[{"data":1,"prerenderedAt":104134},["ShallowReactive",2],{"post-\u002Fblog\u002F2026\u002F0006-markdown-ke-xue-xie-zuo-tong-dian-wen-ti":3,"i-ci:tag":1765,"i-mingcute:time-line":1765,"i-boxicons:location":-1},{"post":4,"nextPost":1774,"prevPost":66715},{"id":5,"title":6,"body":7,"description":13,"draft":1760,"enableCodeHighlight":1761,"enableCodeHightlight":1760,"enableComment":1761,"enableD2":1761,"enableKatex":1761,"extension":1762,"image":123,"important":1760,"location":1763,"meta":1764,"navigation":1761,"ogImage":1765,"path":1766,"seo":1767,"stem":1768,"summary":1769,"tags":1770,"time":1772,"__hash__":1773},"blog\u002Fblog\u002F2026\u002F0006-markdown-ke-xue-xie-zuo-tong-dian-wen-ti.md","Markdown 并不适合科学写作",{"type":8,"value":9,"toc":1748},"minimark",[10,14,17,26,29,32,38,44,47,50,54,60,63,69,72,75,78,81,84,87,90,93,96,99,105,108,111,114,117,159,162,165,172,175,178,181,184,187,190,193,196,199,202,208,211,366,688,699,702,705,708,711,714,717,720,726,837,844,851,854,857,860,867,874,877,880,883,902,905,1020,1027,1030,1033,1143,1169,1175,1181,1190,1193,1199,1202,1209,1323,1430,1434,1437,1440,1451,1568,1571,1575,1578,1584,1587,1597,1600,1607,1610,1613,1616,1619,1622,1625,1632,1739,1744],[11,12,13],"p",{},"写博客了很长一段时间了，但是个人觉得，Markdown 并不适合科学写作。读研究生期间，搞搞科研，有时候会阶段性地总结一下自己的研究 idea，或者梳理自己的知识，就需要系统性地写作总结。这部分我经常写在自己的博客里，就比如之前所发表的博客内容。",[11,15,16],{},"我这个博客网站是基于 Markdown + Unified.js + Nuxt Content 工具链实现的，每篇博客源格式都是 markdown 写成，再编译成 HTML 发表在网页上。",[11,18,19,20,25],{},"但是，在写作过程中，我经常会有种非常别扭且痛苦的感觉。前几天写了一篇文章，",[21,22,24],"a",{"href":23},"\u002Fblog\u002F2026\u002F0005-yin-guo-jie-gou-mo-xing-jian-lun","因果结构模型简论","，这是一篇偏学术和展开论述的文章。",[11,27,28],{},"但是把它们写成 Markdown 博客，却花了我几乎两周的时间去校对和验证。最后精力不支，只能交给 LLM 后仓促发表。类似的，再撰写这类科学写作的文章，Markdown 让我深深感受到了这种文档的不足和局限。",[11,30,31],{},"写作对工具不挑剔，但工具的选择会悄悄影响你写作的组织方式。用记事本写，你倾向于纯线性；用 Notion 写，你可能会不自觉地建数据库、打标签；用 Markdown 写，你会习惯用标题层级来切分内容。",[11,33,34],{},[35,36,37],"strong",{},"一般来说，写作分为几种类型：日常写作、科学写作、技术写作。",[11,39,40,41],{},"三者虽然都叫「写作」，但是背后所使用的行文组织、写作思路等完全不同。",[35,42,43],{},"使用的认知模型完全不同。",[11,45,46],{},"它们对「段落」「证据」「结构」「读者」的预设都不一样。Markdown 的流行，很大程度上是因为它恰好适配了技术写作和一部分日常写作，但科学写作的核心需求它确实覆盖得很差。",[11,48,49],{},"Markdown 与其说「不适合写科学内容」，不如说它的抽象层级主要是「轻量文档标记」，而科学写作本质上更接近「结构化知识建模」。",[51,52,53],"h2",{"id":53},"日常写作",[11,55,56,59],{},[35,57,58],{},"首先是日常写作。"," 日常写作在互联网上随处可见，比如我们写的沟通、记录、表达。比如邮件、笔记、社交媒体、日记等等，它的核心是「交流感受、讲述经验、维持关系」。读者一般是自己或熟人，共享大量语境。",[11,61,62],{},"日常写作是「线性的」。比如：",[64,65,66],"blockquote",{},[11,67,68],{},"今天去了一趟实验室，发现服务器又挂了。折腾了半天，最后发现是 CUDA 环境的问题。",[11,70,71],{},"这样的好处，就是随意、口语化、结构松散，容错率高，歧义靠语境补全。",[11,73,74],{},"它的基本结构就是：想法 → 句子 → 段落 → 文章。",[11,76,77],{},"Markdown 对这种东西非常舒服。标题、粗体、列表、引用，已经足够了。而且这个链条是单向、可增量的。写一段是一段，不必先有全局骨架。这些已经覆盖了日常写作 90% 的标记需求。日常写作本来也不需要那么精确的视觉层级。",[11,79,80],{},"更重要的是，Markdown 的纯文本性让它在任何设备、任何编辑器里都能打开和修改。手机备忘录、VS Code、Obsidian、Notion、Typora，甚至 GitHub 的 issue 框，都能写。这种低门槛 + 跨平台，正好匹配日常写作「随时随地、随手就写」的场景。",[11,82,83],{},"它允许模糊、跳跃、情绪化，结构常常是情绪曲线或联想链条。博客、散文、社交媒体都属于这一类。Markdown 在这里够用，因为它只需要轻量地标记标题、列表、强调、链接。",[11,85,86],{},"作者不需要预先设计结构，想到哪写到哪。读者也不指望从中提取精确知识，能跟上情绪和大致信息就行。逻辑跳了、指代不清、重复啰嗦，都不致命，语境会补全。改一句话不影响全局，不需要回头调整编号、引文、交叉引用。",[11,88,89],{},"所以，对于日常写作，工具要求实际上并不高，任意文本编辑器、笔记软件如 MS Word，Evernote，Notion 都可以轻松应对，甚至手机自带的笔记本 App，Windows 文本编辑器都能应对。",[11,91,92],{},"日常写作还有一个特点：结构可以后补。你先随手写一堆碎片，之后再整理成「标题 + 段落 + 列表」，完全来得及。因为日常写作不依赖精确的交叉引用和编号，结构调整不会引发连锁修改。",[11,94,95],{},"所以，日常写作是三种写作里对工具最宽容、对结构最随意、对修改最不敏感的一类。Markdown 在这里如鱼得水，不是因为它多强大，而是因为日常写作本来就不需要多强大。",[51,97,98],{"id":98},"技术写作",[11,100,101,104],{},[35,102,103],{},"其次是技术写作。"," 技术写作的核心是「让读者完成操作或理解系统」。回答「怎么做」。比如 API 文档、用户手册，核心是让读者准确、高效地完成操作，追求可用性和任务完成率。",[11,106,107],{},"它追求可检索、可复用、可版本控制、可多端发布。文档、API 说明、教程、README 是典型。大多数开源项目的文档、技术博客等等，都属于这种类型。",[11,109,110],{},"技术写作是「操作性的」。技术文档的写作内容，更像是目标、环境、安装、配置、运行、错误处理、结果一连串起来。",[11,112,113],{},"文章的每个部分都是任务导向，模块化。比如，读者可跳读。且每个部分都可以在自己的内部领域展开——这就是典型的树形文章组织。",[11,115,116],{},"因此 Markdown 的标题树非常自然，以一个开源项目的 Github Readme 文档的组织结构为例：",[118,119,124],"pre",{"className":120,"code":121,"language":122,"meta":123,"style":123},"language-markdown shiki shiki-themes github-light github-light github-dark","# Installation\n## Requirements\n## Install\n# Usage\n# Troubleshooting\n","markdown","",[125,126,127,135,141,147,153],"code",{"__ignoreMap":123},[128,129,132],"span",{"class":130,"line":131},"line",1,[128,133,134],{},"# Installation\n",[128,136,138],{"class":130,"line":137},2,[128,139,140],{},"## Requirements\n",[128,142,144],{"class":130,"line":143},3,[128,145,146],{},"## Install\n",[128,148,150],{"class":130,"line":149},4,[128,151,152],{},"# Usage\n",[128,154,156],{"class":130,"line":155},5,[128,157,158],{},"# Troubleshooting\n",[11,160,161],{},"例如，如果读者已经 install 了这个软件，就可以直接跳过 installation 和 requirements 这两章节，直接跳转到 Usage 章节。",[11,163,164],{},"Markdown 的核心模型是树状文档——标题下挂段落和列表，段落和列表之下再无更深的语义结构。就像这样：",[11,166,167],{},[168,169],"img",{"alt":170,"src":171},"Markdown 层次写作模型","https:\u002F\u002Fimage-assets.dreams.plus\u002F202609222216870.png",[11,173,174],{},"Markdown 几乎是为这类写作量身定做的：纯文本、易 diff、易转 HTML、易嵌入代码块。技术写作的「正确性」往往由代码运行结果或操作是否成功来验证，不需要复杂的引注和排版。Markdown 的设计目标不是「表达知识结构」，而是「让纯文本容易读、容易写、容易转 HTML」。它的语法元素——标题、列表、强调、链接、代码块、引用——本质上都是视觉标记，不是语义对象。",[11,176,177],{},"所以 Markdown 甚至非常适合技术写作。例如 GitHub README、API 文档、开发文档，本质上就是让一个人沿着信息路径完成一个任务。",[51,179,180],{"id":180},"科学写作",[11,182,183],{},"但科学写作不是信息排列，而是在构造一个可以被检验的论证系统。核心是提出假设、展示证据、论证结论。",[11,185,186],{},"这一点在技术写作和科学写作里就完全不同了。技术写作的结构往往是预先设计的，科学写作的结构更是由论证逻辑和引用关系约束的。一旦结构变了，引文、图表编号、交叉引用都要跟着变。",[11,188,189],{},"以写一篇论文为例，真正的逻辑并不是「Introduction → Method → Experiment → Conclusion」这样的排版顺序，而更接近：先有一个现象，再追问为什么现有解释不足，进而提出新的问题表述，建立数学模型，推导出模型应当具有的可验证性质，设计方法去利用这个性质，用实验去验证这些性质是否真的存在，检验方法是否真正解决了问题，最后排除其他可能的解释。",[11,191,192],{},"这条链条可以进一步抽象为 Claim → Assumption → Model → Derivation → Prediction → Evidence → Conclusion，这已经不是普通意义上的「文档结构」，而更像一张证明图、因果图或知识图。",[11,194,195],{},"由此可以看到，科学写作其实存在两套结构。读者看到的是表层结构，也就是论文的 IMRaD 结构（引言 - 方法 - 结果 - 讨论），这一线性过程：Introduction、Related Work、Method、Experiments、Conclusion。",[11,197,198],{},"但真正决定论文质量的是深层结构——从 Research Question 出发得到 Claim，Claim 一边连接 Assumption，一边连接 Evidence，Assumption 导向 Model，Evidence 来自 Experiment 并与 Model 互相印证，Model 产生 Prediction，最终汇聚为 Conclusion。",[11,200,201],{},"一个好的论文段落内部也遵循类似的链条：Claim → Reason → Evidence → Interpretation → Connection to next claim。这种写作模型如下图所示",[11,203,204],{},[168,205],{"alt":206,"src":207},"科学写作的写作模型","https:\u002F\u002Fimage-assets.dreams.plus\u002F202609222126754.png",[11,209,210],{},"可以说，科学论文本质上非常接近一种有向图结构，这就产生了一个有意思的矛盾：Markdown 擅长表达「文档树」，而科学写作真正需要表达的是「论证图」。这条链条在认知科学和论证理论里也有对应。比如 Toulmin 的论证模型：Claim、Ground、Warrant、Backing、Qualifier、Rebuttal。",[11,212,213,214,365],{},"这也是为什么 ",[128,215,219,242],{"className":216,"translate":218},[217],"katex","no",[128,220,223],{"className":221},[222],"katex-mathml",[224,225,227],"math",{"xmlns":226},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[228,229,230,237],"semantics",{},[231,232,233],"mrow",{},[234,235,236],"mtext",{},"LaTeX",[238,239,241],"annotation",{"encoding":240},"application\u002Fx-tex","\\LaTeX",[128,243,247],{"className":244,"ariaHidden":246},[245],"katex-html","true",[128,248,251,256],{"className":249},[250],"base",[128,252],{"className":253,"style":255},[254],"strut","height:0.8988em;vertical-align:-0.2155em;",[128,257,261,266,271,303,307],{"className":258},[259,260],"mord","text",[128,262,265],{"className":263},[259,264],"textrm","L",[128,267],{"className":268,"style":270},[269],"mspace","margin-right:-0.36em;",[128,272,275],{"className":273},[274],"vlist-t",[128,276,279],{"className":277},[278],"vlist-r",[128,280,284],{"className":281,"style":283},[282],"vlist","height:0.6833em;",[128,285,287,292],{"style":286},"top:-2.905em;",[128,288],{"className":289,"style":291},[290],"pstrut","height:2.7em;",[128,293,295],{"className":294},[259],[128,296,302],{"className":297},[259,264,298,299,300,301],"mtight","sizing","reset-size6","size3","A",[128,304],{"className":305,"style":306},[269],"margin-right:-0.15em;",[128,308,310,314,318,357,361],{"className":309},[259,260],[128,311,313],{"className":312},[259,264],"T",[128,315],{"className":316,"style":317},[269],"margin-right:-0.1667em;",[128,319,322,348],{"className":320},[274,321],"vlist-t2",[128,323,325,343],{"className":324},[278],[128,326,329],{"className":327,"style":328},[282],"height:0.4678em;",[128,330,332,336],{"style":331},"top:-2.7845em;",[128,333],{"className":334,"style":335},[290],"height:3em;",[128,337,339],{"className":338},[259],[128,340,342],{"className":341},[259,264],"E",[128,344,347],{"className":345},[346],"vlist-s","​",[128,349,351],{"className":350},[278],[128,352,355],{"className":353,"style":354},[282],"height:0.2155em;",[128,356],{},[128,358],{"className":359,"style":360},[269],"margin-right:-0.125em;",[128,362,364],{"className":363},[259,264],"X"," 在科学写作中显得格外强大，且在 互联网时代 Markdown 盛行的情况下仍然未被淘汰的原因。",[11,367,368,471,472,475,476,579,580,683,684,687],{},[128,369,371,384],{"className":370,"translate":218},[217],[128,372,374],{"className":373},[222],[224,375,376],{"xmlns":226},[228,377,378,382],{},[231,379,380],{},[234,381,236],{},[238,383,241],{"encoding":240},[128,385,387],{"className":386,"ariaHidden":246},[245],[128,388,390,393],{"className":389},[250],[128,391],{"className":392,"style":255},[254],[128,394,396,399,402,422,425],{"className":395},[259,260],[128,397,265],{"className":398},[259,264],[128,400],{"className":401,"style":270},[269],[128,403,405],{"className":404},[274],[128,406,408],{"className":407},[278],[128,409,411],{"className":410,"style":283},[282],[128,412,413,416],{"style":286},[128,414],{"className":415,"style":291},[290],[128,417,419],{"className":418},[259],[128,420,302],{"className":421},[259,264,298,299,300,301],[128,423],{"className":424,"style":306},[269],[128,426,428,431,434,465,468],{"className":427},[259,260],[128,429,313],{"className":430},[259,264],[128,432],{"className":433,"style":317},[269],[128,435,437,457],{"className":436},[274,321],[128,438,440,454],{"className":439},[278],[128,441,443],{"className":442,"style":328},[282],[128,444,445,448],{"style":331},[128,446],{"className":447,"style":335},[290],[128,449,451],{"className":450},[259],[128,452,342],{"className":453},[259,264],[128,455,347],{"className":456},[346],[128,458,460],{"className":459},[278],[128,461,463],{"className":462,"style":354},[282],[128,464],{},[128,466],{"className":467,"style":360},[269],[128,469,364],{"className":470},[259,264]," 表面上看起来比 Markdown 古老得多，但它解决的其实不只是排版问题，它隐含的是 ",[35,473,474],{},"科学对象是一等公民"," 这样一种思想。",[128,477,479,492],{"className":478,"translate":218},[217],[128,480,482],{"className":481},[222],[224,483,484],{"xmlns":226},[228,485,486,490],{},[231,487,488],{},[234,489,236],{},[238,491,241],{"encoding":240},[128,493,495],{"className":494,"ariaHidden":246},[245],[128,496,498,501],{"className":497},[250],[128,499],{"className":500,"style":255},[254],[128,502,504,507,510,530,533],{"className":503},[259,260],[128,505,265],{"className":506},[259,264],[128,508],{"className":509,"style":270},[269],[128,511,513],{"className":512},[274],[128,514,516],{"className":515},[278],[128,517,519],{"className":518,"style":283},[282],[128,520,521,524],{"style":286},[128,522],{"className":523,"style":291},[290],[128,525,527],{"className":526},[259],[128,528,302],{"className":529},[259,264,298,299,300,301],[128,531],{"className":532,"style":306},[269],[128,534,536,539,542,573,576],{"className":535},[259,260],[128,537,313],{"className":538},[259,264],[128,540],{"className":541,"style":317},[269],[128,543,545,565],{"className":544},[274,321],[128,546,548,562],{"className":547},[278],[128,549,551],{"className":550,"style":328},[282],[128,552,553,556],{"style":331},[128,554],{"className":555,"style":335},[290],[128,557,559],{"className":558},[259],[128,560,342],{"className":561},[259,264],[128,563,347],{"className":564},[346],[128,566,568],{"className":567},[278],[128,569,571],{"className":570,"style":354},[282],[128,572],{},[128,574],{"className":575,"style":360},[269],[128,577,364],{"className":578},[259,264]," 内置的 equation、theorem、lemma、proof、definition、figure、table、citation、cross-reference、appendix 等等组件，这些东西在 ",[128,581,583,596],{"className":582,"translate":218},[217],[128,584,586],{"className":585},[222],[224,587,588],{"xmlns":226},[228,589,590,594],{},[231,591,592],{},[234,593,236],{},[238,595,241],{"encoding":240},[128,597,599],{"className":598,"ariaHidden":246},[245],[128,600,602,605],{"className":601},[250],[128,603],{"className":604,"style":255},[254],[128,606,608,611,614,634,637],{"className":607},[259,260],[128,609,265],{"className":610},[259,264],[128,612],{"className":613,"style":270},[269],[128,615,617],{"className":616},[274],[128,618,620],{"className":619},[278],[128,621,623],{"className":622,"style":283},[282],[128,624,625,628],{"style":286},[128,626],{"className":627,"style":291},[290],[128,629,631],{"className":630},[259],[128,632,302],{"className":633},[259,264,298,299,300,301],[128,635],{"className":636,"style":306},[269],[128,638,640,643,646,677,680],{"className":639},[259,260],[128,641,313],{"className":642},[259,264],[128,644],{"className":645,"style":317},[269],[128,647,649,669],{"className":648},[274,321],[128,650,652,666],{"className":651},[278],[128,653,655],{"className":654,"style":328},[282],[128,656,657,660],{"style":331},[128,658],{"className":659,"style":335},[290],[128,661,663],{"className":662},[259],[128,664,342],{"className":665},[259,264],[128,667,347],{"className":668},[346],[128,670,672],{"className":671},[278],[128,673,675],{"className":674,"style":354},[282],[128,676],{},[128,678],{"className":679,"style":360},[269],[128,681,364],{"className":682},[259,264]," 里不是普通文本，而是具有实际意义的科学对象（Object）。在科学写作中，讲论证图组织起来的方式，就是 ",[125,685,686],{},"\\ref"," 各个科学对象。",[11,689,690,691,694,695,698],{},"写一个公式并加上 ",[125,692,693],{},"\\label{eq:loss}","，再用 ",[125,696,697],{},"\\ref{eq:loss}"," 去引用它，本质上不是在说「这里有一段数学」，而是在声明这是一个具有编号、引用关系和语义身份的 Equation。此外，在科学写作中，定理环境（theorem）也是很重要的，有时候我会在展开论述的时候，给出一些定义、推论、引理等等。在其他文章部分，会经常 refer 到这些。这样一来，文中就建立起了知识对象之间的引用关系，这已经比 Markdown 里单纯加粗一个 Loss function 高了一个抽象层次。",[11,700,701],{},"而仅 Markdown 则完全做不到这些。在进行科学写作的时候，只能手动去标注哪些是「定理」，用到了哪些部分，然后再手动写出引用位置，实在无法做到随心所欲去 refer 每一个对象。这些对象和关系，在 LaTeX 编译时会被自动编号、自动解析、自动维护。你增删一个公式，所有引用它的地方都会自动更新。这就是「图结构」在工具层面的体现。Markdown 没有这些语义对象。你只能手动写「如公式 (3) 所示」，然后手动维护编号。一旦增删，就是灾难。",[11,703,704],{},"更麻烦的是，科学写作并不是一日之功，很多时候要经过好几天甚至数月时间才能写成文章，在此期间，校对、增删文章时都会重构整个对象引用关系，如果论述过程简单还尚可，对系统性长文，手动维护各个对象之间的关系，简直是灾难级别的事故。",[11,706,707],{},"我个人也尝试去寻找相关工具链，很遗憾，我没有找到任何能适用于科学写作处理的 Markdown 文档工具链。",[11,709,710],{},"虽然社区有一些尝试，比如 Pandoc 的 Markdown 扩展、Quarto、MyST、Jupyter Book，它们确实支持公式、引用、交叉引用。但它们的抽象层级仍然是「文档 + 一些科学标记」，而不是「科学知识图」。它们能让你在 Markdown 里写公式和引用，但无法让你像 LaTeX 那样自然地声明和引用定理、引理、证明、假设、证据。",[11,712,713],{},"更重要的是，它们没有解决上面提到的核心问题：科学写作的深层结构是图，而不是树。工具如果只提供树形结构，写作者就只能手动在脑子里维护图，然后把它压扁成树。这个「压扁」过程，就是让我觉得别扭和痛苦的根源。",[51,715,716],{"id":716},"压扁的代价",[11,718,719],{},"上面说的「压扁」不是一个比喻，它是一件有具体成本的事。",[11,721,722,723],{},"写作并不是「先在脑子里想好一张完整的图，再把它抄成文字」。真实的过程往往相反：图和文本互相塑造。你在写第三段的时候，才想清楚第一段那个 Claim 到底需要什么假设；你在写实验的时候，才发现原来的模型少了一个条件。",[35,724,725],{},"图是在写作过程中长出来的，而 Markdown 要求你在图还没有定形的时候，就把它线性地固定下来。",[11,727,728,729,832,833,836],{},"举一个具体的例子。假设我在写一篇关于因果推断的文章，第三节给出了「后门准则」的定义，第五节有一个命题依赖这个定义，第七节的分析又依赖那个命题。现在我想在第三节中间再插入一个识别性假设。在 ",[128,730,732,745],{"className":731,"translate":218},[217],[128,733,735],{"className":734},[222],[224,736,737],{"xmlns":226},[228,738,739,743],{},[231,740,741],{},[234,742,236],{},[238,744,241],{"encoding":240},[128,746,748],{"className":747,"ariaHidden":246},[245],[128,749,751,754],{"className":750},[250],[128,752],{"className":753,"style":255},[254],[128,755,757,760,763,783,786],{"className":756},[259,260],[128,758,265],{"className":759},[259,264],[128,761],{"className":762,"style":270},[269],[128,764,766],{"className":765},[274],[128,767,769],{"className":768},[278],[128,770,772],{"className":771,"style":283},[282],[128,773,774,777],{"style":286},[128,775],{"className":776,"style":291},[290],[128,778,780],{"className":779},[259],[128,781,302],{"className":782},[259,264,298,299,300,301],[128,784],{"className":785,"style":306},[269],[128,787,789,792,795,826,829],{"className":788},[259,260],[128,790,313],{"className":791},[259,264],[128,793],{"className":794,"style":317},[269],[128,796,798,818],{"className":797},[274,321],[128,799,801,815],{"className":800},[278],[128,802,804],{"className":803,"style":328},[282],[128,805,806,809],{"style":331},[128,807],{"className":808,"style":335},[290],[128,810,812],{"className":811},[259],[128,813,342],{"className":814},[259,264],[128,816,347],{"className":817},[346],[128,819,821],{"className":820},[278],[128,822,824],{"className":823,"style":354},[282],[128,825],{},[128,827],{"className":828,"style":360},[269],[128,830,364],{"className":831},[259,264]," 里这是一个局部操作：加一个 ",[125,834,835],{},"\\label","，被影响的地方编译时会提醒我。在 Markdown 里这是一次全局手术：我得记住哪些地方引用了「上面那个定义」，哪些公式的编号要变，哪些「如公式 (3) 所示」要改成 (4)。而 Markdown 不会告诉我它们在哪里。",[11,838,839,840,843],{},"不过编号错乱其实还不是最贵的部分，因为编辑器至少能搜到。真正贵的是",[35,841,842],{},"关系的丢失","。在 Markdown 里，「这一段是为了支持那个 Claim」这个事实不存在于文件里，它只存在于我的脑子里。今天写的时候当然记得，三个月后回来改的时候就不记得了。",[11,845,846,847,850],{},"这带来一个更隐蔽的后果：",[35,848,849],{},"别人无法验证我的论证","。合作者和审稿人拿到的是一段线性文本，他们只能重新读一遍全文，然后在自己脑子里把这张图重建出来，再检查它成不成立。每个人都要重建一遍。引用是显式的，论证是隐式的。",[11,852,853],{},"所以那种「别扭」的感觉可以更精确地描述：写作时，我的大脑同时在维护两个表征——一张还在变的论证图，和一条正在往前走的文本流——并且要保证它们在每一步都一致。Markdown 为前者提供的支撑是零。它不是不好用，是它根本没打算管这件事。",[51,855,856],{"id":856},"读者也在走这张图",[11,858,859],{},"线性化的成本不只由写作者承担，读者也在付。",[11,861,862,863,866],{},"读一篇论文的真实动作从来不是从头读到尾。读到中间的 Claim，我要翻回前面看那个定义到底是什么；看到「实验表明」，我要跳到结果章节确认；想知道这个结论有多强，我要去附录看证明的边界条件。",[35,864,865],{},"阅读本身就是在图上做遍历","，而且是带随机跳转的遍历。",[11,868,869,870,873],{},"IMRaD 与其说是一种逻辑结构，不如说是",[35,871,872],{},"一种为印刷媒介做的妥协","。纸是顺序的，装订是顺序的，翻页是顺序的，所以我们把一张图压成一条线，然后指望读者自己再把它拆开、重新组装。",[11,875,876],{},"这里有一个有点讽刺的地方：网页其实是天然支持非线性阅读的。折叠、跳转、悬浮预览、双向链接，技术上全都存在。但我们依然在用线性的写作工具，生产线性的制品，再把它放到一个非线性的媒介上。最后得到的，是一篇被伪装成网页的 PDF。",[11,878,879],{},"所以「压扁」这件事，写的人付一次，读的人付一次，每个合作者再各付一次。它是一个被反复征收的成本。",[11,881,882],{},"有人会说，图结构的写作工具不是早就有了吗？Obsidian、Logseq、Roam Research 的双向链接，不就是图吗？",[11,884,885,886,889,890,893,894,897,898,901],{},"是图，但粒度不对。这些工具的节点是",[35,887,888],{},"笔记","，不是",[35,891,892],{},"命题","。",[125,895,896],{},"[[因果推断]]"," 这样一条链接只说了「这两篇相关」，没有说「这篇支持那篇」还是「这篇反驳那篇」。而当边没有类型的时候，一张论证图就退化成了一个共现网络。图上只剩下相关性，可科学写作里最要紧的东西恰恰是",[35,899,900],{},"边的类型","：支持、反驳、假设、推导、检验。",[11,903,904],{},"Zettelkasten 也是同样的情况。它的原意是让想法自由连接、自然涌现，服务于「我该想什么」，而不是「我这个论证成不成立」。卡片之间可以链接，但链接不带论证语义。",[11,906,907,908,911,912,1019],{},"另一个方向是 Pandoc、Quarto、MyST、Jupyter Book 这一类。它们的贡献是实打实的：让你能在 Markdown 里写公式、写 ",[125,909,910],{},"@fig:xxx"," 这样的交叉引用。但它们做的是",[35,913,914,915,1018],{},"把 ",[128,916,918,931],{"className":917,"translate":218},[217],[128,919,921],{"className":920},[222],[224,922,923],{"xmlns":226},[228,924,925,929],{},[231,926,927],{},[234,928,236],{},[238,930,241],{"encoding":240},[128,932,934],{"className":933,"ariaHidden":246},[245],[128,935,937,940],{"className":936},[250],[128,938],{"className":939,"style":255},[254],[128,941,943,946,949,969,972],{"className":942},[259,260],[128,944,265],{"className":945},[259,264],[128,947],{"className":948,"style":270},[269],[128,950,952],{"className":951},[274],[128,953,955],{"className":954},[278],[128,956,958],{"className":957,"style":283},[282],[128,959,960,963],{"style":286},[128,961],{"className":962,"style":291},[290],[128,964,966],{"className":965},[259],[128,967,302],{"className":968},[259,264,298,299,300,301],[128,970],{"className":971,"style":306},[269],[128,973,975,978,981,1012,1015],{"className":974},[259,260],[128,976,313],{"className":977},[259,264],[128,979],{"className":980,"style":317},[269],[128,982,984,1004],{"className":983},[274,321],[128,985,987,1001],{"className":986},[278],[128,988,990],{"className":989,"style":328},[282],[128,991,992,995],{"style":331},[128,993],{"className":994,"style":335},[290],[128,996,998],{"className":997},[259],[128,999,342],{"className":1000},[259,264],[128,1002,347],{"className":1003},[346],[128,1005,1007],{"className":1006},[278],[128,1008,1010],{"className":1009,"style":354},[282],[128,1011],{},[128,1013],{"className":1014,"style":360},[269],[128,1016,364],{"className":1017},[259,264]," 的对象搬进 Markdown 的语法","，并没有动 Markdown 的骨架。文档的骨架依然是一个标题树，对象只是挂在树上的装饰。至于「这个公式是从哪个假设推出来的」这类关系，它们依然没有地方可以放。",[11,1021,1022,1023,1026],{},"两个方向的工具缺的是同一样东西：",[35,1024,1025],{},"它们都没有把「对象」和「关系」变成编辑器里可以直接操作的对象，也没有让文本变成这张图的一个投影。"," 一个是把边的类型丢了，一个是把对象降格成了树的装饰。而科学写作要求这两件事同时成立。",[51,1028,1029],{"id":1029},"科学写作需要什么",[11,1031,1032],{},"如果要认真地解决这件事，工具大概需要具备以下几个性质。这是一张草图，不是一份产品方案。",[11,1034,1035,1038,1039,1142],{},[35,1036,1037],{},"第一，科学对象是一等公民。"," 这一点其实 ",[128,1040,1042,1055],{"className":1041,"translate":218},[217],[128,1043,1045],{"className":1044},[222],[224,1046,1047],{"xmlns":226},[228,1048,1049,1053],{},[231,1050,1051],{},[234,1052,236],{},[238,1054,241],{"encoding":240},[128,1056,1058],{"className":1057,"ariaHidden":246},[245],[128,1059,1061,1064],{"className":1060},[250],[128,1062],{"className":1063,"style":255},[254],[128,1065,1067,1070,1073,1093,1096],{"className":1066},[259,260],[128,1068,265],{"className":1069},[259,264],[128,1071],{"className":1072,"style":270},[269],[128,1074,1076],{"className":1075},[274],[128,1077,1079],{"className":1078},[278],[128,1080,1082],{"className":1081,"style":283},[282],[128,1083,1084,1087],{"style":286},[128,1085],{"className":1086,"style":291},[290],[128,1088,1090],{"className":1089},[259],[128,1091,302],{"className":1092},[259,264,298,299,300,301],[128,1094],{"className":1095,"style":306},[269],[128,1097,1099,1102,1105,1136,1139],{"className":1098},[259,260],[128,1100,313],{"className":1101},[259,264],[128,1103],{"className":1104,"style":317},[269],[128,1106,1108,1128],{"className":1107},[274,321],[128,1109,1111,1125],{"className":1110},[278],[128,1112,1114],{"className":1113,"style":328},[282],[128,1115,1116,1119],{"style":331},[128,1117],{"className":1118,"style":335},[290],[128,1120,1122],{"className":1121},[259],[128,1123,342],{"className":1124},[259,264],[128,1126,347],{"className":1127},[346],[128,1129,1131],{"className":1130},[278],[128,1132,1134],{"className":1133,"style":354},[282],[128,1135],{},[128,1137],{"className":1138,"style":360},[269],[128,1140,364],{"className":1141},[259,264]," 已经做到了，但是其他的写作工具仍然做得不彻底。一个 Definition、一个 Assumption、一个 Claim、一条 Evidence、一个 Prediction，应该是编辑器里真实存在的对象：有稳定 ID，有类型，有内容，而不是一段被加粗的文字。类型本身携带信息——修改一个 Assumption 和修改一个 Definition，后果完全不同。",[11,1144,1145,1148,1149,1152,1153,1152,1156,1152,1159,1152,1162,1152,1165,1168],{},[35,1146,1147],{},"第二，边是有类型的。"," ",[125,1150,1151],{},"supports","、",[125,1154,1155],{},"contradicts",[125,1157,1158],{},"assumes",[125,1160,1161],{},"derives",[125,1163,1164],{},"tests",[125,1166,1167],{},"qualifies","。这是全文最核心的一条。只有节点类型和边的类型同时存在，才配叫论证图；只有节点，那是笔记库；只有无类型的边，那是共现网络。",[11,1170,1171,1174],{},[35,1172,1173],{},"第三，文本是图的一个投影。"," 意思是：论文不是唯一制品，而是某一张图在某一个视图下的渲染结果。同一张图应该能渲染成论文、组会 slides、审稿回复、以及一篇博客。现在的情况是反过来的——文字是本体的全部，图和 slides 都是它的下脚料。",[11,1176,1177,1180],{},[35,1178,1179],{},"第四，视图要可切换。"," 写作时用线性视图，检查覆盖面用大纲视图，审自己的逻辑用图视图。这三个视图必须操作同一份数据，否则又会退回到「手动同步」的老问题里。",[11,1182,1183,1186,1187,1189],{},[35,1184,1185],{},"第五，一致性检查应该上升到语义层。"," 编译器检查 ",[125,1188,686],{}," 指向的 label 是否存在，这是最浅的一层。再往上一层，工具应该能问：这个 Claim 有 Evidence 支撑吗？它的 Assumption 声明了吗？现有的 Evidence 支撑的是不是只是这个 Claim 的弱化版本？结论有没有超出实验能支持的范围？这些问题，本质上就是读者读论文时会问的那几个问题——工具应该先替他们问一遍。",[51,1191,1192],{"id":1192},"为什么这件事一直没做成",[11,1194,1195,1196,893],{},"既然需求这么明确，为什么没有这样的工具？因为",[35,1197,1198],{},"读一张图很便宜，写一张图很贵",[11,1200,1201],{},"一个理想的知识编辑系统，要求作者在想法还没成形的时候就声明「这个支持那个」「这个是从那个推出来的」。但正如前面说的，图是在写作过程中长出来的。要求作者提前声明关系，等于要求他在思考完成之前就交出思考的结论。这个交互本身就是反人性的。",[11,1203,1204,1205,1208],{},"这不是新问题。Bush 在上世纪四十年代设想的 Memex，Nelson 在六十年代提出的 Xanadu，都是「让人在非线性的知识网络里写作」的方案。它们没有普及，原因通常被归为工程难度和商业失败，但我更倾向于另一个解释：",[35,1206,1207],{},"人的思维展开是序列式的，图是事后归纳出来的。"," 我们不是先有图再写文章，而是先写文章才发现图长什么样。任何强迫作者「先建图再写作」的工具，都会在第一步被放弃。",[11,1210,1211,1212,1315,1316,1318,1319,1322],{},"这反过来解释了一件我一直觉得有意思的事：",[128,1213,1215,1228],{"className":1214,"translate":218},[217],[128,1216,1218],{"className":1217},[222],[224,1219,1220],{"xmlns":226},[228,1221,1222,1226],{},[231,1223,1224],{},[234,1225,236],{},[238,1227,241],{"encoding":240},[128,1229,1231],{"className":1230,"ariaHidden":246},[245],[128,1232,1234,1237],{"className":1233},[250],[128,1235],{"className":1236,"style":255},[254],[128,1238,1240,1243,1246,1266,1269],{"className":1239},[259,260],[128,1241,265],{"className":1242},[259,264],[128,1244],{"className":1245,"style":270},[269],[128,1247,1249],{"className":1248},[274],[128,1250,1252],{"className":1251},[278],[128,1253,1255],{"className":1254,"style":283},[282],[128,1256,1257,1260],{"style":286},[128,1258],{"className":1259,"style":291},[290],[128,1261,1263],{"className":1262},[259],[128,1264,302],{"className":1265},[259,264,298,299,300,301],[128,1267],{"className":1268,"style":306},[269],[128,1270,1272,1275,1278,1309,1312],{"className":1271},[259,260],[128,1273,313],{"className":1274},[259,264],[128,1276],{"className":1277,"style":317},[269],[128,1279,1281,1301],{"className":1280},[274,321],[128,1282,1284,1298],{"className":1283},[278],[128,1285,1287],{"className":1286,"style":328},[282],[128,1288,1289,1292],{"style":331},[128,1290],{"className":1291,"style":335},[290],[128,1293,1295],{"className":1294},[259],[128,1296,342],{"className":1297},[259,264],[128,1299,347],{"className":1300},[346],[128,1302,1304],{"className":1303},[278],[128,1305,1307],{"className":1306,"style":354},[282],[128,1308],{},[128,1310],{"className":1311,"style":360},[269],[128,1313,364],{"className":1314},[259,264]," 为什么活到了今天。它并不要求你放弃线性写作，它只要求你在必要的地方声明对象。你可以照常从头写到尾，只在需要的时候加一个 ",[125,1317,835],{},"。它是一个",[35,1320,1321],{},"树骨架 + 少量图边","的混合体。这个折中在工程上极其成功——它把「线性写作」和「图结构」之间的冲突压到了大多数人都能接受的水平。",[11,1324,1325,1326,1429],{},"所以 ",[128,1327,1329,1342],{"className":1328,"translate":218},[217],[128,1330,1332],{"className":1331},[222],[224,1333,1334],{"xmlns":226},[228,1335,1336,1340],{},[231,1337,1338],{},[234,1339,236],{},[238,1341,241],{"encoding":240},[128,1343,1345],{"className":1344,"ariaHidden":246},[245],[128,1346,1348,1351],{"className":1347},[250],[128,1349],{"className":1350,"style":255},[254],[128,1352,1354,1357,1360,1380,1383],{"className":1353},[259,260],[128,1355,265],{"className":1356},[259,264],[128,1358],{"className":1359,"style":270},[269],[128,1361,1363],{"className":1362},[274],[128,1364,1366],{"className":1365},[278],[128,1367,1369],{"className":1368,"style":283},[282],[128,1370,1371,1374],{"style":286},[128,1372],{"className":1373,"style":291},[290],[128,1375,1377],{"className":1376},[259],[128,1378,302],{"className":1379},[259,264,298,299,300,301],[128,1381],{"className":1382,"style":306},[269],[128,1384,1386,1389,1392,1423,1426],{"className":1385},[259,260],[128,1387,313],{"className":1388},[259,264],[128,1390],{"className":1391,"style":317},[269],[128,1393,1395,1415],{"className":1394},[274,321],[128,1396,1398,1412],{"className":1397},[278],[128,1399,1401],{"className":1400,"style":328},[282],[128,1402,1403,1406],{"style":331},[128,1404],{"className":1405,"style":335},[290],[128,1407,1409],{"className":1408},[259],[128,1410,342],{"className":1411},[259,264],[128,1413,347],{"className":1414},[346],[128,1416,1418],{"className":1417},[278],[128,1419,1421],{"className":1420,"style":354},[282],[128,1422],{},[128,1424],{"className":1425,"style":360},[269],[128,1427,364],{"className":1428},[259,264]," 的地位并不只是历史惯性。它在科学写作里没有被淘汰，是因为它是目前唯一一个既把对象和引用做成了语言原语、又不强迫作者放弃线性写作的系统。它的不足也在这里：图边只有引用这一种类型，而且维护成本随文章长度急剧上升——这正是文章开头我花两周校对的原因。",[51,1431,1433],{"id":1432},"在工具出现之前我现在怎么工作","在工具出现之前，我现在怎么工作",[11,1435,1436],{},"没有现成工具，只能用流程凑。我目前的办法是把「图」和「文」分成两层，中间只做一次机械转换。",[11,1438,1439],{},"草图层不管顺序，只管对象和关系。给每个对象一个短 ID：",[1441,1442,1443],"div",{},[168,1444],{"height":1445,"width":1446,"style":1447,"data-d2-theme":1448,"alt":1449,"src":1450},679,1255,"max-width:100%;height:auto","default","以《因果结构模型文章》为例，论证的依赖关系图","data:image\u002Fsvg+xml;base64,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\u002Fmm7\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",[11,1452,1453,1454,1557,1558,1560,1561,1563,1564,1567],{},"然后在成文层，把这些 ID 落成 ",[128,1455,1457,1470],{"className":1456,"translate":218},[217],[128,1458,1460],{"className":1459},[222],[224,1461,1462],{"xmlns":226},[228,1463,1464,1468],{},[231,1465,1466],{},[234,1467,236],{},[238,1469,241],{"encoding":240},[128,1471,1473],{"className":1472,"ariaHidden":246},[245],[128,1474,1476,1479],{"className":1475},[250],[128,1477],{"className":1478,"style":255},[254],[128,1480,1482,1485,1488,1508,1511],{"className":1481},[259,260],[128,1483,265],{"className":1484},[259,264],[128,1486],{"className":1487,"style":270},[269],[128,1489,1491],{"className":1490},[274],[128,1492,1494],{"className":1493},[278],[128,1495,1497],{"className":1496,"style":283},[282],[128,1498,1499,1502],{"style":286},[128,1500],{"className":1501,"style":291},[290],[128,1503,1505],{"className":1504},[259],[128,1506,302],{"className":1507},[259,264,298,299,300,301],[128,1509],{"className":1510,"style":306},[269],[128,1512,1514,1517,1520,1551,1554],{"className":1513},[259,260],[128,1515,313],{"className":1516},[259,264],[128,1518],{"className":1519,"style":317},[269],[128,1521,1523,1543],{"className":1522},[274,321],[128,1524,1526,1540],{"className":1525},[278],[128,1527,1529],{"className":1528,"style":328},[282],[128,1530,1531,1534],{"style":331},[128,1532],{"className":1533,"style":335},[290],[128,1535,1537],{"className":1536},[259],[128,1538,342],{"className":1539},[259,264],[128,1541,347],{"className":1542},[346],[128,1544,1546],{"className":1545},[278],[128,1547,1549],{"className":1548,"style":354},[282],[128,1550],{},[128,1552],{"className":1553,"style":360},[269],[128,1555,364],{"className":1556},[259,264]," 的 ",[125,1559,835],{}," 和 ",[125,1562,686],{},"。