164384,"ariaHidden":394},[393],[363,164386,164388,164391],{"className":164387},[398],[363,164389],{"className":164390,"style":133764},[402],[363,164392,164394],{"className":164393},[407],[363,164395,164397],{"className":164396},[407],[363,164398,2711],{"className":164399},[407,136068]," 与精度 ",[363,164402,164404,164421],{"className":164403,"translate":367},[366],[363,164405,164407],{"className":164406},[371],[373,164408,164409],{"xmlns":375},[377,164410,164411,164419],{},[380,164412,164413],{},[543,164414,164415,164417],{},[383,164416,45101],{},[463,164418,474],{},[387,164420,152251],{"encoding":389},[363,164422,164424],{"className":164423,"ariaHidden":394},[393],[363,164425,164427,164430],{"className":164426},[398],[363,164428],{"className":164429,"style":13721},[402],[363,164431,164433,164436],{"className":164432},[407],[363,164434,45101],{"className":164435,"style":45131},[407,408],[363,164437,164439],{"className":164438},[629],[363,164440,164442,164462],{"className":164441},[633,634],[363,164443,164445,164459],{"className":164444},[638],[363,164446,164448],{"className":164447,"style":11480},[642],[363,164449,164450,164453],{"style":136107},[363,164451],{"className":164452,"style":651},[650],[363,164454,164456],{"className":164455},[655,656,657,658],[363,164457,474],{"className":164458},[407,658],[363,164460,666],{"className":164461},[665],[363,164463,164465],{"className":164464},[638],[363,164466,164468],{"className":164467,"style":8315},[642],[363,164469],{}," 两个正交分量构成","（2.2 节），精度决定围绕 ",[363,164473,164475,164488],{"className":164474,"translate":367},[366],[363,164476,164478],{"className":164477},[371],[373,164479,164480],{"xmlns":375},[377,164481,164482,164486],{},[380,164483,164484],{},[383,164485,2711],{"mathvariant":136008},[387,164487,152212],{"encoding":389},[363,164489,164491],{"className":164490,"ariaHidden":394},[393],[363,164492,164494,164497],{"className":164493},[398],[363,164495],{"className":164496,"style":133764},[402],[363,164498,164500],{"className":164499},[407],[363,164501,164503],{"className":164502},[407],[363,164504,2711],{"className":164505},[407,136068]," 的收缩程度。",[7012,164508,164509,43112,164675,164767,164768,164860],{},[1572,164510,164511,164512,164604,164605,164674],{},"在似然意义上，",[363,164513,164515,164537],{"className":164514,"translate":367},[366],[363,164516,164518],{"className":164517},[371],[373,164519,164520],{"xmlns":375},[377,164521,164522,164534],{},[380,164523,164524,164530,164532],{},[543,164525,164526,164528],{},[383,164527,45101],{},[383,164529,12310],{},[458,164531,5160],{},[463,164533,465],{},[387,164535,164536],{"encoding":389},"\\alpha_i - 1",[363,164538,164540,164595],{"className":164539,"ariaHidden":394},[393],[363,164541,164543,164546,164586,164589,164592],{"className":164542},[398],[363,164544],{"className":164545,"style":145420},[402],[363,164547,164549,164552],{"className":164548},[407],[363,164550,45101],{"className":164551,"style":45131},[407,408],[363,164553,164555],{"className":164554},[629],[363,164556,164558,164578],{"className":164557},[633,634],[363,164559,164561,164575],{"className":164560},[638],[363,164562,164564],{"className":164563,"style":12529},[642],[363,164565,164566,164569],{"style":136107},[363,164567],{"className":164568,"style":651},[650],[363,164570,164572],{"className":164571},[655,656,657,658],[363,164573,12310],{"className":164574},[407,408,658],[363,164576,666],{"className":164577},[665],[363,164579,164581],{"className":164580},[638],[363,164582,164584],{"className":164583,"style":8315},[642],[363,164585],{},[363,164587],{"className":164588,"style":2934},[505],[363,164590,5160],{"className":164591},[2938],[363,164593],{"className":164594,"style":2934},[505],[363,164596,164598,164601],{"className":164597},[398],[363,164599],{"className":164600,"style":520},[402],[363,164602,465],{"className":164603},[407]," 是对数密度中 ",[363,164606,164608,164625],{"className":164607,"translate":367},[366],[363,164609,164611],{"className":164610},[371],[373,164612,164613],{"xmlns":375},[377,164614,164615,164623],{},[380,164616,164617],{},[543,164618,164619,164621],{},[383,164620,1121],{},[383,164622,12310],{},[387,164624,146649],{"encoding":389},[363,164626,164628],{"className":164627,"ariaHidden":394},[393],[363,164629,164631,164634],{"className":164630},[398],[363,164632],{"className":164633,"style":13721},[402],[363,164635,164637,164640],{"className":164636},[407],[363,164638,1121],{"className":164639},[407,408],[363,164641,164643],{"className":164642},[629],[363,164644,164646,164666],{"className":164645},[633,634],[363,164647,164649,164663],{"className":164648},[638],[363,164650,164652],{"className":164651,"style":12529},[642],[363,164653,164654,164657],{"style":730},[363,164655],{"className":164656,"style":651},[650],[363,164658,164660],{"className":164659},[655,656,657,658],[363,164661,12310],{"className":164662},[407,408,658],[363,164664,666],{"className":164665},[665],[363,164667,164669],{"className":164668},[638],[363,164670,164672],{"className":164671,"style":8315},[642],[363,164673],{}," 的指数",[363,164676,164678,164700],{"className":164677,"translate":367},[366],[363,164679,164681],{"className":164680},[371],[373,164682,164683],{"xmlns":375},[377,164684,164685,164697],{},[380,164686,164687,164693,164695],{},[543,164688,164689,164691],{},[383,164690,45101],{},[383,164692,12310],{},[458,164694,7598],{},[463,164696,465],{},[387,164698,164699],{"encoding":389},"\\alpha_i \u003C 1",[363,164701,164703,164758],{"className":164702,"ariaHidden":394},[393],[363,164704,164706,164709,164749,164752,164755],{"className":164705},[398],[363,164707],{"className":164708,"style":134669},[402],[363,164710,164712,164715],{"className":164711},[407],[363,164713,45101],{"className":164714,"style":45131},[407,408],[363,164716,164718],{"className":164717},[629],[363,164719,164721,164741],{"className":164720},[633,634],[363,164722,164724,164738],{"className":164723},[638],[363,164725,164727],{"className":164726,"style":12529},[642],[363,164728,164729,164732],{"style":136107},[363,164730],{"className":164731,"style":651},[650],[363,164733,164735],{"className":164734},[655,656,657,658],[363,164736,12310],{"className":164737},[407,408,658],[363,164739,666],{"className":164740},[665],[363,164742,164744],{"className":164743},[638],[363,164745,164747],{"className":164746,"style":8315},[642],[363,164748],{},[363,164750],{"className":164751,"style":506},[505],[363,164753,7598],{"className":164754},[510],[363,164756],{"className":164757,"style":506},[505],[363,164759,164761,164764],{"className":164760},[398],[363,164762],{"className":164763,"style":520},[402],[363,164765,465],{"className":164766},[407]," 意味着密度在 ",[363,164769,164771,164793],{"className":164770,"translate":367},[366],[363,164772,164774],{"className":164773},[371],[373,164775,164776],{"xmlns":375},[377,164777,164778,164790],{},[380,164779,164780,164786,164788],{},[543,164781,164782,164784],{},[383,164783,1121],{},[383,164785,12310],{},[458,164787,1376],{},[463,164789,474],{},[387,164791,164792],{"encoding":389},"x_i \\to 0",[363,164794,164796,164851],{"className":164795,"ariaHidden":394},[393],[363,164797,164799,164802,164842,164845,164848],{"className":164798},[398],[363,164800],{"className":164801,"style":13721},[402],[363,164803,164805,164808],{"className":164804},[407],[363,164806,1121],{"className":164807},[407,408],[363,164809,164811],{"className":164810},[629],[363,164812,164814,164834],{"className":164813},[633,634],[363,164815,164817,164831],{"className":164816},[638],[363,164818,164820],{"className":164819,"style":12529},[642],[363,164821,164822,164825],{"style":730},[363,164823],{"className":164824,"style":651},[650],[363,164826,164828],{"className":164827},[655,656,657,658],[363,164829,12310],{"className":164830},[407,408,658],[363,164832,666],{"className":164833},[665],[363,164835,164837],{"className":164836},[638],[363,164838,164840],{"className":164839,"style":8315},[642],[363,164841],{},[363,164843],{"className":164844,"style":506},[505],[363,164846,1376],{"className":164847},[510],[363,164849],{"className":164850,"style":506},[505],[363,164852,164854,164857],{"className":164853},[398],[363,164855],{"className":164856,"style":520},[402],[363,164858,474],{"className":164859},[407]," 处发散。",[11,164862,164863,164864,164866,164867,164928],{},"对于",[1572,164865,30033],{},"情形 ",[363,164868,164870,164889],{"className":164869,"translate":367},[366],[363,164871,164873],{"className":164872},[371],[373,164874,164875],{"xmlns":375},[377,164876,164877,164887],{},[380,164878,164879,164881,164883,164885],{},[383,164880,45101],{"mathvariant":136008},[458,164882,471],{},[383,164884,45101],{},[463,164886,465],{"mathvariant":75560},[387,164888,156708],{"encoding":389},[363,164890,164892,164916],{"className":164891,"ariaHidden":394},[393],[363,164893,164895,164898,164907,164910,164913],{"className":164894},[398],[363,164896],{"className":164897,"style":135617},[402],[363,164899,164901],{"className":164900},[407],[363,164902,164904],{"className":164903},[407],[363,164905,45101],{"className":164906},[407,136068],[363,164908],{"className":164909,"style":506},[505],[363,164911,471],{"className":164912},[510],[363,164914],{"className":164915,"style":506},[505],[363,164917,164919,164922,164925],{"className":164918},[398],[363,164920],{"className":164921,"style":520},[402],[363,164923,45101],{"className":164924,"style":45131},[407,408],[363,164926,465],{"className":164927},[407,75905],"，这三重语义给出一条完整的形态谱：",[52839,164930,164931,164948],{},[52842,164932,164933],{},[52845,164934,164935,164939,164942,164945],{},[52848,164936,164938],{"align":164937},"left","参数区间",[52848,164940,164941],{"align":164937},"分布的形态",[52848,164943,164944],{"align":164937},"采样的典型特征",[52848,164946,164947],{"align":164937},"典型用途",[52937,164949,164950,165123,165186],{},[52845,164951,164952,165005,165089,165120],{},[52942,164953,164954],{"align":164937},[363,164955,164957,164975],{"className":164956,"translate":367},[366],[363,164958,164960],{"className":164959},[371],[373,164961,164962],{"xmlns":375},[377,164963,164964,164972],{},[380,164965,164966,164968,164970],{},[383,164967,45101],{},[458,164969,1376],{},[463,164971,474],{},[387,164973,164974],{"encoding":389},"\\alpha \\to 0",[363,164976,164978,164996],{"className":164977,"ariaHidden":394},[393],[363,164979,164981,164984,164987,164990,164993],{"className":164980},[398],[363,164982],{"className":164983,"style":2692},[402],[363,164985,45101],{"className":164986,"style":45131},[407,408],[363,164988],{"className":164989,"style":506},[505],[363,164991,1376],{"className":164992},[510],[363,164994],{"className":164995,"style":506},[505],[363,164997,164999,165002],{"className":164998},[398],[363,165000],{"className":165001,"style":520},[402],[363,165003,474],{"className":165004},[407],[52942,165006,165007,165008,165088],{"align":164937},"质量集中于顶点 ",[363,165009,165011,165033],{"className":165010,"translate":367},[366],[363,165012,165014],{"className":165013},[371],[373,165015,165016],{"xmlns":375},[377,165017,165018,165030],{},[380,165019,165020,165022,165028],{},[458,165021,3245],{"stretchy":460},[543,165023,165024,165026],{},[383,165025,7914],{"mathvariant":75560},[383,165027,12310],{},[458,165029,3255],{"stretchy":460},[387,165031,165032],{"encoding":389},"\\{\\mathbf{e}_i\\}",[363,165034,165036],{"className":165035,"ariaHidden":394},[393],[363,165037,165039,165042,165045,165085],{"className":165038},[398],[363,165040],{"className":165041,"style":487},[402],[363,165043,3245],{"className":165044},[494],[363,165046,165048,165051],{"className":165047},[407],[363,165049,7914],{"className":165050},[407,75905],[363,165052,165054],{"className":165053},[629],[363,165055,165057,165077],{"className":165056},[633,634],[363,165058,165060,165074],{"className":165059},[638],[363,165061,165063],{"className":165062,"style":12529},[642],[363,165064,165065,165068],{"style":730},[363,165066],{"className":165067,"style":651},[650],[363,165069,165071],{"className":165070},[655,656,657,658],[363,165072,12310],{"className":165073},[407,408,658],[363,165075,666],{"className":165076},[665],[363,165078,165080],{"className":165079},[638],[363,165081,165083],{"className":165082,"style":8315},[642],[363,165084],{},[363,165086,3255],{"className":165087},[501]," 邻域",[52942,165090,165091,165092],{"align":164937},"极端稀疏，单个分量接近 ",[363,165093,165095,165108],{"className":165094,"translate":367},[366],[363,165096,165098],{"className":165097},[371],[373,165099,165100],{"xmlns":375},[377,165101,165102,165106],{},[380,165103,165104],{},[463,165105,465],{},[387,165107,465],{"encoding":389},[363,165109,165111],{"className":165110,"ariaHidden":394},[393],[363,165112,165114,165117],{"className":165113},[398],[363,165115],{"className":165116,"style":520},[402],[363,165118,465],{"className":165119},[407],[52942,165121,165122],{"align":164937},"LDA 文档—主题混合（文档只涉少数主题）",[52845,165124,165125,165177,165180,165183],{},[52942,165126,165127],{"align":164937},[363,165128,165130,165147],{"className":165129,"translate":367},[366],[363,165131,165133],{"className":165132},[371],[373,165134,165135],{"xmlns":375},[377,165136,165137,165145],{},[380,165138,165139,165141,165143],{},[383,165140,45101],{},[458,165142,471],{},[463,165144,465],{},[387,165146,156797],{"encoding":389},[363,165148,165150,165168],{"className":165149,"ariaHidden":394},[393],[363,165151,165153,165156,165159,165162,165165],{"className":165152},[398],[363,165154],{"className":165155,"style":2692},[402],[363,165157,45101],{"className":165158,"style":45131},[407,408],[363,165160],{"className":165161,"style":506},[505],[363,165163,471],{"className":165164},[510],[363,165166],{"className":165167,"style":506},[505],[363,165169,165171,165174],{"className":165170},[398],[363,165172],{"className":165173,"style":520},[402],[363,165175,465],{"className":165176},[407],[52942,165178,165179],{"align":164937},"单纯形上的均匀分布",[52942,165181,165182],{"align":164937},"各分量量级相当，无偏好",[52942,165184,165185],{"align":164937},"无信息先验",[52845,165187,165188,165241,165313,165353],{},[52942,165189,165190],{"align":164937},[363,165191,165193,165211],{"className":165192,"translate":367},[366],[363,165194,165196],{"className":165195},[371],[373,165197,165198],{"xmlns":375},[377,165199,165200,165208],{},[380,165201,165202,165204,165206],{},[383,165203,45101],{},[458,165205,3250],{},[463,165207,465],{},[387,165209,165210],{"encoding":389},"\\alpha > 1",[363,165212,165214,165232],{"className":165213,"ariaHidden":394},[393],[363,165215,165217,165220,165223,165226,165229],{"className":165216},[398],[363,165218],{"className":165219,"style":6271},[402],[363,165221,45101],{"className":165222,"style":45131},[407,408],[363,165224],{"className":165225,"style":506},[505],[363,165227,3250],{"className":165228},[510],[363,165230],{"className":165231,"style":506},[505],[363,165233,165235,165238],{"className":165234},[398],[363,165236],{"className":165237,"style":520},[402],[363,165239,465],{"className":165240},[407],[52942,165242,165243,165244,165283,165284,165312],{"align":164937},"集中于中心 ",[363,165245,165247,165265],{"className":165246,"translate":367},[366],[363,165248,165250],{"className":165249},[371],[373,165251,165252],{"xmlns":375},[377,165253,165254,165262],{},[380,165255,165256,165258,165260],{},[463,165257,465],{"mathvariant":75560},[383,165259,1288],{"mathvariant":557},[383,165261,11041],{},[387,165263,165264],{"encoding":389},"\\mathbf{1}\u002FK",[363,165266,165268],{"className":165267,"ariaHidden":394},[393],[363,165269,165271,165274,165277,165280],{"className":165270},[398],[363,165272],{"className":165273,"style":487},[402],[363,165275,465],{"className":165276},[407,75905],[363,165278,1288],{"className":165279},[407],[363,165281,11041],{"className":165282,"style":11129},[407,408],"，随 ",[363,165285,165287,165300],{"className":165286,"translate":367},[366],[363,165288,165290],{"className":165289},[371],[373,165291,165292],{"xmlns":375},[377,165293,165294,165298],{},[380,165295,165296],{},[383,165297,45101],{},[387,165299,49437],{"encoding":389},[363,165301,165303],{"className":165302,"ariaHidden":394},[393],[363,165304,165306,165309],{"className":165305},[398],[363,165307],{"className":165308,"style":2692},[402],[363,165310,45101],{"className":165311,"style":45131},[407,408]," 增大而收缩",[52942,165314,165315,165316,165352],{"align":164937},"各分量接近 ",[363,165317,165319,165337],{"className":165318,"translate":367},[366],[363,165320,165322],{"className":165321},[371],[373,165323,165324],{"xmlns":375},[377,165325,165326,165334],{},[380,165327,165328,165330,165332],{},[463,165329,465],{},[383,165331,1288],{"mathvariant":557},[383,165333,11041],{},[387,165335,165336],{"encoding":389},"1\u002FK",[363,165338,165340],{"className":165339,"ariaHidden":394},[393],[363,165341,165343,165346,165349],{"className":165342},[398],[363,165344],{"className":165345,"style":487},[402],[363,165347,8936],{"className":165348},[407],[363,165350,11041],{"className":165351,"style":11129},[407,408]," 的平滑向量",[52942,165354,165355],{"align":164937},"强正则化、收缩估计",[11,165357,165358,165359,165428,165429,165521,165522,10649,165613,165728,165729,165950],{},"此处必须澄清一个常见但过强的说法：把 ",[363,165360,165362,165379],{"className":165361,"translate":367},[366],[363,165363,165365],{"className":165364},[371],[373,165366,165367],{"xmlns":375},[377,165368,165369,165377],{},[380,165370,165371],{},[543,165372,165373,165375],{},[383,165374,45101],{},[383,165376,12310],{},[387,165378,142548],{"encoding":389},[363,165380,165382],{"className":165381,"ariaHidden":394},[393],[363,165383,165385,165388],{"className":165384},[398],[363,165386],{"className":165387,"style":13721},[402],[363,165389,165391,165394],{"className":165390},[407],[363,165392,45101],{"className":165393,"style":45131},[407,408],[363,165395,165397],{"className":165396},[629],[363,165398,165400,165420],{"className":165399},[633,634],[363,165401,165403,165417],{"className":165402},[638],[363,165404,165406],{"className":165405,"style":12529},[642],[363,165407,165408,165411],{"style":136107},[363,165409],{"className":165410,"style":651},[650],[363,165412,165414],{"className":165413},[655,656,657,658],[363,165415,12310],{"className":165416},[407,408,658],[363,165418,666],{"className":165419},[665],[363,165421,165423],{"className":165422},[638],[363,165424,165426],{"className":165425,"style":8315},[642],[363,165427],{}," 直接称为「观测到的次数」只在 ",[363,165430,165432,165454],{"className":165431,"translate":367},[366],[363,165433,165435],{"className":165434},[371],[373,165436,165437],{"xmlns":375},[377,165438,165439,165451],{},[380,165440,165441,165447,165449],{},[543,165442,165443,165445],{},[383,165444,45101],{},[383,165446,12310],{},[458,165448,7275],{},[463,165450,465],{},[387,165452,165453],{"encoding":389},"\\alpha_i \\ge 1",[363,165455,165457,165512],{"className":165456,"ariaHidden":394},[393],[363,165458,165460,165463,165503,165506,165509],{"className":165459},[398],[363,165461],{"className":165462,"style":155227},[402],[363,165464,165466,165469],{"className":165465},[407],[363,165467,45101],{"className":165468,"style":45131},[407,408],[363,165470,165472],{"className":165471},[629],[363,165473,165475,165495],{"className":165474},[633,634],[363,165476,165478,165492],{"className":165477},[638],[363,165479,165481],{"className":165480,"style":12529},[642],[363,165482,165483,165486],{"style":136107},[363,165484],{"className":165485,"style":651},[650],[363,165487,165489],{"className":165488},[655,656,657,658],[363,165490,12310],{"className":165491},[407,408,658],[363,165493,666],{"className":165494},[665],[363,165496,165498],{"className":165497},[638],[363,165499,165501],{"className":165500,"style":8315},[642],[363,165502],{},[363,165504],{"className":165505,"style":506},[505],[363,165507,7275],{"className":165508},[510],[363,165510],{"className":165511,"style":506},[505],[363,165513,165515,165518],{"className":165514},[398],[363,165516],{"className":165517,"style":520},[402],[363,165519,465],{"className":165520},[407]," 时在字面上成立。当 ",[363,165523,165525,165546],{"className":165524,"translate":367},[366],[363,165526,165528],{"className":165527},[371],[373,165529,165530],{"xmlns":375},[377,165531,165532,165544],{},[380,165533,165534,165540,165542],{},[543,165535,165536,165538],{},[383,165537,45101],{},[383,165539,12310],{},[458,165541,7598],{},[463,165543,465],{},[387,165545,164699],{"encoding":389},[363,165547,165549,165604],{"className":165548,"ariaHidden":394},[393],[363,165550,165552,165555,165595,165598,165601],{"className":165551},[398],[363,165553],{"className":165554,"style":134669},[402],[363,165556,165558,165561],{"className":165557},[407],[363,165559,45101],{"className":165560,"style":45131},[407,408],[363,165562,165564],{"className":165563},[629],[363,165565,165567,165587],{"className":165566},[633,634],[363,165568,165570,165584],{"className":165569},[638],[363,165571,165573],{"className":165572,"style":12529},[642],[363,165574,165575,165578],{"style":136107},[363,165576],{"className":165577,"style":651},[650],[363,165579,165581],{"className":165580},[655,656,657,658],[363,165582,12310],{"className":165583},[407,408,658],[363,165585,666],{"className":165586},[665],[363,165588,165590],{"className":165589},[638],[363,165591,165593],{"className":165592,"style":8315},[642],[363,165594],{},[363,165596],{"className":165597,"style":506},[505],[363,165599,7598],{"className":165600},[510],[363,165602],{"className":165603,"style":506},[505],[363,165605,165607,165610],{"className":165606},[398],[363,165608],{"className":165609,"style":520},[402],[363,165611,465],{"className":165612},[407],[363,165614,165616,165642],{"className":165615,"translate":367},[366],[363,165617,165619],{"className":165618},[371],[373,165620,165621],{"xmlns":375},[377,165622,165623,165639],{},[380,165624,165625,165631,165633,165635,165637],{},[543,165626,165627,165629],{},[383,165628,45101],{},[383,165630,12310],{},[458,165632,5160],{},[463,165634,465],{},[458,165636,7598],{},[463,165638,474],{},[387,165640,165641],{"encoding":389},"\\alpha_i - 1 \u003C 0",[363,165643,165645,165700,165719],{"className":165644,"ariaHidden":394},[393],[363,165646,165648,165651,165691,165694,165697],{"className":165647},[398],[363,165649],{"className":165650,"style":145420},[402],[363,165652,165654,165657],{"className":165653},[407],[363,165655,45101],{"className":165656,"style":45131},[407,408],[363,165658,165660],{"className":165659},[629],[363,165661,165663,165683],{"className":165662},[633,634],[363,165664,165666,165680],{"className":165665},[638],[363,165667,165669],{"className":165668,"style":12529},[642],[363,165670,165671,165674],{"style":136107},[363,165672],{"className":165673,"style":651},[650],[363,165675,165677],{"className":165676},[655,656,657,658],[363,165678,12310],{"className":165679},[407,408,658],[363,165681,666],{"className":165682},[665],[363,165684,165686],{"className":165685},[638],[363,165687,165689],{"className":165688,"style":8315},[642],[363,165690],{},[363,165692],{"className":165693,"style":2934},[505],[363,165695,5160],{"className":165696},[2938],[363,165698],{"className":165699,"style":2934},[505],[363,165701,165703,165707,165710,165713,165716],{"className":165702},[398],[363,165704],{"className":165705,"style":165706},[402],"height:0.6835em;vertical-align:-0.0391em;",[363,165708,465],{"className":165709},[407],[363,165711],{"className":165712,"style":506},[505],[363,165714,7598],{"className":165715},[510],[363,165717],{"className":165718,"style":506},[505],[363,165720,165722,165725],{"className":165721},[398],[363,165723],{"className":165724,"style":520},[402],[363,165726,474],{"className":165727},[407],"，隐含的「先验计数」为负，这在计数语义下不可解释，却对应于密度在边界处的发散——一个在稀疏建模中必不可少的形态。准确的说法是：",[1572,165730,165731,165765,165766,165857,165858,165949],{},[363,165732,165734,165747],{"className":165733,"translate":367},[366],[363,165735,165737],{"className":165736},[371],[373,165738,165739],{"xmlns":375},[377,165740,165741,165745],{},[380,165742,165743],{},[383,165744,45101],{"mathvariant":136008},[387,165746,137027],{"encoding":389},[363,165748,165750],{"className":165749,"ariaHidden":394},[393],[363,165751,165753,165756],{"className":165752},[398],[363,165754],{"className":165755,"style":135617},[402],[363,165757,165759],{"className":165758},[407],[363,165760,165762],{"className":165761},[407],[363,165763,45101],{"className":165764},[407,136068]," 是伪计数概念的连续化，其在 ",[363,165767,165769,165790],{"className":165768,"translate":367},[366],[363,165770,165772],{"className":165771},[371],[373,165773,165774],{"xmlns":375},[377,165775,165776,165788],{},[380,165777,165778,165784,165786],{},[543,165779,165780,165782],{},[383,165781,45101],{},[383,165783,12310],{},[458,165785,7275],{},[463,165787,465],{},[387,165789,165453],{"encoding":389},[363,165791,165793,165848],{"className":165792,"ariaHidden":394},[393],[363,165794,165796,165799,165839,165842,165845],{"className":165795},[398],[363,165797],{"className":165798,"style":155227},[402],[363,165800,165802,165805],{"className":165801},[407],[363,165803,45101],{"className":165804,"style":45131},[407,408],[363,165806,165808],{"className":165807},[629],[363,165809,165811,165831],{"className":165810},[633,634],[363,165812,165814,165828],{"className":165813},[638],[363,165815,165817],{"className":165816,"style":12529},[642],[363,165818,165819,165822],{"style":136107},[363,165820],{"className":165821,"style":651},[650],[363,165823,165825],{"className":165824},[655,656,657,658],[363,165826,12310],{"className":165827},[407,408,658],[363,165829,666],{"className":165830},[665],[363,165832,165834],{"className":165833},[638],[363,165835,165837],{"className":165836,"style":8315},[642],[363,165838],{},[363,165840],{"className":165841,"style":506},[505],[363,165843,7275],{"className":165844},[510],[363,165846],{"className":165847,"style":506},[505],[363,165849,165851,165854],{"className":165850},[398],[363,165852],{"className":165853,"style":520},[402],[363,165855,465],{"className":165856},[407]," 区域退化回字面意义上的计数解释，而在 ",[363,165859,165861,165882],{"className":165860,"translate":367},[366],[363,165862,165864],{"className":165863},[371],[373,165865,165866],{"xmlns":375},[377,165867,165868,165880],{},[380,165869,165870,165876,165878],{},[543,165871,165872,165874],{},[383,165873,45101],{},[383,165875,12310],{},[458,165877,7598],{},[463,165879,465],{},[387,165881,164699],{"encoding":389},[363,165883,165885,165940],{"className":165884,"ariaHidden":394},[393],[363,165886,165888,165891,165931,165934,165937],{"className":165887},[398],[363,165889],{"className":165890,"style":134669},[402],[363,165892,165894,165897],{"className":165893},[407],[363,165895,45101],{"className":165896,"style":45131},[407,408],[363,165898,165900],{"className":165899},[629],[363,165901,165903,165923],{"className":165902},[633,634],[363,165904,165906,165920],{"className":165905},[638],[363,165907,165909],{"className":165908,"style":12529},[642],[363,165910,165911,165914],{"style":136107},[363,165912],{"className":165913,"style":651},[650],[363,165915,165917],{"className":165916},[655,656,657,658],[363,165918,12310],{"className":165919},[407,408,658],[363,165921,666],{"className":165922},[665],[363,165924,165926],{"className":165925},[638],[363,165927,165929],{"className":165928,"style":8315},[642],[363,165930],{},[363,165932],{"className":165933,"style":506},[505],[363,165935,7598],{"className":165936},[510],[363,165938],{"className":165939,"style":506},[505],[363,165941,165943,165946],{"className":165942},[398],[363,165944],{"className":165945,"style":520},[402],[363,165947,465],{"className":165948},[407]," 区域承担的是稀疏性先验的角色。"," 这一区分在 3.4 节将直接决定 EDL 中「证据」一词的适用边界。",[18,165952,165954],{"id":165953},"三主观逻辑到证据深度学习","三、主观逻辑到证据深度学习",[2658,165956,165958],{"id":165957},"_31-主观逻辑的-opinion-表示","3.1 主观逻辑的 opinion 表示",[11,165960,165961,165962,165965],{},"证据深度学习的直接理论前身是 Josang 的",[1572,165963,165964],{},"主观逻辑（subjective logic）","，它为「对一个命题的相信程度」建立了一套带不确定性维度的代数。",[1340,165967,165969,166151,166737],{"title":165968},"定义 3.1（opinion）",[11,165970,165971,165972,166062,166063,166150],{},"在有限域 ",[363,165973,165975,166005],{"className":165974,"translate":367},[366],[363,165976,165978],{"className":165977},[371],[373,165979,165980],{"xmlns":375},[377,165981,165982,166002],{},[380,165983,165984,165986,165988,165990,165992,165994,165996,165998,166000],{},[383,165985,5748],{"mathvariant":944},[458,165987,471],{},[458,165989,3245],{"stretchy":460},[463,165991,465],{},[458,165993,898],{"separator":394},[458,165995,133107],{},[458,165997,898],{"separator":394},[383,165999,11041],{},[458,166001,3255],{"stretchy":460},[387,166003,166004],{"encoding":389},"\\mathcal{Y} = \\{1, \\dots, K\\}",[363,166006,166008,166026],{"className":166007,"ariaHidden":394},[393],[363,166009,166011,166014,166017,166020,166023],{"className":166010},[398],[363,166012],{"className":166013,"style":5797},[402],[363,166015,5748],{"className":166016,"style":5801},[407,971],[363,166018],{"className":166019,"style":506},[505],[363,166021,471],{"className":166022},[510],[363,166024],{"className":166025,"style":506},[505],[363,166027,166029,166032,166035,166038,166041,166044,166047,166050,166053,166056,166059],{"className":166028},[398],[363,166030],{"className":166031,"style":487},[402],[363,166033,3245],{"className":166034},[494],[363,166036,465],{"className":166037},[407],[363,166039,898],{"className":166040},[920],[363,166042],{"className":166043,"style":754},[505],[363,166045,133107],{"className":166046},[758],[363,166048],{"className":166049,"style":754},[505],[363,166051,898],{"className":166052},[920],[363,166054],{"className":166055,"style":754},[505],[363,166057,11041],{"className":166058,"style":11129},[407,408],[363,166060,3255],{"className":166061},[501]," 上的一个 opinion 是三元组 ",[363,166064,166066,166096],{"className":166065,"translate":367},[366],[363,166067,166069],{"className":166068},[371],[373,166070,166071],{"xmlns":375},[377,166072,166073,166093],{},[380,166074,166075,166077,166079,166081,166083,166085,166087,166089,166091],{},[383,166076,100208],{},[458,166078,471],{},[458,166080,461],{"stretchy":460},[383,166082,83174],{"mathvariant":75560},[458,166084,898],{"separator":394},[383,166086,15747],{},[458,166088,898],{"separator":394},[383,166090,45527],{"mathvariant":75560},[458,166092,468],{"stretchy":460},[387,166094,166095],{"encoding":389},"\\omega = (\\mathbf{b}, u, \\mathbf{a})",[363,166097,166099,166117],{"className":166098,"ariaHidden":394},[393],[363,166100,166102,166105,166108,166111,166114],{"className":166101},[398],[363,166103],{"className":166104,"style":2692},[402],[363,166106,100208],{"className":166107,"style":1328},[407,408],[363,166109],{"className":166110,"style":506},[505],[363,166112,471],{"className":166113},[510],[363,166115],{"className":166116,"style":506},[505],[363,166118,166120,166123,166126,166129,166132,166135,166138,166141,166144,166147],{"className":166119},[398],[363,166121],{"className":166122,"style":487},[402],[363,166124,461],{"className":166125},[494],[363,166127,83174],{"className":166128},[407,75905],[363,166130,898],{"className":166131},[920],[363,166133],{"className":166134,"style":754},[505],[363,166136,15747],{"className":166137},[407,408],[363,166139,898],{"className":166140},[920],[363,166142],{"className":166143,"style":754},[505],[363,166145,45527],{"className":166146},[407,75905],[363,166148,468],{"className":166149},[501],"，其中",[10374,166152,166153,166407,166486],{},[7012,166154,166155,166403,166404,10527],{},[363,166156,166158,166212],{"className":166157,"translate":367},[366],[363,166159,166161],{"className":166160},[371],[373,166162,166163],{"xmlns":375},[377,166164,166165,166209],{},[380,166166,166167,166169,166171,166173,166179,166181,166183,166185,166191,166193,166195,166197,166199,166201,166203],{},[383,166168,83174],{"mathvariant":75560},[458,166170,471],{},[458,166172,461],{"stretchy":460},[543,166174,166175,166177],{},[383,166176,83174],{},[463,166178,465],{},[458,166180,898],{"separator":394},[458,166182,133107],{},[458,166184,898],{"separator":394},[543,166186,166187,166189],{},[383,166188,83174],{},[383,166190,11041],{},[458,166192,468],{"stretchy":460},[458,166194,6256],{},[458,166196,578],{"stretchy":460},[463,166198,474],{},[458,166200,898],{"separator":394},[463,166202,465],{},[7161,166204,166205,166207],{},[458,166206,605],{"stretchy":460},[383,166208,11041],{},[387,166210,166211],{"encoding":389},"\\mathbf{b} = (b_1, \\dots, b_K) \\in [0,1]^K",[363,166213,166215,166233,166352],{"className":166214,"ariaHidden":394},[393],[363,166216,166218,166221,166224,166227,166230],{"className":166217},[398],[363,166219],{"className":166220,"style":12944},[402],[363,166222,83174],{"className":166223},[407,75905],[363,166225],{"className":166226,"style":506},[505],[363,166228,471],{"className":166229},[510],[363,166231],{"className":166232,"style":506},[505],[363,166234,166236,166239,166242,166282,166285,166288,166291,166294,166297,166300,166340,166343,166346,166349],{"className":166235},[398],[363,166237],{"className":166238,"style":487},[402],[363,166240,461],{"className":166241},[494],[363,166243,166245,166248],{"className":166244},[407],[363,166246,83174],{"className":166247},[407,408],[363,166249,166251],{"className":166250},[629],[363,166252,166254,166274],{"className":166253},[633,634],[363,166255,166257,166271],{"className":166256},[638],[363,166258,166260],{"className":166259,"style":11480},[642],[363,166261,166262,166265],{"style":730},[363,166263],{"className":166264,"style":651},[650],[363,166266,166268],{"className":166267},[655,656,657,658],[363,166269,465],{"className":166270},[407,658],[363,166272,666],{"className":166273},[665],[363,166275,166277],{"className":166276},[638],[363,166278,166280],{"className":166279,"style":8315},[642],[363,166281],{},[363,166283,898],{"className":166284},[920],[363,166286],{"className":166287,"style":754},[505],[363,166289,133107],{"className":166290},[758],[363,166292],{"className":166293,"style":754},[505],[363,166295,898],{"className":166296},[920],[363,166298],{"className":166299,"style":754},[505],[363,166301,166303,166306],{"className":166302},[407],[363,166304,83174],{"className":166305},[407,408],[363,166307,166309],{"className":166308},[629],[363,166310,166312,166332],{"className":166311},[633,634],[363,166313,166315,166329],{"className":166314},[638],[363,166316,166318],{"className":166317,"style":727},[642],[363,166319,166320,166323],{"style":730},[363,166321],{"className":166322,"style":651},[650],[363,166324,166326],{"className":166325},[655,656,657,658],[363,166327,11041],{"className":166328,"style":11129},[407,408,658],[363,166330,666],{"className":166331},[665],[363,166333,166335],{"className":166334},[638],[363,166336,166338],{"className":166337,"style":8315},[642],[363,166339],{},[363,166341,468],{"className":166342},[501],[363,166344],{"className":166345,"style":506},[505],[363,166347,6256],{"className":166348},[510],[363,166350],{"className":166351,"style":506},[505],[363,166353,166355,166359,166362,166365,166368,166371,166374],{"className":166354},[398],[363,166356],{"className":166357,"style":166358},[402],"height:1.0913em;vertical-align:-0.25em;",[363,166360,578],{"className":166361},[494],[363,166363,474],{"className":166364},[407],[363,166366,898],{"className":166367},[920],[363,166369],{"className":166370,"style":754},[505],[363,166372,465],{"className":166373},[407],[363,166375,166377,166380],{"className":166376},[501],[363,166378,605],{"className":166379},[501],[363,166381,166383],{"className":166382},[629],[363,166384,166386],{"className":166385},[633],[363,166387,166389],{"className":166388},[638],[363,166390,166392],{"className":166391,"style":52432},[642],[363,166393,166394,166397],{"style":7212},[363,166395],{"className":166396,"style":651},[650],[363,166398,166400],{"className":166399},[655,656,657,658],[363,166401,11041],{"className":166402,"style":11129},[407,408,658]," 为",[1572,166405,166406],{},"信念质量（belief mass）",[7012,166408,166409,166403,166483,10527],{},[363,166410,166412,166438],{"className":166411,"translate":367},[366],[363,166413,166415],{"className":166414},[371],[373,166416,166417],{"xmlns":375},[377,166418,166419,166435],{},[380,166420,166421,166423,166425,166427,166429,166431,166433],{},[383,166422,15747],{},[458,166424,6256],{},[458,166426,578],{"stretchy":460},[463,166428,474],{},[458,166430,898],{"separator":394},[463,166432,465],{},[458,166434,605],{"stretchy":460},[387,166436,166437],{"encoding":389},"u \\in [0,1]",[363,166439,166441,166459],{"className":166440,"ariaHidden":394},[393],[363,166442,166444,166447,166450,166453,166456],{"className":166443},[398],[363,166445],{"className":166446,"style":6271},[402],[363,166448,15747],{"className":166449},[407,408],[363,166451],{"className":166452,"style":506},[505],[363,166454,6256],{"className":166455},[510],[363,166457],{"className":166458,"style":506},[505],[363,166460,166462,166465,166468,166471,166474,166477,166480],{"className":166461},[398],[363,166463],{"className":166464,"style":487},[402],[363,166466,578],{"className":166467},[494],[363,166469,474],{"className":166470},[407],[363,166472,898],{"className":166473},[920],[363,166475],{"className":166476,"style":754},[505],[363,166478,465],{"className":166479},[407],[363,166481,605],{"className":166482},[501],[1572,166484,166485],{},"不确定性质量（uncertainty mass）",[7012,166487,166488,3092,166592,166733,166734,10527],{},[363,166489,166491,166521],{"className":166490,"translate":367},[366],[363,166492,166494],{"className":166493},[371],[373,166495,166496],{"xmlns":375},[377,166497,166498,166518],{},[380,166499,166500,166502,166504,166506,166508,166510,166512],{},[383,166501,45527],{"mathvariant":75560},[458,166503,6256],{},[458,166505,578],{"stretchy":460},[463,166507,474],{},[458,166509,898],{"separator":394},[463,166511,465],{},[7161,166513,166514,166516],{},[458,166515,605],{"stretchy":460},[383,166517,11041],{},[387,166519,166520],{"encoding":389},"\\mathbf{a} \\in [0,1]^K",[363,166522,166524,166542],{"className":166523,"ariaHidden":394},[393],[363,166525,166527,166530,166533,166536,166539],{"className":166526},[398],[363,166528],{"className":166529,"style":6271},[402],[363,166531,45527],{"className":166532},[407,75905],[363,166534],{"className":166535,"style":506},[505],[363,166537,6256],{"className":166538},[510],[363,166540],{"className":166541,"style":506},[505],[363,166543,166545,166548,166551,166554,166557,166560,166563],{"className":166544},[398],[363,166546],{"className":166547,"style":166358},[402],[363,166549,578],{"className":166550},[494],[363,166552,474],{"className":166553},[407],[363,166555,898],{"className":166556},[920],[363,166558],{"className":166559,"style":754},[505],[363,166561,465],{"className":166562},[407],[363,166564,166566,166569],{"className":166565},[501],[363,166567,605],{"className":166568},[501],[363,166570,166572],{"className":166571},[629],[363,166573,166575],{"className":166574},[633],[363,166576,166578],{"className":166577},[638],[363,166579,166581],{"className":166580,"style":52432},[642],[363,166582,166583,166586],{"style":7212},[363,166584],{"className":166585,"style":651},[650],[363,166587,166589],{"className":166588},[655,656,657,658],[363,166590,11041],{"className":166591,"style":11129},[407,408,658],[363,166593,166595,166623],{"className":166594,"translate":367},[366],[363,166596,166598],{"className":166597},[371],[373,166599,166600],{"xmlns":375},[377,166601,166602,166620],{},[380,166603,166604,166610,166616,166618],{},[543,166605,166606,166608],{},[458,166607,13808],{},[383,166609,7911],{},[543,166611,166612,166614],{},[383,166613,45527],{},[383,166615,7911],{},[458,166617,471],{},[463,166619,465],{},[387,166621,166622],{"encoding":389},"\\sum_k a_k = 1",[363,166624,166626,166724],{"className":166625,"ariaHidden":394},[393],[363,166627,166629,166632,166672,166675,166715,166718,166721],{"className":166628},[398],[363,166630],{"className":166631,"style":138904},[402],[363,166633,166635,166638],{"className":166634},[1831],[363,166636,13808],{"className":166637,"style":40007},[1831,1832,5963],[363,166639,166641],{"className":166640},[629],[363,166642,166644,166664],{"className":166643},[633,634],[363,166645,166647,166661],{"className":166646},[638],[363,166648,166650],{"className":166649,"style":67358},[642],[363,166651,166652,166655],{"style":40023},[363,166653],{"className":166654,"style":651},[650],[363,166656,166658],{"className":166657},[655,656,657,658],[363,166659,7911],{"className":166660,"style":8614},[407,408,658],[363,166662,666],{"className":166663},[665],[363,166665,166667],{"className":166666},[638],[363,166668,166670],{"className":166669,"style":40042},[642],[363,166671],{},[363,166673],{"className":166674,"style":754},[505],[363,166676,166678,166681],{"className":166677},[407],[363,166679,45527],{"className":166680},[407,408],[363,166682,166684],{"className":166683},[629],[363,166685,166687,166707],{"className":166686},[633,634],[363,166688,166690,166704],{"className":166689},[638],[363,166691,166693],{"className":166692,"style":643},[642],[363,166694,166695,166698],{"style":730},[363,166696],{"className":166697,"style":651},[650],[363,166699,166701],{"className":166700},[655,656,657,658],[363,166702,7911],{"className":166703,"style":8614},[407,408,658],[363,166705,666],{"className":166706},[665],[363,166708,166710],{"className":166709},[638],[363,166711,166713],{"className":166712,"style":8315},[642],[363,166714],{},[363,166716],{"className":166717,"style":506},[505],[363,166719,471],{"className":166720},[510],[363,166722],{"className":166723,"style":506},[505],[363,166725,166727,166730],{"className":166726},[398],[363,166728],{"className":166729,"style":520},[402],[363,166731,465],{"className":166732},[407],"，为",[1572,166735,166736],{},"基准率（base rate）",[11,166738,166739,166740,10527],{},"并满足单纯形约束 ",[363,166741,166743,166783],{"className":166742,"translate":367},[366],[363,166744,166746],{"className":166745},[371],[373,166747,166748],{"xmlns":375},[377,166749,166750,166780],{},[380,166751,166752,166766,166772,166774,166776,166778],{},[7900,166753,166754,166756,166764],{},[458,166755,13808],{},[380,166757,166758,166760,166762],{},[383,166759,7911],{},[458,166761,471],{},[463,166763,465],{},[383,166765,11041],{},[543,166767,166768,166770],{},[383,166769,83174],{},[383,166771,7911],{},[458,166773,2817],{},[383,166775,15747],{},[458,166777,471],{},[463,166779,465],{},[387,166781,166782],{"encoding":389},"\\sum_{k=1}^K b_k + u = 1",[363,166784,166786,166904,166922],{"className":166785,"ariaHidden":394},[393],[363,166787,166789,166792,166852,166855,166895,166898,166901],{"className":166788},[398],[363,166790],{"className":166791,"style":136371},[402],[363,166793,166795,166798],{"className":166794},[1831],[363,166796,13808],{"className":166797,"style":40007},[1831,1832,5963],[363,166799,166801],{"className":166800},[629],[363,166802,166804,166844],{"className":166803},[633,634],[363,166805,166807,166841],{"className":166806},[638],[363,166808,166810,166830],{"className":166809,"style":133494},[642],[363,166811,166812,166815],{"style":40023},[363,166813],{"className":166814,"style":651},[650],[363,166816,166818],{"className":166817},[655,656,657,658],[363,166819,166821,166824,166827],{"className":166820},[407,658],[363,166822,7911],{"className":166823,"style":8614},[407,408,658],[363,166825,471],{"className":166826},[510,658],[363,166828,465],{"className":166829},[407,658],[363,166831,166832,166835],{"style":133517},[363,166833],{"className":166834,"style":651},[650],[363,166836,166838],{"className":166837},[655,656,657,658],[363,166839,11041],{"className":166840,"style":11129},[407,408,658],[363,166842,666],{"className":166843},[665],[363,166845,166847],{"className":166846},[638],[363,166848,166850],{"className":166849,"style":40042},[642],[363,166851],{},[363,166853],{"className":166854,"style":754},[505],[363,166856,166858,166861],{"className":166857},[407],[363,166859,83174],{"className":166860},[407,408],[363,166862,166864],{"className":166863},[629],[363,166865,166867,166887],{"className":166866},[633,634],[363,166868,166870,166884],{"className":166869},[638],[363,166871,166873],{"className":166872,"style":643},[642],[363,166874,166875,166878],{"style":730},[363,166876],{"className":166877,"style":651},[650],[363,166879,166881],{"className":166880},[655,656,657,658],[363,166882,7911],{"className":166883,"style":8614},[407,408,658],[363,166885,666],{"className":166886},[665],[363,166888,166890],{"className":166889},[638],[363,166891,166893],{"className":166892,"style":8315},[642],[363,166894],{},[363,166896],{"className":166897,"style":2934},[505],[363,166899,2817],{"className":166900},[2938],[363,166902],{"className":166903,"style":2934},[505],[363,166905,166907,166910,166913,166916,166919],{"className":166906},[398],[363,166908],{"className":166909,"style":2692},[402],[363,166911,15747],{"className":166912},[407,408],[363,166914],{"className":166915,"style":506},[505],[363,166917,471],{"className":166918},[510],[363,166920],{"className":166921,"style":506},[505],[363,166923,166925,166928],{"className":166924},[398],[363,166926],{"className":166927,"style":520},[402],[363,166929,465],{"className":166930},[407],[11,166932,166933,34172,166961,166964,166965,167166,167167,10649,167266,10527],{},[363,166934,166936,166949],{"className":166935,"translate":367},[366],[363,166937,166939],{"className":166938},[371],[373,166940,166941],{"xmlns":375},[377,166942,166943,166947],{},[380,166944,166945],{},[383,166946,100208],{},[387,166948,101070],{"encoding":389},[363,166950,166952],{"className":166951,"ariaHidden":394},[393],[363,166953,166955,166958],{"className":166954},[398],[363,166956],{"className":166957,"style":2692},[402],[363,166959,100208],{"className":166960,"style":1328},[407,408],[1572,166962,166963],{},"概率投影（probability projection）"," 定义为 ",[363,166966,166968,167004],{"className":166967,"translate":367},[366],[363,166969,166971],{"className":166970},[371],[373,166972,166973],{"xmlns":375},[377,166974,166975,167001],{},[380,166976,166977,166983,166985,166991,166993,166999],{},[543,166978,166979,166981],{},[383,166980,554],{},[383,166982,7911],{},[458,166984,471],{},[543,166986,166987,166989],{},[383,166988,83174],{},[383,166990,7911],{},[458,166992,2817],{},[543,166994,166995,166997],{},[383,166996,45527],{},[383,166998,7911],{},[383,167000,15747],{},[387,167002,167003],{"encoding":389},"P_k = b_k + a_k u",[363,167005,167007,167062,167117],{"className":167006,"ariaHidden":394},[393],[363,167008,167010,167013,167053,167056,167059],{"className":167009},[398],[363,167011],{"className":167012,"style":16308},[402],[363,167014,167016,167019],{"className":167015},[407],[363,167017,554],{"className":167018,"style":682},[407,408],[363,167020,167022],{"className":167021},[629],[363,167023,167025,167045],{"className":167024},[633,634],[363,167026,167028,167042],{"className":167027},[638],[363,167029,167031],{"className":167030,"style":643},[642],[363,167032,167033,167036],{"style":11483},[363,167034],{"className":167035,"style":651},[650],[363,167037,167039],{"className":167038},[655,656,657,658],[363,167040,7911],{"className":167041,"style":8614},[407,408,658],[363,167043,666],{"className":167044},[665],[363,167046,167048],{"className":167047},[638],[363,167049,167051],{"className":167050,"style":8315},[642],[363,167052],{},[363,167054],{"className":167055,"style":506},[505],[363,167057,471],{"className":167058},[510],[363,167060],{"className":167061,"style":506},[505],[363,167063,167065,167068,167108,167111,167114],{"className":167064},[398],[363,167066],{"className":167067,"style":11821},[402],[363,167069,167071,167074],{"className":167070},[407],[363,167072,83174],{"className":167073},[407,408],[363,167075,167077],{"className":167076},[629],[363,167078,167080,167100],{"className":167079},[633,634],[363,167081,167083,167097],{"className":167082},[638],[363,167084,167086],{"className":167085,"style":643},[642],[363,167087,167088,167091],{"style":730},[363,167089],{"className":167090,"style":651},[650],[363,167092,167094],{"className":167093},[655,656,657,658],[363,167095,7911],{"className":167096,"style":8614},[407,408,658],[363,167098,666],{"className":167099},[665],[363,167101,167103],{"className":167102},[638],[363,167104,167106],{"className":167105,"style":8315},[642],[363,167107],{},[363,167109],{"className":167110,"style":2934},[505],[363,167112,2817],{"className":167113},[2938],[363,167115],{"className":167116,"style":2934},[505],[363,167118,167120,167123,167163],{"className":167119},[398],[363,167121],{"className":167122,"style":13721},[402],[363,167124,167126,167129],{"className":167125},[407],[363,167127,45527],{"className":167128},[407,408],[363,167130,167132],{"className":167131},[629],[363,167133,167135,167155],{"className":167134},[633,634],[363,167136,167138,167152],{"className":167137},[638],[363,167139,167141],{"className":167140,"style":643},[642],[363,167142,167143,167146],{"style":730},[363,167144],{"className":167145,"style":651},[650],[363,167147,167149],{"className":167148},[655,656,657,658],[363,167150,7911],{"className":167151,"style":8614},[407,408,658],[363,167153,666],{"className":167154},[665],[363,167156,167158],{"className":167157},[638],[363,167159,167161],{"className":167160,"style":8315},[642],[363,167162],{},[363,167164,15747],{"className":167165},[407,408],"：在不了解具体类别时退回基准率，在有所了解时按信念质量分配。当基准率取均匀值 ",[363,167168,167170,167196],{"className":167169,"translate":367},[366],[363,167171,167173],{"className":167172},[371],[373,167174,167175],{"xmlns":375},[377,167176,167177,167193],{},[380,167178,167179,167185,167187,167189,167191],{},[543,167180,167181,167183],{},[383,167182,45527],{},[383,167184,7911],{},[458,167186,471],{},[463,167188,465],{},[383,167190,1288],{"mathvariant":557},[383,167192,11041],{},[387,167194,167195],{"encoding":389},"a_k = 1\u002FK",[363,167197,167199,167254],{"className":167198,"ariaHidden":394},[393],[363,167200,167202,167205,167245,167248,167251],{"className":167201},[398],[363,167203],{"className":167204,"style":13721},[402],[363,167206,167208,167211],{"className":167207},[407],[363,167209,45527],{"className":167210},[407,408],[363,167212,167214],{"className":167213},[629],[363,167215,167217,167237],{"className":167216},[633,634],[363,167218,167220,167234],{"className":167219},[638],[363,167221,167223],{"className":167222,"style":643},[642],[363,167224,167225,167228],{"style":730},[363,167226],{"className":167227,"style":651},[650],[363,167229,167231],{"className":167230},[655,656,657,658],[363,167232,7911],{"className":167233,"style":8614},[407,408,658],[363,167235,666],{"className":167236},[665],[363,167238,167240],{"className":167239},[638],[363,167241,167243],{"className":167242,"style":8315},[642],[363,167244],{},[363,167246],{"className":167247,"style":506},[505],[363,167249,471],{"className":167250},[510],[363,167252],{"className":167253,"style":506},[505],[363,167255,167257,167260,167263],{"className":167256},[398],[363,167258],{"className":167259,"style":487},[402],[363,167261,8936],{"className":167262},[407],[363,167264,11041],{"className":167265,"style":11129},[407,408],[363,167267,167269,167303],{"className":167268,"translate":367},[366],[363,167270,167272],{"className":167271},[371],[373,167273,167274],{"xmlns":375},[377,167275,167276,167300],{},[380,167277,167278,167284,167286,167292,167294,167296,167298],{},[543,167279,167280,167282],{},[383,167281,554],{},[383,167283,7911],{},[458,167285,471],{},[543,167287,167288,167290],{},[383,167289,83174],{},[383,167291,7911],{},[458,167293,2817],{},[383,167295,15747],{},[383,167297,1288],{"mathvariant":557},[383,167299,11041],{},[387,167301,167302],{"encoding":389},"P_k = b_k + u\u002FK",[363,167304,167306,167361,167416],{"className":167305,"ariaHidden":394},[393],[363,167307,167309,167312,167352,167355,167358],{"className":167308},[398],[363,167310],{"className":167311,"style":16308},[402],[363,167313,167315,167318],{"className":167314},[407],[363,167316,554],{"className":167317,"style":682},[407,408],[363,167319,167321],{"className":167320},[629],[363,167322,167324,167344],{"className":167323},[633,634],[363,167325,167327,167341],{"className":167326},[638],[363,167328,167330],{"className":167329,"style":643},[642],[363,167331,167332,167335],{"style":11483},[363,167333],{"className":167334,"style":651},[650],[363,167336,167338],{"className":167337},[655,656,657,658],[363,167339,7911],{"className":167340,"style":8614},[407,408,658],[363,167342,666],{"className":167343},[665],[363,167345,167347],{"className":167346},[638],[363,167348,167350],{"className":167349,"style":8315},[642],[363,167351],{},[363,167353],{"className":167354,"style":506},[505],[363,167356,471],{"className":167357},[510],[363,167359],{"className":167360,"style":506},[505],[363,167362,167364,167367,167407,167410,167413],{"className":167363},[398],[363,167365],{"className":167366,"style":11821},[402],[363,167368,167370,167373],{"className":167369},[407],[363,167371,83174],{"className":167372},[407,408],[363,167374,167376],{"className":167375},[629],[363,167377,167379,167399],{"className":167378},[633,634],[363,167380,167382,167396],{"className":167381},[638],[363,167383,167385],{"className":167384,"style":643},[642],[363,167386,167387,167390],{"style":730},[363,167388],{"className":167389,"style":651},[650],[363,167391,167393],{"className":167392},[655,656,657,658],[363,167394,7911],{"className":167395,"style":8614},[407,408,658],[363,167397,666],{"className":167398},[665],[363,167400,167402],{"className":167401},[638],[363,167403,167405],{"className":167404,"style":8315},[642],[363,167406],{},[363,167408],{"className":167409,"style":2934},[505],[363,167411,2817],{"className":167412},[2938],[363,167414],{"className":167415,"style":2934},[505],[363,167417,167419,167422,167425,167428],{"className":167418},[398],[363,167420],{"className":167421,"style":487},[402],[363,167423,15747],{"className":167424},[407,408],[363,167426,1288],{"className":167427},[407],[363,167429,11041],{"className":167430,"style":11129},[407,408],[11,167432,167433,167434,167496,167497,167525,167526,167599],{},"定义 3.1 的关键在于：opinion 所栖居的空间是 ",[363,167435,167437,167455],{"className":167436,"translate":367},[366],[363,167438,167440],{"className":167439},[371],[373,167441,167442],{"xmlns":375},[377,167443,167444,167452],{},[380,167445,167446],{},[7161,167447,167448,167450],{},[383,167449,126023],{"mathvariant":557},[383,167451,11041],{},[387,167453,167454],{"encoding":389},"\\Delta^{K}",[363,167456,167458],{"className":167457,"ariaHidden":394},[393],[363,167459,167461,167464],{"className":167460},[398],[363,167462],{"className":167463,"style":52432},[402],[363,167465,167467,167470],{"className":167466},[407],[363,167468,126023],{"className":167469},[407],[363,167471,167473],{"className":167472},[629],[363,167474,167476],{"className":167475},[633],[363,167477,167479],{"className":167478},[638],[363,167480,167482],{"className":167481,"style":52432},[642],[363,167483,167484,167487],{"style":7212},[363,167485],{"className":167486,"style":651},[650],[363,167488,167490],{"className":167489},[655,656,657,658],[363,167491,167493],{"className":167492},[407,658],[363,167494,11041],{"className":167495,"style":11129},[407,408,658],"——一个 ",[363,167498,167500,167513],{"className":167499,"translate":367},[366],[363,167501,167503],{"className":167502},[371],[373,167504,167505],{"xmlns":375},[377,167506,167507,167511],{},[380,167508,167509],{},[383,167510,11041],{},[387,167512,11041],{"encoding":389},[363,167514,167516],{"className":167515,"ariaHidden":394},[393],[363,167517,167519,167522],{"className":167518},[398],[363,167520],{"className":167521,"style":1011},[402],[363,167523,11041],{"className":167524,"style":11129},[407,408]," 维单纯形，比 ",[363,167527,167529,167552],{"className":167528,"translate":367},[366],[363,167530,167532],{"className":167531},[371],[373,167533,167534],{"xmlns":375},[377,167535,167536,167550],{},[380,167537,167538],{},[7161,167539,167540,167542],{},[383,167541,126023],{"mathvariant":557},[380,167543,167544,167546,167548],{},[383,167545,11041],{},[458,167547,5160],{},[463,167549,465],{},[387,167551,134774],{"encoding":389},[363,167553,167555],{"className":167554,"ariaHidden":394},[393],[363,167556,167558,167561],{"className":167557},[398],[363,167559],{"className":167560,"style":52432},[402],[363,167562,167564,167567],{"className":167563},[407],[363,167565,126023],{"className":167566},[407],[363,167568,167570],{"className":167569},[629],[363,167571,167573],{"className":167572},[633],[363,167574,167576],{"className":167575},[638],[363,167577,167579],{"className":167578,"style":52432},[642],[363,167580,167581,167584],{"style":7212},[363,167582],{"className":167583,"style":651},[650],[363,167585,167587],{"className":167586},[655,656,657,658],[363,167588,167590,167593,167596],{"className":167589},[407,658],[363,167591,11041],{"className":167592,"style":11129},[407,408,658],[363,167594,5160],{"className":167595},[2938,658],[363,167597,465],{"className":167598},[407,658]," 多出一个维度。多出来的这一维正是「不确定性」的自由度，而它恰恰是 softmax 输出所没有的。",[2658,167601,167603],{"id":167602},"_32-dirichlet-与-opinion-的双射","3.2 Dirichlet 与 opinion 的双射",[11,167605,167606,167607,10527],{},"主观逻辑与迪利克雷分布之间不存在类比关系，而是存在严格的",[1572,167608,167609],{},"双射",[1340,167611,167613],{"title":167612},"命题 3.2（双射）",[11,167614,167615,167616,167668,167669,167767,167768],{},"设先验权重 ",[363,167617,167619,167638],{"className":167618,"translate":367},[366],[363,167620,167622],{"className":167621},[371],[373,167623,167624],{"xmlns":375},[377,167625,167626,167635],{},[380,167627,167628,167631,167633],{},[383,167629,167630],{},"W",[458,167632,471],{},[383,167634,11041],{},[387,167636,167637],{"encoding":389},"W = K",[363,167639,167641,167659],{"className":167640,"ariaHidden":394},[393],[363,167642,167644,167647,167650,167653,167656],{"className":167643},[398],[363,167645],{"className":167646,"style":1011},[402],[363,167648,167630],{"className":167649,"style":682},[407,408],[363,167651],{"className":167652,"style":506},[505],[363,167654,471],{"className":167655},[510],[363,167657],{"className":167658,"style":506},[505],[363,167660,167662,167665],{"className":167661},[398],[363,167663],{"className":167664,"style":1011},[402],[363,167666,11041],{"className":167667,"style":11129},[407,408],"、基准率 ",[363,167670,167672,167697],{"className":167671,"translate":367},[366],[363,167673,167675],{"className":167674},[371],[373,167676,167677],{"xmlns":375},[377,167678,167679,167695],{},[380,167680,167681,167687,167689,167691,167693],{},[543,167682,167683,167685],{},[383,167684,45527],{},[383,167686,7911],{},[458,167688,471],{},[463,167690,465],{},[383,167692,1288],{"mathvariant":557},[383,167694,11041],{},[387,167696,167195],{"encoding":389},[363,167698,167700,167755],{"className":167699,"ariaHidden":394},[393],[363,167701,167703,167706,167746,167749,167752],{"className":167702},[398],[363,167704],{"className":167705,"style":13721},[402],[363,167707,167709,167712],{"className":167708},[407],[363,167710,45527],{"className":167711},[407,408],[363,167713,167715],{"className":167714},[629],[363,167716,167718,167738],{"className":167717},[633,634],[363,167719,167721,167735],{"className":167720},[638],[363,167722,167724],{"className":167723,"style":643},[642],[363,167725,167726,167729],{"style":730},[363,167727],{"className":167728,"style":651},[650],[363,167730,167732],{"className":167731},[655,656,657,658],[363,167733,7911],{"className":167734,"style":8614},[407,408,658],[363,167736,666],{"className":167737},[665],[363,167739,167741],{"className":167740},[638],[363,167742,167744],{"className":167743,"style":8315},[642],[363,167745],{},[363,167747],{"className":167748,"style":506},[505],[363,167750,471],{"className":167751},[510],[363,167753],{"className":167754,"style":506},[505],[363,167756,167758,167761,167764],{"className":167757},[398],[363,167759],{"className":167760,"style":487},[402],[363,167762,8936],{"className":167763},[407],[363,167765,11041],{"className":167766,"style":11129},[407,408],"。则如下两个映射互逆：\n",[363,167769,167771,167873],{"className":167770,"translate":367},[366],[363,167772,167774],{"className":167773},[371],[373,167775,167776],{"xmlns":375},[377,167777,167778,167870],{},[380,167779,167780,167782,167784,167800,167802,167804,167806,167808,167818,167820,167822,167824,167830,167832,167848,167850,167852,167854,167856,167862,167864],{},[383,167781,83174],{"mathvariant":75560},[458,167783,471],{},[586,167785,167786,167794],{},[380,167787,167788,167790,167792],{},[383,167789,45101],{"mathvariant":136008},[458,167791,5160],{},[463,167793,465],{"mathvariant":75560},[543,167795,167796,167798],{},[383,167797,45101],{},[463,167799,474],{},[458,167801,898],{"separator":394},[505,167803],{"width":3609},[383,167805,15747],{},[458,167807,471],{},[586,167809,167810,167812],{},[383,167811,11041],{},[543,167813,167814,167816],{},[383,167815,45101],{},[463,167817,474],{},[505,167819],{"width":3609},[458,167821,96402],{},[505,167823],{"width":3609},[543,167825,167826,167828],{},[383,167827,45101],{},[383,167829,7911],{},[458,167831,471],{},[586,167833,167834,167846],{},[380,167835,167836,167838,167840],{},[383,167837,11041],{},[1644,167839,1646],{},[543,167841,167842,167844],{},[383,167843,83174],{},[383,167845,7911],{},[383,167847,15747],{},[458,167849,2817],{},[463,167851,465],{},[458,167853,898],{"separator":394},[505,167855],{"width":3609},[543,167857,167858,167860],{},[383,167859,45101],{},[463,167861,474],{},[458,167863,471],{},[586,167865,167866,167868],{},[383,167867,11041],{},[383,167869,15747],{},[387,167871,167872],{"encoding":389},"\\mathbf{b} = \\frac{\\boldsymbol{\\alpha} - \\mathbf{1}}{\\alpha_0}, \\qquad u = \\frac{K}{\\alpha_0} \\qquad \\Longleftrightarrow \\qquad \\alpha_k = \\frac{K\\, b_k}{u} + 1, \\qquad \\alpha_0 = \\frac{K}{u}",[363,167874,167876,167894,168038,168166,168221,168349,168416],{"className":167875,"ariaHidden":394},[393],[363,167877,167879,167882,167885,167888,167891],{"className":167878},[398],[363,167880],{"className":167881,"style":12944},[402],[363,167883,83174],{"className":167884},[407,75905],[363,167886],{"className":167887,"style":506},[505],[363,167889,471],{"className":167890},[510],[363,167892],{"className":167893,"style":506},[505],[363,167895,167897,167900,168017,168020,168023,168026,168029,168032,168035],{"className":167896},[398],[363,167898],{"className":167899,"style":149348},[402],[363,167901,167903,167906,168014],{"className":167902},[407],[363,167904],{"className":167905},[494,789],[363,167907,167909],{"className":167908},[586],[363,167910,167912,168006],{"className":167911},[633,634],[363,167913,167915,168003],{"className":167914},[638],[363,167916,167918,167969,167977],{"className":167917,"style":2871},[642],[363,167919,167920,167923],{"style":2874},[363,167921],{"className":167922,"style":809},[650],[363,167924,167926],{"className":167925},[655,656,657,658],[363,167927,167929],{"className":167928},[407,658],[363,167930,167932,167935],{"className":167931},[407,658],[363,167933,45101],{"className":167934,"style":45131},[407,408,658],[363,167936,167938],{"className":167937},[629],[363,167939,167941,167961],{"className":167940},[633,634],[363,167942,167944,167958],{"className":167943},[638],[363,167945,167947],{"className":167946,"style":137304},[642],[363,167948,167949,167952],{"style":136942},[363,167950],{"className":167951,"style":30553},[650],[363,167953,167955],{"className":167954},[655,30557,10021,658],[363,167956,474],{"className":167957},[407,658],[363,167959,666],{"className":167960},[665],[363,167962,167964],{"className":167963},[638],[363,167965,167967],{"className":167966,"style":40117},[642],[363,167968],{},[363,167970,167971,167974],{"style":821},[363,167972],{"className":167973,"style":809},[650],[363,167975],{"className":167976,"style":829},[828],[363,167978,167979,167982],{"style":2897},[363,167980],{"className":167981,"style":809},[650],[363,167983,167985],{"className":167984},[655,656,657,658],[363,167986,167988,167997,168000],{"className":167987},[407,658],[363,167989,167991],{"className":167990},[407,658],[363,167992,167994],{"className":167993},[407,658],[363,167995,45101],{"className":167996},[407,136068,658],[363,167998,5160],{"className":167999},[2938,658],[363,168001,465],{"className":168002},[407,75905,658],[363,168004,666],{"className":168005},[665],[363,168007,168009],{"className":168008},[638],[363,168010,168012],{"className":168011,"style":40264},[642],[363,168013],{},[363,168015],{"className":168016},[501,789],[363,168018,898],{"className":168019},[920],[363,168021],{"className":168022,"style":3981},[505],[363,168024],{"className":168025,"style":754},[505],[363,168027,15747],{"className":168028},[407,408],[363,168030],{"className":168031,"style":506},[505],[363,168033,471],{"className":168034},[510],[363,168036],{"className":168037,"style":506},[505],[363,168039,168041,168045,168151,168154,168157,168160,168163],{"className":168040},[398],[363,168042],{"className":168043,"style":168044},[402],"height:1.3174em;vertical-align:-0.4451em;",[363,168046,168048,168051,168148],{"className":168047},[407],[363,168049],{"className":168050},[494,789],[363,168052,168054],{"className":168053},[586],[363,168055,168057,168140],{"className":168056},[633,634],[363,168058,168060,168137],{"className":168059},[638],[363,168061,168064,168115,168123],{"className":168062,"style":168063},[642],"height:0.8723em;",[363,168065,168066,168069],{"style":2874},[363,168067],{"className":168068,"style":809},[650],[363,168070,168072],{"className":168071},[655,656,657,658],[363,168073,168075],{"className":168074},[407,658],[363,168076,168078,168081],{"className":168077},[407,658],[363,168079,45101],{"className":168080,"style":45131},[407,408,658],[363,168082,168084],{"className":168083},[629],[363,168085,168087,168107],{"className":168086},[633,634],[363,168088,168090,168104],{"className":168089},[638],[363,168091,168093],{"className":168092,"style":137304},[642],[363,168094,168095,168098],{"style":136942},[363,168096],{"className":168097,"style":30553},[650],[363,168099,168101],{"className":168100},[655,30557,10021,658],[363,168102,474],{"className":168103},[407,658],[363,168105,666],{"className":168106},[665],[363,168108,168110],{"className":168109},[638],[363,168111,168113],{"className":168112,"style":40117},[642],[363,168114],{},[363,168116,168117,168120],{"style":821},[363,168118],{"className":168119,"style":809},[650],[363,168121],{"className":168122,"style":829},[828],[363,168124,168125,168128],{"style":2897},[363,168126],{"className":168127,"style":809},[650],[363,168129,168131],{"className":168130},[655,656,657,658],[363,168132,168134],{"className":168133},[407,658],[363,168135,11041],{"className":168136,"style":11129},[407,408,658],[363,168138,666],{"className":168139},[665],[363,168141,168143],{"className":168142},[638],[363,168144,168146],{"className":168145,"style":40264},[642],[363,168147],{},[363,168149],{"className":168150},[501,789],[363,168152],{"className":168153,"style":3981},[505],[363,168155],{"className":168156,"style":506},[505],[363,168158,96402],{"className":168159},[510],[363,168161],{"className":168162,"style":3981},[505],[363,168164],{"className":168165,"style":506},[505],[363,168167,168169,168172,168212,168215,168218],{"className":168168},[398],[363,168170],{"className":168171,"style":13721},[402],[363,168173,168175,168178],{"className":168174},[407],[363,168176,45101],{"className":168177,"style":45131},[407,408],[363,168179,168181],{"className":168180},[629],[363,168182,168184,168204],{"className":168183},[633,634],[363,168185,168187,168201],{"className":168186},[638],[363,168188,168190],{"className":168189,"style":643},[642],[363,168191,168192,168195],{"style":136107},[363,168193],{"className":168194,"style":651},[650],[363,168196,168198],{"className":168197},[655,656,657,658],[363,168199,7911],{"className":168200,"style":8614},[407,408,658],[363,168202,666],{"className":168203},[665],[363,168205,168207],{"className":168206},[638],[363,168208,168210],{"className":168209,"style":8315},[642],[363,168211],{},[363,168213],{"className":168214,"style":506},[505],[363,168216,471],{"className":168217},[510],[363,168219],{"className":168220,"style":506},[505],[363,168222,168224,168228,168340,168343,168346],{"className":168223},[398],[363,168225],{"className":168226,"style":168227},[402],"height:1.247em;vertical-align:-0.345em;",[363,168229,168231,168234,168337],{"className":168230},[407],[363,168232],{"className":168233},[494,789],[363,168235,168237],{"className":168236},[586],[363,168238,168240,168329],{"className":168239},[633,634],[363,168241,168243,168326],{"className":168242},[638],[363,168244,168247,168261,168269],{"className":168245,"style":168246},[642],"height:0.902em;",[363,168248,168249,168252],{"style":2874},[363,168250],{"className":168251,"style":809},[650],[363,168253,168255],{"className":168254},[655,656,657,658],[363,168256,168258],{"className":168257},[407,658],[363,168259,15747],{"className":168260},[407,408,658],[363,168262,168263,168266],{"style":821},[363,168264],{"className":168265,"style":809},[650],[363,168267],{"className":168268,"style":829},[828],[363,168270,168271,168274],{"style":159912},[363,168272],{"className":168273,"style":809},[650],[363,168275,168277],{"className":168276},[655,656,657,658],[363,168278,168280,168283,168286],{"className":168279},[407,658],[363,168281,11041],{"className":168282,"style":11129},[407,408,658],[363,168284],{"className":168285,"style":42713},[505,658],[363,168287,168289,168292],{"className":168288},[407,658],[363,168290,83174],{"className":168291},[407,408,658],[363,168293,168295],{"className":168294},[629],[363,168296,168298,168318],{"className":168297},[633,634],[363,168299,168301,168315],{"className":168300},[638],[363,168302,168304],{"className":168303,"style":6445},[642],[363,168305,168306,168309],{"style":101564},[363,168307],{"className":168308,"style":30553},[650],[363,168310,168312],{"className":168311},[655,30557,10021,658],[363,168313,7911],{"className":168314,"style":8614},[407,408,658],[363,168316,666],{"className":168317},[665],[363,168319,168321],{"className":168320},[638],[363,168322,168324],{"className":168323,"style":101583},[642],[363,168325],{},[363,168327,666],{"className":168328},[665],[363,168330,168332],{"className":168331},[638],[363,168333,168335],{"className":168334,"style":2919},[642],[363,168336],{},[363,168338],{"className":168339},[501,789],[363,168341],{"className":168342,"style":2934},[505],[363,168344,2817],{"className":168345},[2938],[363,168347],{"className":168348,"style":2934},[505],[363,168350,168352,168355,168358,168361,168364,168367,168407,168410,168413],{"className":168351},[398],[363,168353],{"className":168354,"style":9705},[402],[363,168356,465],{"className":168357},[407],[363,168359,898],{"className":168360},[920],[363,168362],{"className":168363,"style":3981},[505],[363,168365],{"className":168366,"style":754},[505],[363,168368,168370,168373],{"className":168369},[407],[363,168371,45101],{"className":168372,"style":45131},[407,408],[363,168374,168376],{"className":168375},[629],[363,168377,168379,168399],{"className":168378},[633,634],[363,168380,168382,168396],{"className":168381},[638],[363,168383,168385],{"className":168384,"style":11480},[642],[363,168386,168387,168390],{"style":136107},[363,168388],{"className":168389,"style":651},[650],[363,168391,168393],{"className":168392},[655,656,657,658],[363,168394,474],{"className":168395},[407,658],[363,168397,666],{"className":168398},[665],[363,168400,168402],{"className":168401},[638],[363,168403,168405],{"className":168404,"style":8315},[642],[363,168406],{},[363,168408],{"className":168409,"style":506},[505],[363,168411,471],{"className":168412},[510],[363,168414],{"className":168415,"style":506},[505],[363,168417,168419,168423],{"className":168418},[398],[363,168420],{"className":168421,"style":168422},[402],"height:1.2173em;vertical-align:-0.345em;",[363,168424,168426,168429,168488],{"className":168425},[407],[363,168427],{"className":168428},[494,789],[363,168430,168432],{"className":168431},[586],[363,168433,168435,168480],{"className":168434},[633,634],[363,168436,168438,168477],{"className":168437},[638],[363,168439,168441,168455,168463],{"className":168440,"style":168063},[642],[363,168442,168443,168446],{"style":2874},[363,168444],{"className":168445,"style":809},[650],[363,168447,168449],{"className":168448},[655,656,657,658],[363,168450,168452],{"className":168451},[407,658],[363,168453,15747],{"className":168454},[407,408,658],[363,168456,168457,168460],{"style":821},[363,168458],{"className":168459,"style":809},[650],[363,168461],{"className":168462,"style":829},[828],[363,168464,168465,168468],{"style":2897},[363,168466],{"className":168467,"style":809},[650],[363,168469,168471],{"className":168470},[655,656,657,658],[363,168472,168474],{"className":168473},[407,658],[363,168475,11041],{"className":168476,"style":11129},[407,408,658],[363,168478,666],{"className":168479},[665],[363,168481,168483],{"className":168482},[638],[363,168484,168486],{"className":168485,"style":2919},[642],[363,168487],{},[363,168489],{"className":168490},[501,789],[11,168492,168493,168496,168497,168979],{},[1572,168494,168495],{},"验证"," 正向：",[363,168498,168500,168566],{"className":168499,"translate":367},[366],[363,168501,168503],{"className":168502},[371],[373,168504,168505],{"xmlns":375},[377,168506,168507,168563],{},[380,168508,168509,168515,168521,168523,168525,168527,168547,168549,168559,168561],{},[543,168510,168511,168513],{},[458,168512,13808],{},[383,168514,7911],{},[543,168516,168517,168519],{},[383,168518,83174],{},[383,168520,7911],{},[458,168522,2817],{},[383,168524,15747],{},[458,168526,471],{},[586,168528,168529,168541],{},[380,168530,168531,168537,168539],{},[543,168532,168533,168535],{},[383,168534,45101],{},[463,168536,474],{},[458,168538,5160],{},[383,168540,11041],{},[543,168542,168543,168545],{},[383,168544,45101],{},[463,168546,474],{},[458,168548,2817],{},[586,168550,168551,168553],{},[383,168552,11041],{},[543,168554,168555,168557],{},[383,168556,45101],{},[463,168558,474],{},[458,168560,471],{},[463,168562,465],{},[387,168564,168565],{"encoding":389},"\\sum_k b_k + u = \\frac{\\alpha_0 - K}{\\alpha_0} + \\frac{K}{\\alpha_0} = 1",[363,168567,168569,168667,168685,168850,168970],{"className":168568,"ariaHidden":394},[393],[363,168570,168572,168575,168615,168618,168658,168661,168664],{"className":168571},[398],[363,168573],{"className":168574,"style":138904},[402],[363,168576,168578,168581],{"className":168577},[1831],[363,168579,13808],{"className":168580,"style":40007},[1831,1832,5963],[363,168582,168584],{"className":168583},[629],[363,168585,168587,168607],{"className":168586},[633,634],[363,168588,168590,168604],{"className":168589},[638],[363,168591,168593],{"className":168592,"style":67358},[642],[363,168594,168595,168598],{"style":40023},[363,168596],{"className":168597,"style":651},[650],[363,168599,168601],{"className":168600},[655,656,657,658],[363,168602,7911],{"className":168603,"style":8614},[407,408,658],[363,168605,666],{"className":168606},[665],[363,168608,168610],{"className":168609},[638],[363,168611,168613],{"className":168612,"style":40042},[642],[363,168614],{},[363,168616],{"className":168617,"style":754},[505],[363,168619,168621,168624],{"className":168620},[407],[363,168622,83174],{"className":168623},[407,408],[363,168625,168627],{"className":168626},[629],[363,168628,168630,168650],{"className":168629},[633,634],[363,168631,168633,168647],{"className":168632},[638],[363,168634,168636],{"className":168635,"style":643},[642],[363,168637,168638,168641],{"style":730},[363,168639],{"className":168640,"style":651},[650],[363,168642,168644],{"className":168643},[655,656,657,658],[363,168645,7911],{"className":168646,"style":8614},[407,408,658],[363,168648,666],{"className":168649},[665],[363,168651,168653],{"className":168652},[638],[363,168654,168656],{"className":168655,"style":8315},[642],[363,168657],{},[363,168659],{"className":168660,"style":2934},[505],[363,168662,2817],{"className":168663},[2938],[363,168665],{"className":168666,"style":2934},[505],[363,168668,168670,168673,168676,168679,168682],{"className":168669},[398],[363,168671],{"className":168672,"style":2692},[402],[363,168674,15747],{"className":168675},[407,408],[363,168677],{"className":168678,"style":506},[505],[363,168680,471],{"className":168681},[510],[363,168683],{"className":168684,"style":506},[505],[363,168686,168688,168692,168841,168844,168847],{"className":168687},[398],[363,168689],{"className":168690,"style":168691},[402],"height:1.3335em;vertical-align:-0.4451em;",[363,168693,168695,168698,168838],{"className":168694},[407],[363,168696],{"className":168697},[494,789],[363,168699,168701],{"className":168700},[586],[363,168702,168704,168830],{"className":168703},[633,634],[363,168705,168707,168827],{"className":168706},[638],[363,168708,168711,168762,168770],{"className":168709,"style":168710},[642],"height:0.8884em;",[363,168712,168713,168716],{"style":2874},[363,168714],{"className":168715,"style":809},[650],[363,168717,168719],{"className":168718},[655,656,657,658],[363,168720,168722],{"className":168721},[407,658],[363,168723,168725,168728],{"className":168724},[407,658],[363,168726,45101],{"className":168727,"style":45131},[407,408,658],[363,168729,168731],{"className":168730},[629],[363,168732,168734,168754],{"className":168733},[633,634],[363,168735,168737,168751],{"className":168736},[638],[363,168738,168740],{"className":168739,"style":137304},[642],[363,168741,168742,168745],{"style":136942},[363,168743],{"className":168744,"style":30553},[650],[363,168746,168748],{"className":168747},[655,30557,10021,658],[363,168749,474],{"className":168750},[407,658],[363,168752,666],{"className":168753},[665],[363,168755,168757],{"className":168756},[638],[363,168758,168760],{"className":168759,"style":40117},[642],[363,168761],{},[363,168763,168764,168767],{"style":821},[363,168765],{"className":168766,"style":809},[650],[363,168768],{"className":168769,"style":829},[828],[363,168771,168772,168775],{"style":147946},[363,168773],{"className":168774,"style":809},[650],[363,168776,168778],{"className":168777},[655,656,657,658],[363,168779,168781,168821,168824],{"className":168780},[407,658],[363,168782,168784,168787],{"className":168783},[407,658],[363,168785,45101],{"className":168786,"style":45131},[407,408,658],[363,168788,168790],{"className":168789},[629],[363,168791,168793,168813],{"className":168792},[633,634],[363,168794,168796,168810],{"className":168795},[638],[363,168797,168799],{"className":168798,"style":137304},[642],[363,168800,168801,168804],{"style":136942},[363,168802],{"className":168803,"style":30553},[650],[363,168805,168807],{"className":168806},[655,30557,10021,658],[363,168808,474],{"className":168809},[407,658],[363,168811,666],{"className":168812},[665],[363,168814,168816],{"className":168815},[638],[363,168817,168819],{"className":168818,"style":40117},[642],[363,168820],{},[363,168822,5160],{"className":168823},[2938,658],[363,168825,11041],{"className":168826,"style":11129},[407,408,658],[363,168828,666],{"className":168829},[665],[363,168831,168833],{"className":168832},[638],[363,168834,168836],{"className":168835,"style":40264},[642],[363,168837],{},[363,168839],{"className":168840},[501,789],[363,168842],{"className":168843,"style":2934},[505],[363,168845,2817],{"className":168846},[2938],[363,168848],{"className":168849,"style":2934},[505],[363,168851,168853,168856,168961,168964,168967],{"className":168852},[398],[363,168854],{"className":168855,"style":168044},[402],[363,168857,168859,168862,168958],{"className":168858},[407],[363,168860],{"className":168861},[494,789],[363,168863,168865],{"className":168864},[586],[363,168866,168868,168950],{"className":168867},[633,634],[363,168869,168871,168947],{"className":168870},[638],[363,168872,168874,168925,168933],{"className":168873,"style":168063},[642],[363,168875,168876,168879],{"style":2874},[363,168877],{"className":168878,"style":809},[650],[363,168880,168882],{"className":168881},[655,656,657,658],[363,168883,168885],{"className":168884},[407,658],[363,168886,168888,168891],{"className":168887},[407,658],[363,168889,45101],{"className":168890,"style":45131},[407,408,658],[363,168892,168894],{"className":168893},[629],[363,168895,168897,168917],{"className":168896},[633,634],[363,168898,168900,168914],{"className":168899},[638],[363,168901,168903],{"className":168902,"style":137304},[642],[363,168904,168905,168908],{"style":136942},[363,168906],{"className":168907,"style":30553},[650],[363,168909,168911],{"className":168910},[655,30557,10021,658],[363,168912,474],{"className":168913},[407,658],[363,168915,666],{"className":168916},[665],[363,168918,168920],{"className":168919},[638],[363,168921,168923],{"className":168922,"style":40117},[642],[363,168924],{},[363,168926,168927,168930],{"style":821},[363,168928],{"className":168929,"style":809},[650],[363,168931],{"className":168932,"style":829},[828],[363,168934,168935,168938],{"style":2897},[363,168936],{"className":168937,"style":809},[650],[363,168939,168941],{"className":168940},[655,656,657,658],[363,168942,168944],{"className":168943},[407,658],[363,168945,11041],{"className":168946,"style":11129},[407,408,658],[363,168948,666],{"className":168949},[665],[363,168951,168953],{"className":168952},[638],[363,168954,168956],{"className":168955,"style":40264},[642],[363,168957],{},[363,168959],{"className":168960},[501,789],[363,168962],{"className":168963,"style":506},[505],[363,168965,471],{"className":168966},[510],[363,168968],{"className":168969,"style":506},[505],[363,168971,168973,168976],{"className":168972},[398],[363,168974],{"className":168975,"style":520},[402],[363,168977,465],{"className":168978},[407],"，满足定义 3.1 的约束。反向：代入即得恒等。此外，概率投影与迪利克雷期望重合：",[363,168981,168983],{"className":168982,"translate":367},[528],[363,168984,168986,169084],{"className":168985,"translate":367},[366],[363,168987,168989],{"className":168988},[371],[373,168990,168991],{"xmlns":375,"display":537},[377,168992,168993,169081],{},[380,168994,168995,169001,169003,169009,169011,169017,169019,169039,169041,169051,169053,169067,169069,169071,169073,169079],{},[543,168996,168997,168999],{},[383,168998,554],{},[383,169000,7911],{},[458,169002,471],{},[543,169004,169005,169007],{},[383,169006,83174],{},[383,169008,7911],{},[458,169010,2817],{},[586,169012,169013,169015],{},[383,169014,15747],{},[383,169016,11041],{},[458,169018,471],{},[586,169020,169021,169033],{},[380,169022,169023,169029,169031],{},[543,169024,169025,169027],{},[383,169026,45101],{},[383,169028,7911],{},[458,169030,5160],{},[463,169032,465],{},[543,169034,169035,169037],{},[383,169036,45101],{},[463,169038,474],{},[458,169040,2817],{},[586,169042,169043,169045],{},[463,169044,465],{},[543,169046,169047,169049],{},[383,169048,45101],{},[463,169050,474],{},[458,169052,471],{},[586,169054,169055,169061],{},[543,169056,169057,169059],{},[383,169058,45101],{},[383,169060,7911],{},[543,169062,169063,169065],{},[383,169064,45101],{},[463,169066,474],{},[458,169068,471],{},[383,169070,571],{"mathvariant":570},[458,169072,578],{"stretchy":460},[543,169074,169075,169077],{},[383,169076,1121],{},[383,169078,7911],{},[458,169080,605],{"stretchy":460},[387,169082,169083],{"encoding":389},"P_k = b_k + \\frac{u}{K} = \\frac{\\alpha_k - 1}{\\alpha_0} + \\frac{1}{\\alpha_0} = \\frac{\\alpha_k}{\\alpha_0} = \\mathbb{E}[x_k]",[363,169085,169087,169142,169197,169274,169437,169551,169702],{"className":169086,"ariaHidden":394},[393],[363,169088,169090,169093,169133,169136,169139],{"className":169089},[398],[363,169091],{"className":169092,"style":16308},[402],[363,169094,169096,169099],{"className":169095},[407],[363,169097,554],{"className":169098,"style":682},[407,408],[363,169100,169102],{"className":169101},[629],[363,169103,169105,169125],{"className":169104},[633,634],[363,169106,169108,169122],{"className":169107},[638],[363,169109,169111],{"className":169110,"style":643},[642],[363,169112,169113,169116],{"style":11483},[363,169114],{"className":169115,"style":651},[650],[363,169117,169119],{"className":169118},[655,656,657,658],[363,169120,7911],{"className":169121,"style":8614},[407,408,658],[363,169123,666],{"className":169124},[665],[363,169126,169128],{"className":169127},[638],[363,169129,169131],{"className":169130,"style":8315},[642],[363,169132],{},[363,169134],{"className":169135,"style":506},[505],[363,169137,471],{"className":169138},[510],[363,169140],{"className":169141,"style":506},[505],[363,169143,169145,169148,169188,169191,169194],{"className":169144},[398],[363,169146],{"className":169147,"style":11821},[402],[363,169149,169151,169154],{"className":169150},[407],[363,169152,83174],{"className":169153},[407,408],[363,169155,169157],{"className":169156},[629],[363,169158,169160,169180],{"className":169159},[633,634],[363,169161,169163,169177],{"className":169162},[638],[363,169164,169166],{"className":169165,"style":643},[642],[363,169167,169168,169171],{"style":730},[363,169169],{"className":169170,"style":651},[650],[363,169172,169174],{"className":169173},[655,656,657,658],[363,169175,7911],{"className":169176,"style":8614},[407,408,658],[363,169178,666],{"className":169179},[665],[363,169181,169183],{"className":169182},[638],[363,169184,169186],{"className":169185,"style":8315},[642],[363,169187],{},[363,169189],{"className":169190,"style":2934},[505],[363,169192,2817],{"className":169193},[2938],[363,169195],{"className":169196,"style":2934},[505],[363,169198,169200,169203,169265,169268,169271],{"className":169199},[398],[363,169201],{"className":169202,"style":26885},[402],[363,169204,169206,169209,169262],{"className":169205},[407],[363,169207],{"className":169208},[494,789],[363,169210,169212],{"className":169211},[586],[363,169213,169215,169254],{"className":169214},[633,634],[363,169216,169218,169251],{"className":169217},[638],[363,169219,169221,169232,169240],{"className":169220,"style":3901},[642],[363,169222,169223,169226],{"style":805},[363,169224],{"className":169225,"style":809},[650],[363,169227,169229],{"className":169228},[407],[363,169230,11041],{"className":169231,"style":11129},[407,408],[363,169233,169234,169237],{"style":821},[363,169235],{"className":169236,"style":809},[650],[363,169238],{"className":169239,"style":829},[828],[363,169241,169242,169245],{"style":832},[363,169243],{"className":169244,"style":809},[650],[363,169246,169248],{"className":169247},[407],[363,169249,15747],{"className":169250},[407,408],[363,169252,666],{"className":169253},[665],[363,169255,169257],{"className":169256},[638],[363,169258,169260],{"className":169259,"style":4125},[642],[363,169261],{},[363,169263],{"className":169264},[501,789],[363,169266],{"className":169267,"style":506},[505],[363,169269,471],{"className":169270},[510],[363,169272],{"className":169273,"style":506},[505],[363,169275,169277,169280,169428,169431,169434],{"className":169276},[398],[363,169278],{"className":169279,"style":151436},[402],[363,169281,169283,169286,169425],{"className":169282},[407],[363,169284],{"className":169285},[494,789],[363,169287,169289],{"className":169288},[586],[363,169290,169292,169417],{"className":169291},[633,634],[363,169293,169295,169414],{"className":169294},[638],[363,169296,169298,169346,169354],{"className":169297,"style":23236},[642],[363,169299,169300,169303],{"style":805},[363,169301],{"className":169302,"style":809},[650],[363,169304,169306],{"className":169305},[407],[363,169307,169309,169312],{"className":169308},[407],[363,169310,45101],{"className":169311,"style":45131},[407,408],[363,169313,169315],{"className":169314},[629],[363,169316,169318,169338],{"className":169317},[633,634],[363,169319,169321,169335],{"className":169320},[638],[363,169322,169324],{"className":169323,"style":11480},[642],[363,169325,169326,169329],{"style":136107},[363,169327],{"className":169328,"style":651},[650],[363,169330,169332],{"className":169331},[655,656,657,658],[363,169333,474],{"className":169334},[407,658],[363,169336,666],{"className":169337},[665],[363,169339,169341],{"className":169340},[638],[363,169342,169344],{"className":169343,"style":8315},[642],[363,169345],{},[363,169347,169348,169351],{"style":821},[363,169349],{"className":169350,"style":809},[650],[363,169352],{"className":169353,"style":829},[828],[363,169355,169356,169359],{"style":832},[363,169357],{"className":169358,"style":809},[650],[363,169360,169362,169402,169405,169408,169411],{"className":169361},[407],[363,169363,169365,169368],{"className":169364},[407],[363,169366,45101],{"className":169367,"style":45131},[407,408],[363,169369,169371],{"className":169370},[629],[363,169372,169374,169394],{"className":169373},[633,634],[363,169375,169377,169391],{"className":169376},[638],[363,169378,169380],{"className":169379,"style":643},[642],[363,169381,169382,169385],{"style":136107},[363,169383],{"className":169384,"style":651},[650],[363,169386,169388],{"className":169387},[655,656,657,658],[363,169389,7911],{"className":169390,"style":8614},[407,408,658],[363,169392,666],{"className":169393},[665],[363,169395,169397],{"className":169396},[638],[363,169398,169400],{"className":169399,"style":8315},[642],[363,169401],{},[363,169403],{"className":169404,"style":2934},[505],[363,169406,5160],{"className":169407},[2938],[363,169409],{"className":169410,"style":2934},[505],[363,169412,465],{"className":169413},[407],[363,169415,666],{"className":169416},[665],[363,169418,169420],{"className":169419},[638],[363,169421,169423],{"className":169422,"style":125395},[642],[363,169424],{},[363,169426],{"className":169427},[501,789],[363,169429],{"className":169430,"style":2934},[505],[363,169432,2817],{"className":169433},[2938],[363,169435],{"className":169436,"style":2934},[505],[363,169438,169440,169443,169542,169545,169548],{"className":169439},[398],[363,169441],{"className":169442,"style":151436},[402],[363,169444,169446,169449,169539],{"className":169445},[407],[363,169447],{"className":169448},[494,789],[363,169450,169452],{"className":169451},[586],[363,169453,169455,169531],{"className":169454},[633,634],[363,169456,169458,169528],{"className":169457},[638],[363,169459,169461,169509,169517],{"className":169460,"style":23236},[642],[363,169462,169463,169466],{"style":805},[363,169464],{"className":169465,"style":809},[650],[363,169467,169469],{"className":169468},[407],[363,169470,169472,169475],{"className":169471},[407],[363,169473,45101],{"className":169474,"style":45131},[407,408],[363,169476,169478],{"className":169477},[629],[363,169479,169481,169501],{"className":169480},[633,634],[363,169482,169484,169498],{"className":169483},[638],[363,169485,169487],{"className":169486,"style":11480},[642],[363,169488,169489,169492],{"style":136107},[363,169490],{"className":169491,"style":651},[650],[363,169493,169495],{"className":169494},[655,656,657,658],[363,169496,474],{"className":169497},[407,658],[363,169499,666],{"className":169500},[665],[363,169502,169504],{"className":169503},[638],[363,169505,169507],{"className":169506,"style":8315},[642],[363,169508],{},[363,169510,169511,169514],{"style":821},[363,169512],{"className":169513,"style":809},[650],[363,169515],{"className":169516,"style":829},[828],[363,169518,169519,169522],{"style":832},[363,169520],{"className":169521,"style":809},[650],[363,169523,169525],{"className":169524},[407],[363,169526,465],{"className":169527},[407],[363,169529,666],{"className":169530},[665],[363,169532,169534],{"className":169533},[638],[363,169535,169537],{"className":169536,"style":125395},[642],[363,169538],{},[363,169540],{"className":169541},[501,789],[363,169543],{"className":169544,"style":506},[505],[363,169546,471],{"className":169547},[510],[363,169549],{"className":169550,"style":506},[505],[363,169552,169554,169557,169693,169696,169699],{"className":169553},[398],[363,169555],{"className":169556,"style":125255},[402],[363,169558,169560,169563,169690],{"className":169559},[407],[363,169561],{"className":169562},[494,789],[363,169564,169566],{"className":169565},[586],[363,169567,169569,169682],{"className":169568},[633,634],[363,169570,169572,169679],{"className":169571},[638],[363,169573,169575,169623,169631],{"className":169574,"style":3901},[642],[363,169576,169577,169580],{"style":805},[363,169578],{"className":169579,"style":809},[650],[363,169581,169583],{"className":169582},[407],[363,169584,169586,169589],{"className":169585},[407],[363,169587,45101],{"className":169588,"style":45131},[407,408],[363,169590,169592],{"className":169591},[629],[363,169593,169595,169615],{"className":169594},[633,634],[363,169596,169598,169612],{"className":169597},[638],[363,169599,169601],{"className":169600,"style":11480},[642],[363,169602,169603,169606],{"style":136107},[363,169604],{"className":169605,"style":651},[650],[363,169607,169609],{"className":169608},[655,656,657,658],[363,169610,474],{"className":169611},[407,658],[363,169613,666],{"className":169614},[665],[363,169616,169618],{"className":169617},[638],[363,169619,169621],{"className":169620,"style":8315},[642],[363,169622],{},[363,169624,169625,169628],{"style":821},[363,169626],{"className":169627,"style":809},[650],[363,169629],{"className":169630,"style":829},[828],[363,169632,169633,169636],{"style":832},[363,169634],{"className":169635,"style":809},[650],[363,169637,169639],{"className":169638},[407],[363,169640,169642,169645],{"className":169641},[407],[363,169643,45101],{"className":169644,"style":45131},[407,408],[363,169646,169648],{"className":169647},[629],[363,169649,169651,169671],{"className":169650},[633,634],[363,169652,169654,169668],{"className":169653},[638],[363,169655,169657],{"className":169656,"style":643},[642],[363,169658,169659,169662],{"style":136107},[363,169660],{"className":169661,"style":651},[650],[363,169663,169665],{"className":169664},[655,656,657,658],[363,169666,7911],{"className":169667,"style":8614},[407,408,658],[363,169669,666],{"className":169670},[665],[363,169672,169674],{"className":169673},[638],[363,169675,169677],{"className":169676,"style":8315},[642],[363,169678],{},[363,169680,666],{"className":169681},[665],[363,169683,169685],{"className":169684},[638],[363,169686,169688],{"className":169687,"style":125395},[642],[363,169689],{},[363,169691],{"className":169692},[501,789],[363,169694],{"className":169695,"style":506},[505],[363,169697,471],{"className":169698},[510],[363,169700],{"className":169701,"style":506},[505],[363,169703,169705,169708,169711,169714,169754],{"className":169704},[398],[363,169706],{"className":169707,"style":487},[402],[363,169709,571],{"className":169710},[407,714],[363,169712,578],{"className":169713},[494],[363,169715,169717,169720],{"className":169716},[407],[363,169718,1121],{"className":169719},[407,408],[363,169721,169723],{"className":169722},[629],[363,169724,169726,169746],{"className":169725},[633,634],[363,169727,169729,169743],{"className":169728},[638],[363,169730,169732],{"className":169731,"style":643},[642],[363,169733,169734,169737],{"style":730},[363,169735],{"className":169736,"style":651},[650],[363,169738,169740],{"className":169739},[655,656,657,658],[363,169741,7911],{"className":169742,"style":8614},[407,408,658],[363,169744,666],{"className":169745},[665],[363,169747,169749],{"className":169748},[638],[363,169750,169752],{"className":169751,"style":8315},[642],[363,169753],{},[363,169755,605],{"className":169756},[501],[11,169758,169759],{},"其中最后一个等号由命题 2.1 给出。",[11,169761,169762,169763,169766],{},"命题 3.2 是整篇文章的枢纽：它说明",[1572,169764,169765],{},"在单纯形上输出一个概率分布，与在 opinion 空间中输出一个带不确定性度量的判断，是同一件事。"," 于是，「给网络加一个不确定性维度」这一看似需要新架构的任务，被归结为「让网络的输出参数化一个迪利克雷分布」。证据深度学习正是沿着这条路径展开的。",[2658,169768,169770],{"id":169769},"_33-softmax-的翻译不变性与过度自信","3.3 Softmax 的翻译不变性与过度自信",[11,169772,169773,169774,169928,169929,170045,170046,19055,170118,170422],{},"设神经网络 ",[363,169775,169777,169807],{"className":169776,"translate":367},[366],[363,169778,169780],{"className":169779},[371],[373,169781,169782],{"xmlns":375},[377,169783,169784,169804],{},[380,169785,169786,169792,169794,169796,169798],{},[543,169787,169788,169790],{},[383,169789,385],{},[383,169791,101106],{"mathvariant":136008},[458,169793,1362],{},[383,169795,945],{"mathvariant":944},[458,169797,1376],{},[7161,169799,169800,169802],{},[383,169801,1379],{"mathvariant":570},[383,169803,11041],{},[387,169805,169806],{"encoding":389},"f_{\\boldsymbol{\\theta}}: \\mathcal{X} \\to \\mathbb{R}^K",[363,169808,169810,169875,169893],{"className":169809,"ariaHidden":394},[393],[363,169811,169813,169816,169866,169869,169872],{"className":169812},[398],[363,169814],{"className":169815,"style":403},[402],[363,169817,169819,169822],{"className":169818},[407],[363,169820,385],{"className":169821,"style":409},[407,408],[363,169823,169825],{"className":169824},[629],[363,169826,169828,169858],{"className":169827},[633,634],[363,169829,169831,169855],{"className":169830},[638],[363,169832,169834],{"className":169833,"style":643},[642],[363,169835,169836,169839],{"style":27856},[363,169837],{"className":169838,"style":651},[650],[363,169840,169842],{"className":169841},[655,656,657,658],[363,169843,169845],{"className":169844},[407,658],[363,169846,169848],{"className":169847},[407,658],[363,169849,169851],{"className":169850},[407,658],[363,169852,101106],{"className":169853,"style":169854},[407,136068,658],"margin-right:0.0319em;",[363,169856,666],{"className":169857},[665],[363,169859,169861],{"className":169860},[638],[363,169862,169864],{"className":169863,"style":8315},[642],[363,169865],{},[363,169867],{"className":169868,"style":506},[505],[363,169870,1362],{"className":169871},[510],[363,169873],{"className":169874,"style":506},[505],[363,169876,169878,169881,169884,169887,169890],{"className":169877},[398],[363,169879],{"className":169880,"style":1011},[402],[363,169882,945],{"className":169883,"style":972},[407,971],[363,169885],{"className":169886,"style":506},[505],[363,169888,1376],{"className":169889},[510],[363,169891],{"className":169892,"style":506},[505],[363,169894,169896,169899],{"className":169895},[398],[363,169897],{"className":169898,"style":52432},[402],[363,169900,169902,169905],{"className":169901},[407],[363,169903,1379],{"className":169904},[407,714],[363,169906,169908],{"className":169907},[629],[363,169909,169911],{"className":169910},[633],[363,169912,169914],{"className":169913},[638],[363,169915,169917],{"className":169916,"style":52432},[642],[363,169918,169919,169922],{"style":7212},[363,169920],{"className":169921,"style":651},[650],[363,169923,169925],{"className":169924},[655,656,657,658],[363,169926,11041],{"className":169927,"style":11129},[407,408,658]," 输出 logits ",[363,169930,169932,169960],{"className":169931,"translate":367},[366],[363,169933,169935],{"className":169934},[371],[373,169936,169937],{"xmlns":375},[377,169938,169939,169957],{},[380,169940,169941,169943,169945,169951,169953,169955],{},[383,169942,118116],{"mathvariant":75560},[458,169944,471],{},[543,169946,169947,169949],{},[383,169948,385],{},[383,169950,101106],{"mathvariant":136008},[458,169952,461],{"stretchy":460},[383,169954,1121],{"mathvariant":75560},[458,169956,468],{"stretchy":460},[387,169958,169959],{"encoding":389},"\\mathbf{z} = f_{\\boldsymbol{\\theta}}(\\mathbf{x})",[363,169961,169963,169981],{"className":169962,"ariaHidden":394},[393],[363,169964,169966,169969,169972,169975,169978],{"className":169965},[398],[363,169967],{"className":169968,"style":135617},[402],[363,169970,118116],{"className":169971},[407,75905],[363,169973],{"className":169974,"style":506},[505],[363,169976,471],{"className":169977},[510],[363,169979],{"className":169980,"style":506},[505],[363,169982,169984,169987,170036,170039,170042],{"className":169983},[398],[363,169985],{"className":169986,"style":487},[402],[363,169988,169990,169993],{"className":169989},[407],[363,169991,385],{"className":169992,"style":409},[407,408],[363,169994,169996],{"className":169995},[629],[363,169997,169999,170028],{"className":169998},[633,634],[363,170000,170002,170025],{"className":170001},[638],[363,170003,170005],{"className":170004,"style":643},[642],[363,170006,170007,170010],{"style":27856},[363,170008],{"className":170009,"style":651},[650],[363,170011,170013],{"className":170012},[655,656,657,658],[363,170014,170016],{"className":170015},[407,658],[363,170017,170019],{"className":170018},[407,658],[363,170020,170022],{"className":170021},[407,658],[363,170023,101106],{"className":170024,"style":169854},[407,136068,658],[363,170026,666],{"className":170027},[665],[363,170029,170031],{"className":170030},[638],[363,170032,170034],{"className":170033,"style":8315},[642],[363,170035],{},[363,170037,461],{"className":170038},[494],[363,170040,1121],{"className":170041},[407,75905],[363,170043,468],{"className":170044},[501],"，softmax 给出 ",[363,170047,170049,170076],{"className":170048,"translate":367},[366],[363,170050,170052],{"className":170051},[371],[373,170053,170054],{"xmlns":375},[377,170055,170056,170073],{},[380,170057,170058,170060,170062,170065,170067,170069,170071],{},[383,170059,11],{"mathvariant":75560},[458,170061,471],{},[383,170063,170064],{"mathvariant":557},"softmax",[458,170066,4450],{},[458,170068,461],{"stretchy":460},[383,170070,118116],{"mathvariant":75560},[458,170072,468],{"stretchy":460},[387,170074,170075],{"encoding":389},"\\mathbf{p} = \\operatorname{softmax}(\\mathbf{z})",[363,170077,170079,170097],{"className":170078,"ariaHidden":394},[393],[363,170080,170082,170085,170088,170091,170094],{"className":170081},[398],[363,170083],{"className":170084,"style":133764},[402],[363,170086,11],{"className":170087},[407,75905],[363,170089],{"className":170090,"style":506},[505],[363,170092,471],{"className":170093},[510],[363,170095],{"className":170096,"style":506},[505],[363,170098,170100,170103,170109,170112,170115],{"className":170099},[398],[363,170101],{"className":170102,"style":487},[402],[363,170104,170106],{"className":170105},[1831],[363,170107,170064],{"className":170108},[407,33009],[363,170110,461],{"className":170111},[494],[363,170113,118116],{"className":170114},[407,75905],[363,170116,468],{"className":170117},[501],[363,170119,170121,170169],{"className":170120,"translate":367},[366],[363,170122,170124],{"className":170123},[371],[373,170125,170126],{"xmlns":375},[377,170127,170128,170166],{},[380,170129,170130,170136,170138,170148,170150,170156],{},[543,170131,170132,170134],{},[383,170133,11],{},[383,170135,7911],{},[458,170137,471],{},[7161,170139,170140,170142],{},[383,170141,7914],{},[543,170143,170144,170146],{},[383,170145,118116],{},[383,170147,7911],{},[383,170149,1288],{"mathvariant":557},[543,170151,170152,170154],{},[458,170153,13808],{},[383,170155,100360],{},[7161,170157,170158,170160],{},[383,170159,7914],{},[543,170161,170162,170164],{},[383,170163,118116],{},[383,170165,100360],{},[387,170167,170168],{"encoding":389},"p_k = e^{z_k}\u002F\\sum_j e^{z_j}",[363,170170,170172,170227],{"className":170171,"ariaHidden":394},[393],[363,170173,170175,170178,170218,170221,170224],{"className":170174},[398],[363,170176],{"className":170177,"style":2623},[402],[363,170179,170181,170184],{"className":170180},[407],[363,170182,11],{"className":170183},[407,408],[363,170185,170187],{"className":170186},[629],[363,170188,170190,170210],{"className":170189},[633,634],[363,170191,170193,170207],{"className":170192},[638],[363,170194,170196],{"className":170195,"style":643},[642],[363,170197,170198,170201],{"style":730},[363,170199],{"className":170200,"style":651},[650],[363,170202,170204],{"className":170203},[655,656,657,658],[363,170205,7911],{"className":170206,"style":8614},[407,408,658],[363,170208,666],{"className":170209},[665],[363,170211,170213],{"className":170212},[638],[363,170214,170216],{"className":170215,"style":8315},[642],[363,170217],{},[363,170219],{"className":170220,"style":506},[505],[363,170222,471],{"className":170223},[510],[363,170225],{"className":170226,"style":506},[505],[363,170228,170230,170233,170303,170306,170309,170349,170352],{"className":170229},[398],[363,170231],{"className":170232,"style":162540},[402],[363,170234,170236,170239],{"className":170235},[407],[363,170237,7914],{"className":170238},[407,408],[363,170240,170242],{"className":170241},[629],[363,170243,170245],{"className":170244},[633],[363,170246,170248],{"className":170247},[638],[363,170249,170251],{"className":170250,"style":50700},[642],[363,170252,170253,170256],{"style":7212},[363,170254],{"className":170255,"style":651},[650],[363,170257,170259],{"className":170258},[655,656,657,658],[363,170260,170262],{"className":170261},[407,658],[363,170263,170265,170268],{"className":170264},[407,658],[363,170266,118116],{"className":170267,"style":118386},[407,408,658],[363,170269,170271],{"className":170270},[629],[363,170272,170274,170295],{"className":170273},[633,634],[363,170275,170277,170292],{"className":170276},[638],[363,170278,170280],{"className":170279,"style":6445},[642],[363,170281,170283,170286],{"style":170282},"top:-2.3488em;margin-left:-0.044em;margin-right:0.0714em;",[363,170284],{"className":170285,"style":30553},[650],[363,170287,170289],{"className":170288},[655,30557,10021,658],[363,170290,7911],{"className":170291,"style":8614},[407,408,658],[363,170293,666],{"className":170294},[665],[363,170296,170298],{"className":170297},[638],[363,170299,170301],{"className":170300,"style":101583},[642],[363,170302],{},[363,170304,1288],{"className":170305},[407],[363,170307],{"className":170308,"style":754},[505],[363,170310,170312,170315],{"className":170311},[1831],[363,170313,13808],{"className":170314,"style":40007},[1831,1832,5963],[363,170316,170318],{"className":170317},[629],[363,170319,170321,170341],{"className":170320},[633,634],[363,170322,170324,170338],{"className":170323},[638],[363,170325,170327],{"className":170326,"style":40020},[642],[363,170328,170329,170332],{"style":40023},[363,170330],{"className":170331,"style":651},[650],[363,170333,170335],{"className":170334},[655,656,657,658],[363,170336,100360],{"className":170337,"style":100888},[407,408,658],[363,170339,666],{"className":170340},[665],[363,170342,170344],{"className":170343},[638],[363,170345,170347],{"className":170346,"style":162729},[642],[363,170348],{},[363,170350],{"className":170351,"style":754},[505],[363,170353,170355,170358],{"className":170354},[407],[363,170356,7914],{"className":170357},[407,408],[363,170359,170361],{"className":170360},[629],[363,170362,170364],{"className":170363},[633],[363,170365,170367],{"className":170366},[638],[363,170368,170370],{"className":170369,"style":50700},[642],[363,170371,170372,170375],{"style":7212},[363,170373],{"className":170374,"style":651},[650],[363,170376,170378],{"className":170377},[655,656,657,658],[363,170379,170381],{"className":170380},[407,658],[363,170382,170384,170387],{"className":170383},[407,658],[363,170385,118116],{"className":170386,"style":118386},[407,408,658],[363,170388,170390],{"className":170389},[629],[363,170391,170393,170414],{"className":170392},[633,634],[363,170394,170396,170411],{"className":170395},[638],[363,170397,170399],{"className":170398,"style":40095},[642],[363,170400,170402,170405],{"style":170401},"top:-2.357em;margin-left:-0.044em;margin-right:0.0714em;",[363,170403],{"className":170404,"style":30553},[650],[363,170406,170408],{"className":170407},[655,30557,10021,658],[363,170409,100360],{"className":170410,"style":100888},[407,408,658],[363,170412,666],{"className":170413},[665],[363,170415,170417],{"className":170416},[638],[363,170418,170420],{"className":170419,"style":122065},[642],[363,170421],{},"。这一映射存在两个结构性缺陷。",[11,170424,170425,170428,170429,3092,170457,170575,170576,34172,170657,170660,170661,170712,170713,170786,170787,170825],{},[1572,170426,170427],{},"其一，平移不变性抹去了「无信息」这一状态。"," 对任意常数 ",[363,170430,170432,170445],{"className":170431,"translate":367},[366],[363,170433,170435],{"className":170434},[371],[373,170436,170437],{"xmlns":375},[377,170438,170439,170443],{},[380,170440,170441],{},[383,170442,6253],{},[387,170444,6253],{"encoding":389},[363,170446,170448],{"className":170447,"ariaHidden":394},[393],[363,170449,170451,170454],{"className":170450},[398],[363,170452],{"className":170453,"style":2692},[402],[363,170455,6253],{"className":170456},[407,408],[363,170458,170460,170500],{"className":170459,"translate":367},[366],[363,170461,170463],{"className":170462},[371],[373,170464,170465],{"xmlns":375},[377,170466,170467,170497],{},[380,170468,170469,170471,170473,170475,170477,170479,170481,170483,170485,170487,170489,170491,170493,170495],{},[383,170470,170064],{"mathvariant":557},[458,170472,4450],{},[458,170474,461],{"stretchy":460},[383,170476,118116],{"mathvariant":75560},[458,170478,2817],{},[383,170480,6253],{},[463,170482,465],{"mathvariant":75560},[458,170484,468],{"stretchy":460},[458,170486,471],{},[383,170488,170064],{"mathvariant":557},[458,170490,4450],{},[458,170492,461],{"stretchy":460},[383,170494,118116],{"mathvariant":75560},[458,170496,468],{"stretchy":460},[387,170498,170499],{"encoding":389},"\\operatorname{softmax}(\\mathbf{z} + c\\mathbf{1}) = \\operatorname{softmax}(\\mathbf{z})",[363,170501,170503,170530,170554],{"className":170502,"ariaHidden":394},[393],[363,170504,170506,170509,170515,170518,170521,170524,170527],{"className":170505},[398],[363,170507],{"className":170508,"style":487},[402],[363,170510,170512],{"className":170511},[1831],[363,170513,170064],{"className":170514},[407,33009],[363,170516,461],{"className":170517},[494],[363,170519,118116],{"className":170520},[407,75905],[363,170522],{"className":170523,"style":2934},[505],[363,170525,2817],{"className":170526},[2938],[363,170528],{"className":170529,"style":2934},[505],[363,170531,170533,170536,170539,170542,170545,170548,170551],{"className":170532},[398],[363,170534],{"className":170535,"style":487},[402],[363,170537,6253],{"className":170538},[407,408],[363,170540,465],{"className":170541},[407,75905],[363,170543,468],{"className":170544},[501],[363,170546],{"className":170547,"style":506},[505],[363,170549,471],{"className":170550},[510],[363,170552],{"className":170553,"style":506},[505],[363,170555,170557,170560,170566,170569,170572],{"className":170556},[398],[363,170558],{"className":170559,"style":487},[402],[363,170561,170563],{"className":170562},[1831],[363,170564,170064],{"className":170565},[407,33009],[363,170567,461],{"className":170568},[494],[363,170570,118116],{"className":170571},[407,75905],[363,170573,468],{"className":170574},[501],"。因此 logits 的绝对水平不含任何信息，网络的输出只依赖于 ",[363,170577,170579,170601],{"className":170578,"translate":367},[366],[363,170580,170582],{"className":170581},[371],[373,170583,170584],{"xmlns":375},[377,170585,170586,170598],{},[380,170587,170588,170590,170596],{},[458,170589,3245],{"stretchy":460},[543,170591,170592,170594],{},[383,170593,118116],{},[383,170595,7911],{},[458,170597,3255],{"stretchy":460},[387,170599,170600],{"encoding":389},"\\{z_k\\}",[363,170602,170604],{"className":170603,"ariaHidden":394},[393],[363,170605,170607,170610,170613,170654],{"className":170606},[398],[363,170608],{"className":170609,"style":487},[402],[363,170611,3245],{"className":170612},[494],[363,170614,170616,170619],{"className":170615},[407],[363,170617,118116],{"className":170618,"style":118386},[407,408],[363,170620,170622],{"className":170621},[629],[363,170623,170625,170646],{"className":170624},[633,634],[363,170626,170628,170643],{"className":170627},[638],[363,170629,170631],{"className":170630,"style":643},[642],[363,170632,170634,170637],{"style":170633},"top:-2.55em;margin-left:-0.044em;margin-right:0.05em;",[363,170635],{"className":170636,"style":651},[650],[363,170638,170640],{"className":170639},[655,656,657,658],[363,170641,7911],{"className":170642,"style":8614},[407,408,658],[363,170644,666],{"className":170645},[665],[363,170647,170649],{"className":170648},[638],[363,170650,170652],{"className":170651,"style":8315},[642],[363,170653],{},[363,170655,3255],{"className":170656},[501],[1572,170658,170659],{},"相对差","。后果是：",[363,170662,170664,170682],{"className":170663,"translate":367},[366],[363,170665,170667],{"className":170666},[371],[373,170668,170669],{"xmlns":375},[377,170670,170671,170679],{},[380,170672,170673,170675,170677],{},[383,170674,118116],{"mathvariant":75560},[458,170676,471],{},[463,170678,474],{"mathvariant":75560},[387,170680,170681],{"encoding":389},"\\mathbf{z} = \\mathbf{0}",[363,170683,170685,170703],{"className":170684,"ariaHidden":394},[393],[363,170686,170688,170691,170694,170697,170700],{"className":170687},[398],[363,170689],{"className":170690,"style":135617},[402],[363,170692,118116],{"className":170693},[407,75905],[363,170695],{"className":170696,"style":506},[505],[363,170698,471],{"className":170699},[510],[363,170701],{"className":170702,"style":506},[505],[363,170704,170706,170709],{"className":170705},[398],[363,170707],{"className":170708,"style":520},[402],[363,170710,474],{"className":170711},[407,75905],"（「全零 logits」）与 ",[363,170714,170716,170738],{"className":170715,"translate":367},[366],[363,170717,170719],{"className":170718},[371],[373,170720,170721],{"xmlns":375},[377,170722,170723,170735],{},[380,170724,170725,170727,170729,170731,170733],{},[383,170726,118116],{"mathvariant":75560},[458,170728,471],{},[463,170730,117281],{},[458,170732,3646],{},[463,170734,465],{"mathvariant":75560},[387,170736,170737],{"encoding":389},"\\mathbf{z} = 100 \\cdot \\mathbf{1}",[363,170739,170741,170759,170777],{"className":170740,"ariaHidden":394},[393],[363,170742,170744,170747,170750,170753,170756],{"className":170743},[398],[363,170745],{"className":170746,"style":135617},[402],[363,170748,118116],{"className":170749},[407,75905],[363,170751],{"className":170752,"style":506},[505],[363,170754,471],{"className":170755},[510],[363,170757],{"className":170758,"style":506},[505],[363,170760,170762,170765,170768,170771,170774],{"className":170761},[398],[363,170763],{"className":170764,"style":520},[402],[363,170766,117281],{"className":170767},[407],[363,170769],{"className":170770,"style":2934},[505],[363,170772,3646],{"className":170773},[2938],[363,170775],{"className":170776,"style":2934},[505],[363,170778,170780,170783],{"className":170779},[398],[363,170781],{"className":170782,"style":520},[402],[363,170784,465],{"className":170785},[407,75905]," 不可区分，二者都对应均匀分布 ",[363,170788,170790,170807],{"className":170789,"translate":367},[366],[363,170791,170793],{"className":170792},[371],[373,170794,170795],{"xmlns":375},[377,170796,170797,170805],{},[380,170798,170799,170801,170803],{},[463,170800,465],{"mathvariant":75560},[383,170802,1288],{"mathvariant":557},[383,170804,11041],{},[387,170806,165264],{"encoding":389},[363,170808,170810],{"className":170809,"ariaHidden":394},[393],[363,170811,170813,170816,170819,170822],{"className":170812},[398],[363,170814],{"className":170815,"style":487},[402],[363,170817,465],{"className":170818},[407,75905],[363,170820,1288],{"className":170821},[407],[363,170823,11041],{"className":170824,"style":11129},[407,408],"。既然均匀分布既可由「无任何信号」也可由「极其强烈的信号恰好相互抵消」产生，输出端就不可能把前者作为一个可辨识的状态标记出来。",[11,170827,170828,170831,170832,170963,170964,170967,170968,10527],{},[1572,170829,170830],{},"其二，交叉熵的最优解在可分数据上把 logits 推向发散。"," 在训练集线性可分时，以交叉熵为目标的极大似然估计不存在有限最优解：沿方向 ",[363,170833,170835,170871],{"className":170834,"translate":367},[366],[363,170836,170838],{"className":170837},[371],[373,170839,170840],{"xmlns":375},[377,170841,170842,170868],{},[380,170843,170844,170846,170848,170850,170852,170858,170860,170862,170864,170866],{},[383,170845,118116],{"mathvariant":75560},[458,170847,1376],{},[383,170849,6253],{},[1644,170851,1646],{},[7161,170853,170854,170856],{},[383,170855,118116],{"mathvariant":75560},[458,170857,76305],{},[458,170859,898],{"separator":394},[1644,170861,4630],{},[383,170863,6253],{},[458,170865,1376],{},[383,170867,1371],{"mathvariant":557},[387,170869,170870],{"encoding":389},"\\mathbf{z} \\to c\\,\\mathbf{z}^\\star,\\ c \\to \\infty",[363,170872,170874,170892,170954],{"className":170873,"ariaHidden":394},[393],[363,170875,170877,170880,170883,170886,170889],{"className":170876},[398],[363,170878],{"className":170879,"style":135617},[402],[363,170881,118116],{"className":170882},[407,75905],[363,170884],{"className":170885,"style":506},[505],[363,170887,1376],{"className":170888},[510],[363,170890],{"className":170891,"style":506},[505],[363,170893,170895,170898,170901,170904,170933,170936,170939,170942,170945,170948,170951],{"className":170894},[398],[363,170896],{"className":170897,"style":64362},[402],[363,170899,6253],{"className":170900},[407,408],[363,170902],{"className":170903,"style":754},[505],[363,170905,170907,170910],{"className":170906},[407],[363,170908,118116],{"className":170909},[407,75905],[363,170911,170913],{"className":170912},[629],[363,170914,170916],{"className":170915},[633],[363,170917,170919],{"className":170918},[638],[363,170920,170922],{"className":170921,"style":8846},[642],[363,170923,170924,170927],{"style":7212},[363,170925],{"className":170926,"style":651},[650],[363,170928,170930],{"className":170929},[655,656,657,658],[363,170931,76305],{"className":170932},[2938,658],[363,170934,898],{"className":170935},[920],[363,170937,4630],{"className":170938},[505],[363,170940],{"className":170941,"style":754},[505],[363,170943,6253],{"className":170944},[407,408],[363,170946],{"className":170947,"style":506},[505],[363,170949,1376],{"className":170950},[510],[363,170952],{"className":170953,"style":506},[505],[363,170955,170957,170960],{"className":170956},[398],[363,170958],{"className":170959,"style":2692},[402],[363,170961,1371],{"className":170962},[407]," 可将损失单调压向零。换言之，",[1572,170965,170966],{},"过度自信不是训练不足的症状，而是 MLE 在可分数据上的退化解","——模型越是被「训练充分」，其 softmax 输出越接近 one-hot，而这一行为",[1572,170969,170970],{},"完全不受输入是否为分布内样本的约束",[11,170972,170973],{},"两个缺陷合起来解释了 5.1 节的经验事实：以最大 softmax 概率（MSP）作为分布外检测分数存在系统性偏差，因为 softmax 对任何使 logits 相对间距增大的输入都会返回高置信度的断言，而无从表达「这个输入对我而言是陌生的」。",[2658,170975,170977],{"id":170976},"_34-证据参数化","3.4 证据参数化",[11,170979,170980,170981],{},"证据深度学习对上述缺陷的回应是：",[1572,170982,170983],{},"不再用 softmax 把 logits 压缩为概率，而是用非负激活函数把 logits 提升为证据。",[1340,170985,170987],{"title":170986},"定义 3.3（证据网络）",[11,170988,881,170989,171178,171179,171182,171183,171442,171443,171679,171680,10527],{},[363,170990,170992,171028],{"className":170991,"translate":367},[366],[363,170993,170995],{"className":170994},[371],[373,170996,170997],{"xmlns":375},[377,170998,170999,171025],{},[380,171000,171001,171007,171009,171011,171013],{},[543,171002,171003,171005],{},[383,171004,4505],{},[383,171006,101106],{"mathvariant":136008},[458,171008,1362],{},[383,171010,945],{"mathvariant":944},[458,171012,1376],{},[7900,171014,171015,171017,171023],{},[383,171016,1379],{"mathvariant":570},[380,171018,171019,171021],{},[458,171020,7275],{},[463,171022,474],{},[383,171024,11041],{},[387,171026,171027],{"encoding":389},"g_{\\boldsymbol{\\theta}}: \\mathcal{X} \\to \\mathbb{R}_{\\ge 0}^K",[363,171029,171031,171095,171113],{"className":171030,"ariaHidden":394},[393],[363,171032,171034,171037,171086,171089,171092],{"className":171033},[398],[363,171035],{"className":171036,"style":2623},[402],[363,171038,171040,171043],{"className":171039},[407],[363,171041,4505],{"className":171042,"style":1328},[407,408],[363,171044,171046],{"className":171045},[629],[363,171047,171049,171078],{"className":171048},[633,634],[363,171050,171052,171075],{"className":171051},[638],[363,171053,171055],{"className":171054,"style":643},[642],[363,171056,171057,171060],{"style":19190},[363,171058],{"className":171059,"style":651},[650],[363,171061,171063],{"className":171062},[655,656,657,658],[363,171064,171066],{"className":171065},[407,658],[363,171067,171069],{"className":171068},[407,658],[363,171070,171072],{"className":171071},[407,658],[363,171073,101106],{"className":171074,"style":169854},[407,136068,658],[363,171076,666],{"className":171077},[665],[363,171079,171081],{"className":171080},[638],[363,171082,171084],{"className":171083,"style":8315},[642],[363,171085],{},[363,171087],{"className":171088,"style":506},[505],[363,171090,1362],{"className":171091},[510],[363,171093],{"className":171094,"style":506},[505],[363,171096,171098,171101,171104,171107,171110],{"className":171097},[398],[363,171099],{"className":171100,"style":1011},[402],[363,171102,945],{"className":171103,"style":972},[407,971],[363,171105],{"className":171106,"style":506},[505],[363,171108,1376],{"className":171109},[510],[363,171111],{"className":171112,"style":506},[505],[363,171114,171116,171120],{"className":171115},[398],[363,171117],{"className":171118,"style":171119},[402],"height:1.1846em;vertical-align:-0.3433em;",[363,171121,171123,171126],{"className":171122},[407],[363,171124,1379],{"className":171125},[407,714],[363,171127,171129],{"className":171128},[629],[363,171130,171132,171169],{"className":171131},[633,634],[363,171133,171135,171166],{"className":171134},[638],[363,171136,171138,171155],{"className":171137,"style":52432},[642],[363,171139,171140,171143],{"style":136225},[363,171141],{"className":171142,"style":651},[650],[363,171144,171146],{"className":171145},[655,656,657,658],[363,171147,171149,171152],{"className":171148},[407,658],[363,171150,7275],{"className":171151},[510,658],[363,171153,474],{"className":171154},[407,658],[363,171156,171157,171160],{"style":7212},[363,171158],{"className":171159,"style":651},[650],[363,171161,171163],{"className":171162},[655,656,657,658],[363,171164,11041],{"className":171165,"style":11129},[407,408,658],[363,171167,666],{"className":171168},[665],[363,171170,171172],{"className":171171},[638],[363,171173,171176],{"className":171174,"style":171175},[642],"height:0.3433em;",[363,171177],{}," 是由主干网络与",[1572,171180,171181],{},"非负激活函数","复合而成的证据函数，输出 ",[363,171184,171186,171238],{"className":171185,"translate":367},[366],[363,171187,171189],{"className":171188},[371],[373,171190,171191],{"xmlns":375},[377,171192,171193,171235],{},[380,171194,171195,171197,171199,171205,171207,171209,171211,171213,171215,171221,171223,171225,171227,171233],{},[383,171196,7914],{"mathvariant":75560},[458,171198,471],{},[543,171200,171201,171203],{},[383,171202,4505],{},[383,171204,101106],{"mathvariant":136008},[458,171206,461],{"stretchy":460},[383,171208,1121],{"mathvariant":75560},[458,171210,468],{"stretchy":460},[458,171212,471],{},[458,171214,461],{"stretchy":460},[543,171216,171217,171219],{},[383,171218,7914],{},[463,171220,465],{},[458,171222,898],{"separator":394},[458,171224,133107],{},[458,171226,898],{"separator":394},[543,171228,171229,171231],{},[383,171230,7914],{},[383,171232,11041],{},[458,171234,468],{"stretchy":460},[387,171236,171237],{"encoding":389},"\\mathbf{e} = g_{\\boldsymbol{\\theta}}(\\mathbf{x}) = (e_1, \\dots, e_K)",[363,171239,171241,171259,171332],{"className":171240,"ariaHidden":394},[393],[363,171242,171244,171247,171250,171253,171256],{"className":171243},[398],[363,171245],{"className":171246,"style":135617},[402],[363,171248,7914],{"className":171249},[407,75905],[363,171251],{"className":171252,"style":506},[505],[363,171254,471],{"className":171255},[510],[363,171257],{"className":171258,"style":506},[505],[363,171260,171262,171265,171314,171317,171320,171323,171326,171329],{"className":171261},[398],[363,171263],{"className":171264,"style":487},[402],[363,171266,171268,171271],{"className":171267},[407],[363,171269,4505],{"className":171270,"style":1328},[407,408],[363,171272,171274],{"className":171273},[629],[363,171275,171277,171306],{"className":171276},[633,634],[363,171278,171280,171303],{"className":171279},[638],[363,171281,171283],{"className":171282,"style":643},[642],[363,171284,171285,171288],{"style":19190},[363,171286],{"className":171287,"style":651},[650],[363,171289,171291],{"className":171290},[655,656,657,658],[363,171292,171294],{"className":171293},[407,658],[363,171295,171297],{"className":171296},[407,658],[363,171298,171300],{"className":171299},[407,658],[363,171301,101106],{"className":171302,"style":169854},[407,136068,658],[363,171304,666],{"className":171305},[665],[363,171307,171309],{"className":171308},[638],[363,171310,171312],{"className":171311,"style":8315},[642],[363,171313],{},[363,171315,461],{"className":171316},[494],[363,171318,1121],{"className":171319},[407,75905],[363,171321,468],{"className":171322},[501],[363,171324],{"className":171325,"style":506},[505],[363,171327,471],{"className":171328},[510],[363,171330],{"className":171331,"style":506},[505],[363,171333,171335,171338,171341,171381,171384,171387,171390,171393,171396,171399,171439],{"className":171334},[398],[363,171336],{"className":171337,"style":487},[402],[363,171339,461],{"className":171340},[494],[363,171342,171344,171347],{"className":171343},[407],[363,171345,7914],{"className":171346},[407,408],[363,171348,171350],{"className":171349},[629],[363,171351,171353,171373],{"className":171352},[633,634],[363,171354,171356,171370],{"className":171355},[638],[363,171357,171359],{"className":171358,"style":11480},[642],[363,171360,171361,171364],{"style":730},[363,171362],{"className":171363,"style":651},[650],[363,171365,171367],{"className":171366},[655,656,657,658],[363,171368,465],{"className":171369},[407,658],[363,171371,666],{"className":171372},[665],[363,171374,171376],{"className":171375},[638],[363,171377,171379],{"className":171378,"style":8315},[642],[363,171380],{},[363,171382,898],{"className":171383},[920],[363,171385],{"className":171386,"style":754},[505],[363,171388,133107],{"className":171389},[758],[363,171391],{"className":171392,"style":754},[505],[363,171394,898],{"className":171395},[920],[363,171397],{"className":171398,"style":754},[505],[363,171400,171402,171405],{"className":171401},[407],[363,171403,7914],{"className":171404},[407,408],[363,171406,171408],{"className":171407},[629],[363,171409,171411,171431],{"className":171410},[633,634],[363,171412,171414,171428],{"className":171413},[638],[363,171415,171417],{"className":171416,"style":727},[642],[363,171418,171419,171422],{"style":730},[363,171420],{"className":171421,"style":651},[650],[363,171423,171425],{"className":171424},[655,656,657,658],[363,171426,11041],{"className":171427,"style":11129},[407,408,658],[363,171429,666],{"className":171430},[665],[363,171432,171434],{"className":171433},[638],[363,171435,171437],{"className":171436,"style":8315},[642],[363,171438],{},[363,171440,468],{"className":171441},[501],"。迪利克雷参数取为\n",[363,171444,171446,171494],{"className":171445,"translate":367},[366],[363,171447,171449],{"className":171448},[371],[373,171450,171451],{"xmlns":375},[377,171452,171453,171491],{},[380,171454,171455,171461,171463,171469,171471,171473,171475,171477,171479,171481,171483,171485,171487,171489],{},[543,171456,171457,171459],{},[383,171458,45101],{},[383,171460,7911],{},[458,171462,471],{},[543,171464,171465,171467],{},[383,171466,7914],{},[383,171468,7911],{},[458,171470,2817],{},[463,171472,465],{},[458,171474,898],{"separator":394},[505,171476],{"width":3609},[1644,171478,87982],{},[505,171480],{"width":3609},[383,171482,45101],{"mathvariant":136008},[458,171484,471],{},[383,171486,7914],{"mathvariant":75560},[458,171488,2817],{},[463,171490,465],{"mathvariant":75560},[387,171492,171493],{"encoding":389},"\\alpha_k = e_k + 1, \\qquad \\text{即} \\qquad \\boldsymbol{\\alpha} = \\mathbf{e} + \\mathbf{1}",[363,171495,171497,171552,171607,171652,171670],{"className":171496,"ariaHidden":394},[393],[363,171498,171500,171503,171543,171546,171549],{"className":171499},[398],[363,171501],{"className":171502,"style":13721},[402],[363,171504,171506,171509],{"className":171505},[407],[363,171507,45101],{"className":171508,"style":45131},[407,408],[363,171510,171512],{"className":171511},[629],[363,171513,171515,171535],{"className":171514},[633,634],[363,171516,171518,171532],{"className":171517},[638],[363,171519,171521],{"className":171520,"style":643},[642],[363,171522,171523,171526],{"style":136107},[363,171524],{"className":171525,"style":651},[650],[363,171527,171529],{"className":171528},[655,656,657,658],[363,171530,7911],{"className":171531,"style":8614},[407,408,658],[363,171533,666],{"className":171534},[665],[363,171536,171538],{"className":171537},[638],[363,171539,171541],{"className":171540,"style":8315},[642],[363,171542],{},[363,171544],{"className":171545,"style":506},[505],[363,171547,471],{"className":171548},[510],[363,171550],{"className":171551,"style":506},[505],[363,171553,171555,171558,171598,171601,171604],{"className":171554},[398],[363,171556],{"className":171557,"style":145420},[402],[363,171559,171561,171564],{"className":171560},[407],[363,171562,7914],{"className":171563},[407,408],[363,171565,171567],{"className":171566},[629],[363,171568,171570,171590],{"className":171569},[633,634],[363,171571,171573,171587],{"className":171572},[638],[363,171574,171576],{"className":171575,"style":643},[642],[363,171577,171578,171581],{"style":730},[363,171579],{"className":171580,"style":651},[650],[363,171582,171584],{"className":171583},[655,656,657,658],[363,171585,7911],{"className":171586,"style":8614},[407,408,658],[363,171588,666],{"className":171589},[665],[363,171591,171593],{"className":171592},[638],[363,171594,171596],{"className":171595,"style":8315},[642],[363,171597],{},[363,171599],{"className":171600,"style":2934},[505],[363,171602,2817],{"className":171603},[2938],[363,171605],{"className":171606,"style":2934},[505],[363,171608,171610,171613,171616,171619,171622,171625,171631,171634,171643,171646,171649],{"className":171609},[398],[363,171611],{"className":171612,"style":913},[402],[363,171614,465],{"className":171615},[407],[363,171617,898],{"className":171618},[920],[363,171620],{"className":171621,"style":3981},[505],[363,171623],{"className":171624,"style":754},[505],[363,171626,171628],{"className":171627},[407,4945],[363,171629,87982],{"className":171630},[407,4949],[363,171632],{"className":171633,"style":3981},[505],[363,171635,171637],{"className":171636},[407],[363,171638,171640],{"className":171639},[407],[363,171641,45101],{"className":171642},[407,136068],[363,171644],{"className":171645,"style":506},[505],[363,171647,471],{"className":171648},[510],[363,171650],{"className":171651,"style":506},[505],[363,171653,171655,171658,171661,171664,171667],{"className":171654},[398],[363,171656],{"className":171657,"style":4598},[402],[363,171659,7914],{"className":171660},[407,75905],[363,171662],{"className":171663,"style":2934},[505],[363,171665,2817],{"className":171666},[2938],[363,171668],{"className":171669,"style":2934},[505],[363,171671,171673,171676],{"className":171672},[398],[363,171674],{"className":171675,"style":520},[402],[363,171677,465],{"className":171678},[407,75905],"\n网络对输入的预测由此被定义为 ",[363,171681,171683,171705],{"className":171682,"translate":367},[366],[363,171684,171686],{"className":171685},[371],[373,171687,171688],{"xmlns":375},[377,171689,171690,171702],{},[380,171691,171692,171694,171696,171698,171700],{},[383,171693,137065],{"mathvariant":557},[458,171695,4450],{},[458,171697,461],{"stretchy":460},[383,171699,45101],{"mathvariant":136008},[458,171701,468],{"stretchy":460},[387,171703,171704],{"encoding":389},"\\operatorname{Dir}(\\boldsymbol{\\alpha})",[363,171706,171708],{"className":171707,"ariaHidden":394},[393],[363,171709,171711,171714,171720,171723,171732],{"className":171710},[398],[363,171712],{"className":171713,"style":487},[402],[363,171715,171717],{"className":171716},[1831],[363,171718,137065],{"className":171719},[407,33009],[363,171721,461],{"className":171722},[494],[363,171724,171726],{"className":171725},[407],[363,171727,171729],{"className":171728},[407],[363,171730,45101],{"className":171731},[407,136068],[363,171733,468],{"className":171734},[501],[11,171736,171737,171738,171817,171818,171919,171920,171990,171991,172019],{},"参数化的语义可直接由命题 3.2 读出：",[363,171739,171741,171763],{"className":171740,"translate":367},[366],[363,171742,171744],{"className":171743},[371],[373,171745,171746],{"xmlns":375},[377,171747,171748,171760],{},[380,171749,171750,171752,171754,171756,171758],{},[383,171751,7914],{"mathvariant":75560},[458,171753,471],{},[383,171755,45101],{"mathvariant":136008},[458,171757,5160],{},[463,171759,465],{"mathvariant":75560},[387,171761,171762],{"encoding":389},"\\mathbf{e} = \\boldsymbol{\\alpha} - \\mathbf{1}",[363,171764,171766,171784,171808],{"className":171765,"ariaHidden":394},[393],[363,171767,171769,171772,171775,171778,171781],{"className":171768},[398],[363,171770],{"className":171771,"style":135617},[402],[363,171773,7914],{"className":171774},[407,75905],[363,171776],{"className":171777,"style":506},[505],[363,171779,471],{"className":171780},[510],[363,171782],{"className":171783,"style":506},[505],[363,171785,171787,171790,171799,171802,171805],{"className":171786},[398],[363,171788],{"className":171789,"style":4598},[402],[363,171791,171793],{"className":171792},[407],[363,171794,171796],{"className":171795},[407],[363,171797,45101],{"className":171798},[407,136068],[363,171800],{"className":171801,"style":2934},[505],[363,171803,5160],{"className":171804},[2938],[363,171806],{"className":171807,"style":2934},[505],[363,171809,171811,171814],{"className":171810},[398],[363,171812],{"className":171813,"style":520},[402],[363,171815,465],{"className":171816},[407,75905]," 正是",[1572,171819,171820,171821,171918],{},"超出均匀先验 ",[363,171822,171824,171848],{"className":171823,"translate":367},[366],[363,171825,171827],{"className":171826},[371],[373,171828,171829],{"xmlns":375},[377,171830,171831,171845],{},[380,171832,171833,171839,171841,171843],{},[543,171834,171835,171837],{},[383,171836,45527],{},[383,171838,7911],{},[383,171840,167630],{},[458,171842,471],{},[463,171844,465],{},[387,171846,171847],{"encoding":389},"a_k W = 1",[363,171849,171851,171909],{"className":171850,"ariaHidden":394},[393],[363,171852,171854,171857,171897,171900,171903,171906],{"className":171853},[398],[363,171855],{"className":171856,"style":16308},[402],[363,171858,171860,171863],{"className":171859},[407],[363,171861,45527],{"className":171862},[407,408],[363,171864,171866],{"className":171865},[629],[363,171867,171869,171889],{"className":171868},[633,634],[363,171870,171872,171886],{"className":171871},[638],[363,171873,171875],{"className":171874,"style":643},[642],[363,171876,171877,171880],{"style":730},[363,171878],{"className":171879,"style":651},[650],[363,171881,171883],{"className":171882},[655,656,657,658],[363,171884,7911],{"className":171885,"style":8614},[407,408,658],[363,171887,666],{"className":171888},[665],[363,171890,171892],{"className":171891},[638],[363,171893,171895],{"className":171894,"style":8315},[642],[363,171896],{},[363,171898,167630],{"className":171899,"style":682},[407,408],[363,171901],{"className":171902,"style":506},[505],[363,171904,471],{"className":171905},[510],[363,171907],{"className":171908,"style":506},[505],[363,171910,171912,171915],{"className":171911},[398],[363,171913],{"className":171914,"style":520},[402],[363,171916,465],{"className":171917},[407]," 的那部分伪计数","，即 2.6 节意义上「可解释为计数」的区域。这就是「证据」一词的来源：",[363,171921,171923,171941],{"className":171922,"translate":367},[366],[363,171924,171926],{"className":171925},[371],[373,171927,171928],{"xmlns":375},[377,171929,171930,171938],{},[380,171931,171932],{},[543,171933,171934,171936],{},[383,171935,7914],{},[383,171937,7911],{},[387,171939,171940],{"encoding":389},"e_k",[363,171942,171944],{"className":171943,"ariaHidden":394},[393],[363,171945,171947,171950],{"className":171946},[398],[363,171948],{"className":171949,"style":13721},[402],[363,171951,171953,171956],{"className":171952},[407],[363,171954,7914],{"className":171955},[407,408],[363,171957,171959],{"className":171958},[629],[363,171960,171962,171982],{"className":171961},[633,634],[363,171963,171965,171979],{"className":171964},[638],[363,171966,171968],{"className":171967,"style":643},[642],[363,171969,171970,171973],{"style":730},[363,171971],{"className":171972,"style":651},[650],[363,171974,171976],{"className":171975},[655,656,657,658],[363,171977,7911],{"className":171978,"style":8614},[407,408,658],[363,171980,666],{"className":171981},[665],[363,171983,171985],{"className":171984},[638],[363,171986,171988],{"className":171987,"style":8315},[642],[363,171989],{}," 是与类别 ",[363,171992,171994,172007],{"className":171993,"translate":367},[366],[363,171995,171997],{"className":171996},[371],[373,171998,171999],{"xmlns":375},[377,172000,172001,172005],{},[380,172002,172003],{},[383,172004,7911],{},[387,172006,7911],{"encoding":389},[363,172008,172010],{"className":172009,"ariaHidden":394},[393],[363,172011,172013,172016],{"className":172012},[398],[363,172014],{"className":172015,"style":12944},[402],[363,172017,7911],{"className":172018,"style":8614},[407,408]," 相关的、由网络从输入中提取出的支持性观测。",[11,172021,172022],{},"非负激活函数的选择影响显著，值得逐一说明：",[10374,172024,172025,172345,172464,172766],{},[7012,172026,172027,172170,172171,172227,172228,172287,172288,172344],{},[363,172028,172030,172073],{"className":172029,"translate":367},[366],[363,172031,172033],{"className":172032},[371],[373,172034,172035],{"xmlns":375},[377,172036,172037,172070],{},[380,172038,172039,172042,172044,172046,172048,172050,172052,172054,172056,172058,172060,172062,172068],{},[383,172040,172041],{"mathvariant":557},"softplus",[458,172043,4450],{},[458,172045,461],{"stretchy":460},[383,172047,118116],{},[458,172049,468],{"stretchy":460},[458,172051,471],{},[383,172053,4447],{},[458,172055,4450],{},[458,172057,461],{"stretchy":460},[463,172059,465],{},[458,172061,2817],{},[7161,172063,172064,172066],{},[383,172065,7914],{},[383,172067,118116],{},[458,172069,468],{"stretchy":460},[387,172071,172072],{"encoding":389},"\\operatorname{softplus}(z) = \\log(1 + e^z)",[363,172074,172076,172106,172132],{"className":172075,"ariaHidden":394},[393],[363,172077,172079,172082,172088,172091,172094,172097,172100,172103],{"className":172078},[398],[363,172080],{"className":172081,"style":487},[402],[363,172083,172085],{"className":172084},[1831],[363,172086,172041],{"className":172087},[407,33009],[363,172089,461],{"className":172090},[494],[363,172092,118116],{"className":172093,"style":118386},[407,408],[363,172095,468],{"className":172096},[501],[363,172098],{"className":172099,"style":506},[505],[363,172101,471],{"className":172102},[510],[363,172104],{"className":172105,"style":506},[505],[363,172107,172109,172112,172117,172120,172123,172126,172129],{"className":172108},[398],[363,172110],{"className":172111,"style":487},[402],[363,172113,4501,172115],{"className":172114},[1831],[363,172116,4505],{"style":4504},[363,172118,461],{"className":172119},[494],[363,172121,465],{"className":172122},[407],[363,172124],{"className":172125,"style":2934},[505],[363,172127,2817],{"className":172128},[2938],[363,172130],{"className":172131,"style":2934},[505],[363,172133,172135,172138,172167],{"className":172134},[398],[363,172136],{"className":172137,"style":487},[402],[363,172139,172141,172144],{"className":172140},[407],[363,172142,7914],{"className":172143},[407,408],[363,172145,172147],{"className":172146},[629],[363,172148,172150],{"className":172149},[633],[363,172151,172153],{"className":172152},[638],[363,172154,172156],{"className":172155,"style":50700},[642],[363,172157,172158,172161],{"style":7212},[363,172159],{"className":172160,"style":651},[650],[363,172162,172164],{"className":172163},[655,656,657,658],[363,172165,118116],{"className":172166,"style":118386},[407,408,658],[363,172168,468],{"className":172169},[501],"：恒正、处处可微、在 ",[363,172172,172174,172194],{"className":172173,"translate":367},[366],[363,172175,172177],{"className":172176},[371],[373,172178,172179],{"xmlns":375},[377,172180,172181,172191],{},[380,172182,172183,172185,172187,172189],{},[383,172184,118116],{},[458,172186,1376],{},[458,172188,5160],{},[383,172190,1371],{"mathvariant":557},[387,172192,172193],{"encoding":389},"z \\to -\\infty",[363,172195,172197,172215],{"className":172196,"ariaHidden":394},[393],[363,172198,172200,172203,172206,172209,172212],{"className":172199},[398],[363,172201],{"className":172202,"style":2692},[402],[363,172204,118116],{"className":172205,"style":118386},[407,408],[363,172207],{"className":172208,"style":506},[505],[363,172210,1376],{"className":172211},[510],[363,172213],{"className":172214,"style":506},[505],[363,172216,172218,172221,172224],{"className":172217},[398],[363,172219],{"className":172220,"style":4598},[402],[363,172222,5160],{"className":172223},[407],[363,172225,1371],{"className":172226},[407]," 时以 ",[363,172229,172231,172249],{"className":172230,"translate":367},[366],[363,172232,172234],{"className":172233},[371],[373,172235,172236],{"xmlns":375},[377,172237,172238,172246],{},[380,172239,172240],{},[7161,172241,172242,172244],{},[383,172243,7914],{},[383,172245,118116],{},[387,172247,172248],{"encoding":389},"e^z",[363,172250,172252],{"className":172251,"ariaHidden":394},[393],[363,172253,172255,172258],{"className":172254},[398],[363,172256],{"className":172257,"style":50700},[402],[363,172259,172261,172264],{"className":172260},[407],[363,172262,7914],{"className":172263},[407,408],[363,172265,172267],{"className":172266},[629],[363,172268,172270],{"className":172269},[633],[363,172271,172273],{"className":172272},[638],[363,172274,172276],{"className":172275,"style":50700},[642],[363,172277,172278,172281],{"style":7212},[363,172279],{"className":172280,"style":651},[650],[363,172282,172284],{"className":172283},[655,656,657,658],[363,172285,118116],{"className":172286,"style":118386},[407,408,658]," 的速度趋零、在 ",[363,172289,172291,172311],{"className":172290,"translate":367},[366],[363,172292,172294],{"className":172293},[371],[373,172295,172296],{"xmlns":375},[377,172297,172298,172308],{},[380,172299,172300,172302,172304,172306],{},[383,172301,118116],{},[458,172303,1376],{},[458,172305,2817],{},[383,172307,1371],{"mathvariant":557},[387,172309,172310],{"encoding":389},"z \\to +\\infty",[363,172312,172314,172332],{"className":172313,"ariaHidden":394},[393],[363,172315,172317,172320,172323,172326,172329],{"className":172316},[398],[363,172318],{"className":172319,"style":2692},[402],[363,172321,118116],{"className":172322,"style":118386},[407,408],[363,172324],{"className":172325,"style":506},[505],[363,172327,1376],{"className":172328},[510],[363,172330],{"className":172331,"style":506},[505],[363,172333,172335,172338,172341],{"className":172334},[398],[363,172336],{"className":172337,"style":4598},[402],[363,172339,2817],{"className":172340},[407],[363,172342,1371],{"className":172343},[407]," 时线性增长。它既提供了精确的零证据状态，又避免了指数爆炸，是实践中默认的选择。",[7012,172346,172347,172393,172394,172463],{},[363,172348,172350,172372],{"className":172349,"translate":367},[366],[363,172351,172353],{"className":172352},[371],[373,172354,172355],{"xmlns":375},[377,172356,172357,172369],{},[380,172358,172359,172361,172363,172365,172367],{},[383,172360,126281],{},[458,172362,4450],{},[458,172364,461],{"stretchy":460},[383,172366,118116],{},[458,172368,468],{"stretchy":460},[387,172370,172371],{"encoding":389},"\\exp(z)",[363,172373,172375],{"className":172374,"ariaHidden":394},[393],[363,172376,172378,172381,172384,172387,172390],{"className":172377},[398],[363,172379],{"className":172380,"style":487},[402],[363,172382,126281],{"className":172383},[1831],[363,172385,461],{"className":172386},[494],[363,172388,118116],{"className":172389,"style":118386},[407,408],[363,172391,468],{"className":172392},[501],"：严格正、光滑，但无上界，使 ",[363,172395,172397,172414],{"className":172396,"translate":367},[366],[363,172398,172400],{"className":172399},[371],[373,172401,172402],{"xmlns":375},[377,172403,172404,172412],{},[380,172405,172406],{},[543,172407,172408,172410],{},[383,172409,45101],{},[463,172411,474],{},[387,172413,152251],{"encoding":389},[363,172415,172417],{"className":172416,"ariaHidden":394},[393],[363,172418,172420,172423],{"className":172419},[398],[363,172421],{"className":172422,"style":13721},[402],[363,172424,172426,172429],{"className":172425},[407],[363,172427,45101],{"className":172428,"style":45131},[407,408],[363,172430,172432],{"className":172431},[629],[363,172433,172435,172455],{"className":172434},[633,634],[363,172436,172438,172452],{"className":172437},[638],[363,172439,172441],{"className":172440,"style":11480},[642],[363,172442,172443,172446],{"style":136107},[363,172444],{"className":172445,"style":651},[650],[363,172447,172449],{"className":172448},[655,656,657,658],[363,172450,474],{"className":172451},[407,658],[363,172453,666],{"className":172454},[665],[363,172456,172458],{"className":172457},[638],[363,172459,172461],{"className":172460,"style":8315},[642],[363,172462],{}," 可任意大，易造成数值溢出与损失对证据的不稳定响应。",[7012,172465,172466,172516,172517,172568,172569,172661,172662,172665,172666,172736,172737,172765],{},[363,172467,172469,172492],{"className":172468,"translate":367},[366],[363,172470,172472],{"className":172471},[371],[373,172473,172474],{"xmlns":375},[377,172475,172476,172489],{},[380,172477,172478,172481,172483,172485,172487],{},[383,172479,172480],{"mathvariant":557},"ReLU",[458,172482,4450],{},[458,172484,461],{"stretchy":460},[383,172486,118116],{},[458,172488,468],{"stretchy":460},[387,172490,172491],{"encoding":389},"\\operatorname{ReLU}(z)",[363,172493,172495],{"className":172494,"ariaHidden":394},[393],[363,172496,172498,172501,172507,172510,172513],{"className":172497},[398],[363,172499],{"className":172500,"style":487},[402],[363,172502,172504],{"className":172503},[1831],[363,172505,172480],{"className":172506},[407,33009],[363,172508,461],{"className":172509},[494],[363,172511,118116],{"className":172512,"style":118386},[407,408],[363,172514,468],{"className":172515},[501],"：计算廉价，但在 ",[363,172518,172520,172538],{"className":172519,"translate":367},[366],[363,172521,172523],{"className":172522},[371],[373,172524,172525],{"xmlns":375},[377,172526,172527,172535],{},[380,172528,172529,172531,172533],{},[383,172530,118116],{},[458,172532,7598],{},[463,172534,474],{},[387,172536,172537],{"encoding":389},"z \u003C 0",[363,172539,172541,172559],{"className":172540,"ariaHidden":394},[393],[363,172542,172544,172547,172550,172553,172556],{"className":172543},[398],[363,172545],{"className":172546,"style":6271},[402],[363,172548,118116],{"className":172549,"style":118386},[407,408],[363,172551],{"className":172552,"style":506},[505],[363,172554,7598],{"className":172555},[510],[363,172557],{"className":172558,"style":506},[505],[363,172560,172562,172565],{"className":172561},[398],[363,172563],{"className":172564,"style":520},[402],[363,172566,474],{"className":172567},[407]," 处梯度恒为零。处于该区域的单元输出证据 ",[363,172570,172572,172594],{"className":172571,"translate":367},[366],[363,172573,172575],{"className":172574},[371],[373,172576,172577],{"xmlns":375},[377,172578,172579,172591],{},[380,172580,172581,172587,172589],{},[543,172582,172583,172585],{},[383,172584,7914],{},[383,172586,7911],{},[458,172588,471],{},[463,172590,474],{},[387,172592,172593],{"encoding":389},"e_k = 0",[363,172595,172597,172652],{"className":172596,"ariaHidden":394},[393],[363,172598,172600,172603,172643,172646,172649],{"className":172599},[398],[363,172601],{"className":172602,"style":13721},[402],[363,172604,172606,172609],{"className":172605},[407],[363,172607,7914],{"className":172608},[407,408],[363,172610,172612],{"className":172611},[629],[363,172613,172615,172635],{"className":172614},[633,634],[363,172616,172618,172632],{"className":172617},[638],[363,172619,172621],{"className":172620,"style":643},[642],[363,172622,172623,172626],{"style":730},[363,172624],{"className":172625,"style":651},[650],[363,172627,172629],{"className":172628},[655,656,657,658],[363,172630,7911],{"className":172631,"style":8614},[407,408,658],[363,172633,666],{"className":172634},[665],[363,172636,172638],{"className":172637},[638],[363,172639,172641],{"className":172640,"style":8315},[642],[363,172642],{},[363,172644],{"className":172645,"style":506},[505],[363,172647,471],{"className":172648},[510],[363,172650],{"className":172651,"style":506},[505],[363,172653,172655,172658],{"className":172654},[398],[363,172656],{"className":172657,"style":520},[402],[363,172659,474],{"className":172660},[407]," 且",[1572,172663,172664],{},"永远无法通过梯度逃离","——",[363,172667,172669,172687],{"className":172668,"translate":367},[366],[363,172670,172672],{"className":172671},[371],[373,172673,172674],{"xmlns":375},[377,172675,172676,172684],{},[380,172677,172678],{},[543,172679,172680,172682],{},[383,172681,45101],{},[383,172683,7911],{},[387,172685,172686],{"encoding":389},"\\alpha_k",[363,172688,172690],{"className":172689,"ariaHidden":394},[393],[363,172691,172693,172696],{"className":172692},[398],[363,172694],{"className":172695,"style":13721},[402],[363,172697,172699,172702],{"className":172698},[407],[363,172700,45101],{"className":172701,"style":45131},[407,408],[363,172703,172705],{"className":172704},[629],[363,172706,172708,172728],{"className":172707},[633,634],[363,172709,172711,172725],{"className":172710},[638],[363,172712,172714],{"className":172713,"style":643},[642],[363,172715,172716,172719],{"style":136107},[363,172717],{"className":172718,"style":651},[650],[363,172720,172722],{"className":172721},[655,656,657,658],[363,172723,7911],{"className":172724,"style":8614},[407,408,658],[363,172726,666],{"className":172727},[665],[363,172729,172731],{"className":172730},[638],[363,172732,172734],{"className":172733,"style":8315},[642],[363,172735],{}," 被锁在 ",[363,172738,172740,172753],{"className":172739,"translate":367},[366],[363,172741,172743],{"className":172742},[371],[373,172744,172745],{"xmlns":375},[377,172746,172747,172751],{},[380,172748,172749],{},[463,172750,465],{},[387,172752,465],{"encoding":389},[363,172754,172756],{"className":172755,"ariaHidden":394},[393],[363,172757,172759,172762],{"className":172758},[398],[363,172760],{"className":172761,"style":520},[402],[363,172763,465],{"className":172764},[407],"，形成死区。