这样做的好处是：",[35,1565,1566],{},"压扁只发生在最后一步，而且是可逆的","——草图层始终在，任何时候都能回到图上检查。改动时先动草图层，再重新生成文本层的引用，而不是反过来。",[11,1569,1570],{},"诚实地说，这只是把痛苦从脑子里挪到了纸上，并没有消除手动维护。但它至少让「图」变成了一个可以被检查的实体，而不是一个只存在于我记忆里的东西。而且它带来一个意外的收益：这些 ID 本身，恰好可以当作和 LLM 交流的接口。",[51,1572,1574],{"id":1573},"当-llm-进入这张图","当 LLM 进入这张图",[11,1576,1577],{},"回到文章开头那个略显狼狈的结尾：那篇文章我写了两周，最后精力不支，交给了 LLM 仓促发表。",[11,1579,1580,1581],{},"当时我把它当成一次失败。但现在回头看，它其实指出了一个更重要的变化：",[35,1582,1583],{},"LLM 是历史上第一个有可能承担「图维护」这件事的东西。",[11,1585,1586],{},"前面说「写图很贵」，贵在哪里？贵在三件事：声明关系、保持一致、以及结构变动后重新检查下游。这三件事恰好都是 LLM 擅长的。它能读完一段文本后抽出隐含的 Claim 和 Evidence，能在插入新假设之后重新检查所有依赖它的结论，能在你改动一个定义时把下游的引用全部找出来。",[11,1588,1589,1590,1593,1594,893],{},"但这里有一个前提，而且是致命的前提：",[35,1591,1592],{},"LLM 在显式的图上工作，远好于在隐式的图上工作。"," 如果关系从来不曾落在文件里，LLM 也只能像我一样去猜，而且会猜得同样不可靠。所以「把图显式化」这件事的性质变了——它不再纯粹是作者的额外负担，而是让机器能够介入的前提。也许真正可行的分工不是「作者建图、作者维护图」，而是",[35,1595,1596],{},"作者建图、机器维护图",[11,1598,1599],{},"不过有一个反向的危险，值得单独说。LLM 天然擅长生成流畅的线性文本，它会不由自主地把你论证里的裂缝糊上。一段话读起来通顺，和这个论证成不成立，是两件完全不同的事，而 LLM 恰好最擅长制造前者。我用 LLM 校对那篇两周的文章时就吃过这个亏：它把很多衔接不畅的地方改顺了，但那些地方原本的不畅，其实是论证真的没接上。",[11,1601,1602,1603,1606],{},"所以 LLM 在这件事上的正确用法，是当图的审查者，而不是文本的润色者。",[35,1604,1605],{},"让它问我「这个 Claim 的证据在哪里」，而不是问它「这段话怎么写得更好」。"," 前者会暴露问题，后者只会掩盖问题。",[51,1608,1609],{"id":1609},"结语",[11,1611,1612],{},"如果把三种写作对应到三种数据结构，会看得更清楚：日常写作对应的是序列（Sequence），句子接句子，核心是语言流。技术写作对应的是树（Tree），文档下分节，节下分概念与流程，核心是信息层级，Markdown 对此非常合适。",[11,1614,1615],{},"而科学写作对应的则是图（Graph），一个 Claim 由 Evidence 支持、由 Assumption 建立基础、由 Model 推导而来、由 Experiment 加以检验，核心是命题之间的逻辑关系。到了这一层，Markdown 就开始显得太扁平了。",[11,1617,1618],{},"无论是读者还是写作者，实际上一直在追问：这个 Claim 从哪里来的？这个 Assumption 合理吗？这个公式是否真的从前面的定义推出？这个实验是否真的能够验证这个 Claim？这个结果还有没有其他解释？结论有没有超出实验能够支持的范围？所以科学写作，本质上是在维护一张 Claim、Evidence、Reasoning 三者互相印证的关系网络。",[11,1620,1621],{},"这也解释了为什么科学写作写久之后，我会逐渐不满足于 Markdown。",[11,1623,1624],{},"不是因为它不够漂亮，因为真正需要的已经不再是一个好用的文本编辑器，而是一个能够表达定义、命题、假设、推导、证据、引用和论证关系的科学知识编辑系统。",[11,1626,1627,1628,1631],{},"这三种数据结构也解释了前面所有具体的痛苦。序列容错，所以日常写作拿记事本就能对付；树可以局部修改，所以技术文档在 Markdown 里如鱼得水；而",[35,1629,1630],{},"图一旦被压成线，每一次改动都要付出全局的代价","——那两周的校对时间，大部分就是花在这里的。",[11,1633,1634,1635,1738],{},"所以在那个系统出现之前，我大概还会继续用 Markdown 写博客、用 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写论文，并且在两者之间手动维护一张只有我自己看得见的图。这篇文章本身也是用 Markdown 写的——这大概是它最后一个恰当的讽刺。",[64,1740,1741],{},[11,1742,1743],{},"Markdown 的问题不是它表达不了科学内容，而是它把科学内容中最重要的那部分——对象之间的论证关系——降格成了文本。",[1745,1746,1747],"style",{},"html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: 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与其说「不适合写科学内容」，不如说它的抽象层级主要是「轻量文档标记」，而科学写作本质上更接近「结构化知识建模」。",[1771],"thoughts","2026-09-22T22:53:33+08:00","bdCBbBDqfmLRWSRlu3duJ1udbcTOKHpeg3xAyvxH5EM",{"id":1775,"title":1776,"body":1777,"description":66704,"draft":1760,"enableCodeHighlight":1760,"enableCodeHightlight":1760,"enableComment":1761,"enableD2":1760,"enableKatex":1761,"extension":1762,"image":123,"important":1760,"location":1765,"meta":66705,"navigation":1761,"ogImage":1765,"path":66706,"seo":66707,"stem":66708,"summary":66709,"tags":66710,"time":66713,"__hash__":66714},"blog\u002Fblog\u002F2026\u002F0007-dirichlet-distribution-and-evidential-deep-learning.md","Dirichlet 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\\right\\}",[128,2069,2071,2128],{"className":2070,"ariaHidden":246},[245],[128,2072,2074,2078,2119,2122,2125],{"className":2073},[250],[128,2075],{"className":2076,"style":2077},[254],"height:0.8913em;",[128,2079,2081,2084],{"className":2080},[259],[128,2082,1982],{"className":2083},[259],[128,2085,2088],{"className":2086},[2087],"msupsub",[128,2089,2091],{"className":2090},[274],[128,2092,2094],{"className":2093},[278],[128,2095,2097],{"className":2096,"style":2077},[282],[128,2098,2100,2103],{"style":2099},"top:-3.113em;margin-right:0.05em;",[128,2101],{"className":2102,"style":291},[290],[128,2104,2106],{"className":2105},[299,300,301,298],[128,2107,2109,2112,2116],{"className":2108},[259,298],[128,2110,1853],{"className":2111,"style":1924},[259,1873,298],[128,2113,1989],{"className":2114},[2115,298],"mbin",[128,2117,1842],{"className":2118},[259,298],[128,2120],{"className":2121,"style":1878},[269],[128,2123,1994],{"className":2124},[1882],[128,2126],{"className":2127,"style":1878},[269],[128,2129,2131,2135],{"className":2130},[250],[128,2132],{"className":2133,"style":2134},[254],"height:1.8em;vertical-align:-0.65em;",[128,2136,2138,2148,2152,2155,2158,2161,2191,2194,2197,2200,2244,2247,2250,2253,2256,2259,2262,2265,2333,2336,2376,2379,2382,2385,2388],{"className":2137},[1911],[128,2139,2143],{"className":2140,"style":2142},[1896,2141],"delimcenter","top:0em;",[128,2144,1838],{"className":2145},[2146,2147],"delimsizing","size2",[128,2149,11],{"className":2150},[259,2151],"mathbf",[128,2153],{"className":2154,"style":1878},[269],[128,2156,1834],{"className":2157},[1882],[128,2159],{"className":2160,"style":1878},[269],[128,2162,2164,2168],{"className":2163},[259],[128,2165,2009],{"className":2166},[259,2167],"mathbb",[128,2169,2171],{"className":2170},[2087],[128,2172,2174],{"className":2173},[274],[128,2175,2177],{"className":2176},[278],[128,2178,2180],{"className":2179,"style":2077},[282],[128,2181,2182,2185],{"style":2099},[128,2183],{"className":2184,"style":291},[290],[128,2186,2188],{"className":2187},[299,300,301,298],[128,2189,1853],{"className":2190,"style":1924},[259,1873,298],[128,2192],{"className":2193,"style":1878},[269],[128,2195,2014],{"className":2196},[1882],[128,2198],{"className":2199,"style":1878},[269],[128,2201,2203,2206],{"className":2202},[259],[128,2204,11],{"className":2205},[259,1873],[128,2207,2209],{"className":2208},[2087],[128,2210,2212,2235],{"className":2211},[274,321],[128,2213,2215,2232],{"className":2214},[278],[128,2216,2219],{"className":2217,"style":2218},[282],"height:0.3361em;",[128,2220,2222,2225],{"style":2221},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[128,2223],{"className":2224,"style":291},[290],[128,2226,2228],{"className":2227},[299,300,301,298],[128,2229,2022],{"className":2230,"style":2231},[259,1873,298],"margin-right:0.0315em;",[128,2233,347],{"className":2234},[346],[128,2236,2238],{"className":2237},[278],[128,2239,2242],{"className":2240,"style":2241},[282],"height:0.15em;",[128,2243],{},[128,2245],{"className":2246,"style":1878},[269],[128,2248,2025],{"className":2249},[1882],[128,2251],{"className":2252,"style":1878},[269],[128,2254,2028],{"className":2255},[259],[128,2257,1845],{"className":2258},[1903],[128,2260,2033],{"className":2261},[269],[128,2263],{"className":2264,"style":1907},[269],[128,2266,2269,2275],{"className":2267},[2268],"mop",[128,2270,2042],{"className":2271,"style":2274},[2268,2272,2273],"op-symbol","small-op","position:relative;top:0em;",[128,2276,2278],{"className":2277},[2087],[128,2279,2281,2324],{"className":2280},[274,321],[128,2282,2284,2321],{"className":2283},[278],[128,2285,2288,2309],{"className":2286,"style":2287},[282],"height:0.9812em;",[128,2289,2291,2294],{"style":2290},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[128,2292],{"className":2293,"style":291},[290],[128,2295,2297],{"className":2296},[299,300,301,298],[128,2298,2300,2303,2306],{"className":2299},[259,298],[128,2301,2022],{"className":2302,"style":2231},[259,1873,298],[128,2304,1994],{"className":2305},[1882,298],[128,2307,1842],{"className":2308},[259,298],[128,2310,2312,2315],{"style":2311},"top:-3.2029em;margin-right:0.05em;",[128,2313],{"className":2314,"style":291},[290],[128,2316,2318],{"className":2317},[299,300,301,298],[128,2319,1853],{"className":2320,"style":1924},[259,1873,298],[128,2322,347],{"className":2323},[346],[128,2325,2327],{"className":2326},[278],[128,2328,2331],{"className":2329,"style":2330},[282],"height:0.2997em;",[128,2332],{},[128,2334],{"className":2335,"style":1907},[269],[128,2337,2339,2342],{"className":2338},[259],[128,2340,11],{"className":2341},[259,1873],[128,2343,2345],{"className":2344},[2087],[128,2346,2348,2368],{"className":2347},[274,321],[128,2349,2351,2365],{"className":2350},[278],[128,2352,2354],{"className":2353,"style":2218},[282],[128,2355,2356,2359],{"style":2221},[128,2357],{"className":2358,"style":291},[290],[128,2360,2362],{"className":2361},[299,300,301,298],[128,2363,2022],{"className":2364,"style":2231},[259,1873,298],[128,2366,347],{"className":2367},[346],[128,2369,2371],{"className":2370},[278],[128,2372,2374],{"className":2373,"style":2241},[282],[128,2375],{},[128,2377],{"className":2378,"style":1878},[269],[128,2380,1994],{"className":2381},[1882],[128,2383],{"className":2384,"style":1878},[269],[128,2386,1842],{"className":2387},[259],[128,2389,2391],{"className":2390,"style":2142},[1928,2141],[128,2392,1856],{"className":2393},[2146,2147],[11,2395,2396,2397,2400,2401,2462,2463,2527],{},"之中——",[35,2398,2399],{},"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 ",[128,2402,2404,2422],{"className":2403,"translate":218},[217],[128,2405,2407],{"className":2406},[222],[224,2408,2409],{"xmlns":226},[228,2410,2411,2419],{},[231,2412,2413],{},[1977,2414,2415,2417],{},[1795,2416,2009],{"mathvariant":2008},[1795,2418,1853],{},[238,2420,2421],{"encoding":240},"\\mathbb{R}^K",[128,2423,2425],{"className":2424,"ariaHidden":246},[245],[128,2426,2428,2432],{"className":2427},[250],[128,2429],{"className":2430,"style":2431},[254],"height:0.8413em;",[128,2433,2435,2438],{"className":2434},[259],[128,2436,2009],{"className":2437},[259,2167],[128,2439,2441],{"className":2440},[2087],[128,2442,2444],{"className":2443},[274],[128,2445,2447],{"className":2446},[278],[128,2448,2450],{"className":2449,"style":2431},[282],[128,2451,2453,2456],{"style":2452},"top:-3.063em;margin-right:0.05em;",[128,2454],{"className":2455,"style":291},[290],[128,2457,2459],{"className":2458},[299,300,301,298],[128,2460,1853],{"className":2461,"style":1924},[259,1873,298],"，而是一个 ",[128,2464,2466,2490],{"className":2465,"translate":218},[217],[128,2467,2469],{"className":2468},[222],[224,2470,2471],{"xmlns":226},[228,2472,2473,2487],{},[231,2474,2475,2478,2480,2482,2484],{},[1832,2476,2477],{"stretchy":1837},"(",[1795,2479,1853],{},[1832,2481,1989],{},[1840,2483,1842],{},[1832,2485,2486],{"stretchy":1837},")",[238,2488,2489],{"encoding":240},"(K-1)",[128,2491,2493,2515],{"className":2492,"ariaHidden":246},[245],[128,2494,2496,2499,2502,2505,2509,2512],{"className":2495},[250],[128,2497],{"className":2498,"style":1892},[254],[128,2500,2477],{"className":2501},[1896],[128,2503,1853],{"className":2504,"style":1924},[259,1873],[128,2506],{"className":2507,"style":2508},[269],"margin-right:0.2222em;",[128,2510,1989],{"className":2511},[2115],[128,2513],{"className":2514,"style":2508},[269],[128,2516,2518,2521,2524],{"className":2517},[250],[128,2519],{"className":2520,"style":1892},[254],[128,2522,1842],{"className":2523},[259],[128,2525,2486],{"className":2526},[1928]," 维的紧凸集。",[11,2529,2530,2531,2534,2535,1148,2538,2568,2569,2598,2599,893],{},"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",[35,2532,2533],{},"把握","有多大？若把输出建模为单纯形上的一个",[35,2536,2537],{},"确定点",[128,2539,2541,2555],{"className":2540,"translate":218},[217],[128,2542,2544],{"className":2543},[222],[224,2545,2546],{"xmlns":226},[228,2547,2548,2552],{},[231,2549,2550],{},[1795,2551,11],{"mathvariant":2001},[238,2553,2554],{"encoding":240},"\\mathbf{p}",[128,2556,2558],{"className":2557,"ariaHidden":246},[245],[128,2559,2561,2565],{"className":2560},[250],[128,2562],{"className":2563,"style":2564},[254],"height:0.6389em;vertical-align:-0.1944em;",[128,2566,11],{"className":2567},[259,2151],"，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 ",[128,2570,2572,2585],{"className":2571,"translate":218},[217],[128,2573,2575],{"className":2574},[222],[224,2576,2577],{"xmlns":226},[228,2578,2579,2583],{},[231,2580,2581],{},[1840,2582,1842],{},[238,2584,1842],{"encoding":240},[128,2586,2588],{"className":2587,"ariaHidden":246},[245],[128,2589,2591,2595],{"className":2590},[250],[128,2592],{"className":2593,"style":2594},[254],"height:0.6444em;",[128,2596,1842],{"className":2597},[259]," 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 ",[35,2600,2601],{},"迪利克雷分布（Dirichlet distribution）",[11,2603,2604],{},"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。",[51,2606,2608],{"id":2607},"一形式化","一、形式化",[2610,2611,2613],"h3",{"id":2612},"_11-概率单纯形","1.1 概率单纯形",[2615,2616,2618],"theorem",{"title":2617},"定义 1.1（概率单纯形）",[11,2619,2620,2621,2674,2675,2727,2728,3260,3261,893],{},"对整数 ",[128,2622,2624,2643],{"className":2623,"translate":218},[217],[128,2625,2627],{"className":2626},[222],[224,2628,2629],{"xmlns":226},[228,2630,2631,2640],{},[231,2632,2633,2635,2637],{},[1795,2634,1853],{},[1832,2636,2025],{},[1840,2638,2639],{},"2",[238,2641,2642],{"encoding":240},"K \\ge 2",[128,2644,2646,2665],{"className":2645,"ariaHidden":246},[245],[128,2647,2649,2653,2656,2659,2662],{"className":2648},[250],[128,2650],{"className":2651,"style":2652},[254],"height:0.8193em;vertical-align:-0.136em;",[128,2654,1853],{"className":2655,"style":1924},[259,1873],[128,2657],{"className":2658,"style":1878},[269],[128,2660,2025],{"className":2661},[1882],[128,2663],{"className":2664,"style":1878},[269],[128,2666,2668,2671],{"className":2667},[250],[128,2669],{"className":2670,"style":2594},[254],[128,2672,2639],{"className":2673},[259],"，",[128,2676,2678,2696],{"className":2677,"translate":218},[217],[128,2679,2681],{"className":2680},[222],[224,2682,2683],{"xmlns":226},[228,2684,2685,2693],{},[231,2686,2687,2689,2691],{},[1795,2688,1853],{},[1832,2690,1989],{},[1840,2692,1842],{},[238,2694,2695],{"encoding":240},"K-1",[128,2697,2699,2718],{"className":2698,"ariaHidden":246},[245],[128,2700,2702,2706,2709,2712,2715],{"className":2701},[250],[128,2703],{"className":2704,"style":2705},[254],"height:0.7667em;vertical-align:-0.0833em;",[128,2707,1853],{"className":2708,"style":1924},[259,1873],[128,2710],{"className":2711,"style":2508},[269],[128,2713,1989],{"className":2714},[2115],[128,2716],{"className":2717,"style":2508},[269],[128,2719,2721,2724],{"className":2720},[250],[128,2722],{"className":2723,"style":2594},[254],[128,2725,1842],{"className":2726},[259]," 维标准单纯形定义为\n",[128,2729,2731,2841],{"className":2730,"translate":218},[217],[128,2732,2734],{"className":2733},[222],[224,2735,2736],{"xmlns":226},[228,2737,2738,2838],{},[231,2739,2740,2752,2754],{},[1977,2741,2742,2744],{},[1795,2743,1982],{"mathvariant":1981},[231,2745,2746,2748,2750],{},[1795,2747,1853],{},[1832,2749,1989],{},[1840,2751,1842],{},[1832,2753,1994],{},[231,2755,2756,2758,2761,2763,2765,2771,2773,2775,2777,2783,2785,2787,2793,2795,2802,2804,2806,2808,2810,2836],{},[1832,2757,1838],{"fence":246},[1795,2759,2760],{"mathvariant":2001},"x",[1832,2762,1994],{},[1832,2764,2477],{"stretchy":1837},[2016,2766,2767,2769],{},[1795,2768,2760],{},[1840,2770,1842],{},[1832,2772,1845],{"separator":246},[1832,2774,1848],{},[1832,2776,1845],{"separator":246},[2016,2778,2779,2781],{},[1795,2780,2760],{},[1795,2782,1853],{},[1832,2784,2486],{"stretchy":1837},[1832,2786,1834],{},[1977,2788,2789,2791],{},[1795,2790,2009],{"mathvariant":2008},[1795,2792,1853],{},[1832,2794,2014],{},[2016,2796,2797,2799],{},[1795,2798,2760],{},[1795,2800,2801],{},"i",[1832,2803,2025],{},[1840,2805,2028],{},[1832,2807,1845],{"separator":246},[234,2809,2033],{},[2035,2811,2812,2826,2832,2834],{"scriptlevel":2028,"displaystyle":1837},[2038,2813,2814,2816,2824],{},[1832,2815,2042],{},[231,2817,2818,2820,2822],{},[1795,2819,2801],{},[1832,2821,1994],{},[1840,2823,1842],{},[1795,2825,1853],{},[2016,2827,2828,2830],{},[1795,2829,2760],{},[1795,2831,2801],{},[1832,2833,1994],{},[1840,2835,1842],{},[1832,2837,1856],{"fence":246},[238,2839,2840],{"encoding":240},"\\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\\}",[128,2842,2844,2897],{"className":2843,"ariaHidden":246},[245],[128,2845,2847,2850,2888,2891,2894],{"className":2846},[250],[128,2848],{"className":2849,"style":2431},[254],[128,2851,2853,2856],{"className":2852},[259],[128,2854,1982],{"className":2855},[259],[128,2857,2859],{"className":2858},[2087],[128,2860,2862],{"className":2861},[274],[128,2863,2865],{"className":2864},[278],[128,2866,2868],{"className":2867,"style":2431},[282],[128,2869,2870,2873],{"style":2452},[128,2871],{"className":2872,"style":291},[290],[128,2874,2876],{"className":2875},[299,300,301,298],[128,2877,2879,2882,2885],{"className":2878},[259,298],[128,2880,1853],{"className":2881,"style":1924},[259,1873,298],[128,2883,1989],{"className":2884},[2115,298],[128,2886,1842],{"className":2887},[259,298],[128,2889],{"className":2890,"style":1878},[269],[128,2892,1994],{"className":2893},[1882],[128,2895],{"className":2896,"style":1878},[269],[128,2898,2900,2903],{"className":2899},[250],[128,2901],{"className":2902,"style":2134},[254],[128,2904,2906,2912,2915,2918,2921,2924,2927,2968,2971,2974,2977,2980,2983,2986,3027,3030,3033,3036,3039,3068,3071,3074,3077,3118,3121,3124,3127,3130,3133,3136,3139,3199,3202,3242,3245,3248,3251,3254],{"className":2905},[1911],[128,2907,2909],{"className":2908,"style":2142},[1896,2141],[128,2910,1838],{"className":2911},[2146,2147],[128,2913,2760],{"className":2914},[259,2151],[128,2916],{"className":2917,"style":1878},[269],[128,2919,1994],{"className":2920},[1882],[128,2922],{"className":2923,"style":1878},[269],[128,2925,2477],{"className":2926},[1896],[128,2928,2930,2933],{"className":2929},[259],[128,2931,2760],{"className":2932},[259,1873],[128,2934,2936],{"className":2935},[2087],[128,2937,2939,2960],{"className":2938},[274,321],[128,2940,2942,2957],{"className":2941},[278],[128,2943,2946],{"className":2944,"style":2945},[282],"height:0.3011em;",[128,2947,2948,2951],{"style":2221},[128,2949],{"className":2950,"style":291},[290],[128,2952,2954],{"className":2953},[299,300,301,298],[128,2955,1842],{"className":2956},[259,298],[128,2958,347],{"className":2959},[346],[128,2961,2963],{"className":2962},[278],[128,2964,2966],{"className":2965,"style":2241},[282],[128,2967],{},[128,2969,1845],{"className":2970},[1903],[128,2972],{"className":2973,"style":1907},[269],[128,2975,1848],{"className":2976},[1911],[128,2978],{"className":2979,"style":1907},[269],[128,2981,1845],{"className":2982},[1903],[128,2984],{"className":2985,"style":1907},[269],[128,2987,2989,2992],{"className":2988},[259],[128,2990,2760],{"className":2991},[259,1873],[128,2993,2995],{"className":2994},[2087],[128,2996,2998,3019],{"className":2997},[274,321],[128,2999,3001,3016],{"className":3000},[278],[128,3002,3005],{"className":3003,"style":3004},[282],"height:0.3283em;",[128,3006,3007,3010],{"style":2221},[128,3008],{"className":3009,"style":291},[290],[128,3011,3013],{"className":3012},[299,300,301,298],[128,3014,1853],{"className":3015,"style":1924},[259,1873,298],[128,3017,347],{"className":3018},[346],[128,3020,3022],{"className":3021},[278],[128,3023,3025],{"className":3024,"style":2241},[282],[128,3026],{},[128,3028,2486],{"className":3029},[1928],[128,3031],{"className":3032,"style":1878},[269],[128,3034,1834],{"className":3035},[1882],[128,3037],{"className":3038,"style":1878},[269],[128,3040,3042,3045],{"className":3041},[259],[128,3043,2009],{"className":3044},[259,2167],[128,3046,3048],{"className":3047},[2087],[128,3049,3051],{"className":3050},[274],[128,3052,3054],{"className":3053},[278],[128,3055,3057],{"className":3056,"style":2431},[282],[128,3058,3059,3062],{"style":2452},[128,3060],{"className":3061,"style":291},[290],[128,3063,3065],{"className":3064},[299,300,301,298],[128,3066,1853],{"className":3067,"style":1924},[259,1873,298],[128,3069],{"className":3070,"style":1878},[269],[128,3072,2014],{"className":3073},[1882],[128,3075],{"className":3076,"style":1878},[269],[128,3078,3080,3083],{"className":3079},[259],[128,3081,2760],{"className":3082},[259,1873],[128,3084,3086],{"className":3085},[2087],[128,3087,3089,3110],{"className":3088},[274,321],[128,3090,3092,3107],{"className":3091},[278],[128,3093,3096],{"className":3094,"style":3095},[282],"height:0.3117em;",[128,3097,3098,3101],{"style":2221},[128,3099],{"className":3100,"style":291},[290],[128,3102,3104],{"className":3103},[299,300,301,298],[128,3105,2801],{"className":3106},[259,1873,298],[128,3108,347],{"className":3109},[346],[128,3111,3113],{"className":3112},[278],[128,3114,3116],{"className":3115,"style":2241},[282],[128,3117],{},[128,3119],{"className":3120,"style":1878},[269],[128,3122,2025],{"className":3123},[1882],[128,3125],{"className":3126,"style":1878},[269],[128,3128,2028],{"className":3129},[259],[128,3131,1845],{"className":3132},[1903],[128,3134,2033],{"className":3135},[269],[128,3137],{"className":3138,"style":1907},[269],[128,3140,3142,3145],{"className":3141},[2268],[128,3143,2042],{"className":3144,"style":2274},[2268,2272,2273],[128,3146,3148],{"className":3147},[2087],[128,3149,3151,3191],{"className":3150},[274,321],[128,3152,3154,3188],{"className":3153},[278],[128,3155,3157,3177],{"className":3156,"style":2287},[282],[128,3158,3159,3162],{"style":2290},[128,3160],{"className":3161,"style":291},[290],[128,3163,3165],{"className":3164},[299,300,301,298],[128,3166,3168,3171,3174],{"className":3167},[259,298],[128,3169,2801],{"className":3170},[259,1873,298],[128,3172,1994],{"className":3173},[1882,298],[128,3175,1842],{"className":3176},[259,298],[128,3178,3179,3182],{"style":2311},[128,3180],{"className":3181,"style":291},[290],[128,3183,3185],{"className":3184},[299,300,301,298],[128,3186,1853],{"className":3187,"style":1924},[259,1873,298],[128,3189,347],{"className":3190},[346],[128,3192,3194],{"className":3193},[278],[128,3195,3197],{"className":3196,"style":2330},[282],[128,3198],{},[128,3200],{"className":3201,"style":1907},[269],[128,3203,3205,3208],{"className":3204},[259],[128,3206,2760],{"className":3207},[259,1873],[128,3209,3211],{"className":3210},[2087],[128,3212,3214,3234],{"className":3213},[274,321],[128,3215,3217,3231],{"className":3216},[278],[128,3218,3220],{"className":3219,"style":3095},[282],[128,3221,3222,3225],{"style":2221},[128,3223],{"className":3224,"style":291},[290],[128,3226,3228],{"className":3227},[299,300,301,298],[128,3229,2801],{"className":3230},[259,1873,298],[128,3232,347],{"className":3233},[346],[128,3235,3237],{"className":3236},[278],[128,3238,3240],{"className":3239,"style":2241},[282],[128,3241],{},[128,3243],{"className":3244,"style":1878},[269],[128,3246,1994],{"className":3247},[1882],[128,3249],{"className":3250,"style":1878},[269],[128,3252,1842],{"className":3253},[259],[128,3255,3257],{"className":3256,"style":2142},[1928,2141],[128,3258,1856],{"className":3259},[2146,2147],"\n其内部记作 ",[128,3262,3264,3338],{"className":3263,"translate":218},[217],[128,3265,3267],{"className":3266},[222],[224,3268,3269],{"xmlns":226},[228,3270,3271,3335],{},[231,3272,3273,3276,3279,3291,3293,3295,3297,3299,3311,3313,3319,3322,3324,3326,3328,3331,3333],{},[1795,3274,3275],{"mathvariant":1981},"int",[1832,3277,3278],{},"⁡",[1977,3280,3281,3283],{},[1795,3282,1982],{"mathvariant":1981},[231,3284,3285,3287,3289],{},[1795,3286,1853],{},[1832,3288,1989],{},[1840,3290,1842],{},[1832,3292,1994],{},[1832,3294,1838],{"stretchy":1837},[1795,3296,2760],{"mathvariant":2001},[1832,3298,1834],{},[1977,3300,3301,3303],{},[1795,3302,1982],{"mathvariant":1981},[231,3304,3305,3307,3309],{},[1795,3306,1853],{},[1832,3308,1989],{},[1840,3310,1842],{},[1832,3312,2014],{},[2016,3314,3315,3317],{},[1795,3316,2760],{},[1795,3318,2801],{},[1832,3320,3321],{},">",[1840,3323,2028],{},[1832,3325,1845],{"separator":246},[234,3327,2033],{},[1795,3329,3330],{"mathvariant":1981},"∀",[1795,3332,2801],{},[1832,3334,1856],{"stretchy":1837},[238,3336,3337],{"encoding":240},"\\operatorname{int}\\Delta^{K-1} = \\{\\mathbf{x} \\in \\Delta^{K-1} : x_i > 0,\\ \\forall i\\}",[128,3339,3341,3404,3425,3478,3534],{"className":3340,"ariaHidden":246},[245],[128,3342,3344,3347,3354,3357,3395,3398,3401],{"className":3343},[250],[128,3345],{"className":3346,"style":2431},[254],[128,3348,3350],{"className":3349},[2268],[128,3351,3275],{"className":3352},[259,3353],"mathrm",[128,3355],{"className":3356,"style":1907},[269],[128,3358,3360,3363],{"className":3359},[259],[128,3361,1982],{"className":3362},[259],[128,3364,3366],{"className":3365},[2087],[128,3367,3369],{"className":3368},[274],[128,3370,3372],{"className":3371},[278],[128,3373,3375],{"className":3374,"style":2431},[282],[128,3376,3377,3380],{"style":2452},[128,3378],{"className":3379,"style":291},[290],[128,3381,3383],{"className":3382},[299,300,301,298],[128,3384,3386,3389,3392],{"className":3385},[259,298],[128,3387,1853],{"className":3388,"style":1924},[259,1873,298],[128,3390,1989],{"className":3391},[2115,298],[128,3393,1842],{"className":3394},[259,298],[128,3396],{"className":3397,"style":1878},[269],[128,3399,1994],{"className":3400},[1882],[128,3402],{"className":3403,"style":1878},[269],[128,3405,3407,3410,3413,3416,3419,3422],{"className":3406},[250],[128,3408],{"className":3409,"style":1892},[254],[128,3411,1838],{"className":3412},[1896],[128,3414,2760],{"className":3415},[259,2151],[128,3417],{"className":3418,"style":1878},[269],[128,3420,1834],{"className":3421},[1882],[128,3423],{"className":3424,"style":1878},[269],[128,3426,3428,3431,3469,3472,3475],{"className":3427},[250],[128,3429],{"className":3430,"style":2431},[254],[128,3432,3434,3437],{"className":3433},[259],[128,3435,1982],{"className":3436},[259],[128,3438,3440],{"className":3439},[2087],[128,3441,3443],{"className":3442},[274],[128,3444,3446],{"className":3445},[278],[128,3447,3449],{"className":3448,"style":2431},[282],[128,3450,3451,3454],{"style":2452},[128,3452],{"className":3453,"style":291},[290],[128,3455,3457],{"className":3456},[299,300,301,298],[128,3458,3460,3463,3466],{"className":3459},[259,298],[128,3461,1853],{"className":3462,"style":1924},[259,1873,298],[128,3464,1989],{"className":3465},[2115,298],[128,3467,1842],{"className":3468},[259,298],[128,3470],{"className":3471,"style":1878},[269],[128,3473,2014],{"className":3474},[1882],[128,3476],{"className":3477,"style":1878},[269],[128,3479,3481,3485,3525,3528,3531],{"className":3480},[250],[128,3482],{"className":3483,"style":3484},[254],"height:0.6891em;vertical-align:-0.15em;",[128,3486,3488,3491],{"className":3487},[259],[128,3489,2760],{"className":3490},[259,1873],[128,3492,3494],{"className":3493},[2087],[128,3495,3497,3517],{"className":3496},[274,321],[128,3498,3500,3514],{"className":3499},[278],[128,3501,3503],{"className":3502,"style":3095},[282],[128,3504,3505,3508],{"style":2221},[128,3506],{"className":3507,"style":291},[290],[128,3509,3511],{"className":3510},[299,300,301,298],[128,3512,2801],{"className":3513},[259,1873,298],[128,3515,347],{"className":3516},[346],[128,3518,3520],{"className":3519},[278],[128,3521,3523],{"className":3522,"style":2241},[282],[128,3524],{},[128,3526],{"className":3527,"style":1878},[269],[128,3529,3321],{"className":3530},[1882],[128,3532],{"className":3533,"style":1878},[269],[128,3535,3537,3540,3543,3546,3549,3552,3555,3558],{"className":3536},[250],[128,3538],{"className":3539,"style":1892},[254],[128,3541,2028],{"className":3542},[259],[128,3544,1845],{"className":3545},[1903],[128,3547,2033],{"className":3548},[269],[128,3550],{"className":3551,"style":1907},[269],[128,3553,3330],{"className":3554},[259],[128,3556,2801],{"className":3557},[259,1873],[128,3559,1856],{"className":3560},[1928],[11,3562,3563,3637,3638,3696,3697,3838,3839,3890,3891,3943,3944,3996,3997,4025],{},[128,3564,3566,3590],{"className":3565,"translate":218},[217],[128,3567,3569],{"className":3568},[222],[224,3570,3571],{"xmlns":226},[228,3572,3573,3587],{},[231,3574,3575],{},[1977,3576,3577,3579],{},[1795,3578,1982],{"mathvariant":1981},[231,3580,3581,3583,3585],{},[1795,3582,1853],{},[1832,3584,1989],{},[1840,3586,1842],{},[238,3588,3589],{"encoding":240},"\\Delta^{K-1}",[128,3591,3593],{"className":3592,"ariaHidden":246},[245],[128,3594,3596,3599],{"className":3595},[250],[128,3597],{"className":3598,"style":2431},[254],[128,3600,3602,3605],{"className":3601},[259],[128,3603,1982],{"className":3604},[259],[128,3606,3608],{"className":3607},[2087],[128,3609,3611],{"className":3610},[274],[128,3612,3614],{"className":3613},[278],[128,3615,3617],{"className":3616,"style":2431},[282],[128,3618,3619,3622],{"style":2452},[128,3620],{"className":3621,"style":291},[290],[128,3623,3625],{"className":3624},[299,300,301,298],[128,3626,3628,3631,3634],{"className":3627},[259,298],[128,3629,1853],{"className":3630,"style":1924},[259,1873,298],[128,3632,1989],{"className":3633},[2115,298],[128,3635,1842],{"className":3636},[259,298]," 是 ",[128,3639,3641,3658],{"className":3640,"translate":218},[217],[128,3642,3644],{"className":3643},[222],[224,3645,3646],{"xmlns":226},[228,3647,3648,3656],{},[231,3649,3650],{},[1977,3651,3652,3654],{},[1795,3653,2009],{"mathvariant":2008},[1795,3655,1853],{},[238,3657,2421],{"encoding":240},[128,3659,3661],{"className":3660,"ariaHidden":246},[245],[128,3662,3664,3667],{"className":3663},[250],[128,3665],{"className":3666,"style":2431},[254],[128,3668,3670,3673],{"className":3669},[259],[128,3671,2009],{"className":3672},[259,2167],[128,3674,3676],{"className":3675},[2087],[128,3677,3679],{"className":3678},[274],[128,3680,3682],{"className":3681},[278],[128,3683,3685],{"className":3684,"style":2431},[282],[128,3686,3687,3690],{"style":2452},[128,3688],{"className":3689,"style":291},[290],[128,3691,3693],{"className":3692},[299,300,301,298],[128,3694,1853],{"className":3695,"style":1924},[259,1873,298]," 中的紧凸集，其顶点为坐标向量 ",[128,3698,3700,3731],{"className":3699,"translate":218},[217],[128,3701,3703],{"className":3702},[222],[224,3704,3705],{"xmlns":226},[228,3706,3707,3728],{},[231,3708,3709,3716,3718,3720,3722],{},[2016,3710,3711,3714],{},[1795,3712,3713],{"mathvariant":2001},"e",[1840,3715,1842],{},[1832,3717,1845],{"separator":246},[1832,3719,1848],{},[1832,3721,1845],{"separator":246},[2016,3723,3724,3726],{},[1795,3725,3713],{"mathvariant":2001},[1795,3727,1853],{},[238,3729,3730],{"encoding":240},"\\mathbf{e}_1, \\dots, \\mathbf{e}_K",[128,3732,3734],{"className":3733,"ariaHidden":246},[245],[128,3735,3737,3740,3780,3783,3786,3789,3792,3795,3798],{"className":3736},[250],[128,3738],{"className":3739,"style":2564},[254],[128,3741,3743,3746],{"className":3742},[259],[128,3744,3713],{"className":3745},[259,2151],[128,3747,3749],{"className":3748},[2087],[128,3750,3752,3772],{"className":3751},[274,321],[128,3753,3755,3769],{"className":3754},[278],[128,3756,3758],{"className":3757,"style":2945},[282],[128,3759,3760,3763],{"style":2221},[128,3761],{"className":3762,"style":291},[290],[128,3764,3766],{"className":3765},[299,300,301,298],[128,3767,1842],{"className":3768},[259,298],[128,3770,347],{"className":3771},[346],[128,3773,3775],{"className":3774},[278],[128,3776,3778],{"className":3777,"style":2241},[282],[128,3779],{},[128,3781,1845],{"className":3782},[1903],[128,3784],{"className":3785,"style":1907},[269],[128,3787,1848],{"className":3788},[1911],[128,3790],{"className":3791,"style":1907},[269],[128,3793,1845],{"className":3794},[1903],[128,3796],{"className":3797,"style":1907},[269],[128,3799,3801,3804],{"className":3800},[259],[128,3802,3713],{"className":3803},[259,2151],[128,3805,3807],{"className":3806},[2087],[128,3808,3810,3830],{"className":3809},[274,321],[128,3811,3813,3827],{"className":3812},[278],[128,3814,3816],{"className":3815,"style":3004},[282],[128,3817,3818,3821],{"style":2221},[128,3819],{"className":3820,"style":291},[290],[128,3822,3824],{"className":3823},[299,300,301,298],[128,3825,1853],{"className":3826,"style":1924},[259,1873,298],[128,3828,347],{"className":3829},[346],[128,3831,3833],{"className":3832},[278],[128,3834,3836],{"className":3835,"style":2241},[282],[128,3837],{},"。