这使 ReLU 在证据函数中通常劣于 softplus。",[7012,172767,172768,172840,172841,172869],{},[363,172769,172771,172798],{"className":172770,"translate":367},[366],[363,172772,172774],{"className":172773},[371],[373,172775,172776],{"xmlns":375},[377,172777,172778,172795],{},[380,172779,172780,172783,172785,172787,172789,172791,172793],{},[383,172781,172782],{"mathvariant":557},"ELU",[458,172784,4450],{},[458,172786,461],{"stretchy":460},[383,172788,118116],{},[458,172790,468],{"stretchy":460},[458,172792,2817],{},[463,172794,465],{},[387,172796,172797],{"encoding":389},"\\operatorname{ELU}(z) + 1",[363,172799,172801,172831],{"className":172800,"ariaHidden":394},[393],[363,172802,172804,172807,172813,172816,172819,172822,172825,172828],{"className":172803},[398],[363,172805],{"className":172806,"style":487},[402],[363,172808,172810],{"className":172809},[1831],[363,172811,172782],{"className":172812},[407,33009],[363,172814,461],{"className":172815},[494],[363,172817,118116],{"className":172818,"style":118386},[407,408],[363,172820,468],{"className":172821},[501],[363,172823],{"className":172824,"style":2934},[505],[363,172826,2817],{"className":172827},[2938],[363,172829],{"className":172830,"style":2934},[505],[363,172832,172834,172837],{"className":172833},[398],[363,172835],{"className":172836,"style":520},[402],[363,172838,465],{"className":172839},[407],"：具有负饱和下界 ",[363,172842,172844,172857],{"className":172843,"translate":367},[366],[363,172845,172847],{"className":172846},[371],[373,172848,172849],{"xmlns":375},[377,172850,172851,172855],{},[380,172852,172853],{},[463,172854,474],{},[387,172856,474],{"encoding":389},[363,172858,172860],{"className":172859,"ariaHidden":394},[393],[363,172861,172863,172866],{"className":172862},[398],[363,172864],{"className":172865,"style":520},[402],[363,172867,474],{"className":172868},[407],"，梯度在负半轴非零，是介于二者之间的折中。",[2658,172871,172873],{"id":172872},"_35-预测概率与不确定性的解析形式","3.5 预测概率与不确定性的解析形式",[1340,172875,172877],{"title":172876},"命题 3.4（EDL 的预测与不确定性）",[11,172878,172879,172880,173274,173275],{},"在定义 3.3 的参数化下，记总强度 ",[363,172881,172883,172953],{"className":172882,"translate":367},[366],[363,172884,172886],{"className":172885},[371],[373,172887,172888],{"xmlns":375},[377,172889,172890,172950],{},[380,172891,172892,172894,172896,172902,172904,172918,172924,172926,172928,172930,172944],{},[383,172893,26084],{},[458,172895,471],{},[543,172897,172898,172900],{},[383,172899,45101],{},[463,172901,474],{},[458,172903,471],{},[7900,172905,172906,172908,172916],{},[458,172907,13808],{},[380,172909,172910,172912,172914],{},[383,172911,7911],{},[458,172913,471],{},[463,172915,465],{},[383,172917,11041],{},[543,172919,172920,172922],{},[383,172921,45101],{},[383,172923,7911],{},[458,172925,471],{},[383,172927,11041],{},[458,172929,2817],{},[7900,172931,172932,172934,172942],{},[458,172933,13808],{},[380,172935,172936,172938,172940],{},[383,172937,7911],{},[458,172939,471],{},[463,172941,465],{},[383,172943,11041],{},[543,172945,172946,172948],{},[383,172947,7914],{},[383,172949,7911],{},[387,172951,172952],{"encoding":389},"S = \\alpha_0 = \\sum_{k=1}^K \\alpha_k = K + \\sum_{k=1}^K e_k",[363,172954,172956,172974,173029,173147,173165],{"className":172955,"ariaHidden":394},[393],[363,172957,172959,172962,172965,172968,172971],{"className":172958},[398],[363,172960],{"className":172961,"style":1011},[402],[363,172963,26084],{"className":172964,"style":26208},[407,408],[363,172966],{"className":172967,"style":506},[505],[363,172969,471],{"className":172970},[510],[363,172972],{"className":172973,"style":506},[505],[363,172975,172977,172980,173020,173023,173026],{"className":172976},[398],[363,172978],{"className":172979,"style":13721},[402],[363,172981,172983,172986],{"className":172982},[407],[363,172984,45101],{"className":172985,"style":45131},[407,408],[363,172987,172989],{"className":172988},[629],[363,172990,172992,173012],{"className":172991},[633,634],[363,172993,172995,173009],{"className":172994},[638],[363,172996,172998],{"className":172997,"style":11480},[642],[363,172999,173000,173003],{"style":136107},[363,173001],{"className":173002,"style":651},[650],[363,173004,173006],{"className":173005},[655,656,657,658],[363,173007,474],{"className":173008},[407,658],[363,173010,666],{"className":173011},[665],[363,173013,173015],{"className":173014},[638],[363,173016,173018],{"className":173017,"style":8315},[642],[363,173019],{},[363,173021],{"className":173022,"style":506},[505],[363,173024,471],{"className":173025},[510],[363,173027],{"className":173028,"style":506},[505],[363,173030,173032,173035,173095,173098,173138,173141,173144],{"className":173031},[398],[363,173033],{"className":173034,"style":136371},[402],[363,173036,173038,173041],{"className":173037},[1831],[363,173039,13808],{"className":173040,"style":40007},[1831,1832,5963],[363,173042,173044],{"className":173043},[629],[363,173045,173047,173087],{"className":173046},[633,634],[363,173048,173050,173084],{"className":173049},[638],[363,173051,173053,173073],{"className":173052,"style":133494},[642],[363,173054,173055,173058],{"style":40023},[363,173056],{"className":173057,"style":651},[650],[363,173059,173061],{"className":173060},[655,656,657,658],[363,173062,173064,173067,173070],{"className":173063},[407,658],[363,173065,7911],{"className":173066,"style":8614},[407,408,658],[363,173068,471],{"className":173069},[510,658],[363,173071,465],{"className":173072},[407,658],[363,173074,173075,173078],{"style":133517},[363,173076],{"className":173077,"style":651},[650],[363,173079,173081],{"className":173080},[655,656,657,658],[363,173082,11041],{"className":173083,"style":11129},[407,408,658],[363,173085,666],{"className":173086},[665],[363,173088,173090],{"className":173089},[638],[363,173091,173093],{"className":173092,"style":40042},[642],[363,173094],{},[363,173096],{"className":173097,"style":754},[505],[363,173099,173101,173104],{"className":173100},[407],[363,173102,45101],{"className":173103,"style":45131},[407,408],[363,173105,173107],{"className":173106},[629],[363,173108,173110,173130],{"className":173109},[633,634],[363,173111,173113,173127],{"className":173112},[638],[363,173114,173116],{"className":173115,"style":643},[642],[363,173117,173118,173121],{"style":136107},[363,173119],{"className":173120,"style":651},[650],[363,173122,173124],{"className":173123},[655,656,657,658],[363,173125,7911],{"className":173126,"style":8614},[407,408,658],[363,173128,666],{"className":173129},[665],[363,173131,173133],{"className":173132},[638],[363,173134,173136],{"className":173135,"style":8315},[642],[363,173137],{},[363,173139],{"className":173140,"style":506},[505],[363,173142,471],{"className":173143},[510],[363,173145],{"className":173146,"style":506},[505],[363,173148,173150,173153,173156,173159,173162],{"className":173149},[398],[363,173151],{"className":173152,"style":133899},[402],[363,173154,11041],{"className":173155,"style":11129},[407,408],[363,173157],{"className":173158,"style":2934},[505],[363,173160,2817],{"className":173161},[2938],[363,173163],{"className":173164,"style":2934},[505],[363,173166,173168,173171,173231,173234],{"className":173167},[398],[363,173169],{"className":173170,"style":136371},[402],[363,173172,173174,173177],{"className":173173},[1831],[363,173175,13808],{"className":173176,"style":40007},[1831,1832,5963],[363,173178,173180],{"className":173179},[629],[363,173181,173183,173223],{"className":173182},[633,634],[363,173184,173186,173220],{"className":173185},[638],[363,173187,173189,173209],{"className":173188,"style":133494},[642],[363,173190,173191,173194],{"style":40023},[363,173192],{"className":173193,"style":651},[650],[363,173195,173197],{"className":173196},[655,656,657,658],[363,173198,173200,173203,173206],{"className":173199},[407,658],[363,173201,7911],{"className":173202,"style":8614},[407,408,658],[363,173204,471],{"className":173205},[510,658],[363,173207,465],{"className":173208},[407,658],[363,173210,173211,173214],{"style":133517},[363,173212],{"className":173213,"style":651},[650],[363,173215,173217],{"className":173216},[655,656,657,658],[363,173218,11041],{"className":173219,"style":11129},[407,408,658],[363,173221,666],{"className":173222},[665],[363,173224,173226],{"className":173225},[638],[363,173227,173229],{"className":173228,"style":40042},[642],[363,173230],{},[363,173232],{"className":173233,"style":754},[505],[363,173235,173237,173240],{"className":173236},[407],[363,173238,7914],{"className":173239},[407,408],[363,173241,173243],{"className":173242},[629],[363,173244,173246,173266],{"className":173245},[633,634],[363,173247,173249,173263],{"className":173248},[638],[363,173250,173252],{"className":173251,"style":643},[642],[363,173253,173254,173257],{"style":730},[363,173255],{"className":173256,"style":651},[650],[363,173258,173260],{"className":173259},[655,656,657,658],[363,173261,7911],{"className":173262,"style":8614},[407,408,658],[363,173264,666],{"className":173265},[665],[363,173267,173269],{"className":173268},[638],[363,173270,173272],{"className":173271,"style":8315},[642],[363,173273],{},"。则\n",[363,173276,173278,173336],{"className":173277,"translate":367},[366],[363,173279,173281],{"className":173280},[371],[373,173282,173283],{"xmlns":375},[377,173284,173285,173333],{},[380,173286,173287,173293,173295,173297,173299,173305,173307,173309,173319,173321,173323,173325,173327],{},[543,173288,173289,173291],{},[383,173290,11],{},[383,173292,7911],{},[458,173294,471],{},[383,173296,571],{"mathvariant":570},[458,173298,578],{"stretchy":460},[543,173300,173301,173303],{},[383,173302,1121],{},[383,173304,7911],{},[458,173306,605],{"stretchy":460},[458,173308,471],{},[586,173310,173311,173317],{},[543,173312,173313,173315],{},[383,173314,45101],{},[383,173316,7911],{},[383,173318,26084],{},[458,173320,898],{"separator":394},[505,173322],{"width":3609},[383,173324,15747],{},[458,173326,471],{},[586,173328,173329,173331],{},[383,173330,11041],{},[383,173332,26084],{},[387,173334,173335],{"encoding":389},"p_k = \\mathbb{E}[x_k] = \\frac{\\alpha_k}{S}, \\qquad u = \\frac{K}{S}",[363,173337,173339,173394,173458,173590],{"className":173338,"ariaHidden":394},[393],[363,173340,173342,173345,173385,173388,173391],{"className":173341},[398],[363,173343],{"className":173344,"style":2623},[402],[363,173346,173348,173351],{"className":173347},[407],[363,173349,11],{"className":173350},[407,408],[363,173352,173354],{"className":173353},[629],[363,173355,173357,173377],{"className":173356},[633,634],[363,173358,173360,173374],{"className":173359},[638],[363,173361,173363],{"className":173362,"style":643},[642],[363,173364,173365,173368],{"style":730},[363,173366],{"className":173367,"style":651},[650],[363,173369,173371],{"className":173370},[655,656,657,658],[363,173372,7911],{"className":173373,"style":8614},[407,408,658],[363,173375,666],{"className":173376},[665],[363,173378,173380],{"className":173379},[638],[363,173381,173383],{"className":173382,"style":8315},[642],[363,173384],{},[363,173386],{"className":173387,"style":506},[505],[363,173389,471],{"className":173390},[510],[363,173392],{"className":173393,"style":506},[505],[363,173395,173397,173400,173403,173406,173446,173449,173452,173455],{"className":173396},[398],[363,173398],{"className":173399,"style":487},[402],[363,173401,571],{"className":173402},[407,714],[363,173404,578],{"className":173405},[494],[363,173407,173409,173412],{"className":173408},[407],[363,173410,1121],{"className":173411},[407,408],[363,173413,173415],{"className":173414},[629],[363,173416,173418,173438],{"className":173417},[633,634],[363,173419,173421,173435],{"className":173420},[638],[363,173422,173424],{"className":173423,"style":643},[642],[363,173425,173426,173429],{"style":730},[363,173427],{"className":173428,"style":651},[650],[363,173430,173432],{"className":173431},[655,656,657,658],[363,173433,7911],{"className":173434,"style":8614},[407,408,658],[363,173436,666],{"className":173437},[665],[363,173439,173441],{"className":173440},[638],[363,173442,173444],{"className":173443,"style":8315},[642],[363,173445],{},[363,173447,605],{"className":173448},[501],[363,173450],{"className":173451,"style":506},[505],[363,173453,471],{"className":173454},[510],[363,173456],{"className":173457,"style":506},[505],[363,173459,173461,173464,173569,173572,173575,173578,173581,173584,173587],{"className":173460},[398],[363,173462],{"className":173463,"style":161014},[402],[363,173465,173467,173470,173566],{"className":173466},[407],[363,173468],{"className":173469},[494,789],[363,173471,173473],{"className":173472},[586],[363,173474,173476,173558],{"className":173475},[633,634],[363,173477,173479,173555],{"className":173478},[638],[363,173480,173482,173496,173504],{"className":173481,"style":160636},[642],[363,173483,173484,173487],{"style":2874},[363,173485],{"className":173486,"style":809},[650],[363,173488,173490],{"className":173489},[655,656,657,658],[363,173491,173493],{"className":173492},[407,658],[363,173494,26084],{"className":173495,"style":26208},[407,408,658],[363,173497,173498,173501],{"style":821},[363,173499],{"className":173500,"style":809},[650],[363,173502],{"className":173503,"style":829},[828],[363,173505,173506,173509],{"style":159912},[363,173507],{"className":173508,"style":809},[650],[363,173510,173512],{"className":173511},[655,656,657,658],[363,173513,173515],{"className":173514},[407,658],[363,173516,173518,173521],{"className":173517},[407,658],[363,173519,45101],{"className":173520,"style":45131},[407,408,658],[363,173522,173524],{"className":173523},[629],[363,173525,173527,173547],{"className":173526},[633,634],[363,173528,173530,173544],{"className":173529},[638],[363,173531,173533],{"className":173532,"style":6445},[642],[363,173534,173535,173538],{"style":159942},[363,173536],{"className":173537,"style":30553},[650],[363,173539,173541],{"className":173540},[655,30557,10021,658],[363,173542,7911],{"className":173543,"style":8614},[407,408,658],[363,173545,666],{"className":173546},[665],[363,173548,173550],{"className":173549},[638],[363,173551,173553],{"className":173552,"style":101583},[642],[363,173554],{},[363,173556,666],{"className":173557},[665],[363,173559,173561],{"className":173560},[638],[363,173562,173564],{"className":173563,"style":2919},[642],[363,173565],{},[363,173567],{"className":173568},[501,789],[363,173570,898],{"className":173571},[920],[363,173573],{"className":173574,"style":3981},[505],[363,173576],{"className":173577,"style":754},[505],[363,173579,15747],{"className":173580},[407,408],[363,173582],{"className":173583,"style":506},[505],[363,173585,471],{"className":173586},[510],[363,173588],{"className":173589,"style":506},[505],[363,173591,173593,173596],{"className":173592},[398],[363,173594],{"className":173595,"style":168422},[402],[363,173597,173599,173602,173661],{"className":173598},[407],[363,173600],{"className":173601},[494,789],[363,173603,173605],{"className":173604},[586],[363,173606,173608,173653],{"className":173607},[633,634],[363,173609,173611,173650],{"className":173610},[638],[363,173612,173614,173628,173636],{"className":173613,"style":168063},[642],[363,173615,173616,173619],{"style":2874},[363,173617],{"className":173618,"style":809},[650],[363,173620,173622],{"className":173621},[655,656,657,658],[363,173623,173625],{"className":173624},[407,658],[363,173626,26084],{"className":173627,"style":26208},[407,408,658],[363,173629,173630,173633],{"style":821},[363,173631],{"className":173632,"style":809},[650],[363,173634],{"className":173635,"style":829},[828],[363,173637,173638,173641],{"style":2897},[363,173639],{"className":173640,"style":809},[650],[363,173642,173644],{"className":173643},[655,656,657,658],[363,173645,173647],{"className":173646},[407,658],[363,173648,11041],{"className":173649,"style":11129},[407,408,658],[363,173651,666],{"className":173652},[665],[363,173654,173656],{"className":173655},[638],[363,173657,173659],{"className":173658,"style":2919},[642],[363,173660],{},[363,173662],{"className":173663},[501,789],[11,173665,173666,173668,173669,173697,173698,173767,173768,10527],{},[1572,173667,137993],{}," 第一式即命题 2.1。第二式即命题 3.2。对 ",[363,173670,173672,173685],{"className":173671,"translate":367},[366],[363,173673,173675],{"className":173674},[371],[373,173676,173677],{"xmlns":375},[377,173678,173679,173683],{},[380,173680,173681],{},[383,173682,15747],{},[387,173684,15747],{"encoding":389},[363,173686,173688],{"className":173687,"ariaHidden":394},[393],[363,173689,173691,173694],{"className":173690},[398],[363,173692],{"className":173693,"style":2692},[402],[363,173695,15747],{"className":173696},[407,408]," 的推导亦可独立地由聚合性（命题 2.8）得到：若把全部类别合并为一个事件，其迪利克雷参数为 ",[363,173699,173701,173718],{"className":173700,"translate":367},[366],[363,173702,173704],{"className":173703},[371],[373,173705,173706],{"xmlns":375},[377,173707,173708,173716],{},[380,173709,173710],{},[543,173711,173712,173714],{},[383,173713,45101],{},[463,173715,474],{},[387,173717,152251],{"encoding":389},[363,173719,173721],{"className":173720,"ariaHidden":394},[393],[363,173722,173724,173727],{"className":173723},[398],[363,173725],{"className":173726,"style":13721},[402],[363,173728,173730,173733],{"className":173729},[407],[363,173731,45101],{"className":173732,"style":45131},[407,408],[363,173734,173736],{"className":173735},[629],[363,173737,173739,173759],{"className":173738},[633,634],[363,173740,173742,173756],{"className":173741},[638],[363,173743,173745],{"className":173744,"style":11480},[642],[363,173746,173747,173750],{"style":136107},[363,173748],{"className":173749,"style":651},[650],[363,173751,173753],{"className":173752},[655,656,657,658],[363,173754,474],{"className":173755},[407,658],[363,173757,666],{"className":173758},[665],[363,173760,173762],{"className":173761},[638],[363,173763,173765],{"className":173764,"style":8315},[642],[363,173766],{},"，不确定性质量即为 ",[363,173769,173771,173793],{"className":173770,"translate":367},[366],[363,173772,173774],{"className":173773},[371],[373,173775,173776],{"xmlns":375},[377,173777,173778,173790],{},[380,173779,173780,173782,173784],{},[383,173781,11041],{},[383,173783,1288],{"mathvariant":557},[543,173785,173786,173788],{},[383,173787,45101],{},[463,173789,474],{},[387,173791,173792],{"encoding":389},"K\u002F\\alpha_0",[363,173794,173796],{"className":173795,"ariaHidden":394},[393],[363,173797,173799,173802,173805,173808],{"className":173798},[398],[363,173800],{"className":173801,"style":487},[402],[363,173803,11041],{"className":173804,"style":11129},[407,408],[363,173806,1288],{"className":173807},[407],[363,173809,173811,173814],{"className":173810},[407],[363,173812,45101],{"className":173813,"style":45131},[407,408],[363,173815,173817],{"className":173816},[629],[363,173818,173820,173840],{"className":173819},[633,634],[363,173821,173823,173837],{"className":173822},[638],[363,173824,173826],{"className":173825,"style":11480},[642],[363,173827,173828,173831],{"style":136107},[363,173829],{"className":173830,"style":651},[650],[363,173832,173834],{"className":173833},[655,656,657,658],[363,173835,474],{"className":173836},[407,658],[363,173838,666],{"className":173839},[665],[363,173841,173843],{"className":173842},[638],[363,173844,173846],{"className":173845,"style":8315},[642],[363,173847],{},[11,173849,31026,173850,173878],{},[363,173851,173853,173866],{"className":173852,"translate":367},[366],[363,173854,173856],{"className":173855},[371],[373,173857,173858],{"xmlns":375},[377,173859,173860,173864],{},[380,173861,173862],{},[383,173863,15747],{},[387,173865,15747],{"encoding":389},[363,173867,173869],{"className":173868,"ariaHidden":394},[393],[363,173870,173872,173875],{"className":173871},[398],[363,173873],{"className":173874,"style":2692},[402],[363,173876,15747],{"className":173877},[407,408]," 的定义下，预测概率具有一个在解释上极有用的分解：",[363,173880,173882],{"className":173881,"translate":367},[528],[363,173883,173885,173999],{"className":173884,"translate":367},[366],[363,173886,173888],{"className":173887},[371],[373,173889,173890],{"xmlns":375,"display":537},[377,173891,173892,173996],{},[380,173893,173894,173900,173902,173927,173929,173944,173946,173948,173950,173952,173954,173956,173958,173984,173986,173988,173990],{},[543,173895,173896,173898],{},[383,173897,11],{},[383,173899,7911],{},[458,173901,471],{},[6363,173903,173904,173924],{},[6363,173905,173906,173922],{},[586,173907,173908,173920],{},[380,173909,173910,173916,173918],{},[543,173911,173912,173914],{},[383,173913,45101],{},[383,173915,7911],{},[458,173917,5160],{},[463,173919,465],{},[383,173921,26084],{},[458,173923,6387],{"stretchy":394},[1644,173925,173926],{},"证据部分",[458,173928,2817],{},[6363,173930,173931,173941],{},[6363,173932,173933,173939],{},[586,173934,173935,173937],{},[463,173936,465],{},[383,173938,26084],{},[458,173940,6387],{"stretchy":394},[1644,173942,173943],{},"先验部分",[458,173945,471],{},[458,173947,461],{"stretchy":460},[463,173949,465],{},[458,173951,5160],{},[383,173953,15747],{},[458,173955,468],{"stretchy":460},[1644,173957,1646],{},[586,173959,173960,173972],{},[380,173961,173962,173968,173970],{},[543,173963,173964,173966],{},[383,173965,45101],{},[383,173967,7911],{},[458,173969,5160],{},[463,173971,465],{},[380,173973,173974,173980,173982],{},[543,173975,173976,173978],{},[383,173977,45101],{},[463,173979,474],{},[458,173981,5160],{},[383,173983,11041],{},[458,173985,2817],{},[383,173987,15747],{},[458,173989,3646],{},[586,173991,173992,173994],{},[463,173993,465],{},[383,173995,11041],{},[387,173997,173998],{"encoding":389},"p_k = \\underbrace{\\frac{\\alpha_k - 1}{S}}_{\\text{证据部分}} + \\underbrace{\\frac{1}{S}}_{\\text{先验部分}} = (1 - u)\\,\\frac{\\alpha_k - 1}{\\alpha_0 - K} + u \\cdot \\frac{1}{K}",[363,174000,174002,174057,174295,174478,174499,174683,174702],{"className":174001,"ariaHidden":394},[393],[363,174003,174005,174008,174048,174051,174054],{"className":174004},[398],[363,174006],{"className":174007,"style":2623},[402],[363,174009,174011,174014],{"className":174010},[407],[363,174012,11],{"className":174013},[407,408],[363,174015,174017],{"className":174016},[629],[363,174018,174020,174040],{"className":174019},[633,634],[363,174021,174023,174037],{"className":174022},[638],[363,174024,174026],{"className":174025,"style":643},[642],[363,174027,174028,174031],{"style":730},[363,174029],{"className":174030,"style":651},[650],[363,174032,174034],{"className":174033},[655,656,657,658],[363,174035,7911],{"className":174036,"style":8614},[407,408,658],[363,174038,666],{"className":174039},[665],[363,174041,174043],{"className":174042},[638],[363,174044,174046],{"className":174045,"style":8315},[642],[363,174047],{},[363,174049],{"className":174050,"style":506},[505],[363,174052,471],{"className":174053},[510],[363,174055],{"className":174056,"style":506},[505],[363,174058,174060,174064,174286,174289,174292],{"className":174059},[398],[363,174061],{"className":174062,"style":174063},[402],"height:3.3338em;vertical-align:-2.0123em;",[363,174065,174067],{"className":174066},[758,6363],[363,174068,174070,174277],{"className":174069},[633,634],[363,174071,174073,174274],{"className":174072},[638],[363,174074,174076,174094],{"className":174075,"style":23236},[642],[363,174077,174079,174082],{"style":174078},"top:-1.3091em;",[363,174080],{"className":174081,"style":23013},[650],[363,174083,174085],{"className":174084},[655,656,657,658],[363,174086,174088],{"className":174087},[407,658],[363,174089,174091],{"className":174090},[407,4945,658],[363,174092,173926],{"className":174093},[407,4949,658],[363,174095,174097,174100],{"style":174096},"top:-3.3214em;",[363,174098],{"className":174099,"style":23013},[650],[363,174101,174103],{"className":174102},[758,6363],[363,174104,174106,174265],{"className":174105},[633,634],[363,174107,174109,174262],{"className":174108},[638],[363,174110,174112,174143],{"className":174111,"style":23236},[642],[363,174113,174116,174119],{"className":174114,"style":174115},[6654],"top:-1.9874em;",[363,174117],{"className":174118,"style":23013},[650],[363,174120,174122,174129,174136],{"className":174121,"style":6663},[6662],[363,174123,174125],{"className":174124,"style":6668},[6667],[6670,174126,174127],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6676},[6678,174128],{"d":6680},[363,174130,174132],{"className":174131,"style":6668},[6684],[6670,174133,174134],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6687},[6678,174135],{"d":6690},[363,174137,174139],{"className":174138,"style":6668},[6694],[6670,174140,174141],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6697},[6678,174142],{"d":6700},[363,174144,174145,174148],{"style":174096},[363,174146],{"className":174147,"style":23013},[650],[363,174149,174151],{"className":174150},[407],[363,174152,174154,174157,174259],{"className":174153},[407],[363,174155],{"className":174156},[494,789],[363,174158,174160],{"className":174159},[586],[363,174161,174163,174251],{"className":174162},[633,634],[363,174164,174166,174248],{"className":174165},[638],[363,174167,174169,174180,174188],{"className":174168,"style":23236},[642],[363,174170,174171,174174],{"style":805},[363,174172],{"className":174173,"style":809},[650],[363,174175,174177],{"className":174176},[407],[363,174178,26084],{"className":174179,"style":26208},[407,408],[363,174181,174182,174185],{"style":821},[363,174183],{"className":174184,"style":809},[650],[363,174186],{"className":174187,"style":829},[828],[363,174189,174190,174193],{"style":832},[363,174191],{"className":174192,"style":809},[650],[363,174194,174196,174236,174239,174242,174245],{"className":174195},[407],[363,174197,174199,174202],{"className":174198},[407],[363,174200,45101],{"className":174201,"style":45131},[407,408],[363,174203,174205],{"className":174204},[629],[363,174206,174208,174228],{"className":174207},[633,634],[363,174209,174211,174225],{"className":174210},[638],[363,174212,174214],{"className":174213,"style":643},[642],[363,174215,174216,174219],{"style":136107},[363,174217],{"className":174218,"style":651},[650],[363,174220,174222],{"className":174221},[655,656,657,658],[363,174223,7911],{"className":174224,"style":8614},[407,408,658],[363,174226,666],{"className":174227},[665],[363,174229,174231],{"className":174230},[638],[363,174232,174234],{"className":174233,"style":8315},[642],[363,174235],{},[363,174237],{"className":174238,"style":2934},[505],[363,174240,5160],{"className":174241},[2938],[363,174243],{"className":174244,"style":2934},[505],[363,174246,465],{"className":174247},[407],[363,174249,666],{"className":174250},[665],[363,174252,174254],{"className":174253},[638],[363,174255,174257],{"className":174256,"style":4125},[642],[363,174258],{},[363,174260],{"className":174261},[501,789],[363,174263,666],{"className":174264},[665],[363,174266,174268],{"className":174267},[638],[363,174269,174272],{"className":174270,"style":174271},[642],"height:1.334em;",[363,174273],{},[363,174275,666],{"className":174276},[665],[363,174278,174280],{"className":174279},[638],[363,174281,174284],{"className":174282,"style":174283},[642],"height:2.0123em;",[363,174285],{},[363,174287],{"className":174288,"style":2934},[505],[363,174290,2817],{"className":174291},[2938],[363,174293],{"className":174294,"style":2934},[505],[363,174296,174298,174301,174469,174472,174475],{"className":174297},[398],[363,174299],{"className":174300,"style":174063},[402],[363,174302,174304],{"className":174303},[758,6363],[363,174305,174307,174461],{"className":174306},[633,634],[363,174308,174310,174458],{"className":174309},[638],[363,174311,174313,174330],{"className":174312,"style":23236},[642],[363,174314,174315,174318],{"style":174078},[363,174316],{"className":174317,"style":23013},[650],[363,174319,174321],{"className":174320},[655,656,657,658],[363,174322,174324],{"className":174323},[407,658],[363,174325,174327],{"className":174326},[407,4945,658],[363,174328,173943],{"className":174329},[407,4949,658],[363,174331,174332,174335],{"style":174096},[363,174333],{"className":174334,"style":23013},[650],[363,174336,174338],{"className":174337},[758,6363],[363,174339,174341,174450],{"className":174340},[633,634],[363,174342,174344,174447],{"className":174343},[638],[363,174345,174347,174377],{"className":174346,"style":23236},[642],[363,174348,174350,174353],{"className":174349,"style":174115},[6654],[363,174351],{"className":174352,"style":23013},[650],[363,174354,174356,174363,174370],{"className":174355,"style":6663},[6662],[363,174357,174359],{"className":174358,"style":6668},[6667],[6670,174360,174361],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6676},[6678,174362],{"d":6680},[363,174364,174366],{"className":174365,"style":6668},[6684],[6670,174367,174368],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6687},[6678,174369],{"d":6690},[363,174371,174373],{"className":174372,"style":6668},[6694],[6670,174374,174375],{"xmlns":6672,"width":6673,"height":6674,"viewBox":6675,"preserveAspectRatio":6697},[6678,174376],{"d":6700},[363,174378,174379,174382],{"style":174096},[363,174380],{"className":174381,"style":23013},[650],[363,174383,174385],{"className":174384},[407],[363,174386,174388,174391,174444],{"className":174387},[407],[363,174389],{"className":174390},[494,789],[363,174392,174394],{"className":174393},[586],[363,174395,174397,174436],{"className":174396},[633,634],[363,174398,174400,174433],{"className":174399},[638],[363,174401,174403,174414,174422],{"className":174402,"style":23236},[642],[363,174404,174405,174408],{"style":805},[363,174406],{"className":174407,"style":809},[650],[363,174409,174411],{"className":174410},[407],[363,174412,26084],{"className":174413,"style":26208},[407,408],[363,174415,174416,174419],{"style":821},[363,174417],{"className":174418,"style":809},[650],[363,174420],{"className":174421,"style":829},[828],[363,174423,174424,174427],{"style":832},[363,174425],{"className":174426,"style":809},[650],[363,174428,174430],{"className":174429},[407],[363,174431,465],{"className":174432},[407],[363,174434,666],{"className":174435},[665],[363,174437,174439],{"className":174438},[638],[363,174440,174442],{"className":174441,"style":4125},[642],[363,174443],{},[363,174445],{"className":174446},[501,789],[363,174448,666],{"className":174449},[665],[363,174451,174453],{"className":174452},[638],[363,174454,174456],{"className":174455,"style":174271},[642],[363,174457],{},[363,174459,666],{"className":174460},[665],[363,174462,174464],{"className":174463},[638],[363,174465,174467],{"className":174466,"style":174283},[642],[363,174468],{},[363,174470],{"className":174471,"style":506},[505],[363,174473,471],{"className":174474},[510],[363,174476],{"className":174477,"style":506},[505],[363,174479,174481,174484,174487,174490,174493,174496],{"className":174480},[398],[363,174482],{"className":174483,"style":487},[402],[363,174485,461],{"className":174486},[494],[363,174488,465],{"className":174489},[407],[363,174491],{"className":174492,"style":2934},[505],[363,174494,5160],{"className":174495},[2938],[363,174497],{"className":174498,"style":2934},[505],[363,174500,174502,174505,174508,174511,174514,174674,174677,174680],{"className":174501},[398],[363,174503],{"className":174504,"style":151436},[402],[363,174506,15747],{"className":174507},[407,408],[363,174509,468],{"className":174510},[501],[363,174512],{"className":174513,"style":754},[505],[363,174515,174517,174520,174671],{"className":174516},[407],[363,174518],{"className":174519},[494,789],[363,174521,174523],{"className":174522},[586],[363,174524,174526,174663],{"className":174525},[633,634],[363,174527,174529,174660],{"className":174528},[638],[363,174530,174532,174592,174600],{"className":174531,"style":23236},[642],[363,174533,174534,174537],{"style":805},[363,174535],{"className":174536,"style":809},[650],[363,174538,174540,174580,174583,174586,174589],{"className":174539},[407],[363,174541,174543,174546],{"className":174542},[407],[363,174544,45101],{"className":174545,"style":45131},[407,408],[363,174547,174549],{"className":174548},[629],[363,174550,174552,174572],{"className":174551},[633,634],[363,174553,174555,174569],{"className":174554},[638],[363,174556,174558],{"className":174557,"style":11480},[642],[363,174559,174560,174563],{"style":136107},[363,174561],{"className":174562,"style":651},[650],[363,174564,174566],{"className":174565},[655,656,657,658],[363,174567,474],{"className":174568},[407,658],[363,174570,666],{"className":174571},[665],[363,174573,174575],{"className":174574},[638],[363,174576,174578],{"className":174577,"style":8315},[642],[363,174579],{},[363,174581],{"className":174582,"style":2934},[505],[363,174584,5160],{"className":174585},[2938],[363,174587],{"className":174588,"style":2934},[505],[363,174590,11041],{"className":174591,"style":11129},[407,408],[363,174593,174594,174597],{"style":821},[363,174595],{"className":174596,"style":809},[650],[363,174598],{"className":174599,"style":829},[828],[363,174601,174602,174605],{"style":832},[363,174603],{"className":174604,"style":809},[650],[363,174606,174608,174648,174651,174654,174657],{"className":174607},[407],[363,174609,174611,174614],{"className":174610},[407],[363,174612,45101],{"className":174613,"style":45131},[407,408],[363,174615,174617],{"className":174616},[629],[363,174618,174620,174640],{"className":174619},[633,634],[363,174621,174623,174637],{"className":174622},[638],[363,174624,174626],{"className":174625,"style":643},[642],[363,174627,174628,174631],{"style":136107},[363,174629],{"className":174630,"style":651},[650],[363,174632,174634],{"className":174633},[655,656,657,658],[363,174635,7911],{"className":174636,"style":8614},[407,408,658],[363,174638,666],{"className":174639},[665],[363,174641,174643],{"className":174642},[638],[363,174644,174646],{"className":174645,"style":8315},[642],[363,174647],{},[363,174649],{"className":174650,"style":2934},[505],[363,174652,5160],{"className":174653},[2938],[363,174655],{"className":174656,"style":2934},[505],[363,174658,465],{"className":174659},[407],[363,174661,666],{"className":174662},[665],[363,174664,174666],{"className":174665},[638],[363,174667,174669],{"className":174668,"style":125395},[642],[363,174670],{},[363,174672],{"className":174673},[501,789],[363,174675],{"className":174676,"style":2934},[505],[363,174678,2817],{"className":174679},[2938],[363,174681],{"className":174682,"style":2934},[505],[363,174684,174686,174690,174693,174696,174699],{"className":174685},[398],[363,174687],{"className":174688,"style":174689},[402],"height:0.4445em;",[363,174691,15747],{"className":174692},[407,408],[363,174694],{"className":174695,"style":2934},[505],[363,174697,3646],{"className":174698},[2938],[363,174700],{"className":174701,"style":2934},[505],[363,174703,174705,174708],{"className":174704},[398],[363,174706],{"className":174707,"style":26250},[402],[363,174709,174711,174714,174767],{"className":174710},[407],[363,174712],{"className":174713},[494,789],[363,174715,174717],{"className":174716},[586],[363,174718,174720,174759],{"className":174719},[633,634],[363,174721,174723,174756],{"className":174722},[638],[363,174724,174726,174737,174745],{"className":174725,"style":23236},[642],[363,174727,174728,174731],{"style":805},[363,174729],{"className":174730,"style":809},[650],[363,174732,174734],{"className":174733},[407],[363,174735,11041],{"className":174736,"style":11129},[407,408],[363,174738,174739,174742],{"style":821},[363,174740],{"className":174741,"style":809},[650],[363,174743],{"className":174744,"style":829},[828],[363,174746,174747,174750],{"style":832},[363,174748],{"className":174749,"style":809},[650],[363,174751,174753],{"className":174752},[407],[363,174754,465],{"className":174755},[407],[363,174757,666],{"className":174758},[665],[363,174760,174762],{"className":174761},[638],[363,174763,174765],{"className":174764,"style":4125},[642],[363,174766],{},[363,174768],{"className":174769},[501,789],[11,174771,87982,174772,174850,174851,174902,174903,174954],{},[1572,174773,174774,174775,174849],{},"预测概率是「证据归一化的类比例」与「均匀分布」按 ",[363,174776,174778,174804],{"className":174777,"translate":367},[366],[363,174779,174781],{"className":174780},[371],[373,174782,174783],{"xmlns":375},[377,174784,174785,174801],{},[380,174786,174787,174789,174791,174793,174795,174797,174799],{},[458,174788,461],{"stretchy":460},[463,174790,465],{},[458,174792,5160],{},[383,174794,15747],{},[458,174796,898],{"separator":394},[383,174798,15747],{},[458,174800,468],{"stretchy":460},[387,174802,174803],{"encoding":389},"(1-u, u)",[363,174805,174807,174828],{"className":174806,"ariaHidden":394},[393],[363,174808,174810,174813,174816,174819,174822,174825],{"className":174809},[398],[363,174811],{"className":174812,"style":487},[402],[363,174814,461],{"className":174815},[494],[363,174817,465],{"className":174818},[407],[363,174820],{"className":174821,"style":2934},[505],[363,174823,5160],{"className":174824},[2938],[363,174826],{"className":174827,"style":2934},[505],[363,174829,174831,174834,174837,174840,174843,174846],{"className":174830},[398],[363,174832],{"className":174833,"style":487},[402],[363,174835,15747],{"className":174836},[407,408],[363,174838,898],{"className":174839},[920],[363,174841],{"className":174842,"style":754},[505],[363,174844,15747],{"className":174845},[407,408],[363,174847,468],{"className":174848},[501]," 的凸组合","。当证据充分时（",[363,174852,174854,174872],{"className":174853,"translate":367},[366],[363,174855,174857],{"className":174856},[371],[373,174858,174859],{"xmlns":375},[377,174860,174861,174869],{},[380,174862,174863,174865,174867],{},[383,174864,15747],{},[458,174866,1376],{},[463,174868,474],{},[387,174870,174871],{"encoding":389},"u \\to 0",[363,174873,174875,174893],{"className":174874,"ariaHidden":394},[393],[363,174876,174878,174881,174884,174887,174890],{"className":174877},[398],[363,174879],{"className":174880,"style":2692},[402],[363,174882,15747],{"className":174883},[407,408],[363,174885],{"className":174886,"style":506},[505],[363,174888,1376],{"className":174889},[510],[363,174891],{"className":174892,"style":506},[505],[363,174894,174896,174899],{"className":174895},[398],[363,174897],{"className":174898,"style":520},[402],[363,174900,474],{"className":174901},[407],"），预测趋于证据的方向。当证据消失时（",[363,174904,174906,174924],{"className":174905,"translate":367},[366],[363,174907,174909],{"className":174908},[371],[373,174910,174911],{"xmlns":375},[377,174912,174913,174921],{},[380,174914,174915,174917,174919],{},[383,174916,15747],{},[458,174918,1376],{},[463,174920,465],{},[387,174922,174923],{"encoding":389},"u \\to 1",[363,174925,174927,174945],{"className":174926,"ariaHidden":394},[393],[363,174928,174930,174933,174936,174939,174942],{"className":174929},[398],[363,174931],{"className":174932,"style":2692},[402],[363,174934,15747],{"className":174935},[407,408],[363,174937],{"className":174938,"style":506},[505],[363,174940,1376],{"className":174941},[510],[363,174943],{"className":174944,"style":506},[505],[363,174946,174948,174951],{"className":174947},[398],[363,174949],{"className":174950,"style":520},[402],[363,174952,465],{"className":174953},[407],"），预测退回均匀分布。极限行为因此完全符合直觉：",[363,174956,174958],{"className":174957,"translate":367},[528],[363,174959,174961,175066],{"className":174960,"translate":367},[366],[363,174962,174964],{"className":174963},[371],[373,174965,174966],{"xmlns":375,"display":537},[377,174967,174968,175063],{},[380,174969,174970,174972,174974,174976,174978,174980,174982,174984,174986,174988,174990,174992,174994,174996,174998,175000,175003,175005,175007,175015,175017,175019,175021,175023,175025,175027,175029,175031,175033,175035,175037,175039,175041,175043,175045],{},[383,174971,26084],{},[458,174973,1376],{},[383,174975,11041],{},[1644,174977,4630],{},[458,174979,461],{"stretchy":460},[383,174981,7914],{"mathvariant":75560},[458,174983,1376],{},[463,174985,474],{"mathvariant":75560},[458,174987,468],{"stretchy":460},[458,174989,1362],{},[505,174991],{"width":4662},[383,174993,15747],{},[458,174995,1376],{},[463,174997,465],{},[458,174999,898],{"separator":394},[1644,175001,175002],{},"  ",[383,175004,11],{"mathvariant":75560},[458,175006,1376],{},[1602,175008,175009],{"scriptlevel":474,"displaystyle":460},[586,175010,175011,175013],{},[463,175012,465],{},[383,175014,11041],{},[463,175016,465],{"mathvariant":75560},[505,175018],{"width":3609},[505,175020],{"width":3609},[383,175022,26084],{},[458,175024,1376],{},[383,175026,1371],{"mathvariant":557},[458,175028,1362],{},[505,175030],{"width":4662},[383,175032,15747],{},[458,175034,1376],{},[463,175036,474],{},[458,175038,898],{"separator":394},[1644,175040,175002],{},[383,175042,11],{"mathvariant":75560},[458,175044,1376],{},[586,175046,175047,175049],{},[383,175048,7914],{"mathvariant":75560},[380,175050,175051,175057],{},[6363,175052,175053,175055],{},[458,175054,13808],{},[383,175056,100360],{},[543,175058,175059,175061],{},[383,175060,7914],{},[383,175062,100360],{},[387,175064,175065],{"encoding":389},"S \\to K \\ (\\mathbf{e} \\to \\mathbf{0}): \\quad u \\to 1,\\ \\ \\mathbf{p} \\to \\tfrac{1}{K}\\mathbf{1}\n\\qquad\\qquad\nS \\to \\infty: \\quad u \\to 0,\\ \\ \\mathbf{p} \\to \\frac{\\mathbf{e}}{\\sum_j e_j}",[363,175067,175069,175087,175114,175138,175156,175189,175284,175305,175323,175356],{"className":175068,"ariaHidden":394},[393],[363,175070,175072,175075,175078,175081,175084],{"className":175071},[398],[363,175073],{"className":175074,"style":1011},[402],[363,175076,26084],{"className":175077,"style":26208},[407,408],[363,175079],{"className":175080,"style":506},[505],[363,175082,1376],{"className":175083},[510],[363,175085],{"className":175086,"style":506},[505],[363,175088,175090,175093,175096,175099,175102,175105,175108,175111],{"className":175089},[398],[363,175091],{"className":175092,"style":487},[402],[363,175094,11041],{"className":175095,"style":11129},[407,408],[363,175097,4630],{"className":175098},[505],[363,175100,461],{"className":175101},[494],[363,175103,7914],{"className":175104},[407,75905],[363,175106],{"className":175107,"style":506},[505],[363,175109,1376],{"className":175110},[510],[363,175112],{"className":175113,"style":506},[505],[363,175115,175117,175120,175123,175126,175129,175132,175135],{"className":175116},[398],[363,175118],{"className":175119,"style":487},[402],[363,175121,474],{"className":175122},[407,75905],[363,175124,468],{"className":175125},[501],[363,175127],{"className":175128,"style":506},[505],[363,175130,1362],{"className":175131},[510],[363,175133],{"className":175134,"style":88315},[505],[363,175136],{"className":175137,"style":506},[505],[363,175139,175141,175144,175147,175150,175153],{"className":175140},[398],[363,175142],{"className":175143,"style":2692},[402],[363,175145,15747],{"className":175146},[407,408],[363,175148],{"className":175149,"style":506},[505],[363,175151,1376],{"className":175152},[510],[363,175154],{"className":175155,"style":506},[505],[363,175157,175159,175162,175165,175168,175171,175174,175177,175180,175183,175186],{"className":175158},[398],[363,175160],{"className":175161,"style":9705},[402],[363,175163,465],{"className":175164},[407],[363,175166,898],{"className":175167},[920],[363,175169,4630],{"className":175170},[505],[363,175172,4630],{"className":175173},[505],[363,175175],{"className":175176,"style":754},[505],[363,175178,11],{"className":175179},[407,75905],[363,175181],{"className":175182,"style":506},[505],[363,175184,1376],{"className":175185},[510],[363,175187],{"className":175188,"style":506},[505],[363,175190,175192,175195,175263,175266,175269,175272,175275,175278,175281],{"className":175191},[398],[363,175193],{"className":175194,"style":2852},[402],[363,175196,175198,175201,175260],{"className":175197},[407],[363,175199],{"className":175200},[494,789],[363,175202,175204],{"className":175203},[586],[363,175205,175207,175252],{"className":175206},[633,634],[363,175208,175210,175249],{"className":175209},[638],[363,175211,175213,175227,175235],{"className":175212,"style":2871},[642],[363,175214,175215,175218],{"style":2874},[363,175216],{"className":175217,"style":809},[650],[363,175219,175221],{"className":175220},[655,656,657,658],[363,175222,175224],{"className":175223},[407,658],[363,175225,11041],{"className":175226,"style":11129},[407,408,658],[363,175228,175229,175232],{"style":821},[363,175230],{"className":175231,"style":809},[650],[363,175233],{"className":175234,"style":829},[828],[363,175236,175237,175240],{"style":2897},[363,175238],{"className":175239,"style":809},[650],[363,175241,175243],{"className":175242},[655,656,657,658],[363,175244,175246],{"className":175245},[407,658],[363,175247,465],{"className":175248},[407,658],[363,175250,666],{"className":175251},[665],[363,175253,175255],{"className":175254},[638],[363,175256,175258],{"className":175257,"style":2919},[642],[363,175259],{},[363,175261],{"className":175262},[501,789],[363,175264,465],{"className":175265},[407,75905],[363,175267],{"className":175268,"style":3981},[505],[363,175270],{"className":175271,"style":3981},[505],[363,175273,26084],{"className":175274,"style":26208},[407,408],[363,175276],{"className":175277,"style":506},[505],[363,175279,1376],{"className":175280},[510],[363,175282],{"className":175283,"style":506},[505],[363,175285,175287,175290,175293,175296,175299,175302],{"className":175286},[398],[363,175288],{"className":175289,"style":2692},[402],[363,175291,1371],{"className":175292},[407],[363,175294],{"className":175295,"style":506},[505],[363,175297,1362],{"className":175298},[510],[363,175300],{"className":175301,"style":88315},[505],[363,175303],{"className":175304,"style":506},[505],[363,175306,175308,175311,175314,175317,175320],{"className":175307},[398],[363,175309],{"className":175310,"style":2692},[402],[363,175312,15747],{"className":175313},[407,408],[363,175315],{"className":175316,"style":506},[505],[363,175318,1376],{"className":175319},[510],[363,175321],{"className":175322,"style":506},[505],[363,175324,175326,175329,175332,175335,175338,175341,175344,175347,175350,175353],{"className":175325},[398],[363,175327],{"className":175328,"style":9705},[402],[363,175330,474],{"className":175331},[407],[363,175333,898],{"className":175334},[920],[363,175336,4630],{"className":175337},[505],[363,175339,4630],{"className":175340},[505],[363,175342],{"className":175343,"style":754},[505],[363,175345,11],{"className":175346},[407,75905],[363,175348],{"className":175349,"style":506},[505],[363,175351,1376],{"className":175352},[510],[363,175354],{"className":175355,"style":506},[505],[363,175357,175359,175363],{"className":175358},[398],[363,175360],{"className":175361,"style":175362},[402],"height:2.2433em;vertical-align:-1.1218em;",[363,175364,175366,175369,175504],{"className":175365},[407],[363,175367],{"className":175368},[494,789],[363,175370,175372],{"className":175371},[586],[363,175373,175375,175495],{"className":175374},[633,634],[363,175376,175378,175492],{"className":175377},[638],[363,175379,175382,175473,175481],{"className":175380,"style":175381},[642],"height:1.1214em;",[363,175383,175384,175387],{"style":805},[363,175385],{"className":175386,"style":809},[650],[363,175388,175390,175430,175433],{"className":175389},[407],[363,175391,175393,175396],{"className":175392},[1831],[363,175394,13808],{"className":175395,"style":40007},[1831,1832,5963],[363,175397,175399],{"className":175398},[629],[363,175400,175402,175422],{"className":175401},[633,634],[363,175403,175405,175419],{"className":175404},[638],[363,175406,175408],{"className":175407,"style":40020},[642],[363,175409,175410,175413],{"style":40023},[363,175411],{"className":175412,"style":651},[650],[363,175414,175416],{"className":175415},[655,656,657,658],[363,175417,100360],{"className":175418,"style":100888},[407,408,658],[363,175420,666],{"className":175421},[665],[363,175423,175425],{"className":175424},[638],[363,175426,175428],{"className":175427,"style":162729},[642],[363,175429],{},[363,175431],{"className":175432,"style":754},[505],[363,175434,175436,175439],{"className":175435},[407],[363,175437,7914],{"className":175438},[407,408],[363,175440,175442],{"className":175441},[629],[363,175443,175445,175465],{"className":175444},[633,634],[363,175446,175448,175462],{"className":175447},[638],[363,175449,175451],{"className":175450,"style":12529},[642],[363,175452,175453,175456],{"style":730},[363,175454],{"className":175455,"style":651},[650],[363,175457,175459],{"className":175458},[655,656,657,658],[363,175460,100360],{"className":175461,"style":100888},[407,408,658],[363,175463,666],{"className":175464},[665],[363,175466,175468],{"className":175467},[638],[363,175469,175471],{"className":175470,"style":673},[642],[363,175472],{},[363,175474,175475,175478],{"style":821},[363,175476],{"className":175477,"style":809},[650],[363,175479],{"className":175480,"style":829},[828],[363,175482,175483,175486],{"style":832},[363,175484],{"className":175485,"style":809},[650],[363,175487,175489],{"className":175488},[407],[363,175490,7914],{"className":175491},[407,75905],[363,175493,666],{"className":175494},[665],[363,175496,175498],{"className":175497},[638],[363,175499,175502],{"className":175500,"style":175501},[642],"height:1.1218em;",[363,175503],{},[363,175505],{"className":175506},[501,789],[11,175508,175509,175510,9747,175513,175541,175542,175570,175571,175574],{},"命题 3.4 同时也暴露了该参数化的一个",[1572,175511,175512],{},"结构性局限",[363,175514,175516,175529],{"className":175515,"translate":367},[366],[363,175517,175519],{"className":175518},[371],[373,175520,175521],{"xmlns":375},[377,175522,175523,175527],{},[380,175524,175525],{},[383,175526,15747],{},[387,175528,15747],{"encoding":389},[363,175530,175532],{"className":175531,"ariaHidden":394},[393],[363,175533,175535,175538],{"className":175534},[398],[363,175536],{"className":175537,"style":2692},[402],[363,175539,15747],{"className":175540},[407,408]," 只是总强度 ",[363,175543,175545,175558],{"className":175544,"translate":367},[366],[363,175546,175548],{"className":175547},[371],[373,175549,175550],{"xmlns":375},[377,175551,175552,175556],{},[380,175553,175554],{},[383,175555,26084],{},[387,175557,26084],{"encoding":389},[363,175559,175561],{"className":175560,"ariaHidden":394},[393],[363,175562,175564,175567],{"className":175563},[398],[363,175565],{"className":175566,"style":1011},[402],[363,175568,26084],{"className":175569,"style":26208},[407,408]," 的函数，与证据在各类别之间的",[1572,175572,175573],{},"分布","无关。因此 EDL 的不确定性分数无法区分「少量证据集中于一类」与「大量证据均匀分散」，也无法区分「证据落在正确类别上」与「证据落在错误类别上」。这一局限将在 4.5 节与 5.6 节被重新讨论。",[2658,175576,175578],{"id":175577},"_36-不确定性的分解偶然与认知","3.6 不确定性的分解：偶然与认知",[11,175580,175581,175582,175643,175644,175647],{},"命题 3.4 给出的 ",[363,175583,175585,175607],{"className":175584,"translate":367},[366],[363,175586,175588],{"className":175587},[371],[373,175589,175590],{"xmlns":375},[377,175591,175592,175604],{},[380,175593,175594,175596,175598,175600,175602],{},[383,175595,15747],{},[458,175597,471],{},[383,175599,11041],{},[383,175601,1288],{"mathvariant":557},[383,175603,26084],{},[387,175605,175606],{"encoding":389},"u = K\u002FS",[363,175608,175610,175628],{"className":175609,"ariaHidden":394},[393],[363,175611,175613,175616,175619,175622,175625],{"className":175612},[398],[363,175614],{"className":175615,"style":2692},[402],[363,175617,15747],{"className":175618},[407,408],[363,175620],{"className":175621,"style":506},[505],[363,175623,471],{"className":175624},[510],[363,175626],{"className":175627,"style":506},[505],[363,175629,175631,175634,175637,175640],{"className":175630},[398],[363,175632],{"className":175633,"style":487},[402],[363,175635,11041],{"className":175636,"style":11129},[407,408],[363,175638,1288],{"className":175639},[407],[363,175641,26084],{"className":175642,"style":26208},[407,408]," 是一个",[1572,175645,175646],{},"启发式","的不确定性标量。与之相对，Malinin 与 Gales 在 Prior Networks 的工作中给出了一个有信息论根据的分解，它在迪利克雷族内具有闭式解。",[11,175649,881,175650,7147,175732,175838],{},[363,175651,175653,175678],{"className":175652,"translate":367},[366],[363,175654,175656],{"className":175655},[371],[373,175657,175658],{"xmlns":375},[377,175659,175660,175676],{},[380,175661,175662,175664,175666,175668,175670,175672,175674],{},[383,175663,157399],{"mathvariant":136008},[458,175665,9216],{},[383,175667,137065],{"mathvariant":557},[458,175669,4450],{},[458,175671,461],{"stretchy":460},[383,175673,45101],{"mathvariant":136008},[458,175675,468],{"stretchy":460},[387,175677,157414],{"encoding":389},[363,175679,175681,175705],{"className":175680,"ariaHidden":394},[393],[363,175682,175684,175687,175696,175699,175702],{"className":175683},[398],[363,175685],{"className":175686,"style":135617},[402],[363,175688,175690],{"className":175689},[407],[363,175691,175693],{"className":175692},[407],[363,175694,157399],{"className":175695,"style":157433},[407,136068],[363,175697],{"className":175698,"style":506},[505],[363,175700,9216],{"className":175701},[510],[363,175703],{"className":175704,"style":506},[505],[363,175706,175708,175711,175717,175720,175729],{"className":175707},[398],[363,175709],{"className":175710,"style":487},[402],[363,175712,175714],{"className":175713},[1831],[363,175715,137065],{"className":175716},[407,33009],[363,175718,461],{"className":175719},[494],[363,175721,175723],{"className":175722},[407],[363,175724,175726],{"className":175725},[407],[363,175727,45101],{"className":175728},[407,136068],[363,175730,468],{"className":175731},[501],[363,175733,175735,175766],{"className":175734,"translate":367},[366],[363,175736,175738],{"className":175737},[371],[373,175739,175740],{"xmlns":375},[377,175741,175742,175763],{},[380,175743,175744,175746,175748,175750,175752,175755,175757,175759,175761],{},[383,175745,40584],{},[458,175747,5155],{},[383,175749,157399],{"mathvariant":136008},[458,175751,9216],{},[383,175753,175754],{"mathvariant":557},"Cat",[458,175756,4450],{},[458,175758,461],{"stretchy":460},[383,175760,157399],{"mathvariant":136008},[458,175762,468],{"stretchy":460},[387,175764,175765],{"encoding":389},"y \\mid \\boldsymbol{\\pi} \\sim \\operatorname{Cat}(\\boldsymbol{\\pi})",[363,175767,175769,175787,175811],{"className":175768,"ariaHidden":394},[393],[363,175770,175772,175775,175778,175781,175784],{"className":175771},[398],[363,175773],{"className":175774,"style":487},[402],[363,175776,40584],{"className":175777,"style":1328},[407,408],[363,175779],{"className":175780,"style":506},[505],[363,175782,5155],{"className":175783},[510],[363,175785],{"className":175786,"style":506},[505],[363,175788,175790,175793,175802,175805,175808],{"className":175789},[398],[363,175791],{"className":175792,"style":135617},[402],[363,175794,175796],{"className":175795},[407],[363,175797,175799],{"className":175798},[407],[363,175800,157399],{"className":175801,"style":157433},[407,136068],[363,175803],{"className":175804,"style":506},[505],[363,175806,9216],{"className":175807},[510],[363,175809],{"className":175810,"style":506},[505],[363,175812,175814,175817,175823,175826,175835],{"className":175813},[398],[363,175815],{"className":175816,"style":487},[402],[363,175818,175820],{"className":175819},[1831],[363,175821,175754],{"className":175822},[407,33009],[363,175824,461],{"className":175825},[494],[363,175827,175829],{"className":175828},[407],[363,175830,175832],{"className":175831},[407],[363,175833,157399],{"className":175834,"style":157433},[407,136068],[363,175836,468],{"className":175837},[501],"。考虑三个量：",[7009,175840,175841,176190,176343],{},[7012,175842,175843,175846,175847,87128,175925,10527],{},[1572,175844,175845],{},"总不确定性（total uncertainty）","：预测分布的熵 ",[363,175848,175850,175880],{"className":175849,"translate":367},[366],[363,175851,175853],{"className":175852},[371],[373,175854,175855],{"xmlns":375},[377,175856,175857,175877],{},[380,175858,175859,175861,175863,175865,175867,175869,175871,175873,175875],{},[383,175860,34231],{},[458,175862,578],{"stretchy":460},[383,175864,554],{"mathvariant":570},[458,175866,461],{"stretchy":460},[383,175868,40584],{},[458,175870,5155],{},[383,175872,1121],{"mathvariant":75560},[458,175874,468],{"stretchy":460},[458,175876,605],{"stretchy":460},[387,175878,175879],{"encoding":389},"H[\\mathbb{P}(y \\mid \\mathbf{x})]",[363,175881,175883,175913],{"className":175882,"ariaHidden":394},[393],[363,175884,175886,175889,175892,175895,175898,175901,175904,175907,175910],{"className":175885},[398],[363,175887],{"className":175888,"style":487},[402],[363,175890,34231],{"className":175891,"style":34385},[407,408],[363,175893,578],{"className":175894},[494],[363,175896,554],{"className":175897},[407,714],[363,175899,461],{"className":175900},[494],[363,175902,40584],{"className":175903,"style":1328},[407,408],[363,175905],{"className":175906,"style":506},[505],[363,175908,5155],{"className":175909},[510],[363,175911],{"className":175912,"style":506},[505],[363,175914,175916,175919,175922],{"className":175915},[398],[363,175917],{"className":175918,"style":487},[402],[363,175920,1121],{"className":175921},[407,75905],[363,175923,20737],{"className":175924},[501],[363,175926,175928,175980],{"className":175927,"translate":367},[366],[363,175929,175931],{"className":175930},[371],[373,175932,175933],{"xmlns":375},[377,175934,175935,175977],{},[380,175936,175937,175939,175941,175943,175945,175947,175949,175951,175953,175955,175961,175963,175969,175971],{},[383,175938,554],{"mathvariant":570},[458,175940,461],{"stretchy":460},[383,175942,40584],{},[458,175944,471],{},[383,175946,7911],{},[458,175948,5155],{},[383,175950,1121],{"mathvariant":75560},[458,175952,468],{"stretchy":460},[458,175954,471],{},[543,175956,175957,175959],{},[383,175958,11],{},[383,175960,7911],{},[458,175962,471],{},[543,175964,175965,175967],{},[383,175966,45101],{},[383,175968,7911],{},[383,175970,1288],{"mathvariant":557},[543,175972,175973,175975],{},[383,175974,45101],{},[463,175976,474],{},[387,175978,175979],{"encoding":389},"\\mathbb{P}(y = k \\mid \\mathbf{x}) = p_k = \\alpha_k\u002F\\alpha_0",[363,175981,175983,176007,176025,176046,176101],{"className":175982,"ariaHidden":394},[393],[363,175984,175986,175989,175992,175995,175998,176001,176004],{"className":175985},[398],[363,175987],{"className":175988,"style":487},[402],[363,175990,554],{"className":175991},[407,714],[363,175993,461],{"className":175994},[494],[363,175996,40584],{"className":175997,"style":1328},[407,408],[363,175999],{"className":176000,"style":506},[505],[363,176002,471],{"className":176003},[510],[363,176005],{"className":176006,"style":506},[505],[363,176008,176010,176013,176016,176019,176022],{"className":176009},[398],[363,176011],{"className":176012,"style":487},[402],[363,176014,7911],{"className":176015,"style":8614},[407,408],[363,176017],{"className":176018,"style":506},[505],[363,176020,5155],{"className":176021},[510],[363,176023],{"className":176024,"style":506},[505],[363,176026,176028,176031,176034,176037,176040,176043],{"className":176027},[398],[363,176029],{"className":176030,"style":487},[402],[363,176032,1121],{"className":176033},[407,75905],[363,176035,468],{"className":176036},[501],[363,176038],{"className":176039,"style":506},[505],[363,176041,471],{"className":176042},[510],[363,176044],{"className":176045,"style":506},[505],[363,176047,176049,176052,176092,176095,176098],{"className":176048},[398],[363,176050],{"className":176051,"style":2623},[402],[363,176053,176055,176058],{"className":176054},[407],[363,176056,11],{"className":176057},[407,408],[363,176059,176061],{"className":176060},[629],[363,176062,176064,176084],{"className":176063},[633,634],[363,176065,176067,176081],{"className":176066},[638],[363,176068,176070],{"className":176069,"style":643},[642],[363,176071,176072,176075],{"style":730},[363,176073],{"className":176074,"style":651},[650],[363,176076,176078],{"className":176077},[655,656,657,658],[363,176079,7911],{"className":176080,"style":8614},[407,408,658],[363,176082,666],{"className":176083},[665],[363,176085,176087],{"className":176086},[638],[363,176088,176090],{"className":176089,"style":8315},[642],[363,176091],{},[363,176093],{"className":176094,"style":506},[505],[363,176096,471],{"className":176097},[510],[363,176099],{"className":176100,"style":506},[505],[363,176102,176104,176107,176147,176150],{"className":176103},[398],[363,176105],{"className":176106,"style":487},[402],[363,176108,176110,176113],{"className":176109},[407],[363,176111,45101],{"className":176112,"style":45131},[407,408],[363,176114,176116],{"className":176115},[629],[363,176117,176119,176139],{"className":176118},[633,634],[363,176120,176122,176136],{"className":176121},[638],[363,176123,176125],{"className":176124,"style":643},[642],[363,176126,176127,176130],{"style":136107},[363,176128],{"className":176129,"style":651},[650],[363,176131,176133],{"className":176132},[655,656,657,658],[363,176134,7911],{"className":176135,"style":8614},[407,408,658],[363,176137,666],{"className":176138},[665],[363,176140,176142],{"className":176141},[638],[363,176143,176145],{"className":176144,"style":8315},[642],[363,176146],{},[363,176148,1288],{"className":176149},[407],[363,176151,176153,176156],{"className":176152},[407],[363,176154,45101],{"className":176155,"style":45131},[407,408],[363,176157,176159],{"className":176158},[629],[363,176160,176162,176182],{"className":176161},[633,634],[363,176163,176165,176179],{"className":176164},[638],[363,176166,176168],{"className":176167,"style":11480},[642],[363,176169,176170,176173],{"style":136107},[363,176171],{"className":176172,"style":651},[650],[363,176174,176176],{"className":176175},[655,656,657,658],[363,176177,474],{"className":176178},[407,658],[363,176180,666],{"className":176181},[665],[363,176183,176185],{"className":176184},[638],[363,176186,176188],{"className":176187,"style":8315},[642],[363,176189],{},[7012,176191,176192,176195,176196,176230,176231,10527],{},[1572,176193,176194],{},"偶然不确定性（aleatoric uncertainty）","：给定 ",[363,176197,176199,176212],{"className":176198,"translate":367},[366],[363,176200,176202],{"className":176201},[371],[373,176203,176204],{"xmlns":375},[377,176205,176206,176210],{},[380,176207,176208],{},[383,176209,157399],{"mathvariant":136008},[387,176211,157487],{"encoding":389},[363,176213,176215],{"className":176214,"ariaHidden":394},[393],[363,176216,176218,176221],{"className":176217},[398],[363,176219],{"className":176220,"style":135617},[402],[363,176222,176224],{"className":176223},[407],[363,176225,176227],{"className":176226},[407],[363,176228,157399],{"className":176229,"style":157433},[407,136068]," 后仍存在的熵的期望 ",[363,176232,176234,176264],{"className":176233,"translate":367},[366],[363,176235,176237],{"className":176236},[371],[373,176238,176239],{"xmlns":375},[377,176240,176241,176261],{},[380,176242,176243,176249,176251,176253,176255,176257,176259],{},[543,176244,176245,176247],{},[383,176246,571],{"mathvariant":570},[383,176248,157399],{"mathvariant":136008},[458,176250,578],{"stretchy":460},[383,176252,34231],{},[458,176254,461],{"stretchy":460},[383,176256,157399],{"mathvariant":136008},[458,176258,468],{"stretchy":460},[458,176260,605],{"stretchy":460},[387,176262,176263],{"encoding":389},"\\mathbb{E}_{\\boldsymbol{\\pi}}[H(\\boldsymbol{\\pi})]",[363,176265,176267],{"className":176266,"ariaHidden":394},[393],[363,176268,176270,176273,176322,176325,176328,176331,176340],{"className":176269},[398],[363,176271],{"className":176272,"style":487},[402],[363,176274,176276,176279],{"className":176275},[407],[363,176277,571],{"className":176278},[407,714],[363,176280,176282],{"className":176281},[629],[363,176283,176285,176314],{"className":176284},[633,634],[363,176286,176288,176311],{"className":176287},[638],[363,176289,176291],{"className":176290,"style":153717},[642],[363,176292,176293,176296],{"style":730},[363,176294],{"className":176295,"style":651},[650],[363,176297,176299],{"className":176298},[655,656,657,658],[363,176300,176302],{"className":176301},[407,658],[363,176303,176305],{"className":176304},[407,658],[363,176306,176308],{"className":176307},[407,658],[363,176309,157399],{"className":176310,"style":157433},[407,136068,658],[363,176312,666],{"className":176313},[665],[363,176315,176317],{"className":176316},[638],[363,176318,176320],{"className":176319,"style":8315},[642],[363,176321],{},[363,176323,578],{"className":176324},[494],[363,176326,34231],{"className":176327,"style":34385},[407,408],[363,176329,461],{"className":176330},[494],[363,176332,176334],{"className":176333},[407],[363,176335,176337],{"className":176336},[407],[363,176338,157399],{"className":176339,"style":157433},[407,136068],[363,176341,20737],{"className":176342},[501],[7012,176344,176345,176348,176349,2756,176377,176411],{},[1572,176346,176347],{},"认知不确定性（epistemic uncertainty）","：二者的差，即 ",[363,176350,176352,176365],{"className":176351,"translate":367},[366],[363,176353,176355],{"className":176354},[371],[373,176356,176357],{"xmlns":375},[377,176358,176359,176363],{},[380,176360,176361],{},[383,176362,40584],{},[387,176364,40584],{"encoding":389},[363,176366,176368],{"className":176367,"ariaHidden":394},[393],[363,176369,176371,176374],{"className":176370},[398],[363,176372],{"className":176373,"style":2623},[402],[363,176375,40584],{"className":176376,"style":1328},[407,408],[363,176378,176380,176393],{"className":176379,"translate":367},[366],[363,176381,176383],{"className":176382},[371],[373,176384,176385],{"xmlns":375},[377,176386,176387,176391],{},[380,176388,176389],{},[383,176390,157399],{"mathvariant":136008},[387,176392,157487],{"encoding":389},[363,176394,176396],{"className":176395,"ariaHidden":394},[393],[363,176397,176399,176402],{"className":176398},[398],[363,176400],{"className":176401,"style":135617},[402],[363,176403,176405],{"className":176404},[407],[363,176406,176408],{"className":176407},[407],[363,176409,157399],{"className":176410,"style":157433},[407,136068]," 之间的互信息。",[1340,176413,176415],{"title":176414},"命题 3.5（Dirichlet 族内的不确定性分解）",[11,176416,82412,176417,3092,176601,173274,176693,176980,177379],{},[363,176418,176420,176454],{"className":176419,"translate":367},[366],[363,176421,176423],{"className":176422},[371],[373,176424,176425],{"xmlns":375},[377,176426,176427,176451],{},[380,176428,176429,176435,176437,176443,176445],{},[543,176430,176431,176433],{},[383,176432,11],{},[383,176434,7911],{},[458,176436,471],{},[543,176438,176439,176441],{},[383,176440,45101],{},[383,176442,7911],{},[383,176444,1288],{"mathvariant":557},[543,176446,176447,176449],{},[383,176448,45101],{},[463,176450,474],{},[387,176452,176453],{"encoding":389},"p_k = \\alpha_k\u002F\\alpha_0",[363,176455,176457,176512],{"className":176456,"ariaHidden":394},[393],[363,176458,176460,176463,176503,176506,176509],{"className":176459},[398],[363,176461],{"className":176462,"style":2623},[402],[363,176464,176466,176469],{"className":176465},[407],[363,176467,11],{"className":176468},[407,408],[363,176470,176472],{"className":176471},[629],[363,176473,176475,176495],{"className":176474},[633,634],[363,176476,176478,176492],{"className":176477},[638],[363,176479,176481],{"className":176480,"style":643},[642],[363,176482,176483,176486],{"style":730},[363,176484],{"className":176485,"style":651},[650],[363,176487,176489],{"className":176488},[655,656,657,658],[363,176490,7911],{"className":176491,"style":8614},[407,408,658],[363,176493,666],{"className":176494},[665],[363,176496,176498],{"className":176497},[638],[363,176499,176501],{"className":176500,"style":8315},[642],[363,176502],{},[363,176504],{"className":176505,"style":506},[505],[363,176507,471],{"className":176508},[510],[363,176510],{"className":176511,"style":506},[505],[363,176513,176515,176518,176558,176561],{"className":176514},[398],[363,176516],{"className":176517,"style":487},[402],[363,176519,176521,176524],{"className":176520},[407],[363,176522,45101],{"className":176523,"style":45131},[407,408],[363,176525,176527],{"className":176526},[629],[363,176528,176530,176550],{"className":176529},[633,634],[363,176531,176533,176547],{"className":176532},[638],[363,176534,176536],{"className":176535,"style":643},[642],[363,176537,176538,176541],{"style":136107},[363,176539],{"className":176540,"style":651},[650],[363,176542,176544],{"className":176543},[655,656,657,658],[363,176545,7911],{"className":176546,"style":8614},[407,408,658],[363,176548,666],{"className":176549},[665],[363,176551,176553],{"className":176552},[638],[363,176554,176556],{"className":176555,"style":8315},[642],[363,176557],{},[363,176559,1288],{"className":176560},[407],[363,176562,176564,176567],{"className":176563},[407],[363,176565,45101],{"className":176566,"style":45131},[407,408],[363,176568,176570],{"className":176569},[629],[363,176571,176573,176593],{"className":176572},[633,634],[363,176574,176576,176590],{"className":176575},[638],[363,176577,176579],{"className":176578,"style":11480},[642],[363,176580,176581,176584],{"style":136107},[363,176582],{"className":176583,"style":651},[650],[363,176585,176587],{"className":176586},[655,656,657,658],[363,176588,474],{"className":176589},[407,658],[363,176591,666],{"className":176592},[665],[363,176594,176596],{"className":176595},[638],[363,176597,176599],{"className":176598,"style":8315},[642],[363,176600],{},[363,176602,176604,176626],{"className":176603,"translate":367},[366],[363,176605,176607],{"className":176606},[371],[373,176608,176609],{"xmlns":375},[377,176610,176611,176623],{},[380,176612,176613,176615,176617],{},[383,176614,26084],{},[458,176616,471],{},[543,176618,176619,176621],{},[383,176620,45101],{},[463,176622,474],{},[387,176624,176625],{"encoding":389},"S = \\alpha_0",[363,176627,176629,176647],{"className":176628,"ariaHidden":394},[393],[363,176630,176632,176635,176638,176641,176644],{"className":176631},[398],[363,176633],{"className":176634,"style":1011},[402],[363,176636,26084],{"className":176637,"style":26208},[407,408],[363,176639],{"className":176640,"style":506},[505],[363,176642,471],{"className":176643},[510],[363,176645],{"className":176646,"style":506},[505],[363,176648,176650,176653],{"className":176649},[398],[363,176651],{"className":176652,"style":13721},[402],[363,176654,176656,176659],{"className":176655},[407],[363,176657,45101],{"className":176658,"style":45131},[407,408],[363,176660,176662],{"className":176661},[629],[363,176663,176665,176685],{"className":176664},[633,634],[363,176666,176668,176682],{"className":176667},[638],[363,176669,176671],{"className":176670,"style":11480},[642],[363,176672,176673,176676],{"style":136107},[363,176674],{"className":176675,"style":651},[650],[363,176677,176679],{"className":176678},[655,656,657,658],[363,176680,474],{"className":176681},[407,658],[363,176683,666],{"className":176684},[665],[363,176686,176688],{"className":176687},[638],[363,176689,176691],{"className":176690,"style":8315},[642],[363,176692],{},[363,176694,176696,176760],{"className":176695,"translate":367},[366],[363,176697,176699],{"className":176698},[371],[373,176700,176701],{"xmlns":375},[377,176702,176703,176757],{},[380,176704,176705,176707,176709,176711,176713,176715,176717,176719,176721,176723,176725,176727,176741,176747,176749,176751],{},[383,176706,34231],{},[458,176708,578],{"stretchy":460},[383,176710,554],{"mathvariant":570},[458,176712,461],{"stretchy":460},[383,176714,40584],{},[458,176716,5155],{},[383,176718,1121],{"mathvariant":75560},[458,176720,468],{"stretchy":460},[458,176722,605],{"stretchy":460},[458,176724,471],{},[458,176726,5160],{},[7900,176728,176729,176731,176739],{},[458,176730,13808],{},[380,176732,176733,176735,176737],{},[383,176734,7911],{},[458,176736,471],{},[463,176738,465],{},[383,176740,11041],{},[543,176742,176743,176745],{},[383,176744,11],{},[383,176746,7911],{},[383,176748,4447],{},[458,176750,4450],{},[543,176752,176753,176755],{},[383,176754,11],{},[383,176756,7911],{},[387,176758,176759],{"encoding":389},"H[\\mathbb{P}(y \\mid \\mathbf{x})] = -\\sum_{k=1}^K p_k \\log p_k",[363,176761,176763,176793,176814],{"className":176762,"ariaHidden":394},[393],[363,176764,176766,176769,176772,176775,176778,176781,176784,176787,176790],{"className":176765},[398],[363,176767],{"className":176768,"style":487},[402],[363,176770,34231],{"className":176771,"style":34385},[407,408],[363,176773,578],{"className":176774},[494],[363,176776,554],{"className":176777},[407,714],[363,176779,461],{"className":176780},[494],[363,176782,40584],{"className":176783,"style":1328},[407,408],[363,176785],{"className":176786,"style":506},[505],[363,176788,5155],{"className":176789},[510],[363,176791],{"className":176792,"style":506},[505],[363,176794,176796,176799,176802,176805,176808,176811],{"className":176795},[398],[363,176797],{"className":176798,"style":487},[402],[363,176800,1121],{"className":176801},[407,75905],[363,176803,20737],{"className":176804},[501],[363,176806],{"className":176807,"style":506},[505],[363,176809,471],{"className":176810},[510],[363,176812],{"className":176813,"style":506},[505],[363,176815,176817,176820,176823,176826,176886,176889,176929,176932,176937,176940],{"className":176816},[398],[363,176818],{"className":176819,"style":136371},[402],[363,176821,5160],{"className":176822},[407],[363,176824],{"className":176825,"style":754},[505],[363,176827,176829,176832],{"className":176828},[1831],[363,176830,13808],{"className":176831,"style":40007},[1831,1832,5963],[363,176833,176835],{"className":176834},[629],[363,176836,176838,176878],{"className":176837},[633,634],[363,176839,176841,176875],{"className":176840},[638],[363,176842,176844,176864],{"className":176843,"style":133494},[642],[363,176845,176846,176849],{"style":40023},[363,176847],{"className":176848,"style":651},[650],[363,176850,176852],{"className":176851},[655,656,657,658],[363,176853,176855,176858,176861],{"className":176854},[407,658],[363,176856,7911],{"className":176857,"style":8614},[407,408,658],[363,176859,471],{"className":176860},[510,658],[363,176862,465],{"className":176863},[407,658],[363,176865,176866,176869],{"style":133517},[363,176867],{"className":176868,"style":651},[650],[363,176870,176872],{"className":176871},[655,656,657,658],[363,176873,11041],{"className":176874,"style":11129},[407,408,658],[363,176876,666],{"className":176877},[665],[363,176879,176881],{"className":176880},[638],[363,176882,176884],{"className":176883,"style":40042},[642],[363,176885],{},[363,176887],{"className":176888,"style":754},[505],[363,176890,176892,176895],{"className":176891},[407],[363,176893,11],{"className":176894},[407,408],[363,176896,176898],{"className":176897},[629],[363,176899,176901,176921],{"className":176900},[633,634],[363,176902,176904,176918],{"className":176903},[638],[363,176905,176907],{"className":176906,"style":643},[642],[363,176908,176909,176912],{"style":730},[363,176910],{"className":176911,"style":651},[650],[363,176913,176915],{"className":176914},[655,656,657,658],[363,176916,7911],{"className":176917,"style":8614},[407,408,658],[363,176919,666],{"className":176920},[665],[363,176922,176924],{"className":176923},[638],[363,176925,176927],{"className":176926,"style":8315},[642],[363,176928],{},[363,176930],{"className":176931,"style":754},[505],[363,176933,4501,176935],{"className":176934},[1831],[363,176936,4505],{"style":4504},[363,176938],{"className":176939,"style":754},[505],[363,176941,176943,176946],{"className":176942},[407],[363,176944,11],{"className":176945},[407,408],[363,176947,176949],{"className":176948},[629],[363,176950,176952,176972],{"className":176951},[633,634],[363,176953,176955,176969],{"className":176954},[638],[363,176956,176958],{"className":176957,"style":643},[642],[363,176959,176960,176963],{"style":730},[363,176961],{"className":176962,"style":651},[650],[363,176964,176966],{"className":176965},[655,656,657,658],[363,176967,7911],{"className":176968,"style":8614},[407,408,658],[363,176970,666],{"className":176971},[665],[363,176973,176975],{"className":176974},[638],[363,176976,176978],{"className":176977,"style":8315},[642],[363,176979],{},[363,176981,176983,177067],{"className":176982,"translate":367},[366],[363,176984,176986],{"className":176985},[371],[373,176987,176988],{"xmlns":375},[377,176989,176990,177064],{},[380,176991,176992,176998,177000,177002,177004,177006,177008,177010,177012,177014,177016,177018,177020,177022,177024,177026,177040,177046,177048,177050,177052,177058,177060,177062],{},[543,176993,176994,176996],{},[383,176995,571],{"mathvariant":570},[383,176997,157399],{"mathvariant":136008},[458,176999,578],{"stretchy":460},[383,177001,34231],{},[458,177003,461],{"stretchy":460},[383,177005,157399],{"mathvariant":136008},[458,177007,468],{"stretchy":460},[458,177009,605],{"stretchy":460},[458,177011,471],{},[383,177013,155424],{},[458,177015,461],{"stretchy":460},[383,177017,26084],{},[458,177019,2817],{},[463,177021,465],{},[458,177023,468],{"stretchy":460},[458,177025,5160],{},[7900,177027,177028,177030,177038],{},[458,177029,13808],{},[380,177031,177032,177034,177036],{},[383,177033,7911],{},[458,177035,471],{},[463,177037,465],{},[383,177039,11041],{},[543,177041,177042,177044],{},[383,177043,11],{},[383,177045,7911],{},[1644,177047,1646],{},[383,177049,155424],{},[458,177051,461],{"stretchy":460},[543,177053,177054,177056],{},[383,177055,45101],{},[383,177057,7911],{},[458,177059,2817],{},[463,177061,465],{},[458,177063,468],{"stretchy":460},[387,177065,177066],{"encoding":389},"\\mathbb{E}_{\\boldsymbol{\\pi}}[H(\\boldsymbol{\\pi})] = \\psi(S + 1) - \\sum_{k=1}^K p_k \\,\\psi(\\alpha_k + 1)",[363,177068,177070,177155,177179,177200,177367],{"className":177069,"ariaHidden":394},[393],[363,177071,177073,177076,177125,177128,177131,177134,177143,177146,177149,177152],{"className":177072},[398],[363,177074],{"className":177075,"style":487},[402],[363,177077,177079,177082],{"className":177078},[407],[363,177080,571],{"className":177081},[407,714],[363,177083,177085],{"className":177084},[629],[363,177086,177088,177117],{"className":177087},[633,634],[363,177089,177091,177114],{"className":177090},[638],[363,177092,177094],{"className":177093,"style":153717},[642],[363,177095,177096,177099],{"style":730},[363,177097],{"className":177098,"style":651},[650],[363,177100,177102],{"className":177101},[655,656,657,658],[363,177103,177105],{"className":177104},[407,658],[363,177106,177108],{"className":177107},[407,658],[363,177109,177111],{"className":177110},[407,658],[363,177112,157399],{"className":177113,"style":157433},[407,136068,658],[363,177115,666],{"className":177116},[665],[363,177118,177120],{"className":177119},[638],[363,177121,177123],{"className":177122,"style":8315},[642],[363,177124],{},[363,177126,578],{"className":177127},[494],[363,177129,34231],{"className":177130,"style":34385},[407,408],[363,177132,461],{"className":177133},[494],[363,177135,177137],{"className":177136},[407],[363,177138,177140],{"className":177139},[407],[363,177141,157399],{"className":177142,"style":157433},[407,136068],[363,177144,20737],{"className":177145},[501],[363,177147],{"className":177148,"style":506},[505],[363,177150,471],{"className":177151},[510],[363,177153],{"className":177154,"style":506},[505],[363,177156,177158,177161,177164,177167,177170,177173,177176],{"className":177157},[398],[363,177159],{"className":177160,"style":487},[402],[363,177162,155424],{"className":177163,"style":1328},[407,408],[363,177165,461],{"className":177166},[494],[363,177168,26084],{"className":177169,"style":26208},[407,408],[363,177171],{"className":177172,"style":2934},[505],[363,177174,2817],{"className":177175},[2938],[363,177177],{"className":177178,"style":2934},[505],[363,177180,177182,177185,177188,177191,177194,177197],{"className":177181},[398],[363,177183],{"className":177184,"style":487},[402],[363,177186,465],{"className":177187},[407],[363,177189,468],{"className":177190},[501],[363,177192],{"className":177193,"style":2934},[505],[363,177195,5160],{"className":177196},[2938],[363,177198],{"className":177199,"style":2934},[505],[363,177201,177203,177206,177266,177269,177309,177312,177315,177318,177358,177361,177364],{"className":177202},[398],[363,177204],{"className":177205,"style":136371},[402],[363,177207,177209,177212],{"className":177208},[1831],[363,177210,13808],{"className":177211,"style":40007},[1831,1832,5963],[363,177213,177215],{"className":177214},[629],[363,177216,177218,177258],{"className":177217},[633,634],[363,177219,177221,177255],{"className":177220},[638],[363,177222,177224,177244],{"className":177223,"style":133494},[642],[363,177225,177226,177229],{"style":40023},[363,177227],{"className":177228,"style":651},[650],[363,177230,177232],{"className":177231},[655,656,657,658],[363,177233,177235,177238,177241],{"className":177234},[407,658],[363,177236,7911],{"className":177237,"style":8614},[407,408,658],[363,177239,471],{"className":177240},[510,658],[363,177242,465],{"className":177243},[407,658],[363,177245,177246,177249],{"style":133517},[363,177247],{"className":177248,"style":651},[650],[363,177250,177252],{"className":177251},[655,656,657,658],[363,177253,11041],{"className":177254,"style":11129},[407,408,658],[363,177256,666],{"className":177257},[665],[363,177259,177261],{"className":177260},[638],[363,177262,177264],{"className":177263,"style":40042},[642],[363,177265],{},[363,177267],{"className":177268,"style":754},[505],[363,177270,177272,177275],{"className":177271},[407],[363,177273,11],{"className":177274},[407,408],[363,177276,177278],{"className":177277},[629],[363,177279,177281,177301],{"className":177280},[633,634],[363,177282,177284,177298],{"className":177283},[638],[363,177285,177287],{"className":177286,"style":643},[642],[363,177288,177289,177292],{"style":730},[363,177290],{"className":177291,"style":651},[650],[363,177293,177295],{"className":177294},[655,656,657,658],[363,177296,7911],{"className":177297,"style":8614},[407,408,658],[363,177299,666],{"className":177300},[665],[363,177302,177304],{"className":177303},[638],[363,177305,177307],{"className":177306,"style":8315},[642],[363,177308],{},[363,177310],{"className":177311,"style":754},[505],[363,177313,155424],{"className":177314,"style":1328},[407,408],[363,177316,461],{"className":177317},[494],[363,177319,177321,177324],{"className":177320},[407],[363,177322,45101],{"className":177323,"style":45131},[407,408],[363,177325,177327],{"className":177326},[629],[363,177328,177330,177350],{"className":177329},[633,634],[363,177331,177333,177347],{"className":177332},[638],[363,177334,177336],{"className":177335,"style":643},[642],[363,177337,177338,177341],{"style":136107},[363,177339],{"className":177340,"style":651},[650],[363,177342,177344],{"className":177343},[655,656,657,658],[363,177345,7911],{"className":177346,"style":8614},[407,408,658],[363,177348,666],{"className":177349},[665],[363,177351,177353],{"className":177352},[638],[363,177354,177356],{"className":177355,"style":8315},[642],[363,177357],{},[363,177359],{"className":177360,"style":2934},[505],[363,177362,2817],{"className":177363},[2938],[363,177365],{"className":177366,"style":2934},[505],[363,177368,177370,177373,177376],{"className":177369},[398],[363,177371],{"className":177372,"style":487},[402],[363,177374,465],{"className":177375},[407],[363,177377,468],{"className":177378},[501],[363,177380,177382,177514],{"className":177381,"translate":367},[366],[363,177383,177385],{"className":177384},[371],[373,177386,177387],{"xmlns":375},[377,177388,177389,177511],{},[380,177390,177391,177393,177395,177397,177399,177401,177403,177405,177407,177409,177411,177413,177415,177417,177419,177421,177423,177425,177431,177433,177435,177437,177439,177441,177443,177445,177459,177465,177467,177469,177471,177477,177479,177481,177483,177485,177487,177489,177495,177497,177499,177501,177503,177505,177507,177509],{},[383,177392,34215],{},[458,177394,461],{"stretchy":460},[383,177396,40584],{},[458,177398,34222],{"separator":394},[383,177400,157399],{"mathvariant":136008},[458,177402,468],{"stretchy":460},[458,177404,471],{},[383,177406,34231],{},[458,177408,578],{"stretchy":460},[383,177410,554],{"mathvariant":570},[458,177412,461],{"stretchy":460},[383,177414,40584],{},[458,177416,5155],{},[383,177418,1121],{"mathvariant":75560},[458,177420,468],{"stretchy":460},[458,177422,605],{"stretchy":460},[458,177424,5160],{},[543,177426,177427,177429],{},[383,177428,571],{"mathvariant":570},[383,177430,157399],{"mathvariant":136008},[458,177432,578],{"stretchy":460},[383,177434,34231],{},[458,177436,461],{"stretchy":460},[383,177438,157399],{"mathvariant":136008},[458,177440,468],{"stretchy":460},[458,177442,605],{"stretchy":460},[458,177444,471],{},[7900,177446,177447,177449,177457],{},[458,177448,13808],{},[380,177450,177451,177453,177455],{},[383,177452,7911],{},[458,177454,471],{},[463,177456,465],{},[383,177458,11041],{},[543,177460,177461,177463],{},[383,177462,11],{},[383,177464,7911],{},[458,177466,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,177468,155424],{},[458,177470,461],{"stretchy":460},[543,177472,177473,177475],{},[383,177474,45101],{},[383,177476,7911],{},[458,177478,2817],{},[463,177480,465],{},[458,177482,468],{"stretchy":460},[458,177484,5160],{},[383,177486,4447],{},[458,177488,4450],{},[543,177490,177491,177493],{},[383,177492,11],{},[383,177494,7911],{},[458,177496,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,177498,5160],{},[383,177500,155424],{},[458,177502,461],{"stretchy":460},[383,177504,26084],{},[458,177506,2817],{},[463,177508,465],{},[458,177510,468],{"stretchy":460},[387,177512,177513],{"encoding":389},"I(y; \\boldsymbol{\\pi}) = H[\\mathbb{P}(y \\mid \\mathbf{x})] - \\mathbb{E}_{\\boldsymbol{\\pi}}[H(\\boldsymbol{\\pi})] = \\sum_{k=1}^K p_k\\big(\\psi(\\alpha_k + 1) - \\log p_k\\big) - \\psi(S + 1)",[363,177515,177517,177559,177589,177610,177695,177866,177887,177956,177980],{"className":177516,"ariaHidden":394},[393],[363,177518,177520,177523,177526,177529,177532,177535,177538,177547,177550,177553,177556],{"className":177519},[398],[363,177521],{"className":177522,"style":487},[402],[363,177524,34215],{"className":177525,"style":9234},[407,408],[363,177527,461],{"className":177528},[494],[363,177530,40584],{"className":177531,"style":1328},[407,408],[363,177533,34222],{"className":177534},[920],[363,177536],{"className":177537,"style":754},[505],[363,177539,177541],{"className":177540},[407],[363,177542,177544],{"className":177543},[407],[363,177545,157399],{"className":177546,"style":157433},[407,136068],[363,177548,468],{"className":177549},[501],[363,177551],{"className":177552,"style":506},[505],[363,177554,471],{"className":177555},[510],[363,177557],{"className":177558,"style":506},[505],[363,177560,177562,177565,177568,177571,177574,177577,177580,177583,177586],{"className":177561},[398],[363,177563],{"className":177564,"style":487},[402],[363,177566,34231],{"className":177567,"style":34385},[407,408],[363,177569,578],{"className":177570},[494],[363,177572,554],{"className":177573},[407,714],[363,177575,461],{"className":177576},[494],[363,177578,40584],{"className":177579,"style":1328},[407,408],[363,177581],{"className":177582,"style":506},[505],[363,177584,5155],{"className":177585},[510],[363,177587],{"className":177588,"style":506},[505],[363,177590,177592,177595,177598,177601,177604,177607],{"className":177591},[398],[363,177593],{"className":177594,"style":487},[402],[363,177596,1121],{"className":177597},[407,75905],[363,177599,20737],{"className":177600},[501],[363,177602],{"className":177603,"style":2934},[505],[363,177605,5160],{"className":177606},[2938],[363,177608],{"className":177609,"style":2934},[505],[363,177611,177613,177616,177665,177668,177671,177674,177683,177686,177689,177692],{"className":177612},[398],[363,177614],{"className":177615,"style":487},[402],[363,177617,177619,177622],{"className":177618},[407],[363,177620,571],{"className":177621},[407,714],[363,177623,177625],{"className":177624},[629],[363,177626,177628,177657],{"className":177627},[633,634],[363,177629,177631,177654],{"className":177630},[638],[363,177632,177634],{"className":177633,"style":153717},[642],[363,177635,177636,177639],{"style":730},[363,177637],{"className":177638,"style":651},[650],[363,177640,177642],{"className":177641},[655,656,657,658],[363,177643,177645],{"className":177644},[407,658],[363,177646,177648],{"className":177647},[407,658],[363,177649,177651],{"className":177650},[407,658],[363,177652,157399],{"className":177653,"style":157433},[407,136068,658],[363,177655,666],{"className":177656},[665],[363,177658,177660],{"className":177659},[638],[363,177661,177663],{"className":177662,"style":8315},[642],[363,177664],{},[363,177666,578],{"className":177667},[494],[363,177669,34231],{"className":177670,"style":34385},[407,408],[363,177672,461],{"className":177673},[494],[363,177675,177677],{"className":177676},[407],[363,177678,177680],{"className":177679},[407],[363,177681,157399],{"className":177682,"style":157433},[407,136068],[363,177684,20737],{"className":177685},[501],[363,177687],{"className":177688,"style":506},[505],[363,177690,471],{"className":177691},[510],[363,177693],{"className":177694,"style":506},[505],[363,177696,177698,177702,177762,177765,177805,177811,177814,177817,177857,177860,177863],{"className":177697},[398],[363,177699],{"className":177700,"style":177701},[402],"height:1.3312em;vertical-align:-0.35em;",[363,177703,177705,177708],{"className":177704},[1831],[363,177706,13808],{"className":177707,"style":40007},[1831,1832,5963],[363,177709,177711],{"className":177710},[629],[363,177712,177714,177754],{"className":177713},[633,634],[363,177715,177717,177751],{"className":177716},[638],[363,177718,177720,177740],{"className":177719,"style":133494},[642],[363,177721,177722,177725],{"style":40023},[363,177723],{"className":177724,"style":651},[650],[363,177726,177728],{"className":177727},[655,656,657,658],[363,177729,177731,177734,177737],{"className":177730},[407,658],[363,177732,7911],{"className":177733,"style":8614},[407,408,658],[363,177735,471],{"className":177736},[510,658],[363,177738,465],{"className":177739},[407,658],[363,177741,177742,177745],{"style":133517},[363,177743],{"className":177744,"style":651},[650],[363,177746,177748],{"className":177747},[655,656,657,658],[363,177749,11041],{"className":177750,"style":11129},[407,408,658],[363,177752,666],{"className":177753},[665],[363,177755,177757],{"className":177756},[638],[363,177758,177760],{"className":177759,"style":40042},[642],[363,177761],{},[363,177763],{"className":177764,"style":754},[505],[363,177766,177768,177771],{"className":177767},[407],[363,177769,11],{"className":177770},[407,408],[363,177772,177774],{"className":177773},[629],[363,177775,177777,177797],{"className":177776},[633,634],[363,177778,177780,177794],{"className":177779},[638],[363,177781,177783],{"className":177782,"style":643},[642],[363,177784,177785,177788],{"style":730},[363,177786],{"className":177787,"style":651},[650],[363,177789,177791],{"className":177790},[655,656,657,658],[363,177792,7911],{"className":177793,"style":8614},[407,408,658],[363,177795,666],{"className":177796},[665],[363,177798,177800],{"className":177799},[638],[363,177801,177803],{"className":177802,"style":8315},[642],[363,177804],{},[363,177806,177808],{"className":177807},[407],[363,177809,461],{"className":177810},[767,10021],[363,177812,155424],{"className":177813,"style":1328},[407,408],[363,177815,461],{"className":177816},[494],[363,177818,177820,177823],{"className":177819},[407],[363,177821,45101],{"className":177822,"style":45131},[407,408],[363,177824,177826],{"className":177825},[629],[363,177827,177829,177849],{"className":177828},[633,634],[363,177830,177832,177846],{"className":177831},[638],[363,177833,177835],{"className":177834,"style":643},[642],[363,177836,177837,177840],{"style":136107},[363,177838],{"className":177839,"style":651},[650],[363,177841,177843],{"className":177842},[655,656,657,658],[363,177844,7911],{"className":177845,"style":8614},[407,408,658],[363,177847,666],{"className":177848},[665],[363,177850,177852],{"className":177851},[638],[363,177853,177855],{"className":177854,"style":8315},[642],[363,177856],{},[363,177858],{"className":177859,"style":2934},[505],[363,177861,2817],{"className":177862},[2938],[363,177864],{"className":177865,"style":2934},[505],[363,177867,177869,177872,177875,177878,177881,177884],{"className":177868},[398],[363,177870],{"className":177871,"style":487},[402],[363,177873,465],{"className":177874},[407],[363,177876,468],{"className":177877},[501],[363,177879],{"className":177880,"style":2934},[505],[363,177882,5160],{"className":177883},[2938],[363,177885],{"className":177886,"style":2934},[505],[363,177888,177890,177893,177898,177901,177941,177947,177950,177953],{"className":177889},[398],[363,177891],{"className":177892,"style":20910},[402],[363,177894,4501,177896],{"className":177895},[1831],[363,177897,4505],{"style":4504},[363,177899],{"className":177900,"style":754},[505],[363,177902,177904,177907],{"className":177903},[407],[363,177905,11],{"className":177906},[407,408],[363,177908,177910],{"className":177909},[629],[363,177911,177913,177933],{"className":177912},[633,634],[363,177914,177916,177930],{"className":177915},[638],[363,177917,177919],{"className":177918,"style":643},[642],[363,177920,177921,177924],{"style":730},[363,177922],{"className":177923,"style":651},[650],[363,177925,177927],{"className":177926},[655,656,657,658],[363,177928,7911],{"className":177929,"style":8614},[407,408,658],[363,177931,666],{"className":177932},[665],[363,177934,177936],{"className":177935},[638],[363,177937,177939],{"className":177938,"style":8315},[642],[363,177940],{},[363,177942,177944],{"className":177943},[407],[363,177945,468],{"className":177946},[767,10021],[363,177948],{"className":177949,"style":2934},[505],[363,177951,5160],{"className":177952},[2938],[363,177954],{"className":177955,"style":2934},[505],[363,177957,177959,177962,177965,177968,177971,177974,177977],{"className":177958},[398],[363,177960],{"className":177961,"style":487},[402],[363,177963,155424],{"className":177964,"style":1328},[407,408],[363,177966,461],{"className":177967},[494],[363,177969,26084],{"className":177970,"style":26208},[407,408],[363,177972],{"className":177973,"style":2934},[505],[363,177975,2817],{"className":177976},[2938],[363,177978],{"className":177979,"style":2934},[505],[363,177981,177983,177986,177989],{"className":177982},[398],[363,177984],{"className":177985,"style":487},[402],[363,177987,465],{"className":177988},[407],[363,177990,468],{"className":177991},[501],[11,177993,177994,177996,177997,43112,178228,178486,178487,178716,178717,179023,179024,3092,179116,179189,179190,179324,179325,179462],{},[1572,177995,137993],{}," 关键在于 ",[363,177998,178000,178046],{"className":177999,"translate":367},[366],[363,178001,178003],{"className":178002},[371],[373,178004,178005],{"xmlns":375},[377,178006,178007,178043],{},[380,178008,178009,178011,178013,178015,178017,178019,178021,178027,178033,178035,178037],{},[383,178010,34231],{},[458,178012,461],{"stretchy":460},[383,178014,157399],{"mathvariant":136008},[458,178016,468],{"stretchy":460},[458,178018,471],{},[458,178020,5160],{},[543,178022,178023,178025],{},[458,178024,13808],{},[383,178026,7911],{},[543,178028,178029,178031],{},[383,178030,157399],{},[383,178032,7911],{},[383,178034,4447],{},[458,178036,4450],{},[543,178038,178039,178041],{},[383,178040,157399],{},[383,178042,7911],{},[387,178044,178045],{"encoding":389},"H(\\boldsymbol{\\pi}) = -\\sum_k \\pi_k \\log \\pi_k",[363,178047,178049,178082],{"className":178048,"ariaHidden":394},[393],[363,178050,178052,178055,178058,178061,178070,178073,178076,178079],{"className":178051},[398],[363,178053],{"className":178054,"style":487},[402],[363,178056,34231],{"className":178057,"style":34385},[407,408],[363,178059,461],{"className":178060},[494],[363,178062,178064],{"className":178063},[407],[363,178065,178067],{"className":178066},[407],[363,178068,157399],{"className":178069,"style":157433},[407,136068],[363,178071,468],{"className":178072},[501],[363,178074],{"className":178075,"style":506},[505],[363,178077,471],{"className":178078},[510],[363,178080],{"className":178081,"style":506},[505],[363,178083,178085,178088,178091,178094,178134,178137,178177,178180,178185,178188],{"className":178084},[398],[363,178086],{"className":178087,"style":138904},[402],[363,178089,5160],{"className":178090},[407],[363,178092],{"className":178093,"style":754},[505],[363,178095,178097,178100],{"className":178096},[1831],[363,178098,13808],{"className":178099,"style":40007},[1831,1832,5963],[363,178101,178103],{"className":178102},[629],[363,178104,178106,178126],{"className":178105},[633,634],[363,178107,178109,178123],{"className":178108},[638],[363,178110,178112],{"className":178111,"style":67358},[642],[363,178113,178114,178117],{"style":40023},[363,178115],{"className":178116,"style":651},[650],[363,178118,178120],{"className":178119},[655,656,657,658],[363,178121,7911],{"className":178122,"style":8614},[407,408,658],[363,178124,666],{"className":178125},[665],[363,178127,178129],{"className":178128},[638],[363,178130,178132],{"className":178131,"style":40042},[642],[363,178133],{},[363,178135],{"className":178136,"style":754},[505],[363,178138,178140,178143],{"className":178139},[407],[363,178141,157399],{"className":178142,"style":1328},[407,408],[363,178144,178146],{"className":178145},[629],[363,178147,178149,178169],{"className":178148},[633,634],[363,178150,178152,178166],{"className":178151},[638],[363,178153,178155],{"className":178154,"style":643},[642],[363,178156,178157,178160],{"style":19190},[363,178158],{"className":178159,"style":651},[650],[363,178161,178163],{"className":178162},[655,656,657,658],[363,178164,7911],{"className":178165,"style":8614},[407,408,658],[363,178167,666],{"className":178168},[665],[363,178170,178172],{"className":178171},[638],[363,178173,178175],{"className":178174,"style":8315},[642],[363,178176],{},[363,178178],{"className":178179,"style":754},[505],[363,178181,4501,178183],{"className":178182},[1831],[363,178184,4505],{"style":4504},[363,178186],{"className":178187,"style":754},[505],[363,178189,178191,178194],{"className":178190},[407],[363,178192,157399],{"className":178193,"style":1328},[407,408],[363,178195,178197],{"className":178196},[629],[363,178198,178200,178220],{"className":178199},[633,634],[363,178201,178203,178217],{"className":178202},[638],[363,178204,178206],{"className":178205,"style":643},[642],[363,178207,178208,178211],{"style":19190},[363,178209],{"className":178210,"style":651},[650],[363,178212,178214],{"className":178213},[655,656,657,658],[363,178215,7911],{"className":178216,"style":8614},[407,408,658],[363,178218,666],{"className":178219},[665],[363,178221,178223],{"className":178222},[638],[363,178224,178226],{"className":178225,"style":8315},[642],[363,178227],{},[363,178229,178231,178289],{"className":178230,"translate":367},[366],[363,178232,178234],{"className":178233},[371],[373,178235,178236],{"xmlns":375},[377,178237,178238,178286],{},[380,178239,178240,178242,178244,178246,178248,178250,178252,178254,178256,178258,178264,178266,178268,178274,178276,178278,178284],{},[383,178241,571],{"mathvariant":570},[458,178243,578],{"stretchy":460},[383,178245,34231],{},[458,178247,461],{"stretchy":460},[383,178249,157399],{"mathvariant":136008},[458,178251,468],{"stretchy":460},[458,178253,605],{"stretchy":460},[458,178255,471],{},[458,178257,5160],{},[543,178259,178260,178262],{},[458,178261,13808],{},[383,178263,7911],{},[383,178265,571],{"mathvariant":570},[458,178267,578],{"stretchy":460},[543,178269,178270,178272],{},[383,178271,157399],{},[383,178273,7911],{},[383,178275,4447],{},[458,178277,4450],{},[543,178279,178280,178282],{},[383,178281,157399],{},[383,178283,7911],{},[458,178285,605],{"stretchy":460},[387,178287,178288],{"encoding":389},"\\mathbb{E}[H(\\boldsymbol{\\pi})] = -\\sum_k \\mathbb{E}[\\pi_k \\log \\pi_k]",[363,178290,178292,178331],{"className":178291,"ariaHidden":394},[393],[363,178293,178295,178298,178301,178304,178307,178310,178319,178322,178325,178328],{"className":178294},[398],[363,178296],{"className":178297,"style":487},[402],[363,178299,571],{"className":178300},[407,714],[363,178302,578],{"className":178303},[494],[363,178305,34231],{"className":178306,"style":34385},[407,408],[363,178308,461],{"className":178309},[494],[363,178311,178313],{"className":178312},[407],[363,178314,178316],{"className":178315},[407],[363,178317,157399],{"className":178318,"style":157433},[407,136068],[363,178320,20737],{"className":178321},[501],[363,178323],{"className":178324,"style":506},[505],[363,178326,471],{"className":178327},[510],[363,178329],{"className":178330,"style":506},[505],[363,178332,178334,178337,178340,178343,178383,178386,178389,178392,178432,178435,178440,178443,178483],{"className":178333},[398],[363,178335],{"className":178336,"style":138904},[402],[363,178338,5160],{"className":178339},[407],[363,178341],{"className":178342,"style":754},[505],[363,178344,178346,178349],{"className":178345},[1831],[363,178347,13808],{"className":178348,"style":40007},[1831,1832,5963],[363,178350,178352],{"className":178351},[629],[363,178353,178355,178375],{"className":178354},[633,634],[363,178356,178358,178372],{"className":178357},[638],[363,178359,178361],{"className":178360,"style":67358},[642],[363,178362,178363,178366],{"style":40023},[363,178364],{"className":178365,"style":651},[650],[363,178367,178369],{"className":178368},[655,656,657,658],[363,178370,7911],{"className":178371,"style":8614},[407,408,658],[363,178373,666],{"className":178374},[665],[363,178376,178378],{"className":178377},[638],[363,178379,178381],{"className":178380,"style":40042},[642],[363,178382],{},[363,178384],{"className":178385,"style":754},[505],[363,178387,571],{"className":178388},[407,714],[363,178390,578],{"className":178391},[494],[363,178393,178395,178398],{"className":178394},[407],[363,178396,157399],{"className":178397,"style":1328},[407,408],[363,178399,178401],{"className":178400},[629],[363,178402,178404,178424],{"className":178403},[633,634],[363,178405,178407,178421],{"className":178406},[638],[363,178408,178410],{"className":178409,"style":643},[642],[363,178411,178412,178415],{"style":19190},[363,178413],{"className":178414,"style":651},[650],[363,178416,178418],{"className":178417},[655,656,657,658],[363,178419,7911],{"className":178420,"style":8614},[407,408,658],[363,178422,666],{"className":178423},[665],[363,178425,178427],{"className":178426},[638],[363,178428,178430],{"className":178429,"style":8315},[642],[363,178431],{},[363,178433],{"className":178434,"style":754},[505],[363,178436,4501,178438],{"className":178437},[1831],[363,178439,4505],{"style":4504},[363,178441],{"className":178442,"style":754},[505],[363,178444,178446,178449],{"className":178445},[407],[363,178447,157399],{"className":178448,"style":1328},[407,408],[363,178450,178452],{"className":178451},[629],[363,178453,178455,178475],{"className":178454},[633,634],[363,178456,178458,178472],{"className":178457},[638],[363,178459,178461],{"className":178460,"style":643},[642],[363,178462,178463,178466],{"style":19190},[363,178464],{"className":178465,"style":651},[650],[363,178467,178469],{"className":178468},[655,656,657,658],[363,178470,7911],{"className":178471,"style":8614},[407,408,658],[363,178473,666],{"className":178474},[665],[363,178476,178478],{"className":178477},[638],[363,178479,178481],{"className":178480,"style":8315},[642],[363,178482],{},[363,178484,605],{"className":178485},[501],"。由 1.4 节的边缘 Beta 性，",[363,178488,178490,178536],{"className":178489,"translate":367},[366],[363,178491,178493],{"className":178492},[371],[373,178494,178495],{"xmlns":375},[377,178496,178497,178533],{},[380,178498,178499,178505,178507,178509,178511,178513,178519,178521,178523,178525,178531],{},[543,178500,178501,178503],{},[383,178502,157399],{},[383,178504,7911],{},[458,178506,9216],{},[383,178508,145757],{"mathvariant":557},[458,178510,4450],{},[458,178512,461],{"stretchy":460},[543,178514,178515,178517],{},[383,178516,45101],{},[383,178518,7911],{},[458,178520,898],{"separator":394},[383,178522,26084],{},[458,178524,5160],{},[543,178526,178527,178529],{},[383,178528,45101],{},[383,178530,7911],{},[458,178532,468],{"stretchy":460},[387,178534,178535],{"encoding":389},"\\pi_k \\sim \\operatorname{Beta}(\\alpha_k, S - \\alpha_k)",[363,178537,178539,178594,178667],{"className":178538,"ariaHidden":394},[393],[363,178540,178542,178545,178585,178588,178591],{"className":178541},[398],[363,178543],{"className":178544,"style":13721},[402],[363,178546,178548,178551],{"className":178547},[407],[363,178549,157399],{"className":178550,"style":1328},[407,408],[363,178552,178554],{"className":178553},[629],[363,178555,178557,178577],{"className":178556},[633,634],[363,178558,178560,178574],{"className":178559},[638],[363,178561,178563],{"className":178562,"style":643},[642],[363,178564,178565,178568],{"style":19190},[363,178566],{"className":178567,"style":651},[650],[363,178569,178571],{"className":178570},[655,656,657,658],[363,178572,7911],{"className":178573,"style":8614},[407,408,658],[363,178575,666],{"className":178576},[665],[363,178578,178580],{"className":178579},[638],[363,178581,178583],{"className":178582,"style":8315},[642],[363,178584],{},[363,178586],{"className":178587,"style":506},[505],[363,178589,9216],{"className":178590},[510],[363,178592],{"className":178593,"style":506},[505],[363,178595,178597,178600,178606,178609,178649,178652,178655,178658,178661,178664],{"className":178596},[398],[363,178598],{"className":178599,"style":487},[402],[363,178601,178603],{"className":178602},[1831],[363,178604,145757],{"className":178605},[407,33009],[363,178607,461],{"className":178608},[494],[363,178610,178612,178615],{"className":178611},[407],[363,178613,45101],{"className":178614,"style":45131},[407,408],[363,178616,178618],{"className":178617},[629],[363,178619,178621,178641],{"className":178620},[633,634],[363,178622,178624,178638],{"className":178623},[638],[363,178625,178627],{"className":178626,"style":643},[642],[363,178628,178629,178632],{"style":136107},[363,178630],{"className":178631,"style":651},[650],[363,178633,178635],{"className":178634},[655,656,657,658],[363,178636,7911],{"className":178637,"style":8614},[407,408,658],[363,178639,666],{"className":178640},[665],[363,178642,178644],{"className":178643},[638],[363,178645,178647],{"className":178646,"style":8315},[642],[363,178648],{},[363,178650,898],{"className":178651},[920],[363,178653],{"className":178654,"style":754},[505],[363,178656,26084],{"className":178657,"style":26208},[407,408],[363,178659],{"className":178660,"style":2934},[505],[363,178662,5160],{"className":178663},[2938],[363,178665],{"className":178666,"style":2934},[505],[363,178668,178670,178673,178713],{"className":178669},[398],[363,178671],{"className":178672,"style":487},[402],[363,178674,178676,178679],{"className":178675},[407],[363,178677,45101],{"className":178678,"style":45131},[407,408],[363,178680,178682],{"className":178681},[629],[363,178683,178685,178705],{"className":178684},[633,634],[363,178686,178688,178702],{"className":178687},[638],[363,178689,178691],{"className":178690,"style":643},[642],[363,178692,178693,178696],{"style":136107},[363,178694],{"className":178695,"style":651},[650],[363,178697,178699],{"className":178698},[655,656,657,658],[363,178700,7911],{"className":178701,"style":8614},[407,408,658],[363,178703,666],{"className":178704},[665],[363,178706,178708],{"className":178707},[638],[363,178709,178711],{"className":178710,"style":8315},[642],[363,178712],{},[363,178714,468],{"className":178715},[501],"，而对该 Beta 分布有恒等式 ",[363,178718,178720,178794],{"className":178719,"translate":367},[366],[363,178721,178723],{"className":178722},[371],[373,178724,178725],{"xmlns":375},[377,178726,178727,178791],{},[380,178728,178729,178731,178733,178735,178737,178739,178741,178743,178745,178757,178759,178761,178763,178765,178767,178769,178771,178773,178775,178777,178779,178781,178783,178785,178787,178789],{},[383,178730,571],{"mathvariant":570},[458,178732,578],{"stretchy":460},[383,178734,945],{},[383,178736,4447],{},[458,178738,4450],{},[383,178740,945],{},[458,178742,605],{"stretchy":460},[458,178744,471],{},[586,178746,178747,178749],{},[383,178748,45527],{},[380,178750,178751,178753,178755],{},[383,178752,45527],{},[458,178754,2817],{},[383,178756,83174],{},[458,178758,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,178760,155424],{},[458,178762,461],{"stretchy":460},[383,178764,45527],{},[458,178766,2817],{},[463,178768,465],{},[458,178770,468],{"stretchy":460},[458,178772,5160],{},[383,178774,155424],{},[458,178776,461],{"stretchy":460},[383,178778,45527],{},[458,178780,2817],{},[383,178782,83174],{},[458,178784,2817],{},[463,178786,465],{},[458,178788,468],{"stretchy":460},[458,178790,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[387,178792,178793],{"encoding":389},"\\mathbb{E}[X \\log X] = \\frac{a}{a+b}\\big(\\psi(a+1) - \\psi(a+b+1)\\big)",[363,178795,178797,178838,178942,178963,178987,179005],{"className":178796,"ariaHidden":394},[393],[363,178798,178800,178803,178806,178809,178812,178815,178820,178823,178826,178829,178832,178835],{"className":178799},[398],[363,178801],{"className":178802,"style":487},[402],[363,178804,571],{"className":178805},[407,714],[363,178807,578],{"className":178808},[494],[363,178810,945],{"className":178811,"style":9234},[407,408],[363,178813],{"className":178814,"style":754},[505],[363,178816,4501,178818],{"className":178817},[1831],[363,178819,4505],{"style":4504},[363,178821],{"className":178822,"style":754},[505],[363,178824,945],{"className":178825,"style":9234},[407,408],[363,178827,605],{"className":178828},[501],[363,178830],{"className":178831,"style":506},[505],[363,178833,471],{"className":178834},[510],[363,178836],{"className":178837,"style":506},[505],[363,178839,178841,178844,178918,178924,178927,178930,178933,178936,178939],{"className":178840},[398],[363,178842],{"className":178843,"style":111760},[402],[363,178845,178847,178850,178915],{"className":178846},[407],[363,178848],{"className":178849},[494,789],[363,178851,178853],{"className":178852},[586],[363,178854,178856,178907],{"className":178855},[633,634],[363,178857,178859,178904],{"className":178858},[638],[363,178860,178862,178882,178890],{"className":178861,"style":86039},[642],[363,178863,178864,178867],{"style":2874},[363,178865],{"className":178866,"style":809},[650],[363,178868,178870],{"className":178869},[655,656,657,658],[363,178871,178873,178876,178879],{"className":178872},[407,658],[363,178874,45527],{"className":178875},[407,408,658],[363,178877,2817],{"className":178878},[2938,658],[363,178880,83174],{"className":178881},[407,408,658],[363,178883,178884,178887],{"style":821},[363,178885],{"className":178886,"style":809},[650],[363,178888],{"className":178889,"style":829},[828],[363,178891,178892,178895],{"style":2897},[363,178893],{"className":178894,"style":809},[650],[363,178896,178898],{"className":178897},[655,656,657,658],[363,178899,178901],{"className":178900},[407,658],[363,178902,45527],{"className":178903},[407,408,658],[363,178905,666],{"className":178906},[665],[363,178908,178910],{"className":178909},[638],[363,178911,178913],{"className":178912,"style":16776},[642],[363,178914],{},[363,178916],{"className":178917},[501,789],[363,178919,178921],{"className":178920},[407],[363,178922,461],{"className":178923},[767,10021],[363,178925,155424],{"className":178926,"style":1328},[407,408],[363,178928,461],{"className":178929},[494],[363,178931,45527],{"className":178932},[407,408],[363,178934],{"className":178935,"style":2934},[505],[363,178937,2817],{"className":178938},[2938],[363,178940],{"className":178941,"style":2934},[505],[363,178943,178945,178948,178951,178954,178957,178960],{"className":178944},[398],[363,178946],{"className":178947,"style":487},[402],[363,178949,465],{"className":178950},[407],[363,178952,468],{"className":178953},[501],[363,178955],{"className":178956,"style":2934},[505],[363,178958,5160],{"className":178959},[2938],[363,178961],{"className":178962,"style":2934},[505],[363,178964,178966,178969,178972,178975,178978,178981,178984],{"className":178965},[398],[363,178967],{"className":178968,"style":487},[402],[363,178970,155424],{"className":178971,"style":1328},[407,408],[363,178973,461],{"className":178974},[494],[363,178976,45527],{"className":178977},[407,408],[363,178979],{"className":178980,"style":2934},[505],[363,178982,2817],{"className":178983},[2938],[363,178985],{"className":178986,"style":2934},[505],[363,178988,178990,178993,178996,178999,179002],{"className":178989},[398],[363,178991],{"className":178992,"style":15933},[402],[363,178994,83174],{"className":178995},[407,408],[363,178997],{"className":178998,"style":2934},[505],[363,179000,2817],{"className":179001},[2938],[363,179003],{"className":179004,"style":2934},[505],[363,179006,179008,179011,179014,179017],{"className":179007},[398],[363,179009],{"className":179010,"style":20910},[402],[363,179012,465],{"className":179013},[407],[363,179015,468],{"className":179016},[501],[363,179018,179020],{"className":179019},[407],[363,179021,468],{"className":179022},[767,10021],"（此处 ",[363,179025,179027,179049],{"className":179026,"translate":367},[366],[363,179028,179030],{"className":179029},[371],[373,179031,179032],{"xmlns":375},[377,179033,179034,179046],{},[380,179035,179036,179038,179040],{},[383,179037,45527],{},[458,179039,471],{},[543,179041,179042,179044],{},[383,179043,45101],{},[383,179045,7911],{},[387,179047,179048],{"encoding":389},"a = \\alpha_k",[363,179050,179052,179070],{"className":179051,"ariaHidden":394},[393],[363,179053,179055,179058,179061,179064,179067],{"className":179054},[398],[363,179056],{"className":179057,"style":2692},[402],[363,179059,45527],{"className":179060},[407,408],[363,179062],{"className":179063,"style":506},[505],[363,179065,471],{"className":179066},[510],[363,179068],{"className":179069,"style":506},[505],[363,179071,179073,179076],{"className":179072},[398],[363,179074],{"className":179075,"style":13721},[402],[363,179077,179079,179082],{"className":179078},[407],[363,179080,45101],{"className":179081,"style":45131},[407,408],[363,179083,179085],{"className":179084},[629],[363,179086,179088,179108],{"className":179087},[633,634],[363,179089,179091,179105],{"className":179090},[638],[363,179092,179094],{"className":179093,"style":643},[642],[363,179095,179096,179099],{"style":136107},[363,179097],{"className":179098,"style":651},[650],[363,179100,179102],{"className":179101},[655,656,657,658],[363,179103,7911],{"className":179104,"style":8614},[407,408,658],[363,179106,666],{"className":179107},[665],[363,179109,179111],{"className":179110},[638],[363,179112,179114],{"className":179113,"style":8315},[642],[363,179115],{},[363,179117,179119,179141],{"className":179118,"translate":367},[366],[363,179120,179122],{"className":179121},[371],[373,179123,179124],{"xmlns":375},[377,179125,179126,179138],{},[380,179127,179128,179130,179132,179134,179136],{},[383,179129,45527],{},[458,179131,2817],{},[383,179133,83174],{},[458,179135,471],{},[383,179137,26084],{},[387,179139,179140],{"encoding":389},"a + b = S",[363,179142,179144,179162,179180],{"className":179143,"ariaHidden":394},[393],[363,179145,179147,179150,179153,179156,179159],{"className":179146},[398],[363,179148],{"className":179149,"style":4598},[402],[363,179151,45527],{"className":179152},[407,408],[363,179154],{"className":179155,"style":2934},[505],[363,179157,2817],{"className":179158},[2938],[363,179160],{"className":179161,"style":2934},[505],[363,179163,179165,179168,179171,179174,179177],{"className":179164},[398],[363,179166],{"className":179167,"style":12944},[402],[363,179169,83174],{"className":179170},[407,408],[363,179172],{"className":179173,"style":506},[505],[363,179175,471],{"className":179176},[510],[363,179178],{"className":179179,"style":506},[505],[363,179181,179183,179186],{"className":179182},[398],[363,179184],{"className":179185,"style":1011},[402],[363,179187,26084],{"className":179188,"style":26208},[407,408],"）。代入 ",[363,179191,179193,179227],{"className":179192,"translate":367},[366],[363,179194,179196],{"className":179195},[371],[373,179197,179198],{"xmlns":375},[377,179199,179200,179224],{},[380,179201,179202,179204,179206,179208,179210,179212,179214,179216,179218],{},[383,179203,45527],{},[383,179205,1288],{"mathvariant":557},[458,179207,461],{"stretchy":460},[383,179209,45527],{},[458,179211,2817],{},[383,179213,83174],{},[458,179215,468],{"stretchy":460},[458,179217,471],{},[543,179219,179220,179222],{},[383,179221,11],{},[383,179223,7911],{},[387,179225,179226],{"encoding":389},"a\u002F(a+b) = p_k",[363,179228,179230,179257,179278],{"className":179229,"ariaHidden":394},[393],[363,179231,179233,179236,179239,179242,179245,179248,179251,179254],{"className":179232},[398],[363,179234],{"className":179235,"style":487},[402],[363,179237,45527],{"className":179238},[407,408],[363,179240,1288],{"className":179241},[407],[363,179243,461],{"className":179244},[494],[363,179246,45527],{"className":179247},[407,408],[363,179249],{"className":179250,"style":2934},[505],[363,179252,2817],{"className":179253},[2938],[363,179255],{"className":179256,"style":2934},[505],[363,179258,179260,179263,179266,179269,179272,179275],{"className":179259},[398],[363,179261],{"className":179262,"style":487},[402],[363,179264,83174],{"className":179265},[407,408],[363,179267,468],{"className":179268},[501],[363,179270],{"className":179271,"style":506},[505],[363,179273,471],{"className":179274},[510],[363,179276],{"className":179277,"style":506},[505],[363,179279,179281,179284],{"className":179280},[398],[363,179282],{"className":179283,"style":2623},[402],[363,179285,179287,179290],{"className":179286},[407],[363,179288,11],{"className":179289},[407,408],[363,179291,179293],{"className":179292},[629],[363,179294,179296,179316],{"className":179295},[633,634],[363,179297,179299,179313],{"className":179298},[638],[363,179300,179302],{"className":179301,"style":643},[642],[363,179303,179304,179307],{"style":730},[363,179305],{"className":179306,"style":651},[650],[363,179308,179310],{"className":179309},[655,656,657,658],[363,179311,7911],{"className":179312,"style":8614},[407,408,658],[363,179314,666],{"className":179315},[665],[363,179317,179319],{"className":179318},[638],[363,179320,179322],{"className":179321,"style":8315},[642],[363,179323],{}," 即得第二式。互信息由 ",[363,179326,179328,179372],{"className":179327,"translate":367},[366],[363,179329,179331],{"className":179330},[371],[373,179332,179333],{"xmlns":375},[377,179334,179335,179369],{},[380,179336,179337,179339,179341,179343,179345,179347,179349,179351,179353,179355,179357,179359,179361,179363,179365,179367],{},[383,179338,34215],{},[458,179340,471],{},[383,179342,34231],{},[458,179344,578],{"stretchy":460},[383,179346,571],{"mathvariant":570},[1644,179348,1646],{},[383,179350,157399],{"mathvariant":136008},[458,179352,605],{"stretchy":460},[458,179354,5160],{},[383,179356,571],{"mathvariant":570},[458,179358,578],{"stretchy":460},[383,179360,34231],{},[458,179362,461],{"stretchy":460},[383,179364,157399],{"mathvariant":136008},[458,179366,468],{"stretchy":460},[458,179368,605],{"stretchy":460},[387,179370,179371],{"encoding":389},"I = H[\\mathbb{E}\\,\\boldsymbol{\\pi}] - \\mathbb{E}[H(\\boldsymbol{\\pi})]",[363,179373,179375,179393,179432],{"className":179374,"ariaHidden":394},[393],[363,179376,179378,179381,179384,179387,179390],{"className":179377},[398],[363,179379],{"className":179380,"style":1011},[402],[363,179382,34215],{"className":179383,"style":9234},[407,408],[363,179385],{"className":179386,"style":506},[505],[363,179388,471],{"className":179389},[510],[363,179391],{"className":179392,"style":506},[505],[363,179394,179396,179399,179402,179405,179408,179411,179420,179423,179426,179429],{"className":179395},[398],[363,179397],{"className":179398,"style":487},[402],[363,179400,34231],{"className":179401,"style":34385},[407,408],[363,179403,578],{"className":179404},[494],[363,179406,571],{"className":179407},[407,714],[363,179409],{"className":179410,"style":754},[505],[363,179412,179414],{"className":179413},[407],[363,179415,179417],{"className":179416},[407],[363,179418,157399],{"className":179419,"style":157433},[407,136068],[363,179421,605],{"className":179422},[501],[363,179424],{"className":179425,"style":2934},[505],[363,179427,5160],{"className":179428},[2938],[363,179430],{"className":179431,"style":2934},[505],[363,179433,179435,179438,179441,179444,179447,179450,179459],{"className":179434},[398],[363,179436],{"className":179437,"style":487},[402],[363,179439,571],{"className":179440},[407,714],[363,179442,578],{"className":179443},[494],[363,179445,34231],{"className":179446,"style":34385},[407,408],[363,179448,461],{"className":179449},[494],[363,179451,179453],{"className":179452},[407],[363,179454,179456],{"className":179455},[407],[363,179457,157399],{"className":179458,"style":157433},[407,136068],[363,179460,20737],{"className":179461},[501]," 得到。",[11,179464,179465,179466,179469,179470,4200,179533,179584,179585,179645,179646,179675,179676,179704,179705,179708,179709,179737],{},"这一分解的意义在于：",[1572,179467,179468],{},"它把「数据本身的随机性」与「关于类别分布的认知不足」在数学上分离成了两个可分别计算的量。"," 认知项 ",[363,179471,179473,179497],{"className":179472,"translate":367},[366],[363,179474,179476],{"className":179475},[371],[373,179477,179478],{"xmlns":375},[377,179479,179480,179494],{},[380,179481,179482,179484,179486,179488,179490,179492],{},[383,179483,34215],{},[458,179485,461],{"stretchy":460},[383,179487,40584],{},[458,179489,34222],{"separator":394},[383,179491,157399],{"mathvariant":136008},[458,179493,468],{"stretchy":460},[387,179495,179496],{"encoding":389},"I(y;\\boldsymbol{\\pi})",[363,179498,179500],{"className":179499,"ariaHidden":394},[393],[363,179501,179503,179506,179509,179512,179515,179518,179521,179530],{"className":179502},[398],[363,179504],{"className":179505,"style":487},[402],[363,179507,34215],{"className":179508,"style":9234},[407,408],[363,179510,461],{"className":179511},[494],[363,179513,40584],{"className":179514,"style":1328},[407,408],[363,179516,34222],{"className":179517},[920],[363,179519],{"className":179520,"style":754},[505],[363,179522,179524],{"className":179523},[407],[363,179525,179527],{"className":179526},[407],[363,179528,157399],{"className":179529,"style":157433},[407,136068],[363,179531,468],{"className":179532},[501],[363,179534,179536,179554],{"className":179535,"translate":367},[366],[363,179537,179539],{"className":179538},[371],[373,179540,179541],{"xmlns":375},[377,179542,179543,179551],{},[380,179544,179545,179547,179549],{},[383,179546,26084],{},[458,179548,1376],{},[383,179550,1371],{"mathvariant":557},[387,179552,179553],{"encoding":389},"S \\to \\infty",[363,179555,179557,179575],{"className":179556,"ariaHidden":394},[393],[363,179558,179560,179563,179566,179569,179572],{"className":179559},[398],[363,179561],{"className":179562,"style":1011},[402],[363,179564,26084],{"className":179565,"style":26208},[407,408],[363,179567],{"className":179568,"style":506},[505],[363,179570,1376],{"className":179571},[510],[363,179573],{"className":179574,"style":506},[505],[363,179576,179578,179581],{"className":179577},[398],[363,179579],{"className":179580,"style":2692},[402],[363,179582,1371],{"className":179583},[407],"（证据充分）时趋于零，在证据缺失时增大，与 ",[363,179586,179588,179609],{"className":179587,"translate":367},[366],[363,179589,179591],{"className":179590},[371],[373,179592,179593],{"xmlns":375},[377,179594,179595,179607],{},[380,179596,179597,179599,179601,179603,179605],{},[383,179598,15747],{},[458,179600,471],{},[383,179602,11041],{},[383,179604,1288],{"mathvariant":557},[383,179606,26084],{},[387,179608,175606],{"encoding":389},[363,179610,179612,179630],{"className":179611,"ariaHidden":394},[393],[363,179613,179615,179618,179621,179624,179627],{"className":179614},[398],[363,179616],{"className":179617,"style":2692},[402],[363,179619,15747],{"className":179620},[407,408],[363,179622],{"className":179623,"style":506},[505],[363,179625,471],{"className":179626},[510],[363,179628],{"className":179629,"style":506},[505],[363,179631,179633,179636,179639,179642],{"className":179632},[398],[363,179634],{"className":179635,"style":487},[402],[363,179637,11041],{"className":179638,"style":11129},[407,408],[363,179640,1288],{"className":179641},[407],[363,179643,26084],{"className":179644,"style":26208},[407,408]," 的定性行为一致。但它是通过 ",[363,179647,179649,179663],{"className":179648,"translate":367},[366],[363,179650,179652],{"className":179651},[371],[373,179653,179654],{"xmlns":375},[377,179655,179656,179660],{},[380,179657,179658],{},[383,179659,155424],{},[387,179661,179662],{"encoding":389},"\\psi",[363,179664,179666],{"className":179665,"ariaHidden":394},[393],[363,179667,179669,179672],{"className":179668},[398],[363,179670],{"className":179671,"style":403},[402],[363,179673,155424],{"className":179674,"style":1328},[407,408]," 函数的差构造的，捕捉了 ",[363,179677,179679,179692],{"className":179678,"translate":367},[366],[363,179680,179682],{"className":179681},[371],[373,179683,179684],{"xmlns":375},[377,179685,179686,179690],{},[380,179687,179688],{},[383,179689,15747],{},[387,179691,15747],{"encoding":389},[363,179693,179695],{"className":179694,"ariaHidden":394},[393],[363,179696,179698,179701],{"className":179697},[398],[363,179699],{"className":179700,"style":2692},[402],[363,179702,15747],{"className":179703},[407,408]," 所忽略的",[1572,179706,179707],{},"证据分布","信息，因而是比 ",[363,179710,179712,179725],{"className":179711,"translate":367},[366],[363,179713,179715],{"className":179714},[371],[373,179716,179717],{"xmlns":375},[377,179718,179719,179723],{},[380,179720,179721],{},[383,179722,15747],{},[387,179724,15747],{"encoding":389},[363,179726,179728],{"className":179727,"ariaHidden":394},[393],[363,179729,179731,179734],{"className":179730},[398],[363,179732],{"className":179733,"style":2692},[402],[363,179735,15747],{"className":179736},[407,408]," 更精细的分数。",[11,179739,179740,179741,179775,179776,179810,179811,179905,179906,153051,179909,179971,179972,179976,179977,179980],{},"不过，这一分解的「认知」标签必须谨慎对待。它在形式上是「关于 ",[363,179742,179744,179757],{"className":179743,"translate":367},[366],[363,179745,179747],{"className":179746},[371],[373,179748,179749],{"xmlns":375},[377,179750,179751,179755],{},[380,179752,179753],{},[383,179754,157399],{"mathvariant":136008},[387,179756,157487],{"encoding":389},[363,179758,179760],{"className":179759,"ariaHidden":394},[393],[363,179761,179763,179766],{"className":179762},[398],[363,179764],{"className":179765,"style":135617},[402],[363,179767,179769],{"className":179768},[407],[363,179770,179772],{"className":179771},[407],[363,179773,157399],{"className":179774,"style":157433},[407,136068]," 的不确定性」，而 ",[363,179777,179779,179792],{"className":179778,"translate":367},[366],[363,179780,179782],{"className":179781},[371],[373,179783,179784],{"xmlns":375},[377,179785,179786,179790],{},[380,179787,179788],{},[383,179789,157399],{"mathvariant":136008},[387,179791,157487],{"encoding":389},[363,179793,179795],{"className":179794,"ariaHidden":394},[393],[363,179796,179798,179801],{"className":179797},[398],[363,179799],{"className":179800,"style":135617},[402],[363,179802,179804],{"className":179803},[407],[363,179805,179807],{"className":179806},[407],[363,179808,157399],{"className":179809,"style":157433},[407,136068]," 在 EDL 中是 ",[363,179812,179814,179838],{"className":179813,"translate":367},[366],[363,179815,179817],{"className":179816},[371],[373,179818,179819],{"xmlns":375},[377,179820,179821,179835],{},[380,179822,179823,179829,179831,179833],{},[543,179824,179825,179827],{},[383,179826,4505],{},[383,179828,101106],{"mathvariant":136008},[458,179830,461],{"stretchy":460},[383,179832,1121],{"mathvariant":75560},[458,179834,468],{"stretchy":460},[387,179836,179837],{"encoding":389},"g_{\\boldsymbol{\\theta}}(\\mathbf{x})",[363,179839,179841],{"className":179840,"ariaHidden":394},[393],[363,179842,179844,179847,179896,179899,179902],{"className":179843},[398],[363,179845],{"className":179846,"style":487},[402],[363,179848,179850,179853],{"className":179849},[407],[363,179851,4505],{"className":179852,"style":1328},[407,408],[363,179854,179856],{"className":179855},[629],[363,179857,179859,179888],{"className":179858},[633,634],[363,179860,179862,179885],{"className":179861},[638],[363,179863,179865],{"className":179864,"style":643},[642],[363,179866,179867,179870],{"style":19190},[363,179868],{"className":179869,"style":651},[650],[363,179871,179873],{"className":179872},[655,656,657,658],[363,179874,179876],{"className":179875},[407,658],[363,179877,179879],{"className":179878},[407,658],[363,179880,179882],{"className":179881},[407,658],[363,179883,101106],{"className":179884,"style":169854},[407,136068,658],[363,179886,666],{"className":179887},[665],[363,179889,179891],{"className":179890},[638],[363,179892,179894],{"className":179893,"style":8315},[642],[363,179895],{},[363,179897,461],{"className":179898},[494],[363,179900,1121],{"className":179901},[407,75905],[363,179903,468],{"className":179904},[501]," 的输出，是",[1572,179907,179908],{},"网络参数的确定性函数",[363,179910,179912,179935],{"className":179911,"translate":367},[366],[363,179913,179915],{"className":179914},[371],[373,179916,179917],{"xmlns":375},[377,179918,179919,179933],{},[380,179920,179921,179923,179925,179927,179929,179931],{},[383,179922,34215],{},[458,179924,461],{"stretchy":460},[383,179926,40584],{},[458,179928,34222],{"separator":394},[383,179930,157399],{"mathvariant":136008},[458,179932,468],{"stretchy":460},[387,179934,179496],{"encoding":389},[363,179936,179938],{"className":179937,"ariaHidden":394},[393],[363,179939,179941,179944,179947,179950,179953,179956,179959,179968],{"className":179940},[398],[363,179942],{"className":179943,"style":487},[402],[363,179945,34215],{"className":179946,"style":9234},[407,408],[363,179948,461],{"className":179949},[494],[363,179951,40584],{"className":179952,"style":1328},[407,408],[363,179954,34222],{"className":179955},[920],[363,179957],{"className":179958,"style":754},[505],[363,179960,179962],{"className":179961},[407],[363,179963,179965],{"className":179964},[407],[363,179966,157399],{"className":179967,"style":157433},[407,136068],[363,179969,468],{"className":179970},[501]," 度量的是",[179973,179974,179975],"em",{},"类概率向量","的不确定，而不是",[179973,179978,179979],{},"模型参数","的不确定——后者才是贝叶斯认识论意义上的 epistemic uncertainty。二者的距离，正是 4.5 节全部批评的技术根源。",[18,179982,179984],{"id":179983},"四证据深度学习的损失函数","四、证据深度学习的损失函数",[11,179986,179987,179988,180016,180017,180071],{},"EDL 的训练目标不再是「使 ",[363,179989,179991,180004],{"className":179990,"translate":367},[366],[363,179992,179994],{"className":179993},[371],[373,179995,179996],{"xmlns":375},[377,179997,179998,180002],{},[380,179999,180000],{},[383,180001,11],{"mathvariant":75560},[387,180003,133754],{"encoding":389},[363,180005,180007],{"className":180006,"ariaHidden":394},[393],[363,180008,180010,180013],{"className":180009},[398],[363,180011],{"className":180012,"style":133764},[402],[363,180014,11],{"className":180015},[407,75905]," 逼近 one-hot 标签」，而是「使整族 ",[363,180018,180020,180041],{"className":180019,"translate":367},[366],[363,180021,180023],{"className":180022},[371],[373,180024,180025],{"xmlns":375},[377,180026,180027,180039],{},[380,180028,180029,180031,180033,180035,180037],{},[383,180030,137065],{"mathvariant":557},[458,180032,4450],{},[458,180034,461],{"stretchy":460},[383,180036,45101],{"mathvariant":136008},[458,180038,468],{"stretchy":460},[387,180040,171704],{"encoding":389},[363,180042,180044],{"className":180043,"ariaHidden":394},[393],[363,180045,180047,180050,180056,180059,180068],{"className":180046},[398],[363,180048],{"className":180049,"style":487},[402],[363,180051,180053],{"className":180052},[1831],[363,180054,137065],{"className":180055},[407,33009],[363,180057,461],{"className":180058},[494],[363,180060,180062],{"className":180061},[407],[363,180063,180065],{"className":180064},[407],[363,180066,45101],{"className":180067},[407,136068],[363,180069,468],{"className":180070},[501]," 逼近一个理想的分布」。损失函数因此被组织为两项：一项拟合分类目标，一项约束不确定性的行为。",[2658,180073,180075],{"id":180074},"_41-type-ii-极大似然与对数风险","4.1 Type-II 极大似然与对数风险",[11,180077,180078,180079,180082],{},"最自然的构造是极小化对数损失在迪利克雷先验下的",[1572,180080,180081],{},"贝叶斯风险","（亦称 Type-II 极大似然）：",[363,180084,180086],{"className":180085,"translate":367},[528],[363,180087,180089,180146],{"className":180088,"translate":367},[366],[363,180090,180092],{"className":180091},[371],[373,180093,180094],{"xmlns":375,"display":537},[377,180095,180096,180143],{},[380,180097,180098,180105,180107,180127,180129,180131,180133,180135,180141],{},[7161,180099,180100,180102],{},[383,180101,22240],{"mathvariant":944},[1644,180103,180104],{},"NLL",[458,180106,471],{},[543,180108,180109,180111],{},[383,180110,571],{"mathvariant":570},[380,180112,180113,180115,180117,180119,180121,180123,180125],{},[383,180114,157399],{"mathvariant":136008},[458,180116,9216],{},[383,180118,137065],{"mathvariant":557},[458,180120,4450],{},[458,180122,461],{"stretchy":460},[383,180124,45101],{"mathvariant":136008},[458,180126,468],{"stretchy":460},[458,180128,578],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[458,180130,5160],{},[383,180132,4447],{},[458,180134,4450],{},[543,180136,180137,180139],{},[383,180138,157399],{},[383,180140,40584],{},[458,180142,605],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[387,180144,180145],{"encoding":389},"\\mathcal{L}^{\\text{NLL}} = \\mathbb{E}_{\\boldsymbol{\\pi} \\sim \\operatorname{Dir}(\\boldsymbol{\\alpha})}\\big[-\\log \\pi_y\\big]",[363,180147,180149,180199,180293],{"className":180148,"ariaHidden":394},[393],[363,180150,180152,180155,180190,180193,180196],{"className":180151},[398],[363,180153],{"className":180154,"style":38859},[402],[363,180156,180158,180161],{"className":180157},[407],[363,180159,22240],{"className":180160},[407,971],[363,180162,180164],{"className":180163},[629],[363,180165,180167],{"className":180166},[633],[363,180168,180170],{"className":180169},[638],[363,180171,180173],{"className":180172,"style":38859},[642],[363,180174,180175,180178],{"style":8624},[363,180176],{"className":180177,"style":651},[650],[363,180179,180181],{"className":180180},[655,656,657,658],[363,180182,180184],{"className":180183},[407,658],[363,180185,180187],{"className":180186},[407,4945,658],[363,180188,180104],{"className":180189},[407,658],[363,180191],{"className":180192,"style":506},[505],[363,180194,471],{"className":180195},[510],[363,180197],{"className":180198,"style":506},[505],[363,180200,180202,180205,180278,180284,180287,180290],{"className":180201},[398],[363,180203],{"className":180204,"style":119783},[402],[363,180206,180208,180211],{"className":180207},[407],[363,180209,571],{"className":180210},[407,714],[363,180212,180214],{"className":180213},[629],[363,180215,180217,180270],{"className":180216},[633,634],[363,180218,180220,180267],{"className":180219},[638],[363,180221,180223],{"className":180222,"style":6445},[642],[363,180224,180225,180228],{"style":75920},[363,180226],{"className":180227,"style":651},[650],[363,180229,180231],{"className":180230},[655,656,657,658],[363,180232,180234,180243,180246,180252,180255,180264],{"className":180233},[407,658],[363,180235,180237],{"className":180236},[407,658],[363,180238,180240],{"className":180239},[407,658],[363,180241,157399],{"className":180242,"style":157433},[407,136068,658],[363,180244,9216],{"className":180245},[510,658],[363,180247,180249],{"className":180248},[1831,658],[363,180250,137065],{"className":180251},[407,33009,658],[363,180253,461],{"className":180254},[494,658],[363,180256,180258],{"className":180257},[407,658],[363,180259,180261],{"className":180260},[407,658],[363,180262,45101],{"className":180263},[407,136068,658],[363,180265,468],{"className":180266},[501,658],[363,180268,666],{"className":180269},[665],[363,180271,180273],{"className":180272},[638],[363,180274,180276],{"className":180275,"style":6491},[642],[363,180277],{},[363,180279,180281],{"className":180280},[407],[363,180282,578],{"className":180283},[767,10021],[363,180285],{"className":180286,"style":2934},[505],[363,180288,5160],{"className":180289},[2938],[363,180291],{"className":180292,"style":2934},[505],[363,180294,180296,180299,180304,180307,180347],{"className":180295},[398],[363,180297],{"className":180298,"style":20910},[402],[363,180300,4501,180302],{"className":180301},[1831],[363,180303,4505],{"style":4504},[363,180305],{"className":180306,"style":754},[505],[363,180308,180310,180313],{"className":180309},[407],[363,180311,157399],{"className":180312,"style":1328},[407,408],[363,180314,180316],{"className":180315},[629],[363,180317,180319,180339],{"className":180318},[633,634],[363,180320,180322,180336],{"className":180321},[638],[363,180323,180325],{"className":180324,"style":45276},[642],[363,180326,180327,180330],{"style":19190},[363,180328],{"className":180329,"style":651},[650],[363,180331,180333],{"className":180332},[655,656,657,658],[363,180334,40584],{"className":180335,"style":1328},[407,408,658],[363,180337,666],{"className":180338},[665],[363,180340,180342],{"className":180341},[638],[363,180343,180345],{"className":180344,"style":673},[642],[363,180346],{},[363,180348,180350],{"className":180349},[407],[363,180351,605],{"className":180352},[767,10021],[1340,180354,180356],{"title":180355},"命题 4.1（对数风险的闭式）",[11,180357,180358,180359,180387,180388],{},"设真实标签为 ",[363,180360,180362,180375],{"className":180361,"translate":367},[366],[363,180363,180365],{"className":180364},[371],[373,180366,180367],{"xmlns":375},[377,180368,180369,180373],{},[380,180370,180371],{},[383,180372,40584],{},[387,180374,40584],{"encoding":389},[363,180376,180378],{"className":180377,"ariaHidden":394},[393],[363,180379,180381,180384],{"className":180380},[398],[363,180382],{"className":180383,"style":2623},[402],[363,180385,40584],{"className":180386,"style":1328},[407,408],"，则\n",[363,180389,180391,180433],{"className":180390,"translate":367},[366],[363,180392,180394],{"className":180393},[371],[373,180395,180396],{"xmlns":375},[377,180397,180398,180430],{},[380,180399,180400,180406,180408,180410,180412,180414,180416,180418,180420,180422,180428],{},[7161,180401,180402,180404],{},[383,180403,22240],{"mathvariant":944},[1644,180405,180104],{},[458,180407,471],{},[383,180409,155424],{},[458,180411,461],{"stretchy":460},[383,180413,26084],{},[458,180415,468],{"stretchy":460},[458,180417,5160],{},[383,180419,155424],{},[458,180421,461],{"stretchy":460},[543,180423,180424,180426],{},[383,180425,45101],{},[383,180427,40584],{},[458,180429,468],{"stretchy":460},[387,180431,180432],{"encoding":389},"\\mathcal{L}^{\\text{NLL}} = \\psi(S) - \\psi(\\alpha_y)",[363,180434,180436,180486,180513],{"className":180435,"ariaHidden":394},[393],[363,180437,180439,180442,180477,180480,180483],{"className":180438},[398],[363,180440],{"className":180441,"style":52432},[402],[363,180443,180445,180448],{"className":180444},[407],[363,180446,22240],{"className":180447},[407,971],[363,180449,180451],{"className":180450},[629],[363,180452,180454],{"className":180453},[633],[363,180455,180457],{"className":180456},[638],[363,180458,180460],{"className":180459,"style":52432},[642],[363,180461,180462,180465],{"style":7212},[363,180463],{"className":180464,"style":651},[650],[363,180466,180468],{"className":180467},[655,656,657,658],[363,180469,180471],{"className":180470},[407,658],[363,180472,180474],{"className":180473},[407,4945,658],[363,180475,180104],{"className":180476},[407,658],[363,180478],{"className":180479,"style":506},[505],[363,180481,471],{"className":180482},[510],[363,180484],{"className":180485,"style":506},[505],[363,180487,180489,180492,180495,180498,180501,180504,180507,180510],{"className":180488},[398],[363,180490],{"className":180491,"style":487},[402],[363,180493,155424],{"className":180494,"style":1328},[407,408],[363,180496,461],{"className":180497},[494],[363,180499,26084],{"className":180500,"style":26208},[407,408],[363,180502,468],{"className":180503},[501],[363,180505],{"className":180506,"style":2934},[505],[363,180508,5160],{"className":180509},[2938],[363,180511],{"className":180512,"style":2934},[505],[363,180514,180516,180519,180522,180525,180565],{"className":180515},[398],[363,180517],{"className":180518,"style":618},[402],[363,180520,155424],{"className":180521,"style":1328},[407,408],[363,180523,461],{"className":180524},[494],[363,180526,180528,180531],{"className":180527},[407],[363,180529,45101],{"className":180530,"style":45131},[407,408],[363,180532,180534],{"className":180533},[629],[363,180535,180537,180557],{"className":180536},[633,634],[363,180538,180540,180554],{"className":180539},[638],[363,180541,180543],{"className":180542,"style":45276},[642],[363,180544,180545,180548],{"style":136107},[363,180546],{"className":180547,"style":651},[650],[363,180549,180551],{"className":180550},[655,656,657,658],[363,180552,40584],{"className":180553,"style":1328},[407,408,658],[363,180555,666],{"className":180556},[665],[363,180558,180560],{"className":180559},[638],[363,180561,180563],{"className":180562,"style":673},[642],[363,180564],{},[363,180566,468],{"className":180567},[501],[11,180569,180570,180572,180573,180826,180827,180878,180879,180912],{},[1572,180571,137993],{}," 由 ",[363,180574,180576,180632],{"className":180575,"translate":367},[366],[363,180577,180579],{"className":180578},[371],[373,180580,180581],{"xmlns":375},[377,180582,180583,180629],{},[380,180584,180585,180587,180589,180591,180593,180599,180601,180603,180605,180607,180613,180615,180617,180619,180621,180627],{},[383,180586,571],{"mathvariant":570},[458,180588,578],{"stretchy":460},[383,180590,4447],{},[458,180592,4450],{},[543,180594,180595,180597],{},[383,180596,1121],{},[383,180598,7911],{},[458,180600,605],{"stretchy":460},[458,180602,471],{},[383,180604,155424],{},[458,180606,461],{"stretchy":460},[543,180608,180609,180611],{},[383,180610,45101],{},[383,180612,7911],{},[458,180614,468],{"stretchy":460},[458,180616,5160],{},[383,180618,155424],{},[458,180620,461],{"stretchy":460},[543,180622,180623,180625],{},[383,180624,45101],{},[463,180626,474],{},[458,180628,468],{"stretchy":460},[387,180630,180631],{"encoding":389},"\\mathbb{E}[\\log x_k] = \\psi(\\alpha_k) - \\psi(\\alpha_0)",[363,180633,180635,180707,180771],{"className":180634,"ariaHidden":394},[393],[363,180636,180638,180641,180644,180647,180652,180655,180695,180698,180701,180704],{"className":180637},[398],[363,180639],{"className":180640,"style":487},[402],[363,180642,571],{"className":180643},[407,714],[363,180645,578],{"className":180646},[494],[363,180648,4501,180650],{"className":180649},[1831],[363,180651,4505],{"style":4504},[363,180653],{"className":180654,"style":754},[505],[363,180656,180658,180661],{"className":180657},[407],[363,180659,1121],{"className":180660},[407,408],[363,180662,180664],{"className":180663},[629],[363,180665,180667,180687],{"className":180666},[633,634],[363,180668,180670,180684],{"className":180669},[638],[363,180671,180673],{"className":180672,"style":643},[642],[363,180674,180675,180678],{"style":730},[363,180676],{"className":180677,"style":651},[650],[363,180679,180681],{"className":180680},[655,656,657,658],[363,180682,7911],{"className":180683,"style":8614},[407,408,658],[363,180685,666],{"className":180686},[665],[363,180688,180690],{"className":180689},[638],[363,180691,180693],{"className":180692,"style":8315},[642],[363,180694],{},[363,180696,605],{"className":180697},[501],[363,180699],{"className":180700,"style":506},[505],[363,180702,471],{"className":180703},[510],[363,180705],{"className":180706,"style":506},[505],[363,180708,180710,180713,180716,180719,180759,180762,180765,180768],{"className":180709},[398],[363,180711],{"className":180712,"style":487},[402],[363,180714,155424],{"className":180715,"style":1328},[407,408],[363,180717,461],{"className":180718},[494],[363,180720,180722,180725],{"className":180721},[407],[363,180723,45101],{"className":180724,"style":45131},[407,408],[363,180726,180728],{"className":180727},[629],[363,180729,180731,180751],{"className":180730},[633,634],[363,180732,180734,180748],{"className":180733},[638],[363,180735,180737],{"className":180736,"style":643},[642],[363,180738,180739,180742],{"style":136107},[363,180740],{"className":180741,"style":651},[650],[363,180743,180745],{"className":180744},[655,656,657,658],[363,180746,7911],{"className":180747,"style":8614},[407,408,658],[363,180749,666],{"className":180750},[665],[363,180752,180754],{"className":180753},[638],[363,180755,180757],{"className":180756,"style":8315},[642],[363,180758],{},[363,180760,468],{"className":180761},[501],[363,180763],{"className":180764,"style":2934},[505],[363,180766,5160],{"className":180767},[2938],[363,180769],{"className":180770,"style":2934},[505],[363,180772,180774,180777,180780,180783,180823],{"className":180773},[398],[363,180775],{"className":180776,"style":487},[402],[363,180778,155424],{"className":180779,"style":1328},[407,408],[363,180781,461],{"className":180782},[494],[363,180784,180786,180789],{"className":180785},[407],[363,180787,45101],{"className":180788,"style":45131},[407,408],[363,180790,180792],{"className":180791},[629],[363,180793,180795,180815],{"className":180794},[633,634],[363,180796,180798,180812],{"className":180797},[638],[363,180799,180801],{"className":180800,"style":11480},[642],[363,180802,180803,180806],{"style":136107},[363,180804],{"className":180805,"style":651},[650],[363,180807,180809],{"className":180808},[655,656,657,658],[363,180810,474],{"className":180811},[407,658],[363,180813,666],{"className":180814},[665],[363,180816,180818],{"className":180817},[638],[363,180819,180821],{"className":180820,"style":8315},[642],[363,180822],{},[363,180824,468],{"className":180825},[501],"（命题 2.4 的证明中已给出），取 ",[363,180828,180830,180848],{"className":180829,"translate":367},[366],[363,180831,180833],{"className":180832},[371],[373,180834,180835],{"xmlns":375},[377,180836,180837,180845],{},[380,180838,180839,180841,180843],{},[383,180840,7911],{},[458,180842,471],{},[383,180844,40584],{},[387,180846,180847],{"encoding":389},"k = y",[363,180849,180851,180869],{"className":180850,"ariaHidden":394},[393],[363,180852,180854,180857,180860,180863,180866],{"className":180853},[398],[363,180855],{"className":180856,"style":12944},[402],[363,180858,7911],{"className":180859,"style":8614},[407,408],[363,180861],{"className":180862,"style":506},[505],[363,180864,471],{"className":180865},[510],[363,180867],{"className":180868,"style":506},[505],[363,180870,180872,180875],{"className":180871},[398],[363,180873],{"className":180874,"style":2623},[402],[363,180876,40584],{"className":180877,"style":1328},[407,408]," 并乘以 ",[363,180880,180882,180897],{"className":180881,"translate":367},[366],[363,180883,180885],{"className":180884},[371],[373,180886,180887],{"xmlns":375},[377,180888,180889,180895],{},[380,180890,180891,180893],{},[458,180892,5160],{},[463,180894,465],{},[387,180896,49503],{"encoding":389},[363,180898,180900],{"className":180899,"ariaHidden":394},[393],[363,180901,180903,180906,180909],{"className":180902},[398],[363,180904],{"className":180905,"style":12925},[402],[363,180907,5160],{"className":180908},[407],[363,180910,465],{"className":180911},[407]," 即得。",[11,180914,180915],{},"该损失的梯度结构值得注意：",[363,180917,180919],{"className":180918,"translate":367},[528],[363,180920,180922,181049],{"className":180921,"translate":367},[366],[363,180923,180925],{"className":180924},[371],[373,180926,180927],{"xmlns":375,"display":537},[377,180928,180929,181046],{},[380,180930,180931,180954,180956,180962,180964,180966,180968,180970,180976,180978,180984,180986,180988,180990,180992,180994,181016,181018,181024,181026,181028,181030,181032,181034,181036,181038,181040,181042,181044],{},[586,180932,180933,180944],{},[380,180934,180935,180938],{},[383,180936,180937],{"mathvariant":557},"∂",[7161,180939,180940,180942],{},[383,180941,22240],{"mathvariant":944},[1644,180943,180104],{},[380,180945,180946,180948],{},[383,180947,180937],{"mathvariant":557},[543,180949,180950,180952],{},[383,180951,45101],{},[383,180953,40584],{},[458,180955,471],{},[7161,180957,180958,180960],{},[383,180959,155424],{},[458,180961,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,180963,461],{"stretchy":460},[383,180965,26084],{},[458,180967,468],{"stretchy":460},[458,180969,5160],{},[7161,180971,180972,180974],{},[383,180973,155424],{},[458,180975,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,180977,461],{"stretchy":460},[543,180979,180980,180982],{},[383,180981,45101],{},[383,180983,40584],{},[458,180985,468],{"stretchy":460},[458,180987,10299],{},[463,180989,474],{},[458,180991,898],{"separator":394},[505,180993],{"width":3609},[586,180995,180996,181006],{},[380,180997,180998,181000],{},[383,180999,180937],{"mathvariant":557},[7161,181001,181002,181004],{},[383,181003,22240],{"mathvariant":944},[1644,181005,180104],{},[380,181007,181008,181010],{},[383,181009,180937],{"mathvariant":557},[543,181011,181012,181014],{},[383,181013,45101],{},[383,181015,100360],{},[458,181017,471],{},[7161,181019,181020,181022],{},[383,181021,155424],{},[458,181023,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,181025,461],{"stretchy":460},[383,181027,26084],{},[458,181029,468],{"stretchy":460},[458,181031,3250],{},[463,181033,474],{},[505,181035],{"width":4662},[458,181037,461],{"stretchy":460},[383,181039,100360],{},[458,181041,49854],{"mathvariant":557},[383,181043,40584],{},[458,181045,468],{"stretchy":460},[387,181047,181048],{"encoding":389},"\\frac{\\partial \\mathcal{L}^{\\text{NLL}}}{\\partial \\alpha_y} = \\psi'(S) - \\psi'(\\alpha_y) \\le 0,\n\\qquad\n\\frac{\\partial \\mathcal{L}^{\\text{NLL}}}{\\partial \\alpha_j} = \\psi'(S) > 0 \\quad (j \\ne y)",[363,181050,181052,181207,181263,181357,181521,181577,181637],{"className":181051,"ariaHidden":394},[393],[363,181053,181055,181059,181198,181201,181204],{"className":181054},[398],[363,181056],{"className":181057,"style":181058},[402],"height:2.4904em;vertical-align:-0.9721em;",[363,181060,181062,181065,181195],{"className":181061},[407],[363,181063],{"className":181064},[494,789],[363,181066,181068],{"className":181067},[586],[363,181069,181071,181186],{"className":181070},[633,634],[363,181072,181074,181183],{"className":181073},[638],[363,181075,181078,181129,181137],{"className":181076,"style":181077},[642],"height:1.5183em;",[363,181079,181080,181083],{"style":805},[363,181081],{"className":181082,"style":809},[650],[363,181084,181086,181089],{"className":181085},[407],[363,181087,180937],{"className":181088,"style":121511},[407],[363,181090,181092,181095],{"className":181091},[407],[363,181093,45101],{"className":181094,"style":45131},[407,408],[363,181096,181098],{"className":181097},[629],[363,181099,181101,181121],{"className":181100},[633,634],[363,181102,181104,181118],{"className":181103},[638],[363,181105,181107],{"className":181106,"style":45276},[642],[363,181108,181109,181112],{"style":136107},[363,181110],{"className":181111,"style":651},[650],[363,181113,181115],{"className":181114},[655,656,657,658],[363,181116,40584],{"className":181117,"style":1328},[407,408,658],[363,181119,666],{"className":181120},[665],[363,181122,181124],{"className":181123},[638],[363,181125,181127],{"className":181126,"style":673},[642],[363,181128],{},[363,181130,181131,181134],{"style":821},[363,181132],{"className":181133,"style":809},[650],[363,181135],{"className":181136,"style":829},[828],[363,181138,181139,181142],{"style":832},[363,181140],{"className":181141,"style":809},[650],[363,181143,181145,181148],{"className":181144},[407],[363,181146,180937],{"className":181147,"style":121511},[407],[363,181149,181151,181154],{"className":181150},[407],[363,181152,22240],{"className":181153},[407,971],[363,181155,181157],{"className":181156},[629],[363,181158,181160],{"className":181159},[633],[363,181161,181163],{"className":181162},[638],[363,181164,181166],{"className":181165,"style":52432},[642],[363,181167,181168,181171],{"style":7212},[363,181169],{"className":181170,"style":651},[650],[363,181172,181174],{"className":181173},[655,656,657,658],[363,181175,181177],{"className":181176},[407,658],[363,181178,181180],{"className":181179},[407,4945,658],[363,181181,180104],{"className":181182},[407,658],[363,181184,666],{"className":181185},[665],[363,181187,181189],{"className":181188},[638],[363,181190,181193],{"className":181191,"style":181192},[642],"height:0.9721em;",[363,181194],{},[363,181196],{"className":181197},[501,789],[363,181199],{"className":181200,"style":506},[505],[363,181202,471],{"className":181203},[510],[363,181205],{"className":181206,"style":506},[505],[363,181208,181210,181213,181245,181248,181251,181254,181257,181260],{"className":181209},[398],[363,181211],{"className":181212,"style":102528},[402],[363,181214,181216,181219],{"className":181215},[407],[363,181217,155424],{"className":181218,"style":1328},[407,408],[363,181220,181222],{"className":181221},[629],[363,181223,181225],{"className":181224},[633],[363,181226,181228],{"className":181227},[638],[363,181229,181231],{"className":181230,"style":29318},[642],[363,181232,181233,181236],{"style":8624},[363,181234],{"className":181235,"style":651},[650],[363,181237,181239],{"className":181238},[655,656,657,658],[363,181240,181242],{"className":181241},[407,658],[363,181243,7167],{"className":181244},[407,658],[363,181246,461],{"className":181247},[494],[363,181249,26084],{"className":181250,"style":26208},[407,408],[363,181252,468],{"className":181253},[501],[363,181255],{"className":181256,"style":2934},[505],[363,181258,5160],{"className":181259},[2938],[363,181261],{"className":181262,"style":2934},[505],[363,181264,181266,181270,181302,181305,181345,181348,181351,181354],{"className":181265},[398],[363,181267],{"className":181268,"style":181269},[402],"height:1.088em;vertical-align:-0.2861em;",[363,181271,181273,181276],{"className":181272},[407],[363,181274,155424],{"className":181275,"style":1328},[407,408],[363,181277,181279],{"className":181278},[629],[363,181280,181282],{"className":181281},[633],[363,181283,181285],{"className":181284},[638],[363,181286,181288],{"className":181287,"style":29318},[642],[363,181289,181290,181293],{"style":8624},[363,181291],{"className":181292,"style":651},[650],[363,181294,181296],{"className":181295},[655,656,657,658],[363,181297,181299],{"className":181298},[407,658],[363,181300,7167],{"className":181301},[407,658],[363,181303,461],{"className":181304},[494],[363,181306,181308,181311],{"className":181307},[407],[363,181309,45101],{"className":181310,"style":45131},[407,408],[363,181312,181314],{"className":181313},[629],[363,181315,181317,181337],{"className":181316},[633,634],[363,181318,181320,181334],{"className":181319},[638],[363,181321,181323],{"className":181322,"style":45276},[642],[363,181324,181325,181328],{"style":136107},[363,181326],{"className":181327,"style":651},[650],[363,181329,181331],{"className":181330},[655,656,657,658],[363,181332,40584],{"className":181333,"style":1328},[407,408,658],[363,181335,666],{"className":181336},[665],[363,181338,181340],{"className":181339},[638],[363,181341,181343],{"className":181342,"style":673},[642],[363,181344],{},[363,181346,468],{"className":181347},[501],[363,181349],{"className":181350,"style":506},[505],[363,181352,10299],{"className":181353},[510],[363,181355],{"className":181356,"style":506},[505],[363,181358,181360,181363,181366,181369,181372,181375,181512,181515,181518],{"className":181359},[398],[363,181361],{"className":181362,"style":181058},[402],[363,181364,474],{"className":181365},[407],[363,181367,898],{"className":181368},[920],[363,181370],{"className":181371,"style":3981},[505],[363,181373],{"className":181374,"style":754},[505],[363,181376,181378,181381,181509],{"className":181377},[407],[363,181379],{"className":181380},[494,789],[363,181382,181384],{"className":181383},[586],[363,181385,181387,181501],{"className":181386},[633,634],[363,181388,181390,181498],{"className":181389},[638],[363,181391,181393,181444,181452],{"className":181392,"style":181077},[642],[363,181394,181395,181398],{"style":805},[363,181396],{"className":181397,"style":809},[650],[363,181399,181401,181404],{"className":181400},[407],[363,181402,180937],{"className":181403,"style":121511},[407],[363,181405,181407,181410],{"className":181406},[407],[363,181408,45101],{"className":181409,"style":45131},[407,408],[363,181411,181413],{"className":181412},[629],[363,181414,181416,181436],{"className":181415},[633,634],[363,181417,181419,181433],{"className":181418},[638],[363,181420,181422],{"className":181421,"style":12529},[642],[363,181423,181424,181427],{"style":136107},[363,181425],{"className":181426,"style":651},[650],[363,181428,181430],{"className":181429},[655,656,657,658],[363,181431,100360],{"className":181432,"style":100888},[407,408,658],[363,181434,666],{"className":181435},[665],[363,181437,181439],{"className":181438},[638],[363,181440,181442],{"className":181441,"style":673},[642],[363,181443],{},[363,181445,181446,181449],{"style":821},[363,181447],{"className":181448,"style":809},[650],[363,181450],{"className":181451,"style":829},[828],[363,181453,181454,181457],{"style":832},[363,181455],{"className":181456,"style":809},[650],[363,181458,181460,181463],{"className":181459},[407],[363,181461,180937],{"className":181462,"style":121511},[407],[363,181464,181466,181469],{"className":181465},[407],[363,181467,22240],{"className":181468},[407,971],[363,181470,181472],{"className":181471},[629],[363,181473,181475],{"className":181474},[633],[363,181476,181478],{"className":181477},[638],[363,181479,181481],{"className":181480,"style":52432},[642],[363,181482,181483,181486],{"style":7212},[363,181484],{"className":181485,"style":651},[650],[363,181487,181489],{"className":181488},[655,656,657,658],[363,181490,181492],{"className":181491},[407,658],[363,181493,181495],{"className":181494},[407,4945,658],[363,181496,180104],{"className":181497},[407,658],[363,181499,666],{"className":181500},[665],[363,181502,181504],{"className":181503},[638],[363,181505,181507],{"className":181506,"style":181192},[642],[363,181508],{},[363,181510],{"className":181511},[501,789],[363,181513],{"className":181514,"style":506},[505],[363,181516,471],{"className":181517},[510],[363,181519],{"className":181520,"style":506},[505],[363,181522,181524,181527,181559,181562,181565,181568,181571,181574],{"className":181523},[398],[363,181525],{"className":181526,"style":102528},[402],[363,181528,181530,181533],{"className":181529},[407],[363,181531,155424],{"className":181532,"style":1328},[407,408],[363,181534,181536],{"className":181535},[629],[363,181537,181539],{"className":181538},[633],[363,181540,181542],{"className":181541},[638],[363,181543,181545],{"className":181544,"style":29318},[642],[363,181546,181547,181550],{"style":8624},[363,181548],{"className":181549,"style":651},[650],[363,181551,181553],{"className":181552},[655,656,657,658],[363,181554,181556],{"className":181555},[407,658],[363,181557,7167],{"className":181558},[407,658],[363,181560,461],{"className":181561},[494],[363,181563,26084],{"className":181564,"style":26208},[407,408],[363,181566,468],{"className":181567},[501],[363,181569],{"className":181570,"style":506},[505],[363,181572,3250],{"className":181573},[510],[363,181575],{"className":181576,"style":506},[505],[363,181578,181580,181583,181586,181589,181592,181595,181598,181634],{"className":181579},[398],[363,181581],{"className":181582,"style":487},[402],[363,181584,474],{"className":181585},[407],[363,181587],{"className":181588,"style":88315},[505],[363,181590,461],{"className":181591},[494],[363,181593,100360],{"className":181594,"style":100888},[407,408],[363,181596],{"className":181597,"style":506},[505],[363,181599,181601,181628,181631],{"className":181600},[510],[363,181602,181604],{"className":181603},[510],[363,181605,181607],{"className":181606},[407,4747],[363,181608,181610],{"className":181609},[4751],[363,181611,181613,181616,181625],{"className":181612},[4755],[363,181614],{"className":181615,"style":403},[402],[363,181617,181619],{"className":181618},[4762],[363,181620,181622],{"className":181621},[407],[363,181623,4769],{"className":181624},[510],[363,181626],{"className":181627},[4773],[363,181629],{"className":181630},[505,4777],[363,181632,471],{"className":181633},[510],[363,181635],{"className":181636,"style":506},[505],[363,181638,181640,181643,181646],{"className":181639},[398],[363,181641],{"className":181642,"style":487},[402],[363,181644,40584],{"className":181645,"style":1328},[407,408],[363,181647,468],{"className":181648},[501],[11,181650,2597,181651,181713,181714,16142,181717,181787,181788,16142,181791,181861,181862,181931,181932,181960,181961,181989],{},[363,181652,181654,181672],{"className":181653,"translate":367},[366],[363,181655,181657],{"className":181656},[371],[373,181658,181659],{"xmlns":375},[377,181660,181661,181669],{},[380,181662,181663],{},[7161,181664,181665,181667],{},[383,181666,155424],{},[458,181668,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[387,181670,181671],{"encoding":389},"\\psi'",[363,181673,181675],{"className":181674,"ariaHidden":394},[393],[363,181676,181678,181681],{"className":181677},[398],[363,181679],{"className":181680,"style":64508},[402],[363,181682,181684,181687],{"className":181683},[407],[363,181685,155424],{"className":181686,"style":1328},[407,408],[363,181688,181690],{"className":181689},[629],[363,181691,181693],{"className":181692},[633],[363,181694,181696],{"className":181695},[638],[363,181697,181699],{"className":181698,"style":7209},[642],[363,181700,181701,181704],{"style":7212},[363,181702],{"className":181703,"style":651},[650],[363,181705,181707],{"className":181706},[655,656,657,658],[363,181708,181710],{"className":181709},[407,658],[363,181711,7167],{"className":181712},[407,658]," 为 trigamma 函数（恒正、单调递减）。