低维特例给出了全部几何直观：",[128,3840,3842,3860],{"className":3841,"translate":218},[217],[128,3843,3845],{"className":3844},[222],[224,3846,3847],{"xmlns":226},[228,3848,3849,3857],{},[231,3850,3851,3853,3855],{},[1795,3852,1853],{},[1832,3854,1994],{},[1840,3856,2639],{},[238,3858,3859],{"encoding":240},"K = 2",[128,3861,3863,3881],{"className":3862,"ariaHidden":246},[245],[128,3864,3866,3869,3872,3875,3878],{"className":3865},[250],[128,3867],{"className":3868,"style":283},[254],[128,3870,1853],{"className":3871,"style":1924},[259,1873],[128,3873],{"className":3874,"style":1878},[269],[128,3876,1994],{"className":3877},[1882],[128,3879],{"className":3880,"style":1878},[269],[128,3882,3884,3887],{"className":3883},[250],[128,3885],{"className":3886,"style":2594},[254],[128,3888,2639],{"className":3889},[259]," 时它是一维线段，",[128,3892,3894,3913],{"className":3893,"translate":218},[217],[128,3895,3897],{"className":3896},[222],[224,3898,3899],{"xmlns":226},[228,3900,3901,3910],{},[231,3902,3903,3905,3907],{},[1795,3904,1853],{},[1832,3906,1994],{},[1840,3908,3909],{},"3",[238,3911,3912],{"encoding":240},"K = 3",[128,3914,3916,3934],{"className":3915,"ariaHidden":246},[245],[128,3917,3919,3922,3925,3928,3931],{"className":3918},[250],[128,3920],{"className":3921,"style":283},[254],[128,3923,1853],{"className":3924,"style":1924},[259,1873],[128,3926],{"className":3927,"style":1878},[269],[128,3929,1994],{"className":3930},[1882],[128,3932],{"className":3933,"style":1878},[269],[128,3935,3937,3940],{"className":3936},[250],[128,3938],{"className":3939,"style":2594},[254],[128,3941,3909],{"className":3942},[259]," 时是二维三角形，",[128,3945,3947,3966],{"className":3946,"translate":218},[217],[128,3948,3950],{"className":3949},[222],[224,3951,3952],{"xmlns":226},[228,3953,3954,3963],{},[231,3955,3956,3958,3960],{},[1795,3957,1853],{},[1832,3959,1994],{},[1840,3961,3962],{},"4",[238,3964,3965],{"encoding":240},"K = 4",[128,3967,3969,3987],{"className":3968,"ariaHidden":246},[245],[128,3970,3972,3975,3978,3981,3984],{"className":3971},[250],[128,3973],{"className":3974,"style":283},[254],[128,3976,1853],{"className":3977,"style":1924},[259,1873],[128,3979],{"className":3980,"style":1878},[269],[128,3982,1994],{"className":3983},[1882],[128,3985],{"className":3986,"style":1878},[269],[128,3988,3990,3993],{"className":3989},[250],[128,3991],{"className":3992,"style":2594},[254],[128,3994,3962],{"className":3995},[259]," 时是三维四面体。它与 ",[128,3998,4000,4013],{"className":3999,"translate":218},[217],[128,4001,4003],{"className":4002},[222],[224,4004,4005],{"xmlns":226},[228,4006,4007,4011],{},[231,4008,4009],{},[1795,4010,1853],{},[238,4012,1853],{"encoding":240},[128,4014,4016],{"className":4015,"ariaHidden":246},[245],[128,4017,4019,4022],{"className":4018},[250],[128,4020],{"className":4021,"style":283},[254],[128,4023,1853],{"className":4024,"style":1924},[259,1873]," 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。",[11,4027,4028,4029,4186,4187,4412,4413,4443,4444,4504,4505,4660,4661,4734,4735,4809],{},"本文采用如下测度约定：以 ",[128,4030,4032,4068],{"className":4031,"translate":218},[217],[128,4033,4035],{"className":4034},[222],[224,4036,4037],{"xmlns":226},[228,4038,4039,4065],{},[231,4040,4041,4047,4049,4051,4053],{},[2016,4042,4043,4045],{},[1795,4044,2760],{},[1840,4046,1842],{},[1832,4048,1845],{"separator":246},[1832,4050,1848],{},[1832,4052,1845],{"separator":246},[2016,4054,4055,4057],{},[1795,4056,2760],{},[231,4058,4059,4061,4063],{},[1795,4060,1853],{},[1832,4062,1989],{},[1840,4064,1842],{},[238,4066,4067],{"encoding":240},"x_1, \\dots, x_{K-1}",[128,4069,4071],{"className":4070,"ariaHidden":246},[245],[128,4072,4074,4078,4118,4121,4124,4127,4130,4133,4136],{"className":4073},[250],[128,4075],{"className":4076,"style":4077},[254],"height:0.6389em;vertical-align:-0.2083em;",[128,4079,4081,4084],{"className":4080},[259],[128,4082,2760],{"className":4083},[259,1873],[128,4085,4087],{"className":4086},[2087],[128,4088,4090,4110],{"className":4089},[274,321],[128,4091,4093,4107],{"className":4092},[278],[128,4094,4096],{"className":4095,"style":2945},[282],[128,4097,4098,4101],{"style":2221},[128,4099],{"className":4100,"style":291},[290],[128,4102,4104],{"className":4103},[299,300,301,298],[128,4105,1842],{"className":4106},[259,298],[128,4108,347],{"className":4109},[346],[128,4111,4113],{"className":4112},[278],[128,4114,4116],{"className":4115,"style":2241},[282],[128,4117],{},[128,4119,1845],{"className":4120},[1903],[128,4122],{"className":4123,"style":1907},[269],[128,4125,1848],{"className":4126},[1911],[128,4128],{"className":4129,"style":1907},[269],[128,4131,1845],{"className":4132},[1903],[128,4134],{"className":4135,"style":1907},[269],[128,4137,4139,4142],{"className":4138},[259],[128,4140,2760],{"className":4141},[259,1873],[128,4143,4145],{"className":4144},[2087],[128,4146,4148,4177],{"className":4147},[274,321],[128,4149,4151,4174],{"className":4150},[278],[128,4152,4154],{"className":4153,"style":3004},[282],[128,4155,4156,4159],{"style":2221},[128,4157],{"className":4158,"style":291},[290],[128,4160,4162],{"className":4161},[299,300,301,298],[128,4163,4165,4168,4171],{"className":4164},[259,298],[128,4166,1853],{"className":4167,"style":1924},[259,1873,298],[128,4169,1989],{"className":4170},[2115,298],[128,4172,1842],{"className":4173},[259,298],[128,4175,347],{"className":4176},[346],[128,4178,4180],{"className":4179},[278],[128,4181,4184],{"className":4182,"style":4183},[282],"height:0.2083em;",[128,4185],{}," 为自由坐标、",[128,4188,4190,4233],{"className":4189,"translate":218},[217],[128,4191,4193],{"className":4192},[222],[224,4194,4195],{"xmlns":226},[228,4196,4197,4230],{},[231,4198,4199,4205,4207,4209,4211,4224],{},[2016,4200,4201,4203],{},[1795,4202,2760],{},[1795,4204,1853],{},[1832,4206,1994],{},[1840,4208,1842],{},[1832,4210,1989],{},[2016,4212,4213,4215],{},[1832,4214,2042],{},[231,4216,4217,4219,4222],{},[1795,4218,2801],{},[1832,4220,4221],{},"\u003C",[1795,4223,1853],{},[2016,4225,4226,4228],{},[1795,4227,2760],{},[1795,4229,2801],{},[238,4231,4232],{"encoding":240},"x_K = 1 - \\sum_{i\u003CK} x_i",[128,4234,4236,4292,4311],{"className":4235,"ariaHidden":246},[245],[128,4237,4239,4243,4283,4286,4289],{"className":4238},[250],[128,4240],{"className":4241,"style":4242},[254],"height:0.5806em;vertical-align:-0.15em;",[128,4244,4246,4249],{"className":4245},[259],[128,4247,2760],{"className":4248},[259,1873],[128,4250,4252],{"className":4251},[2087],[128,4253,4255,4275],{"className":4254},[274,321],[128,4256,4258,4272],{"className":4257},[278],[128,4259,4261],{"className":4260,"style":3004},[282],[128,4262,4263,4266],{"style":2221},[128,4264],{"className":4265,"style":291},[290],[128,4267,4269],{"className":4268},[299,300,301,298],[128,4270,1853],{"className":4271,"style":1924},[259,1873,298],[128,4273,347],{"className":4274},[346],[128,4276,4278],{"className":4277},[278],[128,4279,4281],{"className":4280,"style":2241},[282],[128,4282],{},[128,4284],{"className":4285,"style":1878},[269],[128,4287,1994],{"className":4288},[1882],[128,4290],{"className":4291,"style":1878},[269],[128,4293,4295,4299,4302,4305,4308],{"className":4294},[250],[128,4296],{"className":4297,"style":4298},[254],"height:0.7278em;vertical-align:-0.0833em;",[128,4300,1842],{"className":4301},[259],[128,4303],{"className":4304,"style":2508},[269],[128,4306,1989],{"className":4307},[2115],[128,4309],{"className":4310,"style":2508},[269],[128,4312,4314,4318,4369,4372],{"className":4313},[250],[128,4315],{"className":4316,"style":4317},[254],"height:1.0771em;vertical-align:-0.3271em;",[128,4319,4321,4324],{"className":4320},[2268],[128,4322,2042],{"className":4323,"style":2274},[2268,2272,2273],[128,4325,4327],{"className":4326},[2087],[128,4328,4330,4360],{"className":4329},[274,321],[128,4331,4333,4357],{"className":4332},[278],[128,4334,4337],{"className":4335,"style":4336},[282],"height:0.1786em;",[128,4338,4339,4342],{"style":2290},[128,4340],{"className":4341,"style":291},[290],[128,4343,4345],{"className":4344},[299,300,301,298],[128,4346,4348,4351,4354],{"className":4347},[259,298],[128,4349,2801],{"className":4350},[259,1873,298],[128,4352,4221],{"className":4353},[1882,298],[128,4355,1853],{"className":4356,"style":1924},[259,1873,298],[128,4358,347],{"className":4359},[346],[128,4361,4363],{"className":4362},[278],[128,4364,4367],{"className":4365,"style":4366},[282],"height:0.3271em;",[128,4368],{},[128,4370],{"className":4371,"style":1907},[269],[128,4373,4375,4378],{"className":4374},[259],[128,4376,2760],{"className":4377},[259,1873],[128,4379,4381],{"className":4380},[2087],[128,4382,4384,4404],{"className":4383},[274,321],[128,4385,4387,4401],{"className":4386},[278],[128,4388,4390],{"className":4389,"style":3095},[282],[128,4391,4392,4395],{"style":2221},[128,4393],{"className":4394,"style":291},[290],[128,4396,4398],{"className":4397},[299,300,301,298],[128,4399,2801],{"className":4400},[259,1873,298],[128,4402,347],{"className":4403},[346],[128,4405,4407],{"className":4406},[278],[128,4408,4410],{"className":4409,"style":2241},[282],[128,4411],{},"，并以 ",[128,4414,4416,4430],{"className":4415,"translate":218},[217],[128,4417,4419],{"className":4418},[222],[224,4420,4421],{"xmlns":226},[228,4422,4423,4427],{},[231,4424,4425],{},[1795,4426,2760],{"mathvariant":2001},[238,4428,4429],{"encoding":240},"\\mathbf{x}",[128,4431,4433],{"className":4432,"ariaHidden":246},[245],[128,4434,4436,4440],{"className":4435},[250],[128,4437],{"className":4438,"style":4439},[254],"height:0.4444em;",[128,4441,2760],{"className":4442},[259,2151]," 上的 ",[128,4445,4447,4468],{"className":4446,"translate":218},[217],[128,4448,4450],{"className":4449},[222],[224,4451,4452],{"xmlns":226},[228,4453,4454,4466],{},[231,4455,4456,4458,4460,4462,4464],{},[1832,4457,2477],{"stretchy":1837},[1795,4459,1853],{},[1832,4461,1989],{},[1840,4463,1842],{},[1832,4465,2486],{"stretchy":1837},[238,4467,2489],{"encoding":240},[128,4469,4471,4492],{"className":4470,"ariaHidden":246},[245],[128,4472,4474,4477,4480,4483,4486,4489],{"className":4473},[250],[128,4475],{"className":4476,"style":1892},[254],[128,4478,2477],{"className":4479},[1896],[128,4481,1853],{"className":4482,"style":1924},[259,1873],[128,4484],{"className":4485,"style":2508},[269],[128,4487,1989],{"className":4488},[2115],[128,4490],{"className":4491,"style":2508},[269],[128,4493,4495,4498,4501],{"className":4494},[250],[128,4496],{"className":4497,"style":1892},[254],[128,4499,1842],{"className":4500},[259],[128,4502,2486],{"className":4503},[1928]," 维 Lebesgue 测度 ",[128,4506,4508,4546],{"className":4507,"translate":218},[217],[128,4509,4511],{"className":4510},[222],[224,4512,4513],{"xmlns":226},[228,4514,4515,4543],{},[231,4516,4517,4520,4526,4529,4531],{},[1795,4518,4519],{"mathvariant":1981},"d",[2016,4521,4522,4524],{},[1795,4523,2760],{},[1840,4525,1842],{},[1832,4527,4528],{},"⋯",[1795,4530,4519],{"mathvariant":1981},[2016,4532,4533,4535],{},[1795,4534,2760],{},[231,4536,4537,4539,4541],{},[1795,4538,1853],{},[1832,4540,1989],{},[1840,4542,1842],{},[238,4544,4545],{"encoding":240},"\\mathrm{d}x_1 \\cdots \\mathrm{d}x_{K-1}",[128,4547,4549],{"className":4548,"ariaHidden":246},[245],[128,4550,4552,4556,4559,4599,4602,4605,4608,4611],{"className":4551},[250],[128,4553],{"className":4554,"style":4555},[254],"height:0.9028em;vertical-align:-0.2083em;",[128,4557,4519],{"className":4558},[259,3353],[128,4560,4562,4565],{"className":4561},[259],[128,4563,2760],{"className":4564},[259,1873],[128,4566,4568],{"className":4567},[2087],[128,4569,4571,4591],{"className":4570},[274,321],[128,4572,4574,4588],{"className":4573},[278],[128,4575,4577],{"className":4576,"style":2945},[282],[128,4578,4579,4582],{"style":2221},[128,4580],{"className":4581,"style":291},[290],[128,4583,4585],{"className":4584},[299,300,301,298],[128,4586,1842],{"className":4587},[259,298],[128,4589,347],{"className":4590},[346],[128,4592,4594],{"className":4593},[278],[128,4595,4597],{"className":4596,"style":2241},[282],[128,4598],{},[128,4600],{"className":4601,"style":1907},[269],[128,4603,4528],{"className":4604},[1911],[128,4606],{"className":4607,"style":1907},[269],[128,4609,4519],{"className":4610},[259,3353],[128,4612,4614,4617],{"className":4613},[259],[128,4615,2760],{"className":4616},[259,1873],[128,4618,4620],{"className":4619},[2087],[128,4621,4623,4652],{"className":4622},[274,321],[128,4624,4626,4649],{"className":4625},[278],[128,4627,4629],{"className":4628,"style":3004},[282],[128,4630,4631,4634],{"style":2221},[128,4632],{"className":4633,"style":291},[290],[128,4635,4637],{"className":4636},[299,300,301,298],[128,4638,4640,4643,4646],{"className":4639},[259,298],[128,4641,1853],{"className":4642,"style":1924},[259,1873,298],[128,4644,1989],{"className":4645},[2115,298],[128,4647,1842],{"className":4648},[259,298],[128,4650,347],{"className":4651},[346],[128,4653,4655],{"className":4654},[278],[128,4656,4658],{"className":4657,"style":4183},[282],[128,4659],{}," 为参考测度。在该约定下 ",[128,4662,4664,4687],{"className":4663,"translate":218},[217],[128,4665,4667],{"className":4666},[222],[224,4668,4669],{"xmlns":226},[228,4670,4671,4685],{},[231,4672,4673],{},[1977,4674,4675,4677],{},[1795,4676,1982],{"mathvariant":1981},[231,4678,4679,4681,4683],{},[1795,4680,1853],{},[1832,4682,1989],{},[1840,4684,1842],{},[238,4686,3589],{"encoding":240},[128,4688,4690],{"className":4689,"ariaHidden":246},[245],[128,4691,4693,4696],{"className":4692},[250],[128,4694],{"className":4695,"style":2431},[254],[128,4697,4699,4702],{"className":4698},[259],[128,4700,1982],{"className":4701},[259],[128,4703,4705],{"className":4704},[2087],[128,4706,4708],{"className":4707},[274],[128,4709,4711],{"className":4710},[278],[128,4712,4714],{"className":4713,"style":2431},[282],[128,4715,4716,4719],{"style":2452},[128,4717],{"className":4718,"style":291},[290],[128,4720,4722],{"className":4721},[299,300,301,298],[128,4723,4725,4728,4731],{"className":4724},[259,298],[128,4726,1853],{"className":4727,"style":1924},[259,1873,298],[128,4729,1989],{"className":4730},[2115,298],[128,4732,1842],{"className":4733},[259,298]," 的体积为 ",[128,4736,4738,4768],{"className":4737,"translate":218},[217],[128,4739,4741],{"className":4740},[222],[224,4742,4743],{"xmlns":226},[228,4744,4745,4765],{},[231,4746,4747,4749,4752,4754,4756,4758,4760,4762],{},[1840,4748,1842],{},[1795,4750,4751],{"mathvariant":1981},"\u002F",[1832,4753,2477],{"stretchy":1837},[1795,4755,1853],{},[1832,4757,1989],{},[1840,4759,1842],{},[1832,4761,2486],{"stretchy":1837},[1832,4763,4764],{"stretchy":1837},"!",[238,4766,4767],{"encoding":240},"1\u002F(K-1)!",[128,4769,4771,4796],{"className":4770,"ariaHidden":246},[245],[128,4772,4774,4777,4781,4784,4787,4790,4793],{"className":4773},[250],[128,4775],{"className":4776,"style":1892},[254],[128,4778,4780],{"className":4779},[259],"1\u002F",[128,4782,2477],{"className":4783},[1896],[128,4785,1853],{"className":4786,"style":1924},[259,1873],[128,4788],{"className":4789,"style":2508},[269],[128,4791,1989],{"className":4792},[2115],[128,4794],{"className":4795,"style":2508},[269],[128,4797,4799,4802,4805],{"className":4798},[250],[128,4800],{"className":4801,"style":1892},[254],[128,4803,1842],{"className":4804},[259],[128,4806,4808],{"className":4807},[1928],")!","，这一点在后文讨论熵时会重新出现。",[2610,4811,4813],{"id":4812},"_12-形式化定义","1.2 形式化定义",[2615,4815,4817],{"title":4816},"定义 1.2（Dirichlet 分布）",[11,4818,4819,4820,5092,5093,5304,5305,5333,5334,5421,5422,5829,5830,5858,5859,5894,5895,5974,5975,5978],{},"设参数向量 ",[128,4821,4823,4877],{"className":4822,"translate":218},[217],[128,4824,4826],{"className":4825},[222],[224,4827,4828],{"xmlns":226},[228,4829,4830,4874],{},[231,4831,4832,4836,4838,4840,4846,4848,4850,4852,4858,4860,4862],{},[1795,4833,4835],{"mathvariant":4834},"bold-italic","α",[1832,4837,1994],{},[1832,4839,2477],{"stretchy":1837},[2016,4841,4842,4844],{},[1795,4843,4835],{},[1840,4845,1842],{},[1832,4847,1845],{"separator":246},[1832,4849,1848],{},[1832,4851,1845],{"separator":246},[2016,4853,4854,4856],{},[1795,4855,4835],{},[1795,4857,1853],{},[1832,4859,2486],{"stretchy":1837},[1832,4861,1834],{},[2038,4863,4864,4866,4872],{},[1795,4865,2009],{"mathvariant":2008},[231,4867,4868,4870],{},[1832,4869,3321],{},[1840,4871,2028],{},[1795,4873,1853],{},[238,4875,4876],{"encoding":240},"\\boldsymbol{\\alpha} = (\\alpha_1, \\dots, \\alpha_K) \\in \\mathbb{R}_{>0}^K",[128,4878,4880,4905,5026],{"className":4879,"ariaHidden":246},[245],[128,4881,4883,4886,4896,4899,4902],{"className":4882},[250],[128,4884],{"className":4885,"style":4439},[254],[128,4887,4889],{"className":4888},[259],[128,4890,4892],{"className":4891},[259],[128,4893,4835],{"className":4894},[259,4895],"boldsymbol",[128,4897],{"className":4898,"style":1878},[269],[128,4900,1994],{"className":4901},[1882],[128,4903],{"className":4904,"style":1878},[269],[128,4906,4908,4911,4914,4956,4959,4962,4965,4968,4971,4974,5014,5017,5020,5023],{"className":4907},[250],[128,4909],{"className":4910,"style":1892},[254],[128,4912,2477],{"className":4913},[1896],[128,4915,4917,4921],{"className":4916},[259],[128,4918,4835],{"className":4919,"style":4920},[259,1873],"margin-right:0.0037em;",[128,4922,4924],{"className":4923},[2087],[128,4925,4927,4948],{"className":4926},[274,321],[128,4928,4930,4945],{"className":4929},[278],[128,4931,4933],{"className":4932,"style":2945},[282],[128,4934,4936,4939],{"style":4935},"top:-2.55em;margin-left:-0.0037em;margin-right:0.05em;",[128,4937],{"className":4938,"style":291},[290],[128,4940,4942],{"className":4941},[299,300,301,298],[128,4943,1842],{"className":4944},[259,298],[128,4946,347],{"className":4947},[346],[128,4949,4951],{"className":4950},[278],[128,4952,4954],{"className":4953,"style":2241},[282],[128,4955],{},[128,4957,1845],{"className":4958},[1903],[128,4960],{"className":4961,"style":1907},[269],[128,4963,1848],{"className":4964},[1911],[128,4966],{"className":4967,"style":1907},[269],[128,4969,1845],{"className":4970},[1903],[128,4972],{"className":4973,"style":1907},[269],[128,4975,4977,4980],{"className":4976},[259],[128,4978,4835],{"className":4979,"style":4920},[259,1873],[128,4981,4983],{"className":4982},[2087],[128,4984,4986,5006],{"className":4985},[274,321],[128,4987,4989,5003],{"className":4988},[278],[128,4990,4992],{"className":4991,"style":3004},[282],[128,4993,4994,4997],{"style":4935},[128,4995],{"className":4996,"style":291},[290],[128,4998,5000],{"className":4999},[299,300,301,298],[128,5001,1853],{"className":5002,"style":1924},[259,1873,298],[128,5004,347],{"className":5005},[346],[128,5007,5009],{"className":5008},[278],[128,5010,5012],{"className":5011,"style":2241},[282],[128,5013],{},[128,5015,2486],{"className":5016},[1928],[128,5018],{"className":5019,"style":1878},[269],[128,5021,1834],{"className":5022},[1882],[128,5024],{"className":5025,"style":1878},[269],[128,5027,5029,5033],{"className":5028},[250],[128,5030],{"className":5031,"style":5032},[254],"height:1.1168em;vertical-align:-0.2755em;",[128,5034,5036,5039],{"className":5035},[259],[128,5037,2009],{"className":5038},[259,2167],[128,5040,5042],{"className":5041},[2087],[128,5043,5045,5083],{"className":5044},[274,321],[128,5046,5048,5080],{"className":5047},[278],[128,5049,5051,5069],{"className":5050,"style":2431},[282],[128,5052,5054,5057],{"style":5053},"top:-2.4519em;margin-left:0em;margin-right:0.05em;",[128,5055],{"className":5056,"style":291},[290],[128,5058,5060],{"className":5059},[299,300,301,298],[128,5061,5063,5066],{"className":5062},[259,298],[128,5064,3321],{"className":5065},[1882,298],[128,5067,2028],{"className":5068},[259,298],[128,5070,5071,5074],{"style":2452},[128,5072],{"className":5073,"style":291},[290],[128,5075,5077],{"className":5076},[299,300,301,298],[128,5078,1853],{"className":5079,"style":1924},[259,1873,298],[128,5081,347],{"className":5082},[346],[128,5084,5086],{"className":5085},[278],[128,5087,5090],{"className":5088,"style":5089},[282],"height:0.2755em;",[128,5091],{},"，记 ",[128,5094,5096,5136],{"className":5095,"translate":218},[217],[128,5097,5099],{"className":5098},[222],[224,5100,5101],{"xmlns":226},[228,5102,5103,5133],{},[231,5104,5105,5111,5113,5127],{},[2016,5106,5107,5109],{},[1795,5108,4835],{},[1840,5110,2028],{},[1832,5112,1994],{},[2038,5114,5115,5117,5125],{},[1832,5116,2042],{},[231,5118,5119,5121,5123],{},[1795,5120,2801],{},[1832,5122,1994],{},[1840,5124,1842],{},[1795,5126,1853],{},[2016,5128,5129,5131],{},[1795,5130,4835],{},[1795,5132,2801],{},[238,5134,5135],{"encoding":240},"\\alpha_0 = \\sum_{i=1}^K \\alpha_i",[128,5137,5139,5194],{"className":5138,"ariaHidden":246},[245],[128,5140,5142,5145,5185,5188,5191],{"className":5141},[250],[128,5143],{"className":5144,"style":4242},[254],[128,5146,5148,5151],{"className":5147},[259],[128,5149,4835],{"className":5150,"style":4920},[259,1873],[128,5152,5154],{"className":5153},[2087],[128,5155,5157,5177],{"className":5156},[274,321],[128,5158,5160,5174],{"className":5159},[278],[128,5161,5163],{"className":5162,"style":2945},[282],[128,5164,5165,5168],{"style":4935},[128,5166],{"className":5167,"style":291},[290],[128,5169,5171],{"className":5170},[299,300,301,298],[128,5172,2028],{"className":5173},[259,298],[128,5175,347],{"className":5176},[346],[128,5178,5180],{"className":5179},[278],[128,5181,5183],{"className":5182,"style":2241},[282],[128,5184],{},[128,5186],{"className":5187,"style":1878},[269],[128,5189,1994],{"className":5190},[1882],[128,5192],{"className":5193,"style":1878},[269],[128,5195,5197,5201,5261,5264],{"className":5196},[250],[128,5198],{"className":5199,"style":5200},[254],"height:1.2809em;vertical-align:-0.2997em;",[128,5202,5204,5207],{"className":5203},[2268],[128,5205,2042],{"className":5206,"style":2274},[2268,2272,2273],[128,5208,5210],{"className":5209},[2087],[128,5211,5213,5253],{"className":5212},[274,321],[128,5214,5216,5250],{"className":5215},[278],[128,5217,5219,5239],{"className":5218,"style":2287},[282],[128,5220,5221,5224],{"style":2290},[128,5222],{"className":5223,"style":291},[290],[128,5225,5227],{"className":5226},[299,300,301,298],[128,5228,5230,5233,5236],{"className":5229},[259,298],[128,5231,2801],{"className":5232},[259,1873,298],[128,5234,1994],{"className":5235},[1882,298],[128,5237,1842],{"className":5238},[259,298],[128,5240,5241,5244],{"style":2311},[128,5242],{"className":5243,"style":291},[290],[128,5245,5247],{"className":5246},[299,300,301,298],[128,5248,1853],{"className":5249,"style":1924},[259,1873,298],[128,5251,347],{"className":5252},[346],[128,5254,5256],{"className":5255},[278],[128,5257,5259],{"className":5258,"style":2330},[282],[128,5260],{},[128,5262],{"className":5263,"style":1907},[269],[128,5265,5267,5270],{"className":5266},[259],[128,5268,4835],{"className":5269,"style":4920},[259,1873],[128,5271,5273],{"className":5272},[2087],[128,5274,5276,5296],{"className":5275},[274,321],[128,5277,5279,5293],{"className":5278},[278],[128,5280,5282],{"className":5281,"style":3095},[282],[128,5283,5284,5287],{"style":4935},[128,5285],{"className":5286,"style":291},[290],[128,5288,5290],{"className":5289},[299,300,301,298],[128,5291,2801],{"className":5292},[259,1873,298],[128,5294,347],{"className":5295},[346],[128,5297,5299],{"className":5298},[278],[128,5300,5302],{"className":5301,"style":2241},[282],[128,5303],{},"。