因此梯度沿两个方向作用：",[1572,181715,181716],{},"提升真实类别的证据",[363,181718,181720,181738],{"className":181719,"translate":367},[366],[363,181721,181723],{"className":181722},[371],[373,181724,181725],{"xmlns":375},[377,181726,181727,181735],{},[380,181728,181729],{},[543,181730,181731,181733],{},[383,181732,45101],{},[383,181734,40584],{},[387,181736,181737],{"encoding":389},"\\alpha_y",[363,181739,181741],{"className":181740,"ariaHidden":394},[393],[363,181742,181744,181747],{"className":181743},[398],[363,181745],{"className":181746,"style":93305},[402],[363,181748,181750,181753],{"className":181749},[407],[363,181751,45101],{"className":181752,"style":45131},[407,408],[363,181754,181756],{"className":181755},[629],[363,181757,181759,181779],{"className":181758},[633,634],[363,181760,181762,181776],{"className":181761},[638],[363,181763,181765],{"className":181764,"style":45276},[642],[363,181766,181767,181770],{"style":136107},[363,181768],{"className":181769,"style":651},[650],[363,181771,181773],{"className":181772},[655,656,657,658],[363,181774,40584],{"className":181775,"style":1328},[407,408,658],[363,181777,666],{"className":181778},[665],[363,181780,181782],{"className":181781},[638],[363,181783,181785],{"className":181784,"style":673},[642],[363,181786],{}," 增大），",[1572,181789,181790],{},"压低其余类别的证据",[363,181792,181794,181812],{"className":181793,"translate":367},[366],[363,181795,181797],{"className":181796},[371],[373,181798,181799],{"xmlns":375},[377,181800,181801,181809],{},[380,181802,181803],{},[543,181804,181805,181807],{},[383,181806,45101],{},[383,181808,100360],{},[387,181810,181811],{"encoding":389},"\\alpha_j",[363,181813,181815],{"className":181814,"ariaHidden":394},[393],[363,181816,181818,181821],{"className":181817},[398],[363,181819],{"className":181820,"style":93305},[402],[363,181822,181824,181827],{"className":181823},[407],[363,181825,45101],{"className":181826,"style":45131},[407,408],[363,181828,181830],{"className":181829},[629],[363,181831,181833,181853],{"className":181832},[633,634],[363,181834,181836,181850],{"className":181835},[638],[363,181837,181839],{"className":181838,"style":12529},[642],[363,181840,181841,181844],{"style":136107},[363,181842],{"className":181843,"style":651},[650],[363,181845,181847],{"className":181846},[655,656,657,658],[363,181848,100360],{"className":181849,"style":100888},[407,408,658],[363,181851,666],{"className":181852},[665],[363,181854,181856],{"className":181855},[638],[363,181857,181859],{"className":181858,"style":673},[642],[363,181860],{}," 减小）。第二条作用有一个退化倾向：若标签之外的证据可被任意压低而不受惩罚，网络便有动机把 ",[363,181863,181865,181882],{"className":181864,"translate":367},[366],[363,181866,181868],{"className":181867},[371],[373,181869,181870],{"xmlns":375},[377,181871,181872,181880],{},[380,181873,181874],{},[543,181875,181876,181878],{},[383,181877,45101],{},[383,181879,100360],{},[387,181881,181811],{"encoding":389},[363,181883,181885],{"className":181884,"ariaHidden":394},[393],[363,181886,181888,181891],{"className":181887},[398],[363,181889],{"className":181890,"style":93305},[402],[363,181892,181894,181897],{"className":181893},[407],[363,181895,45101],{"className":181896,"style":45131},[407,408],[363,181898,181900],{"className":181899},[629],[363,181901,181903,181923],{"className":181902},[633,634],[363,181904,181906,181920],{"className":181905},[638],[363,181907,181909],{"className":181908,"style":12529},[642],[363,181910,181911,181914],{"style":136107},[363,181912],{"className":181913,"style":651},[650],[363,181915,181917],{"className":181916},[655,656,657,658],[363,181918,100360],{"className":181919,"style":100888},[407,408,658],[363,181921,666],{"className":181922},[665],[363,181924,181926],{"className":181925},[638],[363,181927,181929],{"className":181928,"style":673},[642],[363,181930],{}," 全部驱向 ",[363,181933,181935,181948],{"className":181934,"translate":367},[366],[363,181936,181938],{"className":181937},[371],[373,181939,181940],{"xmlns":375},[377,181941,181942,181946],{},[380,181943,181944],{},[463,181945,465],{},[387,181947,465],{"encoding":389},[363,181949,181951],{"className":181950,"ariaHidden":394},[393],[363,181952,181954,181957],{"className":181953},[398],[363,181955],{"className":181956,"style":520},[402],[363,181958,465],{"className":181959},[407],"，从而收缩总证据 ",[363,181962,181964,181977],{"className":181963,"translate":367},[366],[363,181965,181967],{"className":181966},[371],[373,181968,181969],{"xmlns":375},[377,181970,181971,181975],{},[380,181972,181973],{},[383,181974,26084],{},[387,181976,26084],{"encoding":389},[363,181978,181980],{"className":181979,"ariaHidden":394},[393],[363,181981,181983,181986],{"className":181982},[398],[363,181984],{"className":181985,"style":1011},[402],[363,181987,26084],{"className":181988,"style":26208},[407,408],"——这正是 4.3 节引入正则项的直接原因。",[1340,181991,181993],{"title":181992},"推论 4.2（与插值交叉熵的关系）",[11,181994,181995,182060,182061],{},[363,181996,181998,182016],{"className":181997,"translate":367},[366],[363,181999,182001],{"className":182000},[371],[373,182002,182003],{"xmlns":375},[377,182004,182005,182013],{},[380,182006,182007],{},[7161,182008,182009,182011],{},[383,182010,22240],{"mathvariant":944},[1644,182012,180104],{},[387,182014,182015],{"encoding":389},"\\mathcal{L}^{\\text{NLL}}",[363,182017,182019],{"className":182018,"ariaHidden":394},[393],[363,182020,182022,182025],{"className":182021},[398],[363,182023],{"className":182024,"style":52432},[402],[363,182026,182028,182031],{"className":182027},[407],[363,182029,22240],{"className":182030},[407,971],[363,182032,182034],{"className":182033},[629],[363,182035,182037],{"className":182036},[633],[363,182038,182040],{"className":182039},[638],[363,182041,182043],{"className":182042,"style":52432},[642],[363,182044,182045,182048],{"style":7212},[363,182046],{"className":182047,"style":651},[650],[363,182049,182051],{"className":182050},[655,656,657,658],[363,182052,182054],{"className":182053},[407,658],[363,182055,182057],{"className":182056},[407,4945,658],[363,182058,180104],{"className":182059},[407,658]," 是 one-hot 标签下插值交叉熵的 Jensen 上界：\n",[363,182062,182064,182168],{"className":182063,"translate":367},[366],[363,182065,182067],{"className":182066},[371],[373,182068,182069],{"xmlns":375},[377,182070,182071,182165],{},[380,182072,182073,182079,182081,182083,182085,182087,182093,182095,182101,182125,182127,182129,182131,182147,182149,182151,182153,182155,182157,182159],{},[7161,182074,182075,182077],{},[383,182076,22240],{"mathvariant":944},[1644,182078,180104],{},[458,182080,471],{},[458,182082,5160],{},[383,182084,4447],{},[458,182086,4450],{},[543,182088,182089,182091],{},[383,182090,11],{},[383,182092,40584],{},[458,182094,2817],{},[586,182096,182097,182099],{},[463,182098,465],{},[463,182100,2810],{},[380,182102,182103,182105,182115,182117,182123],{},[458,182104,461],{"fence":394},[586,182106,182107,182109],{},[463,182108,465],{},[543,182110,182111,182113],{},[383,182112,45101],{},[383,182114,40584],{},[458,182116,5160],{},[586,182118,182119,182121],{},[463,182120,465],{},[383,182122,26084],{},[458,182124,468],{"fence":394},[458,182126,2817],{},[383,182128,19568],{},[1644,182130,1651],{},[380,182132,182133,182135,182145],{},[458,182134,461],{"fence":394},[7161,182136,182137,182139],{},[383,182138,26084],{},[380,182140,182141,182143],{},[458,182142,5160],{},[463,182144,2810],{},[458,182146,468],{"fence":394},[1644,182148,4630],{},[458,182150,7275],{},[1644,182152,4630],{},[458,182154,5160],{},[383,182156,4447],{},[458,182158,4450],{},[543,182160,182161,182163],{},[383,182162,11],{},[383,182164,40584],{},[387,182166,182167],{"encoding":389},"\\mathcal{L}^{\\text{NLL}} = -\\log p_y + \\frac{1}{2}\\left(\\frac{1}{\\alpha_y} - \\frac{1}{S}\\right) + O\\!\\left(S^{-2}\\right) \\ \\ge \\ -\\log p_y",[363,182169,182171,182221,182290,182574,182654],{"className":182170,"ariaHidden":394},[393],[363,182172,182174,182177,182212,182215,182218],{"className":182173},[398],[363,182175],{"className":182176,"style":52432},[402],[363,182178,182180,182183],{"className":182179},[407],[363,182181,22240],{"className":182182},[407,971],[363,182184,182186],{"className":182185},[629],[363,182187,182189],{"className":182188},[633],[363,182190,182192],{"className":182191},[638],[363,182193,182195],{"className":182194,"style":52432},[642],[363,182196,182197,182200],{"style":7212},[363,182198],{"className":182199,"style":651},[650],[363,182201,182203],{"className":182202},[655,656,657,658],[363,182204,182206],{"className":182205},[407,658],[363,182207,182209],{"className":182208},[407,4945,658],[363,182210,180104],{"className":182211},[407,658],[363,182213],{"className":182214,"style":506},[505],[363,182216,471],{"className":182217},[510],[363,182219],{"className":182220,"style":506},[505],[363,182222,182224,182227,182230,182233,182238,182241,182281,182284,182287],{"className":182223},[398],[363,182225],{"className":182226,"style":153698},[402],[363,182228,5160],{"className":182229},[407],[363,182231],{"className":182232,"style":754},[505],[363,182234,4501,182236],{"className":182235},[1831],[363,182237,4505],{"style":4504},[363,182239],{"className":182240,"style":754},[505],[363,182242,182244,182247],{"className":182243},[407],[363,182245,11],{"className":182246},[407,408],[363,182248,182250],{"className":182249},[629],[363,182251,182253,182273],{"className":182252},[633,634],[363,182254,182256,182270],{"className":182255},[638],[363,182257,182259],{"className":182258,"style":45276},[642],[363,182260,182261,182264],{"style":730},[363,182262],{"className":182263,"style":651},[650],[363,182265,182267],{"className":182266},[655,656,657,658],[363,182268,40584],{"className":182269,"style":1328},[407,408,658],[363,182271,666],{"className":182272},[665],[363,182274,182276],{"className":182275},[638],[363,182277,182279],{"className":182278,"style":673},[642],[363,182280],{},[363,182282],{"className":182283,"style":2934},[505],[363,182285,2817],{"className":182286},[2938],[363,182288],{"className":182289,"style":2934},[505],[363,182291,182293,182296,182364,182367,182565,182568,182571],{"className":182292},[398],[363,182294],{"className":182295,"style":68464},[402],[363,182297,182299,182302,182361],{"className":182298},[407],[363,182300],{"className":182301},[494,789],[363,182303,182305],{"className":182304},[586],[363,182306,182308,182353],{"className":182307},[633,634],[363,182309,182311,182350],{"className":182310},[638],[363,182312,182314,182328,182336],{"className":182313,"style":2871},[642],[363,182315,182316,182319],{"style":2874},[363,182317],{"className":182318,"style":809},[650],[363,182320,182322],{"className":182321},[655,656,657,658],[363,182323,182325],{"className":182324},[407,658],[363,182326,2810],{"className":182327},[407,658],[363,182329,182330,182333],{"style":821},[363,182331],{"className":182332,"style":809},[650],[363,182334],{"className":182335,"style":829},[828],[363,182337,182338,182341],{"style":2897},[363,182339],{"className":182340,"style":809},[650],[363,182342,182344],{"className":182343},[655,656,657,658],[363,182345,182347],{"className":182346},[407,658],[363,182348,465],{"className":182349},[407,658],[363,182351,666],{"className":182352},[665],[363,182354,182356],{"className":182355},[638],[363,182357,182359],{"className":182358,"style":2919},[642],[363,182360],{},[363,182362],{"className":182363},[501,789],[363,182365],{"className":182366,"style":754},[505],[363,182368,182370,182376,182482,182485,182488,182491,182559],{"className":182369},[758],[363,182371,182373],{"className":182372,"style":763},[494,762],[363,182374,461],{"className":182375},[767,4067],[363,182377,182379,182382,182479],{"className":182378},[407],[363,182380],{"className":182381},[494,789],[363,182383,182385],{"className":182384},[586],[363,182386,182388,182470],{"className":182387},[633,634],[363,182389,182391,182467],{"className":182390},[638],[363,182392,182394,182445,182453],{"className":182393,"style":2871},[642],[363,182395,182396,182399],{"style":2874},[363,182397],{"className":182398,"style":809},[650],[363,182400,182402],{"className":182401},[655,656,657,658],[363,182403,182405],{"className":182404},[407,658],[363,182406,182408,182411],{"className":182407},[407,658],[363,182409,45101],{"className":182410,"style":45131},[407,408,658],[363,182412,182414],{"className":182413},[629],[363,182415,182417,182437],{"className":182416},[633,634],[363,182418,182420,182434],{"className":182419},[638],[363,182421,182423],{"className":182422,"style":74609},[642],[363,182424,182425,182428],{"style":136942},[363,182426],{"className":182427,"style":30553},[650],[363,182429,182431],{"className":182430},[655,30557,10021,658],[363,182432,40584],{"className":182433,"style":1328},[407,408,658],[363,182435,666],{"className":182436},[665],[363,182438,182440],{"className":182439},[638],[363,182441,182443],{"className":182442,"style":122065},[642],[363,182444],{},[363,182446,182447,182450],{"style":821},[363,182448],{"className":182449,"style":809},[650],[363,182451],{"className":182452,"style":829},[828],[363,182454,182455,182458],{"style":2897},[363,182456],{"className":182457,"style":809},[650],[363,182459,182461],{"className":182460},[655,656,657,658],[363,182462,182464],{"className":182463},[407,658],[363,182465,465],{"className":182466},[407,658],[363,182468,666],{"className":182469},[665],[363,182471,182473],{"className":182472},[638],[363,182474,182477],{"className":182475,"style":182476},[642],"height:0.5423em;",[363,182478],{},[363,182480],{"className":182481},[501,789],[363,182483],{"className":182484,"style":2934},[505],[363,182486,5160],{"className":182487},[2938],[363,182489],{"className":182490,"style":2934},[505],[363,182492,182494,182497,182556],{"className":182493},[407],[363,182495],{"className":182496},[494,789],[363,182498,182500],{"className":182499},[586],[363,182501,182503,182548],{"className":182502},[633,634],[363,182504,182506,182545],{"className":182505},[638],[363,182507,182509,182523,182531],{"className":182508,"style":2871},[642],[363,182510,182511,182514],{"style":2874},[363,182512],{"className":182513,"style":809},[650],[363,182515,182517],{"className":182516},[655,656,657,658],[363,182518,182520],{"className":182519},[407,658],[363,182521,26084],{"className":182522,"style":26208},[407,408,658],[363,182524,182525,182528],{"style":821},[363,182526],{"className":182527,"style":809},[650],[363,182529],{"className":182530,"style":829},[828],[363,182532,182533,182536],{"style":2897},[363,182534],{"className":182535,"style":809},[650],[363,182537,182539],{"className":182538},[655,656,657,658],[363,182540,182542],{"className":182541},[407,658],[363,182543,465],{"className":182544},[407,658],[363,182546,666],{"className":182547},[665],[363,182549,182551],{"className":182550},[638],[363,182552,182554],{"className":182553,"style":2919},[642],[363,182555],{},[363,182557],{"className":182558},[501,789],[363,182560,182562],{"className":182561,"style":763},[501,762],[363,182563,468],{"className":182564},[767,4067],[363,182566],{"className":182567,"style":2934},[505],[363,182569,2817],{"className":182570},[2938],[363,182572],{"className":182573,"style":2934},[505],[363,182575,182577,182580,182583,182586,182589,182639,182642,182645,182648,182651],{"className":182576},[398],[363,182578],{"className":182579,"style":20910},[402],[363,182581,19568],{"className":182582,"style":625},[407,408],[363,182584],{"className":182585,"style":1859},[505],[363,182587],{"className":182588,"style":754},[505],[363,182590,182592,182598,182633],{"className":182591},[758],[363,182593,182595],{"className":182594,"style":763},[494,762],[363,182596,461],{"className":182597},[767,10021],[363,182599,182601,182604],{"className":182600},[407],[363,182602,26084],{"className":182603,"style":26208},[407,408],[363,182605,182607],{"className":182606},[629],[363,182608,182610],{"className":182609},[633],[363,182611,182613],{"className":182612},[638],[363,182614,182616],{"className":182615,"style":20375},[642],[363,182617,182618,182621],{"style":7212},[363,182619],{"className":182620,"style":651},[650],[363,182622,182624],{"className":182623},[655,656,657,658],[363,182625,182627,182630],{"className":182626},[407,658],[363,182628,5160],{"className":182629},[407,658],[363,182631,2810],{"className":182632},[407,658],[363,182634,182636],{"className":182635,"style":763},[501,762],[363,182637,468],{"className":182638},[767,10021],[363,182640,4630],{"className":182641},[505],[363,182643],{"className":182644,"style":506},[505],[363,182646,7275],{"className":182647},[510],[363,182649,4630],{"className":182650},[505],[363,182652],{"className":182653,"style":506},[505],[363,182655,182657,182660,182663,182666,182671,182674],{"className":182656},[398],[363,182658],{"className":182659,"style":153698},[402],[363,182661,5160],{"className":182662},[407],[363,182664],{"className":182665,"style":754},[505],[363,182667,4501,182669],{"className":182668},[1831],[363,182670,4505],{"style":4504},[363,182672],{"className":182673,"style":754},[505],[363,182675,182677,182680],{"className":182676},[407],[363,182678,11],{"className":182679},[407,408],[363,182681,182683],{"className":182682},[629],[363,182684,182686,182706],{"className":182685},[633,634],[363,182687,182689,182703],{"className":182688},[638],[363,182690,182692],{"className":182691,"style":45276},[642],[363,182693,182694,182697],{"style":730},[363,182695],{"className":182696,"style":651},[650],[363,182698,182700],{"className":182699},[655,656,657,658],[363,182701,40584],{"className":182702,"style":1328},[407,408,658],[363,182704,666],{"className":182705},[665],[363,182707,182709],{"className":182708},[638],[363,182710,182712],{"className":182711,"style":673},[642],[363,182713],{},[11,182715,182716,182718,182719,43112,182981,183130,183131,183384,183385,183478],{},[1572,182717,137993],{}," 由 Jensen 不等式 ",[363,182720,182722,182780],{"className":182721,"translate":367},[366],[363,182723,182725],{"className":182724},[371],[373,182726,182727],{"xmlns":375},[377,182728,182729,182777],{},[380,182730,182731,182733,182735,182737,182739,182745,182747,182749,182751,182753,182755,182757,182763,182765,182767,182769,182771],{},[383,182732,571],{"mathvariant":570},[458,182734,578],{"stretchy":460},[383,182736,4447],{},[458,182738,4450],{},[543,182740,182741,182743],{},[383,182742,157399],{},[383,182744,40584],{},[458,182746,605],{"stretchy":460},[458,182748,10299],{},[383,182750,4447],{},[458,182752,4450],{},[383,182754,571],{"mathvariant":570},[458,182756,578],{"stretchy":460},[543,182758,182759,182761],{},[383,182760,157399],{},[383,182762,40584],{},[458,182764,605],{"stretchy":460},[458,182766,471],{},[383,182768,4447],{},[458,182770,4450],{},[543,182772,182773,182775],{},[383,182774,11],{},[383,182776,40584],{},[387,182778,182779],{"encoding":389},"\\mathbb{E}[\\log \\pi_y] \\le \\log \\mathbb{E}[\\pi_y] = \\log p_y",[363,182781,182783,182855,182927],{"className":182782,"ariaHidden":394},[393],[363,182784,182786,182789,182792,182795,182800,182803,182843,182846,182849,182852],{"className":182785},[398],[363,182787],{"className":182788,"style":618},[402],[363,182790,571],{"className":182791},[407,714],[363,182793,578],{"className":182794},[494],[363,182796,4501,182798],{"className":182797},[1831],[363,182799,4505],{"style":4504},[363,182801],{"className":182802,"style":754},[505],[363,182804,182806,182809],{"className":182805},[407],[363,182807,157399],{"className":182808,"style":1328},[407,408],[363,182810,182812],{"className":182811},[629],[363,182813,182815,182835],{"className":182814},[633,634],[363,182816,182818,182832],{"className":182817},[638],[363,182819,182821],{"className":182820,"style":45276},[642],[363,182822,182823,182826],{"style":19190},[363,182824],{"className":182825,"style":651},[650],[363,182827,182829],{"className":182828},[655,656,657,658],[363,182830,40584],{"className":182831,"style":1328},[407,408,658],[363,182833,666],{"className":182834},[665],[363,182836,182838],{"className":182837},[638],[363,182839,182841],{"className":182840,"style":673},[642],[363,182842],{},[363,182844,605],{"className":182845},[501],[363,182847],{"className":182848,"style":506},[505],[363,182850,10299],{"className":182851},[510],[363,182853],{"className":182854,"style":506},[505],[363,182856,182858,182861,182866,182869,182872,182875,182915,182918,182921,182924],{"className":182857},[398],[363,182859],{"className":182860,"style":618},[402],[363,182862,4501,182864],{"className":182863},[1831],[363,182865,4505],{"style":4504},[363,182867],{"className":182868,"style":754},[505],[363,182870,571],{"className":182871},[407,714],[363,182873,578],{"className":182874},[494],[363,182876,182878,182881],{"className":182877},[407],[363,182879,157399],{"className":182880,"style":1328},[407,408],[363,182882,182884],{"className":182883},[629],[363,182885,182887,182907],{"className":182886},[633,634],[363,182888,182890,182904],{"className":182889},[638],[363,182891,182893],{"className":182892,"style":45276},[642],[363,182894,182895,182898],{"style":19190},[363,182896],{"className":182897,"style":651},[650],[363,182899,182901],{"className":182900},[655,656,657,658],[363,182902,40584],{"className":182903,"style":1328},[407,408,658],[363,182905,666],{"className":182906},[665],[363,182908,182910],{"className":182909},[638],[363,182911,182913],{"className":182912,"style":673},[642],[363,182914],{},[363,182916,605],{"className":182917},[501],[363,182919],{"className":182920,"style":506},[505],[363,182922,471],{"className":182923},[510],[363,182925],{"className":182926,"style":506},[505],[363,182928,182930,182933,182938,182941],{"className":182929},[398],[363,182931],{"className":182932,"style":153698},[402],[363,182934,4501,182936],{"className":182935},[1831],[363,182937,4505],{"style":4504},[363,182939],{"className":182940,"style":754},[505],[363,182942,182944,182947],{"className":182943},[407],[363,182945,11],{"className":182946},[407,408],[363,182948,182950],{"className":182949},[629],[363,182951,182953,182973],{"className":182952},[633,634],[363,182954,182956,182970],{"className":182955},[638],[363,182957,182959],{"className":182958,"style":45276},[642],[363,182960,182961,182964],{"style":730},[363,182962],{"className":182963,"style":651},[650],[363,182965,182967],{"className":182966},[655,656,657,658],[363,182968,40584],{"className":182969,"style":1328},[407,408,658],[363,182971,666],{"className":182972},[665],[363,182974,182976],{"className":182975},[638],[363,182977,182979],{"className":182978,"style":673},[642],[363,182980],{},[363,182982,182984,183016],{"className":182983,"translate":367},[366],[363,182985,182987],{"className":182986},[371],[373,182988,182989],{"xmlns":375},[377,182990,182991,183013],{},[380,182992,182993,182999,183001,183003,183005,183007],{},[7161,182994,182995,182997],{},[383,182996,22240],{"mathvariant":944},[1644,182998,180104],{},[458,183000,7275],{},[458,183002,5160],{},[383,183004,4447],{},[458,183006,4450],{},[543,183008,183009,183011],{},[383,183010,11],{},[383,183012,40584],{},[387,183014,183015],{"encoding":389},"\\mathcal{L}^{\\text{NLL}} \\ge -\\log p_y",[363,183017,183019,183070],{"className":183018,"ariaHidden":394},[393],[363,183020,183022,183026,183061,183064,183067],{"className":183021},[398],[363,183023],{"className":183024,"style":183025},[402],"height:0.9773em;vertical-align:-0.136em;",[363,183027,183029,183032],{"className":183028},[407],[363,183030,22240],{"className":183031},[407,971],[363,183033,183035],{"className":183034},[629],[363,183036,183038],{"className":183037},[633],[363,183039,183041],{"className":183040},[638],[363,183042,183044],{"className":183043,"style":52432},[642],[363,183045,183046,183049],{"style":7212},[363,183047],{"className":183048,"style":651},[650],[363,183050,183052],{"className":183051},[655,656,657,658],[363,183053,183055],{"className":183054},[407,658],[363,183056,183058],{"className":183057},[407,4945,658],[363,183059,180104],{"className":183060},[407,658],[363,183062],{"className":183063,"style":506},[505],[363,183065,7275],{"className":183066},[510],[363,183068],{"className":183069,"style":506},[505],[363,183071,183073,183076,183079,183082,183087,183090],{"className":183072},[398],[363,183074],{"className":183075,"style":153698},[402],[363,183077,5160],{"className":183078},[407],[363,183080],{"className":183081,"style":754},[505],[363,183083,4501,183085],{"className":183084},[1831],[363,183086,4505],{"style":4504},[363,183088],{"className":183089,"style":754},[505],[363,183091,183093,183096],{"className":183092},[407],[363,183094,11],{"className":183095},[407,408],[363,183097,183099],{"className":183098},[629],[363,183100,183102,183122],{"className":183101},[633,634],[363,183103,183105,183119],{"className":183104},[638],[363,183106,183108],{"className":183107,"style":45276},[642],[363,183109,183110,183113],{"style":730},[363,183111],{"className":183112,"style":651},[650],[363,183114,183116],{"className":183115},[655,656,657,658],[363,183117,40584],{"className":183118,"style":1328},[407,408,658],[363,183120,666],{"className":183121},[665],[363,183123,183125],{"className":183124},[638],[363,183126,183128],{"className":183127,"style":673},[642],[363,183129],{},"。渐近展开由 ",[363,183132,183134,183192],{"className":183133,"translate":367},[366],[363,183135,183137],{"className":183136},[371],[373,183138,183139],{"xmlns":375},[377,183140,183141,183189],{},[380,183142,183143,183145,183147,183149,183151,183153,183155,183157,183159,183161,183171,183173,183175,183177,183187],{},[383,183144,155424],{},[458,183146,461],{"stretchy":460},[383,183148,45527],{},[458,183150,468],{"stretchy":460},[458,183152,471],{},[383,183154,4447],{},[458,183156,4450],{},[383,183158,45527],{},[458,183160,5160],{},[586,183162,183163,183165],{},[463,183164,465],{},[380,183166,183167,183169],{},[463,183168,2810],{},[383,183170,45527],{},[458,183172,2817],{},[383,183174,19568],{},[458,183176,461],{"stretchy":460},[7161,183178,183179,183181],{},[383,183180,45527],{},[380,183182,183183,183185],{},[458,183184,5160],{},[463,183186,2810],{},[458,183188,468],{"stretchy":460},[387,183190,183191],{"encoding":389},"\\psi(a) = \\log a - \\frac{1}{2a} + O(a^{-2})",[363,183193,183195,183222,183248,183334],{"className":183194,"ariaHidden":394},[393],[363,183196,183198,183201,183204,183207,183210,183213,183216,183219],{"className":183197},[398],[363,183199],{"className":183200,"style":487},[402],[363,183202,155424],{"className":183203,"style":1328},[407,408],[363,183205,461],{"className":183206},[494],[363,183208,45527],{"className":183209},[407,408],[363,183211,468],{"className":183212},[501],[363,183214],{"className":183215,"style":506},[505],[363,183217,471],{"className":183218},[510],[363,183220],{"className":183221,"style":506},[505],[363,183223,183225,183228,183233,183236,183239,183242,183245],{"className":183224},[398],[363,183226],{"className":183227,"style":403},[402],[363,183229,4501,183231],{"className":183230},[1831],[363,183232,4505],{"style":4504},[363,183234],{"className":183235,"style":754},[505],[363,183237,45527],{"className":183238},[407,408],[363,183240],{"className":183241,"style":2934},[505],[363,183243,5160],{"className":183244},[2938],[363,183246],{"className":183247,"style":2934},[505],[363,183249,183251,183254,183325,183328,183331],{"className":183250},[398],[363,183252],{"className":183253,"style":2852},[402],[363,183255,183257,183260,183322],{"className":183256},[407],[363,183258],{"className":183259},[494,789],[363,183261,183263],{"className":183262},[586],[363,183264,183266,183314],{"className":183265},[633,634],[363,183267,183269,183311],{"className":183268},[638],[363,183270,183272,183289,183297],{"className":183271,"style":2871},[642],[363,183273,183274,183277],{"style":2874},[363,183275],{"className":183276,"style":809},[650],[363,183278,183280],{"className":183279},[655,656,657,658],[363,183281,183283,183286],{"className":183282},[407,658],[363,183284,2810],{"className":183285},[407,658],[363,183287,45527],{"className":183288},[407,408,658],[363,183290,183291,183294],{"style":821},[363,183292],{"className":183293,"style":809},[650],[363,183295],{"className":183296,"style":829},[828],[363,183298,183299,183302],{"style":2897},[363,183300],{"className":183301,"style":809},[650],[363,183303,183305],{"className":183304},[655,656,657,658],[363,183306,183308],{"className":183307},[407,658],[363,183309,465],{"className":183310},[407,658],[363,183312,666],{"className":183313},[665],[363,183315,183317],{"className":183316},[638],[363,183318,183320],{"className":183319,"style":2919},[642],[363,183321],{},[363,183323],{"className":183324},[501,789],[363,183326],{"className":183327,"style":2934},[505],[363,183329,2817],{"className":183330},[2938],[363,183332],{"className":183333,"style":2934},[505],[363,183335,183337,183340,183343,183346,183381],{"className":183336},[398],[363,183338],{"className":183339,"style":20350},[402],[363,183341,19568],{"className":183342,"style":625},[407,408],[363,183344,461],{"className":183345},[494],[363,183347,183349,183352],{"className":183348},[407],[363,183350,45527],{"className":183351},[407,408],[363,183353,183355],{"className":183354},[629],[363,183356,183358],{"className":183357},[633],[363,183359,183361],{"className":183360},[638],[363,183362,183364],{"className":183363,"style":20375},[642],[363,183365,183366,183369],{"style":7212},[363,183367],{"className":183368,"style":651},[650],[363,183370,183372],{"className":183371},[655,656,657,658],[363,183373,183375,183378],{"className":183374},[407,658],[363,183376,5160],{"className":183377},[407,658],[363,183379,2810],{"className":183380},[407,658],[363,183382,468],{"className":183383},[501]," 给出，而 ",[363,183386,183388,183410],{"className":183387,"translate":367},[366],[363,183389,183391],{"className":183390},[371],[373,183392,183393],{"xmlns":375},[377,183394,183395,183407],{},[380,183396,183397,183403,183405],{},[543,183398,183399,183401],{},[383,183400,45101],{},[383,183402,40584],{},[458,183404,10299],{},[383,183406,26084],{},[387,183408,183409],{"encoding":389},"\\alpha_y \\le S",[363,183411,183413,183469],{"className":183412,"ariaHidden":394},[393],[363,183414,183416,183420,183460,183463,183466],{"className":183415},[398],[363,183417],{"className":183418,"style":183419},[402],"height:0.9221em;vertical-align:-0.2861em;",[363,183421,183423,183426],{"className":183422},[407],[363,183424,45101],{"className":183425,"style":45131},[407,408],[363,183427,183429],{"className":183428},[629],[363,183430,183432,183452],{"className":183431},[633,634],[363,183433,183435,183449],{"className":183434},[638],[363,183436,183438],{"className":183437,"style":45276},[642],[363,183439,183440,183443],{"style":136107},[363,183441],{"className":183442,"style":651},[650],[363,183444,183446],{"className":183445},[655,656,657,658],[363,183447,40584],{"className":183448,"style":1328},[407,408,658],[363,183450,666],{"className":183451},[665],[363,183453,183455],{"className":183454},[638],[363,183456,183458],{"className":183457,"style":673},[642],[363,183459],{},[363,183461],{"className":183462,"style":506},[505],[363,183464,10299],{"className":183465},[510],[363,183467],{"className":183468,"style":506},[505],[363,183470,183472,183475],{"className":183471},[398],[363,183473],{"className":183474,"style":1011},[402],[363,183476,26084],{"className":183477,"style":26208},[407,408]," 保证修正项非负。",[11,183480,183481,183482,183485,183486,183514],{},"推论 4.2 揭示了一个在文献中常被忽略的事实：",[1572,183483,183484],{},"EDL 的对数损失并非多项—迪利克雷边缘似然的负对数，而是它加上一个显式的、随证据稀缺而增大的修正项。"," 该项在 ",[363,183487,183489,183502],{"className":183488,"translate":367},[366],[363,183490,183492],{"className":183491},[371],[373,183493,183494],{"xmlns":375},[377,183495,183496,183500],{},[380,183497,183498],{},[383,183499,26084],{},[387,183501,26084],{"encoding":389},[363,183503,183505],{"className":183504,"ariaHidden":394},[393],[363,183506,183508,183511],{"className":183507},[398],[363,183509],{"className":183510,"style":1011},[402],[363,183512,26084],{"className":183513,"style":26208},[407,408]," 大时消失，在证据不足时提供额外压力，其作用与下一小节方差惩罚项在平方损失中的地位完全平行。",[2658,183516,183518],{"id":183517},"_42-平方损失的贝叶斯风险","4.2 平方损失的贝叶斯风险",[11,183520,183521],{},"Sensoy 等人的原始工作采用了平方损失而非对数损失，其闭式更为直观。",[1340,183523,183525],{"title":183524},"命题 4.3（平方风险的闭式）",[11,183526,881,183527,183556,183557],{},[363,183528,183530,183544],{"className":183529,"translate":367},[366],[363,183531,183533],{"className":183532},[371],[373,183534,183535],{"xmlns":375},[377,183536,183537,183541],{},[380,183538,183539],{},[383,183540,40584],{"mathvariant":75560},[387,183542,183543],{"encoding":389},"\\mathbf{y}",[363,183545,183547],{"className":183546,"ariaHidden":394},[393],[363,183548,183550,183553],{"className":183549},[398],[363,183551],{"className":183552,"style":133764},[402],[363,183554,40584],{"className":183555,"style":162090},[407,75905]," 为 one-hot 标签，则\n",[363,183558,183560,183685],{"className":183559,"translate":367},[366],[363,183561,183563],{"className":183562},[371],[373,183564,183565],{"xmlns":375},[377,183566,183567,183682],{},[380,183568,183569,183576,183578,183584,183604,183606,183620],{},[7161,183570,183571,183573],{},[383,183572,22240],{"mathvariant":944},[1644,183574,183575],{},"MSE",[458,183577,471],{},[543,183579,183580,183582],{},[383,183581,571],{"mathvariant":570},[383,183583,157399],{"mathvariant":136008},[380,183585,183586,183588,183590,183592,183594,183596,183602],{},[458,183587,578],{"fence":394},[383,183589,558],{"mathvariant":557},[383,183591,40584],{"mathvariant":75560},[458,183593,5160],{},[383,183595,157399],{"mathvariant":136008},[7161,183597,183598,183600],{},[383,183599,558],{"mathvariant":557},[463,183601,2810],{},[458,183603,605],{"fence":394},[458,183605,471],{},[7900,183607,183608,183610,183618],{},[458,183609,13808],{},[380,183611,183612,183614,183616],{},[383,183613,7911],{},[458,183615,471],{},[463,183617,465],{},[383,183619,11041],{},[380,183621,183622,183624,183626,183632,183634,183640,183646,183648,183680],{},[458,183623,578],{"fence":394},[458,183625,461],{"stretchy":460},[543,183627,183628,183630],{},[383,183629,40584],{},[383,183631,7911],{},[458,183633,5160],{},[543,183635,183636,183638],{},[383,183637,11],{},[383,183639,7911],{},[7161,183641,183642,183644],{},[458,183643,468],{"stretchy":460},[463,183645,2810],{},[458,183647,2817],{},[586,183649,183650,183672],{},[380,183651,183652,183658,183660,183662,183664,183670],{},[543,183653,183654,183656],{},[383,183655,11],{},[383,183657,7911],{},[458,183659,461],{"stretchy":460},[463,183661,465],{},[458,183663,5160],{},[543,183665,183666,183668],{},[383,183667,11],{},[383,183669,7911],{},[458,183671,468],{"stretchy":460},[380,183673,183674,183676,183678],{},[383,183675,26084],{},[458,183677,2817],{},[463,183679,465],{},[458,183681,605],{"fence":394},[387,183683,183684],{"encoding":389},"\\mathcal{L}^{\\text{MSE}} = \\mathbb{E}_{\\boldsymbol{\\pi}}\\left[\\|\\mathbf{y} - \\boldsymbol{\\pi}\\|^2\\right] = \\sum_{k=1}^K \\left[(y_k - p_k)^2 + \\frac{p_k(1 - p_k)}{S + 1}\\right]",[363,183686,183688,183738,183873],{"className":183687,"ariaHidden":394},[393],[363,183689,183691,183694,183729,183732,183735],{"className":183690},[398],[363,183692],{"className":183693,"style":52432},[402],[363,183695,183697,183700],{"className":183696},[407],[363,183698,22240],{"className":183699},[407,971],[363,183701,183703],{"className":183702},[629],[363,183704,183706],{"className":183705},[633],[363,183707,183709],{"className":183708},[638],[363,183710,183712],{"className":183711,"style":52432},[642],[363,183713,183714,183717],{"style":7212},[363,183715],{"className":183716,"style":651},[650],[363,183718,183720],{"className":183719},[655,656,657,658],[363,183721,183723],{"className":183722},[407,658],[363,183724,183726],{"className":183725},[407,4945,658],[363,183727,183575],{"className":183728},[407,658],[363,183730],{"className":183731,"style":506},[505],[363,183733,471],{"className":183734},[510],[363,183736],{"className":183737,"style":506},[505],[363,183739,183741,183744,183793,183796,183864,183867,183870],{"className":183740},[398],[363,183742],{"className":183743,"style":20910},[402],[363,183745,183747,183750],{"className":183746},[407],[363,183748,571],{"className":183749},[407,714],[363,183751,183753],{"className":183752},[629],[363,183754,183756,183785],{"className":183755},[633,634],[363,183757,183759,183782],{"className":183758},[638],[363,183760,183762],{"className":183761,"style":153717},[642],[363,183763,183764,183767],{"style":730},[363,183765],{"className":183766,"style":651},[650],[363,183768,183770],{"className":183769},[655,656,657,658],[363,183771,183773],{"className":183772},[407,658],[363,183774,183776],{"className":183775},[407,658],[363,183777,183779],{"className":183778},[407,658],[363,183780,157399],{"className":183781,"style":157433},[407,136068,658],[363,183783,666],{"className":183784},[665],[363,183786,183788],{"className":183787},[638],[363,183789,183791],{"className":183790,"style":8315},[642],[363,183792],{},[363,183794],{"className":183795,"style":754},[505],[363,183797,183799,183805,183808,183811,183814,183817,183820,183829,183858],{"className":183798},[758],[363,183800,183802],{"className":183801,"style":763},[494,762],[363,183803,578],{"className":183804},[767,10021],[363,183806,558],{"className":183807},[407],[363,183809,40584],{"className":183810,"style":162090},[407,75905],[363,183812],{"className":183813,"style":2934},[505],[363,183815,5160],{"className":183816},[2938],[363,183818],{"className":183819,"style":2934},[505],[363,183821,183823],{"className":183822},[407],[363,183824,183826],{"className":183825},[407],[363,183827,157399],{"className":183828,"style":157433},[407,136068],[363,183830,183832,183835],{"className":183831},[407],[363,183833,558],{"className":183834},[407],[363,183836,183838],{"className":183837},[629],[363,183839,183841],{"className":183840},[633],[363,183842,183844],{"className":183843},[638],[363,183845,183847],{"className":183846,"style":20375},[642],[363,183848,183849,183852],{"style":7212},[363,183850],{"className":183851,"style":651},[650],[363,183853,183855],{"className":183854},[655,656,657,658],[363,183856,2810],{"className":183857},[407,658],[363,183859,183861],{"className":183860,"style":763},[501,762],[363,183862,605],{"className":183863},[767,10021],[363,183865],{"className":183866,"style":506},[505],[363,183868,471],{"className":183869},[510],[363,183871],{"className":183872,"style":506},[505],[363,183874,183876,183879,183939,183942],{"className":183875},[398],[363,183877],{"className":183878,"style":68464},[402],[363,183880,183882,183885],{"className":183881},[1831],[363,183883,13808],{"className":183884,"style":40007},[1831,1832,5963],[363,183886,183888],{"className":183887},[629],[363,183889,183891,183931],{"className":183890},[633,634],[363,183892,183894,183928],{"className":183893},[638],[363,183895,183897,183917],{"className":183896,"style":133494},[642],[363,183898,183899,183902],{"style":40023},[363,183900],{"className":183901,"style":651},[650],[363,183903,183905],{"className":183904},[655,656,657,658],[363,183906,183908,183911,183914],{"className":183907},[407,658],[363,183909,7911],{"className":183910,"style":8614},[407,408,658],[363,183912,471],{"className":183913},[510,658],[363,183915,465],{"className":183916},[407,658],[363,183918,183919,183922],{"style":133517},[363,183920],{"className":183921,"style":651},[650],[363,183923,183925],{"className":183924},[655,656,657,658],[363,183926,11041],{"className":183927,"style":11129},[407,408,658],[363,183929,666],{"className":183930},[665],[363,183932,183934],{"className":183933},[638],[363,183935,183937],{"className":183936,"style":40042},[642],[363,183938],{},[363,183940],{"className":183941,"style":754},[505],[363,183943,183945,183951,183954,183994,183997,184000,184003,184043,184072,184075,184078,184081,184244],{"className":183944},[758],[363,183946,183948],{"className":183947,"style":763},[494,762],[363,183949,578],{"className":183950},[767,4067],[363,183952,461],{"className":183953},[494],[363,183955,183957,183960],{"className":183956},[407],[363,183958,40584],{"className":183959,"style":1328},[407,408],[363,183961,183963],{"className":183962},[629],[363,183964,183966,183986],{"className":183965},[633,634],[363,183967,183969,183983],{"className":183968},[638],[363,183970,183972],{"className":183971,"style":643},[642],[363,183973,183974,183977],{"style":19190},[363,183975],{"className":183976,"style":651},[650],[363,183978,183980],{"className":183979},[655,656,657,658],[363,183981,7911],{"className":183982,"style":8614},[407,408,658],[363,183984,666],{"className":183985},[665],[363,183987,183989],{"className":183988},[638],[363,183990,183992],{"className":183991,"style":8315},[642],[363,183993],{},[363,183995],{"className":183996,"style":2934},[505],[363,183998,5160],{"className":183999},[2938],[363,184001],{"className":184002,"style":2934},[505],[363,184004,184006,184009],{"className":184005},[407],[363,184007,11],{"className":184008},[407,408],[363,184010,184012],{"className":184011},[629],[363,184013,184015,184035],{"className":184014},[633,634],[363,184016,184018,184032],{"className":184017},[638],[363,184019,184021],{"className":184020,"style":643},[642],[363,184022,184023,184026],{"style":730},[363,184024],{"className":184025,"style":651},[650],[363,184027,184029],{"className":184028},[655,656,657,658],[363,184030,7911],{"className":184031,"style":8614},[407,408,658],[363,184033,666],{"className":184034},[665],[363,184036,184038],{"className":184037},[638],[363,184039,184041],{"className":184040,"style":8315},[642],[363,184042],{},[363,184044,184046,184049],{"className":184045},[501],[363,184047,468],{"className":184048},[501],[363,184050,184052],{"className":184051},[629],[363,184053,184055],{"className":184054},[633],[363,184056,184058],{"className":184057},[638],[363,184059,184061],{"className":184060,"style":20375},[642],[363,184062,184063,184066],{"style":7212},[363,184064],{"className":184065,"style":651},[650],[363,184067,184069],{"className":184068},[655,656,657,658],[363,184070,2810],{"className":184071},[407,658],[363,184073],{"className":184074,"style":2934},[505],[363,184076,2817],{"className":184077},[2938],[363,184079],{"className":184080,"style":2934},[505],[363,184082,184084,184087,184241],{"className":184083},[407],[363,184085],{"className":184086},[494,789],[363,184088,184090],{"className":184089},[586],[363,184091,184093,184233],{"className":184092},[633,634],[363,184094,184096,184230],{"className":184095},[638],[363,184097,184099,184119,184127],{"className":184098,"style":26740},[642],[363,184100,184101,184104],{"style":2874},[363,184102],{"className":184103,"style":809},[650],[363,184105,184107],{"className":184106},[655,656,657,658],[363,184108,184110,184113,184116],{"className":184109},[407,658],[363,184111,26084],{"className":184112,"style":26208},[407,408,658],[363,184114,2817],{"className":184115},[2938,658],[363,184117,465],{"className":184118},[407,658],[363,184120,184121,184124],{"style":821},[363,184122],{"className":184123,"style":809},[650],[363,184125],{"className":184126,"style":829},[828],[363,184128,184129,184132],{"style":26765},[363,184130],{"className":184131,"style":809},[650],[363,184133,184135],{"className":184134},[655,656,657,658],[363,184136,184138,184178,184181,184184,184187,184227],{"className":184137},[407,658],[363,184139,184141,184144],{"className":184140},[407,658],[363,184142,11],{"className":184143},[407,408,658],[363,184145,184147],{"className":184146},[629],[363,184148,184150,184170],{"className":184149},[633,634],[363,184151,184153,184167],{"className":184152},[638],[363,184154,184156],{"className":184155,"style":6445},[642],[363,184157,184158,184161],{"style":101564},[363,184159],{"className":184160,"style":30553},[650],[363,184162,184164],{"className":184163},[655,30557,10021,658],[363,184165,7911],{"className":184166,"style":8614},[407,408,658],[363,184168,666],{"className":184169},[665],[363,184171,184173],{"className":184172},[638],[363,184174,184176],{"className":184175,"style":101583},[642],[363,184177],{},[363,184179,461],{"className":184180},[494,658],[363,184182,465],{"className":184183},[407,658],[363,184185,5160],{"className":184186},[2938,658],[363,184188,184190,184193],{"className":184189},[407,658],[363,184191,11],{"className":184192},[407,408,658],[363,184194,184196],{"className":184195},[629],[363,184197,184199,184219],{"className":184198},[633,634],[363,184200,184202,184216],{"className":184201},[638],[363,184203,184205],{"className":184204,"style":6445},[642],[363,184206,184207,184210],{"style":101564},[363,184208],{"className":184209,"style":30553},[650],[363,184211,184213],{"className":184212},[655,30557,10021,658],[363,184214,7911],{"className":184215,"style":8614},[407,408,658],[363,184217,666],{"className":184218},[665],[363,184220,184222],{"className":184221},[638],[363,184223,184225],{"className":184224,"style":101583},[642],[363,184226],{},[363,184228,468],{"className":184229},[501,658],[363,184231,666],{"className":184232},[665],[363,184234,184236],{"className":184235},[638],[363,184237,184239],{"className":184238,"style":16776},[642],[363,184240],{},[363,184242],{"className":184243},[501,789],[363,184245,184247],{"className":184246,"style":763},[501,762],[363,184248,605],{"className":184249},[767,4067],[11,184251,184252,184254,184255,184689,184690,185250],{},[1572,184253,137993],{}," 逐项展开：",[363,184256,184258,184338],{"className":184257,"translate":367},[366],[363,184259,184261],{"className":184260},[371],[373,184262,184263],{"xmlns":375},[377,184264,184265,184335],{},[380,184266,184267,184269,184271,184273,184279,184281,184287,184293,184295,184297,184299,184305,184307,184313,184319,184321,184323,184325,184327,184333],{},[383,184268,571],{"mathvariant":570},[458,184270,578],{"stretchy":460},[458,184272,461],{"stretchy":460},[543,184274,184275,184277],{},[383,184276,40584],{},[383,184278,7911],{},[458,184280,5160],{},[543,184282,184283,184285],{},[383,184284,157399],{},[383,184286,7911],{},[7161,184288,184289,184291],{},[458,184290,468],{"stretchy":460},[463,184292,2810],{},[458,184294,605],{"stretchy":460},[458,184296,471],{},[458,184298,461],{"stretchy":460},[543,184300,184301,184303],{},[383,184302,40584],{},[383,184304,7911],{},[458,184306,5160],{},[543,184308,184309,184311],{},[383,184310,11],{},[383,184312,7911],{},[7161,184314,184315,184317],{},[458,184316,468],{"stretchy":460},[463,184318,2810],{},[458,184320,2817],{},[383,184322,147639],{"mathvariant":557},[458,184324,4450],{},[458,184326,461],{"stretchy":460},[543,184328,184329,184331],{},[383,184330,157399],{},[383,184332,7911],{},[458,184334,468],{"stretchy":460},[387,184336,184337],{"encoding":389},"\\mathbb{E}[(y_k - \\pi_k)^2] = (y_k - p_k)^2 + \\operatorname{Var}(\\pi_k)",[363,184339,184341,184402,184489,184547,184631],{"className":184340,"ariaHidden":394},[393],[363,184342,184344,184347,184350,184353,184393,184396,184399],{"className":184343},[398],[363,184345],{"className":184346,"style":487},[402],[363,184348,571],{"className":184349},[407,714],[363,184351,123276],{"className":184352},[494],[363,184354,184356,184359],{"className":184355},[407],[363,184357,40584],{"className":184358,"style":1328},[407,408],[363,184360,184362],{"className":184361},[629],[363,184363,184365,184385],{"className":184364},[633,634],[363,184366,184368,184382],{"className":184367},[638],[363,184369,184371],{"className":184370,"style":643},[642],[363,184372,184373,184376],{"style":19190},[363,184374],{"className":184375,"style":651},[650],[363,184377,184379],{"className":184378},[655,656,657,658],[363,184380,7911],{"className":184381,"style":8614},[407,408,658],[363,184383,666],{"className":184384},[665],[363,184386,184388],{"className":184387},[638],[363,184389,184391],{"className":184390,"style":8315},[642],[363,184392],{},[363,184394],{"className":184395,"style":2934},[505],[363,184397,5160],{"className":184398},[2938],[363,184400],{"className":184401,"style":2934},[505],[363,184403,184405,184408,184448,184477,184480,184483,184486],{"className":184404},[398],[363,184406],{"className":184407,"style":20350},[402],[363,184409,184411,184414],{"className":184410},[407],[363,184412,157399],{"className":184413,"style":1328},[407,408],[363,184415,184417],{"className":184416},[629],[363,184418,184420,184440],{"className":184419},[633,634],[363,184421,184423,184437],{"className":184422},[638],[363,184424,184426],{"className":184425,"style":643},[642],[363,184427,184428,184431],{"style":19190},[363,184429],{"className":184430,"style":651},[650],[363,184432,184434],{"className":184433},[655,656,657,658],[363,184435,7911],{"className":184436,"style":8614},[407,408,658],[363,184438,666],{"className":184439},[665],[363,184441,184443],{"className":184442},[638],[363,184444,184446],{"className":184445,"style":8315},[642],[363,184447],{},[363,184449,184451,184454],{"className":184450},[501],[363,184452,468],{"className":184453},[501],[363,184455,184457],{"className":184456},[629],[363,184458,184460],{"className":184459},[633],[363,184461,184463],{"className":184462},[638],[363,184464,184466],{"className":184465,"style":20375},[642],[363,184467,184468,184471],{"style":7212},[363,184469],{"className":184470,"style":651},[650],[363,184472,184474],{"className":184473},[655,656,657,658],[363,184475,2810],{"className":184476},[407,658],[363,184478,605],{"className":184479},[501],[363,184481],{"className":184482,"style":506},[505],[363,184484,471],{"className":184485},[510],[363,184487],{"className":184488,"style":506},[505],[363,184490,184492,184495,184498,184538,184541,184544],{"className":184491},[398],[363,184493],{"className":184494,"style":487},[402],[363,184496,461],{"className":184497},[494],[363,184499,184501,184504],{"className":184500},[407],[363,184502,40584],{"className":184503,"style":1328},[407,408],[363,184505,184507],{"className":184506},[629],[363,184508,184510,184530],{"className":184509},[633,634],[363,184511,184513,184527],{"className":184512},[638],[363,184514,184516],{"className":184515,"style":643},[642],[363,184517,184518,184521],{"style":19190},[363,184519],{"className":184520,"style":651},[650],[363,184522,184524],{"className":184523},[655,656,657,658],[363,184525,7911],{"className":184526,"style":8614},[407,408,658],[363,184528,666],{"className":184529},[665],[363,184531,184533],{"className":184532},[638],[363,184534,184536],{"className":184535,"style":8315},[642],[363,184537],{},[363,184539],{"className":184540,"style":2934},[505],[363,184542,5160],{"className":184543},[2938],[363,184545],{"className":184546,"style":2934},[505],[363,184548,184550,184553,184593,184622,184625,184628],{"className":184549},[398],[363,184551],{"className":184552,"style":20350},[402],[363,184554,184556,184559],{"className":184555},[407],[363,184557,11],{"className":184558},[407,408],[363,184560,184562],{"className":184561},[629],[363,184563,184565,184585],{"className":184564},[633,634],[363,184566,184568,184582],{"className":184567},[638],[363,184569,184571],{"className":184570,"style":643},[642],[363,184572,184573,184576],{"style":730},[363,184574],{"className":184575,"style":651},[650],[363,184577,184579],{"className":184578},[655,656,657,658],[363,184580,7911],{"className":184581,"style":8614},[407,408,658],[363,184583,666],{"className":184584},[665],[363,184586,184588],{"className":184587},[638],[363,184589,184591],{"className":184590,"style":8315},[642],[363,184592],{},[363,184594,184596,184599],{"className":184595},[501],[363,184597,468],{"className":184598},[501],[363,184600,184602],{"className":184601},[629],[363,184603,184605],{"className":184604},[633],[363,184606,184608],{"className":184607},[638],[363,184609,184611],{"className":184610,"style":20375},[642],[363,184612,184613,184616],{"style":7212},[363,184614],{"className":184615,"style":651},[650],[363,184617,184619],{"className":184618},[655,656,657,658],[363,184620,2810],{"className":184621},[407,658],[363,184623],{"className":184624,"style":2934},[505],[363,184626,2817],{"className":184627},[2938],[363,184629],{"className":184630,"style":2934},[505],[363,184632,184634,184637,184643,184646,184686],{"className":184633},[398],[363,184635],{"className":184636,"style":487},[402],[363,184638,184640],{"className":184639},[1831],[363,184641,147639],{"className":184642},[407,33009],[363,184644,461],{"className":184645},[494],[363,184647,184649,184652],{"className":184648},[407],[363,184650,157399],{"className":184651,"style":1328},[407,408],[363,184653,184655],{"className":184654},[629],[363,184656,184658,184678],{"className":184657},[633,634],[363,184659,184661,184675],{"className":184660},[638],[363,184662,184664],{"className":184663,"style":643},[642],[363,184665,184666,184669],{"style":19190},[363,184667],{"className":184668,"style":651},[650],[363,184670,184672],{"className":184671},[655,656,657,658],[363,184673,7911],{"className":184674,"style":8614},[407,408,658],[363,184676,666],{"className":184677},[665],[363,184679,184681],{"className":184680},[638],[363,184682,184684],{"className":184683,"style":8315},[642],[363,184685],{},[363,184687,468],{"className":184688},[501],"。由命题 2.1，",[363,184691,184693,184797],{"className":184692,"translate":367},[366],[363,184694,184696],{"className":184695},[371],[373,184697,184698],{"xmlns":375},[377,184699,184700,184794],{},[380,184701,184702,184704,184706,184708,184714,184716,184718,184760,184762],{},[383,184703,147639],{"mathvariant":557},[458,184705,4450],{},[458,184707,461],{"stretchy":460},[543,184709,184710,184712],{},[383,184711,157399],{},[383,184713,7911],{},[458,184715,468],{"stretchy":460},[458,184717,471],{},[586,184719,184720,184742],{},[380,184721,184722,184728,184730,184732,184734,184740],{},[543,184723,184724,184726],{},[383,184725,45101],{},[383,184727,7911],{},[458,184729,461],{"stretchy":460},[383,184731,26084],{},[458,184733,5160],{},[543,184735,184736,184738],{},[383,184737,45101],{},[383,184739,7911],{},[458,184741,468],{"stretchy":460},[380,184743,184744,184750,184752,184754,184756,184758],{},[7161,184745,184746,184748],{},[383,184747,26084],{},[463,184749,2810],{},[458,184751,461],{"stretchy":460},[383,184753,26084],{},[458,184755,2817],{},[463,184757,465],{},[458,184759,468],{"stretchy":460},[458,184761,471],{},[586,184763,184764,184786],{},[380,184765,184766,184772,184774,184776,184778,184784],{},[543,184767,184768,184770],{},[383,184769,11],{},[383,184771,7911],{},[458,184773,461],{"stretchy":460},[463,184775,465],{},[458,184777,5160],{},[543,184779,184780,184782],{},[383,184781,11],{},[383,184783,7911],{},[458,184785,468],{"stretchy":460},[380,184787,184788,184790,184792],{},[383,184789,26084],{},[458,184791,2817],{},[463,184793,465],{},[387,184795,184796],{"encoding":389},"\\operatorname{Var}(\\pi_k) = \\frac{\\alpha_k(S - \\alpha_k)}{S^2(S+1)} = \\frac{p_k(1-p_k)}{S+1}",[363,184798,184800,184867,185080],{"className":184799,"ariaHidden":394},[393],[363,184801,184803,184806,184812,184815,184855,184858,184861,184864],{"className":184802},[398],[363,184804],{"className":184805,"style":487},[402],[363,184807,184809],{"className":184808},[1831],[363,184810,147639],{"className":184811},[407,33009],[363,184813,461],{"className":184814},[494],[363,184816,184818,184821],{"className":184817},[407],[363,184819,157399],{"className":184820,"style":1328},[407,408],[363,184822,184824],{"className":184823},[629],[363,184825,184827,184847],{"className":184826},[633,634],[363,184828,184830,184844],{"className":184829},[638],[363,184831,184833],{"className":184832,"style":643},[642],[363,184834,184835,184838],{"style":19190},[363,184836],{"className":184837,"style":651},[650],[363,184839,184841],{"className":184840},[655,656,657,658],[363,184842,7911],{"className":184843,"style":8614},[407,408,658],[363,184845,666],{"className":184846},[665],[363,184848,184850],{"className":184849},[638],[363,184851,184853],{"className":184852,"style":8315},[642],[363,184854],{},[363,184856,468],{"className":184857},[501],[363,184859],{"className":184860,"style":506},[505],[363,184862,471],{"className":184863},[510],[363,184865],{"className":184866,"style":506},[505],[363,184868,184870,184873,185071,185074,185077],{"className":184869},[398],[363,184871],{"className":184872,"style":150425},[402],[363,184874,184876,184879,185068],{"className":184875},[407],[363,184877],{"className":184878},[494,789],[363,184880,184882],{"className":184881},[586],[363,184883,184885,185060],{"className":184884},[633,634],[363,184886,184888,185057],{"className":184887},[638],[363,184889,184891,184946,184954],{"className":184890,"style":26740},[642],[363,184892,184893,184896],{"style":2874},[363,184894],{"className":184895,"style":809},[650],[363,184897,184899],{"className":184898},[655,656,657,658],[363,184900,184902,184931,184934,184937,184940,184943],{"className":184901},[407,658],[363,184903,184905,184908],{"className":184904},[407,658],[363,184906,26084],{"className":184907,"style":26208},[407,408,658],[363,184909,184911],{"className":184910},[629],[363,184912,184914],{"className":184913},[633],[363,184915,184917],{"className":184916},[638],[363,184918,184920],{"className":184919,"style":45806},[642],[363,184921,184922,184925],{"style":45809},[363,184923],{"className":184924,"style":30553},[650],[363,184926,184928],{"className":184927},[655,30557,10021,658],[363,184929,2810],{"className":184930},[407,658],[363,184932,461],{"className":184933},[494,658],[363,184935,26084],{"className":184936,"style":26208},[407,408,658],[363,184938,2817],{"className":184939},[2938,658],[363,184941,465],{"className":184942},[407,658],[363,184944,468],{"className":184945},[501,658],[363,184947,184948,184951],{"style":821},[363,184949],{"className":184950,"style":809},[650],[363,184952],{"className":184953,"style":829},[828],[363,184955,184956,184959],{"style":26765},[363,184957],{"className":184958,"style":809},[650],[363,184960,184962],{"className":184961},[655,656,657,658],[363,184963,184965,185005,185008,185011,185014,185054],{"className":184964},[407,658],[363,184966,184968,184971],{"className":184967},[407,658],[363,184969,45101],{"className":184970,"style":45131},[407,408,658],[363,184972,184974],{"className":184973},[629],[363,184975,184977,184997],{"className":184976},[633,634],[363,184978,184980,184994],{"className":184979},[638],[363,184981,184983],{"className":184982,"style":6445},[642],[363,184984,184985,184988],{"style":159942},[363,184986],{"className":184987,"style":30553},[650],[363,184989,184991],{"className":184990},[655,30557,10021,658],[363,184992,7911],{"className":184993,"style":8614},[407,408,658],[363,184995,666],{"className":184996},[665],[363,184998,185000],{"className":184999},[638],[363,185001,185003],{"className":185002,"style":101583},[642],[363,185004],{},[363,185006,461],{"className":185007},[494,658],[363,185009,26084],{"className":185010,"style":26208},[407,408,658],[363,185012,5160],{"className":185013},[2938,658],[363,185015,185017,185020],{"className":185016},[407,658],[363,185018,45101],{"className":185019,"style":45131},[407,408,658],[363,185021,185023],{"className":185022},[629],[363,185024,185026,185046],{"className":185025},[633,634],[363,185027,185029,185043],{"className":185028},[638],[363,185030,185032],{"className":185031,"style":6445},[642],[363,185033,185034,185037],{"style":159942},[363,185035],{"className":185036,"style":30553},[650],[363,185038,185040],{"className":185039},[655,30557,10021,658],[363,185041,7911],{"className":185042,"style":8614},[407,408,658],[363,185044,666],{"className":185045},[665],[363,185047,185049],{"className":185048},[638],[363,185050,185052],{"className":185051,"style":101583},[642],[363,185053],{},[363,185055,468],{"className":185056},[501,658],[363,185058,666],{"className":185059},[665],[363,185061,185063],{"className":185062},[638],[363,185064,185066],{"className":185065,"style":45949},[642],[363,185067],{},[363,185069],{"className":185070},[501,789],[363,185072],{"className":185073,"style":506},[505],[363,185075,471],{"className":185076},[510],[363,185078],{"className":185079,"style":506},[505],[363,185081,185083,185087],{"className":185082},[398],[363,185084],{"className":185085,"style":185086},[402],"height:1.4133em;vertical-align:-0.4033em;",[363,185088,185090,185093,185247],{"className":185089},[407],[363,185091],{"className":185092},[494,789],[363,185094,185096],{"className":185095},[586],[363,185097,185099,185239],{"className":185098},[633,634],[363,185100,185102,185236],{"className":185101},[638],[363,185103,185105,185125,185133],{"className":185104,"style":26740},[642],[363,185106,185107,185110],{"style":2874},[363,185108],{"className":185109,"style":809},[650],[363,185111,185113],{"className":185112},[655,656,657,658],[363,185114,185116,185119,185122],{"className":185115},[407,658],[363,185117,26084],{"className":185118,"style":26208},[407,408,658],[363,185120,2817],{"className":185121},[2938,658],[363,185123,465],{"className":185124},[407,658],[363,185126,185127,185130],{"style":821},[363,185128],{"className":185129,"style":809},[650],[363,185131],{"className":185132,"style":829},[828],[363,185134,185135,185138],{"style":26765},[363,185136],{"className":185137,"style":809},[650],[363,185139,185141],{"className":185140},[655,656,657,658],[363,185142,185144,185184,185187,185190,185193,185233],{"className":185143},[407,658],[363,185145,185147,185150],{"className":185146},[407,658],[363,185148,11],{"className":185149},[407,408,658],[363,185151,185153],{"className":185152},[629],[363,185154,185156,185176],{"className":185155},[633,634],[363,185157,185159,185173],{"className":185158},[638],[363,185160,185162],{"className":185161,"style":6445},[642],[363,185163,185164,185167],{"style":101564},[363,185165],{"className":185166,"style":30553},[650],[363,185168,185170],{"className":185169},[655,30557,10021,658],[363,185171,7911],{"className":185172,"style":8614},[407,408,658],[363,185174,666],{"className":185175},[665],[363,185177,185179],{"className":185178},[638],[363,185180,185182],{"className":185181,"style":101583},[642],[363,185183],{},[363,185185,461],{"className":185186},[494,658],[363,185188,465],{"className":185189},[407,658],[363,185191,5160],{"className":185192},[2938,658],[363,185194,185196,185199],{"className":185195},[407,658],[363,185197,11],{"className":185198},[407,408,658],[363,185200,185202],{"className":185201},[629],[363,185203,185205,185225],{"className":185204},[633,634],[363,185206,185208,185222],{"className":185207},[638],[363,185209,185211],{"className":185210,"style":6445},[642],[363,185212,185213,185216],{"style":101564},[363,185214],{"className":185215,"style":30553},[650],[363,185217,185219],{"className":185218},[655,30557,10021,658],[363,185220,7911],{"className":185221,"style":8614},[407,408,658],[363,185223,666],{"className":185224},[665],[363,185226,185228],{"className":185227},[638],[363,185229,185231],{"className":185230,"style":101583},[642],[363,185232],{},[363,185234,468],{"className":185235},[501,658],[363,185237,666],{"className":185238},[665],[363,185240,185242],{"className":185241},[638],[363,185243,185245],{"className":185244,"style":16776},[642],[363,185246],{},[363,185248],{"className":185249},[501,789],"。求和即得。",[11,185252,185253,185254,185257,185258,185328,185329,185332,185333,185481,185482,185533],{},"该损失的两项具有不同的角色。",[1572,185255,185256],{},"第一项是拟合项","：在 ",[363,185259,185261,185279],{"className":185260,"translate":367},[366],[363,185262,185264],{"className":185263},[371],[373,185265,185266],{"xmlns":375},[377,185267,185268,185276],{},[380,185269,185270],{},[543,185271,185272,185274],{},[383,185273,11],{},[383,185275,7911],{},[387,185277,185278],{"encoding":389},"p_k",[363,185280,185282],{"className":185281,"ariaHidden":394},[393],[363,185283,185285,185288],{"className":185284},[398],[363,185286],{"className":185287,"style":2623},[402],[363,185289,185291,185294],{"className":185290},[407],[363,185292,11],{"className":185293},[407,408],[363,185295,185297],{"className":185296},[629],[363,185298,185300,185320],{"className":185299},[633,634],[363,185301,185303,185317],{"className":185302},[638],[363,185304,185306],{"className":185305,"style":643},[642],[363,185307,185308,185311],{"style":730},[363,185309],{"className":185310,"style":651},[650],[363,185312,185314],{"className":185313},[655,656,657,658],[363,185315,7911],{"className":185316,"style":8614},[407,408,658],[363,185318,666],{"className":185319},[665],[363,185321,185323],{"className":185322},[638],[363,185324,185326],{"className":185325,"style":8315},[642],[363,185327],{}," 退化为确定性预测时，它退化为 one-hot 编码下的均方误差。",[1572,185330,185331],{},"第二项是方差惩罚项","：它正比于每个分量的伯努利方差 ",[363,185334,185336,185368],{"className":185335,"translate":367},[366],[363,185337,185339],{"className":185338},[371],[373,185340,185341],{"xmlns":375},[377,185342,185343,185365],{},[380,185344,185345,185351,185353,185355,185357,185363],{},[543,185346,185347,185349],{},[383,185348,11],{},[383,185350,7911],{},[458,185352,461],{"stretchy":460},[463,185354,465],{},[458,185356,5160],{},[543,185358,185359,185361],{},[383,185360,11],{},[383,185362,7911],{},[458,185364,468],{"stretchy":460},[387,185366,185367],{"encoding":389},"p_k(1-p_k)",[363,185369,185371,185432],{"className":185370,"ariaHidden":394},[393],[363,185372,185374,185377,185417,185420,185423,185426,185429],{"className":185373},[398],[363,185375],{"className":185376,"style":487},[402],[363,185378,185380,185383],{"className":185379},[407],[363,185381,11],{"className":185382},[407,408],[363,185384,185386],{"className":185385},[629],[363,185387,185389,185409],{"className":185388},[633,634],[363,185390,185392,185406],{"className":185391},[638],[363,185393,185395],{"className":185394,"style":643},[642],[363,185396,185397,185400],{"style":730},[363,185398],{"className":185399,"style":651},[650],[363,185401,185403],{"className":185402},[655,656,657,658],[363,185404,7911],{"className":185405,"style":8614},[407,408,658],[363,185407,666],{"className":185408},[665],[363,185410,185412],{"className":185411},[638],[363,185413,185415],{"className":185414,"style":8315},[642],[363,185416],{},[363,185418,461],{"className":185419},[494],[363,185421,465],{"className":185422},[407],[363,185424],{"className":185425,"style":2934},[505],[363,185427,5160],{"className":185428},[2938],[363,185430],{"className":185431,"style":2934},[505],[363,185433,185435,185438,185478],{"className":185434},[398],[363,185436],{"className":185437,"style":487},[402],[363,185439,185441,185444],{"className":185440},[407],[363,185442,11],{"className":185443},[407,408],[363,185445,185447],{"className":185446},[629],[363,185448,185450,185470],{"className":185449},[633,634],[363,185451,185453,185467],{"className":185452},[638],[363,185454,185456],{"className":185455,"style":643},[642],[363,185457,185458,185461],{"style":730},[363,185459],{"className":185460,"style":651},[650],[363,185462,185464],{"className":185463},[655,656,657,658],[363,185465,7911],{"className":185466,"style":8614},[407,408,658],[363,185468,666],{"className":185469},[665],[363,185471,185473],{"className":185472},[638],[363,185474,185476],{"className":185475,"style":8315},[642],[363,185477],{},[363,185479,468],{"className":185480},[501],"，反比于总证据 ",[363,185483,185485,185503],{"className":185484,"translate":367},[366],[363,185486,185488],{"className":185487},[371],[373,185489,185490],{"xmlns":375},[377,185491,185492,185500],{},[380,185493,185494,185496,185498],{},[383,185495,26084],{},[458,185497,2817],{},[463,185499,465],{},[387,185501,185502],{"encoding":389},"S + 1",[363,185504,185506,185524],{"className":185505,"ariaHidden":394},[393],[363,185507,185509,185512,185515,185518,185521],{"className":185508},[398],[363,185510],{"className":185511,"style":133899},[402],[363,185513,26084],{"className":185514,"style":26208},[407,408],[363,185516],{"className":185517,"style":2934},[505],[363,185519,2817],{"className":185520},[2938],[363,185522],{"className":185523,"style":2934},[505],[363,185525,185527,185530],{"className":185526},[398],[363,185528],{"className":185529,"style":520},[402],[363,185531,465],{"className":185532},[407],"。其作用是双重的：",[7009,185535,185536,185572],{},[7012,185537,185538,185539,185567,185568,185571],{},"当证据稀缺（",[363,185540,185542,185555],{"className":185541,"translate":367},[366],[363,185543,185545],{"className":185544},[371],[373,185546,185547],{"xmlns":375},[377,185548,185549,185553],{},[380,185550,185551],{},[383,185552,26084],{},[387,185554,26084],{"encoding":389},[363,185556,185558],{"className":185557,"ariaHidden":394},[393],[363,185559,185561,185564],{"className":185560},[398],[363,185562],{"className":185563,"style":1011},[402],[363,185565,26084],{"className":185566,"style":26208},[407,408]," 小）时，方差项较大，迫使模型",[1572,185569,185570],{},"不得","以低方差的方式给出尖锐预测——这是一种自适应的软惩罚，其强度由数据本身决定，而非人为设定的超参数。",[7012,185573,185574,185575,2756,185603,185672,185673,185701],{},"当证据变化时，",[363,185576,185578,185591],{"className":185577,"translate":367},[366],[363,185579,185581],{"className":185580},[371],[373,185582,185583],{"xmlns":375},[377,185584,185585,185589],{},[380,185586,185587],{},[383,185588,26084],{},[387,185590,26084],{"encoding":389},[363,185592,185594],{"className":185593,"ariaHidden":394},[393],[363,185595,185597,185600],{"className":185596},[398],[363,185598],{"className":185599,"style":1011},[402],[363,185601,26084],{"className":185602,"style":26208},[407,408],[363,185604,185606,185623],{"className":185605,"translate":367},[366],[363,185607,185609],{"className":185608},[371],[373,185610,185611],{"xmlns":375},[377,185612,185613,185621],{},[380,185614,185615],{},[543,185616,185617,185619],{},[383,185618,11],{},[383,185620,7911],{},[387,185622,185278],{"encoding":389},[363,185624,185626],{"className":185625,"ariaHidden":394},[393],[363,185627,185629,185632],{"className":185628},[398],[363,185630],{"className":185631,"style":2623},[402],[363,185633,185635,185638],{"className":185634},[407],[363,185636,11],{"className":185637},[407,408],[363,185639,185641],{"className":185640},[629],[363,185642,185644,185664],{"className":185643},[633,634],[363,185645,185647,185661],{"className":185646},[638],[363,185648,185650],{"className":185649,"style":643},[642],[363,185651,185652,185655],{"style":730},[363,185653],{"className":185654,"style":651},[650],[363,185656,185658],{"className":185657},[655,656,657,658],[363,185659,7911],{"className":185660,"style":8614},[407,408,658],[363,185662,666],{"className":185663},[665],[363,185665,185667],{"className":185666},[638],[363,185668,185670],{"className":185669,"style":8315},[642],[363,185671],{}," 同时进入两项，形成张力：增大 ",[363,185674,185676,185689],{"className":185675,"translate":367},[366],[363,185677,185679],{"className":185678},[371],[373,185680,185681],{"xmlns":375},[377,185682,185683,185687],{},[380,185684,185685],{},[383,185686,26084],{},[387,185688,26084],{"encoding":389},[363,185690,185692],{"className":185691,"ariaHidden":394},[393],[363,185693,185695,185698],{"className":185694},[398],[363,185696],{"className":185697,"style":1011},[402],[363,185699,26084],{"className":185700,"style":26208},[407,408]," 可以压低方差项，却会强化拟合项。因此最优解不会退化为「证据全为零」的平凡解。",[2658,185703,185705],{"id":185704},"_43-证据正则化与退火-kl","4.3 证据正则化与退火 KL",[11,185707,185708,185709,185712,185713,185790,185791,185794],{},"仅有拟合损失仍不足以约束错误预测上的证据。原因在于 4.1 节的梯度分析：拟合项只对",[1572,185710,185711],{},"真实类别","的证据给出直接的提升压力，而对错误类别上的证据，它只通过 ",[363,185714,185716,185740],{"className":185715,"translate":367},[366],[363,185717,185719],{"className":185718},[371],[373,185720,185721],{"xmlns":375},[377,185722,185723,185737],{},[380,185724,185725,185731,185733,185735],{},[7161,185726,185727,185729],{},[383,185728,155424],{},[458,185730,7167],{"mathvariant":557,"lspace":1594,"rspace":1594},[458,185732,461],{"stretchy":460},[383,185734,26084],{},[458,185736,468],{"stretchy":460},[387,185738,185739],{"encoding":389},"\\psi'(S)",[363,185741,185743],{"className":185742,"ariaHidden":394},[393],[363,185744,185746,185749,185781,185784,185787],{"className":185745},[398],[363,185747],{"className":185748,"style":7190},[402],[363,185750,185752,185755],{"className":185751},[407],[363,185753,155424],{"className":185754,"style":1328},[407,408],[363,185756,185758],{"className":185757},[629],[363,185759,185761],{"className":185760},[633],[363,185762,185764],{"className":185763},[638],[363,185765,185767],{"className":185766,"style":7209},[642],[363,185768,185769,185772],{"style":7212},[363,185770],{"className":185771,"style":651},[650],[363,185773,185775],{"className":185774},[655,656,657,658],[363,185776,185778],{"className":185777},[407,658],[363,185779,7167],{"className":185780},[407,658],[363,185782,461],{"className":185783},[494],[363,185785,26084],{"className":185786,"style":26208},[407,408],[363,185788,468],{"className":185789},[501]," 给出一个整体的压制信号，这一信号与证据在各类别间的分配无关。后果是：",[1572,185792,185793],{},"当一个样本被错误分类时，网络可以通过在错误类别上堆积证据来降低损失","，而这恰恰是我们希望惩罚的行为。",[11,185796,185797],{},"正则项的构造基于一个「反事实」的迪利克雷参数：抹去真实类别的证据，保留其余。",[1340,185799,185801],{"title":185800},"定义 4.4（反事实参数与证据正则）",[11,185802,185803,185804,185979,185980,186008,186009],{},"令 ",[363,185805,185807,185846],{"className":185806,"translate":367},[366],[363,185808,185810],{"className":185809},[371],[373,185811,185812],{"xmlns":375},[377,185813,185814,185843],{},[380,185815,185816,185822,185824,185826,185828,185830,185832,185834,185836,185838,185841],{},[12158,185817,185818,185820],{"accent":394},[383,185819,45101],{"mathvariant":136008},[458,185821,12164],{},[458,185823,471],{},[383,185825,40584],{"mathvariant":75560},[458,185827,2817],{},[458,185829,461],{"stretchy":460},[463,185831,465],{"mathvariant":75560},[458,185833,5160],{},[383,185835,40584],{"mathvariant":75560},[458,185837,468],{"stretchy":460},[458,185839,185840],{},"⊙",[383,185842,45101],{"mathvariant":136008},[387,185844,185845],{"encoding":389},"\\tilde{\\boldsymbol{\\alpha}} = \\mathbf{y} + (\\mathbf{1} - \\mathbf{y}) \\odot \\boldsymbol{\\alpha}",[363,185847,185849,185904,185922,185943,185964],{"className":185848,"ariaHidden":394},[393],[363,185850,185852,185856,185895,185898,185901],{"className":185851},[398],[363,185853],{"className":185854,"style":185855},[402],"height:0.6813em;",[363,185857,185859],{"className":185858},[407,12198],[363,185860,185862],{"className":185861},[633],[363,185863,185865],{"className":185864},[638],[363,185866,185868,185882],{"className":185867,"style":185855},[642],[363,185869,185870,185873],{"style":12210},[363,185871],{"className":185872,"style":809},[650],[363,185874,185876],{"className":185875},[407],[363,185877,185879],{"className":185878},[407],[363,185880,45101],{"className":185881},[407,136068],[363,185883,185885,185888],{"style":185884},"top:-3.3634em;",[363,185886],{"className":185887,"style":809},[650],[363,185889,185892],{"className":185890,"style":185891},[12226],"left:-0.25em;",[363,185893,12164],{"className":185894},[407],[363,185896],{"className":185897,"style":506},[505],[363,185899,471],{"className":185900},[510],[363,185902],{"className":185903,"style":506},[505],[363,185905,185907,185910,185913,185916,185919],{"className":185906},[398],[363,185908],{"className":185909,"style":40668},[402],[363,185911,40584],{"className":185912,"style":162090},[407,75905],[363,185914],{"className":185915,"style":2934},[505],[363,185917,2817],{"className":185918},[2938],[363,185920],{"className":185921,"style":2934},[505],[363,185923,185925,185928,185931,185934,185937,185940],{"className":185924},[398],[363,185926],{"className":185927,"style":487},[402],[363,185929,461],{"className":185930},[494],[363,185932,465],{"className":185933},[407,75905],[363,185935],{"className":185936,"style":2934},[505],[363,185938,5160],{"className":185939},[2938],[363,185941],{"className":185942,"style":2934},[505],[363,185944,185946,185949,185952,185955,185958,185961],{"className":185945},[398],[363,185947],{"className":185948,"style":487},[402],[363,185950,40584],{"className":185951,"style":162090},[407,75905],[363,185953,468],{"className":185954},[501],[363,185956],{"className":185957,"style":2934},[505],[363,185959,185840],{"className":185960},[2938],[363,185962],{"className":185963,"style":2934},[505],[363,185965,185967,185970],{"className":185966},[398],[363,185968],{"className":185969,"style":135617},[402],[363,185971,185973],{"className":185972},[407],[363,185974,185976],{"className":185975},[407],[363,185977,45101],{"className":185978},[407,136068],"，即把真实类别处的参数置为 ",[363,185981,185983,185996],{"className":185982,"translate":367},[366],[363,185984,185986],{"className":185985},[371],[373,185987,185988],{"xmlns":375},[377,185989,185990,185994],{},[380,185991,185992],{},[463,185993,465],{},[387,185995,465],{"encoding":389},[363,185997,185999],{"className":185998,"ariaHidden":394},[393],[363,186000,186002,186005],{"className":186001},[398],[363,186003],{"className":186004,"style":520},[402],[363,186006,465],{"className":186007},[407],"、其余保持不变。证据正则项定义为\n",[363,186010,186012,186073],{"className":186011,"translate":367},[366],[363,186013,186015],{"className":186014},[371],[373,186016,186017],{"xmlns":375},[377,186018,186019,186070],{},[380,186020,186021,186028,186030,186032,186034],{},[7161,186022,186023,186025],{},[383,186024,22240],{"mathvariant":944},[1644,186026,186027],{},"reg",[458,186029,471],{},[383,186031,33010],{"mathvariant":557},[458,186033,4450],{},[380,186035,186036,186038,186040,186042,186044,186050,186052,186054,186056,186058,186060,186062,186064,186066,186068],{},[458,186037,578],{"fence":394},[383,186039,137065],{"mathvariant":557},[458,186041,4450],{},[458,186043,461],{"stretchy":460},[12158,186045,186046,186048],{"accent":394},[383,186047,45101],{"mathvariant":136008},[458,186049,12164],{},[458,186051,468],{"stretchy":460},[1644,186053,1646],{},[458,186055,558],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[1644,186057,1646],{},[383,186059,137065],{"mathvariant":557},[458,186061,4450],{},[458,186063,461],{"stretchy":460},[463,186065,465],{"mathvariant":75560},[458,186067,468],{"stretchy":460},[458,186069,605],{"fence":394},[387,186071,186072],{"encoding":389},"\\mathcal{L}^{\\text{reg}} = \\operatorname{KL}\\left[\\operatorname{Dir}(\\tilde{\\boldsymbol{\\alpha}}) \\,\\big\\|\\, \\operatorname{Dir}(\\mathbf{1})\\right]",[363,186074,186076,186126],{"className":186075,"ariaHidden":394},[393],[363,186077,186079,186082,186117,186120,186123],{"className":186078},[398],[363,186080],{"className":186081,"style":1011},[402],[363,186083,186085,186088],{"className":186084},[407],[363,186086,22240],{"className":186087},[407,971],[363,186089,186091],{"className":186090},[629],[363,186092,186094],{"className":186093},[633],[363,186095,186097],{"className":186096},[638],[363,186098,186100],{"className":186099,"style":50700},[642],[363,186101,186102,186105],{"style":7212},[363,186103],{"className":186104,"style":651},[650],[363,186106,186108],{"className":186107},[655,656,657,658],[363,186109,186111],{"className":186110},[407,658],[363,186112,186114],{"className":186113},[407,4945,658],[363,186115,186027],{"className":186116},[407,658],[363,186118],{"className":186119,"style":506},[505],[363,186121,471],{"className":186122},[510],[363,186124],{"className":186125,"style":506},[505],[363,186127,186129,186132,186138,186141],{"className":186128},[398],[363,186130],{"className":186131,"style":20910},[402],[363,186133,186135],{"className":186134},[1831],[363,186136,33010],{"className":186137},[407,33009],[363,186139],{"className":186140,"style":754},[505],[363,186142,186144,186150,186156,186159,186196,186199,186202,186239,186242,186245,186251,186254,186257,186260],{"className":186143},[758],[363,186145,186147],{"className":186146,"style":763},[494,762],[363,186148,578],{"className":186149},[767,10021],[363,186151,186153],{"className":186152},[1831],[363,186154,137065],{"className":186155},[407,33009],[363,186157,461],{"className":186158},[494],[363,186160,186162],{"className":186161},[407,12198],[363,186163,186165],{"className":186164},[633],[363,186166,186168],{"className":186167},[638],[363,186169,186171,186185],{"className":186170,"style":185855},[642],[363,186172,186173,186176],{"style":12210},[363,186174],{"className":186175,"style":809},[650],[363,186177,186179],{"className":186178},[407],[363,186180,186182],{"className":186181},[407],[363,186183,45101],{"className":186184},[407,136068],[363,186186,186187,186190],{"style":185884},[363,186188],{"className":186189,"style":809},[650],[363,186191,186193],{"className":186192,"style":185891},[12226],[363,186194,12164],{"className":186195},[407],[363,186197,468],{"className":186198},[501],[363,186200],{"className":186201,"style":754},[505],[363,186203,186205],{"className":186204},[407],[363,186206,186208],{"className":186207},[767,15176],[363,186209,186211,186231],{"className":186210},[633,634],[363,186212,186214,186228],{"className":186213},[638],[363,186215,186217],{"className":186216,"style":15186},[642],[363,186218,186219,186222],{"style":15189},[363,186220],{"className":186221,"style":15193},[650],[363,186223,186224],{"style":15196},[6670,186225,186226],{"xmlns":6672,"width":15199,"height":9797,"viewBox":15200},[6678,186227],{"d":15203},[363,186229,666],{"className":186230},[665],[363,186232,186234],{"className":186233},[638],[363,186235,186237],{"className":186236,"style":15213},[642],[363,186238],{},[363,186240],{"className":186241,"style":754},[505],[363,186243],{"className":186244,"style":754},[505],[363,186246,186248],{"className":186247},[1831],[363,186249,137065],{"className":186250},[407,33009],[363,186252,461],{"className":186253},[494],[363,186255,465],{"className":186256},[407,75905],[363,186258,468],{"className":186259},[501],[363,186261,186263],{"className":186262,"style":763},[501,762],[363,186264,605],{"className":186265},[767,10021],[11,186267,5924,186268,186317,186318,186405],{},[363,186269,186271,186293],{"className":186270,"translate":367},[366],[363,186272,186274],{"className":186273},[371],[373,186275,186276],{"xmlns":375},[377,186277,186278,186290],{},[380,186279,186280,186282,186284,186286,186288],{},[383,186281,137065],{"mathvariant":557},[458,186283,4450],{},[458,186285,461],{"stretchy":460},[463,186287,465],{"mathvariant":75560},[458,186289,468],{"stretchy":460},[387,186291,186292],{"encoding":389},"\\operatorname{Dir}(\\mathbf{1})",[363,186294,186296],{"className":186295,"ariaHidden":394},[393],[363,186297,186299,186302,186308,186311,186314],{"className":186298},[398],[363,186300],{"className":186301,"style":487},[402],[363,186303,186305],{"className":186304},[1831],[363,186306,137065],{"className":186307},[407,33009],[363,186309,461],{"className":186310},[494],[363,186312,465],{"className":186313},[407,75905],[363,186315,468],{"className":186316},[501]," 正是无信息均匀先验。该 KL 散度只依赖于非目标类别上的证据：若网络在错误类别上给出大量证据，",[363,186319,186321,186347],{"className":186320,"translate":367},[366],[363,186322,186324],{"className":186323},[371],[373,186325,186326],{"xmlns":375},[377,186327,186328,186344],{},[380,186329,186330,186332,186334,186336,186342],{},[383,186331,137065],{"mathvariant":557},[458,186333,4450],{},[458,186335,461],{"stretchy":460},[12158,186337,186338,186340],{"accent":394},[383,186339,45101],{"mathvariant":136008},[458,186341,12164],{},[458,186343,468],{"stretchy":460},[387,186345,186346],{"encoding":389},"\\operatorname{Dir}(\\tilde{\\boldsymbol{\\alpha}})",[363,186348,186350],{"className":186349,"ariaHidden":394},[393],[363,186351,186353,186356,186362,186365,186402],{"className":186352},[398],[363,186354],{"className":186355,"style":487},[402],[363,186357,186359],{"className":186358},[1831],[363,186360,137065],{"className":186361},[407,33009],[363,186363,461],{"className":186364},[494],[363,186366,186368],{"className":186367},[407,12198],[363,186369,186371],{"className":186370},[633],[363,186372,186374],{"className":186373},[638],[363,186375,186377,186391],{"className":186376,"style":185855},[642],[363,186378,186379,186382],{"style":12210},[363,186380],{"className":186381,"style":809},[650],[363,186383,186385],{"className":186384},[407],[363,186386,186388],{"className":186387},[407],[363,186389,45101],{"className":186390},[407,136068],[363,186392,186393,186396],{"style":185884},[363,186394],{"className":186395,"style":809},[650],[363,186397,186399],{"className":186398,"style":185891},[12226],[363,186400,12164],{"className":186401},[407],[363,186403,468],{"className":186404},[501]," 将显著偏离均匀分布，KL 随之增大。",[1340,186407,186409],{"title":186408},"命题 4.5（Dirichlet 的 KL 散度）",[11,186410,14608,186411,137612,186551,187237,187238,187295,187296,187382,187383],{},[363,186412,186414,186446],{"className":186413,"translate":367},[366],[363,186415,186417],{"className":186416},[371],[373,186418,186419],{"xmlns":375},[377,186420,186421,186443],{},[380,186422,186423,186425,186427,186429,186431],{},[383,186424,45101],{"mathvariant":136008},[458,186426,898],{"separator":394},[383,186428,84464],{"mathvariant":136008},[458,186430,6256],{},[7900,186432,186433,186435,186441],{},[383,186434,1379],{"mathvariant":570},[380,186436,186437,186439],{},[458,186438,3250],{},[463,186440,474],{},[383,186442,11041],{},[387,186444,186445],{"encoding":389},"\\boldsymbol{\\alpha}, \\boldsymbol{\\beta} \\in \\mathbb{R}_{>0}^K",[363,186447,186449,186488],{"className":186448,"ariaHidden":394},[393],[363,186450,186452,186455,186464,186467,186470,186479,186482,186485],{"className":186451},[398],[363,186453],{"className":186454,"style":403},[402],[363,186456,186458],{"className":186457},[407],[363,186459,186461],{"className":186460},[407],[363,186462,45101],{"className":186463},[407,136068],[363,186465,898],{"className":186466},[920],[363,186468],{"className":186469,"style":754},[505],[363,186471,186473],{"className":186472},[407],[363,186474,186476],{"className":186475},[407],[363,186477,84464],{"className":186478,"style":150142},[407,136068],[363,186480],{"className":186481,"style":506},[505],[363,186483,6256],{"className":186484},[510],[363,186486],{"className":186487,"style":506},[505],[363,186489,186491,186494],{"className":186490},[398],[363,186492],{"className":186493,"style":136204},[402],[363,186495,186497,186500],{"className":186496},[407],[363,186498,1379],{"className":186499},[407,714],[363,186501,186503],{"className":186502},[629],[363,186504,186506,186543],{"className":186505},[633,634],[363,186507,186509,186540],{"className":186508},[638],[363,186510,186512,186529],{"className":186511,"style":52432},[642],[363,186513,186514,186517],{"style":136225},[363,186515],{"className":186516,"style":651},[650],[363,186518,186520],{"className":186519},[655,656,657,658],[363,186521,186523,186526],{"className":186522},[407,658],[363,186524,3250],{"className":186525},[510,658],[363,186527,474],{"className":186528},[407,658],[363,186530,186531,186534],{"style":7212},[363,186532],{"className":186533,"style":651},[650],[363,186535,186537],{"className":186536},[655,656,657,658],[363,186538,11041],{"className":186539,"style":11129},[407,408,658],[363,186541,666],{"className":186542},[665],[363,186544,186546],{"className":186545},[638],[363,186547,186549],{"className":186548,"style":136261},[642],[363,186550],{},[363,186552,186554,186694],{"className":186553,"translate":367},[366],[363,186555,186557],{"className":186556},[371],[373,186558,186559],{"xmlns":375},[377,186560,186561,186691],{},[380,186562,186563,186565,186567,186599,186601,186603,186605,186627,186629,186643,186645,186651,186653,186659,186661,186663,186665,186667,186673,186675,186677,186679,186681,186687,186689],{},[383,186564,33010],{"mathvariant":557},[458,186566,4450],{},[380,186568,186569,186571,186573,186575,186577,186579,186581,186583,186585,186587,186589,186591,186593,186595,186597],{},[458,186570,578],{"fence":394},[383,186572,137065],{"mathvariant":557},[458,186574,4450],{},[458,186576,461],{"stretchy":460},[383,186578,45101],{"mathvariant":136008},[458,186580,468],{"stretchy":460},[1644,186582,1646],{},[458,186584,558],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[1644,186586,1646],{},[383,186588,137065],{"mathvariant":557},[458,186590,4450],{},[458,186592,461],{"stretchy":460},[383,186594,84464],{"mathvariant":136008},[458,186596,468],{"stretchy":460},[458,186598,605],{"fence":394},[458,186600,471],{},[383,186602,4447],{},[458,186604,4450],{},[586,186606,186607,186617],{},[380,186608,186609,186611,186613,186615],{},[383,186610,39638],{},[458,186612,461],{"stretchy":460},[383,186614,84464],{"mathvariant":136008},[458,186616,468],{"stretchy":460},[380,186618,186619,186621,186623,186625],{},[383,186620,39638],{},[458,186622,461],{"stretchy":460},[383,186624,45101],{"mathvariant":136008},[458,186626,468],{"stretchy":460},[458,186628,2817],{},[7900,186630,186631,186633,186641],{},[458,186632,13808],{},[380,186634,186635,186637,186639],{},[383,186636,7911],{},[458,186638,471],{},[463,186640,465],{},[383,186642,11041],{},[458,186644,461],{"stretchy":460},[543,186646,186647,186649],{},[383,186648,45101],{},[383,186650,7911],{},[458,186652,5160],{},[543,186654,186655,186657],{},[383,186656,84464],{},[383,186658,7911],{},[458,186660,468],{"stretchy":460},[458,186662,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,186664,155424],{},[458,186666,461],{"stretchy":460},[543,186668,186669,186671],{},[383,186670,45101],{},[383,186672,7911],{},[458,186674,468],{"stretchy":460},[458,186676,5160],{},[383,186678,155424],{},[458,186680,461],{"stretchy":460},[543,186682,186683,186685],{},[383,186684,45101],{},[463,186686,474],{},[458,186688,468],{"stretchy":460},[458,186690,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[387,186692,186693],{"encoding":389},"\\operatorname{KL}\\left[\\operatorname{Dir}(\\boldsymbol{\\alpha}) \\,\\big\\|\\, \\operatorname{Dir}(\\boldsymbol{\\beta})\\right] = \\log\\frac{B(\\boldsymbol{\\beta})}{B(\\boldsymbol{\\alpha})} + \\sum_{k=1}^K (\\alpha_k - \\beta_k)\\big(\\psi(\\alpha_k) - \\psi(\\alpha_0)\\big)",[363,186695,186697,186824,186945,187063,187176],{"className":186696,"ariaHidden":394},[393],[363,186698,186700,186703,186709,186712,186815,186818,186821],{"className":186699},[398],[363,186701],{"className":186702,"style":20910},[402],[363,186704,186706],{"className":186705},[1831],[363,186707,33010],{"className":186708},[407,33009],[363,186710],{"className":186711,"style":754},[505],[363,186713,186715,186721,186727,186730,186739,186742,186745,186782,186785,186788,186794,186797,186806,186809],{"className":186714},[758],[363,186716,186718],{"className":186717,"style":763},[494,762],[363,186719,578],{"className":186720},[767,10021],[363,186722,186724],{"className":186723},[1831],[363,186725,137065],{"className":186726},[407,33009],[363,186728,461],{"className":186729},[494],[363,186731,186733],{"className":186732},[407],[363,186734,186736],{"className":186735},[407],[363,186737,45101],{"className":186738},[407,136068],[363,186740,468],{"className":186741},[501],[363,186743],{"className":186744,"style":754},[505],[363,186746,186748],{"className":186747},[407],[363,186749,186751],{"className":186750},[767,15176],[363,186752,186754,186774],{"className":186753},[633,634],[363,186755,186757,186771],{"className":186756},[638],[363,186758,186760],{"className":186759,"style":15186},[642],[363,186761,186762,186765],{"style":15189},[363,186763],{"className":186764,"style":15193},[650],[363,186766,186767],{"style":15196},[6670,186768,186769],{"xmlns":6672,"width":15199,"height":9797,"viewBox":15200},[6678,186770],{"d":15203},[363,186772,666],{"className":186773},[665],[363,186775,186777],{"className":186776},[638],[363,186778,186780],{"className":186779,"style":15213},[642],[363,186781],{},[363,186783],{"className":186784,"style":754},[505],[363,186786],{"className":186787,"style":754},[505],[363,186789,186791],{"className":186790},[1831],[363,186792,137065],{"className":186793},[407,33009],[363,186795,461],{"className":186796},[494],[363,186798,186800],{"className":186799},[407],[363,186801,186803],{"className":186802},[407],[363,186804,84464],{"className":186805,"style":150142},[407,136068],[363,186807,468],{"className":186808},[501],[363,186810,186812],{"className":186811,"style":763},[501,762],[363,186813,605],{"className":186814},[767,10021],[363,186816],{"className":186817,"style":506},[505],[363,186819,471],{"className":186820},[510],[363,186822],{"className":186823,"style":506},[505],[363,186825,186827,186830,186835,186838,186936,186939,186942],{"className":186826},[398],[363,186828],{"className":186829,"style":150425},[402],[363,186831,4501,186833],{"className":186832},[1831],[363,186834,4505],{"style":4504},[363,186836],{"className":186837,"style":754},[505],[363,186839,186841,186844,186933],{"className":186840},[407],[363,186842],{"className":186843},[494,789],[363,186845,186847],{"className":186846},[586],[363,186848,186850,186925],{"className":186849},[633,634],[363,186851,186853,186922],{"className":186852},[638],[363,186854,186856,186885,186893],{"className":186855,"style":26740},[642],[363,186857,186858,186861],{"style":2874},[363,186859],{"className":186860,"style":809},[650],[363,186862,186864],{"className":186863},[655,656,657,658],[363,186865,186867,186870,186873,186882],{"className":186866},[407,658],[363,186868,39638],{"className":186869,"style":39734},[407,408,658],[363,186871,461],{"className":186872},[494,658],[363,186874,186876],{"className":186875},[407,658],[363,186877,186879],{"className":186878},[407,658],[363,186880,45101],{"className":186881},[407,136068,658],[363,186883,468],{"className":186884},[501,658],[363,186886,186887,186890],{"style":821},[363,186888],{"className":186889,"style":809},[650],[363,186891],{"className":186892,"style":829},[828],[363,186894,186895,186898],{"style":26765},[363,186896],{"className":186897,"style":809},[650],[363,186899,186901],{"className":186900},[655,656,657,658],[363,186902,186904,186907,186910,186919],{"className":186903},[407,658],[363,186905,39638],{"className":186906,"style":39734},[407,408,658],[363,186908,461],{"className":186909},[494,658],[363,186911,186913],{"className":186912},[407,658],[363,186914,186916],{"className":186915},[407,658],[363,186917,84464],{"className":186918,"style":150142},[407,136068,658],[363,186920,468],{"className":186921},[501,658],[363,186923,666],{"className":186924},[665],[363,186926,186928],{"className":186927},[638],[363,186929,186931],{"className":186930,"style":45949},[642],[363,186932],{},[363,186934],{"className":186935},[501,789],[363,186937],{"className":186938,"style":2934},[505],[363,186940,2817],{"className":186941},[2938],[363,186943],{"className":186944,"style":2934},[505],[363,186946,186948,186951,187011,187014,187054,187057,187060],{"className":186947},[398],[363,186949],{"className":186950,"style":136371},[402],[363,186952,186954,186957],{"className":186953},[1831],[363,186955,13808],{"className":186956,"style":40007},[1831,1832,5963],[363,186958,186960],{"className":186959},[629],[363,186961,186963,187003],{"className":186962},[633,634],[363,186964,186966,187000],{"className":186965},[638],[363,186967,186969,186989],{"className":186968,"style":133494},[642],[363,186970,186971,186974],{"style":40023},[363,186972],{"className":186973,"style":651},[650],[363,186975,186977],{"className":186976},[655,656,657,658],[363,186978,186980,186983,186986],{"className":186979},[407,658],[363,186981,7911],{"className":186982,"style":8614},[407,408,658],[363,186984,471],{"className":186985},[510,658],[363,186987,465],{"className":186988},[407,658],[363,186990,186991,186994],{"style":133517},[363,186992],{"className":186993,"style":651},[650],[363,186995,186997],{"className":186996},[655,656,657,658],[363,186998,11041],{"className":186999,"style":11129},[407,408,658],[363,187001,666],{"className":187002},[665],[363,187004,187006],{"className":187005},[638],[363,187007,187009],{"className":187008,"style":40042},[642],[363,187010],{},[363,187012,461],{"className":187013},[494],[363,187015,187017,187020],{"className":187016},[407],[363,187018,45101],{"className":187019,"style":45131},[407,408],[363,187021,187023],{"className":187022},[629],[363,187024,187026,187046],{"className":187025},[633,634],[363,187027,187029,187043],{"className":187028},[638],[363,187030,187032],{"className":187031,"style":643},[642],[363,187033,187034,187037],{"style":136107},[363,187035],{"className":187036,"style":651},[650],[363,187038,187040],{"className":187039},[655,656,657,658],[363,187041,7911],{"className":187042,"style":8614},[407,408,658],[363,187044,666],{"className":187045},[665],[363,187047,187049],{"className":187048},[638],[363,187050,187052],{"className":187051,"style":8315},[642],[363,187053],{},[363,187055],{"className":187056,"style":2934},[505],[363,187058,5160],{"className":187059},[2938],[363,187061],{"className":187062,"style":2934},[505],[363,187064,187066,187069,187109,187112,187118,187121,187124,187164,187167,187170,187173],{"className":187065},[398],[363,187067],{"className":187068,"style":20910},[402],[363,187070,187072,187075],{"className":187071},[407],[363,187073,84464],{"className":187074,"style":84686},[407,408],[363,187076,187078],{"className":187077},[629],[363,187079,187081,187101],{"className":187080},[633,634],[363,187082,187084,187098],{"className":187083},[638],[363,187085,187087],{"className":187086,"style":643},[642],[363,187088,187089,187092],{"style":150221},[363,187090],{"className":187091,"style":651},[650],[363,187093,187095],{"className":187094},[655,656,657,658],[363,187096,7911],{"className":187097,"style":8614},[407,408,658],[363,187099,666],{"className":187100},[665],[363,187102,187104],{"className":187103},[638],[363,187105,187107],{"className":187106,"style":8315},[642],[363,187108],{},[363,187110,468],{"className":187111},[501],[363,187113,187115],{"className":187114},[407],[363,187116,461],{"className":187117},[767,10021],[363,187119,155424],{"className":187120,"style":1328},[407,408],[363,187122,461],{"className":187123},[494],[363,187125,187127,187130],{"className":187126},[407],[363,187128,45101],{"className":187129,"style":45131},[407,408],[363,187131,187133],{"className":187132},[629],[363,187134,187136,187156],{"className":187135},[633,634],[363,187137,187139,187153],{"className":187138},[638],[363,187140,187142],{"className":187141,"style":643},[642],[363,187143,187144,187147],{"style":136107},[363,187145],{"className":187146,"style":651},[650],[363,187148,187150],{"className":187149},[655,656,657,658],[363,187151,7911],{"className":187152,"style":8614},[407,408,658],[363,187154,666],{"className":187155},[665],[363,187157,187159],{"className":187158},[638],[363,187160,187162],{"className":187161,"style":8315},[642],[363,187163],{},[363,187165,468],{"className":187166},[501],[363,187168],{"className":187169,"style":2934},[505],[363,187171,5160],{"className":187172},[2938],[363,187174],{"className":187175,"style":2934},[505],[363,187177,187179,187182,187185,187188,187228,187231],{"className":187178},[398],[363,187180],{"className":187181,"style":20910},[402],[363,187183,155424],{"className":187184,"style":1328},[407,408],[363,187186,461],{"className":187187},[494],[363,187189,187191,187194],{"className":187190},[407],[363,187192,45101],{"className":187193,"style":45131},[407,408],[363,187195,187197],{"className":187196},[629],[363,187198,187200,187220],{"className":187199},[633,634],[363,187201,187203,187217],{"className":187202},[638],[363,187204,187206],{"className":187205,"style":11480},[642],[363,187207,187208,187211],{"style":136107},[363,187209],{"className":187210,"style":651},[650],[363,187212,187214],{"className":187213},[655,656,657,658],[363,187215,474],{"className":187216},[407,658],[363,187218,666],{"className":187219},[665],[363,187221,187223],{"className":187222},[638],[363,187224,187226],{"className":187225,"style":8315},[642],[363,187227],{},[363,187229,468],{"className":187230},[501],[363,187232,187234],{"className":187233},[407],[363,187235,468],{"className":187236},[767,10021],"\n特别地，取 ",[363,187239,187241,187259],{"className":187240,"translate":367},[366],[363,187242,187244],{"className":187243},[371],[373,187245,187246],{"xmlns":375},[377,187247,187248,187256],{},[380,187249,187250,187252,187254],{},[383,187251,84464],{"mathvariant":136008},[458,187253,471],{},[463,187255,465],{"mathvariant":75560},[387,187257,187258],{"encoding":389},"\\boldsymbol{\\beta} = \\mathbf{1}",[363,187260,187262,187286],{"className":187261,"ariaHidden":394},[393],[363,187263,187265,187268,187277,187280,187283],{"className":187264},[398],[363,187266],{"className":187267,"style":403},[402],[363,187269,187271],{"className":187270},[407],[363,187272,187274],{"className":187273},[407],[363,187275,84464],{"className":187276,"style":150142},[407,136068],[363,187278],{"className":187279,"style":506},[505],[363,187281,471],{"className":187282},[510],[363,187284],{"className":187285,"style":506},[505],[363,187287,187289,187292],{"className":187288},[398],[363,187290],{"className":187291,"style":520},[402],[363,187293,465],{"className":187294},[407,75905],"（此时 ",[363,187297,187299,187333],{"className":187298,"translate":367},[366],[363,187300,187302],{"className":187301},[371],[373,187303,187304],{"xmlns":375},[377,187305,187306,187330],{},[380,187307,187308,187310,187312,187314,187316,187318,187320,187322,187324,187326,187328],{},[383,187309,39638],{},[458,187311,461],{"stretchy":460},[463,187313,465],{"mathvariant":75560},[458,187315,468],{"stretchy":460},[458,187317,471],{},[463,187319,465],{},[383,187321,1288],{"mathvariant":557},[383,187323,137171],{"mathvariant":557},[458,187325,461],{"stretchy":460},[383,187327,11041],{},[458,187329,468],{"stretchy":460},[387,187331,187332],{"encoding":389},"B(\\mathbf{1}) = 1\u002F\\Gamma(K)",[363,187334,187336,187363],{"className":187335,"ariaHidden":394},[393],[363,187337,187339,187342,187345,187348,187351,187354,187357,187360],{"className":187338},[398],[363,187340],{"className":187341,"style":487},[402],[363,187343,39638],{"className":187344,"style":39734},[407,408],[363,187346,461],{"className":187347},[494],[363,187349,465],{"className":187350},[407,75905],[363,187352,468],{"className":187353},[501],[363,187355],{"className":187356,"style":506},[505],[363,187358,471],{"className":187359},[510],[363,187361],{"className":187362,"style":506},[505],[363,187364,187366,187369,187373,187376,187379],{"className":187365},[398],[363,187367],{"className":187368,"style":487},[402],[363,187370,187372],{"className":187371},[407],"1\u002FΓ",[363,187374,461],{"className":187375},[494],[363,187377,11041],{"className":187378,"style":11129},[407,408],[363,187380,468],{"className":187381},[501],"）得\n",[363,187384,187386,187548],{"className":187385,"translate":367},[366],[363,187387,187389],{"className":187388},[371],[373,187390,187391],{"xmlns":375},[377,187392,187393,187545],{},[380,187394,187395,187401,187403,187405,187407,187409,187411,187421,187423,187425,187439,187441,187443,187445,187447,187457,187459,187461,187463,187465,187467,187469,187471,187473,187475,187489,187491,187501,187503,187505,187507,187509,187511,187513,187523,187525,187527,187529,187531,187541,187543],{},[7161,187396,187397,187399],{},[383,187398,22240],{"mathvariant":944},[1644,187400,186027],{},[458,187402,471],{},[383,187404,4447],{},[458,187406,4450],{},[383,187408,137171],{"mathvariant":557},[458,187410,461],{"stretchy":460},[543,187412,187413,187419],{},[12158,187414,187415,187417],{"accent":394},[383,187416,45101],{},[458,187418,12164],{},[463,187420,474],{},[458,187422,468],{"stretchy":460},[458,187424,5160],{},[7900,187426,187427,187429,187437],{},[458,187428,13808],{},[380,187430,187431,187433,187435],{},[383,187432,7911],{},[458,187434,471],{},[463,187436,465],{},[383,187438,11041],{},[383,187440,4447],{},[458,187442,4450],{},[383,187444,137171],{"mathvariant":557},[458,187446,461],{"stretchy":460},[543,187448,187449,187455],{},[12158,187450,187451,187453],{"accent":394},[383,187452,45101],{},[458,187454,12164],{},[383,187456,7911],{},[458,187458,468],{"stretchy":460},[458,187460,5160],{},[383,187462,4447],{},[458,187464,4450],{},[383,187466,137171],{"mathvariant":557},[458,187468,461],{"stretchy":460},[383,187470,11041],{},[458,187472,468],{"stretchy":460},[458,187474,2817],{},[7900,187476,187477,187479,187487],{},[458,187478,13808],{},[380,187480,187481,187483,187485],{},[383,187482,7911],{},[458,187484,471],{},[463,187486,465],{},[383,187488,11041],{},[458,187490,461],{"stretchy":460},[543,187492,187493,187499],{},[12158,187494,187495,187497],{"accent":394},[383,187496,45101],{},[458,187498,12164],{},[383,187500,7911],{},[458,187502,5160],{},[463,187504,465],{},[458,187506,468],{"stretchy":460},[458,187508,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,187510,155424],{},[458,187512,461],{"stretchy":460},[543,187514,187515,187521],{},[12158,187516,187517,187519],{"accent":394},[383,187518,45101],{},[458,187520,12164],{},[383,187522,7911],{},[458,187524,468],{"stretchy":460},[458,187526,5160],{},[383,187528,155424],{},[458,187530,461],{"stretchy":460},[543,187532,187533,187539],{},[12158,187534,187535,187537],{"accent":394},[383,187536,45101],{},[458,187538,12164],{},[463,187540,474],{},[458,187542,468],{"stretchy":460},[458,187544,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[387,187546,187547],{"encoding":389},"\\mathcal{L}^{\\text{reg}} = \\log\\Gamma(\\tilde{\\alpha}_0) - \\sum_{k=1}^K \\log\\Gamma(\\tilde{\\alpha}_k) - \\log\\Gamma(K) + \\sum_{k=1}^K (\\tilde{\\alpha}_k - 1)\\big(\\psi(\\tilde{\\alpha}_k) - \\psi(\\tilde{\\alpha}_0)\\big)",[363,187549,187551,187601,187703,187866,187901,188047,188151],{"className":187550,"ariaHidden":394},[393],[363,187552,187554,187557,187592,187595,187598],{"className":187553},[398],[363,187555],{"className":187556,"style":1011},[402],[363,187558,187560,187563],{"className":187559},[407],[363,187561,22240],{"className":187562},[407,971],[363,187564,187566],{"className":187565},[629],[363,187567,187569],{"className":187568},[633],[363,187570,187572],{"className":187571},[638],[363,187573,187575],{"className":187574,"style":50700},[642],[363,187576,187577,187580],{"style":7212},[363,187578],{"className":187579,"style":651},[650],[363,187581,187583],{"className":187582},[655,656,657,658],[363,187584,187586],{"className":187585},[407,658],[363,187587,187589],{"className":187588},[407,4945,658],[363,187590,186027],{"className":187591},[407,658],[363,187593],{"className":187594,"style":506},[505],[363,187596,471],{"className":187597},[510],[363,187599],{"className":187600,"style":506},[505],[363,187602,187604,187607,187612,187615,187618,187621,187691,187694,187697,187700],{"className":187603},[398],[363,187605],{"className":187606,"style":487},[402],[363,187608,4501,187610],{"className":187609},[1831],[363,187611,4505],{"style":4504},[363,187613],{"className":187614,"style":754},[505],[363,187616,137171],{"className":187617},[407],[363,187619,461],{"className":187620},[494],[363,187622,187624,187657],{"className":187623},[407],[363,187625,187627],{"className":187626},[407,12198],[363,187628,187630],{"className":187629},[633],[363,187631,187633],{"className":187632},[638],[363,187634,187636,187644],{"className":187635,"style":52240},[642],[363,187637,187638,187641],{"style":12210},[363,187639],{"className":187640,"style":809},[650],[363,187642,45101],{"className":187643,"style":45131},[407,408],[363,187645,187647,187650],{"style":187646},"top:-3.35em;",[363,187648],{"className":187649,"style":809},[650],[363,187651,187654],{"className":187652,"style":187653},[12226],"left:-0.2222em;",[363,187655,12164],{"className":187656},[407],[363,187658,187660],{"className":187659},[629],[363,187661,187663,187683],{"className":187662},[633,634],[363,187664,187666,187680],{"className":187665},[638],[363,187667,187669],{"className":187668,"style":11480},[642],[363,187670,187671,187674],{"style":136107},[363,187672],{"className":187673,"style":651},[650],[363,187675,187677],{"className":187676},[655,656,657,658],[363,187678,474],{"className":187679},[407,658],[363,187681,666],{"className":187682},[665],[363,187684,187686],{"className":187685},[638],[363,187687,187689],{"className":187688,"style":8315},[642],[363,187690],{},[363,187692,468],{"className":187693},[501],[363,187695],{"className":187696,"style":2934},[505],[363,187698,5160],{"className":187699},[2938],[363,187701],{"className":187702,"style":2934},[505],[363,187704,187706,187709,187769,187772,187777,187780,187783,187786,187854,187857,187860,187863],{"className":187705},[398],[363,187707],{"className":187708,"style":136371},[402],[363,187710,187712,187715],{"className":187711},[1831],[363,187713,13808],{"className":187714,"style":40007},[1831,1832,5963],[363,187716,187718],{"className":187717},[629],[363,187719,187721,187761],{"className":187720},[633,634],[363,187722,187724,187758],{"className":187723},[638],[363,187725,187727,187747],{"className":187726,"style":133494},[642],[363,187728,187729,187732],{"style":40023},[363,187730],{"className":187731,"style":651},[650],[363,187733,187735],{"className":187734},[655,656,657,658],[363,187736,187738,187741,187744],{"className":187737},[407,658],[363,187739,7911],{"className":187740,"style":8614},[407,408,658],[363,187742,471],{"className":187743},[510,658],[363,187745,465],{"className":187746},[407,658],[363,187748,187749,187752],{"style":133517},[363,187750],{"className":187751,"style":651},[650],[363,187753,187755],{"className":187754},[655,656,657,658],[363,187756,11041],{"className":187757,"style":11129},[407,408,658],[363,187759,666],{"className":187760},[665],[363,187762,187764],{"className":187763},[638],[363,187765,187767],{"className":187766,"style":40042},[642],[363,187768],{},[363,187770],{"className":187771,"style":754},[505],[363,187773,4501,187775],{"className":187774},[1831],[363,187776,4505],{"style":4504},[363,187778],{"className":187779,"style":754},[505],[363,187781,137171],{"className":187782},[407],[363,187784,461],{"className":187785},[494],[363,187787,187789,187820],{"className":187788},[407],[363,187790,187792],{"className":187791},[407,12198],[363,187793,187795],{"className":187794},[633],[363,187796,187798],{"className":187797},[638],[363,187799,187801,187809],{"className":187800,"style":52240},[642],[363,187802,187803,187806],{"style":12210},[363,187804],{"className":187805,"style":809},[650],[363,187807,45101],{"className":187808,"style":45131},[407,408],[363,187810,187811,187814],{"style":187646},[363,187812],{"className":187813,"style":809},[650],[363,187815,187817],{"className":187816,"style":187653},[12226],[363,187818,12164],{"className":187819},[407],[363,187821,187823],{"className":187822},[629],[363,187824,187826,187846],{"className":187825},[633,634],[363,187827,187829,187843],{"className":187828},[638],[363,187830,187832],{"className":187831,"style":643},[642],[363,187833,187834,187837],{"style":136107},[363,187835],{"className":187836,"style":651},[650],[363,187838,187840],{"className":187839},[655,656,657,658],[363,187841,7911],{"className":187842,"style":8614},[407,408,658],[363,187844,666],{"className":187845},[665],[363,187847,187849],{"className":187848},[638],[363,187850,187852],{"className":187851,"style":8315},[642],[363,187853],{},[363,187855,468],{"className":187856},[501],[363,187858],{"className":187859,"style":2934},[505],[363,187861,5160],{"className":187862},[2938],[363,187864],{"className":187865,"style":2934},[505],[363,187867,187869,187872,187877,187880,187883,187886,187889,187892,187895,187898],{"className":187868},[398],[363,187870],{"className":187871,"style":487},[402],[363,187873,4501,187875],{"className":187874},[1831],[363,187876,4505],{"style":4504},[363,187878],{"className":187879,"style":754},[505],[363,187881,137171],{"className":187882},[407],[363,187884,461],{"className":187885},[494],[363,187887,11041],{"className":187888,"style":11129},[407,408],[363,187890,468],{"className":187891},[501],[363,187893],{"className":187894,"style":2934},[505],[363,187896,2817],{"className":187897},[2938],[363,187899],{"className":187900,"style":2934},[505],[363,187902,187904,187907,187967,187970,188038,188041,188044],{"className":187903},[398],[363,187905],{"className":187906,"style":136371},[402],[363,187908,187910,187913],{"className":187909},[1831],[363,187911,13808],{"className":187912,"style":40007},[1831,1832,5963],[363,187914,187916],{"className":187915},[629],[363,187917,187919,187959],{"className":187918},[633,634],[363,187920,187922,187956],{"className":187921},[638],[363,187923,187925,187945],{"className":187924,"style":133494},[642],[363,187926,187927,187930],{"style":40023},[363,187928],{"className":187929,"style":651},[650],[363,187931,187933],{"className":187932},[655,656,657,658],[363,187934,187936,187939,187942],{"className":187935},[407,658],[363,187937,7911],{"className":187938,"style":8614},[407,408,658],[363,187940,471],{"className":187941},[510,658],[363,187943,465],{"className":187944},[407,658],[363,187946,187947,187950],{"style":133517},[363,187948],{"className":187949,"style":651},[650],[363,187951,187953],{"className":187952},[655,656,657,658],[363,187954,11041],{"className":187955,"style":11129},[407,408,658],[363,187957,666],{"className":187958},[665],[363,187960,187962],{"className":187961},[638],[363,187963,187965],{"className":187964,"style":40042},[642],[363,187966],{},[363,187968,461],{"className":187969},[494],[363,187971,187973,188004],{"className":187972},[407],[363,187974,187976],{"className":187975},[407,12198],[363,187977,187979],{"className":187978},[633],[363,187980,187982],{"className":187981},[638],[363,187983,187985,187993],{"className":187984,"style":52240},[642],[363,187986,187987,187990],{"style":12210},[363,187988],{"className":187989,"style":809},[650],[363,187991,45101],{"className":187992,"style":45131},[407,408],[363,187994,187995,187998],{"style":187646},[363,187996],{"className":187997,"style":809},[650],[363,187999,188001],{"className":188000,"style":187653},[12226],[363,188002,12164],{"className":188003},[407],[363,188005,188007],{"className":188006},[629],[363,188008,188010,188030],{"className":188009},[633,634],[363,188011,188013,188027],{"className":188012},[638],[363,188014,188016],{"className":188015,"style":643},[642],[363,188017,188018,188021],{"style":136107},[363,188019],{"className":188020,"style":651},[650],[363,188022,188024],{"className":188023},[655,656,657,658],[363,188025,7911],{"className":188026,"style":8614},[407,408,658],[363,188028,666],{"className":188029},[665],[363,188031,188033],{"className":188032},[638],[363,188034,188036],{"className":188035,"style":8315},[642],[363,188037],{},[363,188039],{"className":188040,"style":2934},[505],[363,188042,5160],{"className":188043},[2938],[363,188045],{"className":188046,"style":2934},[505],[363,188048,188050,188053,188056,188059,188065,188068,188071,188139,188142,188145,188148],{"className":188049},[398],[363,188051],{"className":188052,"style":20910},[402],[363,188054,465],{"className":188055},[407],[363,188057,468],{"className":188058},[501],[363,188060,188062],{"className":188061},[407],[363,188063,461],{"className":188064},[767,10021],[363,188066,155424],{"className":188067,"style":1328},[407,408],[363,188069,461],{"className":188070},[494],[363,188072,188074,188105],{"className":188073},[407],[363,188075,188077],{"className":188076},[407,12198],[363,188078,188080],{"className":188079},[633],[363,188081,188083],{"className":188082},[638],[363,188084,188086,188094],{"className":188085,"style":52240},[642],[363,188087,188088,188091],{"style":12210},[363,188089],{"className":188090,"style":809},[650],[363,188092,45101],{"className":188093,"style":45131},[407,408],[363,188095,188096,188099],{"style":187646},[363,188097],{"className":188098,"style":809},[650],[363,188100,188102],{"className":188101,"style":187653},[12226],[363,188103,12164],{"className":188104},[407],[363,188106,188108],{"className":188107},[629],[363,188109,188111,188131],{"className":188110},[633,634],[363,188112,188114,188128],{"className":188113},[638],[363,188115,188117],{"className":188116,"style":643},[642],[363,188118,188119,188122],{"style":136107},[363,188120],{"className":188121,"style":651},[650],[363,188123,188125],{"className":188124},[655,656,657,658],[363,188126,7911],{"className":188127,"style":8614},[407,408,658],[363,188129,666],{"className":188130},[665],[363,188132,188134],{"className":188133},[638],[363,188135,188137],{"className":188136,"style":8315},[642],[363,188138],{},[363,188140,468],{"className":188141},[501],[363,188143],{"className":188144,"style":2934},[505],[363,188146,5160],{"className":188147},[2938],[363,188149],{"className":188150,"style":2934},[505],[363,188152,188154,188157,188160,188163,188231,188234],{"className":188153},[398],[363,188155],{"className":188156,"style":20910},[402],[363,188158,155424],{"className":188159,"style":1328},[407,408],[363,188161,461],{"className":188162},[494],[363,188164,188166,188197],{"className":188165},[407],[363,188167,188169],{"className":188168},[407,12198],[363,188170,188172],{"className":188171},[633],[363,188173,188175],{"className":188174},[638],[363,188176,188178,188186],{"className":188177,"style":52240},[642],[363,188179,188180,188183],{"style":12210},[363,188181],{"className":188182,"style":809},[650],[363,188184,45101],{"className":188185,"style":45131},[407,408],[363,188187,188188,188191],{"style":187646},[363,188189],{"className":188190,"style":809},[650],[363,188192,188194],{"className":188193,"style":187653},[12226],[363,188195,12164],{"className":188196},[407],[363,188198,188200],{"className":188199},[629],[363,188201,188203,188223],{"className":188202},[633,634],[363,188204,188206,188220],{"className":188205},[638],[363,188207,188209],{"className":188208,"style":11480},[642],[363,188210,188211,188214],{"style":136107},[363,188212],{"className":188213,"style":651},[650],[363,188215,188217],{"className":188216},[655,656,657,658],[363,188218,474],{"className":188219},[407,658],[363,188221,666],{"className":188222},[665],[363,188224,188226],{"className":188225},[638],[363,188227,188229],{"className":188228,"style":8315},[642],[363,188230],{},[363,188232,468],{"className":188233},[501],[363,188235,188237],{"className":188236},[407],[363,188238,468],{"className":188239},[767,10021],[11,188241,188242,188244,188245,188512,188513,2756,188816,189243],{},[1572,188243,137993],{}," 由指数族的一般 KL 公式：",[363,188246,188248,188298],{"className":188247,"translate":367},[366],[363,188249,188251],{"className":188250},[371],[373,188252,188253],{"xmlns":375},[377,188254,188255,188295],{},[380,188256,188257,188259,188261,188263,188269,188271,188273,188275,188281,188283,188285,188287,188293],{},[383,188258,33010],{"mathvariant":557},[458,188260,4450],{},[458,188262,471],{},[543,188264,188265,188267],{},[383,188266,571],{"mathvariant":570},[383,188268,45101],{"mathvariant":136008},[458,188270,578],{"stretchy":460},[383,188272,4447],{},[458,188274,4450],{},[543,188276,188277,188279],{},[383,188278,11],{},[383,188280,45101],{"mathvariant":136008},[458,188282,5160],{},[383,188284,4447],{},[458,188286,4450],{},[543,188288,188289,188291],{},[383,188290,11],{},[383,188292,84464],{"mathvariant":136008},[458,188294,605],{"stretchy":460},[387,188296,188297],{"encoding":389},"\\operatorname{KL} = \\mathbb{E}_{\\boldsymbol{\\alpha}}[\\log p_{\\boldsymbol{\\alpha}} - \\log p_{\\boldsymbol{\\beta}}]",[363,188299,188301,188322,188446],{"className":188300,"ariaHidden":394},[393],[363,188302,188304,188307,188313,188316,188319],{"className":188303},[398],[363,188305],{"className":188306,"style":1011},[402],[363,188308,188310],{"className":188309},[1831],[363,188311,33010],{"className":188312},[407,33009],[363,188314],{"className":188315,"style":506},[505],[363,188317,471],{"className":188318},[510],[363,188320],{"className":188321,"style":506},[505],[363,188323,188325,188328,188377,188380,188385,188388,188437,188440,188443],{"className":188324},[398],[363,188326],{"className":188327,"style":487},[402],[363,188329,188331,188334],{"className":188330},[407],[363,188332,571],{"className":188333},[407,714],[363,188335,188337],{"className":188336},[629],[363,188338,188340,188369],{"className":188339},[633,634],[363,188341,188343,188366],{"className":188342},[638],[363,188344,188346],{"className":188345,"style":153717},[642],[363,188347,188348,188351],{"style":730},[363,188349],{"className":188350,"style":651},[650],[363,188352,188354],{"className":188353},[655,656,657,658],[363,188355,188357],{"className":188356},[407,658],[363,188358,188360],{"className":188359},[407,658],[363,188361,188363],{"className":188362},[407,658],[363,188364,45101],{"className":188365},[407,136068,658],[363,188367,666],{"className":188368},[665],[363,188370,188372],{"className":188371},[638],[363,188373,188375],{"className":188374,"style":8315},[642],[363,188376],{},[363,188378,578],{"className":188379},[494],[363,188381,4501,188383],{"className":188382},[1831],[363,188384,4505],{"style":4504},[363,188386],{"className":188387,"style":754},[505],[363,188389,188391,188394],{"className":188390},[407],[363,188392,11],{"className":188393},[407,408],[363,188395,188397],{"className":188396},[629],[363,188398,188400,188429],{"className":188399},[633,634],[363,188401,188403,188426],{"className":188402},[638],[363,188404,188406],{"className":188405,"style":153717},[642],[363,188407,188408,188411],{"style":730},[363,188409],{"className":188410,"style":651},[650],[363,188412,188414],{"className":188413},[655,656,657,658],[363,188415,188417],{"className":188416},[407,658],[363,188418,188420],{"className":188419},[407,658],[363,188421,188423],{"className":188422},[407,658],[363,188424,45101],{"className":188425},[407,136068,658],[363,188427,666],{"className":188428},[665],[363,188430,188432],{"className":188431},[638],[363,188433,188435],{"className":188434,"style":8315},[642],[363,188436],{},[363,188438],{"className":188439,"style":2934},[505],[363,188441,5160],{"className":188442},[2938],[363,188444],{"className":188445,"style":2934},[505],[363,188447,188449,188452,188457,188460,188509],{"className":188448},[398],[363,188450],{"className":188451,"style":618},[402],[363,188453,4501,188455],{"className":188454},[1831],[363,188456,4505],{"style":4504},[363,188458],{"className":188459,"style":754},[505],[363,188461,188463,188466],{"className":188462},[407],[363,188464,11],{"className":188465},[407,408],[363,188467,188469],{"className":188468},[629],[363,188470,188472,188501],{"className":188471},[633,634],[363,188473,188475,188498],{"className":188474},[638],[363,188476,188478],{"className":188477,"style":643},[642],[363,188479,188480,188483],{"style":730},[363,188481],{"className":188482,"style":651},[650],[363,188484,188486],{"className":188485},[655,656,657,658],[363,188487,188489],{"className":188488},[407,658],[363,188490,188492],{"className":188491},[407,658],[363,188493,188495],{"className":188494},[407,658],[363,188496,84464],{"className":188497,"style":150142},[407,136068,658],[363,188499,666],{"className":188500},[665],[363,188502,188504],{"className":188503},[638],[363,188505,188507],{"className":188506,"style":673},[642],[363,188508],{},[363,188510,605],{"className":188511},[501],"。代入 1.2 节的密度并利用 ",[363,188514,188516,188576],{"className":188515,"translate":367},[366],[363,188517,188519],{"className":188518},[371],[373,188520,188521],{"xmlns":375},[377,188522,188523,188573],{},[380,188524,188525,188531,188533,188535,188537,188543,188545,188547,188549,188551,188557,188559,188561,188563,188565,188571],{},[543,188526,188527,188529],{},[383,188528,571],{"mathvariant":570},[383,188530,45101],{"mathvariant":136008},[458,188532,578],{"stretchy":460},[383,188534,4447],{},[458,188536,4450],{},[543,188538,188539,188541],{},[383,188540,1121],{},[383,188542,7911],{},[458,188544,605],{"stretchy":460},[458,188546,471],{},[383,188548,155424],{},[458,188550,461],{"stretchy":460},[543,188552,188553,188555],{},[383,188554,45101],{},[383,188556,7911],{},[458,188558,468],{"stretchy":460},[458,188560,5160],{},[383,188562,155424],{},[458,188564,461],{"stretchy":460},[543,188566,188567,188569],{},[383,188568,45101],{},[463,188570,474],{},[458,188572,468],{"stretchy":460},[387,188574,188575],{"encoding":389},"\\mathbb{E}_{\\boldsymbol{\\alpha}}[\\log x_k] = \\psi(\\alpha_k) - \\psi(\\alpha_0)",[363,188577,188579,188697,188761],{"className":188578,"ariaHidden":394},[393],[363,188580,188582,188585,188634,188637,188642,188645,188685,188688,188691,188694],{"className":188581},[398],[363,188583],{"className":188584,"style":487},[402],[363,188586,188588,188591],{"className":188587},[407],[363,188589,571],{"className":188590},[407,714],[363,188592,188594],{"className":188593},[629],[363,188595,188597,188626],{"className":188596},[633,634],[363,188598,188600,188623],{"className":188599},[638],[363,188601,188603],{"className":188602,"style":153717},[642],[363,188604,188605,188608],{"style":730},[363,188606],{"className":188607,"style":651},[650],[363,188609,188611],{"className":188610},[655,656,657,658],[363,188612,188614],{"className":188613},[407,658],[363,188615,188617],{"className":188616},[407,658],[363,188618,188620],{"className":188619},[407,658],[363,188621,45101],{"className":188622},[407,136068,658],[363,188624,666],{"className":188625},[665],[363,188627,188629],{"className":188628},[638],[363,188630,188632],{"className":188631,"style":8315},[642],[363,188633],{},[363,188635,578],{"className":188636},[494],[363,188638,4501,188640],{"className":188639},[1831],[363,188641,4505],{"style":4504},[363,188643],{"className":188644,"style":754},[505],[363,188646,188648,188651],{"className":188647},[407],[363,188649,1121],{"className":188650},[407,408],[363,188652,188654],{"className":188653},[629],[363,188655,188657,188677],{"className":188656},[633,634],[363,188658,188660,188674],{"className":188659},[638],[363,188661,188663],{"className":188662,"style":643},[642],[363,188664,188665,188668],{"style":730},[363,188666],{"className":188667,"style":651},[650],[363,188669,188671],{"className":188670},[655,656,657,658],[363,188672,7911],{"className":188673,"style":8614},[407,408,658],[363,188675,666],{"className":188676},[665],[363,188678,188680],{"className":188679},[638],[363,188681,188683],{"className":188682,"style":8315},[642],[363,188684],{},[363,188686,605],{"className":188687},[501],[363,188689],{"className":188690,"style":506},[505],[363,188692,471],{"className":188693},[510],[363,188695],{"className":188696,"style":506},[505],[363,188698,188700,188703,188706,188709,188749,188752,188755,188758],{"className":188699},[398],[363,188701],{"className":188702,"style":487},[402],[363,188704,155424],{"className":188705,"style":1328},[407,408],[363,188707,461],{"className":188708},[494],[363,188710,188712,188715],{"className":188711},[407],[363,188713,45101],{"className":188714,"style":45131},[407,408],[363,188716,188718],{"className":188717},[629],[363,188719,188721,188741],{"className":188720},[633,634],[363,188722,188724,188738],{"className":188723},[638],[363,188725,188727],{"className":188726,"style":643},[642],[363,188728,188729,188732],{"style":136107},[363,188730],{"className":188731,"style":651},[650],[363,188733,188735],{"className":188734},[655,656,657,658],[363,188736,7911],{"className":188737,"style":8614},[407,408,658],[363,188739,666],{"className":188740},[665],[363,188742,188744],{"className":188743},[638],[363,188745,188747],{"className":188746,"style":8315},[642],[363,188748],{},[363,188750,468],{"className":188751},[501],[363,188753],{"className":188754,"style":2934},[505],[363,188756,5160],{"className":188757},[2938],[363,188759],{"className":188760,"style":2934},[505],[363,188762,188764,188767,188770,188773,188813],{"className":188763},[398],[363,188765],{"className":188766,"style":487},[402],[363,188768,155424],{"className":188769,"style":1328},[407,408],[363,188771,461],{"className":188772},[494],[363,188774,188776,188779],{"className":188775},[407],[363,188777,45101],{"className":188778,"style":45131},[407,408],[363,188780,188782],{"className":188781},[629],[363,188783,188785,188805],{"className":188784},[633,634],[363,188786,188788,188802],{"className":188787},[638],[363,188789,188791],{"className":188790,"style":11480},[642],[363,188792,188793,188796],{"style":136107},[363,188794],{"className":188795,"style":651},[650],[363,188797,188799],{"className":188798},[655,656,657,658],[363,188800,474],{"className":188801},[407,658],[363,188803,666],{"className":188804},[665],[363,188806,188808],{"className":188807},[638],[363,188809,188811],{"className":188810,"style":8315},[642],[363,188812],{},[363,188814,468],{"className":188815},[501],[363,188817,188819,188909],{"className":188818,"translate":367},[366],[363,188820,188822],{"className":188821},[371],[373,188823,188824],{"xmlns":375},[377,188825,188826,188906],{},[380,188827,188828,188834,188836,188838,188840,188842,188848,188850,188852,188854,188856,188862,188864,188866,188868,188870,188872,188878,188880,188882,188884,188886,188888,188890,188892,188894,188896,188898,188904],{},[543,188829,188830,188832],{},[458,188831,13808],{},[383,188833,7911],{},[383,188835,571],{"mathvariant":570},[458,188837,578],{"stretchy":460},[383,188839,4447],{},[458,188841,4450],{},[543,188843,188844,188846],{},[383,188845,1121],{},[383,188847,7911],{},[458,188849,605],{"stretchy":460},[458,188851,471],{},[383,188853,155424],{},[458,188855,461],{"stretchy":460},[543,188857,188858,188860],{},[383,188859,45101],{},[463,188861,474],{},[458,188863,468],{"stretchy":460},[458,188865,5160],{},[383,188867,11041],{},[383,188869,155424],{},[458,188871,461],{"stretchy":460},[543,188873,188874,188876],{},[383,188875,45101],{},[463,188877,474],{},[458,188879,468],{"stretchy":460},[458,188881,471],{},[458,188883,5160],{},[458,188885,461],{"stretchy":460},[383,188887,11041],{},[458,188889,5160],{},[463,188891,465],{},[458,188893,468],{"stretchy":460},[383,188895,155424],{},[458,188897,461],{"stretchy":460},[543,188899,188900,188902],{},[383,188901,45101],{},[463,188903,474],{},[458,188905,468],{"stretchy":460},[387,188907,188908],{"encoding":389},"\\sum_k \\mathbb{E}[\\log x_k] = \\psi(\\alpha_0) - K\\psi(\\alpha_0) = -(K-1)\\psi(\\alpha_0)",[363,188910,188912,189027,189091,189158,189182],{"className":188911,"ariaHidden":394},[393],[363,188913,188915,188918,188958,188961,188964,188967,188972,188975,189015,189018,189021,189024],{"className":188914},[398],[363,188916],{"className":188917,"style":138904},[402],[363,188919,188921,188924],{"className":188920},[1831],[363,188922,13808],{"className":188923,"style":40007},[1831,1832,5963],[363,188925,188927],{"className":188926},[629],[363,188928,188930,188950],{"className":188929},[633,634],[363,188931,188933,188947],{"className":188932},[638],[363,188934,188936],{"className":188935,"style":67358},[642],[363,188937,188938,188941],{"style":40023},[363,188939],{"className":188940,"style":651},[650],[363,188942,188944],{"className":188943},[655,656,657,658],[363,188945,7911],{"className":188946,"style":8614},[407,408,658],[363,188948,666],{"className":188949},[665],[363,188951,188953],{"className":188952},[638],[363,188954,188956],{"className":188955,"style":40042},[642],[363,188957],{},[363,188959],{"className":188960,"style":754},[505],[363,188962,571],{"className":188963},[407,714],[363,188965,578],{"className":188966},[494],[363,188968,4501,188970],{"className":188969},[1831],[363,188971,4505],{"style":4504},[363,188973],{"className":188974,"style":754},[505],[363,188976,188978,188981],{"className":188977},[407],[363,188979,1121],{"className":188980},[407,408],[363,188982,188984],{"className":188983},[629],[363,188985,188987,189007],{"className":188986},[633,634],[363,188988,188990,189004],{"className":188989},[638],[363,188991,188993],{"className":188992,"style":643},[642],[363,188994,188995,188998],{"style":730},[363,188996],{"className":188997,"style":651},[650],[363,188999,189001],{"className":189000},[655,656,657,658],[363,189002,7911],{"className":189003,"style":8614},[407,408,658],[363,189005,666],{"className":189006},[665],[363,189008,189010],{"className":189009},[638],[363,189011,189013],{"className":189012,"style":8315},[642],[363,189014],{},[363,189016,605],{"className":189017},[501],[363,189019],{"className":189020,"style":506},[505],[363,189022,471],{"className":189023},[510],[363,189025],{"className":189026,"style":506},[505],[363,189028,189030,189033,189036,189039,189079,189082,189085,189088],{"className":189029},[398],[363,189031],{"className":189032,"style":487},[402],[363,189034,155424],{"className":189035,"style":1328},[407,408],[363,189037,461],{"className":189038},[494],[363,189040,189042,189045],{"className":189041},[407],[363,189043,45101],{"className":189044,"style":45131},[407,408],[363,189046,189048],{"className":189047},[629],[363,189049,189051,189071],{"className":189050},[633,634],[363,189052,189054,189068],{"className":189053},[638],[363,189055,189057],{"className":189056,"style":11480},[642],[363,189058,189059,189062],{"style":136107},[363,189060],{"className":189061,"style":651},[650],[363,189063,189065],{"className":189064},[655,656,657,658],[363,189066,474],{"className":189067},[407,658],[363,189069,666],{"className":189070},[665],[363,189072,189074],{"className":189073},[638],[363,189075,189077],{"className":189076,"style":8315},[642],[363,189078],{},[363,189080,468],{"className":189081},[501],[363,189083],{"className":189084,"style":2934},[505],[363,189086,5160],{"className":189087},[2938],[363,189089],{"className":189090,"style":2934},[505],[363,189092,189094,189097,189100,189103,189106,189146,189149,189152,189155],{"className":189093},[398],[363,189095],{"className":189096,"style":487},[402],[363,189098,11041],{"className":189099,"style":11129},[407,408],[363,189101,155424],{"className":189102,"style":1328},[407,408],[363,189104,461],{"className":189105},[494],[363,189107,189109,189112],{"className":189108},[407],[363,189110,45101],{"className":189111,"style":45131},[407,408],[363,189113,189115],{"className":189114},[629],[363,189116,189118,189138],{"className":189117},[633,634],[363,189119,189121,189135],{"className":189120},[638],[363,189122,189124],{"className":189123,"style":11480},[642],[363,189125,189126,189129],{"style":136107},[363,189127],{"className":189128,"style":651},[650],[363,189130,189132],{"className":189131},[655,656,657,658],[363,189133,474],{"className":189134},[407,658],[363,189136,666],{"className":189137},[665],[363,189139,189141],{"className":189140},[638],[363,189142,189144],{"className":189143,"style":8315},[642],[363,189145],{},[363,189147,468],{"className":189148},[501],[363,189150],{"className":189151,"style":506},[505],[363,189153,471],{"className":189154},[510],[363,189156],{"className":189157,"style":506},[505],[363,189159,189161,189164,189167,189170,189173,189176,189179],{"className":189160},[398],[363,189162],{"className":189163,"style":487},[402],[363,189165,5160],{"className":189166},[407],[363,189168,461],{"className":189169},[494],[363,189171,11041],{"className":189172,"style":11129},[407,408],[363,189174],{"className":189175,"style":2934},[505],[363,189177,5160],{"className":189178},[2938],[363,189180],{"className":189181,"style":2934},[505],[363,189183,189185,189188,189191,189194,189197,189200,189240],{"className":189184},[398],[363,189186],{"className":189187,"style":487},[402],[363,189189,465],{"className":189190},[407],[363,189192,468],{"className":189193},[501],[363,189195,155424],{"className":189196,"style":1328},[407,408],[363,189198,461],{"className":189199},[494],[363,189201,189203,189206],{"className":189202},[407],[363,189204,45101],{"className":189205,"style":45131},[407,408],[363,189207,189209],{"className":189208},[629],[363,189210,189212,189232],{"className":189211},[633,634],[363,189213,189215,189229],{"className":189214},[638],[363,189216,189218],{"className":189217,"style":11480},[642],[363,189219,189220,189223],{"style":136107},[363,189221],{"className":189222,"style":651},[650],[363,189224,189226],{"className":189225},[655,656,657,658],[363,189227,474],{"className":189228},[407,658],[363,189230,666],{"className":189231},[665],[363,189233,189235],{"className":189234},[638],[363,189236,189238],{"className":189237,"style":8315},[642],[363,189239],{},[363,189241,468],{"className":189242},[501]," 即可化简。",[11,189245,189246,189247,9747],{},"总损失为两项的加权和，其中权重按训练步",[1572,189248,189249],{},"退火",[363,189251,189253],{"className":189252,"translate":367},[528],[363,189254,189256,189334],{"className":189255,"translate":367},[366],[363,189257,189259],{"className":189258},[371],[373,189260,189261],{"xmlns":375,"display":537},[377,189262,189263,189331],{},[380,189264,189265,189267,189269,189276,189278,189284,189286,189292,189294,189296,189302,189304,189306,189308,189310],{},[383,189266,22240],{"mathvariant":944},[458,189268,471],{},[7161,189270,189271,189273],{},[383,189272,22240],{"mathvariant":944},[1644,189274,189275],{},"fit",[458,189277,2817],{},[543,189279,189280,189282],{},[383,189281,11686],{},[383,189283,1116],{},[1644,189285,1646],{},[7161,189287,189288,189290],{},[383,189289,22240],{"mathvariant":944},[1644,189291,186027],{},[458,189293,898],{"separator":394},[505,189295],{"width":3609},[543,189297,189298,189300],{},[383,189299,11686],{},[383,189301,1116],{},[458,189303,471],{},[383,189305,51955],{},[458,189307,4450],{},[1644,189309,1651],{},[380,189311,189312,189314,189316,189318,189329],{},[458,189313,461],{"fence":394},[463,189315,465],{},[458,189317,898],{"separator":394},[586,189319,189320,189322],{},[383,189321,1116],{},[543,189323,189324,189326],{},[383,189325,5739],{},[1644,189327,189328],{},"anneal",[458,189330,468],{"fence":394},[387,189332,189333],{"encoding":389},"\\mathcal{L} = \\mathcal{L}^{\\text{fit}} + \\lambda_t \\,\\mathcal{L}^{\\text{reg}},\n\\qquad\n\\lambda_t = \\min\\!