若随机向量 ",[128,5306,5308,5321],{"className":5307,"translate":218},[217],[128,5309,5311],{"className":5310},[222],[224,5312,5313],{"xmlns":226},[228,5314,5315,5319],{},[231,5316,5317],{},[1795,5318,2760],{"mathvariant":2001},[238,5320,4429],{"encoding":240},[128,5322,5324],{"className":5323,"ariaHidden":246},[245],[128,5325,5327,5330],{"className":5326},[250],[128,5328],{"className":5329,"style":4439},[254],[128,5331,2760],{"className":5332},[259,2151]," 取值于 ",[128,5335,5337,5365],{"className":5336,"translate":218},[217],[128,5338,5340],{"className":5339},[222],[224,5341,5342],{"xmlns":226},[228,5343,5344,5362],{},[231,5345,5346,5348,5350],{},[1795,5347,3275],{"mathvariant":1981},[1832,5349,3278],{},[1977,5351,5352,5354],{},[1795,5353,1982],{"mathvariant":1981},[231,5355,5356,5358,5360],{},[1795,5357,1853],{},[1832,5359,1989],{},[1840,5361,1842],{},[238,5363,5364],{"encoding":240},"\\operatorname{int}\\Delta^{K-1}",[128,5366,5368],{"className":5367,"ariaHidden":246},[245],[128,5369,5371,5374,5380,5383],{"className":5370},[250],[128,5372],{"className":5373,"style":2431},[254],[128,5375,5377],{"className":5376},[2268],[128,5378,3275],{"className":5379},[259,3353],[128,5381],{"className":5382,"style":1907},[269],[128,5384,5386,5389],{"className":5385},[259],[128,5387,1982],{"className":5388},[259],[128,5390,5392],{"className":5391},[2087],[128,5393,5395],{"className":5394},[274],[128,5396,5398],{"className":5397},[278],[128,5399,5401],{"className":5400,"style":2431},[282],[128,5402,5403,5406],{"style":2452},[128,5404],{"className":5405,"style":291},[290],[128,5407,5409],{"className":5408},[299,300,301,298],[128,5410,5412,5415,5418],{"className":5411},[259,298],[128,5413,1853],{"className":5414,"style":1924},[259,1873,298],[128,5416,1989],{"className":5417},[2115,298],[128,5419,1842],{"className":5420},[259,298],"，且关于上述参考测度的密度为\n",[128,5423,5425,5502],{"className":5424,"translate":218},[217],[128,5426,5428],{"className":5427},[222],[224,5429,5430],{"xmlns":226},[228,5431,5432,5499],{},[231,5433,5434,5437,5439,5441,5444,5446,5448,5450,5466,5481],{},[1795,5435,5436],{},"f",[1832,5438,2477],{"stretchy":1837},[1795,5440,2760],{"mathvariant":2001},[1832,5442,5443],{},"∣",[1795,5445,4835],{"mathvariant":4834},[1832,5447,2486],{"stretchy":1837},[1832,5449,1994],{},[5451,5452,5453,5455],"mfrac",{},[1840,5454,1842],{},[231,5456,5457,5460,5462,5464],{},[1795,5458,5459],{},"B",[1832,5461,2477],{"stretchy":1837},[1795,5463,4835],{"mathvariant":4834},[1832,5465,2486],{"stretchy":1837},[2038,5467,5468,5471,5479],{},[1832,5469,5470],{},"∏",[231,5472,5473,5475,5477],{},[1795,5474,2801],{},[1832,5476,1994],{},[1840,5478,1842],{},[1795,5480,1853],{},[2038,5482,5483,5485,5487],{},[1795,5484,2760],{},[1795,5486,2801],{},[231,5488,5489,5495,5497],{},[2016,5490,5491,5493],{},[1795,5492,4835],{},[1795,5494,2801],{},[1832,5496,1989],{},[1840,5498,1842],{},[238,5500,5501],{"encoding":240},"f(\\mathbf{x} \\mid \\boldsymbol{\\alpha}) = \\frac{1}{B(\\boldsymbol{\\alpha})} \\prod_{i=1}^K x_i^{\\alpha_i - 1}",[128,5503,5505,5530,5557],{"className":5504,"ariaHidden":246},[245],[128,5506,5508,5511,5515,5518,5521,5524,5527],{"className":5507},[250],[128,5509],{"className":5510,"style":1892},[254],[128,5512,5436],{"className":5513,"style":5514},[259,1873],"margin-right:0.1076em;",[128,5516,2477],{"className":5517},[1896],[128,5519,2760],{"className":5520},[259,2151],[128,5522],{"className":5523,"style":1878},[269],[128,5525,5443],{"className":5526},[1882],[128,5528],{"className":5529,"style":1878},[269],[128,5531,5533,5536,5545,5548,5551,5554],{"className":5532},[250],[128,5534],{"className":5535,"style":1892},[254],[128,5537,5539],{"className":5538},[259],[128,5540,5542],{"className":5541},[259],[128,5543,4835],{"className":5544},[259,4895],[128,5546,2486],{"className":5547},[1928],[128,5549],{"className":5550,"style":1878},[269],[128,5552,1994],{"className":5553},[1882],[128,5555],{"className":5556,"style":1878},[269],[128,5558,5560,5564,5656,5659,5719,5722],{"className":5559},[250],[128,5561],{"className":5562,"style":5563},[254],"height:1.5012em;vertical-align:-0.52em;",[128,5565,5567,5571,5653],{"className":5566},[259],[128,5568],{"className":5569},[1896,5570],"nulldelimiter",[128,5572,5574],{"className":5573},[5451],[128,5575,5577,5644],{"className":5576},[274,321],[128,5578,5580,5641],{"className":5579},[278],[128,5581,5584,5615,5626],{"className":5582,"style":5583},[282],"height:0.8451em;",[128,5585,5587,5590],{"style":5586},"top:-2.655em;",[128,5588],{"className":5589,"style":335},[290],[128,5591,5593],{"className":5592},[299,300,301,298],[128,5594,5596,5600,5603,5612],{"className":5595},[259,298],[128,5597,5459],{"className":5598,"style":5599},[259,1873,298],"margin-right:0.0502em;",[128,5601,2477],{"className":5602},[1896,298],[128,5604,5606],{"className":5605},[259,298],[128,5607,5609],{"className":5608},[259,298],[128,5610,4835],{"className":5611},[259,4895,298],[128,5613,2486],{"className":5614},[1928,298],[128,5616,5618,5621],{"style":5617},"top:-3.23em;",[128,5619],{"className":5620,"style":335},[290],[128,5622],{"className":5623,"style":5625},[5624],"frac-line","border-bottom-width:0.04em;",[128,5627,5629,5632],{"style":5628},"top:-3.394em;",[128,5630],{"className":5631,"style":335},[290],[128,5633,5635],{"className":5634},[299,300,301,298],[128,5636,5638],{"className":5637},[259,298],[128,5639,1842],{"className":5640},[259,298],[128,5642,347],{"className":5643},[346],[128,5645,5647],{"className":5646},[278],[128,5648,5651],{"className":5649,"style":5650},[282],"height:0.52em;",[128,5652],{},[128,5654],{"className":5655},[1928,5570],[128,5657],{"className":5658,"style":1907},[269],[128,5660,5662,5665],{"className":5661},[2268],[128,5663,5470],{"className":5664,"style":2274},[2268,2272,2273],[128,5666,5668],{"className":5667},[2087],[128,5669,5671,5711],{"className":5670},[274,321],[128,5672,5674,5708],{"className":5673},[278],[128,5675,5677,5697],{"className":5676,"style":2287},[282],[128,5678,5679,5682],{"style":2290},[128,5680],{"className":5681,"style":291},[290],[128,5683,5685],{"className":5684},[299,300,301,298],[128,5686,5688,5691,5694],{"className":5687},[259,298],[128,5689,2801],{"className":5690},[259,1873,298],[128,5692,1994],{"className":5693},[1882,298],[128,5695,1842],{"className":5696},[259,298],[128,5698,5699,5702],{"style":2311},[128,5700],{"className":5701,"style":291},[290],[128,5703,5705],{"className":5704},[299,300,301,298],[128,5706,1853],{"className":5707,"style":1924},[259,1873,298],[128,5709,347],{"className":5710},[346],[128,5712,5714],{"className":5713},[278],[128,5715,5717],{"className":5716,"style":2330},[282],[128,5718],{},[128,5720],{"className":5721,"style":1907},[269],[128,5723,5725,5728],{"className":5724},[259],[128,5726,2760],{"className":5727},[259,1873],[128,5729,5731],{"className":5730},[2087],[128,5732,5734,5820],{"className":5733},[274,321],[128,5735,5737,5817],{"className":5736},[278],[128,5738,5741,5753],{"className":5739,"style":5740},[282],"height:0.896em;",[128,5742,5744,5747],{"style":5743},"top:-2.4231em;margin-left:0em;margin-right:0.05em;",[128,5745],{"className":5746,"style":291},[290],[128,5748,5750],{"className":5749},[299,300,301,298],[128,5751,2801],{"className":5752},[259,1873,298],[128,5754,5756,5759],{"style":5755},"top:-3.1449em;margin-right:0.05em;",[128,5757],{"className":5758,"style":291},[290],[128,5760,5762],{"className":5761},[299,300,301,298],[128,5763,5765,5811,5814],{"className":5764},[259,298],[128,5766,5768,5771],{"className":5767},[259,298],[128,5769,4835],{"className":5770,"style":4920},[259,1873,298],[128,5772,5774],{"className":5773},[2087],[128,5775,5777,5802],{"className":5776},[274,321],[128,5778,5780,5799],{"className":5779},[278],[128,5781,5784],{"className":5782,"style":5783},[282],"height:0.3281em;",[128,5785,5787,5791],{"style":5786},"top:-2.357em;margin-left:-0.0037em;margin-right:0.0714em;",[128,5788],{"className":5789,"style":5790},[290],"height:2.5em;",[128,5792,5796],{"className":5793},[299,5794,5795,298],"res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",[128,5831,5833,5846],{"className":5832,"translate":218},[217],[128,5834,5836],{"className":5835},[222],[224,5837,5838],{"xmlns":226},[228,5839,5840,5844],{},[231,5841,5842],{},[1795,5843,2760],{"mathvariant":2001},[238,5845,4429],{"encoding":240},[128,5847,5849],{"className":5848,"ariaHidden":246},[245],[128,5850,5852,5855],{"className":5851},[250],[128,5853],{"className":5854,"style":4439},[254],[128,5856,2760],{"className":5857},[259,2151]," 服从参数为 ",[128,5860,5862,5876],{"className":5861,"translate":218},[217],[128,5863,5865],{"className":5864},[222],[224,5866,5867],{"xmlns":226},[228,5868,5869,5873],{},[231,5870,5871],{},[1795,5872,4835],{"mathvariant":4834},[238,5874,5875],{"encoding":240},"\\boldsymbol{\\alpha}",[128,5877,5879],{"className":5878,"ariaHidden":246},[245],[128,5880,5882,5885],{"className":5881},[250],[128,5883],{"className":5884,"style":4439},[254],[128,5886,5888],{"className":5887},[259],[128,5889,5891],{"className":5890},[259],[128,5892,4835],{"className":5893},[259,4895]," 的迪利克雷分布，记作 ",[128,5896,5898,5926],{"className":5897,"translate":218},[217],[128,5899,5901],{"className":5900},[222],[224,5902,5903],{"xmlns":226},[228,5904,5905,5923],{},[231,5906,5907,5909,5912,5915,5917,5919,5921],{},[1795,5908,2760],{"mathvariant":2001},[1832,5910,5911],{},"∼",[1795,5913,5914],{"mathvariant":1981},"Dir",[1832,5916,3278],{},[1832,5918,2477],{"stretchy":1837},[1795,5920,4835],{"mathvariant":4834},[1832,5922,2486],{"stretchy":1837},[238,5924,5925],{"encoding":240},"\\mathbf{x} \\sim \\operatorname{Dir}(\\boldsymbol{\\alpha})",[128,5927,5929,5947],{"className":5928,"ariaHidden":246},[245],[128,5930,5932,5935,5938,5941,5944],{"className":5931},[250],[128,5933],{"className":5934,"style":4439},[254],[128,5936,2760],{"className":5937},[259,2151],[128,5939],{"className":5940,"style":1878},[269],[128,5942,5911],{"className":5943},[1882],[128,5945],{"className":5946,"style":1878},[269],[128,5948,5950,5953,5959,5962,5971],{"className":5949},[250],[128,5951],{"className":5952,"style":1892},[254],[128,5954,5956],{"className":5955},[2268],[128,5957,5914],{"className":5958},[259,3353],[128,5960,2477],{"className":5961},[1896],[128,5963,5965],{"className":5964},[259],[128,5966,5968],{"className":5967},[259],[128,5969,4835],{"className":5970},[259,4895],[128,5972,2486],{"className":5973},[1928],"。其中归一化常数为",[35,5976,5977],{},"多元 Beta 函数",[128,5979,5981,6050],{"className":5980,"translate":218},[217],[128,5982,5984],{"className":5983},[222],[224,5985,5986],{"xmlns":226},[228,5987,5988,6047],{},[231,5989,5990,5992,5994,5996,5998,6000],{},[1795,5991,5459],{},[1832,5993,2477],{"stretchy":1837},[1795,5995,4835],{"mathvariant":4834},[1832,5997,2486],{"stretchy":1837},[1832,5999,1994],{},[5451,6001,6002,6031],{},[231,6003,6004,6018,6021,6023,6029],{},[2038,6005,6006,6008,6016],{},[1832,6007,5470],{},[231,6009,6010,6012,6014],{},[1795,6011,2801],{},[1832,6013,1994],{},[1840,6015,1842],{},[1795,6017,1853],{},[1795,6019,6020],{"mathvariant":1981},"Γ",[1832,6022,2477],{"stretchy":1837},[2016,6024,6025,6027],{},[1795,6026,4835],{},[1795,6028,2801],{},[1832,6030,2486],{"stretchy":1837},[231,6032,6033,6035],{},[1795,6034,6020],{"mathvariant":1981},[231,6036,6037,6039,6045],{},[1832,6038,2477],{"fence":246},[2016,6040,6041,6043],{},[1795,6042,4835],{},[1840,6044,2028],{},[1832,6046,2486],{"fence":246},[238,6048,6049],{"encoding":240},"B(\\boldsymbol{\\alpha}) = \\frac{\\prod_{i=1}^K \\Gamma(\\alpha_i)}{\\Gamma\\left(\\alpha_0\\right)}",[128,6051,6053,6086],{"className":6052,"ariaHidden":246},[245],[128,6054,6056,6059,6062,6065,6074,6077,6080,6083],{"className":6055},[250],[128,6057],{"className":6058,"style":1892},[254],[128,6060,5459],{"className":6061,"style":5599},[259,1873],[128,6063,2477],{"className":6064},[1896],[128,6066,6068],{"className":6067},[259],[128,6069,6071],{"className":6070},[259],[128,6072,4835],{"className":6073},[259,4895],[128,6075,2486],{"className":6076},[1928],[128,6078],{"className":6079,"style":1878},[269],[128,6081,1994],{"className":6082},[1882],[128,6084],{"className":6085,"style":1878},[269],[128,6087,6089,6093],{"className":6088},[250],[128,6090],{"className":6091,"style":6092},[254],"height:1.6984em;vertical-align:-0.52em;",[128,6094,6096,6099,6330],{"className":6095},[259],[128,6097],{"className":6098},[1896,5570],[128,6100,6102],{"className":6101},[5451],[128,6103,6105,6322],{"className":6104},[274,321],[128,6106,6108,6319],{"className":6107},[278],[128,6109,6112,6182,6190],{"className":6110,"style":6111},[282],"height:1.1784em;",[128,6113,6114,6117],{"style":5586},[128,6115],{"className":6116,"style":335},[290],[128,6118,6120],{"className":6119},[299,300,301,298],[128,6121,6123,6126],{"className":6122},[259,298],[128,6124,6020],{"className":6125},[259,298],[128,6127,6129,6135,6176],{"className":6128},[1911,298],[128,6130,6132],{"className":6131,"style":2142},[1896,298,2141],[128,6133,2477],{"className":6134},[298],[128,6136,6138,6141],{"className":6137},[259,298],[128,6139,4835],{"className":6140,"style":4920},[259,1873,298],[128,6142,6144],{"className":6143},[2087],[128,6145,6147,6168],{"className":6146},[274,321],[128,6148,6150,6165],{"className":6149},[278],[128,6151,6154],{"className":6152,"style":6153},[282],"height:0.3173em;",[128,6155,6156,6159],{"style":5786},[128,6157],{"className":6158,"style":5790},[290],[128,6160,6162],{"className":6161},[299,5794,5795,298],[128,6163,2028],{"className":6164},[259,298],[128,6166,347],{"className":6167},[346],[128,6169,6171],{"className":6170},[278],[128,6172,6174],{"className":6173,"style":5808},[282],[128,6175],{},[128,6177,6179],{"className":6178,"style":2142},[1928,298,2141],[128,6180,2486],{"className":6181},[298],[128,6183,6184,6187],{"style":5617},[128,6185],{"className":6186,"style":335},[290],[128,6188],{"className":6189,"style":5625},[5624],[128,6191,6193,6196],{"style":6192},"top:-3.535em;",[128,6194],{"className":6195,"style":335},[290],[128,6197,6199],{"className":6198},[299,300,301,298],[128,6200,6202,6266,6270,6273,6276,6316],{"className":6201},[259,298],[128,6203,6205,6208],{"className":6204},[2268,298],[128,6206,5470],{"className":6207,"style":2274},[2268,2272,2273,298],[128,6209,6211],{"className":6210},[2087],[128,6212,6214,6257],{"className":6213},[274,321],[128,6215,6217,6254],{"className":6216},[278],[128,6218,6221,6242],{"className":6219,"style":6220},[282],"height:0.9191em;",[128,6222,6224,6227],{"style":6223},"top:-2.1786em;margin-left:0em;margin-right:0.0714em;",[128,6225],{"className":6226,"style":5790},[290],[128,6228,6230],{"className":6229},[299,5794,5795,298],[128,6231,6233,6236,6239],{"className":6232},[259,298],[128,6234,2801],{"className":6235},[259,1873,298],[128,6237,1994],{"className":6238},[1882,298],[128,6240,1842],{"className":6241},[259,298],[128,6243,6245,6248],{"style":6244},"top:-2.931em;margin-right:0.0714em;",[128,6246],{"className":6247,"style":5790},[290],[128,6249,6251],{"className":6250},[299,5794,5795,298],[128,6252,1853],{"className":6253,"style":1924},[259,1873,298],[128,6255,347],{"className":6256},[346],[128,6258,6260],{"className":6259},[278],[128,6261,6264],{"className":6262,"style":6263},[282],"height:0.3214em;",[128,6265],{},[128,6267],{"className":6268,"style":6269},[269,298],"margin-right:0.1952em;",[128,6271,6020],{"className":6272},[259,298],[128,6274,2477],{"className":6275},[1896,298],[128,6277,6279,6282],{"className":6278},[259,298],[128,6280,4835],{"className":6281,"style":4920},[259,1873,298],[128,6283,6285],{"className":6284},[2087],[128,6286,6288,6308],{"className":6287},[274,321],[128,6289,6291,6305],{"className":6290},[278],[128,6292,6294],{"className":6293,"style":5783},[282],[128,6295,6296,6299],{"style":5786},[128,6297],{"className":6298,"style":5790},[290],[128,6300,6302],{"className":6301},[299,5794,5795,298],[128,6303,2801],{"className":6304},[259,1873,298],[128,6306,347],{"className":6307},[346],[128,6309,6311],{"className":6310},[278],[128,6312,6314],{"className":6313,"style":5808},[282],[128,6315],{},[128,6317,2486],{"className":6318},[1928,298],[128,6320,347],{"className":6321},[346],[128,6323,6325],{"className":6324},[278],[128,6326,6328],{"className":6327,"style":5650},[282],[128,6329],{},[128,6331],{"className":6332},[1928,5570],[11,6334,6335],{},"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。",[2615,6337,6339],{"title":6338},"命题 1.3（归一化恒等式）",[11,6340,6341,6342,6464,6465],{},"对任意 ",[128,6343,6345,6373],{"className":6344,"translate":218},[217],[128,6346,6348],{"className":6347},[222],[224,6349,6350],{"xmlns":226},[228,6351,6352,6370],{},[231,6353,6354,6356,6358],{},[1795,6355,4835],{"mathvariant":4834},[1832,6357,1834],{},[2038,6359,6360,6362,6368],{},[1795,6361,2009],{"mathvariant":2008},[231,6363,6364,6366],{},[1832,6365,3321],{},[1840,6367,2028],{},[1795,6369,1853],{},[238,6371,6372],{"encoding":240},"\\boldsymbol{\\alpha} \\in \\mathbb{R}_{>0}^K",[128,6374,6376,6401],{"className":6375,"ariaHidden":246},[245],[128,6377,6379,6383,6392,6395,6398],{"className":6378},[250],[128,6380],{"className":6381,"style":6382},[254],"height:0.5782em;vertical-align:-0.0391em;",[128,6384,6386],{"className":6385},[259],[128,6387,6389],{"className":6388},[259],[128,6390,4835],{"className":6391},[259,4895],[128,6393],{"className":6394,"style":1878},[269],[128,6396,1834],{"className":6397},[1882],[128,6399],{"className":6400,"style":1878},[269],[128,6402,6404,6407],{"className":6403},[250],[128,6405],{"className":6406,"style":5032},[254],[128,6408,6410,6413],{"className":6409},[259],[128,6411,2009],{"className":6412},[259,2167],[128,6414,6416],{"className":6415},[2087],[128,6417,6419,6456],{"className":6418},[274,321],[128,6420,6422,6453],{"className":6421},[278],[128,6423,6425,6442],{"className":6424,"style":2431},[282],[128,6426,6427,6430],{"style":5053},[128,6428],{"className":6429,"style":291},[290],[128,6431,6433],{"className":6432},[299,300,301,298],[128,6434,6436,6439],{"className":6435},[259,298],[128,6437,3321],{"className":6438},[1882,298],[128,6440,2028],{"className":6441},[259,298],[128,6443,6444,6447],{"style":2452},[128,6445],{"className":6446,"style":291},[290],[128,6448,6450],{"className":6449},[299,300,301,298],[128,6451,1853],{"className":6452,"style":1924},[259,1873,298],[128,6454,347],{"className":6455},[346],[128,6457,6459],{"className":6458},[278],[128,6460,6462],{"className":6461,"style":5089},[282],[128,6463],{},"，\n",[128,6466,6468,6546],{"className":6467,"translate":218},[217],[128,6469,6471],{"className":6470},[222],[224,6472,6473],{"xmlns":226},[228,6474,6475,6543],{},[231,6476,6477,6494,6508,6526,6529,6531,6533,6535,6537,6539,6541],{},[2016,6478,6479,6482],{},[1832,6480,6481],{},"∫",[1977,6483,6484,6486],{},[1795,6485,1982],{"mathvariant":1981},[231,6487,6488,6490,6492],{},[1795,6489,1853],{},[1832,6491,1989],{},[1840,6493,1842],{},[2038,6495,6496,6498,6506],{},[1832,6497,5470],{},[231,6499,6500,6502,6504],{},[1795,6501,2801],{},[1832,6503,1994],{},[1840,6505,1842],{},[1795,6507,1853],{},[2038,6509,6510,6512,6514],{},[1795,6511,2760],{},[1795,6513,2801],{},[231,6515,6516,6522,6524],{},[2016,6517,6518,6520],{},[1795,6519,4835],{},[1795,6521,2801],{},[1832,6523,1989],{},[1840,6525,1842],{},[234,6527,6528],{}," ",[1795,6530,4519],{"mathvariant":1981},[1795,6532,2760],{"mathvariant":2001},[1832,6534,1994],{},[1795,6536,5459],{},[1832,6538,2477],{"stretchy":1837},[1795,6540,4835],{"mathvariant":4834},[1832,6542,2486],{"stretchy":1837},[238,6544,6545],{"encoding":240},"\\int_{\\Delta^{K-1}} \\prod_{i=1}^K x_i^{\\alpha_i - 1} \\,\\mathrm{d}\\mathbf{x} = B(\\boldsymbol{\\alpha})",[128,6547,6549,6821],{"className":6548,"ariaHidden":246},[245],[128,6550,6552,6556,6640,6643,6703,6706,6803,6806,6809,6812,6815,6818],{"className":6551},[250],[128,6553],{"className":6554,"style":6555},[254],"height:1.3371em;vertical-align:-0.3558em;",[128,6557,6559,6563],{"className":6558},[2268],[128,6560,6481],{"className":6561,"style":6562},[2268,2272,2273],"margin-right:0.1945em;position:relative;top:-0.0006em;",[128,6564,6566],{"className":6565},[2087],[128,6567,6569,6631],{"className":6568},[274,321],[128,6570,6572,6628],{"className":6571},[278],[128,6573,6576],{"className":6574,"style":6575},[282],"height:0.186em;",[128,6577,6579,6582],{"style":6578},"top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;",[128,6580],{"className":6581,"style":291},[290],[128,6583,6585],{"className":6584},[299,300,301,298],[128,6586,6588],{"className":6587},[259,298],[128,6589,6591,6594],{"className":6590},[259,298],[128,6592,1982],{"className":6593},[259,298],[128,6595,6597],{"className":6596},[2087],[128,6598,6600],{"className":6599},[274],[128,6601,6603],{"className":6602},[278],[128,6604,6607],{"className":6605,"style":6606},[282],"height:0.7741em;",[128,6608,6610,6613],{"style":6609},"top:-2.786em;margin-right:0.0714em;",[128,6611],{"className":6612,"style":5790},[290],[128,6614,6616],{"className":6615},[299,5794,5795,298],[128,6617,6619,6622,6625],{"className":6618},[259,298],[128,6620,1853],{"className":6621,"style":1924},[259,1873,298],[128,6623,1989],{"className":6624},[2115,298],[128,6626,1842],{"className":6627},[259,298],[128,6629,347],{"className":6630},[346],[128,6632,6634],{"className":6633},[278],[128,6635,6638],{"className":6636,"style":6637},[282],"height:0.3558em;",[128,6639],{},[128,6641],{"className":6642,"style":1907},[269],[128,6644,6646,6649],{"className":6645},[2268],[128,6647,5470],{"className":6648,"style":2274},[2268,2272,2273],[128,6650,6652],{"className":6651},[2087],[128,6653,6655,6695],{"className":6654},[274,321],[128,6656,6658,6692],{"className":6657},[278],[128,6659,6661,6681],{"className":6660,"style":2287},[282],[128,6662,6663,6666],{"style":2290},[128,6664],{"className":6665,"style":291},[290],[128,6667,6669],{"className":6668},[299,300,301,298],[128,6670,6672,6675,6678],{"className":6671},[259,298],[128,6673,2801],{"className":6674},[259,1873,298],[128,6676,1994],{"className":6677},[1882,298],[128,6679,1842],{"className":6680},[259,298],[128,6682,6683,6686],{"style":2311},[128,6684],{"className":6685,"style":291},[290],[128,6687,6689],{"className":6688},[299,300,301,298],[128,6690,1853],{"className":6691,"style":1924},[259,1873,298],[128,6693,347],{"className":6694},[346],[128,6696,6698],{"className":6697},[278],[128,6699,6701],{"className":6700,"style":2330},[282],[128,6702],{},[128,6704],{"className":6705,"style":1907},[269],[128,6707,6709,6712],{"className":6708},[259],[128,6710,2760],{"className":6711},[259,1873],[128,6713,6715],{"className":6714},[2087],[128,6716,6718,6795],{"className":6717},[274,321],[128,6719,6721,6792],{"className":6720},[278],[128,6722,6724,6735],{"className":6723,"style":5740},[282],[128,6725,6726,6729],{"style":5743},[128,6727],{"className":6728,"style":291},[290],[128,6730,6732],{"className":6731},[299,300,301,298],[128,6733,2801],{"className":6734},[259,1873,298],[128,6736,6737,6740],{"style":5755},[128,6738],{"className":6739,"style":291},[290],[128,6741,6743],{"className":6742},[299,300,301,298],[128,6744,6746,6786,6789],{"className":6745},[259,298],[128,6747,6749,6752],{"className":6748},[259,298],[128,6750,4835],{"className":6751,"style":4920},[259,1873,298],[128,6753,6755],{"className":6754},[2087],[128,6756,6758,6778],{"className":6757},[274,321],[128,6759,6761,6775],{"className":6760},[278],[128,6762,6764],{"className":6763,"style":5783},[282],[128,6765,6766,6769],{"style":5786},[128,6767],{"className":6768,"style":5790},[290],[128,6770,6772],{"className":6771},[299,5794,5795,298],[128,6773,2801],{"className":6774},[259,1873,298],[128,6776,347],{"className":6777},[346],[128,6779,6781],{"className":6780},[278],[128,6782,6784],{"className":6783,"style":5808},[282],[128,6785],{},[128,6787,1989],{"className":6788},[2115,298],[128,6790,1842],{"className":6791},[259,298],[128,6793,347],{"className":6794},[346],[128,6796,6798],{"className":6797},[278],[128,6799,6801],{"className":6800,"style":5826},[282],[128,6802],{},[128,6804],{"className":6805,"style":1907},[269],[128,6807,4519],{"className":6808},[259,3353],[128,6810,2760],{"className":6811},[259,2151],[128,6813],{"className":6814,"style":1878},[269],[128,6816,1994],{"className":6817},[1882],[128,6819],{"className":6820,"style":1878},[269],[128,6822,6824,6827,6830,6833,6842],{"className":6823},[250],[128,6825],{"className":6826,"style":1892},[254],[128,6828,5459],{"className":6829,"style":5599},[259,1873],[128,6831,2477],{"className":6832},[1896],[128,6834,6836],{"className":6835},[259],[128,6837,6839],{"className":6838},[259],[128,6840,4835],{"className":6841},[259,4895],[128,6843,2486],{"className":6844},[1928],[11,6846,6847,6850,6851,6944],{},[35,6848,6849],{},"证明"," 考虑 ",[128,6852,6854,6878],{"className":6853,"translate":218},[217],[128,6855,6857],{"className":6856},[222],[224,6858,6859],{"xmlns":226},[228,6860,6861,6875],{},[231,6862,6863],{},[2038,6864,6865,6867,6873],{},[1795,6866,2009],{"mathvariant":2008},[231,6868,6869,6871],{},[1832,6870,3321],{},[1840,6872,2028],{},[1795,6874,1853],{},[238,6876,6877],{"encoding":240},"\\mathbb{R}_{>0}^K",[128,6879,6881],{"className":6880,"ariaHidden":246},[245],[128,6882,6884,6887],{"className":6883},[250],[128,6885],{"className":6886,"style":5032},[254],[128,6888,6890,6893],{"className":6889},[259],[128,6891,2009],{"className":6892},[259,2167],[128,6894,6896],{"className":6895},[2087],[128,6897,6899,6936],{"className":6898},[274,321],[128,6900,6902,6933],{"className":6901},[278],[128,6903,6905,6922],{"className":6904,"style":2431},[282],[128,6906,6907,6910],{"style":5053},[128,6908],{"className":6909,"style":291},[290],[128,6911,6913],{"className":6912},[299,300,301,298],[128,6914,6916,6919],{"className":6915},[259,298],[128,6917,3321],{"className":6918},[1882,298],[128,6920,2028],{"className":6921},[259,298],[128,6923,6924,6927],{"style":2452},[128,6925],{"className":6926,"style":291},[290],[128,6928,6930],{"className":6929},[299,300,301,298],[128,6931,1853],{"className":6932,"style":1924},[259,1873,298],[128,6934,347],{"className":6935},[346],[128,6937,6939],{"className":6938},[278],[128,6940,6942],{"className":6941,"style":5089},[282],[128,6943],{}," 上的 Gamma 积分之积：",[128,6946,6948],{"className":6947,"translate":218},[1962],[128,6949,6951,7061],{"className":6950,"translate":218},[217],[128,6952,6954],{"className":6953},[222],[224,6955,6956],{"xmlns":226,"display":1971},[228,6957,6958,7058],{},[231,6959,6960,6975,6977,6979,6985,6987,6989,7005,7019,7038,7052,7054,7056],{},[6961,6962,6963,6965,6973],"munderover",{},[1832,6964,5470],{},[231,6966,6967,6969,6971],{},[1795,6968,2801],{},[1832,6970,1994],{},[1840,6972,1842],{},[1795,6974,1853],{},[1795,6976,6020],{"mathvariant":1981},[1832,6978,2477],{"stretchy":1837},[2016,6980,6981,6983],{},[1795,6982,4835],{},[1795,6984,2801],{},[1832,6986,2486],{"stretchy":1837},[1832,6988,1994],{},[2016,6990,6991,6993],{},[1832,6992,6481],{},[2038,6994,6995,6997,7003],{},[1795,6996,2009],{"mathvariant":2008},[231,6998,6999,7001],{},[1832,7000,3321],{},[1840,7002,2028],{},[1795,7004,1853],{},[6961,7006,7007,7009,7017],{},[1832,7008,5470],{},[231,7010,7011,7013,7015],{},[1795,7012,2801],{},[1832,7014,1994],{},[1840,7016,1842],{},[1795,7018,1853],{},[2038,7020,7021,7024,7026],{},[1795,7022,7023],{},"t",[1795,7025,2801],{},[231,7027,7028,7034,7036],{},[2016,7029,7030,7032],{},[1795,7031,4835],{},[1795,7033,2801],{},[1832,7035,1989],{},[1840,7037,1842],{},[1977,7039,7040,7042],{},[1795,7041,3713],{},[231,7043,7044,7046],{},[1832,7045,1989],{},[2016,7047,7048,7050],{},[1795,7049,7023],{},[1795,7051,2801],{},[234,7053,6528],{},[1795,7055,4519],{"mathvariant":1981},[1795,7057,7023],{"mathvariant":2001},[238,7059,7060],{"encoding":240},"\\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}",[128,7062,7064,7204],{"className":7063,"ariaHidden":246},[245],[128,7065,7067,7071,7143,7146,7149,7152,7192,7195,7198,7201],{"className":7066},[250],[128,7068],{"className":7069,"style":7070},[254],"height:3.106em;vertical-align:-1.2777em;",[128,7072,7075],{"className":7073},[2268,7074],"op-limits",[128,7076,7078,7134],{"className":7077},[274,321],[128,7079,7081,7131],{"className":7080},[278],[128,7082,7085,7107,7119],{"className":7083,"style":7084},[282],"height:1.8283em;",[128,7086,7088,7092],{"style":7087},"top:-1.8723em;margin-left:0em;",[128,7089],{"className":7090,"style":7091},[290],"height:3.05em;",[128,7093,7095],{"className":7094},[299,300,301,298],[128,7096,7098,7101,7104],{"className":7097},[259,298],[128,7099,2801],{"className":7100},[259,1873,298],[128,7102,1994],{"className":7103},[1882,298],[128,7105,1842],{"className":7106},[259,298],[128,7108,7110,7113],{"style":7109},"top:-3.05em;",[128,7111],{"className":7112,"style":7091},[290],[128,7114,7115],{},[128,7116,5470],{"className":7117},[2268,2272,7118],"large-op",[128,7120,7122,7125],{"style":7121},"top:-4.3em;margin-left:0em;",[128,7123],{"className":7124,"style":7091},[290],[128,7126,7128],{"className":7127},[299,300,301,298],[128,7129,1853],{"className":7130,"style":1924},[259,1873,298],[128,7132,347],{"className":7133},[346],[128,7135,7137],{"className":7136},[278],[128,7138,7141],{"className":7139,"style":7140},[282],"height:1.2777em;",[128,7142],{},[128,7144],{"className":7145,"style":1907},[269],[128,7147,6020],{"className":7148},[259],[128,7150,2477],{"className":7151},[1896],[128,7153,7155,7158],{"className":7154},[259],[128,7156,4835],{"className":7157,"style":4920},[259,1873],[128,7159,7161],{"className":7160},[2087],[128,7162,7164,7184],{"className":7163},[274,321],[128,7165,7167,7181],{"className":7166},[278],[128,7168,7170],{"className":7169,"style":3095},[282],[128,7171,7172,7175],{"style":4935},[128,7173],{"className":7174,"style":291},[290],[128,7176,7178],{"className":7177},[299,300,301,298],[128,7179,2801],{"className":7180},[259,1873,298],[128,7182,347],{"className":7183},[346],[128,7185,7187],{"className":7186},[278],[128,7188,7190],{"className":7189,"style":2241},[282],[128,7191],{},[128,7193,2486],{"className":7194},[1928],[128,7196],{"className":7197,"style":1878},[269],[128,7199,1994],{"className":7200},[1882],[128,7202],{"className":7203,"style":1878},[269],[128,7205,7207,7210,7315,7318,7382,7385,7482,7556,7559,7562],{"className":7206},[250],[128,7208],{"className":7209,"style":7070},[254],[128,7211,7213,7217],{"className":7212},[2268],[128,7214,6481],{"className":7215,"style":7216},[2268,2272,7118],"margin-right:0.4445em;position:relative;top:-0.0011em;",[128,7218,7220],{"className":7219},[2087],[128,7221,7223,7306],{"className":7222},[274,321],[128,7224,7226,7303],{"className":7225},[278],[128,7227,7230],{"className":7228,"style":7229},[282],"height:-0.3289em;",[128,7231,7233,7236],{"style":7232},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[128,7234