\\left(1, \\frac{t}{T_{\\text{anneal}}}\\right)",[363,189335,189337,189355,189406,189550],{"className":189336,"ariaHidden":394},[393],[363,189338,189340,189343,189346,189349,189352],{"className":189339},[398],[363,189341],{"className":189342,"style":1011},[402],[363,189344,22240],{"className":189345},[407,971],[363,189347],{"className":189348,"style":506},[505],[363,189350,471],{"className":189351},[510],[363,189353],{"className":189354,"style":506},[505],[363,189356,189358,189362,189397,189400,189403],{"className":189357},[398],[363,189359],{"className":189360,"style":189361},[402],"height:0.9824em;vertical-align:-0.0833em;",[363,189363,189365,189368],{"className":189364},[407],[363,189366,22240],{"className":189367},[407,971],[363,189369,189371],{"className":189370},[629],[363,189372,189374],{"className":189373},[633],[363,189375,189377],{"className":189376},[638],[363,189378,189380],{"className":189379,"style":48211},[642],[363,189381,189382,189385],{"style":8624},[363,189383],{"className":189384,"style":651},[650],[363,189386,189388],{"className":189387},[655,656,657,658],[363,189389,189391],{"className":189390},[407,658],[363,189392,189394],{"className":189393},[407,4945,658],[363,189395,189275],{"className":189396},[407,658],[363,189398],{"className":189399,"style":2934},[505],[363,189401,2817],{"className":189402},[2938],[363,189404],{"className":189405,"style":2934},[505],[363,189407,189409,189413,189454,189457,189492,189495,189498,189501,189541,189544,189547],{"className":189408},[398],[363,189410],{"className":189411,"style":189412},[402],"height:0.9088em;vertical-align:-0.1944em;",[363,189414,189416,189419],{"className":189415},[407],[363,189417,11686],{"className":189418},[407,408],[363,189420,189422],{"className":189421},[629],[363,189423,189425,189446],{"className":189424},[633,634],[363,189426,189428,189443],{"className":189427},[638],[363,189429,189432],{"className":189430,"style":189431},[642],"height:0.2806em;",[363,189433,189434,189437],{"style":730},[363,189435],{"className":189436,"style":651},[650],[363,189438,189440],{"className":189439},[655,656,657,658],[363,189441,1116],{"className":189442},[407,408,658],[363,189444,666],{"className":189445},[665],[363,189447,189449],{"className":189448},[638],[363,189450,189452],{"className":189451,"style":8315},[642],[363,189453],{},[363,189455],{"className":189456,"style":754},[505],[363,189458,189460,189463],{"className":189459},[407],[363,189461,22240],{"className":189462},[407,971],[363,189464,189466],{"className":189465},[629],[363,189467,189469],{"className":189468},[633],[363,189470,189472],{"className":189471},[638],[363,189473,189475],{"className":189474,"style":46258},[642],[363,189476,189477,189480],{"style":8624},[363,189478],{"className":189479,"style":651},[650],[363,189481,189483],{"className":189482},[655,656,657,658],[363,189484,189486],{"className":189485},[407,658],[363,189487,189489],{"className":189488},[407,4945,658],[363,189490,186027],{"className":189491},[407,658],[363,189493,898],{"className":189494},[920],[363,189496],{"className":189497,"style":3981},[505],[363,189499],{"className":189500,"style":754},[505],[363,189502,189504,189507],{"className":189503},[407],[363,189505,11686],{"className":189506},[407,408],[363,189508,189510],{"className":189509},[629],[363,189511,189513,189533],{"className":189512},[633,634],[363,189514,189516,189530],{"className":189515},[638],[363,189517,189519],{"className":189518,"style":189431},[642],[363,189520,189521,189524],{"style":730},[363,189522],{"className":189523,"style":651},[650],[363,189525,189527],{"className":189526},[655,656,657,658],[363,189528,1116],{"className":189529},[407,408,658],[363,189531,666],{"className":189532},[665],[363,189534,189536],{"className":189535},[638],[363,189537,189539],{"className":189538,"style":8315},[642],[363,189540],{},[363,189542],{"className":189543,"style":506},[505],[363,189545,471],{"className":189546},[510],[363,189548],{"className":189549,"style":506},[505],[363,189551,189553,189556,189559,189562,189565],{"className":189552},[398],[363,189554],{"className":189555,"style":707},[402],[363,189557,51955],{"className":189558},[1831],[363,189560],{"className":189561,"style":1859},[505],[363,189563],{"className":189564,"style":754},[505],[363,189566,189568,189574,189577,189580,189583,189688],{"className":189567},[758],[363,189569,189571],{"className":189570,"style":763},[494,762],[363,189572,461],{"className":189573},[767,657],[363,189575,465],{"className":189576},[407],[363,189578,898],{"className":189579},[920],[363,189581],{"className":189582,"style":754},[505],[363,189584,189586,189589,189685],{"className":189585},[407],[363,189587],{"className":189588},[494,789],[363,189590,189592],{"className":189591},[586],[363,189593,189595,189677],{"className":189594},[633,634],[363,189596,189598,189674],{"className":189597},[638],[363,189599,189601,189655,189663],{"className":189600,"style":71402},[642],[363,189602,189603,189606],{"style":805},[363,189604],{"className":189605,"style":809},[650],[363,189607,189609],{"className":189608},[407],[363,189610,189612,189615],{"className":189611},[407],[363,189613,5739],{"className":189614,"style":682},[407,408],[363,189616,189618],{"className":189617},[629],[363,189619,189621,189647],{"className":189620},[633,634],[363,189622,189624,189644],{"className":189623},[638],[363,189625,189627],{"className":189626,"style":643},[642],[363,189628,189629,189632],{"style":11483},[363,189630],{"className":189631,"style":651},[650],[363,189633,189635],{"className":189634},[655,656,657,658],[363,189636,189638],{"className":189637},[407,658],[363,189639,189641],{"className":189640},[407,4945,658],[363,189642,189328],{"className":189643},[407,658],[363,189645,666],{"className":189646},[665],[363,189648,189650],{"className":189649},[638],[363,189651,189653],{"className":189652,"style":8315},[642],[363,189654],{},[363,189656,189657,189660],{"style":821},[363,189658],{"className":189659,"style":809},[650],[363,189661],{"className":189662,"style":829},[828],[363,189664,189665,189668],{"style":832},[363,189666],{"className":189667,"style":809},[650],[363,189669,189671],{"className":189670},[407],[363,189672,1116],{"className":189673},[407,408],[363,189675,666],{"className":189676},[665],[363,189678,189680],{"className":189679},[638],[363,189681,189683],{"className":189682,"style":125395},[642],[363,189684],{},[363,189686],{"className":189687},[501,789],[363,189689,189691],{"className":189690,"style":763},[501,762],[363,189692,468],{"className":189693},[767,657],[11,189695,189696,189697,189789,189790,189882,189883,189912],{},"退火的设计意图是分工时段的划分：训练初期 ",[363,189698,189700,189722],{"className":189699,"translate":367},[366],[363,189701,189703],{"className":189702},[371],[373,189704,189705],{"xmlns":375},[377,189706,189707,189719],{},[380,189708,189709,189715,189717],{},[543,189710,189711,189713],{},[383,189712,11686],{},[383,189714,1116],{},[458,189716,33306],{},[463,189718,474],{},[387,189720,189721],{"encoding":389},"\\lambda_t \\approx 0",[363,189723,189725,189780],{"className":189724,"ariaHidden":394},[393],[363,189726,189728,189731,189771,189774,189777],{"className":189727},[398],[363,189729],{"className":189730,"style":11821},[402],[363,189732,189734,189737],{"className":189733},[407],[363,189735,11686],{"className":189736},[407,408],[363,189738,189740],{"className":189739},[629],[363,189741,189743,189763],{"className":189742},[633,634],[363,189744,189746,189760],{"className":189745},[638],[363,189747,189749],{"className":189748,"style":189431},[642],[363,189750,189751,189754],{"style":730},[363,189752],{"className":189753,"style":651},[650],[363,189755,189757],{"className":189756},[655,656,657,658],[363,189758,1116],{"className":189759},[407,408,658],[363,189761,666],{"className":189762},[665],[363,189764,189766],{"className":189765},[638],[363,189767,189769],{"className":189768,"style":8315},[642],[363,189770],{},[363,189772],{"className":189773,"style":506},[505],[363,189775,33306],{"className":189776},[510],[363,189778],{"className":189779,"style":506},[505],[363,189781,189783,189786],{"className":189782},[398],[363,189784],{"className":189785,"style":520},[402],[363,189787,474],{"className":189788},[407],"，网络可以自由地按拟合损失调整证据的量级，避免在证据尚未成形时被正则项过早地压向零。训练后期 ",[363,189791,189793,189815],{"className":189792,"translate":367},[366],[363,189794,189796],{"className":189795},[371],[373,189797,189798],{"xmlns":375},[377,189799,189800,189812],{},[380,189801,189802,189808,189810],{},[543,189803,189804,189806],{},[383,189805,11686],{},[383,189807,1116],{},[458,189809,1376],{},[463,189811,465],{},[387,189813,189814],{"encoding":389},"\\lambda_t \\to 1",[363,189816,189818,189873],{"className":189817,"ariaHidden":394},[393],[363,189819,189821,189824,189864,189867,189870],{"className":189820},[398],[363,189822],{"className":189823,"style":11821},[402],[363,189825,189827,189830],{"className":189826},[407],[363,189828,11686],{"className":189829},[407,408],[363,189831,189833],{"className":189832},[629],[363,189834,189836,189856],{"className":189835},[633,634],[363,189837,189839,189853],{"className":189838},[638],[363,189840,189842],{"className":189841,"style":189431},[642],[363,189843,189844,189847],{"style":730},[363,189845],{"className":189846,"style":651},[650],[363,189848,189850],{"className":189849},[655,656,657,658],[363,189851,1116],{"className":189852},[407,408,658],[363,189854,666],{"className":189855},[665],[363,189857,189859],{"className":189858},[638],[363,189860,189862],{"className":189861,"style":8315},[642],[363,189863],{},[363,189865],{"className":189866,"style":506},[505],[363,189868,1376],{"className":189869},[510],[363,189871],{"className":189872,"style":506},[505],[363,189874,189876,189879],{"className":189875},[398],[363,189877],{"className":189878,"style":520},[402],[363,189880,465],{"className":189881},[407],"，正则项接管，迫使模型对错误预测给出高不确定性。消融实验一致表明，缺少退火（即使用常数 ",[363,189884,189886,189900],{"className":189885,"translate":367},[366],[363,189887,189889],{"className":189888},[371],[373,189890,189891],{"xmlns":375},[377,189892,189893,189897],{},[380,189894,189895],{},[383,189896,11686],{},[387,189898,189899],{"encoding":389},"\\lambda",[363,189901,189903],{"className":189902,"ariaHidden":394},[393],[363,189904,189906,189909],{"className":189905},[398],[363,189907],{"className":189908,"style":12944},[402],[363,189910,11686],{"className":189911},[407,408],"）会显著损害性能——这与该设计的解释相符，而非仅仅是超参数调优的产物。",[2658,189914,189916],{"id":189915},"_44-统一视角与变体","4.4 统一视角与变体",[11,189918,189919],{},"上述两项可以统一在一个更一般的框架下。所有基于 EDL 的拟合损失都具有形式",[363,189921,189923],{"className":189922,"translate":367},[528],[363,189924,189926,189985],{"className":189925,"translate":367},[366],[363,189927,189929],{"className":189928},[371],[373,189930,189931],{"xmlns":375,"display":537},[377,189932,189933,189982],{},[380,189934,189935,189941,189943,189963],{},[7161,189936,189937,189939],{},[383,189938,22240],{"mathvariant":944},[1644,189940,189275],{},[458,189942,471],{},[543,189944,189945,189947],{},[383,189946,571],{"mathvariant":570},[380,189948,189949,189951,189953,189955,189957,189959,189961],{},[383,189950,157399],{"mathvariant":136008},[458,189952,9216],{},[383,189954,137065],{"mathvariant":557},[458,189956,4450],{},[458,189958,461],{"stretchy":460},[383,189960,45101],{"mathvariant":136008},[458,189962,468],{"stretchy":460},[380,189964,189965,189967,189970,189972,189974,189976,189978,189980],{},[458,189966,578],{"fence":394},[383,189968,189969],{"mathvariant":557},"ℓ",[458,189971,461],{"stretchy":460},[383,189973,40584],{"mathvariant":75560},[458,189975,898],{"separator":394},[383,189977,157399],{"mathvariant":136008},[458,189979,468],{"stretchy":460},[458,189981,605],{"fence":394},[387,189983,189984],{"encoding":389},"\\mathcal{L}^{\\text{fit}} = \\mathbb{E}_{\\boldsymbol{\\pi} \\sim \\operatorname{Dir}(\\boldsymbol{\\alpha})}\\left[\\ell(\\mathbf{y}, \\boldsymbol{\\pi})\\right]",[363,189986,189988,190038],{"className":189987,"ariaHidden":394},[393],[363,189989,189991,189994,190029,190032,190035],{"className":189990},[398],[363,189992],{"className":189993,"style":48211},[402],[363,189995,189997,190000],{"className":189996},[407],[363,189998,22240],{"className":189999},[407,971],[363,190001,190003],{"className":190002},[629],[363,190004,190006],{"className":190005},[633],[363,190007,190009],{"className":190008},[638],[363,190010,190012],{"className":190011,"style":48211},[642],[363,190013,190014,190017],{"style":8624},[363,190015],{"className":190016,"style":651},[650],[363,190018,190020],{"className":190019},[655,656,657,658],[363,190021,190023],{"className":190022},[407,658],[363,190024,190026],{"className":190025},[407,4945,658],[363,190027,189275],{"className":190028},[407,658],[363,190030],{"className":190031,"style":506},[505],[363,190033,471],{"className":190034},[510],[363,190036],{"className":190037,"style":506},[505],[363,190039,190041,190044,190117,190120],{"className":190040},[398],[363,190042],{"className":190043,"style":6426},[402],[363,190045,190047,190050],{"className":190046},[407],[363,190048,571],{"className":190049},[407,714],[363,190051,190053],{"className":190052},[629],[363,190054,190056,190109],{"className":190055},[633,634],[363,190057,190059,190106],{"className":190058},[638],[363,190060,190062],{"className":190061,"style":6445},[642],[363,190063,190064,190067],{"style":75920},[363,190065],{"className":190066,"style":651},[650],[363,190068,190070],{"className":190069},[655,656,657,658],[363,190071,190073,190082,190085,190091,190094,190103],{"className":190072},[407,658],[363,190074,190076],{"className":190075},[407,658],[363,190077,190079],{"className":190078},[407,658],[363,190080,157399],{"className":190081,"style":157433},[407,136068,658],[363,190083,9216],{"className":190084},[510,658],[363,190086,190088],{"className":190087},[1831,658],[363,190089,137065],{"className":190090},[407,33009,658],[363,190092,461],{"className":190093},[494,658],[363,190095,190097],{"className":190096},[407,658],[363,190098,190100],{"className":190099},[407,658],[363,190101,45101],{"className":190102},[407,136068,658],[363,190104,468],{"className":190105},[501,658],[363,190107,666],{"className":190108},[665],[363,190110,190112],{"className":190111},[638],[363,190113,190115],{"className":190114,"style":6491},[642],[363,190116],{},[363,190118],{"className":190119,"style":754},[505],[363,190121,190123,190126,190129,190132,190135,190138,190141,190150,190153],{"className":190122},[758],[363,190124,578],{"className":190125,"style":763},[494,762],[363,190127,189969],{"className":190128},[407],[363,190130,461],{"className":190131},[494],[363,190133,40584],{"className":190134,"style":162090},[407,75905],[363,190136,898],{"className":190137},[920],[363,190139],{"className":190140,"style":754},[505],[363,190142,190144],{"className":190143},[407],[363,190145,190147],{"className":190146},[407],[363,190148,157399],{"className":190149,"style":157433},[407,136068],[363,190151,468],{"className":190152},[501],[363,190154,605],{"className":190155,"style":763},[501,762],[11,190157,87982,190158,190191,190192,190304,190305,190424],{},[1572,190159,190160,190161,190190],{},"对某个一阶损失 ",[363,190162,190164,190178],{"className":190163,"translate":367},[366],[363,190165,190167],{"className":190166},[371],[373,190168,190169],{"xmlns":375},[377,190170,190171,190175],{},[380,190172,190173],{},[383,190174,189969],{"mathvariant":557},[387,190176,190177],{"encoding":389},"\\ell",[363,190179,190181],{"className":190180,"ariaHidden":394},[393],[363,190182,190184,190187],{"className":190183},[398],[363,190185],{"className":190186,"style":12944},[402],[363,190188,189969],{"className":190189},[407]," 的先验期望","。取 ",[363,190193,190195,190223],{"className":190194,"translate":367},[366],[363,190196,190198],{"className":190197},[371],[373,190199,190200],{"xmlns":375},[377,190201,190202,190220],{},[380,190203,190204,190206,190208,190210,190212,190214],{},[383,190205,189969],{"mathvariant":557},[458,190207,471],{},[458,190209,5160],{},[383,190211,4447],{},[458,190213,4450],{},[543,190215,190216,190218],{},[383,190217,157399],{},[383,190219,40584],{},[387,190221,190222],{"encoding":389},"\\ell = -\\log \\pi_y",[363,190224,190226,190244],{"className":190225,"ariaHidden":394},[393],[363,190227,190229,190232,190235,190238,190241],{"className":190228},[398],[363,190230],{"className":190231,"style":12944},[402],[363,190233,189969],{"className":190234},[407],[363,190236],{"className":190237,"style":506},[505],[363,190239,471],{"className":190240},[510],[363,190242],{"className":190243,"style":506},[505],[363,190245,190247,190250,190253,190256,190261,190264],{"className":190246},[398],[363,190248],{"className":190249,"style":153698},[402],[363,190251,5160],{"className":190252},[407],[363,190254],{"className":190255,"style":754},[505],[363,190257,4501,190259],{"className":190258},[1831],[363,190260,4505],{"style":4504},[363,190262],{"className":190263,"style":754},[505],[363,190265,190267,190270],{"className":190266},[407],[363,190268,157399],{"className":190269,"style":1328},[407,408],[363,190271,190273],{"className":190272},[629],[363,190274,190276,190296],{"className":190275},[633,634],[363,190277,190279,190293],{"className":190278},[638],[363,190280,190282],{"className":190281,"style":45276},[642],[363,190283,190284,190287],{"style":19190},[363,190285],{"className":190286,"style":651},[650],[363,190288,190290],{"className":190289},[655,656,657,658],[363,190291,40584],{"className":190292,"style":1328},[407,408,658],[363,190294,666],{"className":190295},[665],[363,190297,190299],{"className":190298},[638],[363,190300,190302],{"className":190301,"style":673},[642],[363,190303],{}," 得命题 4.1 的 digamma 形式。取 ",[363,190306,190308,190338],{"className":190307,"translate":367},[366],[363,190309,190311],{"className":190310},[371],[373,190312,190313],{"xmlns":375},[377,190314,190315,190335],{},[380,190316,190317,190319,190321,190323,190325,190327,190329],{},[383,190318,189969],{"mathvariant":557},[458,190320,471],{},[383,190322,558],{"mathvariant":557},[383,190324,40584],{"mathvariant":75560},[458,190326,5160],{},[383,190328,157399],{"mathvariant":136008},[7161,190330,190331,190333],{},[383,190332,558],{"mathvariant":557},[463,190334,2810],{},[387,190336,190337],{"encoding":389},"\\ell = \\|\\mathbf{y} - \\boldsymbol{\\pi}\\|^2",[363,190339,190341,190359,190380],{"className":190340,"ariaHidden":394},[393],[363,190342,190344,190347,190350,190353,190356],{"className":190343},[398],[363,190345],{"className":190346,"style":12944},[402],[363,190348,189969],{"className":190349},[407],[363,190351],{"className":190352,"style":506},[505],[363,190354,471],{"className":190355},[510],[363,190357],{"className":190358,"style":506},[505],[363,190360,190362,190365,190368,190371,190374,190377],{"className":190361},[398],[363,190363],{"className":190364,"style":487},[402],[363,190366,558],{"className":190367},[407],[363,190369,40584],{"className":190370,"style":162090},[407,75905],[363,190372],{"className":190373,"style":2934},[505],[363,190375,5160],{"className":190376},[2938],[363,190378],{"className":190379,"style":2934},[505],[363,190381,190383,190386,190395],{"className":190382},[398],[363,190384],{"className":190385,"style":20350},[402],[363,190387,190389],{"className":190388},[407],[363,190390,190392],{"className":190391},[407],[363,190393,157399],{"className":190394,"style":157433},[407,136068],[363,190396,190398,190401],{"className":190397},[407],[363,190399,558],{"className":190400},[407],[363,190402,190404],{"className":190403},[629],[363,190405,190407],{"className":190406},[633],[363,190408,190410],{"className":190409},[638],[363,190411,190413],{"className":190412,"style":20375},[642],[363,190414,190415,190418],{"style":7212},[363,190416],{"className":190417,"style":651},[650],[363,190419,190421],{"className":190420},[655,656,657,658],[363,190422,2810],{"className":190423},[407,658]," 得命题 4.3 的平方形式。这一视角把「EDL 的损失设计」转化为「选择哪个一阶损失并在迪利克雷族上求其贝叶斯风险」的标准问题，从而使新损失的设计有章可循。",[11,190426,190427],{},"在此基础上，文献中出现的主要变体可归入三类：",[7009,190429,190430,190536,190546],{},[7012,190431,190432,190435,190436,190506,190507,190535],{},[1572,190433,190434],{},"正则方式不同","。除 4.3 节的 KL 正则外，也有工作直接以「认知不确定性应随证据增加而衰减」作为约束，或对证据施加 ",[363,190437,190439,190457],{"className":190438,"translate":367},[366],[363,190440,190442],{"className":190441},[371],[373,190443,190444],{"xmlns":375},[377,190445,190446,190454],{},[380,190447,190448],{},[543,190449,190450,190452],{},[383,190451,22240],{},[463,190453,2810],{},[387,190455,190456],{"encoding":389},"L_2",[363,190458,190460],{"className":190459,"ariaHidden":394},[393],[363,190461,190463,190466],{"className":190462},[398],[363,190464],{"className":190465,"style":16308},[402],[363,190467,190469,190472],{"className":190468},[407],[363,190470,22240],{"className":190471},[407,408],[363,190473,190475],{"className":190474},[629],[363,190476,190478,190498],{"className":190477},[633,634],[363,190479,190481,190495],{"className":190480},[638],[363,190482,190484],{"className":190483,"style":11480},[642],[363,190485,190486,190489],{"style":730},[363,190487],{"className":190488,"style":651},[650],[363,190490,190492],{"className":190491},[655,656,657,658],[363,190493,2810],{"className":190494},[407,658],[363,190496,666],{"className":190497},[665],[363,190499,190501],{"className":190500},[638],[363,190502,190504],{"className":190503,"style":8315},[642],[363,190505],{}," 惩罚。其共同目标都是阻止 ",[363,190508,190510,190523],{"className":190509,"translate":367},[366],[363,190511,190513],{"className":190512},[371],[373,190514,190515],{"xmlns":375},[377,190516,190517,190521],{},[380,190518,190519],{},[383,190520,26084],{},[387,190522,26084],{"encoding":389},[363,190524,190526],{"className":190525,"ariaHidden":394},[393],[363,190527,190529,190532],{"className":190528},[398],[363,190530],{"className":190531,"style":1011},[402],[363,190533,26084],{"className":190534,"style":26208},[407,408]," 的退化。",[7012,190537,190538,190541,190542,190545],{},[1572,190539,190540],{},"监督方式不同","。Prior Networks 不在期望风险上训练，而是显式地构造一个",[1572,190543,190544],{},"目标迪利克雷分布","（例如：分布内样本用尖锐的 Dirichlet 匹配、分布外样本用平坦的 Dirichlet 匹配），并在分布层面直接计算 KL。这需要分布外样本来定义目标，因此换取的是更强的不确定性控制与更弱的即插即用性。",[7012,190547,190548,190551],{},[1572,190549,190550],{},"回归情形的推广","。把分类的迪利克雷替换为 Normal-Inverse-Gamma 先验，即得 Deep Evidential Regression（5.5 节）。",[11,190553,190554,190555,190558,190559,190562],{},"统一框架也澄清了一个理论定位问题：EDL 与贝叶斯神经网络（BNN）、深度集成（deep ensembles）、MC Dropout 属于",[1572,190556,190557],{},"不同的","不确定性来源。后三者通过对网络参数（或其近似后验）的分布求积分得到预测分布。EDL 则在固定的参数点估计上，对",[1572,190560,190561],{},"输出层的二阶分布","求积分。二者的区分不是工程实现上的，而是概率模型结构上的，这正是下一小节批评的出发点。",[2658,190564,190566],{"id":190565},"_45-使用边界","4.5 使用边界",[11,190568,190569],{},"EDL 在实践中表现良好，但其理论地位常被过度解读。把边界集中列出，与前文的正式推导互为对照：",[7009,190571,190572,191481,191611,191877,191938],{},[7012,190573,190574,190577,190578,190887,190888,190957,190958,10527,191173,191176,191177,191360,191361,2756,191389,191451,191452,191480],{},[1572,190575,190576],{},"它不是贝叶斯不确定性。"," 严格的后验预测分布应由对网络参数的边缘化给出：\n",[363,190579,190581,190666],{"className":190580,"translate":367},[366],[363,190582,190584],{"className":190583},[371],[373,190585,190586],{"xmlns":375},[377,190587,190588,190663],{},[380,190589,190590,190592,190594,190596,190598,190600,190602,190604,190606,190608,190611,190613,190615,190617,190619,190621,190623,190625,190627,190629,190631,190633,190635,190637,190639,190641,190643,190645,190647,190649,190651,190653,190655,190657,190659,190661],{},[383,190591,11],{},[458,190593,461],{"stretchy":460},[383,190595,40584],{},[458,190597,5155],{},[383,190599,1121],{"mathvariant":75560},[458,190601,898],{"separator":394},[383,190603,547],{"mathvariant":944},[458,190605,468],{"stretchy":460},[458,190607,471],{},[458,190609,190610],{},"∬",[383,190612,11],{},[458,190614,461],{"stretchy":460},[383,190616,40584],{},[458,190618,5155],{},[383,190620,157399],{"mathvariant":136008},[458,190622,468],{"stretchy":460},[1644,190624,1646],{},[383,190626,11],{},[458,190628,461],{"stretchy":460},[383,190630,157399],{"mathvariant":136008},[458,190632,5155],{},[383,190634,101106],{"mathvariant":136008},[458,190636,468],{"stretchy":460},[1644,190638,1646],{},[383,190640,11],{},[458,190642,461],{"stretchy":460},[383,190644,101106],{"mathvariant":136008},[458,190646,5155],{},[383,190648,547],{"mathvariant":944},[458,190650,468],{"stretchy":460},[1644,190652,1646],{},[383,190654,592],{"mathvariant":557},[383,190656,157399],{"mathvariant":136008},[1644,190658,1646],{},[383,190660,592],{"mathvariant":557},[383,190662,101106],{"mathvariant":136008},[387,190664,190665],{"encoding":389},"p(y \\mid \\mathbf{x}, \\mathcal{D}) = \\iint p(y \\mid \\boldsymbol{\\pi})\\,p(\\boldsymbol{\\pi} \\mid \\boldsymbol{\\theta})\\,p(\\boldsymbol{\\theta} \\mid \\mathcal{D})\\,\\mathrm{d}\\boldsymbol{\\pi}\\,\\mathrm{d}\\boldsymbol{\\theta}",[363,190667,190669,190693,190723,190755,190800,190845],{"className":190668,"ariaHidden":394},[393],[363,190670,190672,190675,190678,190681,190684,190687,190690],{"className":190671},[398],[363,190673],{"className":190674,"style":487},[402],[363,190676,11],{"className":190677},[407,408],[363,190679,461],{"className":190680},[494],[363,190682,40584],{"className":190683,"style":1328},[407,408],[363,190685],{"className":190686,"style":506},[505],[363,190688,5155],{"className":190689},[510],[363,190691],{"className":190692,"style":506},[505],[363,190694,190696,190699,190702,190705,190708,190711,190714,190717,190720],{"className":190695},[398],[363,190697],{"className":190698,"style":487},[402],[363,190700,1121],{"className":190701},[407,75905],[363,190703,898],{"className":190704},[920],[363,190706],{"className":190707,"style":754},[505],[363,190709,547],{"className":190710,"style":625},[407,971],[363,190712,468],{"className":190713},[501],[363,190715],{"className":190716,"style":506},[505],[363,190718,471],{"className":190719},[510],[363,190721],{"className":190722,"style":506},[505],[363,190724,190726,190730,190734,190737,190740,190743,190746,190749,190752],{"className":190725},[398],[363,190727],{"className":190728,"style":190729},[402],"height:1.111em;vertical-align:-0.306em;",[363,190731,190610],{"className":190732,"style":190733},[1831,1832,5963],"margin-right:0.1945em;position:relative;top:-0.0005em;",[363,190735],{"className":190736,"style":754},[505],[363,190738,11],{"className":190739},[407,408],[363,190741,461],{"className":190742},[494],[363,190744,40584],{"className":190745,"style":1328},[407,408],[363,190747],{"className":190748,"style":506},[505],[363,190750,5155],{"className":190751},[510],[363,190753],{"className":190754,"style":506},[505],[363,190756,190758,190761,190770,190773,190776,190779,190782,190791,190794,190797],{"className":190757},[398],[363,190759],{"className":190760,"style":487},[402],[363,190762,190764],{"className":190763},[407],[363,190765,190767],{"className":190766},[407],[363,190768,157399],{"className":190769,"style":157433},[407,136068],[363,190771,468],{"className":190772},[501],[363,190774],{"className":190775,"style":754},[505],[363,190777,11],{"className":190778},[407,408],[363,190780,461],{"className":190781},[494],[363,190783,190785],{"className":190784},[407],[363,190786,190788],{"className":190787},[407],[363,190789,157399],{"className":190790,"style":157433},[407,136068],[363,190792],{"className":190793,"style":506},[505],[363,190795,5155],{"className":190796},[510],[363,190798],{"className":190799,"style":506},[505],[363,190801,190803,190806,190815,190818,190821,190824,190827,190836,190839,190842],{"className":190802},[398],[363,190804],{"className":190805,"style":487},[402],[363,190807,190809],{"className":190808},[407],[363,190810,190812],{"className":190811},[407],[363,190813,101106],{"className":190814,"style":169854},[407,136068],[363,190816,468],{"className":190817},[501],[363,190819],{"className":190820,"style":754},[505],[363,190822,11],{"className":190823},[407,408],[363,190825,461],{"className":190826},[494],[363,190828,190830],{"className":190829},[407],[363,190831,190833],{"className":190832},[407],[363,190834,101106],{"className":190835,"style":169854},[407,136068],[363,190837],{"className":190838,"style":506},[505],[363,190840,5155],{"className":190841},[510],[363,190843],{"className":190844,"style":506},[505],[363,190846,190848,190851,190854,190857,190860,190863,190872,190875,190878],{"className":190847},[398],[363,190849],{"className":190850,"style":487},[402],[363,190852,547],{"className":190853,"style":625},[407,971],[363,190855,468],{"className":190856},[501],[363,190858],{"className":190859,"style":754},[505],[363,190861,592],{"className":190862},[407,33009],[363,190864,190866],{"className":190865},[407],[363,190867,190869],{"className":190868},[407],[363,190870,157399],{"className":190871,"style":157433},[407,136068],[363,190873],{"className":190874,"style":754},[505],[363,190876,592],{"className":190877},[407,33009],[363,190879,190881],{"className":190880},[407],[363,190882,190884],{"className":190883},[407],[363,190885,101106],{"className":190886,"style":169854},[407,136068],"\n而 EDL 以点估计 ",[363,190889,190891,190909],{"className":190890,"translate":367},[366],[363,190892,190894],{"className":190893},[371],[373,190895,190896],{"xmlns":375},[377,190897,190898,190906],{},[380,190899,190900],{},[12158,190901,190902,190904],{"accent":394},[383,190903,101106],{"mathvariant":136008},[458,190905,100285],{},[387,190907,190908],{"encoding":389},"\\hat{\\boldsymbol{\\theta}}",[363,190910,190912],{"className":190911,"ariaHidden":394},[393],[363,190913,190915,190919],{"className":190914},[398],[363,190916],{"className":190917,"style":190918},[402],"height:0.9579em;",[363,190920,190922],{"className":190921},[407,12198],[363,190923,190925],{"className":190924},[633],[363,190926,190928],{"className":190927},[638],[363,190929,190931,190945],{"className":190930,"style":190918},[642],[363,190932,190933,190936],{"style":12210},[363,190934],{"className":190935,"style":809},[650],[363,190937,190939],{"className":190938},[407],[363,190940,190942],{"className":190941},[407],[363,190943,101106],{"className":190944,"style":169854},[407,136068],[363,190946,190948,190951],{"style":190947},"top:-3.2634em;",[363,190949],{"className":190950,"style":809},[650],[363,190952,190954],{"className":190953,"style":185891},[12226],[363,190955,100285],{"className":190956},[407]," 替换外层积分，取 ",[363,190959,190961,191015],{"className":190960,"translate":367},[366],[363,190962,190964],{"className":190963},[371],[373,190965,190966],{"xmlns":375},[377,190967,190968,191012],{},[380,190969,190970,190972,190974,190976,190978,190980,190982,190984,190986,190988,190990,190992,190994,190996,190998,191000,191002,191008,191010],{},[383,190971,11],{},[458,190973,461],{"stretchy":460},[383,190975,157399],{"mathvariant":136008},[458,190977,5155],{},[383,190979,1121],{"mathvariant":75560},[458,190981,468],{"stretchy":460},[458,190983,471],{},[383,190985,137065],{"mathvariant":557},[458,190987,4450],{},[458,190989,461],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[383,190991,157399],{"mathvariant":136008},[458,190993,34222],{"separator":394},[383,190995,45101],{"mathvariant":136008},[458,190997,461],{"stretchy":460},[383,190999,1121],{"mathvariant":75560},[458,191001,34222],{"separator":394},[12158,191003,191004,191006],{"accent":394},[383,191005,101106],{"mathvariant":136008},[458,191007,100285],{},[458,191009,468],{"stretchy":460},[458,191011,468],{"fence":460,"stretchy":394,"minsize":9797,"maxsize":9797},[387,191013,191014],{"encoding":389},"p(\\boldsymbol{\\pi} \\mid \\mathbf{x}) = \\operatorname{Dir}\\big(\\boldsymbol{\\pi}; \\boldsymbol{\\alpha}(\\mathbf{x}; \\hat{\\boldsymbol{\\theta}})\\big)",[363,191016,191018,191048,191069],{"className":191017,"ariaHidden":394},[393],[363,191019,191021,191024,191027,191030,191039,191042,191045],{"className":191020},[398],[363,191022],{"className":191023,"style":487},[402],[363,191025,11],{"className":191026},[407,408],[363,191028,461],{"className":191029},[494],[363,191031,191033],{"className":191032},[407],[363,191034,191036],{"className":191035},[407],[363,191037,157399],{"className":191038,"style":157433},[407,136068],[363,191040],{"className":191041,"style":506},[505],[363,191043,5155],{"className":191044},[510],[363,191046],{"className":191047,"style":506},[505],[363,191049,191051,191054,191057,191060,191063,191066],{"className":191050},[398],[363,191052],{"className":191053,"style":487},[402],[363,191055,1121],{"className":191056},[407,75905],[363,191058,468],{"className":191059},[501],[363,191061],{"className":191062,"style":506},[505],[363,191064,471],{"className":191065},[510],[363,191067],{"className":191068,"style":506},[505],[363,191070,191072,191076,191082,191085,191091,191100,191103,191106,191115,191118,191121,191124,191127,191164,191167],{"className":191071},[398],[363,191073],{"className":191074,"style":191075},[402],"height:1.3079em;vertical-align:-0.35em;",[363,191077,191079],{"className":191078},[1831],[363,191080,137065],{"className":191081},[407,33009],[363,191083],{"className":191084,"style":754},[505],[363,191086,191088],{"className":191087},[407],[363,191089,461],{"className":191090},[767,10021],[363,191092,191094],{"className":191093},[407],[363,191095,191097],{"className":191096},[407],[363,191098,157399],{"className":191099,"style":157433},[407,136068],[363,191101,34222],{"className":191102},[920],[363,191104],{"className":191105,"style":754},[505],[363,191107,191109],{"className":191108},[407],[363,191110,191112],{"className":191111},[407],[363,191113,45101],{"className":191114},[407,136068],[363,191116,461],{"className":191117},[494],[363,191119,1121],{"className":191120},[407,75905],[363,191122,34222],{"className":191123},[920],[363,191125],{"className":191126,"style":754},[505],[363,191128,191130],{"className":191129},[407,12198],[363,191131,191133],{"className":191132},[633],[363,191134,191136],{"className":191135},[638],[363,191137,191139,191153],{"className":191138,"style":190918},[642],[363,191140,191141,191144],{"style":12210},[363,191142],{"className":191143,"style":809},[650],[363,191145,191147],{"className":191146},[407],[363,191148,191150],{"className":191149},[407],[363,191151,101106],{"className":191152,"style":169854},[407,136068],[363,191154,191155,191158],{"style":190947},[363,191156],{"className":191157,"style":809},[650],[363,191159,191161],{"className":191160,"style":185891},[12226],[363,191162,100285],{"className":191163},[407],[363,191165,468],{"className":191166},[501],[363,191168,191170],{"className":191169},[407],[363,191171,468],{"className":191172},[767,10021],[1572,191174,191175],{},"结果是一个插值（plug-in）估计","，其内层积分给出 ",[363,191178,191180,191213],{"className":191179,"translate":367},[366],[363,191181,191183],{"className":191182},[371],[373,191184,191185],{"xmlns":375},[377,191186,191187,191211],{},[380,191188,191189,191195,191197,191203,191205],{},[543,191190,191191,191193],{},[383,191192,11],{},[383,191194,7911],{},[458,191196,471],{},[543,191198,191199,191201],{},[383,191200,45101],{},[383,191202,7911],{},[383,191204,1288],{"mathvariant":557},[543,191206,191207,191209],{},[383,191208,45101],{},[463,191210,474],{},[387,191212,176453],{"encoding":389},[363,191214,191216,191271],{"className":191215,"ariaHidden":394},[393],[363,191217,191219,191222,191262,191265,191268],{"className":191218},[398],[363,191220],{"className":191221,"style":2623},[402],[363,191223,191225,191228],{"className":191224},[407],[363,191226,11],{"className":191227},[407,408],[363,191229,191231],{"className":191230},[629],[363,191232,191234,191254],{"className":191233},[633,634],[363,191235,191237,191251],{"className":191236},[638],[363,191238,191240],{"className":191239,"style":643},[642],[363,191241,191242,191245],{"style":730},[363,191243],{"className":191244,"style":651},[650],[363,191246,191248],{"className":191247},[655,656,657,658],[363,191249,7911],{"className":191250,"style":8614},[407,408,658],[363,191252,666],{"className":191253},[665],[363,191255,191257],{"className":191256},[638],[363,191258,191260],{"className":191259,"style":8315},[642],[363,191261],{},[363,191263],{"className":191264,"style":506},[505],[363,191266,471],{"className":191267},[510],[363,191269],{"className":191270,"style":506},[505],[363,191272,191274,191277,191317,191320],{"className":191273},[398],[363,191275],{"className":191276,"style":487},[402],[363,191278,191280,191283],{"className":191279},[407],[363,191281,45101],{"className":191282,"style":45131},[407,408],[363,191284,191286],{"className":191285},[629],[363,191287,191289,191309],{"className":191288},[633,634],[363,191290,191292,191306],{"className":191291},[638],[363,191293,191295],{"className":191294,"style":643},[642],[363,191296,191297,191300],{"style":136107},[363,191298],{"className":191299,"style":651},[650],[363,191301,191303],{"className":191302},[655,656,657,658],[363,191304,7911],{"className":191305,"style":8614},[407,408,658],[363,191307,666],{"className":191308},[665],[363,191310,191312],{"className":191311},[638],[363,191313,191315],{"className":191314,"style":8315},[642],[363,191316],{},[363,191318,1288],{"className":191319},[407],[363,191321,191323,191326],{"className":191322},[407],[363,191324,45101],{"className":191325,"style":45131},[407,408],[363,191327,191329],{"className":191328},[629],[363,191330,191332,191352],{"className":191331},[633,634],[363,191333,191335,191349],{"className":191334},[638],[363,191336,191338],{"className":191337,"style":11480},[642],[363,191339,191340,191343],{"style":136107},[363,191341],{"className":191342,"style":651},[650],[363,191344,191346],{"className":191345},[655,656,657,658],[363,191347,474],{"className":191348},[407,658],[363,191350,666],{"className":191351},[665],[363,191353,191355],{"className":191354},[638],[363,191356,191358],{"className":191357,"style":8315},[642],[363,191359],{},"（由聚合性），确实正确。但外层积分被抛弃，",[363,191362,191364,191377],{"className":191363,"translate":367},[366],[363,191365,191367],{"className":191366},[371],[373,191368,191369],{"xmlns":375},[377,191370,191371,191375],{},[380,191372,191373],{},[383,191374,15747],{},[387,191376,15747],{"encoding":389},[363,191378,191380],{"className":191379,"ariaHidden":394},[393],[363,191381,191383,191386],{"className":191382},[398],[363,191384],{"className":191385,"style":2692},[402],[363,191387,15747],{"className":191388},[407,408],[363,191390,191392,191415],{"className":191391,"translate":367},[366],[363,191393,191395],{"className":191394},[371],[373,191396,191397],{"xmlns":375},[377,191398,191399,191413],{},[380,191400,191401,191403,191405,191407,191409,191411],{},[383,191402,34215],{},[458,191404,461],{"stretchy":460},[383,191406,40584],{},[458,191408,34222],{"separator":394},[383,191410,157399],{"mathvariant":136008},[458,191412,468],{"stretchy":460},[387,191414,179496],{"encoding":389},[363,191416,191418],{"className":191417,"ariaHidden":394},[393],[363,191419,191421,191424,191427,191430,191433,191436,191439,191448],{"className":191420},[398],[363,191422],{"className":191423,"style":487},[402],[363,191425,34215],{"className":191426,"style":9234},[407,408],[363,191428,461],{"className":191429},[494],[363,191431,40584],{"className":191432,"style":1328},[407,408],[363,191434,34222],{"className":191435},[920],[363,191437],{"className":191438,"style":754},[505],[363,191440,191442],{"className":191441},[407],[363,191443,191445],{"className":191444},[407],[363,191446,157399],{"className":191447,"style":157433},[407,136068],[363,191449,468],{"className":191450},[501]," 所度量的是「对输出分布的把握」，而非「对模型的把握」。二者在分布外输入上可以严重分歧：一个被错误训练的网络可以以极低的 ",[363,191453,191455,191468],{"className":191454,"translate":367},[366],[363,191456,191458],{"className":191457},[371],[373,191459,191460],{"xmlns":375},[377,191461,191462,191466],{},[380,191463,191464],{},[383,191465,15747],{},[387,191467,15747],{"encoding":389},[363,191469,191471],{"className":191470,"ariaHidden":394},[393],[363,191472,191474,191477],{"className":191473},[398],[363,191475],{"className":191476,"style":2692},[402],[363,191478,15747],{"className":191479},[407,408]," 输出一个错误的类别。",[7012,191482,191483,191486,191487,191547,191548,191610],{},[1572,191484,191485],{},"不确定性分数丢弃了证据的分布信息。"," 如 3.5 节所述，",[363,191488,191490,191511],{"className":191489,"translate":367},[366],[363,191491,191493],{"className":191492},[371],[373,191494,191495],{"xmlns":375},[377,191496,191497,191509],{},[380,191498,191499,191501,191503,191505,191507],{},[383,191500,15747],{},[458,191502,471],{},[383,191504,11041],{},[383,191506,1288],{"mathvariant":557},[383,191508,26084],{},[387,191510,175606],{"encoding":389},[363,191512,191514,191532],{"className":191513,"ariaHidden":394},[393],[363,191515,191517,191520,191523,191526,191529],{"className":191516},[398],[363,191518],{"className":191519,"style":2692},[402],[363,191521,15747],{"className":191522},[407,408],[363,191524],{"className":191525,"style":506},[505],[363,191527,471],{"className":191528},[510],[363,191530],{"className":191531,"style":506},[505],[363,191533,191535,191538,191541,191544],{"className":191534},[398],[363,191536],{"className":191537,"style":487},[402],[363,191539,11041],{"className":191540,"style":11129},[407,408],[363,191542,1288],{"className":191543},[407],[363,191545,26084],{"className":191546,"style":26208},[407,408]," 仅是总证据的函数。它无法表达「证据分散但充分」与「证据集中但贫乏」的区别，也无法区分证据落在何类。",[363,191549,191551,191574],{"className":191550,"translate":367},[366],[363,191552,191554],{"className":191553},[371],[373,191555,191556],{"xmlns":375},[377,191557,191558,191572],{},[380,191559,191560,191562,191564,191566,191568,191570],{},[383,191561,34215],{},[458,191563,461],{"stretchy":460},[383,191565,40584],{},[458,191567,34222],{"separator":394},[383,191569,157399],{"mathvariant":136008},[458,191571,468],{"stretchy":460},[387,191573,179496],{"encoding":389},[363,191575,191577],{"className":191576,"ariaHidden":394},[393],[363,191578,191580,191583,191586,191589,191592,191595,191598,191607],{"className":191579},[398],[363,191581],{"className":191582,"style":487},[402],[363,191584,34215],{"className":191585,"style":9234},[407,408],[363,191587,461],{"className":191588},[494],[363,191590,40584],{"className":191591,"style":1328},[407,408],[363,191593,34222],{"className":191594},[920],[363,191596],{"className":191597,"style":754},[505],[363,191599,191601],{"className":191600},[407],[363,191602,191604],{"className":191603},[407],[363,191605,157399],{"className":191606,"style":157433},[407,136068],[363,191608,468],{"className":191609},[501]," 缓解了这一点，但仍不引入任何关于模型参数的信息。",[7012,191612,191613,191616,191617,191872,191873,191876],{},[1572,191614,191615],{},"拟合损失带有一个与强度耦合的偏置。"," 推论 4.2 表明，对数形式等价于交叉熵加上 ",[363,191618,191620,191662],{"className":191619,"translate":367},[366],[363,191621,191623],{"className":191622},[371],[373,191624,191625],{"xmlns":375},[377,191626,191627,191659],{},[380,191628,191629,191631,191645,191647,191657],{},[458,191630,461],{"stretchy":460},[586,191632,191633,191635],{},[463,191634,465],{},[380,191636,191637,191639],{},[463,191638,2810],{},[543,191640,191641,191643],{},[383,191642,45101],{},[383,191644,40584],{},[458,191646,5160],{},[586,191648,191649,191651],{},[463,191650,465],{},[380,191652,191653,191655],{},[463,191654,2810],{},[383,191656,26084],{},[458,191658,468],{"stretchy":460},[387,191660,191661],{"encoding":389},"(\\frac{1}{2\\alpha_y} - \\frac{1}{2S})",[363,191663,191665,191792],{"className":191664,"ariaHidden":394},[393],[363,191666,191668,191672,191675,191783,191786,191789],{"className":191667},[398],[363,191669],{"className":191670,"style":191671},[402],"height:1.3874em;vertical-align:-0.5423em;",[363,191673,461],{"className":191674},[494],[363,191676,191678,191681,191780],{"className":191677},[407],[363,191679],{"className":191680},[494,789],[363,191682,191684],{"className":191683},[586],[363,191685,191687,191772],{"className":191686},[633,634],[363,191688,191690,191769],{"className":191689},[638],[363,191691,191693,191747,191755],{"className":191692,"style":2871},[642],[363,191694,191695,191698],{"style":2874},[363,191696],{"className":191697,"style":809},[650],[363,191699,191701],{"className":191700},[655,656,657,658],[363,191702,191704,191707],{"className":191703},[407,658],[363,191705,2810],{"className":191706},[407,658],[363,191708,191710,191713],{"className":191709},[407,658],[363,191711,45101],{"className":191712,"style":45131},[407,408,658],[363,191714,191716],{"className":191715},[629],[363,191717,191719,191739],{"className":191718},[633,634],[363,191720,191722,191736],{"className":191721},[638],[363,191723,191725],{"className":191724,"style":74609},[642],[363,191726,191727,191730],{"style":136942},[363,191728],{"className":191729,"style":30553},[650],[363,191731,191733],{"className":191732},[655,30557,10021,658],[363,191734,40584],{"className":191735,"style":1328},[407,408,658],[363,191737,666],{"className":191738},[665],[363,191740,191742],{"className":191741},[638],[363,191743,191745],{"className":191744,"style":122065},[642],[363,191746],{},[363,191748,191749,191752],{"style":821},[363,191750],{"className":191751,"style":809},[650],[363,191753],{"className":191754,"style":829},[828],[363,191756,191757,191760],{"style":2897},[363,191758],{"className":191759,"style":809},[650],[363,191761,191763],{"className":191762},[655,656,657,658],[363,191764,191766],{"className":191765},[407,658],[363,191767,465],{"className":191768},[407,658],[363,191770,666],{"className":191771},[665],[363,191773,191775],{"className":191774},[638],[363,191776,191778],{"className":191777,"style":182476},[642],[363,191779],{},[363,191781],{"className":191782},[501,789],[363,191784],{"className":191785,"style":2934},[505],[363,191787,5160],{"className":191788},[2938],[363,191790],{"className":191791,"style":2934},[505],[363,191793,191795,191798,191869],{"className":191794},[398],[363,191796],{"className":191797,"style":2852},[402],[363,191799,191801,191804,191866],{"className":191800},[407],[363,191802],{"className":191803},[494,789],[363,191805,191807],{"className":191806},[586],[363,191808,191810,191858],{"className":191809},[633,634],[363,191811,191813,191855],{"className":191812},[638],[363,191814,191816,191833,191841],{"className":191815,"style":2871},[642],[363,191817,191818,191821],{"style":2874},[363,191819],{"className":191820,"style":809},[650],[363,191822,191824],{"className":191823},[655,656,657,658],[363,191825,191827,191830],{"className":191826},[407,658],[363,191828,2810],{"className":191829},[407,658],[363,191831,26084],{"className":191832,"style":26208},[407,408,658],[363,191834,191835,191838],{"style":821},[363,191836],{"className":191837,"style":809},[650],[363,191839],{"className":191840,"style":829},[828],[363,191842,191843,191846],{"style":2897},[363,191844],{"className":191845,"style":809},[650],[363,191847,191849],{"className":191848},[655,656,657,658],[363,191850,191852],{"className":191851},[407,658],[363,191853,465],{"className":191854},[407,658],[363,191856,666],{"className":191857},[665],[363,191859,191861],{"className":191860},[638],[363,191862,191864],{"className":191863,"style":2919},[642],[363,191865],{},[363,191867],{"className":191868},[501,789],[363,191870,468],{"className":191871},[501]," 的修正。因此损失的最小值并不位于「插值交叉熵的最优解」，而是位于一个把证据量级也纳入权衡的点上。这不是缺陷本身，但它意味着",[1572,191874,191875],{},"EDL 的优化目标与「拟合条件分布」并非同一个目标","，将其损失解释为似然的做法在术语上应作区分。",[7012,191878,191879,191882,191883,191937],{},[1572,191880,191881],{},"「以损失最小化实现不确定性量化」这一范式受到根本性质疑。"," 有研究指出，当认知不确定性被定义为某个二阶损失（即关于 ",[363,191884,191886,191907],{"className":191885,"translate":367},[366],[363,191887,191889],{"className":191888},[371],[373,191890,191891],{"xmlns":375},[377,191892,191893,191905],{},[380,191894,191895,191897,191899,191901,191903],{},[383,191896,137065],{"mathvariant":557},[458,191898,4450],{},[458,191900,461],{"stretchy":460},[383,191902,45101],{"mathvariant":136008},[458,191904,468],{"stretchy":460},[387,191906,171704],{"encoding":389},[363,191908,191910],{"className":191909,"ariaHidden":394},[393],[363,191911,191913,191916,191922,191925,191934],{"className":191912},[398],[363,191914],{"className":191915,"style":487},[402],[363,191917,191919],{"className":191918},[1831],[363,191920,137065],{"className":191921},[407,33009],[363,191923,461],{"className":191924},[494],[363,191926,191928],{"className":191927},[407],[363,191929,191931],{"className":191930},[407],[363,191932,45101],{"className":191933},[407,136068],[363,191935,468],{"className":191936},[501]," 的泛函）的极小化者时，损失可以在与真实认知状态无关的第二阶分布上取得同一最小值，从而该极小化者一般并不落在具有正确认知解释的分布上。换言之，「损失小」并不蕴含「认知不确定性估计正确」。这一批评与本条前三点在方向上是独立的：即便接受 EDL 的目标函数，其最优解也未必具有所宣称的语义。",[7012,191939,191940,191943,191944,192060,192061,192089,192090,10527],{},[1572,191941,191942],{},"它对主干特征的可分性有隐含依赖。"," 证据由 ",[363,191945,191947,191975],{"className":191946,"translate":367},[366],[363,191948,191950],{"className":191949},[371],[373,191951,191952],{"xmlns":375},[377,191953,191954,191972],{},[380,191955,191956,191958,191960,191966,191968,191970],{},[383,191957,7914],{"mathvariant":75560},[458,191959,471],{},[543,191961,191962,191964],{},[383,191963,4505],{},[383,191965,101106],{"mathvariant":136008},[458,191967,461],{"stretchy":460},[383,191969,1121],{"mathvariant":75560},[458,191971,468],{"stretchy":460},[387,191973,191974],{"encoding":389},"\\mathbf{e} = g_{\\boldsymbol{\\theta}}(\\mathbf{x})",[363,191976,191978,191996],{"className":191977,"ariaHidden":394},[393],[363,191979,191981,191984,191987,191990,191993],{"className":191980},[398],[363,191982],{"className":191983,"style":135617},[402],[363,191985,7914],{"className":191986},[407,75905],[363,191988],{"className":191989,"style":506},[505],[363,191991,471],{"className":191992},[510],[363,191994],{"className":191995,"style":506},[505],[363,191997,191999,192002,192051,192054,192057],{"className":191998},[398],[363,192000],{"className":192001,"style":487},[402],[363,192003,192005,192008],{"className":192004},[407],[363,192006,4505],{"className":192007,"style":1328},[407,408],[363,192009,192011],{"className":192010},[629],[363,192012,192014,192043],{"className":192013},[633,634],[363,192015,192017,192040],{"className":192016},[638],[363,192018,192020],{"className":192019,"style":643},[642],[363,192021,192022,192025],{"style":19190},[363,192023],{"className":192024,"style":651},[650],[363,192026,192028],{"className":192027},[655,656,657,658],[363,192029,192031],{"className":192030},[407,658],[363,192032,192034],{"className":192033},[407,658],[363,192035,192037],{"className":192036},[407,658],[363,192038,101106],{"className":192039,"style":169854},[407,136068,658],[363,192041,666],{"className":192042},[665],[363,192044,192046],{"className":192045},[638],[363,192047,192049],{"className":192048,"style":8315},[642],[363,192050],{},[363,192052,461],{"className":192053},[494],[363,192055,1121],{"className":192056},[407,75905],[363,192058,468],{"className":192059},[501]," 给出，因此 ",[363,192062,192064,192077],{"className":192063,"translate":367},[366],[363,192065,192067],{"className":192066},[371],[373,192068,192069],{"xmlns":375},[377,192070,192071,192075],{},[380,192072,192073],{},[383,192074,1121],{"mathvariant":75560},[387,192076,135607],{"encoding":389},[363,192078,192080],{"className":192079,"ariaHidden":394},[393],[363,192081,192083,192086],{"className":192082},[398],[363,192084],{"className":192085,"style":135617},[402],[363,192087,1121],{"className":192088},[407,75905]," 落在分布外时能否给出低证据，完全取决于特征提取器是否把该区域映射到低响应区。若主干网络对分布外输入仍产生高幅 logits，EDL 的不确定性同样失效——",[1572,192091,192092],{},"它把 OOD 问题从输出层转移到了特征层，而非解决它",[11,192094,192095,192096,192099],{},"综合以上点，恰当的使用立场是：",[1572,192097,192098],{},"把 EDL 视为一种参数高效、结构可解释的不确定性启发式，而非贝叶斯推理的替代品。"," 它在「单次前向代价下同时输出预测与不确定性」这一约束下的性价比是突出的。但凡是论断依赖于「该不确定性具有贝叶斯后验语义」的场合，都应改回到对参数做边缘化的方法，或至少给出与后者的对照实验。",[18,192101,192103],{"id":192102},"五应用","五、应用",[2658,192105,192107],{"id":192106},"_51-分布外检测与开放集识别","5.1 分布外检测与开放集识别",[11,192109,192110,192111,175643,192171,192174,192175,192203,192204,192235],{},"由命题 3.4，",[363,192112,192114,192135],{"className":192113,"translate":367},[366],[363,192115,192117],{"className":192116},[371],[373,192118,192119],{"xmlns":375},[377,192120,192121,192133],{},[380,192122,192123,192125,192127,192129,192131],{},[383,192124,15747],{},[458,192126,471],{},[383,192128,11041],{},[383,192130,1288],{"mathvariant":557},[383,192132,26084],{},[387,192134,175606],{"encoding":389},[363,192136,192138,192156],{"className":192137,"ariaHidden":394},[393],[363,192139,192141,192144,192147,192150,192153],{"className":192140},[398],[363,192142],{"className":192143,"style":2692},[402],[363,192145,15747],{"className":192146},[407,408],[363,192148],{"className":192149,"style":506},[505],[363,192151,471],{"className":192152},[510],[363,192154],{"className":192155,"style":506},[505],[363,192157,192159,192162,192165,192168],{"className":192158},[398],[363,192160],{"className":192161,"style":487},[402],[363,192163,11041],{"className":192164,"style":11129},[407,408],[363,192166,1288],{"className":192167},[407],[363,192169,26084],{"className":192170,"style":26208},[407,408],[1572,192172,192173],{},"单调反比于总证据","的量，因此可以直接充当分布外（OOD）分数：",[363,192176,192178,192191],{"className":192177,"translate":367},[366],[363,192179,192181],{"className":192180},[371],[373,192182,192183],{"xmlns":375},[377,192184,192185,192189],{},[380,192186,192187],{},[383,192188,15747],{},[387,192190,15747],{"encoding":389},[363,192192,192194],{"className":192193,"ariaHidden":394},[393],[363,192195,192197,192200],{"className":192196},[398],[363,192198],{"className":192199,"style":2692},[402],[363,192201,15747],{"className":192202},[407,408]," 高意味着输入未能激活任何类别的证据。以阈值 ",[363,192205,192207,192222],{"className":192206,"translate":367},[366],[363,192208,192210],{"className":192209},[371],[373,192211,192212],{"xmlns":375},[377,192213,192214,192219],{},[380,192215,192216],{},[383,192217,192218],{},"τ",[387,192220,192221],{"encoding":389},"\\tau",[363,192223,192225],{"className":192224,"ariaHidden":394},[393],[363,192226,192228,192231],{"className":192227},[398],[363,192229],{"className":192230,"style":2692},[402],[363,192232,192218],{"className":192233,"style":192234},[407,408],"margin-right:0.1132em;"," 作拒识判决",[363,192237,192239],{"className":192238,"translate":367},[528],[363,192240,192242,192354],{"className":192241,"translate":367},[366],[363,192243,192245],{"className":192244},[371],[373,192246,192247],{"xmlns":375,"display":537},[377,192248,192249,192351],{},[380,192250,192251,192257,192259,192261,192263,192265],{},[12158,192252,192253,192255],{"accent":394},[383,192254,40584],{},[458,192256,100285],{},[458,192258,461],{"stretchy":460},[383,192260,1121],{"mathvariant":75560},[458,192262,468],{"stretchy":460},[458,192264,471],{},[380,192266,192267,192269],{},[458,192268,3245],{"fence":394},[1590,192270,192271,192320],{"rowspacing":4660,"columnalign":4661,"columnspacing":4662},[1596,192272,192273,192302],{},[1599,192274,192275],{},[1602,192276,192277],{"scriptlevel":474,"displaystyle":460},[380,192278,192279,192282,192284,192294,192300],{},[383,192280,192281],{},"arg",[458,192283,4450],{},[543,192285,192286,192292],{},[380,192287,192288,192290],{},[383,192289,52734],{},[458,192291,4450],{},[383,192293,7911],{},[543,192295,192296,192298],{},[383,192297,11],{},[383,192299,7911],{},[458,192301,898],{"separator":394},[1599,192303,192304],{},[1602,192305,192306],{"scriptlevel":474,"displaystyle":460},[380,192307,192308,192310,192312,192314,192316,192318],{},[383,192309,15747],{},[458,192311,461],{"stretchy":460},[383,192313,1121],{"mathvariant":75560},[458,192315,468],{"stretchy":460},[458,192317,10299],{},[383,192319,192218],{},[1596,192321,192322,192333],{},[1599,192323,192324],{},[1602,192325,192326],{"scriptlevel":474,"displaystyle":460},[380,192327,192328,192331],{},[1644,192329,192330],{},"reject",[458,192332,898],{"separator":394},[1599,192334,192335],{},[1602,192336,192337],{"scriptlevel":474,"displaystyle":460},[380,192338,192339,192341,192343,192345,192347,192349],{},[383,192340,15747],{},[458,192342,461],{"stretchy":460},[383,192344,1121],{"mathvariant":75560},[458,192346,468],{"stretchy":460},[458,192348,3250],{},[383,192350,192218],{},[387,192352,192353],{"encoding":389},"\\hat{y}(\\mathbf{x}) = \\begin{cases} \\arg\\max_k p_k, & u(\\mathbf{x}) \\le \\tau \\\\ \\text{reject}, & u(\\mathbf{x}) > \\tau \\end{cases}",[363,192355,192357,192424],{"className":192356,"ariaHidden":394},[393],[363,192358,192360,192363,192406,192409,192412,192415,192418,192421],{"className":192359},[398],[363,192361],{"className":192362,"style":487},[402],[363,192364,192366],{"className":192365},[407,12198],[363,192367,192369,192398],{"className":192368},[633,634],[363,192370,192372,192395],{"className":192371},[638],[363,192373,192375,192383],{"className":192374,"style":12944},[642],[363,192376,192377,192380],{"style":12210},[363,192378],{"className":192379,"style":809},[650],[363,192381,40584],{"className":192382,"style":1328},[407,408],[363,192384,192385,192388],{"style":12210},[363,192386],{"className":192387,"style":809},[650],[363,192389,192392],{"className":192390,"style":192391},[12226],"left:-0.1944em;",[363,192393,100285],{"className":192394},[407],[363,192396,666],{"className":192397},[665],[363,192399,192401],{"className":192400},[638],[363,192402,192404],{"className":192403,"style":12654},[642],[363,192405],{},[363,192407,461],{"className":192408},[494],[363,192410,1121],{"className":192411},[407,75905],[363,192413,468],{"className":192414},[501],[363,192416],{"className":192417,"style":506},[505],[363,192419,471],{"className":192420},[510],[363,192422],{"className":192423,"style":506},[505],[363,192425,192427,192431],{"className":192426},[398],[363,192428],{"className":192429,"style":192430},[402],"height:3em;vertical-align:-1.25em;",[363,192432,192434,192440,192683],{"className":192433},[758],[363,192435,192437],{"className":192436,"style":763},[494,762],[363,192438,3245],{"className":192439},[767,4894],[363,192441,192443],{"className":192442},[407],[363,192444,192446,192593,192596],{"className":192445},[1590],[363,192447,192449],{"className":192448},[1798],[363,192450,192452,192584],{"className":192451},[633,634],[363,192453,192455,192581],{"className":192454},[638],[363,192456,192459,192563],{"className":192457,"style":192458},[642],"height:1.69em;",[363,192460,192462,192465],{"style":192461},"top:-3.69em;",[363,192463],{"className":192464,"style":4920},[650],[363,192466,192468,192474,192477,192517,192520,192560],{"className":192467},[407],[363,192469,192471,192472],{"className":192470},[1831],"ar",[363,192473,4505],{"style":4504},[363,192475],{"className":192476,"style":754},[505],[363,192478,192480,192483],{"className":192479},[1831],[363,192481,52734],{"className":192482},[1831],[363,192484,192486],{"className":192485},[629],[363,192487,192489,192509],{"className":192488},[633,634],[363,192490,192492,192506],{"className":192491},[638],[363,192493,192495],{"className":192494,"style":643},[642],[363,192496,192497,192500],{"style":52793},[363,192498],{"className":192499,"style":651},[650],[363,192501,192503],{"className":192502},[655,656,657,658],[363,192504,7911],{"className":192505,"style":8614},[407,408,658],[363,192507,666],{"className":192508},[665],[363,192510,192512],{"className":192511},[638],[363,192513,192515],{"className":192514,"style":8315},[642],[363,192516],{},[363,192518],{"className":192519,"style":754},[505],[363,192521,192523,192526],{"className":192522},[407],[363,192524,11],{"className":192525},[407,408],[363,192527,192529],{"className":192528},[629],[363,192530,192532,192552],{"className":192531},[633,634],[363,192533,192535,192549],{"className":192534},[638],[363,192536,192538],{"className":192537,"style":643},[642],[363,192539,192540,192543],{"style":730},[363,192541],{"className":192542,"style":651},[650],[363,192544,192546],{"className":192545},[655,656,657,658],[363,192547,7911],{"className":192548,"style":8614},[407,408,658],[363,192550,666],{"className":192551},[665],[363,192553,192555],{"className":192554},[638],[363,192556,192558],{"className":192557,"style":8315},[642],[363,192559],{},[363,192561,898],{"className":192562},[920],[363,192564,192566,192569],{"style":192565},"top:-2.25em;",[363,192567],{"className":192568,"style":4920},[650],[363,192570,192572,192578],{"className":192571},[407],[363,192573,192575],{"className":192574},[407,4945],[363,192576,192330],{"className":192577},[407],[363,192579,898],{"className":192580},[920],[363,192582,666],{"className":192583},[665],[363,192585,192587],{"className":192586},[638],[363,192588,192591],{"className":192589,"style":192590},[642],"height:1.19em;",[363,192592],{},[363,192594],{"className":192595,"style":4969},[4968],[363,192597,192599],{"className":192598},[1798],[363,192600,192602,192675],{"className":192601},[633,634],[363,192603,192605,192672],{"className":192604},[638],[363,192606,192608,192640],{"className":192607,"style":192458},[642],[363,192609,192610,192613],{"style":192461},[363,192611],{"className":192612,"style":4920},[650],[363,192614,192616,192619,192622,192625,192628,192631,192634,192637],{"className":192615},[407],[363,192617,15747],{"className":192618},[407,408],[363,192620,461],{"className":192621},[494],[363,192623,1121],{"className":192624},[407,75905],[363,192626,468],{"className":192627},[501],[363,192629],{"className":192630,"style":506},[505],[363,192632,10299],{"className":192633},[510],[363,192635],{"className":192636,"style":506},[505],[363,192638,192218],{"className":192639,"style":192234},[407,408],[363,192641,192642,192645],{"style":192565},[363,192643],{"className":192644,"style":4920},[650],[363,192646,192648,192651,192654,192657,192660,192663,192666,192669],{"className":192647},[407],[363,192649,15747],{"className":192650},[407,408],[363,192652,461],{"className":192653},[494],[363,192655,1121],{"className":192656},[407,75905],[363,192658,468],{"className":192659},[501],[363,192661],{"className":192662,"style":506},[505],[363,192664,3250],{"className":192665},[510],[363,192667],{"className":192668,"style":506},[505],[363,192670,192218],{"className":192671,"style":192234},[407,408],[363,192673,666],{"className":192674},[665],[363,192676,192678],{"className":192677},[638],[363,192679,192681],{"className":192680,"style":192590},[642],[363,192682],{},[363,192684],{"className":192685},[501,789],[11,192687,192688,192689,192896],{},"即得开放集分类器。与之竞争的分数包括最大 softmax 概率（MSP）、预测熵、ODIN 的温度与输入扰动、Mahalanobis 距离，以及能量分数 ",[363,192690,192692,192737],{"className":192691,"translate":367},[366],[363,192693,192695],{"className":192694},[371],[373,192696,192697],{"xmlns":375},[377,192698,192699,192734],{},[380,192700,192701,192704,192706,192708,192710,192712,192714,192716,192718,192724],{},[383,192702,192703],{"mathvariant":557},"LSE",[458,192705,4450],{},[458,192707,461],{"stretchy":460},[383,192709,118116],{"mathvariant":75560},[458,192711,468],{"stretchy":460},[458,192713,471],{},[383,192715,4447],{},[458,192717,4450],{},[543,192719,192720,192722],{},[458,192721,13808],{},[383,192723,7911],{},[7161,192725,192726,192728],{},[383,192727,7914],{},[543,192729,192730,192732],{},[383,192731,118116],{},[383,192733,7911],{},[387,192735,192736],{"encoding":389},"\\operatorname{LSE}(\\mathbf{z}) = \\log\\sum_k e^{z_k}",[363,192738,192740,192770],{"className":192739,"ariaHidden":394},[393],[363,192741,192743,192746,192752,192755,192758,192761,192764,192767],{"className":192742},[398],[363,192744],{"className":192745,"style":487},[402],[363,192747,192749],{"className":192748},[1831],[363,192750,192703],{"className":192751},[407,33009],[363,192753,461],{"className":192754},[494],[363,192756,118116],{"className":192757},[407,75905],[363,192759,468],{"className":192760},[501],[363,192762],{"className":192763,"style":506},[505],[363,192765,471],{"className":192766},[510],[363,192768],{"className":192769,"style":506},[505],[363,192771,192773,192776,192781,192784,192824,192827],{"className":192772},[398],[363,192774],{"className":192775,"style":138904},[402],[363,192777,4501,192779],{"className":192778},[1831],[363,192780,4505],{"style":4504},[363,192782],{"className":192783,"style":754},[505],[363,192785,192787,192790],{"className":192786},[1831],[363,192788,13808],{"className":192789,"style":40007},[1831,1832,5963],[363,192791,192793],{"className":192792},[629],[363,192794,192796,192816],{"className":192795},[633,634],[363,192797,192799,192813],{"className":192798},[638],[363,192800,192802],{"className":192801,"style":67358},[642],[363,192803,192804,192807],{"style":40023},[363,192805],{"className":192806,"style":651},[650],[363,192808,192810],{"className":192809},[655,656,657,658],[363,192811,7911],{"className":192812,"style":8614},[407,408,658],[363,192814,666],{"className":192815},[665],[363,192817,192819],{"className":192818},[638],[363,192820,192822],{"className":192821,"style":40042},[642],[363,192823],{},[363,192825],{"className":192826,"style":754},[505],[363,192828,192830,192833],{"className":192829},[407],[363,192831,7914],{"className":192832},[407,408],[363,192834,192836],{"className":192835},[629],[363,192837,192839],{"className":192838},[633],[363,192840,192842],{"className":192841},[638],[363,192843,192845],{"className":192844,"style":50700},[642],[363,192846,192847,192850],{"style":7212},[363,192848],{"className":192849,"style":651},[650],[363,192851,192853],{"className":192852},[655,656,657,658],[363,192854,192856],{"className":192855},[407,658],[363,192857,192859,192862],{"className":192858},[407,658],[363,192860,118116],{"className":192861,"style":118386},[407,408,658],[363,192863,192865],{"className":192864},[629],[363,192866,192868,192888],{"className":192867},[633,634],[363,192869,192871,192885],{"className":192870},[638],[363,192872,192874],{"className":192873,"style":6445},[642],[363,192875,192876,192879],{"style":170282},[363,192877],{"className":192878,"style":30553},[650],[363,192880,192882],{"className":192881},[655,30557,10021,658],[363,192883,7911],{"className":192884,"style":8614},[407,408,658],[363,192886,666],{"className":192887},[665],[363,192889,192891],{"className":192890},[638],[363,192892,192894],{"className":192893,"style":101583},[642],[363,192895],{},"。将它们在性质上加以对照：",[52839,192898,192899,192915],{},[52842,192900,192901],{},[52845,192902,192903,192906,192909,192912],{},[52848,192904,192905],{"align":164937},"分数",[52848,192907,192908],{"align":164937},"依赖的结构",[52848,192910,192911],{"align":164937},"是否需要 OOD 数据",[52848,192913,192914],{"align":164937},"不确定性语汇",[52937,192916,192917,192930,192943,192956],{},[52845,192918,192919,192922,192925,192927],{},[52942,192920,192921],{"align":164937},"MSP \u002F 熵",[52942,192923,192924],{"align":164937},"softmax 输出",[52942,192926,53102],{"align":164937},[52942,192928,192929],{"align":164937},"无（受 3.3 节缺陷支配）",[52845,192931,192932,192935,192938,192940],{},[52942,192933,192934],{"align":164937},"Mahalanobis",[52942,192936,192937],{"align":164937},"各特征层的类条件高斯",[52942,192939,53102],{"align":164937},[52942,192941,192942],{"align":164937},"距离，几何语义",[52845,192944,192945,192948,192951,192953],{},[52942,192946,192947],{"align":164937},"能量分数",[52942,192949,192950],{"align":164937},"logits 的对数配分",[52942,192952,53102],{"align":164937},[52942,192954,192955],{"align":164937},"无显式不确定性",[52845,192957,192958,192991,193022,193026],{},[52942,192959,192960],{"align":164937},[1572,192961,192962,192963],{},"EDL 的 ",[363,192964,192966,192979],{"className":192965,"translate":367},[366],[363,192967,192969],{"className":192968},[371],[373,192970,192971],{"xmlns":375},[377,192972,192973,192977],{},[380,192974,192975],{},[383,192976,15747],{},[387,192978,15747],{"encoding":389},[363,192980,192982],{"className":192981,"ariaHidden":394},[393],[363,192983,192985,192988],{"className":192984},[398],[363,192986],{"className":192987,"style":2692},[402],[363,192989,15747],{"className":192990},[407,408],[52942,192992,192993,192994],{"align":164937},"迪利克雷总强度 ",[363,192995,192997,193010],{"className":192996,"translate":367},[366],[363,192998,193000],{"className":192999},[371],[373,193001,193002],{"xmlns":375},[377,193003,193004,193008],{},[380,193005,193006],{},[383,193007,26084],{},[387,193009,26084],{"encoding":389},[363,193011,193013],{"className":193012,"ariaHidden":394},[393],[363,193014,193016,193019],{"className":193015},[398],[363,193017],{"className":193018,"style":1011},[402],[363,193020,26084],{"className":193021,"style":26208},[407,408],[52942,193023,193024],{"align":164937},[1572,193025,53102],{},[52942,193027,193028],{"align":164937},"证据缺失量，可解释",[11,193030,193031,193032,193035],{},"EDL 在此项比较中的结构性优势在于两点。第一，它的不确定性是",[1572,193033,193034],{},"训练目标的一部分","（由 4.3 节的正则项直接优化），而非对训练好的网络做事后加工的产物。第二，它给出的是类概率向量的分布，因此可以在不接触任何 OOD 样本的前提下产生 OOD 分数——这是先验网络之外少有的性质（先验网络需要 OOD 样本以构造目标分布）。",[11,193037,193038],{},"限度同样明确：如 4.5 节第 5 点所述，其成败取决于特征空间的可分性。评价应使用 AUROC、AUPR（In\u002FOut 与 Out\u002FIn 分别报告）、FPR@95TPR 以及开放集风险—覆盖曲线，而非仅报单一的准确率。",[2658,193040,193042],{"id":193041},"_52-校准与选择性预测","5.2 校准与选择性预测",[11,193044,193045,193048,193049,193267],{},[1572,193046,193047],{},"校准","关心的是 ",[363,193050,193052,193096],{"className":193051,"translate":367},[366],[363,193053,193055],{"className":193054},[371],[373,193056,193057],{"xmlns":375},[377,193058,193059,193093],{},[380,193060,193061,193063,193065,193071,193073,193075,193077,193083,193085,193087,193089,193091],{},[383,193062,554],{"mathvariant":570},[458,193064,461],{"stretchy":460},[12158,193066,193067,193069],{"accent":394},[383,193068,40584],{},[458,193070,100285],{},[458,193072,471],{},[383,193074,40584],{},[458,193076,5155],{},[12158,193078,193079,193081],{"accent":394},[383,193080,11],{},[458,193082,100285],{},[458,193084,471],{},[383,193086,1291],{},[458,193088,468],{"stretchy":460},[458,193090,471],{},[383,193092,1291],{},[387,193094,193095],{"encoding":389},"\\mathbb{P}(\\hat{y} = y \\mid \\hat{p} = q) = q",[363,193097,193099,193162,193180,193237,193258],{"className":193098,"ariaHidden":394},[393],[363,193100,193102,193105,193108,193111,193153,193156,193159],{"className":193101},[398],[363,193103],{"className":193104,"style":487},[402],[363,193106,554],{"className":193107},[407,714],[363,193109,461],{"className":193110},[494],[363,193112,193114],{"className":193113},[407,12198],[363,193115,193117,193145],{"className":193116},[633,634],[363,193118,193120,193142],{"className":193119},[638],[363,193121,193123,193131],{"className":193122,"style":12944},[642],[363,193124,193125,193128],{"style":12210},[363,193126],{"className":193127,"style":809},[650],[363,193129,40584],{"className":193130,"style":1328},[407,408],[363,193132,193133,193136],{"style":12210},[363,193134],{"className":193135,"style":809},[650],[363,193137,193139],{"className":193138,"style":192391},[12226],[363,193140,100285],{"className":193141},[407],[363,193143,666],{"className":193144},[665],[363,193146,193148],{"className":193147},[638],[363,193149,193151],{"className":193150,"style":12654},[642],[363,193152],{},[363,193154],{"className":193155,"style":506},[505],[363,193157,471],{"className":193158},[510],[363,193160],{"className":193161,"style":506},[505],[363,193163,193165,193168,193171,193174,193177],{"className":193164},[398],[363,193166],{"className":193167,"style":487},[402],[363,193169,40584],{"className":193170,"style":1328},[407,408],[363,193172],{"className":193173,"style":506},[505],[363,193175,5155],{"className":193176},[510],[363,193178],{"className":193179,"style":506},[505],[363,193181,193183,193186,193228,193231,193234],{"className":193182},[398],[363,193184],{"className":193185,"style":403},[402],[363,193187,193189],{"className":193188},[407,12198],[363,193190,193192,193220],{"className":193191},[633,634],[363,193193,193195,193217],{"className":193194},[638],[363,193196,193198,193206],{"className":193197,"style":12944},[642],[363,193199,193200,193203],{"style":12210},[363,193201],{"className":193202,"style":809},[650],[363,193204,11],{"className":193205},[407,408],[363,193207,193208,193211],{"style":12210},[363,193209],{"className":193210,"style":809},[650],[363,193212,193214],{"className":193213,"style":12462},[12226],[363,193215,100285],{"className":193216},[407],[363,193218,666],{"className":193219},[665],[363,193221,193223],{"className":193222},[638],[363,193224,193226],{"className":193225,"style":12654},[642],[363,193227],{},[363,193229],{"className":193230,"style":506},[505],[363,193232,471],{"className":193233},[510],[363,193235],{"className":193236,"style":506},[505],[363,193238,193240,193243,193246,193249,193252,193255],{"className":193239},[398],[363,193241],{"className":193242,"style":487},[402],[363,193244,1291],{"className":193245,"style":1328},[407,408],[363,193247,468],{"className":193248},[501],[363,193250],{"className":193251,"style":506},[505],[363,193253,471],{"className":193254},[510],[363,193256],{"className":193257,"style":506},[505],[363,193259,193261,193264],{"className":193260},[398],[363,193262],{"className":193263,"style":2623},[402],[363,193265,1291],{"className":193266,"style":1328},[407,408]," 是否成立，常用期望校准误差",[363,193269,193271],{"className":193270,"translate":367},[528],[363,193272,193274,193359],{"className":193273,"translate":367},[366],[363,193275,193277],{"className":193276},[371],[373,193278,193279],{"xmlns":375,"display":537},[377,193280,193281,193356],{},[380,193282,193283,193286,193288,193302,193318,193320,193322,193325,193327,193329,193335,193337,193339,193342,193344,193346,193352,193354],{},[1644,193284,193285],{},"ECE",[458,193287,471],{},[48667,193289,193290,193292,193300],{},[458,193291,13808],{},[380,193293,193294,193296,193298],{},[383,193295,26670],{},[458,193297,471],{},[463,193299,465],{},[383,193301,25914],{},[586,193303,193304,193316],{},[380,193305,193306,193308,193314],{},[383,193307,5155],{"mathvariant":557},[543,193309,193310,193312],{},[383,193311,39638],{"mathvariant":944},[383,193313,26670],{},[383,193315,5155],{"mathvariant":557},[383,193317,82643],{},[1644,193319,1646],{},[458,193321,5155],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[383,193323,193324],{"mathvariant":557},"acc",[458,193326,4450],{},[458,193328,461],{"stretchy":460},[543,193330,193331,193333],{},[383,193332,39638],{"mathvariant":944},[383,193334,26670],{},[458,193336,468],{"stretchy":460},[458,193338,5160],{},[383,193340,193341],{"mathvariant":557},"conf",[458,193343,4450],{},[458,193345,461],{"stretchy":460},[543,193347,193348,193350],{},[383,193349,39638],{"mathvariant":944},[383,193351,26670],{},[458,193353,468],{"stretchy":460},[458,193355,5155],{"fence":460,"stretchy":394,"minsize":17786,"maxsize":17786},[387,193357,193358],{"encoding":389},"\\text{ECE} = \\sum_{m=1}^{M} \\frac{|\\mathcal{B}_m|}{n}\\,\\Big|\\operatorname{acc}(\\mathcal{B}_m) - \\operatorname{conf}(\\mathcal{B}_m)\\Big|",[363,193360,193362,193383,193673],{"className":193361,"ariaHidden":394},[393],[363,193363,193365,193368,193374,193377,193380],{"className":193364},[398],[363,193366],{"className":193367,"style":1011},[402],[363,193369,193371],{"className":193370},[407,4945],[363,193372,193285],{"className":193373},[407],[363,193375],{"className":193376,"style":506},[505],[363,193378,471],{"className":193379},[510],[363,193381],{"className":193382,"style":506},[505],[363,193384,193386,193390,193459,193462,193569,193572,193609,193612,193618,193621,193661,193664,193667,193670],{"className":193385},[398],[363,193387],{"className":193388,"style":193389},[402],"height:3.0954em;vertical-align:-1.2671em;",[363,193391,193393],{"className":193392},[1831,14063],[363,193394,193396,193450],{"className":193395},[633,634],[363,193397,193399,193447],{"className":193398},[638],[363,193400,193402,193423,193433],{"className":193401,"style":138225},[642],[363,193403,193405,193408],{"style":193404},"top:-1.8829em;margin-left:0em;",[363,193406],{"className":193407,"style":14080},[650],[363,193409,193411],{"className":193410},[655,656,657,658],[363,193412,193414,193417,193420],{"className":193413},[407,658],[363,193415,26670],{"className":193416},[407,408,658],[363,193418,471],{"className":193419},[510,658],[363,193421,465],{"className":193422},[407,658],[363,193424,193425,193428],{"style":14089},[363,193426],{"className":193427,"style":14080},[650],[363,193429,193430],{},[363,193431,13808],{"className":193432},[1831,1832,1833],[363,193434,193435,193438],{"style":100671},[363,193436],{"className":193437,"style":14080},[650],[363,193439,193441],{"className":193440},[655,656,657,658],[363,193442,193444],{"className":193443},[407,658],[363,193445,25914],{"className":193446,"style":25948},[407,408,658],[363,193448,666],{"className":193449},[665],[363,193451,193453],{"className":193452},[638],[363,193454,193457],{"className":193455,"style":193456},[642],"height:1.2671em;",[363,193458],{},[363,193460],{"className":193461,"style":754},[505],[363,193463,193465,193468,193566],{"className":193464},[407],[363,193466],{"className":193467},[494,789],[363,193469,193471],{"className":193470},[586],[363,193472,193474,193558],{"className":193473},[633,634],[363,193475,193477,193555],{"className":193476},[638],[363,193478,193480,193491,193499],{"className":193479,"style":1890},[642],[363,193481,193482,193485],{"style":805},[363,193483],{"className":193484,"style":809},[650],[363,193486,193488],{"className":193487},[407],[363,193489,82643],{"className":193490},[407,408],[363,193492,193493,193496],{"style":821},[363,193494],{"className":193495,"style":809},[650],[363,193497],{"className":193498,"style":829},[828],[363,193500,193501,193504],{"style":832},[363,193502],{"className":193503,"style":809},[650],[363,193505,193507,193510,193552],{"className":193506},[407],[363,193508,5155],{"className":193509},[407],[363,193511,193513,193517],{"className":193512},[407],[363,193514,39638],{"className":193515,"style":193516},[407,971],"margin-right:0.0304em;",[363,193518,193520],{"className":193519},[629],[363,193521,193523,193544],{"className":193522},[633,634],[363,193524,193526,193541],{"className":193525},[638],[363,193527,193529],{"className":193528,"style":45276},[642],[363,193530,193532,193535],{"style":193531},"top:-2.55em;margin-left:-0.0304em;margin-right:0.05em;",[363,193533],{"className":193534,"style":651},[650],[363,193536,193538],{"className":193537},[655,656,657,658],[363,193539,26670],{"className":193540},[407,408,658],[363,193542,666],{"className":193543},[665],[363,193545,193547],{"className":193546},[638],[363,193548,193550],{"className":193549,"style":8315},[642],[363,193551],{},[363,193553,5155],{"className":193554},[407],[363,193556,666],{"className":193557},[665],[363,193559,193561],{"className":193560},[638],[363,193562,193564],{"className":193563,"style":4125},[642],[363,193565],{},[363,193567],{"className":193568},[501,789],[363,193570],{"className":193571,"style":754},[505],[363,193573,193575],{"className":193574},[407],[363,193576,193578],{"className":193577},[767,15176],[363,193579,193581,193601],{"className":193580},[633,634],[363,193582,193584,193598],{"className":193583},[638],[363,193585,193587],{"className":193586,"style":85862},[642],[363,193588,193589,193592],{"style":73871},[363,193590],{"className":193591,"style":82934},[650],[363,193593,193594],{"style":115849},[6670,193595,193596],{"xmlns":6672,"width":35398,"height":17786,"viewBox":115852},[6678,193597],{"d":115855},[363,193599,666],{"className":193600},[665],[363,193602,193604],{"className":193603},[638],[363,193605,193607],{"className":193606,"style":85886},[642],[363,193608],{},[363,193610],{"className":193611,"style":754},[505],[363,193613,193615],{"className":193614},[1831],[363,193616,193324],{"className":193617},[407,33009],[363,193619,461],{"className":193620},[494],[363,193622,193624,193627],{"className":193623},[407],[363,193625,39638],{"className":193626,"style":193516},[407,971],[363,193628,193630],{"className":193629},[629],[363,193631,193633,193653],{"className":193632},[633,634],[363,193634,193636,193650],{"className":193635},[638],[363,193637,193639],{"className":193638,"style":45276},[642],[363,193640,193641,193644],{"style":193531},[363,193642],{"className":193643,"style":651},[650],[363,193645,193647],{"className":193646},[655,656,657,658],[363,193648,26670],{"className":193649},[407,408,658],[363,193651,666],{"className":193652},[665],[363,193654,193656],{"className":193655},[638],[363,193657,193659],{"className":193658,"style":8315},[642],[363,193660],{},[363,193662,468],{"className":193663},[501],[363,193665],{"className":193666,"style":2934},[505],[363,193668,5160],{"className":193669},[2938],[363,193671],{"className":193672,"style":2934},[505],[363,193674,193676,193679,193685,193688,193728,193731],{"className":193675},[398],[363,193677],{"className":193678,"style":68464},[402],[363,193680,193682],{"className":193681},[1831],[363,193683,193341],{"className":193684,"style":95181},[407,33009],[363,193686,461],{"className":193687},[494],[363,193689,193691,193694],{"className":193690},[407],[363,193692,39638],{"className":193693,"style":193516},[407,971],[363,193695,193697],{"className":193696},[629],[363,193698,193700,193720],{"className":193699},[633,634],[363,193701,193703,193717],{"className":193702},[638],[363,193704,193706],{"className":193705,"style":45276},[642],[363,193707,193708,193711],{"style":193531},[363,193709],{"className":193710,"style":651},[650],[363,193712,193714],{"className":193713},[655,656,657,658],[363,193715,26670],{"className":193716},[407,408,658],[363,193718,666],{"className":193719},[665],[363,193721,193723],{"className":193722},[638],[363,193724,193726],{"className":193725,"style":8315},[642],[363,193727],{},[363,193729,468],{"className":193730},[501],[363,193732,193734],{"className":193733},[407],[363,193735,193737],{"className":193736},[767,15176],[363,193738,193740,193760],{"className":193739},[633,634],[363,193741,193743,193757],{"className":193742},[638],[363,193744,193746],{"className":193745,"style":85862},[642],[363,193747,193748,193751],{"style":73871},[363,193749],{"className":193750,"style":82934},[650],[363,193752,193753],{"style":115849},[6670,193754,193755],{"xmlns":6672,"width":35398,"height":17786,"viewBox":115852},[6678,193756],{"d":115855},[363,193758,666],{"className":193759},[665],[363,193761,193763],{"className":193762},[638],[363,193764,193766],{"className":193765,"style":85886},[642],[363,193767],{},[11,193769,193770,193771,193841],{},"度量，其中 ",[363,193772,193774,193792],{"className":193773,"translate":367},[366],[363,193775,193777],{"className":193776},[371],[373,193778,193779],{"xmlns":375},[377,193780,193781,193789],{},[380,193782,193783],{},[543,193784,193785,193787],{},[383,193786,39638],{"mathvariant":944},[383,193788,26670],{},[387,193790,193791],{"encoding":389},"\\mathcal{B}_m",[363,193793,193795],{"className":193794,"ariaHidden":394},[393],[363,193796,193798,193801],{"className":193797},[398],[363,193799],{"className":193800,"style":16308},[402],[363,193802,193804,193807],{"className":193803},[407],[363,193805,39638],{"className":193806,"style":193516},[407,971],[363,193808,193810],{"className":193809},[629],[363,193811,193813,193833],{"className":193812},[633,634],[363,193814,193816,193830],{"className":193815},[638],[363,193817,193819],{"className":193818,"style":45276},[642],[363,193820,193821,193824],{"style":193531},[363,193822],{"className":193823,"style":651},[650],[363,193825,193827],{"className":193826},[655,656,657,658],[363,193828,26670],{"className":193829},[407,408,658],[363,193831,666],{"className":193832},[665],[363,193834,193836],{"className":193835},[638],[363,193837,193839],{"className":193838,"style":8315},[642],[363,193840],{}," 是置信度分箱。EDL 的训练目标隐含地抑制了 3.3 节所述的 logits 发散退化，因此在若干基准上比 MSP 更校准。但这不是免费的：如 4.5 节第 7 点，EDL 的一阶校准同样需要验证，不应默认成立。",[11,193843,193844,2627,193847,193875,193876,193942,193943,193975,193976,194004,194005,194067],{},[1572,193845,193846],{},"选择性预测（selective prediction）",[363,193848,193850,193863],{"className":193849,"translate":367},[366],[363,193851,193853],{"className":193852},[371],[373,193854,193855],{"xmlns":375},[377,193856,193857,193861],{},[380,193858,193859],{},[383,193860,15747],{},[387,193862,15747],{"encoding":389},[363,193864,193866],{"className":193865,"ariaHidden":394},[393],[363,193867,193869,193872],{"className":193868},[398],[363,193870],{"className":193871,"style":2692},[402],[363,193873,15747],{"className":193874},[407,408]," 的更自然的落点。经典 Chow 规则指出，在已知真实后验 ",[363,193877,193879,193903],{"className":193878,"translate":367},[366],[363,193880,193882],{"className":193881},[371],[373,193883,193884],{"xmlns":375},[377,193885,193886,193900],{},[380,193887,193888,193890,193892,193894,193896,193898],{},[383,193889,11],{},[458,193891,461],{"stretchy":460},[383,193893,40584],{},[458,193895,5155],{},[383,193897,1121],{"mathvariant":75560},[458,193899,468],{"stretchy":460},[387,193901,193902],{"encoding":389},"p(y \\mid \\mathbf{x})",[363,193904,193906,193930],{"className":193905,"ariaHidden":394},[393],[363,193907,193909,193912,193915,193918,193921,193924,193927],{"className":193908},[398],[363,193910],{"className":193911,"style":487},[402],[363,193913,11],{"className":193914},[407,408],[363,193916,461],{"className":193917},[494],[363,193919,40584],{"className":193920,"style":1328},[407,408],[363,193922],{"className":193923,"style":506},[505],[363,193925,5155],{"className":193926},[510],[363,193928],{"className":193929,"style":506},[505],[363,193931,193933,193936,193939],{"className":193932},[398],[363,193934],{"className":193935,"style":487},[402],[363,193937,1121],{"className":193938},[407,75905],[363,193940,468],{"className":193941},[501]," 时，最优拒识策略是「当最大后验概率低于某阈值时拒识」，其最优性",[1572,193944,193945,193946,193974],{},"依赖于 ",[363,193947,193949,193962],{"className":193948,"translate":367},[366],[363,193950,193952],{"className":193951},[371],[373,193953,193954],{"xmlns":375},[377,193955,193956,193960],{},[380,193957,193958],{},[383,193959,11],{},[387,193961,11],{"encoding":389},[363,193963,193965],{"className":193964,"ariaHidden":394},[393],[363,193966,193968,193971],{"className":193967},[398],[363,193969],{"className":193970,"style":2623},[402],[363,193972,11],{"className":193973},[407,408]," 本身的正确性","。EDL 提供了一条与之互补的路径：直接使用二阶量 ",[363,193977,193979,193992],{"className":193978,"translate":367},[366],[363,193980,193982],{"className":193981},[371],[373,193983,193984],{"xmlns":375},[377,193985,193986,193990],{},[380,193987,193988],{},[383,193989,15747],{},[387,193991,15747],{"encoding":389},[363,193993,193995],{"className":193994,"ariaHidden":394},[393],[363,193996,193998,194001],{"className":193997},[398],[363,193999],{"className":194000,"style":2692},[402],[363,194002,15747],{"className":194003},[407,408]," 或 ",[363,194006,194008,194031],{"className":194007,"translate":367},[366],[363,194009,194011],{"className":194010},[371],[373,194012,194013],{"xmlns":375},[377,194014,194015,194029],{},[380,194016,194017,194019,194021,194023,194025,194027],{},[383,194018,34215],{},[458,194020,461],{"stretchy":460},[383,194022,40584],{},[458,194024,34222],{"separator":394},[383,194026,157399],{"mathvariant":136008},[458,194028,468],{"stretchy":460},[387,194030,179496],{"encoding":389},[363,194032,194034],{"className":194033,"ariaHidden":394},[393],[363,194035,194037,194040,194043,194046,194049,194052,194055,194064],{"className":194036},[398],[363,194038],{"className":194039,"style":487},[402],[363,194041,34215],{"className":194042,"style":9234},[407,408],[363,194044,461],{"className":194045},[494],[363,194047,40584],{"className":194048,"style":1328},[407,408],[363,194050,34222],{"className":194051},[920],[363,194053],{"className":194054,"style":754},[505],[363,194056,194058],{"className":194057},[407],[363,194059,194061],{"className":194060},[407],[363,194062,157399],{"className":194063,"style":157433},[407,136068],[363,194065,468],{"className":194066},[501]," 作为拒识分数，从而绕开对一阶校准的依赖。其代价是引入了一个新的、校准状况未知的量。实践中应同时考察两条路径并报告风险—覆盖曲线下的面积（AURC）。",[2658,194069,194071],{"id":194070},"_53-主动学习与半监督学习","5.3 主动学习与半监督学习",[11,194073,194074,194077,194078,194004,194122,194200,194201,194229,194230,194258,194259,194262,194263,194291],{},[1572,194075,194076],{},"主动学习。"," 采集函数可以直接取 ",[363,194079,194081,194101],{"className":194080,"translate":367},[366],[363,194082,194084],{"className":194083},[371],[373,194085,194086],{"xmlns":375},[377,194087,194088,194098],{},[380,194089,194090,194092,194094,194096],{},[383,194091,15747],{},[458,194093,461],{"stretchy":460},[383,194095,1121],{"mathvariant":75560},[458,194097,468],{"stretchy":460},[387,194099,194100],{"encoding":389},"u(\\mathbf{x})",[363,194102,194104],{"className":194103,"ariaHidden":394},[393],[363,194105,194107,194110,194113,194116,194119],{"className":194106},[398],[363,194108],{"className":194109,"style":487},[402],[363,194111,15747],{"className":194112},[407,408],[363,194114,461],{"className":194115},[494],[363,194117,1121],{"className":194118},[407,75905],[363,194120,468],{"className":194121},[501],[363,194123,194125,194155],{"className":194124,"translate":367},[366],[363,194126,194128],{"className":194127},[371],[373,194129,194130],{"xmlns":375},[377,194131,194132,194152],{},[380,194133,194134,194136,194138,194140,194142,194144,194146,194148,194150],{},[383,194135,34215],{},[458,194137,461],{"stretchy":460},[383,194139,40584],{},[458,194141,34222],{"separator":394},[383,194143,157399],{"mathvariant":136008},[458,194145,468],{"stretchy":460},[458,194147,461],{"stretchy":460},[383,194149,1121],{"mathvariant":75560},[458,194151,468],{"stretchy":460},[387,194153,194154],{"encoding":389},"I(y;\\boldsymbol{\\pi})(\\mathbf{x})",[363,194156,194158],{"className":194157,"ariaHidden":394},[393],[363,194159,194161,194164,194167,194170,194173,194176,194179,194188,194191,194194,194197],{"className":194160},[398],[363,194162],{"className":194163,"style":487},[402],[363,194165,34215],{"className":194166,"style":9234},[407,408],[363,194168,461],{"className":194169},[494],[363,194171,40584],{"className":194172,"style":1328},[407,408],[363,194174,34222],{"className":194175},[920],[363,194177],{"className":194178,"style":754},[505],[363,194180,194182],{"className":194181},[407],[363,194183,194185],{"className":194184},[407],[363,194186,157399],{"className":194187,"style":157433},[407,136068],[363,194189,468],{"className":194190},[501],[363,194192,461],{"className":194193},[494],[363,194195,1121],{"className":194196},[407,75905],[363,194198,468],{"className":194199},[501],"：前者是「总证据最少」，后者是「关于类概率的知识增益最大」。选择 ",[363,194202,194204,194217],{"className":194203,"translate":367},[366],[363,194205,194207],{"className":194206},[371],[373,194208,194209],{"xmlns":375},[377,194210,194211,194215],{},[380,194212,194213],{},[383,194214,34215],{},[387,194216,34215],{"encoding":389},[363,194218,194220],{"className":194219,"ariaHidden":394},[393],[363,194221,194223,194226],{"className":194222},[398],[363,194224],{"className":194225,"style":1011},[402],[363,194227,34215],{"className":194228,"style":9234},[407,408]," 而非 ",[363,194231,194233,194246],{"className":194232,"translate":367},[366],[363,194234,194236],{"className":194235},[371],[373,194237,194238],{"xmlns":375},[377,194239,194240,194244],{},[380,194241,194242],{},[383,194243,15747],{},[387,194245,15747],{"encoding":389},[363,194247,194249],{"className":194248,"ariaHidden":394},[393],[363,194250,194252,194255],{"className":194251},[398],[363,194253],{"className":194254,"style":2692},[402],[363,194256,15747],{"className":194257},[407,408]," 的好处在于它同时考虑证据的量与分布，等价于 BALD 在迪利克雷族内的闭式对应物。EDL 在此场景的最大优势是",[1572,194260,194261],{},"代价","：一次前向即可得到采集分数，无需 MC 采样、无需多次前向、无需集成子模型。其风险同样直接来自 4.5 节第 1 点：若 ",[363,194264,194266,194279],{"className":194265,"translate":367},[366],[363,194267,194269],{"className":194268},[371],[373,194270,194271],{"xmlns":375},[377,194272,194273,194277],{},[380,194274,194275],{},[383,194276,15747],{},[387,194278,15747],{"encoding":389},[363,194280,194282],{"className":194281,"ariaHidden":394},[393],[363,194283,194285,194288],{"className":194284},[398],[363,194286],{"className":194287,"style":2692},[402],[363,194289,15747],{"className":194290},[407,408]," 因特征层的原因而系统性高估某些区域，主动学习会持续采样这些区域，形成采样偏差。缓解办法是在采集函数中叠加批内多样性项。",[11,194293,194294,194297,194298,194326,194327,194378,194379,194407],{},[1572,194295,194296],{},"半监督与伪标签。"," 伪标签流程中，",[363,194299,194301,194314],{"className":194300,"translate":367},[366],[363,194302,194304],{"className":194303},[371],[373,194305,194306],{"xmlns":375},[377,194307,194308,194312],{},[380,194309,194310],{},[383,194311,15747],{},[387,194313,15747],{"encoding":389},[363,194315,194317],{"className":194316,"ariaHidden":394},[393],[363,194318,194320,194323],{"className":194319},[398],[363,194321],{"className":194322,"style":2692},[402],[363,194324,15747],{"className":194325},[407,408]," 提供了比「最大概率」更细的过滤准则：取 ",[363,194328,194330,194348],{"className":194329,"translate":367},[366],[363,194331,194333],{"className":194332},[371],[373,194334,194335],{"xmlns":375},[377,194336,194337,194345],{},[380,194338,194339,194341,194343],{},[383,194340,15747],{},[458,194342,7598],{},[383,194344,192218],{},[387,194346,194347],{"encoding":389},"u \u003C \\tau",[363,194349,194351,194369],{"className":194350,"ariaHidden":394},[393],[363,194352,194354,194357,194360,194363,194366],{"className":194353},[398],[363,194355],{"className":194356,"style":6271},[402],[363,194358,15747],{"className":194359},[407,408],[363,194361],{"className":194362,"style":506},[505],[363,194364,7598],{"className":194365},[510],[363,194367],{"className":194368,"style":506},[505],[363,194370,194372,194375],{"className":194371},[398],[363,194373],{"className":194374,"style":2692},[402],[363,194376,192218],{"className":194377,"style":192234},[407,408]," 的样本赋予伪标签，可以同时排除「概率高但实为分布外」的样本——这正是 MSP 过滤所无法处理的失败模式。反之，当 ",[363,194380,194382,194395],{"className":194381,"translate":367},[366],[363,194383,194385],{"className":194384},[371],[373,194386,194387],{"xmlns":375},[377,194388,194389,194393],{},[380,194390,194391],{},[383,194392,192218],{},[387,194394,192221],{"encoding":389},[363,194396,194398],{"className":194397,"ariaHidden":394},[393],[363,194399,194401,194404],{"className":194400},[398],[363,194402],{"className":194403,"style":2692},[402],[363,194405,192218],{"className":194406,"style":192234},[407,408]," 过紧时，模型会倾向于只在自己已经熟悉的区域采样伪标签，导致训练集分布收缩、对稀有模式进一步失明。该权衡与 5.6 节讨论的长尾问题同源。",[2658,194409,194411],{"id":194410},"_54-安全关键场景","5.4 安全关键场景",[11,194413,194414,194415,9747],{},"在医学影像、自动驾驶与工业质检等场景中，「放弃预测并移交人类」是一个具有明确成本结构的决策，而非纯粹的统计操作。EDL 在这里的价值不是给出更准的标签，而是提供一个",[1572,194416,194417],{},"可嵌入决策规则的二阶量",[10374,194419,194420,194510,194568,194603],{},[7012,194421,194422,194425,194426,194480,194481,194509],{},[1572,194423,194424],{},"分割与体素级不确定性","：对每个体素输出 ",[363,194427,194429,194450],{"className":194428,"translate":367},[366],[363,194430,194432],{"className":194431},[371],[373,194433,194434],{"xmlns":375},[377,194435,194436,194448],{},[380,194437,194438,194440,194442,194444,194446],{},[383,194439,137065],{"mathvariant":557},[458,194441,4450],{},[458,194443,461],{"stretchy":460},[383,194445,45101],{"mathvariant":136008},[458,194447,468],{"stretchy":460},[387,194449,171704],{"encoding":389},[363,194451,194453],{"className":194452,"ariaHidden":394},[393],[363,194454,194456,194459,194465,194468,194477],{"className":194455},[398],[363,194457],{"className":194458,"style":487},[402],[363,194460,194462],{"className":194461},[1831],[363,194463,137065],{"className":194464},[407,33009],[363,194466,461],{"className":194467},[494],[363,194469,194471],{"className":194470},[407],[363,194472,194474],{"className":194473},[407],[363,194475,45101],{"className":194476},[407,136068],[363,194478,468],{"className":194479},[501],"，得到逐像素的 ",[363,194482,194484,194497],{"className":194483,"translate":367},[366],[363,194485,194487],{"className":194486},[371],[373,194488,194489],{"xmlns":375},[377,194490,194491,194495],{},[380,194492,194493],{},[383,194494,15747],{},[387,194496,15747],{"encoding":389},[363,194498,194500],{"className":194499,"ariaHidden":394},[393],[363,194501,194503,194506],{"className":194502},[398],[363,194504],{"className":194505,"style":2692},[402],[363,194507,15747],{"className":194508},[407,408],"，可据此生成「需人工复核区域」的掩码。",[7012,194511,194512,194515,194516,194567],{},[1572,194513,194514],{},"转诊（referral）机制","：将 ",[363,194517,194519,194537],{"className":194518,"translate":367},[366],[363,194520,194522],{"className":194521},[371],[373,194523,194524],{"xmlns":375},[377,194525,194526,194534],{},[380,194527,194528,194530,194532],{},[383,194529,15747],{},[458,194531,3250],{},[383,194533,192218],{},[387,194535,194536],{"encoding":389},"u > \\tau",[363,194538,194540,194558],{"className":194539,"ariaHidden":394},[393],[363,194541,194543,194546,194549,194552,194555],{"className":194542},[398],[363,194544],{"className":194545,"style":6271},[402],[363,194547,15747],{"className":194548},[407,408],[363,194550],{"className":194551,"style":506},[505],[363,194553,3250],{"className":194554},[510],[363,194556],{"className":194557,"style":506},[505],[363,194559,194561,194564],{"className":194560},[398],[363,194562],{"className":194563,"style":2692},[402],[363,194565,192218],{"className":194566,"style":192234},[407,408]," 的样本路由至专家，使自动化系统在其能力边界处显式地退出。",[7012,194569,194570,194573,194574,194602],{},[1572,194571,194572],{},"开放集动作识别","：视频中存在未见动作时，",[363,194575,194577,194590],{"className":194576,"translate":367},[366],[363,194578,194580],{"className":194579},[371],[373,194581,194582],{"xmlns":375},[377,194583,194584,194588],{},[380,194585,194586],{},[383,194587,15747],{},[387,194589,15747],{"encoding":389},[363,194591,194593],{"className":194592,"ariaHidden":394},[393],[363,194594,194596,194599],{"className":194595},[398],[363,194597],{"className":194598,"style":2692},[402],[363,194600,15747],{"className":194601},[407,408]," 提供拒绝信号。",[7012,194604,194605,194608],{},[1572,194606,194607],{},"分子性质预测与虚拟筛选","：在化学空间中标识训练分布之外的候选物，避免对高不确定性的预测投入昂贵的实验验证。",[11,194610,194611,194612,194615,194616,194644],{},"这些应用的共同点是：",[1572,194613,194614],{},"错误的代价不对称，且「不预测」是允许的动作。"," 这也划定了 EDL 不适用的场合——当系统必须对所有输入给出一个标签、且拒识没有对应的动作时，",[363,194617,194619,194632],{"className":194618,"translate":367},[366],[363,194620,194622],{"className":194621},[371],[373,194623,194624],{"xmlns":375},[377,194625,194626,194630],{},[380,194627,194628],{},[383,194629,15747],{},[387,194631,15747],{"encoding":389},[363,194633,194635],{"className":194634,"ariaHidden":394},[393],[363,194636,194638,194641],{"className":194637},[398],[363,194639],{"className":194640,"style":2692},[402],[363,194642,15747],{"className":194643},[407,408]," 至多是一个监控指标。",[2658,194646,194648],{"id":194647},"_55-回归情形的推广","5.5 回归情形的推广",[11,194650,194651,194652,9747],{},"分类的目标是单纯形上的向量，回归的目标是实数。相应地把迪利克雷替换为",[1572,194653,194654],{},"正态—逆 Gamma（Normal-Inverse-Gamma, NIG）先验",[363,194656,194658],{"className":194657,"translate":367},[528],[363,194659,194661,194734],{"className":194660,"translate":367},[366],[363,194662,194664],{"className":194663},[371],[373,194665,194666],{"xmlns":375,"display":537},[377,194667,194668,194731],{},[380,194669,194670,194672,194674,194676,194678,194699,194701,194703,194709,194711,194721,194723,194725,194727,194729],{},[383,194671,2711],{},[458,194673,9216],{},[383,194675,38631],{"mathvariant":944},[1644,194677,1651],{},[380,194679,194680,194682,194684,194686,194697],{},[458,194681,461],{"fence":394},[383,194683,121421],{},[458,194685,898],{"separator":394},[586,194687,194688,194694],{},[7161,194689,194690,194692],{},[383,194691,2679],{},[463,194693,2810],{},[383,194695,194696],{},"υ",[458,194698,468],{"fence":394},[458,194700,898],{"separator":394},[505,194702],{"width":3609},[7161,194704,194705,194707],{},[383,194706,2679],{},[463,194708,2810],{},[458,194710,9216],{},[7161,194712,194713,194715],{},[383,194714,137171],{"mathvariant":557},[380,194716,194717,194719],{},[458,194718,5160],{},[463,194720,465],{},[458,194722,461],{"stretchy":460},[383,194724,45101],{},[458,194726,898],{"separator":394},[383,194728,84464],{},[458,194730,468],{"stretchy":460},[387,194732,194733],{"encoding":389},"\\mu \\sim \\mathcal{N}\\!\\left(\\gamma, \\frac{\\sigma^2}{\\upsilon}\\right),\n\\qquad\n\\sigma^2 \\sim \\Gamma^{-1}(\\alpha, \\beta)",[363,194735,194737,194755,194933],{"className":194736,"ariaHidden":394},[393],[363,194738,194740,194743,194746,194749,194752],{"className":194739},[398],[363,194741],{"className":194742,"style":2623},[402],[363,194744,2711],{"className":194745},[407,408],[363,194747],{"className":194748,"style":506},[505],[363,194750,9216],{"className":194751},[510],[363,194753],{"className":194754,"style":506},[505],[363,194756,194758,194761,194765,194768,194771,194883,194886,194889,194892,194895,194924,194927,194930],{"className":194757},[398],[363,194759],{"className":194760,"style":87605},[402],[363,194762,38631],{"className":194763,"style":194764},[407,971],"margin-right:0.1474em;",[363,194766],{"className":194767,"style":1859},[505],[363,194769],{"className":194770,"style":754},[505],[363,194772,194774,194780,194783,194786,194789,194877],{"className":194773},[758],[363,194775,194777],{"className":194776,"style":763},[494,762],[363,194778,461],{"className":194779},[767,657],[363,194781,121421],{"className":194782,"style":121511},[407,408],[363,194784,898],{"className":194785},[920],[363,194787],{"className":194788,"style":754},[505],[363,194790,194792,194795,194874],{"className":194791},[407],[363,194793],{"className":194794},[494,789],[363,194796,194798],{"className":194797},[586],[363,194799,194801,194866],{"className":194800},[633,634],[363,194802,194804,194863],{"className":194803},[638],[363,194805,194807,194818,194826],{"className":194806,"style":38070},[642],[363,194808,194809,194812],{"style":805},[363,194810],{"className":194811,"style":809},[650],[363,194813,194815],{"className":194814},[407],[363,194816,194696],{"className":194817,"style":1328},[407,408],[363,194819,194820,194823],{"style":821},[363,194821],{"className":194822,"style":809},[650],[363,194824],{"className":194825,"style":829},[828],[363,194827,194828,194831],{"style":832},[363,194829],{"className":194830,"style":809},[650],[363,194832,194834],{"className":194833},[407],[363,194835,194837,194840],{"className":194836},[407],[363,194838,2679],{"className":194839,"style":1328},[407,408],[363,194841,194843],{"className":194842},[629],[363,194844,194846],{"className":194845},[633],[363,194847,194849],{"className":194848},[638],[363,194850,194852],{"className":194851,"style":20375},[642],[363,194853,194854,194857],{"style":7212},[363,194855],{"className":194856,"style":651},[650],[363,194858,194860],{"className":194859},[655,656,657,658],[363,194861,2810],{"className":194862},[407,658],[363,194864,666],{"className":194865},[665],[363,194867,194869],{"className":194868},[638],[363,194870,194872],{"className":194871,"style":4125},[642],[363,194873],{},[363,194875],{"className":194876},[501,789],[363,194878,194880],{"className":194879,"style":763},[501,762],[363,194881,468],{"className":194882},[767,657],[363,194884],{"className":194885,"style":754},[505],[363,194887,898],{"className":194888},[920],[363,194890],{"className":194891,"style":3981},[505],[363,194893],{"className":194894,"style":754},[505],[363,194896,194898,194901],{"className":194897},[407],[363,194899,2679],{"className":194900,"style":1328},[407,408],[363,194902,194904],{"className":194903},[629],[363,194905,194907],{"className":194906},[633],[363,194908,194910],{"className":194909},[638],[363,194911,194913],{"className":194912,"style":20082},[642],[363,194914,194915,194918],{"style":8624},[363,194916],{"className":194917,"style":651},[650],[363,194919,194921],{"className":194920},[655,656,657,658],[363,194922,2810],{"className":194923},[407,658],[363,194925],{"className":194926,"style":506},[505],[363,194928,9216],{"className":194929},[510],[363,194931],{"className":194932,"style":506},[505],[363,194934,194936,194939,194974,194977,194980,194983,194986,194989],{"className":194935},[398],[363,194937],{"className":194938,"style":37598},[402],[363,194940,194942,194945],{"className":194941},[407],[363,194943,137171],{"className":194944},[407],[363,194946,194948],{"className":194947},[629],[363,194949,194951],{"className":194950},[633],[363,194952,194954],{"className":194953},[638],[363,194955,194957],{"className":194956,"style":20082},[642],[363,194958,194959,194962],{"style":8624},[363,194960],{"className":194961,"style":651},[650],[363,194963,194965],{"className":194964},[655,656,657,658],[363,194966,194968,194971],{"className":194967},[407,658],[363,194969,5160],{"className":194970},[407,658],[363,194972,465],{"className":194973},[407,658],[363,194975,461],{"className":194976},[494],[363,194978,45101],{"className":194979,"style":45131},[407,408],[363,194981,898],{"className":194982},[920],[363,194984],{"className":194985,"style":754},[505],[363,194987,84464],{"className":194988,"style":84686},[407,408],[363,194990,468],{"className":194991},[501],[11,194993,194994,194995,195073,195074,195108,195109,195137,195138,195209,195210,195293,195294,195414,195415,195108,195448,195476],{},"网络对每个输入输出四元组 ",[363,194996,194998,195028],{"className":194997,"translate":367},[366],[363,194999,195001],{"className":195000},[371],[373,195002,195003],{"xmlns":375},[377,195004,195005,195025],{},[380,195006,195007,195009,195011,195013,195015,195017,195019,195021,195023],{},[458,195008,461],{"stretchy":460},[383,195010,121421],{},[458,195012,898],{"separator":394},[383,195014,194696],{},[458,195016,898],{"separator":394},[383,195018,45101],{},[458,195020,898],{"separator":394},[383,195022,84464],{},[458,195024,468],{"stretchy":460},[387,195026,195027],{"encoding":389},"(\\gamma, \\upsilon, \\alpha, \\beta)",[363,195029,195031],{"className":195030,"ariaHidden":394},[393],[363,195032,195034,195037,195040,195043,195046,195049,195052,195055,195058,195061,195064,195067,195070],{"className":195033},[398],[363,195035],{"className":195036,"style":487},[402],[363,195038,461],{"className":195039},[494],[363,195041,121421],{"className":195042,"style":121511},[407,408],[363,195044,898],{"className":195045},[920],[363,195047],{"className":195048,"style":754},[505],[363,195050,194696],{"className":195051,"style":1328},[407,408],[363,195053,898],{"className":195054},[920],[363,195056],{"className":195057,"style":754},[505],[363,195059,45101],{"className":195060,"style":45131},[407,408],[363,195062,898],{"className":195063},[920],[363,195065],{"className":195066,"style":754},[505],[363,195068,84464],{"className":195069,"style":84686},[407,408],[363,195071,468],{"className":195072},[501],"，边缘预测为自由度 ",[363,195075,195077,195093],{"className":195076,"translate":367},[366],[363,195078,195080],{"className":195079},[371],[373,195081,195082],{"xmlns":375},[377,195083,195084,195090],{},[380,195085,195086,195088],{},[463,195087,2810],{},[383,195089,45101],{},[387,195091,195092],{"encoding":389},"2\\alpha",[363,195094,195096],{"className":195095,"ariaHidden":394},[393],[363,195097,195099,195102,195105],{"className":195098},[398],[363,195100],{"className":195101,"style":520},[402],[363,195103,2810],{"className":195104},[407],[363,195106,45101],{"className":195107,"style":45131},[407,408]," 的 Student-",[363,195110,195112,195125],{"className":195111,"translate":367},[366],[363,195113,195115],{"className":195114},[371],[373,195116,195117],{"xmlns":375},[377,195118,195119,195123],{},[380,195120,195121],{},[383,195122,1116],{},[387,195124,1116],{"encoding":389},[363,195126,195128],{"className":195127,"ariaHidden":394},[393],[363,195129,195131,195134],{"className":195130},[398],[363,195132],{"className":195133,"style":5690},[402],[363,195135,1116],{"className":195136},[407,408]," 分布。其预测方差可精确分解为偶然部分 ",[363,195139,195141,195167],{"className":195140,"translate":367},[366],[363,195142,195144],{"className":195143},[371],[373,195145,195146],{"xmlns":375},[377,195147,195148,195164],{},[380,195149,195150,195152,195154,195156,195158,195160,195162],{},[383,195151,84464],{},[383,195153,1288],{"mathvariant":557},[458,195155,461],{"stretchy":460},[383,195157,45101],{},[458,195159,5160],{},[463,195161,465],{},[458,195163,468],{"stretchy":460},[387,195165,195166],{"encoding":389},"\\beta\u002F(\\alpha - 1)",[363,195168,195170,195197],{"className":195169,"ariaHidden":394},[393],[363,195171,195173,195176,195179,195182,195185,195188,195191,195194],{"className":195172},[398],[363,195174],{"className":195175,"style":487},[402],[363,195177,84464],{"className":195178,"style":84686},[407,408],[363,195180,1288],{"className":195181},[407],[363,195183,461],{"className":195184},[494],[363,195186,45101],{"className":195187,"style":45131},[407,408],[363,195189],{"className":195190,"style":2934},[505],[363,195192,5160],{"className":195193},[2938],[363,195195],{"className":195196,"style":2934},[505],[363,195198,195200,195203,195206],{"className":195199},[398],[363,195201],{"className":195202,"style":487},[402],[363,195204,465],{"className":195205},[407],[363,195207,468],{"className":195208},[501]," 与认知部分 ",[363,195211,195213,195245],{"className":195212,"translate":367},[366],[363,195214,195216],{"className":195215},[371],[373,195217,195218],{"xmlns":375},[377,195219,195220,195242],{},[380,195221,195222,195224,195226,195228,195230,195232,195234,195236,195238,195240],{},[383,195223,84464],{},[383,195225,1288],{"mathvariant":557},[458,195227,578],{"stretchy":460},[383,195229,194696],{},[458,195231,461],{"stretchy":460},[383,195233,45101],{},[458,195235,5160],{},[463,195237,465],{},[458,195239,468],{"stretchy":460},[458,195241,605],{"stretchy":460},[387,195243,195244],{"encoding":389},"\\beta\u002F[\\upsilon(\\alpha - 1)]",[363,195246,195248,195281],{"className":195247,"ariaHidden":394},[393],[363,195249,195251,195254,195257,195260,195263,195266,195269,195272,195275,195278],{"className":195250},[398],[363,195252],{"className":195253,"style":487},[402],[363,195255,84464],{"className":195256,"style":84686},[407,408],[363,195258,1288],{"className":195259},[407],[363,195261,578],{"className":195262},[494],[363,195264,194696],{"className":195265,"style":1328},[407,408],[363,195267,461],{"className":195268},[494],[363,195270,45101],{"className":195271,"style":45131},[407,408],[363,195273],{"className":195274,"style":2934},[505],[363,195276,5160],{"className":195277},[2938],[363,195279],{"className":195280,"style":2934},[505],[363,195282,195284,195287,195290],{"className":195283},[398],[363,195285],{"className":195286,"style":487},[402],[363,195288,465],{"className":195289},[407],[363,195291,20737],{"className":195292},[501],"，二者之和 ",[363,195295,195297,195339],{"className":195296,"translate":367},[366],[363,195298,195300],{"className":195299},[371],[373,195301,195302],{"xmlns":375},[377,195303,195304,195336],{},[380,195305,195306,195308,195310,195312,195314,195316,195318,195320,195322,195324,195326,195328,195330,195332,195334],{},[383,195307,84464],{},[458,195309,461],{"stretchy":460},[383,195311,194696],{},[458,195313,2817],{},[463,195315,465],{},[458,195317,468],{"stretchy":460},[383,195319,1288],{"mathvariant":557},[458,195321,578],{"stretchy":460},[383,195323,194696],{},[458,195325,461],{"stretchy":460},[383,195327,45101],{},[458,195329,5160],{},[463,195331,465],{},[458,195333,468],{"stretchy":460},[458,195335,605],{"stretchy":460},[387,195337,195338],{"encoding":389},"\\beta(\\upsilon + 1)\u002F[\\upsilon(\\alpha - 1)]",[363,195340,195342,195366,195402],{"className":195341,"ariaHidden":394},[393],[363,195343,195345,195348,195351,195354,195357,195360,195363],{"className":195344},[398],[363,195346],{"className":195347,"style":487},[402],[363,195349,84464],{"className":195350,"style":84686},[407,408],[363,195352,461],{"className":195353},[494],[363,195355,194696],{"className":195356,"style":1328},[407,408],[363,195358],{"className":195359,"style":2934},[505],[363,195361,2817],{"className":195362},[2938],[363,195364],{"className":195365,"style":2934},[505],[363,195367,195369,195372,195375,195378,195381,195384,195387,195390,195393,195396,195399],{"className":195368},[398],[363,195370],{"className":195371,"style":487},[402],[363,195373,465],{"className":195374},[407],[363,195376,468],{"className":195377},[501],[363,195379,1288],{"className":195380},[407],[363,195382,578],{"className":195383},[494],[363,195385,194696],{"className":195386,"style":1328},[407,408],[363,195388,461],{"className":195389},[494],[363,195391,45101],{"className":195392,"style":45131},[407,408],[363,195394],{"className":195395,"style":2934},[505],[363,195397,5160],{"className":195398},[2938],[363,195400],{"className":195401,"style":2934},[505],[363,195403,195405,195408,195411],{"className":195404},[398],[363,195406],{"className":195407,"style":487},[402],[363,195409,465],{"className":195410},[407],[363,195412,20737],{"className":195413},[501]," 即自由度 ",[363,195416,195418,195433],{"className":195417,"translate":367},[366],[363,195419,195421],{"className":195420},[371],[373,195422,195423],{"xmlns":375},[377,195424,195425,195431],{},[380,195426,195427,195429],{},[463,195428,2810],{},[383,195430,45101],{},[387,195432,195092],{"encoding":389},[363,195434,195436],{"className":195435,"ariaHidden":394},[393],[363,195437,195439,195442,195445],{"className":195438},[398],[363,195440],{"className":195441,"style":520},[402],[363,195443,2810],{"className":195444},[407],[363,195446,45101],{"className":195447,"style":45131},[407,408],[363,195449,195451,195464],{"className":195450,"translate":367},[366],[363,195452,195454],{"className":195453},[371],[373,195455,195456],{"xmlns":375},[377,195457,195458,195462],{},[380,195459,195460],{},[383,195461,1116],{},[387,195463,1116],{"encoding":389},[363,195465,195467],{"className":195466,"ariaHidden":394},[393],[363,195468,195470,195473],{"className":195469},[398],[363,195471],{"className":195472,"style":5690},[402],[363,195474,1116],{"className":195475},[407,408]," 分布的方差，形式上与命题 3.5 的分解对应。该推广在分子性质预测、三维重建与不确定性感知的姿态估计中均有应用。",[11,195478,195479],{},"需要指出的是，这一推广的理论状况比分类情形更受争议：有后续研究指出，此类模型所报告的「认知」分量并不随训练数据的增加而按预期衰减，其与偶然分量的分离缺乏理论保证。因此 4.5 节的谨慎立场在回归情形下应进一步加强。",[2658,195481,195483],{"id":195482},"_56-与原型学习超球面几何的融合","5.6 与原型学习、超球面几何的融合",[11,195485,195486,195487,195649,195650,195799,195800,195958,195959,196099],{},"最后讨论一个尚未定型、但在方法上自然的方向：把 EDL 与基于原型的超球面表示学习结合。设主干网络输出归一化特征 ",[363,195488,195490,195528],{"className":195489,"translate":367},[366],[363,195491,195493],{"className":195492},[371],[373,195494,195495],{"xmlns":375},[377,195496,195497,195525],{},[380,195498,195499,195505,195507,195509,195511,195513],{},[543,195500,195501,195503],{},[383,195502,385],{"mathvariant":75560},[383,195504,101106],{"mathvariant":136008},[458,195506,461],{"stretchy":460},[383,195508,1121],{"mathvariant":75560},[458,195510,468],{"stretchy":460},[458,195512,6256],{},[7161,195514,195515,195517],{},[383,195516,26084],{"mathvariant":570},[380,195518,195519,195521,195523],{},[383,195520,592],{},[458,195522,5160],{},[463,195524,465],{},[387,195526,195527],{"encoding":389},"\\mathbf{f}_{\\boldsymbol{\\theta}}(\\mathbf{x}) \\in \\mathbb{S}^{d-1}",[363,195529,195531,195605],{"className":195530,"ariaHidden":394},[393],[363,195532,195534,195537,195587,195590,195593,195596,195599,195602],{"className":195533},[398],[363,195535],{"className":195536,"style":487},[402],[363,195538,195540,195543],{"className":195539},[407],[363,195541,385],{"className":195542,"style":25948},[407,75905],[363,195544,195546],{"className":195545},[629],[363,195547,195549,195579],{"className":195548},[633,634],[363,195550,195552,195576],{"className":195551},[638],[363,195553,195555],{"className":195554,"style":643},[642],[363,195556,195558,195561],{"style":195557},"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;",[363,195559],{"className":195560,"style":651},[650],[363,195562,195564],{"className":195563},[655,656,657,658],[363,195565,195567],{"className":195566},[407,658],[363,195568,195570],{"className":195569},[407,658],[363,195571,195573],{"className":195572},[407,658],[363,195574,101106],{"className":195575,"style":169854},[407,136068,658],[363,195577,666],{"className":195578},[665],[363,195580,195582],{"className":195581},[638],[363,195583,195585],{"className":195584,"style":8315},[642],[363,195586],{},[363,195588,461],{"className":195589},[494],[363,195591,1121],{"className":195592},[407,75905],[363,195594,468],{"className":195595},[501],[363,195597],{"className":195598,"style":506},[505],[363,195600,6256],{"className":195601},[510],[363,195603],{"className":195604,"style":506},[505],[363,195606,195608,195611],{"className":195607},[398],[363,195609],{"className":195610,"style":47901},[402],[363,195612,195614,195617],{"className":195613},[407],[363,195615,26084],{"className":195616},[407,714],[363,195618,195620],{"className":195619},[629],[363,195621,195623],{"className":195622},[633],[363,195624,195626],{"className":195625},[638],[363,195627,195629],{"className":195628,"style":47901},[642],[363,195630,195631,195634],{"style":7212},[363,195632],{"className":195633,"style":651},[650],[363,195635,195637],{"className":195636},[655,656,657,658],[363,195638,195640,195643,195646],{"className":195639},[407,658],[363,195641,592],{"className":195642},[407,408,658],[363,195644,5160],{"className":195645},[2938,658],[363,195647,465],{"className":195648},[407,658],"，各类原型为 ",[363,195651,195653,195690],{"className":195652,"translate":367},[366],[363,195654,195656],{"className":195655},[371],[373,195657,195658],{"xmlns":375},[377,195659,195660,195687],{},[380,195661,195662,195664,195670,195672,195675],{},[458,195663,3245],{"stretchy":460},[543,195665,195666,195668],{},[383,195667,163132],{"mathvariant":75560},[383,195669,7911],{},[458,195671,3255],{"stretchy":460},[458,195673,195674],{},"⊂",[7161,195676,195677,195679],{},[383,195678,26084],{"mathvariant":570},[380,195680,195681,195683,195685],{},[383,195682,592],{},[458,195684,5160],{},[463,195686,465],{},[387,195688,195689],{"encoding":389},"\\{\\mathbf{v}_k\\} \\subset \\mathbb{S}^{d-1}",[363,195691,195693,195755],{"className":195692,"ariaHidden":394},[393],[363,195694,195696,195699,195702,195743,195746,195749,195752],{"className":195695},[398],[363,195697],{"className":195698,"style":487},[402],[363,195700,3245],{"className":195701},[494],[363,195703,195705,195708],{"className":195704},[407],[363,195706,163132],{"className":195707,"style":162090},[407,75905],[363,195709,195711],{"className":195710},[629],[363,195712,195714,195735],{"className":195713},[633,634],[363,195715,195717,195732],{"className":195716},[638],[363,195718,195720],{"className":195719,"style":643},[642],[363,195721,195723,195726],{"style":195722},"top:-2.55em;margin-left:-0.016em;margin-right:0.05em;",[363,195724],{"className":195725,"style":651},[650],[363,195727,195729],{"className":195728},[655,656,657,658],[363,195730,7911],{"className":195731,"style":8614},[407,408,658],[363,195733,666],{"className":195734},[665],[363,195736,195738],{"className":195737},[638],[363,195739,195741],{"className":195740,"style":8315},[642],[363,195742],{},[363,195744,3255],{"className":195745},[501],[363,195747],{"className":195748,"style":506},[505],[363,195750,195674],{"className":195751},[510],[363,195753],{"className":195754,"style":506},[505],[363,195756,195758,195761],{"className":195757},[398],[363,195759],{"className":195760,"style":47901},[402],[363,195762,195764,195767],{"className":195763},[407],[363,195765,26084],{"className":195766},[407,714],[363,195768,195770],{"className":195769},[629],[363,195771,195773],{"className":195772},[633],[363,195774,195776],{"className":195775},[638],[363,195777,195779],{"className":195778,"style":47901},[642],[363,195780,195781,195784],{"style":7212},[363,195782],{"className":195783,"style":651},[650],[363,195785,195787],{"className":195786},[655,656,657,658],[363,195788,195790,195793,195796],{"className":195789},[407,658],[363,195791,592],{"className":195792},[407,408,658],[363,195794,5160],{"className":195795},[2938,658],[363,195797,465],{"className":195798},[407,658],"，相似度 ",[363,195801,195803,195839],{"className":195802,"translate":367},[366],[363,195804,195806],{"className":195805},[371],[373,195807,195808],{"xmlns":375},[377,195809,195810,195836],{},[380,195811,195812,195818,195820,195823,195825,195827,195833],{},[543,195813,195814,195816],{},[383,195815,7908],{},[383,195817,7911],{},[458,195819,471],{},[458,195821,195822],{"stretchy":460},"⟨",[383,195824,385],{"mathvariant":75560},[458,195826,898],{"separator":394},[543,195828,195829,195831],{},[383,195830,163132],{"mathvariant":75560},[383,195832,7911],{},[458,195834,195835],{"stretchy":460},"⟩",[387,195837,195838],{"encoding":389},"s_k = \\langle \\mathbf{f}, \\mathbf{v}_k \\rangle",[363,195840,195842,195897],{"className":195841,"ariaHidden":394},[393],[363,195843,195845,195848,195888,195891,195894],{"className":195844},[398],[363,195846],{"className":195847,"style":13721},[402],[363,195849,195851,195854],{"className":195850},[407],[363,195852,7908],{"className":195853},[407,408],[363,195855,195857],{"className":195856},[629],[363,195858,195860,195880],{"className":195859},[633,634],[363,195861,195863,195877],{"className":195862},[638],[363,195864,195866],{"className":195865,"style":643},[642],[363,195867,195868,195871],{"style":730},[363,195869],{"className":195870,"style":651},[650],[363,195872,195874],{"className":195873},[655,656,657,658],[363,195875,7911],{"className":195876,"style":8614},[407,408,658],[363,195878,666],{"className":195879},[665],[363,195881,195883],{"className":195882},[638],[363,195884,195886],{"className":195885,"style":8315},[642],[363,195887],{},[363,195889],{"className":195890,"style":506},[505],[363,195892,471],{"className":195893},[510],[363,195895],{"className":195896,"style":506},[505],[363,195898,195900,195903,195906,195909,195912,195915,195955],{"className":195899},[398],[363,195901],{"className":195902,"style":487},[402],[363,195904,195822],{"className":195905},[494],[363,195907,385],{"className":195908,"style":25948},[407,75905],[363,195910,898],{"className":195911},[920],[363,195913],{"className":195914,"style":754},[505],[363,195916,195918,195921],{"className":195917},[407],[363,195919,163132],{"className":195920,"style":162090},[407,75905],[363,195922,195924],{"className":195923},[629],[363,195925,195927,195947],{"className":195926},[633,634],[363,195928,195930,195944],{"className":195929},[638],[363,195931,195933],{"className":195932,"style":643},[642],[363,195934,195935,195938],{"style":195722},[363,195936],{"className":195937,"style":651},[650],[363,195939,195941],{"className":195940},[655,656,657,658],[363,195942,7911],{"className":195943,"style":8614},[407,408,658],[363,195945,666],{"className":195946},[665],[363,195948,195950],{"className":195949},[638],[363,195951,195953],{"className":195952,"style":8315},[642],[363,195954],{},[363,195956,195835],{"className":195957},[501],"。传统原型方法以 ",[363,195960,195962,195991],{"className":195961,"translate":367},[366],[363,195963,195965],{"className":195964},[371],[373,195966,195967],{"xmlns":375},[377,195968,195969,195988],{},[380,195970,195971,195977,195979,195982],{},[543,195972,195973,195975],{},[383,195974,118116],{"mathvariant":75560},[383,195976,7911],{},[458,195978,471],{},[383,195980,195981],{},"κ",[543,195983,195984,195986],{},[383,195985,7908],{},[383,195987,7911],{},[387,195989,195990],{"encoding":389},"\\mathbf{z}_k = \\kappa s_k",[363,195992,195994,196050],{"className":195993,"ariaHidden":394},[393],[363,195995,195997,196001,196041,196044,196047],{"className":195996},[398],[363,195998],{"className":195999,"style":196000},[402],"height:0.5944em;vertical-align:-0.15em;",[363,196002,196004,196007],{"className":196003},[407],[363,196005,118116],{"className":196006},[407,75905],[363,196008,196010],{"className":196009},[629],[363,196011,196013,196033],{"className":196012},[633,634],[363,196014,196016,196030],{"className":196015},[638],[363,196017,196019],{"className":196018,"style":643},[642],[363,196020,196021,196024],{"style":730},[363,196022],{"className":196023,"style":651},[650],[363,196025,196027],{"className":196026},[655,656,657,658],[363,196028,7911],{"className":196029,"style":8614},[407,408,658],[363,196031,666],{"className":196032},[665],[363,196034,196036],{"className":196035},[638],[363,196037,196039],{"className":196038,"style":8315},[642],[363,196040],{},[363,196042],{"className":196043,"style":506},[505],[363,196045,471],{"className":196046},[510],[363,196048],{"className":196049,"style":506},[505],[363,196051,196053,196056,196059],{"className":196052},[398],[363,196054],{"className":196055,"style":13721},[402],[363,196057,195981],{"className":196058},[407,408],[363,196060,196062,196065],{"className":196061},[407],[363,196063,7908],{"className":196064},[407,408],[363,196066,196068],{"className":196067},[629],[363,196069,196071,196091],{"className":196070},[633,634],[363,196072,196074,196088],{"className":196073},[638],[363,196075,196077],{"className":196076,"style":643},[642],[363,196078,196079,196082],{"style":730},[363,196080],{"className":196081,"style":651},[650],[363,196083,196085],{"className":196084},[655,656,657,658],[363,196086,7911],{"className":196087,"style":8614},[407,408,658],[363,196089,666],{"className":196090},[665],[363,196092,196094],{"className":196093},[638],[363,196095,196097],{"className":196096,"style":8315},[642],[363,196098],{}," 作为 logits 并配 softmax 交叉熵，由 3.3 节，这仍受平移不变性与 logits 发散两项缺陷的支配。",[11,196101,196102],{},"一个直接的融合方案是把相似度送入证据函数：",[363,196104,196106],{"className":196105,"translate":367},[528],[363,196107,196109,196219],{"className":196108,"translate":367},[366],[363,196110,196112],{"className":196111},[371],[373,196113,196114],{"xmlns":375,"display":537},[377,196115,196116,196216],{},[380,196117,196118,196124,196126,196128,196130,196132,196134,196140,196142,196144,196146,196152,196154,196156,196158,196160,196162,196164,196166,196172,196174,196176,196178,196180,196182,196184,196186,196200,196202,196204,196206,196208,196214],{},[543,196119,196120,196122],{},[383,196121,7914],{},[383,196123,7911],{},[458,196125,471],{},[383,196127,4505],{},[458,196129,461],{"stretchy":460},[383,196131,195981],{},[1644,196133,1646],{},[543,196135,196136,196138],{},[383,196137,7908],{},[383,196139,7911],{},[458,196141,468],{"stretchy":460},[458,196143,898],{"separator":394},[505,196145],{"width":3609},[543,196147,196148,196150],{},[383,196149,45101],{},[383,196151,7911],{},[458,196153,471],{},[463,196155,465],{},[458,196157,2817],{},[383,196159,4505],{},[458,196161,461],{"stretchy":460},[383,196163,195981],{},[1644,196165,1646],{},[543,196167,196168,196170],{},[383,196169,7908],{},[383,196171,7911],{},[458,196173,468],{"stretchy":460},[458,196175,898],{"separator":394},[505,196177],{"width":3609},[383,196179,26084],{},[458,196181,471],{},[383,196183,11041],{},[458,196185,2817],{},[48667,196187,196188,196190,196198],{},[458,196189,13808],{},[380,196191,196192,196194,196196],{},[383,196193,7911],{},[458,196195,471],{},[463,196197,465],{},[383,196199,11041],{},[383,196201,4505],{},[458,196203,461],{"stretchy":460},[383,196205,195981],{},[1644,196207,1646],{},[543,196209,196210,196212],{},[383,196211,7908],{},[383,196213,7911],{},[458,196215,468],{"stretchy":460},[387,196217,196218],{"encoding":389},"e_k = g(\\kappa\\, s_k), \\qquad \\alpha_k = 1 + g(\\kappa\\, s_k), \\qquad S = K + \\sum_{k=1}^K g(\\kappa\\, s_k)",[363,196220,196222,196277,196396,196414,196496,196514],{"className":196221,"ariaHidden":394},[393],[363,196223,196225,196228,196268,196271,196274],{"className":196224},[398],[363,196226],{"className":196227,"style":13721},[402],[363,196229,196231,196234],{"className":196230},[407],[363,196232,7914],{"className":196233},[407,408],[363,196235,196237],{"className":196236},[629],[363,196238,196240,196260],{"className":196239},[633,634],[363,196241,196243,196257],{"className":196242},[638],[363,196244,196246],{"className":196245,"style":643},[642],[363,196247,196248,196251],{"style":730},[363,196249],{"className":196250,"style":651},[650],[363,196252,196254],{"className":196253},[655,656,657,658],[363,196255,7911],{"className":196256,"style":8614},[407,408,658],[363,196258,666],{"className":196259},[665],[363,196261,196263],{"className":196262},[638],[363,196264,196266],{"className":196265,"style":8315},[642],[363,196267],{},[363,196269],{"className":196270,"style":506},[505],[363,196272,471],{"className":196273},[510],[363,196275],{"className":196276,"style":506},[505],[363,196278,196280,196283,196286,196289,196292,196295,196335,196338,196341,196344,196347,196387,196390,196393],{"className":196279},[398],[363,196281],{"className":196282,"style":487},[402],[363,196284,4505],{"className":196285,"style":1328},[407,408],[363,196287,461],{"className":196288},[494],[363,196290,195981],{"className":196291},[407,408],[363,196293],{"className":196294,"style":754},[505],[363,196296,196298,196301],{"className":196297},[407],[363,196299,7908],{"className":196300},[407,408],[363,196302,196304],{"className":196303},[629],[363,196305,196307,196327],{"className":196306},[633,634],[363,196308,196310,196324],{"className":196309},[638],[363,196311,196313],{"className":196312,"style":643},[642],[363,196314,196315,196318],{"style":730},[363,196316],{"className":196317,"style":651},[650],[363,196319,196321],{"className":196320},[655,656,657,658],[363,196322,7911],{"className":196323,"style":8614},[407,408,658],[363,196325,666],{"className":196326},[665],[363,196328,196330],{"className":196329},[638],[363,196331,196333],{"className":196332,"style":8315},[642],[363,196334],{},[363,196336,468],{"className":196337},[501],[363,196339,898],{"className":196340},[920],[363,196342],{"className":196343,"style":3981},[505],[363,196345],{"className":196346,"style":754},[505],[363,196348,196350,196353],{"className":196349},[407],[363,196351,45101],{"className":196352,"style":45131},[407,408],[363,196354,196356],{"className":196355},[629],[363,196357,196359,196379],{"className":196358},[633,634],[363,196360,196362,196376],{"className":196361},[638],[363,196363,196365],{"className":196364,"style":643},[642],[363,196366,196367,196370],{"style":136107},[363,196368],{"className":196369,"style":651},[650],[363,196371,196373],{"className":196372},[655,656,657,658],[363,196374,7911],{"className":196375,"style":8614},[407,408,658],[363,196377,666],{"className":196378},[665],[363,196380,196382],{"className":196381},[638],[363,196383,196385],{"className":196384,"style":8315},[642],[363,196386],{},[363,196388],{"className":196389,"style":506},[505],[363,196391,471],{"className":196392},[510],[363,196394],{"className":196395,"style":506},[505],[363,196397,196399,196402,196405,196408,196411],{"className":196398},[398],[363,196400],{"className":196401,"style":12925},[402],[363,196403,465],{"className":196404},[407],[363,196406],{"className":196407,"style":2934},[505],[363,196409,2817],{"className":196410},[2938],[363,196412],{"className":196413,"style":2934},[505],[363,196415,196417,196420,196423,196426,196429,196432,196472,196475,196478,196481,196484,196487,196490,196493],{"className":196416},[398],[363,196418],{"className":196419,"style":487},[402],[363,196421,4505],{"className":196422,"style":1328},[407,408],[363,196424,461],{"className":196425},[494],[363,196427,195981],{"className":196428},[407,408],[363,196430],{"className":196431,"style":754},[505],[363,196433,196435,196438],{"className":196434},[407],[363,196436,7908],{"className":196437},[407,408],[363,196439,196441],{"className":196440},[629],[363,196442,196444,196464],{"className":196443},[633,634],[363,196445,196447,196461],{"className":196446},[638],[363,196448,196450],{"className":196449,"style":643},[642],[363,196451,196452,196455],{"style":730},[363,196453],{"className":196454,"style":651},[650],[363,196456,196458],{"className":196457},[655,656,657,658],[363,196459,7911],{"className":196460,"style":8614},[407,408,658],[363,196462,666],{"className":196463},[665],[363,196465,196467],{"className":196466},[638],[363,196468,196470],{"className":196469,"style":8315},[642],[363,196471],{},[363,196473,468],{"className":196474},[501],[363,196476,898],{"className":196477},[920],[363,196479],{"className":196480,"style":3981},[505],[363,196482],{"className":196483,"style":754},[505],[363,196485,26084],{"className":196486,"style":26208},[407,408],[363,196488],{"className":196489,"style":506},[505],[363,196491,471],{"className":196492},[510],[363,196494],{"className":196495,"style":506},[505],[363,196497,196499,196502,196505,196508,196511],{"className":196498},[398],[363,196500],{"className":196501,"style":133899},[402],[363,196503,11041],{"className":196504,"style":11129},[407,408],[363,196506],{"className":196507,"style":2934},[505],[363,196509,2817],{"className":196510},[2938],[363,196512],{"className":196513,"style":2934},[505],[363,196515,196517,196521,196587,196590,196593,196596,196599,196602,196642],{"className":196516},[398],[363,196518],{"className":196519,"style":196520},[402],"height:3.1304em;vertical-align:-1.3021em;",[363,196522,196524],{"className":196523},[1831,14063],[363,196525,196527,196578],{"className":196526},[633,634],[363,196528,196530,196575],{"className":196529},[638],[363,196531,196533,196554,196564],{"className":196532,"style":138225},[642],[363,196534,196536,196539],{"style":196535},"top:-1.8479em;margin-left:0em;",[363,196537],{"className":196538,"style":14080},[650],[363,196540,196542],{"className":196541},[655,656,657,658],[363,196543,196545,196548,196551],{"className":196544},[407,658],[363,196546,7911],{"className":196547,"style":8614},[407,408,658],[363,196549,471],{"className":196550},[510,658],[363,196552,465],{"className":196553},[407,658],[363,196555,196556,196559],{"style":14089},[363,196557],{"className":196558,"style":14080},[650],[363,196560,196561],{},[363,196562,13808],{"className":196563},[1831,1832,1833],[363,196565,196566,196569],{"style":100671},[363,196567],{"className":196568,"style":14080},[650],[363,196570,196572],{"className":196571},[655,656,657,658],[363,196573,11041],{"className":196574,"style":11129},[407,408,658],[363,196576,666],{"className":196577},[665],[363,196579,196581],{"className":196580},[638],[363,196582,196585],{"className":196583,"style":196584},[642],"height:1.3021em;",[363,196586],{},[363,196588],{"className":196589,"style":754},[505],[363,196591,4505],{"className":196592,"style":1328},[407,408],[363,196594,461],{"className":196595},[494],[363,196597,195981],{"className":196598},[407,408],[363,196600],{"className":196601,"style":754},[505],[363,196603,196605,196608],{"className":196604},[407],[363,196606,7908],{"className":196607},[407,408],[363,196609,196611],{"className":196610},[629],[363,196612,196614,196634],{"className":196613},[633,634],[363,196615,196617,196631],{"className":196616},[638],[363,196618,196620],{"className":196619,"style":643},[642],[363,196621,196622,196625],{"style":730},[363,196623],{"className":196624,"style":651},[650],[363,196626,196628],{"className":196627},[655,656,657,658],[363,196629,7911],{"className":196630,"style":8614},[407,408,658],[363,196632,666],{"className":196633},[665],[363,196635,196637],{"className":196636},[638],[363,196638,196640],{"className":196639,"style":8315},[642],[363,196641],{},[363,196643,468],{"className":196644},[501],[11,196646,2597,196647,196675,196676,196705,196706,196776,196777,196805,196806,196834,196835,196904,196905,10527,196955],{},[363,196648,196650,196663],{"className":196649,"translate":367},[366],[363,196651,196653],{"className":196652},[371],[373,196654,196655],{"xmlns":375},[377,196656,196657,196661],{},[380,196658,196659],{},[383,196660,4505],{},[387,196662,4505],{"encoding":389},[363,196664,196666],{"className":196665,"ariaHidden":394},[393],[363,196667,196669,196672],{"className":196668},[398],[363,196670],{"className":196671,"style":2623},[402],[363,196673,4505],{"className":196674,"style":1328},[407,408]," 取 3.4 节的非负激活，",[363,196677,196679,196693],{"className":196678,"translate":367},[366],[363,196680,196682],{"className":196681},[371],[373,196683,196684],{"xmlns":375},[377,196685,196686,196690],{},[380,196687,196688],{},[383,196689,195981],{},[387,196691,196692],{"encoding":389},"\\kappa",[363,196694,196696],{"className":196695,"ariaHidden":394},[393],[363,196697,196699,196702],{"className":196698},[398],[363,196700],{"className":196701,"style":2692},[402],[363,196703,195981],{"className":196704},[407,408]," 沿用 vMF 分布的集中参数语义。该构造把几何与不确定性直接挂钩：特征落在某原型附近时，",[363,196707,196709,196727],{"className":196708,"translate":367},[366],[363,196710,196712],{"className":196711},[371],[373,196713,196714],{"xmlns":375},[377,196715,196716,196724],{},[380,196717,196718],{},[543,196719,196720,196722],{},[383,196721,7908],{},[383,196723,7911],{},[387,196725,196726],{"encoding":389},"s_k",[363,196728,196730],{"className":196729,"ariaHidden":394},[393],[363,196731,196733,196736],{"className":196732},[398],[363,196734],{"className":196735,"style":13721},[402],[363,196737,196739,196742],{"className":196738},[407],[363,196740,7908],{"className":196741},[407,408],[363,196743,196745],{"className":196744},[629],[363,196746,196748,196768],{"className":196747},[633,634],[363,196749,196751,196765],{"className":196750},[638],[363,196752,196754],{"className":196753,"style":643},[642],[363,196755,196756,196759],{"style":730},[363,196757],{"className":196758,"style":651},[650],[363,196760,196762],{"className":196761},[655,656,657,658],[363,196763,7911],{"className":196764,"style":8614},[407,408,658],[363,196766,666],{"className":196767},[665],[363,196769,196771],{"className":196770},[638],[363,196772,196774],{"className":196773,"style":8315},[642],[363,196775],{}," 接近 ",[363,196778,196780,196793],{"className":196779,"translate":367},[366],[363,196781,196783],{"className":196782},[371],[373,196784,196785],{"xmlns":375},[377,196786,196787,196791],{},[380,196788,196789],{},[463,196790,465],{},[387,196792,465],{"encoding":389},[363,196794,196796],{"className":196795,"ariaHidden":394},[393],[363,196797,196799,196802],{"className":196798},[398],[363,196800],{"className":196801,"style":520},[402],[363,196803,465],{"className":196804},[407],"、证据充分、",[363,196807,196809,196822],{"className":196808,"translate":367},[366],[363,196810,196812],{"className":196811},[371],[373,196813,196814],{"xmlns":375},[377,196815,196816,196820],{},[380,196817,196818],{},[383,196819,15747],{},[387,196821,15747],{"encoding":389},[363,196823,196825],{"className":196824,"ariaHidden":394},[393],[363,196826,196828,196831],{"className":196827},[398],[363,196829],{"className":196830,"style":2692},[402],[363,196832,15747],{"className":196833},[407,408]," 小。特征落在所有原型之外（其与全部原型的相似度均低或为负）时，各 ",[363,196836,196838,196855],{"className":196837,"translate":367},[366],[363,196839,196841],{"className":196840},[371],[373,196842,196843],{"xmlns":375},[377,196844,196845,196853],{},[380,196846,196847],{},[543,196848,196849,196851],{},[383,196850,7914],{},[383,196852,7911],{},[387,196854,171940],{"encoding":389},[363,196856,196858],{"className":196857,"ariaHidden":394},[393],[363,196859,196861,196864],{"className":196860},[398],[363,196862],{"className":196863,"style":13721},[402],[363,196865,196867,196870],{"className":196866},[407],[363,196868,7914],{"className":196869},[407,408],[363,196871,196873],{"className":196872},[629],[363,196874,196876,196896],{"className":196875},[633,634],[363,196877,196879,196893],{"className":196878},[638],[363,196880,196882],{"className":196881,"style":643},[642],[363,196883,196884,196887],{"style":730},[363,196885],{"className":196886,"style":651},[650],[363,196888,196890],{"className":196889},[655,656,657,658],[363,196891,7911],{"className":196892,"style":8614},[407,408,658],[363,196894,666],{"className":196895},[665],[363,196897,196899],{"className":196898},[638],[363,196900,196902],{"className":196901,"style":8315},[642],[363,196903],{}," 同时趋零、",[363,196906,196908,196925],{"className":196907,"translate":367},[366],[363,196909,196911],{"className":196910},[371],[373,196912,196913],{"xmlns":375},[377,196914,196915,196923],{},[380,196916,196917,196919,196921],{},[383,196918,15747],{},[458,196920,1376],{},[463,196922,465],{},[387,196924,174923],{"encoding":389},[363,196926,196928,196946],{"className":196927,"ariaHidden":394},[393],[363,196929,196931,196934,196937,196940,196943],{"className":196930},[398],[363,196932],{"className":196933,"style":2692},[402],[363,196935,15747],{"className":196936},[407,408],[363,196938],{"className":196939,"style":506},[505],[363,196941,1376],{"className":196942},[510],[363,196944],{"className":196945,"style":506},[505],[363,196947,196949,196952],{"className":196948},[398],[363,196950],{"className":196951,"style":520},[402],[363,196953,465],{"className":196954},[407],[1572,196956,196957],{},"「离原型远」与「证据不足」在此被同一个机制表达。",[11,196959,196960,196961,196964,196965,196968,196969,197041,197042,197070,197071,197074,197075,197109],{},"但这一构造的成立范围必须严格界定。迪利克雷分布定义在",[1572,196962,196963],{},"类概率单纯形","上，原型方法定义在",[1572,196966,196967],{},"球面特征空间","上，二者的「不确定性」不是同一个对象：前者是关于类概率向量的二阶分布，后者是关于特征位置的一阶几何量。",[363,196970,196972,196996],{"className":196971,"translate":367},[366],[363,196973,196975],{"className":196974},[371],[373,196976,196977],{"xmlns":375},[377,196978,196979,196993],{},[380,196980,196981,196983,196985,196987,196989,196991],{},[383,196982,1121],{"mathvariant":75560},[458,196984,9031],{},[383,196986,45101],{"mathvariant":136008},[458,196988,461],{"stretchy":460},[383,196990,1121],{"mathvariant":75560},[458,196992,468],{"stretchy":460},[387,196994,196995],{"encoding":389},"\\mathbf{x} \\mapsto \\boldsymbol{\\alpha}(\\mathbf{x})",[363,196997,196999,197017],{"className":196998,"ariaHidden":394},[393],[363,197000,197002,197005,197008,197011,197014],{"className":197001},[398],[363,197003],{"className":197004,"style":84306},[402],[363,197006,1121],{"className":197007},[407,75905],[363,197009],{"className":197010,"style":506},[505],[363,197012,9031],{"className":197013},[510],[363,197015],{"className":197016,"style":506},[505],[363,197018,197020,197023,197032,197035,197038],{"className":197019},[398],[363,197021],{"className":197022,"style":487},[402],[363,197024,197026],{"className":197025},[407],[363,197027,197029],{"className":197028},[407],[363,197030,45101],{"className":197031},[407,136068],[363,197033,461],{"className":197034},[494],[363,197036,1121],{"className":197037},[407,75905],[363,197039,468],{"className":197040},[501]," 仍然是一个点估计的映射，因此 4.5 节第 1 点的批评在此完全适用——",[363,197043,197045,197058],{"className":197044,"translate":367},[366],[363,197046,197048],{"className":197047},[371],[373,197049,197050],{"xmlns":375},[377,197051,197052,197056],{},[380,197053,197054],{},[383,197055,15747],{},[387,197057,15747],{"encoding":389},[363,197059,197061],{"className":197060,"ariaHidden":394},[393],[363,197062,197064,197067],{"className":197063},[398],[363,197065],{"className":197066,"style":2692},[402],[363,197068,15747],{"className":197069},[407,408]," 度量的是「特征到原型的距离」，而不是「模型对该映射的把握」。要真正结合二者，需要构造（特征空间，类概率空间）的",[1572,197072,197073],{},"联合","模型，例如令 ",[363,197076,197078,197091],{"className":197077,"translate":367},[366],[363,197079,197081],{"className":197080},[371],[373,197082,197083],{"xmlns":375},[377,197084,197085,197089],{},[380,197086,197087],{},[383,197088,45101],{"mathvariant":136008},[387,197090,137027],{"encoding":389},[363,197092,197094],{"className":197093,"ariaHidden":394},[393],[363,197095,197097,197100],{"className":197096},[398],[363,197098],{"className":197099,"style":135617},[402],[363,197101,197103],{"className":197102},[407],[363,197104,197106],{"className":197105},[407],[363,197107,45101],{"className":197108},[407,136068]," 自身携带分布（层级模型），或以 vMF 构造特征的生成式模型、以迪利克雷构造其上的分类头，使两个不确定性来源可以在同一层级结构中分别标识。",[11,197111,197112],{},"即便在当前的简化形式下，该方向仍有两个值得推进的具体问题：",[7009,197114,197115,197179],{},[7012,197116,197117,197120,197121,197149,197150,197178],{},[1572,197118,197119],{},"长尾与稀有类。"," 稀有类的原型天然缺乏证据支撑，",[363,197122,197124,197137],{"className":197123,"translate":367},[366],[363,197125,197127],{"className":197126},[371],[373,197128,197129],{"xmlns":375},[377,197130,197131,197135],{},[380,197132,197133],{},[383,197134,15747],{},[387,197136,15747],{"encoding":389},[363,197138,197140],{"className":197139,"ariaHidden":394},[393],[363,197141,197143,197146],{"className":197142},[398],[363,197144],{"className":197145,"style":2692},[402],[363,197147,15747],{"className":197148},[407,408]," 更高。这既可以被用作保护机制（在损失中对高 ",[363,197151,197153,197166],{"className":197152,"translate":367},[366],[363,197154,197156],{"className":197155},[371],[373,197157,197158],{"xmlns":375},[377,197159,197160,197164],{},[380,197161,197162],{},[383,197163,15747],{},[387,197165,15747],{"encoding":389},[363,197167,197169],{"className":197168,"ariaHidden":394},[393],[363,197170,197172,197175],{"className":197171},[398],[363,197173],{"className":197174,"style":2692},[402],[363,197176,15747],{"className":197177},[407,408]," 样本降低梯度权重），也可能加剧对稀有类的欠拟合（模型学会用「不确定」来逃避稀有类）。二者孰占主导是一个可以实验判定的问题。",[7012,197180,197181,197184,197185,194004,197213,197275,197276],{},[1572,197182,197183],{},"与开集\u002F分布外任务的重叠。"," 在代码漏洞检测这类任务中，异常样本（漏洞）与正常样本在特征空间中高度重叠，其本质是开集问题而非单纯的类别不平衡。",[363,197186,197188,197201],{"className":197187,"translate":367},[366],[363,197189,197191],{"className":197190},[371],[373,197192,197193],{"xmlns":375},[377,197194,197195,197199],{},[380,197196,197197],{},[383,197198,15747],{},[387,197200,15747],{"encoding":389},[363,197202,197204],{"className":197203,"ariaHidden":394},[393],[363,197205,197207,197210],{"className":197206},[398],[363,197208],{"className":197209,"style":2692},[402],[363,197211,15747],{"className":197212},[407,408],[363,197214,197216,197239],{"className":197215,"translate":367},[366],[363,197217,197219],{"className":197218},[371],[373,197220,197221],{"xmlns":375},[377,197222,197223,197237],{},[380,197224,197225,197227,197229,197231,197233,197235],{},[383,197226,34215],{},[458,197228,461],{"stretchy":460},[383,197230,40584],{},[458,197232,34222],{"separator":394},[383,197234,157399],{"mathvariant":136008},[458,197236,468],{"stretchy":460},[387,197238,179496],{"encoding":389},[363,197240,197242],{"className":197241,"ariaHidden":394},[393],[363,197243,197245,197248,197251,197254,197257,197260,197263,197272],{"className":197244},[398],[363,197246],{"className":197247,"style":487},[402],[363,197249,34215],{"className":197250,"style":9234},[407,408],[363,197252,461],{"className":197253},[494],[363,197255,40584],{"className":197256,"style":1328},[407,408],[363,197258,34222],{"className":197259},[920],[363,197261],{"className":197262,"style":754},[505],[363,197264,197266],{"className":197265},[407],[363,197267,197269],{"className":197268},[407],[363,197270,157399],{"className":197271,"style":157433},[407,136068],[363,197273,468],{"className":197274},[501]," 可用作告警与拒识的分数，但必须与 4.5 节第 5 点的前提一并验证：",[1572,197277,197278],{},"只有当特征提取器确实把漏洞样本映射到低证据区时，这一机制才成立，而这正是需要独立验证的假设。",[18,197280,197281],{"id":197281},"结语",[11,197283,197284],{},"回顾全文，迪利克雷分布在本文中依次扮演了三个层次的角色：",[10374,197286,197287,197397,197403],{},[7012,197288,197289,197292,197293,164400,197327,197396],{},[1572,197290,197291],{},"作为单纯形上的分布","，它是「关于概率的概率」这一二阶对象的标准载体，其参数由方向 ",[363,197294,197296,197309],{"className":197295,"translate":367},[366],[363,197297,197299],{"className":197298},[371],[373,197300,197301],{"xmlns":375},[377,197302,197303,197307],{},[380,197304,197305],{},[383,197306,2711],{"mathvariant":136008},[387,197308,152212],{"encoding":389},[363,197310,197312],{"className":197311,"ariaHidden":394},[393],[363,197313,197315,197318],{"className":197314},[398],[363,197316],{"className":197317,"style":133764},[402],[363,197319,197321],{"className":197320},[407],[363,197322,197324],{"className":197323},[407],[363,197325,2711],{"className":197326},[407,136068],[363,197328,197330,197347],{"className":197329,"translate":367},[366],[363,197331,197333],{"className":197332},[371],[373,197334,197335],{"xmlns":375},[377,197336,197337,197345],{},[380,197338,197339],{},[543,197340,197341,197343],{},[383,197342,45101],{},[463,197344,474],{},[387,197346,152251],{"encoding":389},[363,197348,197350],{"className":197349,"ariaHidden":394},[393],[363,197351,197353,197356],{"className":197352},[398],[363,197354],{"className":197355,"style":13721},[402],[363,197357,197359,197362],{"className":197358},[407],[363,197360,45101],{"className":197361,"style":45131},[407,408],[363,197363,197365],{"className":197364},[629],[363,197366,197368,197388],{"className":197367},[633,634],[363,197369,197371,197385],{"className":197370},[638],[363,197372,197374],{"className":197373,"style":11480},[642],[363,197375,197376,197379],{"style":136107},[363,197377],{"className":197378,"style":651},[650],[363,197380,197382],{"className":197381},[655,656,657,658],[363,197383,474],{"className":197384},[407,658],[363,197386,666],{"className":197387},[665],[363,197389,197391],{"className":197390},[638],[363,197392,197394],{"className":197393,"style":8315},[642],[363,197395],{}," 两个正交分量构成（命题 2.2）。",[7012,197398,197399,197402],{},[1572,197400,197401],{},"作为多项分布的共轭先验","，它把贝叶斯更新化简为一次向量加法（命题 2.5），并在聚合性、中立性与 stick-breaking 构造下形成一个结构完整、边界清晰的分布族（命题 2.8、2.9）。",[7012,197404,197405,197408],{},[1572,197406,197407],{},"作为神经网络的输出层","，经由与主观逻辑的严格双射（命题 3.2），它把分类器的输出从「单纯形上的点」提升为「单纯形上的分布」，从而首次让「我不知道」成为一个可表示、可优化的对象。",[11,197410,197411,197412,197415,197416,197476],{},"证据深度学习的核心洞见可以压缩为一句话：",[1572,197413,197414],{},"softmax 的平移不变性丢弃了 logits 的绝对水平，因而无法表示无信息状态。证据函数不是平移不变的，它把这一被丢弃的自由度重新赋值为「证据的量级」。"," 命题 3.4 中 ",[363,197417,197419,197440],{"className":197418,"translate":367},[366],[363,197420,197422],{"className":197421},[371],[373,197423,197424],{"xmlns":375},[377,197425,197426,197438],{},[380,197427,197428,197430,197432,197434,197436],{},[383,197429,15747],{},[458,197431,471],{},[383,197433,11041],{},[383,197435,1288],{"mathvariant":557},[383,197437,26084],{},[387,197439,175606],{"encoding":389},[363,197441,197443,197461],{"className":197442,"ariaHidden":394},[393],[363,197444,197446,197449,197452,197455,197458],{"className":197445},[398],[363,197447],{"className":197448,"style":2692},[402],[363,197450,15747],{"className":197451},[407,408],[363,197453],{"className":197454,"style":506},[505],[363,197456,471],{"className":197457},[510],[363,197459],{"className":197460,"style":506},[505],[363,197462,197464,197467,197470,197473],{"className":197463},[398],[363,197465],{"className":197466,"style":487},[402],[363,197468,11041],{"className":197469,"style":11129},[407,408],[363,197471,1288],{"className":197472},[407],[363,197474,26084],{"className":197475,"style":26208},[407,408]," 的全部行为——证据充分时趋于确定、证据消失时退回均匀——都是这一重新赋值的直接后果。",[11,197478,197479],{},"配合 4.3 节的退火 KL 正则，模型不仅被要求「预测得对」，还被要求「在预测错时承认自己不确定」。",[11,197481,197482,197483,197485,197486,197514,197515],{},"但本文同样花了相当篇幅界定这一范式的边界。EDL 的不确定性是",[1572,197484,175646],{},"的，不是贝叶斯后验不确定性：它以点估计替换了对网络参数的边缘化，因而度量的是对输出分布的把握而非对模型的把握（4.5 节第 1 点）。",[363,197487,197489,197502],{"className":197488,"translate":367},[366],[363,197490,197492],{"className":197491},[371],[373,197493,197494],{"xmlns":375},[377,197495,197496,197500],{},[380,197497,197498],{},[383,197499,15747],{},[387,197501,15747],{"encoding":389},[363,197503,197505],{"className":197504,"ariaHidden":394},[393],[363,197506,197508,197511],{"className":197507},[398],[363,197509],{"className":197510,"style":2692},[402],[363,197512,15747],{"className":197513},[407,408]," 丢弃了证据在类别间的分布信息（第 2 点）。其拟合损失带有与证据量级耦合的偏置，不等同于边缘似然（第 3 点）。并且「以损失最小化实现不确定性量化」这一范式本身受到根本性质疑（第 4 点）。这些限制并不取消该方法的实用价值——在单次前向的代价约束下同时给出预测与不确定性，其性价比是突出的——但它们决定了正确的使用姿态：",[1572,197516,197517],{},"在需要二阶量的场合使用它，在需要后验语义的场合验证它，并在两者都不确定时，回到对参数做边缘化的方法上去。",[11,197519,197520,197521,197524],{},"最后应当记住的是，不确定性量化的可靠程度，与因果推断一样，",[1572,197522,197523],{},"等于你愿意且能够承担的假设的强度","。迪利克雷分布给出的是一个精确而优美的数学结构。把一个精确的结构接到一个近似的映射（神经网络）上，得到的精确性只属于前者。识别出哪一部分是定理、哪一部分是启发式，是使用这套工具时最有价值的一步。",{"title":330,"searchDepth":331,"depth":331,"links":197526},[197527,197533,197541,197549,197556,197564],{"id":133806,"depth":331,"text":133807,"children":197528},[197529,197530,197531,197532],{"id":133810,"depth":132979,"text":133811},{"id":135986,"depth":132979,"text":135987},{"id":142211,"depth":132979,"text":142212},{"id":145320,"depth":132979,"text":145321},{"id":147462,"depth":331,"text":147463,"children":197534},[197535,197536,197537,197538,197539,197540],{"id":147466,"depth":132979,"text":147467},{"id":152191,"depth":132979,"text":152192},{"id":154430,"depth":132979,"text":154431},{"id":157377,"depth":132979,"text":157378},{"id":161505,"depth":132979,"text":161506},{"id":164179,"depth":132979,"text":164180},{"id":165953,"depth":331,"text":165954,"children":197542},[197543,197544,197545,197546,197547,197548],{"id":165957,"depth":132979,"text":165958},{"id":167602,"depth":132979,"text":167603},{"id":169769,"depth":132979,"text":169770},{"id":170976,"depth":132979,"text":170977},{"id":172872,"depth":132979,"text":172873},{"id":175577,"depth":132979,"text":175578},{"id":179983,"depth":331,"text":179984,"children":197550},[197551,197552,197553,197554,197555],{"id":180074,"depth":132979,"text":180075},{"id":183517,"depth":132979,"text":183518},{"id":185704,"depth":132979,"text":185705},{"id":189915,"depth":132979,"text":189916},{"id":190565,"depth":132979,"text":190566},{"id":192102,"depth":331,"text":192103,"children":197557},[197558,197559,197560,197561,197562,197563],{"id":192106,"depth":132979,"text":192107},{"id":193041,"depth":132979,"text":193042},{"id":194070,"depth":132979,"text":194071},{"id":194410,"depth":132979,"text":194411},{"id":194647,"depth":132979,"text":194648},{"id":195482,"depth":132979,"text":195483},{"id":197281,"depth":331,"text":197281},"设 X\\mathcal{X}X 为输入空间，y∈{1,…,K}y \\in \\{1, \\dots, K\\}y∈{1,…,K} 为类别标签。一个 KKK 分类器的输出在数学上究竟是什么？若要求它给出「属于各类别的概率」，则输出必须落在",{},"\u002Fblog\u002F2026\u002F0007-dirichlet-distribution-and-evidential-deep-learning",{"title":133048,"description":197565},"blog\u002F2026\u002F0007-dirichlet-distribution-and-evidential-deep-learning","Dirichlet 是单纯形上的分布、多项分布的共轭先验，也是「关于概率的概率」这一二阶对象的自然载体。本文先给出它在定义、矩结构、共轭更新与分裂构造上的完整形式化，神经网络的输出重解释为证据并参数化迪利克雷分布，推导证据深度学习的对数损失等应用。",[133042,197572],"machine-learning","2026-10-01T18:52:06+08:00","PklX79kbgmXizMsWGOJ3PcHWRm9JgKQrfILpGImulBA",1794483698432]