],{"className":7235,"style":291},[290],[128,7237,7239],{"className":7238},[299,300,301,298],[128,7240,7242],{"className":7241},[259,298],[128,7243,7245,7248],{"className":7244},[259,298],[128,7246,2009],{"className":7247},[259,2167,298],[128,7249,7251],{"className":7250},[2087],[128,7252,7254,7294],{"className":7253},[274,321],[128,7255,7257,7291],{"className":7256},[278],[128,7258,7261,7279],{"className":7259,"style":7260},[282],"height:0.8329em;",[128,7262,7264,7267],{"style":7263},"top:-2.1885em;margin-left:0em;margin-right:0.0714em;",[128,7265],{"className":7266,"style":5790},[290],[128,7268,7270],{"className":7269},[299,5794,5795,298],[128,7271,7273,7276],{"className":7272},[259,298],[128,7274,3321],{"className":7275},[1882,298],[128,7277,2028],{"className":7278},[259,298],[128,7280,7282,7285],{"style":7281},"top:-2.8448em;margin-right:0.0714em;",[128,7283],{"className":7284,"style":5790},[290],[128,7286,7288],{"className":7287},[299,5794,5795,298],[128,7289,1853],{"className":7290,"style":1924},[259,1873,298],[128,7292,347],{"className":7293},[346],[128,7295,7297],{"className":7296},[278],[128,7298,7301],{"className":7299,"style":7300},[282],"height:0.3394em;",[128,7302],{},[128,7304,347],{"className":7305},[346],[128,7307,7309],{"className":7308},[278],[128,7310,7313],{"className":7311,"style":7312},[282],"height:1.1496em;",[128,7314],{},[128,7316],{"className":7317,"style":1907},[269],[128,7319,7321],{"className":7320},[2268,7074],[128,7322,7324,7374],{"className":7323},[274,321],[128,7325,7327,7371],{"className":7326},[278],[128,7328,7330,7350,7360],{"className":7329,"style":7084},[282],[128,7331,7332,7335],{"style":7087},[128,7333],{"className":7334,"style":7091},[290],[128,7336,7338],{"className":7337},[299,300,301,298],[128,7339,7341,7344,7347],{"className":7340},[259,298],[128,7342,2801],{"className":7343},[259,1873,298],[128,7345,1994],{"className":7346},[1882,298],[128,7348,1842],{"className":7349},[259,298],[128,7351,7352,7355],{"style":7109},[128,7353],{"className":7354,"style":7091},[290],[128,7356,7357],{},[128,7358,5470],{"className":7359},[2268,2272,7118],[128,7361,7362,7365],{"style":7121},[128,7363],{"className":7364,"style":7091},[290],[128,7366,7368],{"className":7367},[299,300,301,298],[128,7369,1853],{"className":7370,"style":1924},[259,1873,298],[128,7372,347],{"className":7373},[346],[128,7375,7377],{"className":7376},[278],[128,7378,7380],{"className":7379,"style":7140},[282],[128,7381],{},[128,7383],{"className":7384,"style":1907},[269],[128,7386,7388,7391],{"className":7387},[259],[128,7389,7023],{"className":7390},[259,1873],[128,7392,7394],{"className":7393},[2087],[128,7395,7397,7474],{"className":7396},[274,321],[128,7398,7400,7471],{"className":7399},[278],[128,7401,7403,7414],{"className":7402,"style":5740},[282],[128,7404,7405,7408],{"style":5743},[128,7406],{"className":7407,"style":291},[290],[128,7409,7411],{"className":7410},[299,300,301,298],[128,7412,2801],{"className":7413},[259,1873,298],[128,7415,7416,7419],{"style":5755},[128,7417],{"className":7418,"style":291},[290],[128,7420,7422],{"className":7421},[299,300,301,298],[128,7423,7425,7465,7468],{"className":7424},[259,298],[128,7426,7428,7431],{"className":7427},[259,298],[128,7429,4835],{"className":7430,"style":4920},[259,1873,298],[128,7432,7434],{"className":7433},[2087],[128,7435,7437,7457],{"className":7436},[274,321],[128,7438,7440,7454],{"className":7439},[278],[128,7441,7443],{"className":7442,"style":5783},[282],[128,7444,7445,7448],{"style":5786},[128,7446],{"className":7447,"style":5790},[290],[128,7449,7451],{"className":7450},[299,5794,5795,298],[128,7452,2801],{"className":7453},[259,1873,298],[128,7455,347],{"className":7456},[346],[128,7458,7460],{"className":7459},[278],[128,7461,7463],{"className":7462,"style":5808},[282],[128,7464],{},[128,7466,1989],{"className":7467},[2115,298],[128,7469,1842],{"className":7470},[259,298],[128,7472,347],{"className":7473},[346],[128,7475,7477],{"className":7476},[278],[128,7478,7480],{"className":7479,"style":5826},[282],[128,7481],{},[128,7483,7485,7488],{"className":7484},[259],[128,7486,3713],{"className":7487},[259,1873],[128,7489,7491],{"className":7490},[2087],[128,7492,7494],{"className":7493},[274],[128,7495,7497],{"className":7496},[278],[128,7498,7501],{"className":7499,"style":7500},[282],"height:0.8436em;",[128,7502,7503,7506],{"style":2099},[128,7504],{"className":7505,"style":291},[290],[128,7507,7509],{"className":7508},[299,300,301,298],[128,7510,7512,7515],{"className":7511},[259,298],[128,7513,1989],{"className":7514},[259,298],[128,7516,7518,7521],{"className":7517},[259,298],[128,7519,7023],{"className":7520},[259,1873,298],[128,7522,7524],{"className":7523},[2087],[128,7525,7527,7548],{"className":7526},[274,321],[128,7528,7530,7545],{"className":7529},[278],[128,7531,7533],{"className":7532,"style":5783},[282],[128,7534,7536,7539],{"style":7535},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[128,7537],{"className":7538,"style":5790},[290],[128,7540,7542],{"className":7541},[299,5794,5795,298],[128,7543,2801],{"className":7544},[259,1873,298],[128,7546,347],{"className":7547},[346],[128,7549,7551],{"className":7550},[278],[128,7552,7554],{"className":7553,"style":5808},[282],[128,7555],{},[128,7557],{"className":7558,"style":1907},[269],[128,7560,4519],{"className":7561},[259,3353],[128,7563,7023],{"className":7564},[259,2151],[11,7566,7567,7568,7713,7714,1152,7880,7976,7977,8099,8100,8150,8151,8469],{},"作变量替换 ",[128,7569,7571,7602],{"className":7570,"translate":218},[217],[128,7572,7574],{"className":7573},[222],[224,7575,7576],{"xmlns":226},[228,7577,7578,7599],{},[231,7579,7580,7586,7588,7591,7593],{},[2016,7581,7582,7584],{},[1795,7583,7023],{},[1795,7585,2801],{},[1832,7587,1994],{},[1795,7589,7590],{},"s",[234,7592,6528],{},[2016,7594,7595,7597],{},[1795,7596,2760],{},[1795,7598,2801],{},[238,7600,7601],{"encoding":240},"t_i = s\\, x_i",[128,7603,7605,7661],{"className":7604,"ariaHidden":246},[245],[128,7606,7608,7612,7652,7655,7658],{"className":7607},[250],[128,7609],{"className":7610,"style":7611},[254],"height:0.7651em;vertical-align:-0.15em;",[128,7613,7615,7618],{"className":7614},[259],[128,7616,7023],{"className":7617},[259,1873],[128,7619,7621],{"className":7620},[2087],[128,7622,7624,7644],{"className":7623},[274,321],[128,7625,7627,7641],{"className":7626},[278],[128,7628,7630],{"className":7629,"style":3095},[282],[128,7631,7632,7635],{"style":2221},[128,7633],{"className":7634,"style":291},[290],[128,7636,7638],{"className":7637},[299,300,301,298],[128,7639,2801],{"className":7640},[259,1873,298],[128,7642,347],{"className":7643},[346],[128,7645,7647],{"className":7646},[278],[128,7648,7650],{"className":7649,"style":2241},[282],[128,7651],{},[128,7653],{"className":7654,"style":1878},[269],[128,7656,1994],{"className":7657},[1882],[128,7659],{"className":7660,"style":1878},[269],[128,7662,7664,7667,7670,7673],{"className":7663},[250],[128,7665],{"className":7666,"style":4242},[254],[128,7668,7590],{"className":7669},[259,1873],[128,7671],{"className":7672,"style":1907},[269],[128,7674,7676,7679],{"className":7675},[259],[128,7677,2760],{"className":7678},[259,1873],[128,7680,7682],{"className":7681},[2087],[128,7683,7685,7705],{"className":7684},[274,321],[128,7686,7688,7702],{"className":7687},[278],[128,7689,7691],{"className":7690,"style":3095},[282],[128,7692,7693,7696],{"style":2221},[128,7694],{"className":7695,"style":291},[290],[128,7697,7699],{"className":7698},[299,300,301,298],[128,7700,2801],{"className":7701},[259,1873,298],[128,7703,347],{"className":7704},[346],[128,7706,7708],{"className":7707},[278],[128,7709,7711],{"className":7710,"style":2241},[282],[128,7712],{},"，其中 ",[128,7715,7717,7749],{"className":7716,"translate":218},[217],[128,7718,7720],{"className":7719},[222],[224,7721,7722],{"xmlns":226},[228,7723,7724,7746],{},[231,7725,7726,7728,7730,7736,7742,7744],{},[1795,7727,7590],{},[1832,7729,1994],{},[2016,7731,7732,7734],{},[1832,7733,2042],{},[1795,7735,2801],{},[2016,7737,7738,7740],{},[1795,7739,7023],{},[1795,7741,2801],{},[1832,7743,3321],{},[1840,7745,2028],{},[238,7747,7748],{"encoding":240},"s = \\sum_i t_i > 0",[128,7750,7752,7771,7871],{"className":7751,"ariaHidden":246},[245],[128,7753,7755,7759,7762,7765,7768],{"className":7754},[250],[128,7756],{"className":7757,"style":7758},[254],"height:0.4306em;",[128,7760,7590],{"className":7761},[259,1873],[128,7763],{"className":7764,"style":1878},[269],[128,7766,1994],{"className":7767},[1882],[128,7769],{"className":7770,"style":1878},[269],[128,7772,7774,7778,7819,7822,7862,7865,7868],{"className":7773},[250],[128,7775],{"className":7776,"style":7777},[254],"height:1.0497em;vertical-align:-0.2997em;",[128,7779,7781,7784],{"className":7780},[2268],[128,7782,2042],{"className":7783,"style":2274},[2268,2272,2273],[128,7785,7787],{"className":7786},[2087],[128,7788,7790,7811],{"className":7789},[274,321],[128,7791,7793,7808],{"className":7792},[278],[128,7794,7797],{"className":7795,"style":7796},[282],"height:0.162em;",[128,7798,7799,7802],{"style":2290},[128,7800],{"className":7801,"style":291},[290],[128,7803,7805],{"className":7804},[299,300,301,298],[128,7806,2801],{"className":7807},[259,1873,298],[128,7809,347],{"className":7810},[346],[128,7812,7814],{"className":7813},[278],[128,7815,7817],{"className":7816,"style":2330},[282],[128,7818],{},[128,7820],{"className":7821,"style":1907},[269],[128,7823,7825,7828],{"className":7824},[259],[128,7826,7023],{"className":7827},[259,1873],[128,7829,7831],{"className":7830},[2087],[128,7832,7834,7854],{"className":7833},[274,321],[128,7835,7837,7851],{"className":7836},[278],[128,7838,7840],{"className":7839,"style":3095},[282],[128,7841,7842,7845],{"style":2221},[128,7843],{"className":7844,"style":291},[290],[128,7846,7848],{"className":7847},[299,300,301,298],[128,7849,2801],{"className":7850},[259,1873,298],[128,7852,347],{"className":7853},[346],[128,7855,7857],{"className":7856},[278],[128,7858,7860],{"className":7859,"style":2241},[282],[128,7861],{},[128,7863],{"className":7864,"style":1878},[269],[128,7866,3321],{"className":7867},[1882],[128,7869],{"className":7870,"style":1878},[269],[128,7872,7874,7877],{"className":7873},[250],[128,7875],{"className":7876,"style":2594},[254],[128,7878,2028],{"className":7879},[259],[128,7881,7883,7911],{"className":7882,"translate":218},[217],[128,7884,7886],{"className":7885},[222],[224,7887,7888],{"xmlns":226},[228,7889,7890,7908],{},[231,7891,7892,7894,7896],{},[1795,7893,2760],{"mathvariant":2001},[1832,7895,1834],{},[1977,7897,7898,7900],{},[1795,7899,1982],{"mathvariant":1981},[231,7901,7902,7904,7906],{},[1795,7903,1853],{},[1832,7905,1989],{},[1840,7907,1842],{},[238,7909,7910],{"encoding":240},"\\mathbf{x} \\in \\Delta^{K-1}",[128,7912,7914,7932],{"className":7913,"ariaHidden":246},[245],[128,7915,7917,7920,7923,7926,7929],{"className":7916},[250],[128,7918],{"className":7919,"style":6382},[254],[128,7921,2760],{"className":7922},[259,2151],[128,7924],{"className":7925,"style":1878},[269],[128,7927,1834],{"className":7928},[1882],[128,7930],{"className":7931,"style":1878},[269],[128,7933,7935,7938],{"className":7934},[250],[128,7936],{"className":7937,"style":2431},[254],[128,7939,7941,7944],{"className":7940},[259],[128,7942,1982],{"className":7943},[259],[128,7945,7947],{"className":7946},[2087],[128,7948,7950],{"className":7949},[274],[128,7951,7953],{"className":7952},[278],[128,7954,7956],{"className":7955,"style":2431},[282],[128,7957,7958,7961],{"style":2452},[128,7959],{"className":7960,"style":291},[290],[128,7962,7964],{"className":7963},[299,300,301,298],[128,7965,7967,7970,7973],{"className":7966},[259,298],[128,7968,1853],{"className":7969,"style":1924},[259,1873,298],[128,7971,1989],{"className":7972},[2115,298],[128,7974,1842],{"className":7975},[259,298],"。该替换的 Jacobi 行列式绝对值为 ",[128,7978,7980,8018],{"className":7979,"translate":218},[217],[128,7981,7983],{"className":7982},[222],[224,7984,7985],{"xmlns":226},[228,7986,7987,8015],{},[231,7988,7989,7991,7994,7996,7999,8001,8003],{},[1795,7990,5443],{"mathvariant":1981},[1795,7992,7993],{},"det",[1832,7995,3278],{},[1795,7997,7998],{},"J",[1795,8000,5443],{"mathvariant":1981},[1832,8002,1994],{},[1977,8004,8005,8007],{},[1795,8006,7590],{},[231,8008,8009,8011,8013],{},[1795,8010,1853],{},[1832,8012,1989],{},[1840,8014,1842],{},[238,8016,8017],{"encoding":240},"|\\det J| = s^{K-1}",[128,8019,8021,8055],{"className":8020,"ariaHidden":246},[245],[128,8022,8024,8027,8030,8033,8036,8039,8043,8046,8049,8052],{"className":8023},[250],[128,8025],{"className":8026,"style":1892},[254],[128,8028,5443],{"className":8029},[259],[128,8031],{"className":8032,"style":1907},[269],[128,8034,7993],{"className":8035},[2268],[128,8037],{"className":8038,"style":1907},[269],[128,8040,7998],{"className":8041,"style":8042},[259,1873],"margin-right:0.0962em;",[128,8044,5443],{"className":8045},[259],[128,8047],{"className":8048,"style":1878},[269],[128,8050,1994],{"className":8051},[1882],[128,8053],{"className":8054,"style":1878},[269],[128,8056,8058,8061],{"className":8057},[250],[128,8059],{"className":8060,"style":2431},[254],[128,8062,8064,8067],{"className":8063},[259],[128,8065,7590],{"className":8066},[259,1873],[128,8068,8070],{"className":8069},[2087],[128,8071,8073],{"className":8072},[274],[128,8074,8076],{"className":8075},[278],[128,8077,8079],{"className":8078,"style":2431},[282],[128,8080,8081,8084],{"style":2452},[128,8082],{"className":8083,"style":291},[290],[128,8085,8087],{"className":8086},[299,300,301,298],[128,8088,8090,8093,8096],{"className":8089},[259,298],[128,8091,1853],{"className":8092,"style":1924},[259,1873,298],[128,8094,1989],{"className":8095},[2115,298],[128,8097,1842],{"className":8098},[259,298],"（可由 ",[128,8101,8103,8120],{"className":8102,"translate":218},[217],[128,8104,8106],{"className":8105},[222],[224,8107,8108],{"xmlns":226},[228,8109,8110,8118],{},[231,8111,8112,8114,8116],{},[1795,8113,1853],{},[1832,8115,1994],{},[1840,8117,2639],{},[238,8119,3859],{"encoding":240},[128,8121,8123,8141],{"className":8122,"ariaHidden":246},[245],[128,8124,8126,8129,8132,8135,8138],{"className":8125},[250],[128,8127],{"className":8128,"style":283},[254],[128,8130,1853],{"className":8131,"style":1924},[259,1873],[128,8133],{"className":8134,"style":1878},[269],[128,8136,1994],{"className":8137},[1882],[128,8139],{"className":8140,"style":1878},[269],[128,8142,8144,8147],{"className":8143},[250],[128,8145],{"className":8146,"style":2594},[254],[128,8148,2639],{"className":8149},[259]," 时的 ",[128,8152,8154,8230],{"className":8153,"translate":218},[217],[128,8155,8157],{"className":8156},[222],[224,8158,8159],{"xmlns":226},[228,8160,8161,8227],{},[231,8162,8163,8165,8167,8221,8223,8225],{},[1795,8164,7993],{},[1832,8166,3278],{},[231,8168,8169,8171,8219],{},[1832,8170,2477],{"fence":246},[8172,8173,8177,8197],"mtable",{"rowspacing":8174,"columnalign":8175,"columnspacing":8176},"0.16em","center center","1em",[8178,8179,8180,8191],"mtr",{},[8181,8182,8183],"mtd",{},[2035,8184,8185],{"scriptlevel":2028,"displaystyle":1837},[2016,8186,8187,8189],{},[1795,8188,2760],{},[1840,8190,1842],{},[8181,8192,8193],{},[2035,8194,8195],{"scriptlevel":2028,"displaystyle":1837},[1795,8196,7590],{},[8178,8198,8199,8209],{},[8181,8200,8201],{},[2035,8202,8203],{"scriptlevel":2028,"displaystyle":1837},[2016,8204,8205,8207],{},[1795,8206,2760],{},[1840,8208,2639],{},[8181,8210,8211],{},[2035,8212,8213],{"scriptlevel":2028,"displaystyle":1837},[231,8214,8215,8217],{},[1832,8216,1989],{},[1795,8218,7590],{},[1832,8220,2486],{"fence":246},[1832,8222,1994],{},[1832,8224,1989],{},[1795,8226,7590],{},[238,8228,8229],{"encoding":240},"\\det\\begin{pmatrix} x_1 & s \\\\ x_2 & -s\\end{pmatrix} = -s",[128,8231,8233,8456],{"className":8232,"ariaHidden":246},[245],[128,8234,8236,8240,8243,8246,8447,8450,8453],{"className":8235},[250],[128,8237],{"className":8238,"style":8239},[254],"height:2.4em;vertical-align:-0.95em;",[128,8241,7993],{"className":8242},[2268],[128,8244],{"className":8245,"style":1907},[269],[128,8247,8249,8255,8441],{"className":8248},[1911],[128,8250,8252],{"className":8251,"style":2142},[1896,2141],[128,8253,2477],{"className":8254},[2146,301],[128,8256,8258],{"className":8257},[259],[128,8259,8261,8385,8390,8393],{"className":8260},[8172],[128,8262,8265],{"className":8263},[8264],"col-align-c",[128,8266,8268,8376],{"className":8267},[274,321],[128,8269,8271,8373],{"className":8270},[278],[128,8272,8275,8324],{"className":8273,"style":8274},[282],"height:1.45em;",[128,8276,8278,8281],{"style":8277},"top:-3.61em;",[128,8279],{"className":8280,"style":335},[290],[128,8282,8284],{"className":8283},[259],[128,8285,8287,8290],{"className":8286},[259],[128,8288,2760],{"className":8289},[259,1873],[128,8291,8293],{"className":8292},[2087],[128,8294,8296,8316],{"className":8295},[274,321],[128,8297,8299,8313],{"className":8298},[278],[128,8300,8302],{"className":8301,"style":2945},[282],[128,8303,8304,8307],{"style":2221},[128,8305],{"className":8306,"style":291},[290],[128,8308,8310],{"className":8309},[299,300,301,298],[128,8311,1842],{"className":8312},[259,298],[128,8314,347],{"className":8315},[346],[128,8317,8319],{"className":8318},[278],[128,8320,8322],{"className":8321,"style":2241},[282],[128,8323],{},[128,8325,8327,8330],{"style":8326},"top:-2.41em;",[128,8328],{"className":8329,"style":335},[290],[128,8331,8333],{"className":8332},[259],[128,8334,8336,8339],{"className":8335},[259],[128,8337,2760],{"className":8338},[259,1873],[128,8340,8342],{"className":8341},[2087],[128,8343,8345,8365],{"className":8344},[274,321],[128,8346,8348,8362],{"className":8347},[278],[128,8349,8351],{"className":8350,"style":2945},[282],[128,8352,8353,8356],{"style":2221},[128,8354],{"className":8355,"style":291},[290],[128,8357,8359],{"className":8358},[299,300,301,298],[128,8360,2639],{"className":8361},[259,298],[128,8363,347],{"className":8364},[346],[128,8366,8368],{"className":8367},[278],[128,8369,8371],{"className":8370,"style":2241},[282],[128,8372],{},[128,8374,347],{"className":8375},[346],[128,8377,8379],{"className":8378},[278],[128,8380,8383],{"className":8381,"style":8382},[282],"height:0.95em;",[128,8384],{},[128,8386],{"className":8387,"style":8389},[8388],"arraycolsep","width:0.5em;",[128,8391],{"className":8392,"style":8389},[8388],[128,8394,8396],{"className":8395},[8264],[128,8397,8399,8433],{"className":8398},[274,321],[128,8400,8402,8430],{"className":8401},[278],[128,8403,8405,8416],{"className":8404,"style":8274},[282],[128,8406,8407,8410],{"style":8277},[128,8408],{"className":8409,"style":335},[290],[128,8411,8413],{"className":8412},[259],[128,8414,7590],{"className":8415},[259,1873],[128,8417,8418,8421],{"style":8326},[128,8419],{"className":8420,"style":335},[290],[128,8422,8424,8427],{"className":8423},[259],[128,8425,1989],{"className":8426},[259],[128,8428,7590],{"className":8429},[259,1873],[128,8431,347],{"className":8432},[346],[128,8434,8436],{"className":8435},[278],[128,8437,8439],{"className":8438,"style":8382},[282],[128,8440],{},[128,8442,8444],{"className":8443,"style":2142},[1928,2141],[128,8445,2486],{"className":8446},[2146,301],[128,8448],{"className":8449,"style":1878},[269],[128,8451,1994],{"className":8452},[1882],[128,8454],{"className":8455,"style":1878},[269],[128,8457,8459,8463,8466],{"className":8458},[250],[128,8460],{"className":8461,"style":8462},[254],"height:0.6667em;vertical-align:-0.0833em;",[128,8464,1989],{"className":8465},[259],[128,8467,7590],{"className":8468},[259,1873]," 归纳验证）。代入得",[128,8471,8473],{"className":8472,"translate":218},[1962],[128,8474,8476,8633],{"className":8475,"translate":218},[217],[128,8477,8479],{"className":8478},[222],[224,8480,8481],{"xmlns":226,"display":1971},[228,8482,8483,8630],{},[231,8484,8485,8499,8501,8503,8509,8511,8513,8522,8525,8527,8543,8555,8569,8571,8573,8579,8595,8618,8620,8622,8624,8626,8628],{},[6961,8486,8487,8489,8497],{},[1832,8488,5470],{},[231,8490,8491,8493,8495],{},[1795,8492,2801],{},[1832,8494,1994],{},[1840,8496,1842],{},[1795,8498,1853],{},[1795,8500,6020],{"mathvariant":1981},[1832,8502,2477],{"stretchy":1837},[2016,8504,8505,8507],{},[1795,8506,4835],{},[1795,8508,2801],{},[1832,8510,2486],{"stretchy":1837},[1832,8512,1994],{},[2038,8514,8515,8517,8519],{},[1832,8516,6481],{},[1840,8518,2028],{},[1795,8520,8521],{"mathvariant":1981},"∞",[234,8523,8524],{}," ⁣",[234,8526,8524],{},[2016,8528,8529,8531],{},[1832,8530,6481],{},[1977,8532,8533,8535],{},[1795,8534,1982],{"mathvariant":1981},[231,8536,8537,8539,8541],{},[1795,8538,1853],{},[1832,8540,1989],{},[1840,8542,1842],{},[1977,8544,8545,8547],{},[1795,8546,7590],{},[231,8548,8549,8551,8553],{},[1795,8550,1853],{},[1832,8552,1989],{},[1840,8554,1842],{},[6961,8556,8557,8559,8567],{},[1832,8558,5470],{},[231,8560,8561,8563,8565],{},[1795,8562,2801],{},[1832,8564,1994],{},[1840,8566,1842],{},[1795,8568,1853],{},[1832,8570,2477],{"stretchy":1837},[1795,8572,7590],{},[2016,8574,8575,8577],{},[1795,8576,2760],{},[1795,8578,2801],{},[1977,8580,8581,8583],{},[1832,8582,2486],{"stretchy":1837},[231,8584,8585,8591,8593],{},[2016,8586,8587,8589],{},[1795,8588,4835],{},[1795,8590,2801],{},[1832,8592,1989],{},[1840,8594,1842],{},[1977,8596,8597,8599],{},[1795,8598,3713],{},[231,8600,8601,8603,8605,8612],{},[1832,8602,1989],{},[1795,8604,7590],{},[8606,8607,8608,8610],"munder",{},[1832,8609,2042],{},[1795,8611,2801],{},[2016,8613,8614,8616],{},[1795,8615,2760],{},[1795,8617,2801],{},[234,8619,6528],{},[1795,8621,4519],{"mathvariant":1981},[1795,8623,2760],{"mathvariant":2001},[234,8625,6528],{},[1795,8627,4519],{"mathvariant":1981},[1795,8629,7590],{},[238,8631,8632],{"encoding":240},"\\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",[128,8634,8636,8767],{"className":8635,"ariaHidden":246},[245],[128,8637,8639,8642,8706,8709,8712,8715,8755,8758,8761,8764],{"className":8638},[250],[128,8640],{"className":8641,"style":7070},[254],[128,8643,8645],{"className":8644},[2268,7074],[128,8646,8648,8698],{"className":8647},[274,321],[128,8649,8651,8695],{"className":8650},[278],[128,8652,8654,8674,8684],{"className":8653,"style":7084},[282],[128,8655,8656,8659],{"style":7087},[128,8657],{"className":8658,"style":7091},[290],[128,8660,8662],{"className":8661},[299,300,301,298],[128,8663,8665,8668,8671],{"className":8664},[259,298],[128,8666,2801],{"className":8667},[259,1873,298],[128,8669,1994],{"className":8670},[1882,298],[128,8672,1842],{"className":8673},[259,298],[128,8675,8676,8679],{"style":7109},[128,8677],{"className":8678,"style":7091},[290],[128,8680,8681],{},[128,8682,5470],{"className":8683},[2268,2272,7118],[128,8685,8686,8689],{"style":7121},[128,8687],{"className":8688,"style":7091},[290],[128,8690,8692],{"className":8691},[299,300,301,298],[128,8693,1853],{"className":8694,"style":1924},[259,1873,298],[128,8696,347],{"className":8697},[346],[128,8699,8701],{"className":8700},[278],[128,8702,8704],{"className":8703,"style":7140},[282],[128,8705],{},[128,8707],{"className":8708,"style":1907},[269],[128,8710,6020],{"className":8711},[259],[128,8713,2477],{"className":8714},[1896],[128,8716,8718,8721],{"className":8717},[259],[128,8719,4835],{"className":8720,"style":4920},[259,1873],[128,8722,8724],{"className":8723},[2087],[128,8725,8727,8747],{"className":8726},[274,321],[128,8728,8730,8744],{"className":8729},[278],[128,8731,8733],{"className":8732,"style":3095},[282],[128,8734,8735,8738],{"style":4935},[128,8736],{"className":8737,"style":291},[290],[128,8739,8741],{"className":8740},[299,300,301,298],[128,8742,2801],{"className":8743},[259,1873,298],[128,8745,347],{"className":8746},[346],[128,8748,8750],{"className":8749},[278],[128,8751,8753],{"className":8752,"style":2241},[282],[128,8754],{},[128,8756,2486],{"className":8757},[1928],[128,8759],{"className":8760,"style":1878},[269],[128,8762,1994],{"className":8763},[1882],[128,8765],{"className":8766,"style":1878},[269],[128,8768,8770,8773,8827,8830,8833,8836,8915,8918,8956,8959,9023,9026,9029,9069,9145,9268,9271,9274,9277,9280,9283],{"className":8769},[250],[128,8771],{"className":8772,"style":7070},[254],[128,8774,8776,8779],{"className":8775},[2268],[128,8777,6481],{"className":8778,"style":7216},[2268,2272,7118],[128,8780,8782],{"className":8781},[2087],[128,8783,8785,8818],{"className":8784},[274,321],[128,8786,8788,8815],{"className":8787},[278],[128,8789,8792,8803],{"className":8790,"style":8791},[282],"height:1.4143em;",[128,8793,8794,8797],{"style":7232},[128,8795],{"className":8796,"style":291},[290],[128,8798,8800],{"className":8799},[299,300,301,298],[128,8801,2028],{"className":8802},[259,298],[128,8804,8806,8809],{"style":8805},"top:-3.8129em;margin-right:0.05em;",[128,8807],{"className":8808,"style":291},[290],[128,8810,8812],{"className":8811},[299,300,301,298],[128,8813,8521],{"className":8814},[259,298],[128,8816,347],{"className":8817},[346],[128,8819,8821],{"className":8820},[278],[128,8822,8825],{"className":8823,"style":8824},[282],"height:0.9119em;",[128,8826],{},[128,8828],{"className":8829,"style":317},[269],[128,8831],{"className":8832,"style":317},[269],[128,8834],{"className":8835,"style":1907},[269],[128,8837,8839,8842],{"className":8838},[2268],[128,8840,6481],{"className":8841,"style":7216},[2268,2272,7118],[128,8843,8845],{"className":8844},[2087],[128,8846,8848,8907],{"className":8847},[274,321],[128,8849,8851,8904],{"className":8850},[278],[128,8852,8855],{"className":8853,"style":8854},[282],"height:-0.3701em;",[128,8856,8857,8860],{"style":7232},[128,8858],{"className":8859,"style":291},[290],[128,8861,8863],{"className":8862},[299,300,301,298],[128,8864,8866],{"className":8865},[259,298],[128,8867,8869,8872],{"className":8868},[259,298],[128,8870,1982],{"className":8871},[259,298],[128,8873,8875],{"className":8874},[2087],[128,8876,8878],{"className":8877},[274],[128,8879,8881],{"className":8880},[278],[128,8882,8884],{"className":8883,"style":6606},[282],[128,8885,8886,8889],{"style":6609},[128,8887],{"className":8888,"style":5790},[290],[128,8890,8892],{"className":8891},[299,5794,5795,298],[128,8893,8895,8898,8901],{"className":8894},[259,298],[128,8896,1853],{"className":8897,"style":1924},[259,1873,298],[128,8899,1989],{"className":8900},[2115,298],[128,8902,1842],{"className":8903},[259,298],[128,8905,347],{"className":8906},[346],[128,8908,8910],{"className":8909},[278],[128,8911,8913],{"className":8912,"style":8824},[282],[128,8914],{},[128,8916],{"className":8917,"style":1907},[269],[128,8919,8921,8924],{"className":8920},[259],[128,8922,7590],{"className":8923},[259,1873],[128,8925,8927],{"className":8926},[2087],[128,8928,8930],{"className":8929},[274],[128,8931,8933],{"className":8932},[278],[128,8934,8936],{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1",[128,9321,9323,9421],{"className":9322,"ariaHidden":246},[245],[128,9324,9326,9329,9369,9372,9412,9415,9418],{"className":9325},[250],[128,9327],{"className":9328,"style":7777},[254],[128,9330,9332,9335],{"className":9331},[2268],[128,9333,2042],{"className":9334,"style":2274},[2268,2272,2273],[128,9336,9338],{"className":9337},[2087],[128,9339,9341,9361],{"className":9340},[274,321],[128,9342,9344,9358],{"className":9343},[278],[128,9345,9347],{"className":9346,"style":7796},[282],[128,9348,9349,9352],{"style":2290},[128,9350],{"className":9351,"style":291},[290],[128,9353,9355],{"className":9354},[299,300,301,298],[128,9356,2801],{"className":9357},[259,1873,298],[128,9359,347],{"className":9360},[346],[128,9362,9364],{"className":9363},[278],[128,9365,9367],{"className":9366,"style":2330},[282],[128,9368],{},[128,9370],{"className":9371,"style":1907},[269],[128,9373,9375,9378],{"className":9374},[259],[128,9376,2760],{"className":9377},[259,1873],[128,9379,9381],{"className":9380},[2087],[128,9382,9384,9404],{"className":9383},[274,321],[128,9385,9387,9401],{"className":9386},[278],[128,9388,9390],{"className":9389,"style":3095},[282],[128,9391,9392,9395],{"style":2221},[128,9393],{"className":9394,"style":291},[290],[128,9396,9398],{"className":9397},[299,300,301,298],[128,9399,2801],{"className":9400},[259,1873,298],[128,9402,347],{"className":9403},[346],[128,9405,9407],{"className":9406},[278],[128,9408,9410],{"className":9409,"style":2241},[282],[128,9411],{},[128,9413],{"className":9414,"style":1878},[269],[128,9416,1994],{"className":9417},[1882],[128,9419],{"className":9420,"style":1878},[269],[128,9422,9424,9427],{"className":9423},[250],[128,9425],{"className":9426,"style":2594},[254],[128,9428,1842],{"className":9429},[259],"，被积函数中的 ",[128,9432,9434,9447],{"className":9433,"translate":218},[217],[128,9435,9437],{"className":9436},[222],[224,9438,9439],{"xmlns":226},[228,9440,9441,9445],{},[231,9442,9443],{},[1795,9444,7590],{},[238,9446,7590],{"encoding":240},[128,9448,9450],{"className":9449,"ariaHidden":246},[245],[128,9451,9453,9456],{"className":9452},[250],[128,9454],{"className":9455,"style":7758},[254],[128,9457,7590],{"className":9458},[259,1873]," 因子合并为 ",[128,9461,9463,9518],{"className":9462,"translate":218},[217],[128,9464,9466],{"className":9465},[222],[224,9467,9468],{"xmlns":226},[228,9469,9470,9515],{},[231,9471,9472,9497,9499],{},[1977,9473,9474,9476],{},[1795,9475,7590],{},[231,9477,9478,9480,9482,9484,9487,9493,9495],{},[1795,9479,1853],{},[1832,9481,1989],{},[1840,9483,1842],{},[1832,9485,9486],{},"+",[2016,9488,9489,9491],{},[1795,9490,4835],{},[1840,9492,2028],{},[1832,9494,1989],{},[1795,9496,1853],{},[1832,9498,1994],{},[1977,9500,9501,9503],{},[1795,9502,7590],{},[231,9504,9505,9511,9513],{},[2016,9506,9507,9509],{},[1795,9508,4835],{},[1840,9510,2028],{},[1832,9512,1989],{},[1840,9514,1842],{},[238,9516,9517],{"encoding":240},"s^{K - 1 + \\alpha_0 - K} = s^{\\alpha_0 - 1}",[128,9519,9521,9623],{"className":9520,"ariaHidden":246},[245],[128,9522,9524,9527,9614,9617,9620],{"className":9523},[250],[128,9525],{"className":9526,"style":2431},[254],[128,9528,9530,9533],{"className":9529},[259],[128,9531,7590],{"className":9532},[259,1873],[128,9534,9536],{"className":9535},[2087],[128,9537,9539],{"className":9538},[274],[128,9540,9542],{"className":9541},[278],[128,9543,9545],{"className":9544,"style":2431},[282],[128,9546,9547,9550],{"style":2452},[128,9548],{"className":9549,"style":291},[290],[128,9551,9553],{"className":9552},[299,300,301,298],[128,9554,9556,9559,9562,9565,9568,9608,9611],{"className":9555},[259,298],[128,9557,1853],{"className":9558,"style":1924},[259,1873,298],[128,9560,1989],{"className":9561},[2115,298],[128,9563,1842],{"className":9564},[259,298],[128,9566,9486],{"className":9567},[2115,298],[128,9569,9571,9574],{"className":9570},[259,298],[128,9572,4835],{"className":9573,"style":4920},[259,1873,298],[128,9575,9577],{"className":9576},[2087],[128,9578,9580,9600],{"className":9579},[274,321],[128,9581,9583,9597],{"className":9582},[278],[128,9584,9586],{"className":9585,"style":6153},[282],[128,9587,9588,9591],{"style":5786},[128,9589],{"className":9590,"style":5790},[290],[128,9592,9594],{"className":9593},[299,5794,5795,298],[128,9595,2028],{"className":9596},[259,298],[128,9598,347],{"className":9599},[346],[128,9601,9603],{"className":9602},[278],[128,9604,9606],{"className":9605,"style":5808},[282],[128,9607],{},[128,9609,1989],{"className":9610},[2115,298],[128,9612,1853],{"className":9613,"style":1924},[259,1873,298],[128,9615],{"className":9616,"style":1878},[269],[128,9618,1994],{"className":9619},[1882],[128,9621],{"className":9622,"style":1878},[269],[128,9624,9626,9630],{"className":9625},[250],[128,9627],{"className":9628,"style":9629},[254],"height:0.8141em;",[128,9631,9633,9636],{"className":9632},[259],[128,9634,7590],{"className":9635},[259,1873],[128,9637,9639],{"className":9638},[2087],[128,9640,9642],{"className":9641},[274],[128,9643,9645],{"className":9644},[278],[128,9646,9648],{"className":9647,"style":9629},[282],[128,9649,9650,9653],{"style":2452},[128,9651],{"className":9652,"style":291},[290],[128,9654,9656],{"className":9655},[299,300,301,298],[128,9657,9659,9699,9702],{"className":9658},[259,298],[128,9660,9662,9665],{"className":9661},[259,298],[128,9663,4835],{"className":9664,"style":4920},[259,1873,298],[128,9666,9668],{"className":9667},[2087],[128,9669,9671,9691],{"className":9670},[274,321],[128,9672,9674,9688],{"className":9673},[278],[128,9675,9677],{"className":9676,"style":6153},[282],[128,9678,9679,9682],{"style":5786},[128,9680],{"className":9681,"style":5790},[290],[128,9683,9685],{"className":9684},[299,5794,5795,298],[128,9686,2028],{"className":9687},[259,298],[128,9689,347],{"className":9690},[346],[128,9692,9694],{"className":9693},[278],[128,9695,9697],{"className":9696,"style":5808},[282],[128,9698],{},[128,9700,1989],{"className":9701},[2115,298],[128,9703,1842],{"className":9704},[259,298],"，指数因子合并为 ",[128,9707,9709,9731],{"className":9708,"translate":218},[217],[128,9710,9712],{"className":9711},[222],[224,9713,9714],{"xmlns":226},[228,9715,9716,9728],{},[231,9717,9718],{},[1977,9719,9720,9722],{},[1795,9721,3713],{},[231,9723,9724,9726],{},[1832,9725,1989],{},[1795,9727,7590],{},[238,9729,9730],{"encoding":240},"e^{-s}",[128,9732,9734],{"className":9733,"ariaHidden":246},[245],[128,9735,9737,9741],{"className":9736},[250],[128,9738],{"className":9739,"style":9740},[254],"height:0.7713em;",[128,9742,9744,9747],{"className":9743},[259],[128,9745,3713],{"className":9746},[259,1873],[128,9748,9750],{"className":9749},[2087],[128,9751,9753],{"className":9752},[274],[128,9754,9756],{"className":9755},[278],[128,9757,9759],{"className":9758,"style":9740},[282],[128,9760,9761,9764],{"style":2452},[128,9762],{"className":9763,"style":291},[290],[128,9765,9767],{"className":9766},[299,300,301,298],[128,9768,9770,9773],{"className":9769},[259,298],[128,9771,1989],{"className":9772},[259,298],[128,9774,7590],{"className":9775},[259,1873,298],"，二者均与 ",[128,9778,9780,9793],{"className":9779,"translate":218},[217],[128,9781,9783],{"className":9782},[222],[224,9784,9785],{"xmlns":226},[228,9786,9787,9791],{},[231,9788,9789],{},[1795,9790,2760],{"mathvariant":2001},[238,9792,4429],{"encoding":240},[128,9794,9796],{"className":9795,"ariaHidden":246},[245],[128,9797,9799,9802],{"className":9798},[250],[128,9800],{"className":9801,"style":4439},[254],[128,9803,2760],{"className":9804},[259,2151]," 解耦：",[128,9807,9809],{"className":9808,"translate":218},[1962],[128,9810,9812,10029],{"className":9811,"translate":218},[217],[128,9813,9815],{"className":9814},[222],[224,9816,9817],{"xmlns":226,"display":1971},[228,9818,9819,10026],{},[231,9820,9821,9835,9837,9839,9845,9847,9849,9895,9955,9957,9960,9962,9964,9970,9972,9988,10002,10020,10022,10024],{},[6961,9822,9823,9825,9833],{},[1832,9824,5470],{},[231,9826,9827,9829,9831],{},[1795,9828,2801],{},[1832,9830,1994],{},[1840,9832,1842],{},[1795,9834,1853],{},[1795,9836,6020],{"mathvariant":1981},[1832,9838,2477],{"stretchy":1837},[2016,9840,9841,9843],{},[1795,9842,4835],{},[1795,9844,2801],{},[1832,9846,2486],{"stretchy":1837},[1832,9848,1994],{},[231,9850,9851,9853,9861,9877,9887,9889,9891,9893],{},[1832,9852,2477],{"fence":246},[2038,9854,9855,9857,9859],{},[1832,9856,6481],{},[1840,9858,2028],{},[1795,9860,8521],{"mathvariant":1981},[1977,9862,9863,9865],{},[1795,9864,7590],{},[231,9866,9867,9873,9875],{},[2016,9868,9869,9871],{},[1795,9870,4835],{},[1840,9872,2028],{},[1832,9874,1989],{},[1840,9876,1842],{},[1977,9878,9879,9881],{},[1795,9880,3713],{},[231,9882,9883,9885],{},[1832,9884,1989],{},[1795,9886,7590],{},[234,9888,6528],{},[1795,9890,4519],{"mathvariant":1981},[1795,9892,7590],{},[1832,9894,2486],{"fence":246},[231,9896,9897,9899,9915,9929,9947,9949,9951,9953],{},[1832,9898,2477],{"fence":246},[2016,9900,9901,9903],{},[1832,9902,6481],{},[1977,9904,9905,9907],{},[1795,9906,1982],{"mathvariant":1981},[231,9908,9909,9911,9913],{},[1795,9910,1853],{},[1832,9912,1989],{},[1840,9914,1842],{},[6961,9916,9917,9919,9927],{},[1832,9918,5470],{},[231,9920,9921,9923,9925],{},[1795,9922,2801],{},[1832,9924,1994],{},[1840,9926,1842],{},[1795,9928,1853],{},[2038,9930,9931,9933,9935],{},[1795,9932,2760],{},[1795,9934,2801],{},[231,9936,9937,9943,9945],{},[2016,9938,9939,9941],{},[1795,9940,4835],{},[1795,9942,2801],{},[1832,9944,1989],{},[1840,9946,1842],{},[234,9948,6528],{},[1795,9950,4519],{"mathvariant":1981},[1795,9952,2760],{"mathvariant":2001},[1832,9954,2486],{"fence":246},[1832,9956,1994],{},[269,9958],{"linebreak":9959},"newline",[1795,9961,6020],{"mathvariant":1981},[1832,9963,2477],{"stretchy":1837},[2016,9965,9966,9968],{},[1795,9967,4835],{},[1840,9969,2028],{},[1832,9971,2486],{"stretchy":1837},[2016,9973,9974,9976],{},[1832,9975,6481],{},[1977,9977,9978,9980],{},[1795,9979,1982],{"mathvariant":1981},[231,9981,9982,9984,9986],{},[1795,9983,1853],{},[1832,9985,1989],{},[1840,9987,1842],{},[6961,9989,9990,9992,10000],{},[1832,9991,5470],{},[231,9993,9994,9996,9998],{},[1795,9995,2801],{},[1832,9997,1994],{},[1840,9999,1842],{},[1795,10001,1853],{},[2038,10003,10004,10006,10008],{},[1795,10005,2760],{},[1795,10007,2801],{},[231,10009,10010,10016,10018],{},[2016,10011,10012,10014],{},[1795,10013,4835],{},[1795,10015,2801],{},[1832,10017,1989],{},[1840,10019,1842],{},[234,10021,6528],{},[1795,10023,4519],{"mathvariant":1981},[1795,10025,2760],{"mathvariant":2001},[238,10027,10028],{"encoding":240},"\\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} 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即得结论。",[11,11042,11043,11044,11072,11073,11101,11102,11105],{},"命题 1.3 的证明过程本身包含了比结论更多的信息：",[128,11045,11047,11060],{"className":11046,"translate":218},[217],[128,11048,11050],{"className":11049},[222],[224,11051,11052],{"xmlns":226},[228,11053,11054,11058],{},[231,11055,11056],{},[1795,11057,7590],{},[238,11059,7590],{"encoding":240},[128,11061,11063],{"className":11062,"ariaHidden":246},[245],[128,11064,11066,11069],{"className":11065},[250],[128,11067],{"className":11068,"style":7758},[254],[128,11070,7590],{"className":11071},[259,1873]," 与 ",[128,11074,11076,11089],{"className":11075,"translate":218},[217],[128,11077,11079],{"className":11078},[222],[224,11080,11081],{"xmlns":226},[228,11082,11083,11087],{},[231,11084,11085],{},[1795,11086,2760],{"mathvariant":2001},[238,11088,4429],{"encoding":240},[128,11090,11092],{"className":11091,"ariaHidden":246},[245],[128,11093,11095,11098],{"className":11094},[250],[128,11096],{"className":11097,"style":4439},[254],[128,11099,2760],{"className":11100},[259,2151]," 的",[35,11103,11104],{},"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。",[2610,11107,11109],{"id":11108},"_13-生成性刻画gamma-商表示","1.3 生成性刻画：Gamma 商表示",[2615,11111,11113],{"title":11112},"命题 1.4（Gamma 商表示）",[11,11114,1781,11115,11259,11260,11427,11428,11498,11499,11527,11528,12056,12057,12133,12134,7713,12213,893],{},[128,11116,11118,11149],{"className":11117,"translate":218},[217],[128,11119,11121],{"className":11120},[222],[224,11122,11123],{"xmlns":226},[228,11124,11125,11146],{},[231,11126,11127,11134,11136,11138,11140],{},[2016,11128,11129,11132],{},[1795,11130,11131],{},"γ",[1840,11133,1842],{},[1832,11135,1845],{"separator":246},[1832,11137,1848],{},[1832,11139,1845],{"separator":246},[2016,11141,11142,11144],{},[1795,11143,11131],{},[1795,11145,1853],{},[238,11147,11148],{"encoding":240},"\\gamma_1, \\dots, \\gamma_K",[128,11150,11152],{"className":11151,"ariaHidden":246},[245],[128,11153,11155,11159,11201,11204,11207,11210,11213,11216,11219],{"className":11154},[250],[128,11156],{"className":11157,"style":11158},[254],"height:0.625em;vertical-align:-0.1944em;",[128,11160,11162,11166],{"className":11161},[259],[128,11163,11131],{"className":11164,"style":11165},[259,1873],"margin-right:0.0556em;",[128,11167,11169],{"className":11168},[2087],[128,11170,11172,11193],{"className":11171},[274,321],[128,11173,11175,11190],{"className":11174},[278],[128,11176,11178],{"className":11177,"style":2945},[282],[128,11179,11181,11184],{"style":11180},"top:-2.55em;margin-left:-0.0556em;margin-right:0.05em;",[128,11182],{"className":11183,"style":291},[290],[128,11185,11187],{"className":11186},[299,300,301,298],[128,11188,1842],{"className":11189},[259,298],[128,11191,347],{"className":11192},[346],[128,11194,11196],{"className":11195},[278],[128,11197,11199],{"className":11198,"style":2241},[282],[128,11200],{},[128,11202,1845],{"className":11203},[1903],[128,11205],{"className":11206,"style":1907},[269],[128,11208,1848],{"className":11209},[1911],[128,11211],{"className":11212,"style":1907},[269],[128,11214,1845],{"className":11215},[1903],[128,11217],{"className":11218,"style":1907},[269],[128,11220,11222,11225],{"className":11221},[259],[128,11223,11131],{"className":11224,"style":11165},[259,1873],[128,11226,11228],{"className":11227},[2087],[128,11229,11231,11251],{"className":11230},[274,321],[128,11232,11234,11248],{"className":11233},[278],[128,11235,11237],{"className":11236,"style":3004},[282],[128,11238,11239,11242],{"style":11180},[128,11240],{"className":11241,"style":291},[290],[128,11243,11245],{"className":11244},[299,300,301,298],[128,11246,1853],{"className":11247,"style":1924},[259,1873,298],[128,11249,347],{"className":11250},[346],[128,11252,11254],{"className":11253},[278],[128,11255,11257],{"className":11256,"style":2241},[282],[128,11258],{}," 相互独立且 ",[128,11261,11263,11302],{"className":11262,"translate":218},[217],[128,11264,11266],{"className":11265},[222],[224,11267,11268],{"xmlns":226},[228,11269,11270,11299],{},[231,11271,11272,11278,11280,11283,11285,11287,11293,11295,11297],{},[2016,11273,11274,11276],{},[1795,11275,11131],{},[1795,11277,2801],{},[1832,11279,5911],{},[1795,11281,11282],{"mathvariant":1981},"Gamma",[1832,11284,3278],{},[1832,11286,2477],{"stretchy":1837},[2016,11288,11289,11291],{},[1795,11290,4835],{},[1795,11292,2801],{},[1832,11294,1845],{"separator":246},[1840,11296,1842],{},[1832,11298,2486],{"stretchy":1837},[238,11300,11301],{"encoding":240},"\\gamma_i \\sim \\operatorname{Gamma}(\\alpha_i, 1)",[128,11303,11305,11360],{"className":11304,"ariaHidden":246},[245],[128,11306,11308,11311,11351,11354,11357],{"className":11307},[250],[128,11309],{"className":11310,"style":11158},[254],[128,11312,11314,11317],{"className":11313},[259],[128,11315,11131],{"className":11316,"style":11165},[259,1873],[128,11318,11320],{"className":11319},[2087],[128,11321,11323,11343],{"className":11322},[274,321],[128,11324,11326,11340],{"className":11325},[278],[128,11327,11329],{"className":11328,"style":3095},[282],[128,11330,11331,11334],{"style":11180},[128,11332],{"className":11333,"style":291},[290],[128,11335,11337],{"className":11336},[299,300,301,298],[128,11338,2801],{"className":11339},[259,1873,298],[128,11341,347],{"className":11342},[346],[128,11344,11346],{"className":11345},[278],[128,11347,11349],{"className":11348,"style":2241},[282],[128,11350],{},[128,11352],{"className":11353,"style":1878},[269],[128,11355,5911],{"className":11356},[1882],[128,11358],{"className":11359,"style":1878},[269],[128,11361,11363,11366,11372,11375,11415,11418,11421,11424],{"className":11362},[250],[128,11364],{"className":11365,"style":1892},[254],[128,11367,11369],{"className":11368},[2268],[128,11370,11282],{"className":11371},[259,3353],[128,11373,2477],{"className":11374},[1896],[128,11376,11378,11381],{"className":11377},[259],[128,11379,4835],{"className":11380,"style":4920},[259,1873],[128,11382,11384],{"className":11383},[2087],[128,11385,11387,11407],{"className":11386},[274,321],[128,11388,11390,11404],{"className":11389},[278],[128,11391,11393],{"className":11392,"style":3095},[282],[128,11394,11395,11398],{"style":4935},[128,11396],{"className":11397,"style":291},[290],[128,11399,11401],{"className":11400},[299,300,301,298],[128,11402,2801],{"className":11403},[259,1873,298],[128,11405,347],{"className":11406},[346],[128,11408,11410],{"className":11409},[278],[128,11411,11413],{"className":11412,"style":2241},[282],[128,11414],{},[128,11416,1845],{"className":11417},[1903],[128,11419],{"className":11420,"style":1907},[269],[128,11422,1842],{"className":11423},[259],[128,11425,2486],{"className":11426},[1928],"（形状 ",[128,11429,11431,11449],{"className":11430,"translate":218},[217],[128,11432,11434],{"className":11433},[222],[224,11435,11436],{"xmlns":226},[228,11437,11438,11446],{},[231,11439,11440],{},[2016,11441,11442,11444],{},[1795,11443,4835],{},[1795,11445,2801],{},[238,11447,11448],{"encoding":240},"\\alpha_i",[128,11450,11452],{"className":11451,"ariaHidden":246},[245],[128,11453,11455,11458],{"className":11454},[250],[128,11456],{"className":11457,"style":4242},[254],[128,11459,11461,11464],{"className":11460},[259],[128,11462,4835],{"className":11463,"style":4920},[259,1873],[128,11465,11467],{"className":11466},[2087],[128,11468,11470,11490],{"className":11469},[274,321],[128,11471,11473,11487],{"className":11472},[278],[128,11474,11476],{"className":11475,"style":3095},[282],[128,11477,11478,11481],{"style":4935},[128,11479],{"className":11480,"style":291},[290],[128,11482,11484],{"className":11483},[299,300,301,298],[128,11485,2801],{"className":11486},[259,1873,298],[128,11488,347],{"className":11489},[346],[128,11491,11493],{"className":11492},[278],[128,11494,11496],{"className":11495,"style":2241},[282],[128,11497],{},"、率 ",[128,11500,11502,11515],{"className":11501,"translate":218},[217],[128,11503,11505],{"className":11504},[222],[224,11506,11507],{"xmlns":226},[228,11508,11509,11513],{},[231,11510,11511],{},[1840,11512,1842],{},[238,11514,1842],{"encoding":240},[128,11516,11518],{"className":11517,"ariaHidden":246},[245],[128,11519,11521,11524],{"className":11520},[250],[128,11522],{"className":11523,"style":2594},[254],[128,11525,1842],{"className":11526},[259],"）。令\n",[128,11529,11531,11620],{"className":11530,"translate":218},[217],[128,11532,11534],{"className":11533},[222],[224,11535,11536],{"xmlns":226},[228,11537,11538,11617],{},[231,11539,11540,11542,11544,11558,11564,11566,11569,11575,11577,11587,11589,11591,11593,11595,11597,11603,11605,11607,11609,11615],{},[1795,11541,7590],{},[1832,11543,1994],{},[2038,11545,11546,11548,11556],{},[1832,11547,2042],{},[231,11549,11550,11552,11554],{},[1795,11551,2801],{},[1832,11553,1994],{},[1840,11555,1842],{},[1795,11557,1853],{},[2016,11559,11560,11562],{},[1795,11561,11131],{},[1795,11563,2801],{},[1832,11565,1845],{"separator":246},[269,11567],{"width":11568},"2em",[2016,11570,11571,11573],{},[1795,11572,2760],{},[1795,11574,2801],{},[1832,11576,1994],{},[5451,11578,11579,11585],{},[2016,11580,11581,11583],{},[1795,11582,11131],{},[1795,11584,2801],{},[1795,11586,7590],{},[1832,11588,1845],{"separator":246},[269,11590],{"width":11568},[1795,11592,2760],{"mathvariant":2001},[1832,11594,1994],{},[1832,11596,2477],{"stretchy":1837},[2016,11598,11599,11601],{},[1795,11600,2760],{},[1840,11602,1842],{},[1832,11604,1845],{"separator":246},[1832,11606,1848],{},[1832,11608,1845],{"separator":246},[2016,11610,11611,11613],{},[1795,11612,2760],{},[1795,11614,1853],{},[1832,11616,2486],{"stretchy":1837},[238,11618,11619],{"encoding":240},"s = \\sum_{i=1}^K \\gamma_i, \\qquad x_i = \\frac{\\gamma_i}{s}, \\qquad \\mathbf{x} = (x_1, \\dots, x_K)",[128,11621,11623,11641,11809,11946],{"className":11622,"ariaHidden":246},[245],[128,11624,11626,11629,11632,11635,11638],{"className":11625},[250],[128,11627],{"className":11628,"style":7758},[254],[128,11630,7590],{"className":11631},[259,1873],[128,11633],{"className":11634,"style":1878},[269],[128,11636,1994],{"className":11637},[1882],[128,11639],{"className":11640,"style":1878},[269],[128,11642,11644,11647,11707,11710,11750,11753,11757,11760,11800,11803,11806],{"className":11643},[250],[128,11645],{"className":11646,"style":5200},[254],[128,11648,11650,11653],{"className":11649},[2268],[128,11651,2042],{"className":11652,"style":2274},[2268,2272,2273],[128,11654,11656],{"className":11655},[2087],[128,11657,11659,11699],{"className":11658},[274,321],[128,11660,11662,11696],{"className":11661},[278],[128,11663,11665,11685],{"className":11664,"style":2287},[282],[128,11666,11667,11670],{"style":2290},[128,11668],{"className":11669,"style":291},[290],[128,11671,11673],{"className":11672},[299,300,301,298],[128,11674,11676,11679,11682],{"className":11675},[259,298],[128,11677,2801],{"className":11678},[259,1873,298],[128,11680,1994],{"className":11681},[1882,298],[128,11683,1842],{"className":11684},[259,298],[128,11686,11687,11690],{"style":2311},[128,11688],{"className":11689,"style":291},[290],[128,11691,11693],{"className":11692},[299,300,301,298],[128,11694,1853],{"className":11695,"style":1924},[259,1873,298],[128,11697,347],{"className":11698},[346],[128,11700,11702],{"className":11701},[278],[128,11703,11705],{"className":11704,"style":2330},[282],[128,11706],{},[128,11708],{"className":11709,"style":1907},[269],[128,11711,11713,11716],{"className":11712},[259],[128,11714,11131],{"className":11715,"style":11165},[259,1873],[128,11717,11719],{"className":11718},[2087],[128,11720,11722,11742],{"className":11721},[274,321],[128,11723,11725,11739],{"className":11724},[278],[128,11726,11728],{"className":11727,"style":3095},[282],[128,11729,11730,11733],{"style":11180},[128,11731],{"className":11732,"style":291},[290],[128,11734,11736],{"className":11735},[299,300,301,298],[128,11737,2801],{"className":11738},[259,1873,298],[128,11740,347],{"className":11741},[346],[128,11743,11745],{"className":11744},[278],[128,11746,11748],{"className":11747,"style":2241},[282],[128,11749],{},[128,11751,1845],{"className":11752},[1903],[128,11754],{"className":11755,"style":11756},[269],"margin-right:2em;",[128,11758],{"className":11759,"style":1907},[269],[128,11761,11763,11766],{"className":11762},[259],[128,11764,2760],{"className":11765},[259,1873],[128,11767,11769],{"className":11768},[2087],[128,11770,11772,11792],{"className":11771},[274,321],[128,11773,11775,11789],{"className":11774},[278],[128,11776,11778],{"className":11777,"style":3095},[282],[128,11779,11780,11783],{"style":2221},[128,11781],{"className":11782,"style":291},[290],[128,11784,11786],{"className":11785},[299,300,301,298],[128,11787,2801],{"className":11788},[259,1873,298],[128,11790,347],{"className":11791},[346],[128,11793,11795],{"className":11794},[278],[128,11796,11798],{"className":11797,"style":2241},[282],[128,11799],{},[128,11801],{"className":11802,"style":1878},[269],[128,11804,1994],{"className":11805},[1882],[128,11807],{"className":11808,"style":1878},[269],[128,11810,11812,11816,11925,11928,11931,11934,11937,11940,11943],{"className":11811},[250],[128,11813],{"className":11814,"style":11815},[254],"height:1.0925em;vertical-align:-0.345em;",[128,11817,11819,11822,11922],{"className":11818},[259],[128,11820],{"className":11821},[1896,5570],[128,11823,11825],{"className":11824},[5451],[128,11826,11828,11913],{"className":11827},[274,321],[128,11829,11831,11910],{"className":11830},[278],[128,11832,11835,11849,11857],{"className":11833,"style":11834},[282],"height:0.7475em;",[128,11836,11837,11840],{"style":5586},[128,11838],{"className":11839,"style":335},[290],[128,11841,11843],{"className":11842},[299,300,301,298],[128,11844,11846],{"className":11845},[259,298],[128,11847,7590],{"className":11848},[259,1873,298],[128,11850,11851,11854],{"style":5617},[128,11852],{"className":11853,"style":335},[290],[128,11855],{"className":11856,"style":5625},[5624],[128,11858,11860,11863],{"style":11859},"top:-3.4461em;",[128,11861],{"className":11862,"style":335},[290],[128,11864,11866],{"className":11865},[299,300,301,298],[128,11867,11869],{"className":11868},[259,298],[128,11870,11872,11875],{"className":11871},[259,298],[128,11873,11131],{"className":11874,"style":11165},[259,1873,298],[128,11876,11878],{"className":11877},[2087],[128,11879,11881,11902],{"className":11880},[274,321],[128,11882,11884,11899],{"className":11883},[278],[128,11885,11887],{"className":11886,"style":5783},[282],[128,11888,11890,11893],{"style":11889},"top:-2.357em;margin-left:-0.0556em;margin-right:0.0714em;",[128,11891],{"className":11892,"style":5790},[290],[128,11894,11896],{"className":11895},[299,5794,5795,298],[128,11897,2801],{"className":11898},[259,1873,298],[128,11900,347],{"className":11901},[346],[128,11903,11905],{"className":11904},[278],[128,11906,11908],{"className":11907,"style":5808},[282],[128,11909],{},[128,11911,347],{"className":11912},[346],[128,11914,11916],{"className":11915},[278],[128,11917,11920],{"className":11918,"style":11919},[282],"height:0.345em;",[128,11921],{},[128,11923],{"className":11924},[1928,5570],[128,11926,1845],{"className":11927},[1903],[128,11929],{"className":11930,"style":11756},[269],[128,11932],{"className":11933,"style":1907},[269],[128,11935,2760],{"className":11936},[259,2151],[128,11938],{"className":11939,"style":1878},[269],[128,11941,1994],{"className":11942},[1882],[128,11944],{"className":11945,"style":1878},[269],[128,11947,11949,11952,11955,11995,11998,12001,12004,12007,12010,12013,12053],{"className":11948},[250],[128,11950],{"className":11951,"style":1892},[254],[128,11953,2477],{"className":11954},[1896],[128,11956,11958,11961],{"className":11957},[259],[128,11959,2760],{"className":11960},[259,1873],[128,11962,11964],{"className":11963},[2087],[128,11965,11967,11987],{"className":11966},[274,321],[128,11968,11970,11984],{"className":11969},[278],[128,11971,11973],{"className":11972,"style":2945},[282],[128,11974,11975,11978],{"style":2221},[128,11976],{"className":11977,"style":291},[290],[128,11979,11981],{"className":11980},[299,300,301,298],[128,11982,1842],{"className":11983},[259,298],[128,11985,347],{"className":11986},[346],[128,11988,11990],{"className":11989},[278],[128,11991,11993],{"className":11992,"style":2241},[282],[128,11994],{},[128,11996,1845],{"className":11997},[1903],[128,11999],{"className":12000,"style":1907},[269],[128,12002,1848],{"className":12003},[1911],[128,12005],{"className":12006,"style":1907},[269],[128,12008,1845],{"className":12009},[1903],[128,12011],{"className":12012,"style":1907},[269],[128,12014,12016,12019],{"className":12015},[259],[128,12017,2760],{"className":12018},[259,1873],[128,12020,12022],{"className":12021},[2087],[128,12023,12025,12045],{"className":12024},[274,321],[128,12026,12028,12042],{"className":12027},[278],[128,12029,12031],{"className":12030,"style":3004},[282],[128,12032,12033,12036],{"style":2221},[128,12034],{"className":12035,"style":291},[290],[128,12037,12039],{"className":12038},[299,300,301,298],[128,12040,1853],{"className":12041,"style":1924},[259,1873,298],[128,12043,347],{"className":12044},[346],[128,12046,12048],{"className":12047},[278],[128,12049,12051],{"className":12050,"style":2241},[282],[128,12052],{},[128,12054,2486],{"className":12055},[1928],"\n则 ",[128,12058,12060,12085],{"className":12059,"translate":218},[217],[128,12061,12063],{"className":12062},[222],[224,12064,12065],{"xmlns":226},[228,12066,12067,12083],{},[231,12068,12069,12071,12073,12075,12077,12079,12081],{},[1795,12070,2760],{"mathvariant":2001},[1832,12072,5911],{},[1795,12074,5914],{"mathvariant":1981},[1832,12076,3278],{},[1832,12078,2477],{"stretchy":1837},[1795,12080,4835],{"mathvariant":4834},[1832,12082,2486],{"stretchy":1837},[238,12084,5925],{"encoding":240},[128,12086,12088,12106],{"className":12087,"ariaHidden":246},[245],[128,12089,12091,12094,12097,12100,12103],{"className":12090},[250],[128,12092],{"className":12093,"style":4439},[254],[128,12095,2760],{"className":12096},[259,2151],[128,12098],{"className":12099,"style":1878},[269],[128,12101,5911],{"className":12102},[1882],[128,12104],{"className":12105,"style":1878},[269],[128,12107,12109,12112,12118,12121,12130],{"className":12108},[250],[128,12110],{"className":12111,"style":1892},[254],[128,12113,12115],{"className":12114},[2268],[128,12116,5914],{"className":12117},[259,3353],[128,12119,2477],{"className":12120},[1896],[128,12122,12124],{"className":12123},[259],[128,12125,12127],{"className":12126},[259],[128,12128,4835],{"className":12129},[259,4895],[128,12131,2486],{"className":12132},[1928],"，且 ",[128,12135,12137,12164],{"className":12136,"translate":218},[217],[128,12138,12140],{"className":12139},[222],[224,12141,12142],{"xmlns":226},[228,12143,12144,12161],{},[231,12145,12146,12148,12151,12153,12155,12157,12159],{},[1795,12147,2760],{"mathvariant":2001},[1832,12149,12150],{},"⊥",[234,12152,8524],{},[234,12154,8524],{},[234,12156,8524],{},[1832,12158,12150],{},[1795,12160,7590],{},[238,12162,12163],{"encoding":240},"\\mathbf{x} \\perp\\!\\!\\!\\perp s",[128,12165,12167,12192,12204],{"className":12166,"ariaHidden":246},[245],[128,12168,12170,12174,12177,12180,12183,12186,12189],{"className":12169},[250],[128,12171],{"className":12172,"style":12173},[254],"height:0.6944em;",[128,12175,2760],{"className":12176},[259,2151],[128,12178],{"className":12179,"style":1878},[269],[128,12181,12150],{"className":12182},[1882],[128,12184],{"className":12185,"style":317},[269],[128,12187],{"className":12188,"style":317},[269],[128,12190],{"className":12191,"style":317},[269],[128,12193,12195,12198,12201],{"className":12194},[250],[128,12196],{"className":12197,"style":12173},[254],[128,12199,12150],{"className":12200},[1882],[128,12202],{"className":12203,"style":1878},[269],[128,12205,12207,12210],{"className":12206},[250],[128,12208],{"className":12209,"style":7758},[254],[128,12211,7590],{"className":12212},[259,1873],[128,12214,12216,12250],{"className":12215,"translate":218},[217],[128,12217,12219],{"className":12218},[222],[224,12220,12221],{"xmlns":226},[228,12222,12223,12247],{},[231,12224,12225,12227,12229,12231,12233,12235,12241,12243,12245],{},[1795,12226,7590],{},[1832,12228,5911],{},[1795,12230,11282],{"mathvariant":1981},[1832,12232,3278],{},[1832,12234,2477],{"stretchy":1837},[2016,12236,12237,12239],{},[1795,12238,4835],{},[1840,12240,2028],{},[1832,12242,1845],{"separator":246},[1840,12244,1842],{},[1832,12246,2486],{"stretchy":1837},[238,12248,12249],{"encoding":240},"s \\sim \\operatorname{Gamma}(\\alpha_0, 1)",[128,12251,12253,12271],{"className":12252,"ariaHidden":246},[245],[128,12254,12256,12259,12262,12265,12268],{"className":12255},[250],[128,12257],{"className":12258,"style":7758},[254],[128,12260,7590],{"className":12261},[259,1873],[128,12263],{"className":12264,"style":1878},[269],[128,12266,5911],{"className":12267},[1882],[128,12269],{"className":12270,"style":1878},[269],[128,12272,12274,12277,12283,12286,12326,12329,12332,12335],{"className":12273},[250],[128,12275],{"className":12276,"style":1892},[254],[128,12278,12280],{"className":12279},[2268],[128,12281,11282],{"className":12282},[259,3353],[128,12284,2477],{"className":12285},[1896],[128,12287,12289,12292],{"className":12288},[259],[128,12290,4835],{"className":12291,"style":4920},[259,1873],[128,12293,12295],{"className":12294},[2087],[128,12296,12298,12318],{"className":12297},[274,321],[128,12299,12301,12315],{"className":12300},[278],[128,12302,12304],{"className":12303,"style":2945},[282],[128,12305,12306,12309],{"style":4935},[128,12307],{"className":12308,"style":291},[290],[128,12310,12312],{"className":12311},[299,300,301,298],[128,12313,2028],{"className":12314},[259,298],[128,12316,347],{"className":12317},[346],[128,12319,12321],{"className":12320},[278],[128,12322,12324],{"className":12323,"style":2241},[282],[128,12325],{},[128,12327,1845],{"className":12328},[1903],[128,12330],{"className":12331,"style":1907},[269],[128,12333,1842],{"className":12334},[259],[128,12336,2486],{"className":12337},[1928],[11,12339,12340,12342,12343,12379,12380,12720,12721,12859],{},[35,12341,6849],{}," 由独立性，",[128,12344,12346,12360],{"className":12345,"translate":218},[217],[128,12347,12349],{"className":12348},[222],[224,12350,12351],{"xmlns":226},[228,12352,12353,12357],{},[231,12354,12355],{},[1795,12356,11131],{"mathvariant":4834},[238,12358,12359],{"encoding":240},"\\boldsymbol{\\gamma}",[128,12361,12363],{"className":12362,"ariaHidden":246},[245],[128,12364,12366,12369],{"className":12365},[250],[128,12367],{"className":12368,"style":2564},[254],[128,12370,12372],{"className":12371},[259],[128,12373,12375],{"className":12374},[259],[128,12376,11131],{"className":12377,"style":12378},[259,4895],"margin-right:0.0639em;"," 的联合密度为 ",[128,12381,12383,12447],{"className":12382,"translate":218},[217],[128,12384,12386],{"className":12385},[222],[224,12387,12388],{"xmlns":226},[228,12389,12390,12444],{},[231,12391,12392,12398,12416,12430,12432,12434,12436,12442],{},[2016,12393,12394,12396],{},[1832,12395,5470],{},[1795,12397,2801],{},[2038,12399,12400,12402,12404],{},[1795,12401,11131],{},[1795,12403,2801],{},[231,12405,12406,12412,12414],{},[2016,12407,12408,12410],{},[1795,12409,4835],{},[1795,12411,2801],{},[1832,12413,1989],{},[1840,12415,1842],{},[1977,12417,12418,12420],{},[1795,12419,3713],{},[231,12421,12422,12424],{},[1832,12423,1989],{},[2016,12425,12426,12428],{},[1795,12427,11131],{},[1795,12429,2801],{},[1795,12431,4751],{"mathvariant":1981},[1795,12433,6020],{"mathvariant":1981},[1832,12435,2477],{"stretchy":1837},[2016,12437,12438,12440],{},[1795,12439,4835],{},[1795,12441,2801],{},[1832,12443,2486],{"stretchy":1837},[238,12445,12446],{"encoding":240},"\\prod_i \\gamma_i^{\\alpha_i - 1} e^{-\\gamma_i} \u002F \\Gamma(\\alpha_i)",[128,12448,12450],{"className":12449,"ariaHidden":246},[245],[128,12451,12453,12457,12497,12500,12598,12670,12674,12677,12717],{"className":12452},[250],[128,12454],{"className":12455,"style":12456},[254],"height:1.1957em;vertical-align:-0.2997em;",[128,12458,12460,12463],{"className":12459},[2268],[128,12461,5470],{"className":12462,"style":2274},[2268,2272,2273],[128,12464,12466],{"className":12465},[2087],[128,12467,12469,12489],{"className":12468},[274,321],[128,12470,12472,12486],{"className":12471},[278],[128,12473,12475],{"className":12474,"style":7796},[282],[128,12476,12477,12480],{"style":2290},[128,12478],{"className":12479,"style":291},[290],[128,12481,12483],{"className":12482},[299,300,301,298],[128,12484,2801],{"className":12485},[259,1873,298],[128,12487,347],{"className":12488},[346],[128,12490,12492],{"className":12491},[278],[128,12493,12495],{"className":12494,"style":2330},[282],[128,12496],{},[128,12498],{"className":12499,"style":1907},[269],[128,12501,12503,12506],{"className":12502},[259],[128,12504,11131],{"className":12505,"style":11165},[259,1873],[128,12507,12509],{"className":12508},[2087],[128,12510,12512,12590],{"className":12511},[274,321],[128,12513,12515,12587],{"className":12514},[278],[128,12516,12518,12530],{"className":12517,"style":5740},[282],[128,12519,12521,12524],{"style":12520},"top:-2.4231em;margin-left:-0.0556em;margin-right:0.05em;",[128,12522],{"className":12523,"style":291},[290],[128,12525,12527],{"className":12526},[299,300,301,298],[128,12528,2801],{"className":12529},[259,1873,298],[128,12531,12532,12535],{"style":5755},[128,12533],{"className":12534,"style":291},[290],[128,12536,12538],{"className":12537},[299,300,301,298],[128,12539,12541,12581,12584],{"className":12540},[259,298],[128,12542,12544,12547],{"className":12543},[259,298],[128,12545,4835],{"className":12546,"style":4920},[259,1873,298],[128,12548,12550],{"className":12549},[2087],[128,12551,12553,12573],{"className":12552},[274,321],[128,12554,12556,12570],{"className":12555},[278],[128,12557,12559],{"className":12558,"style":5783},[282],[128,12560,12561,12564],{"style":5786},[128,12562],{"className":12563,"style":5790},[290],[128,12565,12567],{"className":12566},[299,5794,5795,298],[128,12568,2801],{"className":12569},[259,1873,298],[128,12571,347],{"className":12572},[346],[128,12574,12576],{"className":12575},[278],[128,12577,12579],{"className":12578,"style":5808},[282],[128,12580],{},[128,12582,1989],{"className":12583},[2115,298],[128,12585,1842],{"className":12586},[259,298],[128,12588,347],{"className":12589},[346],[128,12591,12593],{"className":12592},[278],[128,12594,12596],{"className":12595,"style":5826},[282],[128,12597],{},[128,12599,12601,12604],{"className":12600},[259],[128,12602,3713],{"className":12603},[259,1873],[128,12605,12607],{"className":12606},[2087],[128,12608,12610],{"className":12609},[274],[128,12611,12613],{"className":12612},[278],[128,12614,12616],{"className":12615,"style":9740},[282],[128,12617,12618,12621],{"style":2452},[128,12619],{"className":12620,"style":291},[290],[128,12622,12624],{"className":12623},[299,300,301,298],[128,12625,12627,12630],{"className":12626},[259,298],[128,12628,1989],{"className":12629},[259,298],[128,12631,12633,12636],{"className":12632},[259,298],[128,12634,11131],{"className":12635,"style":11165},[259,1873,298],[128,12637,12639],{"className":12638},[2087],[128,12640,12642,12662],{"className":12641},[274,321],[128,12643,12645,12659],{"className":12644},[278],[128,12646,12648],{"className":12647,"style":5783},[282],[128,12649,12650,12653],{"style":11889},[128,12651],{"className":12652,"style":5790},[290],[128,12654,12656],{"className":12655},[299,5794,5795,298],[128,12657,2801],{"className":12658},[259,1873,298],[128,12660,347],{"className":12661},[346],[128,12663,12665],{"className":12664},[278],[128,12666,12668],{"className":12667,"style":5808},[282],[128,12669],{},[128,12671,12673],{"className":12672},[259],"\u002FΓ",[128,12675,2477],{"className":12676},[1896],[128,12678,12680,12683],{"className":12679},[259],[128,12681,4835],{"className":12682,"style":4920},[259,1873],[128,12684,12686],{"className":12685},[2087],[128,12687,12689,12709],{"className":12688},[274,321],[128,12690,12692,12706],{"className":12691},[278],[128,12693,12695],{"className":12694,"style":3095},[282],[128,12696,12697,12700],{"style":4935},[128,12698],{"className":12699,"style":291},[290],[128,12701,12703],{"className":12702},[299,300,301,298],[128,12704,2801],{"className":12705},[259,1873,298],[128,12707,347],{"className":12708},[346],[128,12710,12712],{"className":12711},[278],[128,12713,12715],{"className":12714,"style":2241},[282],[128,12716],{},[128,12718,2486],{"className":12719},[1928],"。施行与命题 1.3 相同的替换 ",[128,12722,12724,12752],{"className":12723,"translate":218},[217],[128,12725,12727],{"className":12726},[222],[224,12728,12729],{"xmlns":226},[228,12730,12731,12749],{},[231,12732,12733,12739,12741,12743],{},[2016,12734,12735,12737],{},[1795,12736,11131],{},[1795,12738,2801],{},[1832,12740,1994],{},[1795,12742,7590],{},[2016,12744,12745,12747],{},[1795,12746,2760],{},[1795,12748,2801],{},[238,12750,12751],{"encoding":240},"\\gamma_i = s x_i",[128,12753,12755,12810],{"className":12754,"ariaHidden":246},[245],[128,12756,12758,12761,12801,12804,12807],{"className":12757},[250],[128,12759],{"className":12760,"style":11158},[254],[128,12762,12764,12767],{"className":12763},[259],[128,12765,11131],{"className":12766,"style":11165},[259,1873],[128,12768,12770],{"className":12769},[2087],[128,12771,12773,12793],{"className":12772},[274,321],[128,12774,12776,12790],{"className":12775},[278],[128,12777,12779],{"className":12778,"style":3095},[282],[128,12780,12781,12784],{"style":11180},[128,12782],{"className":12783,"style":291},[290],[128,12785,12787],{"className":12786},[299,300,301,298],[128,12788,2801],{"className":12789},[259,1873,298],[128,12791,347],{"className":12792},[346],[128,12794,12796],{"className":12795},[278],[128,12797,12799],{"className":12798,"style":2241},[282],[128,12800],{},[128,12802],{"className":12803,"style":1878},[269],[128,12805,1994],{"className":12806},[1882],[128,12808],{"className":12809,"style":1878},[269],[128,12811,12813,12816,12819],{"className":12812},[250],[128,12814],{"className":12815,"style":4242},[254],[128,12817,7590],{"className":12818},[259,1873],[128,12820,12822,12825],{"className":12821},[259],[128,12823,2760],{"className":12824},[259,1873],[128,12826,12828],{"className":12827},[2087],[128,12829,12831,12851],{"className":12830},[274,321],[128,12832,12834,12848],{"className":12833},[278],[128,12835,12837],{"className":12836,"style":3095},[282],[128,12838,12839,12842],{"style":2221},[128,12840],{"className":12841,"style":291},[290],[128,12843,12845],{"className":12844},[299,300,301,298],[128,12846,2801],{"className":12847},[259,1873,298],[128,12849,347],{"className":12850},[346],[128,12852,12854],{"className":12853},[278],[128,12855,12857],{"className":12856,"style":2241},[282],[128,12858],{},"，联合密度变换为",[128,12861,12863],{"className":12862,"translate":218},[1962],[128,12864,12866,13056],{"className":12865,"translate":218},[217],[128,12867,12869],{"className":12868},[222],[224,12870,12871],{"xmlns":226,"display":1971},[228,12872,12873,13053],{},[231,12874,12875,12877,12879,12881,12883,12885,12887,12889,12933,12936,13012,13014,13016,13018,13020,13022,13025,13031,13033,13035,13037,13039,13041,13043,13045,13047,13049,13051],{},[1795,12876,11],{},[1832,12878,2477],{"stretchy":1837},[1795,12880,7590],{},[1832,12882,1845],{"separator":246},[1795,12884,2760],{"mathvariant":2001},[1832,12886,2486],{"stretchy":1837},[1832,12888,1994],{},[5451,12890,12891,12919],{},[231,12892,12893,12909],{},[1977,12894,12895,12897],{},[1795,12896,7590],{},[231,12898,12899,12905,12907],{},[2016,12900,12901,12903],{},[1795,12902,4835],{},[1840,12904,2028],{},[1832,12906,1989],{},[1840,12908,1842],{},[1977,12910,12911,12913],{},[1795,12912,3713],{},[231,12914,12915,12917],{},[1832,12916,1989],{},[1795,12918,7590],{},[231,12920,12921,12923,12925,12931],{},[1795,12922,6020],{"mathvariant":1981},[1832,12924,2477],{"stretchy":1837},[2016,12926,12927,12929],{},[1795,12928,4835],{},[1840,12930,2028],{},[1832,12932,2486],{"stretchy":1837},[1832,12934,12935],{},"⋅",[5451,12937,12938,12984],{},[231,12939,12940,12942,12944,12950,12952,12966],{},[1795,12941,6020],{"mathvariant":1981},[1832,12943,2477],{"stretchy":1837},[2016,12945,12946,12948],{},[1795,12947,4835],{},[1840,12949,2028],{},[1832,12951,2486],{"stretchy":1837},[6961,12953,12954,12956,12964],{},[1832,12955,5470],{},[231,12957,12958,12960,12962],{},[1795,12959,2801],{},[1832,12961,1994],{},[1840,12963,1842],{},[1795,12965,1853],{},[2038,12967,12968,12970,12972],{},[1795,12969,2760],{},[1795,12971,2801],{},[231,12973,12974,12980,12982],{},[2016,12975,12976,12978],{},[1795,12977,4835],{},[1795,12979,2801],{},[1832,12981,1989],{},[1840,12983,1842],{},[231,12985,12986,13000,13002,13004,13010],{},[6961,12987,12988,12990,12998],{},[1832,12989,5470],{},[231,12991,12992,12994,12996],{},[1795,12993,2801],{},[1832,12995,1994],{},[1840,12997,1842],{},[1795,12999,1853],{},[1795,13001,6020],{"mathvariant":1981},[1832,13003,2477],{"stretchy":1837},[2016,13005,13006,13008],{},[1795,13007,4835],{},[1795,13009,2801],{},[1832,13011,2486],{"stretchy":1837},[1832,13013,1994],{},[1795,13015,11282],{"mathvariant":1981},[1832,13017,3278],{},[1832,13019,2477],{"stretchy":1837},[1795,13021,7590],{},[1832,13023,13024],{"separator":246},";",[2016,13026,13027,13029],{},[1795,13028,4835],{},[1840,13030,2028],{},[1832,13032,1845],{"separator":246},[1840,13034,1842],{},[1832,13036,2486],{"stretchy":1837},[1832,13038,12935],{},[1795,13040,5914],{"mathvariant":1981},[1832,13042,3278],{},[1832,13044,2477],{"stretchy":1837},[1795,13046,2760],{"mathvariant":2001},[1832,13048,13024],{"separator":246},[1795,13050,4835],{"mathvariant":4834},[1832,13052,2486],{"stretchy":1837},[238,13054,13055],{"encoding":240},"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}; 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",[128,13855,13857,13870],{"className":13856,"translate":218},[217],[128,13858,13860],{"className":13859},[222],[224,13861,13862],{"xmlns":226},[228,13863,13864,13868],{},[231,13865,13866],{},[1795,13867,7590],{},[238,13869,7590],{"encoding":240},[128,13871,13873],{"className":13872,"ariaHidden":246},[245],[128,13874,13876,13879],{"className":13875},[250],[128,13877],{"className":13878,"style":7758},[254],[128,13880,7590],{"className":13881},[259,1873]," 与仅含 ",[128,13884,13886,13899],{"className":13885,"translate":218},[217],[128,13887,13889],{"className":13888},[222],[224,13890,13891],{"xmlns":226},[228,13892,13893,13897],{},[231,13894,13895],{},[1795,13896,2760],{"mathvariant":2001},[238,13898,4429],{"encoding":240},[128,13900,13902],{"className":13901,"ariaHidden":246},[245],[128,13903,13905,13908],{"className":13904},[250],[128,13906],{"className":13907,"style":4439},[254],[128,13909,2760],{"className":13910},[259,2151]," 的两个因子的乘积，故 ",[128,13913,13915,13928],{"className":13914,"translate":218},[217],[128,13916,13918],{"className":13917},[222],[224,13919,13920],{"xmlns":226},[228,13921,13922,13926],{},[231,13923,13924],{},[1795,13925,7590],{},[238,13927,7590],{"encoding":240},[128,13929,13931],{"className":13930,"ariaHidden":246},[245],[128,13932,13934,13937],{"className":13933},[250],[128,13935],{"className":13936,"style":7758},[254],[128,13938,7590],{"className":13939},[259,1873],[128,13941,13943,13956],{"className":13942,"translate":218},[217],[128,13944,13946],{"className":13945},[222],[224,13947,13948],{"xmlns":226},[228,13949,13950,13954],{},[231,13951,13952],{},[1795,13953,2760],{"mathvariant":2001},[238,13955,4429],{"encoding":240},[128,13957,13959],{"className":13958,"ariaHidden":246},[245],[128,13960,13962,13965],{"className":13961},[250],[128,13963],{"className":13964,"style":4439},[254],[128,13966,2760],{"className":13967},[259,2151]," 独立，且各自的边缘分布如命题所述。",[11,13970,13971,13972,14018,14019,14047,14048,14230,14231,14234],{},"命题 1.4 给出了三条即时的推论。其一，它提供了一个 ",[128,13973,13975,13996],{"className":13974,"translate":218},[217],[128,13976,13978],{"className":13977},[222],[224,13979,13980],{"xmlns":226},[228,13981,13982,13993],{},[231,13983,13984,13987,13989,13991],{},[1795,13985,13986],{},"O",[1832,13988,2477],{"stretchy":1837},[1795,13990,1853],{},[1832,13992,2486],{"stretchy":1837},[238,13994,13995],{"encoding":240},"O(K)",[128,13997,13999],{"className":13998,"ariaHidden":246},[245],[128,14000,14002,14005,14009,14012,14015],{"className":14001},[250],[128,14003],{"className":14004,"style":1892},[254],[128,14006,13986],{"className":14007,"style":14008},[259,1873],"margin-right:0.0278em;",[128,14010,2477],{"className":14011},[1896],[128,14013,1853],{"className":14014,"style":1924},[259,1873],[128,14016,2486],{"className":14017},[1928]," 的精确采样算法：独立抽取 ",[128,14020,14022,14035],{"className":14021,"translate":218},[217],[128,14023,14025],{"className":14024},[222],[224,14026,14027],{"xmlns":226},[228,14028,14029,14033],{},[231,14030,14031],{},[1795,14032,1853],{},[238,14034,1853],{"encoding":240},[128,14036,14038],{"className":14037,"ariaHidden":246},[245],[128,14039,14041,14044],{"className":14040},[250],[128,14042],{"className":14043,"style":283},[254],[128,14045,1853],{"className":14046,"style":1924},[259,1873]," 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 ",[128,14049,14051,14083],{"className":14050,"translate":218},[217],[128,14052,14054],{"className":14053},[222],[224,14055,14056],{"xmlns":226},[228,14057,14058,14080],{},[231,14059,14060,14066,14068,14074],{},[2016,14061,14062,14064],{},[1795,14063,4835],{},[1840,14065,2028],{},[1832,14067,1994],{},[2016,14069,14070,14072],{},[1832,14071,2042],{},[1795,14073,2801],{},[2016,14075,14076,14078],{},[1795,14077,4835],{},[1795,14079,2801],{},[238,14081,14082],{"encoding":240},"\\alpha_0 = \\sum_i \\alpha_i",[128,14084,14086,14141],{"className":14085,"ariaHidden":246},[245],[128,14087,14089,14092,14132,14135,14138],{"className":14088},[250],[128,14090],{"className":14091,"style":4242},[254],[128,14093,14095,14098],{"className":14094},[259],[128,14096,4835],{"className":14097,"style":4920},[259,1873],[128,14099,14101],{"className":14100},[2087],[128,14102,14104,14124],{"className":14103},[274,321],[128,14105,14107,14121],{"className":14106},[278],[128,14108,14110],{"className":14109,"style":2945},[282],[128,14111,14112,14115],{"style":4935},[128,14113],{"className":14114,"style":291},[290],[128,14116,14118],{"className":14117},[299,300,301,298],[128,14119,2028],{"className":14120},[259,298],[128,14122,347],{"className":14123},[346],[128,14125,14127],{"className":14126},[278],[128,14128,14130],{"className":14129,"style":2241},[282],[128,14131],{},[128,14133],{"className":14134,"style":1878},[269],[128,14136,1994],{"className":14137},[1882],[128,14139],{"className":14140,"style":1878},[269],[128,14142,14144,14147,14187,14190],{"className":14143},[250],[128,14145],{"className":14146,"style":7777},[254],[128,14148,14150,14153],{"className":14149},[2268],[128,14151,2042],{"className":14152,"style":2274},[2268,2272,2273],[128,14154,14156],{"className":14155},[2087],[128,14157,14159,14179],{"className":14158},[274,321],[128,14160,14162,14176],{"className":14161},[278],[128,14163,14165],{"className":14164,"style":7796},[282],[128,14166,14167,14170],{"style":2290},[128,14168],{"className":14169,"style":291},[290],[128,14171,14173],{"className":14172},[299,300,301,298],[128,14174,2801],{"className":14175},[259,1873,298],[128,14177,347],{"className":14178},[346],[128,14180,14182],{"className":14181},[278],[128,14183,14185],{"className":14184,"style":2330},[282],[128,14186],{},[128,14188],{"className":14189,"style":1907},[269],[128,14191,14193,14196],{"className":14192},[259],[128,14194,4835],{"className":14195,"style":4920},[259,1873],[128,14197,14199],{"className":14198},[2087],[128,14200,14202,14222],{"className":14201},[274,321],[128,14203,14205,14219],{"className":14204},[278],[128,14206,14208],{"className":14207,"style":3095},[282],[128,14209,14210,14213],{"style":4935},[128,14211],{"className":14212,"style":291},[290],[128,14214,14216],{"className":14215},[299,300,301,298],[128,14217,2801],{"className":14218},[259,1873,298],[128,14220,347],{"className":14221},[346],[128,14223,14225],{"className":14224},[278],[128,14226,14228],{"className":14227,"style":2241},[282],[128,14229],{}," 在概率意义上是",[35,14232,14233],{},"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。",[2610,14236,14238],{"id":14237},"_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",[11,14240,14241,14244,14245,14295,14296,14452,14453,14523],{},[35,14242,14243],{},"退化到 Beta 分布。"," 当 ",[128,14246,14248,14265],{"className":14247,"translate":218},[217],[128,14249,14251],{"className":14250},[222],[224,14252,14253],{"xmlns":226},[228,14254,14255,14263],{},[231,14256,14257,14259,14261],{},[1795,14258,1853],{},[1832,14260,1994],{},[1840,14262,2639],{},[238,14264,3859],{"encoding":240},[128,14266,14268,14286],{"className":14267,"ariaHidden":246},[245],[128,14269,14271,14274,14277,14280,14283],{"className":14270},[250],[128,14272],{"className":14273,"style":283},[254],[128,14275,1853],{"className":14276,"style":1924},[259,1873],[128,14278],{"className":14279,"style":1878},[269],[128,14281,1994],{"className":14282},[1882],[128,14284],{"className":14285,"style":1878},[269],[128,14287,14289,14292],{"className":14288},[250],[128,14290],{"className":14291,"style":2594},[254],[128,14293,2639],{"className":14294},[259]," 时，约束 ",[128,14297,14299,14329],{"className":14298,"translate":218},[217],[128,14300,14302],{"className":14301},[222],[224,14303,14304],{"xmlns":226},[228,14305,14306,14326],{},[231,14307,14308,14314,14316,14322,14324],{},[2016,14309,14310,14312],{},[1795,14311,2760],{},[1840,14313,1842],{},[1832,14315,9486],{},[2016,14317,14318,14320],{},[1795,14319,2760],{},[1840,14321,2639],{},[1832,14323,1994],{},[1840,14325,1842],{},[238,14327,14328],{"encoding":240},"x_1 + x_2 = 1",[128,14330,14332,14388,14443],{"className":14331,"ariaHidden":246},[245],[128,14333,14335,14339,14379,14382,14385],{"className":14334},[250],[128,14336],{"className":14337,"style":14338},[254],"height:0.7333em;vertical-align:-0.15em;",[128,14340,14342,14345],{"className":14341},[259],[128,14343,2760],{"className":14344},[259,1873],[128,14346,14348],{"className":14347},[2087],[128,14349,14351,14371],{"className":14350},[274,321],[128,14352,14354,14368],{"className":14353},[278],[128,14355,14357],{"className":14356,"style":2945},[282],[128,14358,14359,14362],{"style":2221},[128,14360],{"className":14361,"style":291},[290],[128,14363,14365],{"className":14364},[299,300,301,298],[128,14366,1842],{"className":14367},[259,298],[128,14369,347],{"className":14370},[346],[128,14372,14374],{"className":14373},[278],[128,14375,14377],{"className":14376,"style":2241},[282],[128,14378],{},[128,14380],{"className":14381,"style":2508},[269],[128,14383,9486],{"className":14384},[2115],[128,14386],{"className":14387,"style":2508},[269],[128,14389,14391,14394,14434,14437,14440],{"className":14390},[250],[128,14392],{"className":14393,"style":4242},[254],[128,14395,14397,14400],{"className":14396},[259],[128,14398,2760],{"className":14399},[259,1873],[128,14401,14403],{"className":14402},[2087],[128,14404,14406,14426],{"className":14405},[274,321],[128,14407,14409,14423],{"className":14408},[278],[128,14410,14412],{"className":14411,"style":2945},[282],[128,14413,14414,14417],{"style":2221},[128,14415],{"className":14416,"style":291},[290],[128,14418,14420],{"className":14419},[299,300,301,298],[128,14421,2639],{"className":14422},[259,298],[128,14424,347],{"className":14425},[346],[128,14427,14429],{"className":14428},[278],[128,14430,14432],{"className":14431,"style":2241},[282],[128,14433],{},[128,14435],{"className":14436,"style":1878},[269],[128,14438,1994],{"className":14439},[1882],[128,14441],{"className":14442,"style":1878},[269],[128,14444,14446,14449],{"className":14445},[250],[128,14447],{"className":14448,"style":2594},[254],[128,14450,1842],{"className":14451},[259]," 使分布由单一变量 ",[128,14454,14456,14474],{"className":14455,"translate":218},[217],[128,14457,14459],{"className":14458},[222],[224,14460,14461],{"xmlns":226},[228,14462,14463,14471],{},[231,14464,14465],{},[2016,14466,14467,14469],{},[1795,14468,2760],{},[1840,14470,1842],{},[238,14472,14473],{"encoding":240},"x_1",[128,14475,14477],{"className":14476,"ariaHidden":246},[245],[128,14478,14480,14483],{"className":14479},[250],[128,14481],{"className":14482,"style":4242},[254],[128,14484,14486,14489],{"className":14485},[259],[128,14487,2760],{"className":14488},[259,1873],[128,14490,14492],{"className":14491},[2087],[128,14493,14495,14515],{"className":14494},[274,321],[128,14496,14498,14512],{"className":14497},[278],[128,14499,14501],{"className":14500,"style":2945},[282],[128,14502,14503,14506],{"style":2221},[128,14504],{"className":14505,"style":291},[290],[128,14507,14509],{"className":14508},[299,300,301,298],[128,14510,1842],{"className":14511},[259,298],[128,14513,347],{"className":14514},[346],[128,14516,14518],{"className":14517},[278],[128,14519,14521],{"className":14520,"style":2241},[282],[128,14522],{}," 完全决定，密度退化为",[128,14525,14527],{"className":14526,"translate":218},[1962],[128,14528,14530,14701],{"className":14529,"translate":218},[217],[128,14531,14533],{"className":14532},[222],[224,14534,14535],{"xmlns":226,"display":1971},[228,14536,14537,14698],{},[231,14538,14539,14541,14543,14549,14551,14557,14559,14565,14567,14569,14641,14643,14645,14648,14650,14652,14654,14656,14662,14664,14670,14672,14675,14678,14680,14682,14688,14690,14696],{},[1795,14540,5436],{},[1832,14542,2477],{"stretchy":1837},[2016,14544,14545,14547],{},[1795,14546,2760],{},[1840,14548,1842],{},[1832,14550,5443],{},[2016,14552,14553,14555],{},[1795,14554,4835],{},[1840,14556,1842],{},[1832,14558,1845],{"separator":246},[2016,14560,14561,14563],{},[1795,14562,4835],{},[1840,14564,2639],{},[1832,14566,2486],{"stretchy":1837},[1832,14568,1994],{},[5451,14570,14571,14619],{},[231,14572,14573,14591,14593,14595,14597,14603],{},[2038,14574,14575,14577,14579],{},[1795,14576,2760],{},[1840,14578,1842],{},[231,14580,14581,14587,14589],{},[2016,14582,14583,14585],{},[1795,14584,4835],{},[1840,14586,1842],{},[1832,14588,1989],{},[1840,14590,1842],{},[1832,14592,2477],{"stretchy":1837},[1840,14594,1842],{},[1832,14596,1989],{},[2016,14598,14599,14601],{},[1795,14600,2760],{},[1840,14602,1842],{},[1977,14604,14605,14607],{},[1832,14606,2486],{"stretchy":1837},[231,14608,14609,14615,14617],{},[2016,14610,14611,14613],{},[1795,14612,4835],{},[1840,14614,2639],{},[1832,14616,1989],{},[1840,14618,1842],{},[231,14620,14621,14623,14625,14631,14633,14639],{},[1795,14622,5459],{},[1832,14624,2477],{"stretchy":1837},[2016,14626,14627,14629],{},[1795,14628,4835],{},[1840,14630,1842],{},[1832,14632,1845],{"separator":246},[2016,14634,14635,14637],{},[1795,14636,4835],{},[1840,14638,2639],{},[1832,14640,2486],{"stretchy":1837},[1832,14642,1845],{"separator":246},[269,14644],{"width":11568},[234,14646,14647],{},"即",[269,14649],{"width":11568},[1795,14651,5914],{"mathvariant":1981},[1832,14653,3278],{},[1832,14655,2477],{"stretchy":1837},[2016,14657,14658,14660],{},[1795,14659,4835],{},[1840,14661,1842],{},[1832,14663,1845],{"separator":246},[2016,14665,14666,14668],{},[1795,14667,4835],{},[1840,14669,2639],{},[1832,14671,2486],{"stretchy":1837},[1832,14673,14674],{},"≡",[1795,14676,14677],{"mathvariant":1981},"Beta",[1832,14679,3278],{},[1832,14681,2477],{"stretchy":1837},[2016,14683,14684,14686],{},[1795,14685,4835],{},[1840,14687,1842],{},[1832,14689,1845],{"separator":246},[2016,14691,14692,14694],{},[1795,14693,4835],{},[1840,14695,2639],{},[1832,14697,2486],{"stretchy":1837},[238,14699,14700],{"encoding":240},"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)",[128,14702,14704,14765,14869,15386],{"className":14703,"ariaHidden":246},[245],[128,14705,14707,14710,14713,14716,14756,14759,14762],{"className":14706},[250],[128,14708],{"className":14709,"style":1892},[254],[128,14711,5436],{"className":14712,"style":5514},[259,1873],[128,14714,2477],{"className":14715},[1896],[128,14717,14719,14722],{"className":14718},[259],[128,14720,2760],{"className":14721},[259,1873],[128,14723,14725],{"className":14724},[2087],[128,14726,14728,14748],{"className":14727},[274,321],[128,14729,14731,14745],{"className":14730},[278],[128,14732,14734],{"className":14733,"style":2945},[282],[128,14735,14736,14739],{"style":2221},[128,14737],{"className":14738,"style":291},[290],[128,14740,14742],{"className":14741},[299,300,301,298],[128,14743,1842],{"className":14744},[259,298],[128,14746,347],{"className":14747},[346],[128,14749,14751],{"className":14750},[278],[128,14752,14754],{"className":14753,"style":2241},[282],[128,14755],{},[128,14757],{"className":14758,"style":1878},[269],[128,14760,5443],{"className":14761},[1882],[128,14763],{"className":14764,"style":1878},[269],[128,14766,14768,14771,14811,14814,14817,14857,14860,14863,14866],{"className":14767},[250],[128,14769],{"className":14770,"style":1892},[254],[128,14772,14774,14777],{"className":14773},[259],[128,14775,4835],{"className":14776,"style":4920},[259,1873],[128,14778,14780],{"className":14779},[2087],[128,14781,14783,14803],{"className":14782},[274,321],[128,14784,14786,14800],{"className":14785},[278],[128,14787,14789],{"className":14788,"style":2945},[282],[128,14790,14791,14794],{"style":4935},[128,14792],{"className":14793,"style":291},[290],[128,14795,14797],{"className":14796},[299,300,301,298],[128,14798,1842],{"className":14799},[259,298],[128,14801,347],{"className":14802},[346],[128,14804,14806],{"className":14805},[278],[128,14807,14809],{"className":14808,"style":2241},[282],[128,14810],{},[128,14812,1845],{"className":14813},[1903],[128,14815],{"className":14816,"style":1907},[269],[128,14818,14820,14823],{"className":14819},[259],[128,14821,4835],{"className":14822,"style":4920},[259,1873],[128,14824,14826],{"className":14825},[2087],[128,14827,14829,14849],{"className":14828},[274,321],[128,14830,14832,14846],{"className":14831},[278],[128,14833,14835],{"className":14834,"style":2945},[282],[128,14836,14837,14840],{"style":4935},[128,14838],{"className":14839,"style":291},[290],[128,14841,14843],{"className":14842},[299,300,301,298],[128,14844,2639],{"className":14845},[259,298],[128,14847,347],{"className":14848},[346],[128,14850,14852],{"className":14851},[278],[128,14853,14855],{"className":14854,"style":2241},[282],[128,14856],{},[128,14858,2486],{"className":14859},[1928],[128,14861],{"className":14862,"style":1878},[269],[128,14864,1994],{"className":14865},[1882],[128,14867],{"className":14868,"style":1878},[269],[128,14870,14872,14876,15257,15260,15263,15266,15273,15276,15279,15285,15288,15328,15331,15334,15374,15377,15380,15383],{"className":14871},[250],[128,14873],{"className":14874,"style":14875},[254],"height:2.509em;vertical-align:-0.936em;",[128,14877,14879,14882,15254],{"className":14878},[259],[128,14880],{"className":14881},[1896,5570],[128,14883,14885],{"className":14884},[5451],[128,14886,14888,15246],{"className":14887},[274,321],[128,14889,14891,15243],{"className":14890},[278],[128,14892,14895,14998,15006],{"className":14893,"style":14894},[282],"height:1.573em;",[128,14896,14897,14900],{"style":13123},[128,14898],{"className":14899,"style":335},[290],[128,14901,14903,14906,14909,14949,14952,14955,14995],{"className":14902},[259],[128,14904,5459],{"className":14905,"style":5599},[259,1873],[128,14907,2477],{"className":14908},[1896],[128,14910,14912,14915],{"className":14911},[259],[128,14913,4835],{"className":14914,"style":4920},[259,1873],[128,14916,14918],{"className":14917},[2087],[128,14919,14921,14941],{"className":14920},[274,321],[128,14922,14924,14938],{"className":14923},[278],[128,14925,14927],{"className":14926,"style":2945},[282],[128,14928,14929,14932],{"style":4935},[128,14930],{"className":14931,"style":291},[290],[128,14933,14935],{"className":14934},[299,300,301,298],[128,14936,1842],{"className":14937},[259,298],[128,14939,347],{"className":14940},[346],[128,14942,14944],{"className":14943},[278],[128,14945,14947],{"className":14946,"style":2241},[282],[128,14948],{},[128,14950,1845],{"className":14951},[1903],[128,14953],{"className":14954,"style":1907},[269],[128,14956,14958,14961],{"className":14957},[259],[128,14959,4835],{"className":14960,"style":4920},[259,1873],[128,14962,14964],{"className":14963},[2087],[128,14965,14967,14987],{"className":14966},[274,321],[128,14968,14970,14984],{"className":14969},[278],[128,14971,14973],{"className":14972,"style":2945},[282],[128,14974,14975,14978],{"style":4935},[128,14976],{"className":14977,"style":291},[290],[128,14979,14981],{"className":14980},[299,300,301,298],[128,14982,2639],{"className":14983},[259,298],[128,14985,347],{"className":14986},[346],[128,14988,14990],{"className":14989},[278],[128,14991,14993],{"className":14992,"style":2241},[282],[128,14994],{},[128,14996,2486],{"className":14997},[1928],[128,14999,15000,15003],{"style":5617},[128,15001],{"className":15002,"style":335},[290],[128,15004],{"className":15005,"style":5625},[5624],[128,15007,15008,15011],{"style":13189},[128,15009],{"className":15010,"style":335},[290],[128,15012,15014,15113,15116,15119,15122,15125,15128,15168],{"className":15013},[259],[128,15015,15017,15020],{"className":15016},[259],[128,15018,2760],{"className":15019},[259,1873],[128,15021,15023],{"className":15022},[2087],[128,15024,15026,15104],{"className":15025},[274,321],[128,15027,15029,15101],{"className":15028},[278],[128,15030,15032,15044],{"className":15031,"style":5740},[282],[128,15033,15035,15038],{"style":15034},"top:-2.4337em;margin-left:0em;margin-right:0.05em;",[128,15036],{"className":15037,"style":291},[290],[128,15039,15041],{"className":15040},[299,300,301,298],[128,15042,1842],{"className":15043},[259,298],[128,15045,15046,15049],{"style":5755},[128,15047],{"className":15048,"style":291},[290],[128,15050,15052],{"className":15051},[299,300,301,298],[128,15053,15055,15095,15098],{"className":15054},[259,298],[128,15056,15058,15061],{"className":15057},[259,298],[128,15059,4835],{"className":15060,"style":4920},[259,1873,298],[128,15062,15064],{"className":15063},[2087],[128,15065,15067,15087],{"className":15066},[274,321],[128,15068,15070,15084],{"className":15069},[278],[128,15071,15073],{"className":15072,"style":6153},[282],[128,15074,15075,15078],{"style":5786},[128,15076],{"className":15077,"style":5790},[290],[128,15079,15081],{"className":15080},[299,5794,5795,298],[128,15082,1842],{"className":15083},[259,298],[128,15085,347],{"className":15086},[346],[128,15088,15090],{"className":15089},[278],[128,15091,15093],{"className":15092,"style":5808},[282],[128,15094],{},[128,15096,1989],{"className":15097},[2115,298],[128,15099,1842],{"className":15100},[259,298],[128,15102,347],{"className":15103},[346],[128,15105,15107],{"className":15106},[278],[128,15108,15111],{"className":15109,"style":15110},[282],"height:0.2663em;",[128,15112],{},[128,15114,2477],{"className":15115},[1896],[128,15117,1842],{"className":15118},[259],[128,15120],{"className":15121,"style":2508},[269],[128,15123,1989],{"className":15124},[2115],[128,15126],{"className":15127,"style":2508},[269],[128,15129,15131,15134],{"className":15130},[259],[128,15132,2760],{"className":15133},[259,1873],[128,15135,15137],{"className":15136},[2087],[128,15138,15140,15160],{"className":15139},[274,321],[128,15141,15143,15157],{"className":15142},[278],[128,15144,15146],{"className":15145,"style":2945},[282],[128,15147,15148,15151],{"style":2221},[128,15149],{"className":15150,"style":291},[290],[128,15152,15154],{"className":15153},[299,300,301,298],[128,15155,1842],{"className":15156},[259,298],[128,15158,347],{"className":15159},[346],[128,15161,15163],{"className":15162},[278],[128,15164,15166],{"className":15165,"style":2241},[282],[128,15167],{},[128,15169,15171,15174],{"className":15170},[1928],[128,15172,2486],{"className":15173},[1928],[128,15175,15177],{"className":15176},[2087],[128,15178,15180],{"className":15179},[274],[128,15181,15183],{"className":15182},[278],[128,15184,15186],{"className":15185,"style":9629},[282],[128,15187,15188,15191],{"style":2452},[128,15189],{"className":15190,"style":291},[290],[128,15192,15194],{"className":15193},[299,300,301,298],[128,15195,15197,15237,15240],{"className":15196},[259,298],[128,15198,15200,15203],{"className":15199},[259,298],[128,15201,4835],{"className":15202,"style":4920},[259,1873,298],[128,15204,15206],{"className":15205},[2087],[128,15207,15209,15229],{"className":15208},[274,321],[128,15210,15212,15226],{"className":15211},[278],[128,15213,15215],{"className":15214,"style":6153},[282],[128,15216,15217,15220],{"style":5786},[128,15218],{"className":15219,"style":5790},[290],[128,15221,15223],{"className":15222},[299,5794,5795,298],[128,15224,2639],{"className":15225},[259,298],[128,15227,347],{"className":15228},[346],[128,15230,15232],{"className":15231},[278],[128,15233,15235],{"className":15234,"style":5808},[282],[128,15236],{},[128,15238,1989],{"className":15239},[2115,298],[128,15241,1842],{"className":15242},[259,298],[128,15244,347],{"className":15245},[346],[128,15247,15249],{"className":15248},[278],[128,15250,15252],{"className":15251,"style":13315},[282],[128,15253],{},[128,15255],{"className":15256},[1928,5570],[128,15258,1845],{"className":15259},[1903],[128,15261],{"className":15262,"style":11756},[269],[128,15264],{"className":15265,"style":1907},[269],[128,15267,15269],{"className":15268},[259,260],[128,15270,14647],{"className":15271},[259,15272],"cjk_fallback",[128,15274],{"className":15275,"style":11756},[269],[128,15277],{"className":15278,"style":1907},[269],[128,15280,15282],{"className":15281},[2268],[128,15283,5914],{"className":15284},[259,3353],[128,15286,2477],{"className":15287},[1896],[128,15289,15291,15294],{"className":15290},[259],[128,15292,4835],{"className":15293,"style":4920},[259,1873],[128,15295,15297],{"className":15296},[2087],[128,15298,15300,15320],{"className":15299},[274,321],[128,15301,15303,15317],{"className":15302},[278],[128,15304,15306],{"className":15305,"style":2945},[282],[128,15307,15308,15311],{"style":4935},[128,15309],{"className":15310,"style":291},[290],[128,15312,15314],{"className":15313},[299,300,301,298],[128,15315,1842],{"className":15316},[259,298],[128,15318,347],{"className":15319},[346],[128,15321,15323],{"className":15322},[278],[128,15324,15326],{"className":15325,"style":2241},[282],[128,15327],{},[128,15329,1845],{"className":15330},[1903],[128,15332],{"className":15333,"style":1907},[269],[128,15335,15337,15340],{"className":15336},[259],[128,15338,4835],{"className":15339,"style":4920},[259,1873],[128,15341,15343],{"className":15342},[2087],[128,15344,15346,15366],{"className":15345},[274,321],[128,15347,15349,15363],{"className":15348},[278],[128,15350,15352],{"className":15351,"style":2945},[282],[128,15353,15354,15357],{"style":4935},[128,15355],{"className":15356,"style":291},[290],[128,15358,15360],{"className":15359},[299,300,301,298],[128,15361,2639],{"className":15362},[259,298],[128,15364,347],{"className":15365},[346],[128,15367,15369],{"className":15368},[278],[128,15370,15372],{"className":15371,"style":2241},[282],[128,15373],{},[128,15375,2486],{"className":15376},[1928],[128,15378],{"className":15379,"style":1878},[269],[128,15381,14674],{"className":15382},[1882],[128,15384],{"className":15385,"style":1878},[269],[128,15387,15389,15392,15398,15401,15441,15444,15447,15487],{"className":15388},[250],[128,15390],{"className":15391,"style":1892},[254],[128,15393,15395],{"className":15394},[2268],[128,15396,14677],{"className":15397},[259,3353],[128,15399,2477],{"className":15400},[1896],[128,15402,15404,15407],{"className":15403},[259],[128,15405,4835],{"className":15406,"style":4920},[259,1873],[128,15408,15410],{"className":15409},[2087],[128,15411,15413,15433],{"className":15412},[274,321],[128,15414,15416,15430],{"className":15415},[278],[128,15417,15419],{"className":15418,"style":2945},[282],[128,15420,15421,15424],{"style":4935},[128,15422],{"className":15423,"style":291},[290],[128,15425,15427],{"className":15426},[299,300,301,298],[128,15428,1842],{"className":15429},[259,298],[128,15431,347],{"className":15432},[346],[128,15434,15436],{"className":15435},[278],[128,15437,15439],{"className":15438,"style":2241},[282],[128,15440],{},[128,15442,1845],{"className":15443},[1903],[128,15445],{"className":15446,"style":1907},[269],[128,15448,15450,15453],{"className":15449},[259],[128,15451,4835],{"className":15452,"style":4920},[259,1873],[128,15454,15456],{"className":15455},[2087],[128,15457,15459,15479],{"className":15458},[274,321],[128,15460,15462,15476],{"className":15461},[278],[128,15463,15465],{"className":15464,"style":2945},[282],[128,15466,15467,15470],{"style":4935},[128,15468],{"className":15469,"style":291},[290],[128,15471,15473],{"className":15472},[299,300,301,298],[128,15474,2639],{"className":15475},[259,298],[128,15477,347],{"className":15478},[346],[128,15480,15482],{"className":15481},[278],[128,15483,15485],{"className":15484,"style":2241},[282],[128,15486],{},[128,15488,2486],{"className":15489},[1928],[11,15491,15492,15493,15544],{},"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 ",[128,15494,15496,15514],{"className":15495,"translate":218},[217],[128,15497,15499],{"className":15498},[222],[224,15500,15501],{"xmlns":226},[228,15502,15503,15511],{},[231,15504,15505,15507,15509],{},[1795,15506,1853],{},[1832,15508,1994],{},[1840,15510,2639],{},[238,15512,15513],{"encoding":240},"K=2",[128,15515,15517,15535],{"className":15516,"ariaHidden":246},[245],[128,15518,15520,15523,15526,15529,15532],{"className":15519},[250],[128,15521],{"className":15522,"style":283},[254],[128,15524,1853],{"className":15525,"style":1924},[259,1873],[128,15527],{"className":15528,"style":1878},[269],[128,15530,1994],{"className":15531},[1882],[128,15533],{"className":15534,"style":1878},[269],[128,15536,15538,15541],{"className":15537},[250],[128,15539],{"className":15540,"style":2594},[254],[128,15542,2639],{"className":15543},[259]," 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。",[11,15546,15547,15550,15551,15621,15622,15829,15830,15983,15984,16150,16151,16220],{},[35,15548,15549],{},"边缘分布仍为 Beta。"," 更一般地，任意单个分量 ",[128,15552,15554,15572],{"className":15553,"translate":218},[217],[128,15555,15557],{"className":15556},[222],[224,15558,15559],{"xmlns":226},[228,15560,15561,15569],{},[231,15562,15563],{},[2016,15564,15565,15567],{},[1795,15566,2760],{},[1795,15568,2801],{},[238,15570,15571],{"encoding":240},"x_i",[128,15573,15575],{"className":15574,"ariaHidden":246},[245],[128,15576,15578,15581],{"className":15577},[250],[128,15579],{"className":15580,"style":4242},[254],[128,15582,15584,15587],{"className":15583},[259],[128,15585,2760],{"className":15586},[259,1873],[128,15588,15590],{"className":15589},[2087],[128,15591,15593,15613],{"className":15592},[274,321],[128,15594,15596,15610],{"className":15595},[278],[128,15597,15599],{"className":15598,"style":3095},[282],[128,15600,15601,15604],{"style":2221},[128,15602],{"className":15603,"style":291},[290],[128,15605,15607],{"className":15606},[299,300,301,298],[128,15608,2801],{"className":15609},[259,1873,298],[128,15611,347],{"className":15612},[346],[128,15614,15616],{"className":15615},[278],[128,15617,15619],{"className":15618,"style":2241},[282],[128,15620],{}," 的边缘分布是 ",[128,15623,15625,15667],{"className":15624,"translate":218},[217],[128,15626,15628],{"className":15627},[222],[224,15629,15630],{"xmlns":226},[228,15631,15632,15664],{},[231,15633,15634,15636,15638,15640,15646,15648,15654,15656,15662],{},[1795,15635,14677],{"mathvariant":1981},[1832,15637,3278],{},[1832,15639,2477],{"stretchy":1837},[2016,15641,15642,15644],{},[1795,15643,4835],{},[1795,15645,2801],{},[1832,15647,1845],{"separator":246},[2016,15649,15650,15652],{},[1795,15651,4835],{},[1840,15653,2028],{},[1832,15655,1989],{},[2016,15657,15658,15660],{},[1795,15659,4835],{},[1795,15661,2801],{},[1832,15663,2486],{"stretchy":1837},[238,15665,15666],{"encoding":240},"\\operatorname{Beta}(\\alpha_i, \\alpha_0 - \\alpha_i)",[128,15668,15670,15780],{"className":15669,"ariaHidden":246},[245],[128,15671,15673,15676,15682,15685,15725,15728,15731,15771,15774,15777],{"className":15672},[250],[128,15674],{"className":15675,"style":1892},[254],[128,15677,15679],{"className":15678},[2268],[128,15680,14677],{"className":15681},[259,3353],[128,15683,2477],{"className":15684},[1896],[128,15686,15688,15691],{"className":15687},[259],[128,15689,4835],{"className":15690,"style":4920},[259,1873],[128,15692,15694],{"className":15693},[2087],[128,15695,15697,15717],{"className":15696},[274,321],[128,15698,15700,15714],{"className":15699},[278],[128,15701,15703],{"className":15702,"style":3095},[282],[128,15704,15705,15708],{"style":4935},[128,15706],{"className":15707,"style":291},[290],[128,15709,15711],{"className":15710},[299,300,301,298],[128,15712,2801],{"className":15713},[259,1873,298],[128,15715,347],{"className":15716},[346],[128,15718,15720],{"className":15719},[278],[128,15721,15723],{"className":15722,"style":2241},[282],[128,15724],{},[128,15726,1845],{"className":15727},[1903],[128,15729],{"className":15730,"style":1907},[269],[128,15732,15734,15737],{"className":15733},[259],[128,15735,4835],{"className":15736,"style":4920},[259,1873],[128,15738,15740],{"className":15739},[2087],[128,15741,15743,15763],{"className":15742},[274,321],[128,15744,15746,15760],{"className":15745},[278],[128,15747,15749],{"className":15748,"style":2945},[282],[128,15750,15751,15754],{"style":4935},[128,15752],{"className":15753,"style":291},[290],[128,15755,15757],{"className":15756},[299,300,301,298],[128,15758,2028],{"className":15759},[259,298],[128,15761,347],{"className":15762},[346],[128,15764,15766],{"className":15765},[278],[128,15767,15769],{"className":15768,"style":2241},[282],[128,15770],{},[128,15772],{"className":15773,"style":2508},[269],[128,15775,1989],{"className":15776},[2115],[128,15778],{"className":15779,"style":2508},[269],[128,15781,15783,15786,15826],{"className":15782},[250],[128,15784],{"className":15785,"style":1892},[254],[128,15787,15789,15792],{"className":15788},[259],[128,15790,4835],{"className":15791,"style":4920},[259,1873],[128,15793,15795],{"className":15794},[2087],[128,15796,15798,15818],{"className":15797},[274,321],[128,15799,15801,15815],{"className":15800},[278],[128,15802,15804],{"className":15803,"style":3095},[282],[128,15805,15806,15809],{"style":4935},[128,15807],{"className":15808,"style":291},[290],[128,15810,15812],{"className":15811},[299,300,301,298],[128,15813,2801],{"className":15814},[259,1873,298],[128,15816,347],{"className":15817},[346],[128,15819,15821],{"className":15820},[278],[128,15822,15824],{"className":15823,"style":2241},[282],[128,15825],{},[128,15827,2486],{"className":15828},[1928],"。这一点可由命题 1.4 直接看出：",[128,15831,15833,15867],{"className":15832,"translate":218},[217],[128,15834,15836],{"className":15835},[222],[224,15837,15838],{"xmlns":226},[228,15839,15840,15864],{},[231,15841,15842,15848,15850,15856,15858,15860,15862],{},[2016,15843,15844,15846],{},[1795,15845,2760],{},[1795,15847,2801],{},[1832,15849,1994],{},[2016,15851,15852,15854],{},[1795,15853,11131],{},[1795,15855,2801],{},[1795,15857,4751],{"mathvariant":1981},[1832,15859,2477],{"stretchy":1837},[1795,15861,7590],{},[1832,15863,2486],{"stretchy":1837},[238,15865,15866],{"encoding":240},"x_i = \\gamma_i \u002F (s)",[128,15868,15870,15925],{"className":15869,"ariaHidden":246},[245],[128,15871,15873,15876,15916,15919,15922],{"className":15872},[250],[128,15874],{"className":15875,"style":4242},[254],[128,15877,15879,15882],{"className":15878},[259],[128,15880,2760],{"className":15881},[259,1873],[128,15883,15885],{"className":15884},[2087],[128,15886,15888,15908],{"className":15887},[274,321],[128,15889,15891,15905],{"className":15890},[278],[128,15892,15894],{"className":15893,"style":3095},[282],[128,15895,15896,15899],{"style":2221},[128,15897],{"className":15898,"style":291},[290],[128,15900,15902],{"className":15901},[299,300,301,298],[128,15903,2801],{"className":15904},[259,1873,298],[128,15906,347],{"className":15907},[346],[128,15909,15911],{"className":15910},[278],[128,15912,15914],{"className":15913,"style":2241},[282],[128,15915],{},[128,15917],{"className":15918,"style":1878},[269],[128,15920,1994],{"className":15921},[1882],[128,15923],{"className":15924,"style":1878},[269],[128,15926,15928,15931,15971,15974,15977,15980],{"className":15927},[250],[128,15929],{"className":15930,"style":1892},[254],[128,15932,15934,15937],{"className":15933},[259],[128,15935,11131],{"className":15936,"style":11165},[259,1873],[128,15938,15940],{"className":15939},[2087],[128,15941,15943,15963],{"className":15942},[274,321],[128,15944,15946,15960],{"className":15945},[278],[128,15947,15949],{"className":15948,"style":3095},[282],[128,15950,15951,15954],{"style":11180},[128,15952],{"className":15953,"style":291},[290],[128,15955,15957],{"className":15956},[299,300,301,298],[128,15958,2801],{"className":15959},[259,1873,298],[128,15961,347],{"className":15962},[346],[128,15964,15966],{"className":15965},[278],[128,15967,15969],{"className":15968,"style":2241},[282],[128,15970],{},[128,15972,4751],{"className":15973},[259],[128,15975,2477],{"className":15976},[1896],[128,15978,7590],{"className":15979},[259,1873],[128,15981,2486],{"className":15982},[1928],"，而 ",[128,15985,15987,16021],{"className":15986,"translate":218},[217],[128,15988,15990],{"className":15989},[222],[224,15991,15992],{"xmlns":226},[228,15993,15994,16018],{},[231,15995,15996,16002,16004,16006,16008,16010,16016],{},[2016,15997,15998,16000],{},[1795,15999,11131],{},[1795,16001,2801],{},[1832,16003,12150],{},[1832,16005,2477],{"stretchy":1837},[1795,16007,7590],{},[1832,16009,1989],{},[2016,16011,16012,16014],{},[1795,16013,11131],{},[1795,16015,2801],{},[1832,16017,2486],{"stretchy":1837},[238,16019,16020],{"encoding":240},"\\gamma_i \\perp (s - \\gamma_i)",[128,16022,16024,16080,16101],{"className":16023,"ariaHidden":246},[245],[128,16025,16027,16031,16071,16074,16077],{"className":16026},[250],[128,16028],{"className":16029,"style":16030},[254],"height:0.8889em;vertical-align:-0.1944em;",[128,16032,16034,16037],{"className":16033},[259],[128,16035,11131],{"className":16036,"style":11165},[259,1873],[128,16038,16040],{"className":16039},[2087],[128,16041,16043,16063],{"className":16042},[274,321],[128,16044,16046,16060],{"className":16045},[278],[128,16047,16049],{"className":16048,"style":3095},[282],[128,16050,16051,16054],{"style":11180},[128,16052],{"className":16053,"style":291},[290],[128,16055,16057],{"className":16056},[299,300,301,298],[128,16058,2801],{"className":16059},[259,1873,298],[128,16061,347],{"className":16062},[346],[128,16064,16066],{"className":16065},[278],[128,16067,16069],{"className":16068,"style":2241},[282],[128,16070],{},[128,16072],{"className":16073,"style":1878},[269],[128,16075,12150],{"className":16076},[1882],[128,16078],{"className":16079,"style":1878},[269],[128,16081,16083,16086,16089,16092,16095,16098],{"className":16082},[250],[128,16084],{"className":16085,"style":1892},[254],[128,16087,2477],{"className":16088},[1896],[128,16090,7590],{"className":16091},[259,1873],[128,16093],{"className":16094,"style":2508},[269],[128,16096,1989],{"className":16097},[2115],[128,16099],{"className":16100,"style":2508},[269],[128,16102,16104,16107,16147],{"className":16103},[250],[128,16105],{"className":16106,"style":1892},[254],[128,16108,16110,16113],{"className":16109},[259],[128,16111,11131],{"className":16112,"style":11165},[259,1873],[128,16114,16116],{"className":16115},[2087],[128,16117,16119,16139],{"className":16118},[274,321],[128,16120,16122,16136],{"className":16121},[278],[128,16123,16125],{"className":16124,"style":3095},[282],[128,16126,16127,16130],{"style":11180},[128,16128],{"className":16129,"style":291},[290],[128,16131,16133],{"className":16132},[299,300,301,298],[128,16134,2801],{"className":16135},[259,1873,298],[128,16137,347],{"className":16138},[346],[128,16140,16142],{"className":16141},[278],[128,16143,16145],{"className":16144,"style":2241},[282],[128,16146],{},[128,16148,2486],{"className":16149},[1928],"，故 ",[128,16152,16154,16171],{"className":16153,"translate":218},[217],[128,16155,16157],{"className":16156},[222],[224,16158,16159],{"xmlns":226},[228,16160,16161,16169],{},[231,16162,16163],{},[2016,16164,16165,16167],{},[1795,16166,2760],{},[1795,16168,2801],{},[238,16170,15571],{"encoding":240},[128,16172,16174],{"className":16173,"ariaHidden":246},[245],[128,16175,16177,16180],{"className":16176},[250],[128,16178],{"className":16179,"style":4242},[254],[128,16181,16183,16186],{"className":16182},[259],[128,16184,2760],{"className":16185},[259,1873],[128,16187,16189],{"className":16188},[2087],[128,16190,16192,16212],{"className":16191},[274,321],[128,16193,16195,16209],{"className":16194},[278],[128,16196,16198],{"className":16197,"style":3095},[282],[128,16199,16200,16203],{"style":2221},[128,16201],{"className":16202,"style":291},[290],[128,16204,16206],{"className":16205},[299,300,301,298],[128,16207,2801],{"className":16208},[259,1873,298],[128,16210,347],{"className":16211},[346],[128,16213,16215],{"className":16214},[278],[128,16216,16218],{"className":16217,"style":2241},[282],[128,16219],{}," 是相互独立的两个 Gamma 变量之比，其分布为 Beta。",[11,16222,16223,16226,16227,16230,16231,16265,16266,16296,16297,893,16384],{},[35,16224,16225],{},"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",[35,16228,16229],{},"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」",[128,16232,16234,16247],{"className":16233,"translate":218},[217],[128,16235,16237],{"className":16236},[222],[224,16238,16239],{"xmlns":226},[228,16240,16241,16245],{},[231,16242,16243],{},[1795,16244,4835],{"mathvariant":4834},[238,16246,5875],{"encoding":240},[128,16248,16250],{"className":16249,"ariaHidden":246},[245],[128,16251,16253,16256],{"className":16252},[250],[128,16254],{"className":16255,"style":4439},[254],[128,16257,16259],{"className":16258},[259],[128,16260,16262],{"className":16261},[259],[128,16263,4835],{"className":16264},[259,4895]," 描述对各类别出现次数的初始信念，则观测到计数 ",[128,16267,16269,16284],{"className":16268,"translate":218},[217],[128,16270,16272],{"className":16271},[222],[224,16273,16274],{"xmlns":226},[228,16275,16276,16281],{},[231,16277,16278],{},[1795,16279,16280],{"mathvariant":2001},"n",[238,16282,16283],{"encoding":240},"\\mathbf{n}",[128,16285,16287],{"className":16286,"ariaHidden":246},[245],[128,16288,16290,16293],{"className":16289},[250],[128,16291],{"className":16292,"style":4439},[254],[128,16294,16280],{"className":16295},[259,2151]," 后，信念的更新只是 ",[128,16298,16300,16323],{"className":16299,"translate":218},[217],[128,16301,16303],{"className":16302},[222],[224,16304,16305],{"xmlns":226},[228,16306,16307,16320],{},[231,16308,16309,16311,16314,16316,16318],{},[1795,16310,4835],{"mathvariant":4834},[1832,16312,16313],{},"↦",[1795,16315,4835],{"mathvariant":4834},[1832,16317,9486],{},[1795,16319,16280],{"mathvariant":2001},[238,16321,16322],{"encoding":240},"\\boldsymbol{\\alpha} \\mapsto \\boldsymbol{\\alpha} + \\mathbf{n}",[128,16324,16326,16351,16375],{"className":16325,"ariaHidden":246},[245],[128,16327,16329,16333,16342,16345,16348],{"className":16328},[250],[128,16330],{"className":16331,"style":16332},[254],"height:0.522em;vertical-align:-0.011em;",[128,16334,16336],{"className":16335},[259],[128,16337,16339],{"className":16338},[259],[128,16340,4835],{"className":16341},[259,4895],[128,16343],{"className":16344,"style":1878},[269],[128,16346,16313],{"className":16347},[1882],[128,16349],{"className":16350,"style":1878},[269],[128,16352,16354,16357,16366,16369,16372],{"className":16353},[250],[128,16355],{"className":16356,"style":8462},[254],[128,16358,16360],{"className":16359},[259],[128,16361,16363],{"className":16362},[259],[128,16364,4835],{"className":16365},[259,4895],[128,16367],{"className":16368,"style":2508},[269],[128,16370,9486],{"className":16371},[2115],[128,16373],{"className":16374,"style":2508},[269],[128,16376,16378,16381],{"className":16377},[250],[128,16379],{"className":16380,"style":4439},[254],[128,16382,16280],{"className":16383},[259,2151],[35,16385,16386],{},"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。",[51,16388,16390],{"id":16389},"二解析性质","二、解析性质",[2610,16392,16394],{"id":16393},"_21-矩结构","2.1 矩结构",[2615,16396,16398],{"title":16397},"命题 2.1（期望、方差与协方差）",[11,16399,1781,16400,16476,16477,16522],{},[128,16401,16403,16428],{"className":16402,"translate":218},[217],[128,16404,16406],{"className":16405},[222],[224,16407,16408],{"xmlns":226},[228,16409,16410,16426],{},[231,16411,16412,16414,16416,16418,16420,16422,16424],{},[1795,16413,2760],{"mathvariant":2001},[1832,16415,5911],{},[1795,16417,5914],{"mathvariant":1981},[1832,16419,3278],{},[1832,16421,2477],{"stretchy":1837},[1795,16423,4835],{"mathvariant":4834},[1832,16425,2486],{"stretchy":1837},[238,16427,5925],{"encoding":240},[128,16429,16431,16449],{"className":16430,"ariaHidden":246},[245],[128,16432,16434,16437,16440,16443,16446],{"className":16433},[250],[128,16435],{"className":16436,"style":4439},[254],[128,16438,2760],{"className":16439},[259,2151],[128,16441],{"className":16442,"style":1878},[269],[128,16444,5911],{"className":16445},[1882],[128,16447],{"className":16448,"style":1878},[269],[128,16450,16452,16455,16461,16464,16473],{"className":16451},[250],[128,16453],{"className":16454,"style":1892},[254],[128,16456,16458],{"className":16457},[2268],[128,16459,5914],{"className":16460},[259,3353],[128,16462,2477],{"className":16463},[1896],[128,16465,16467],{"className":16466},[259],[128,16468,16470],{"className":16469},[259],[128,16471,4835],{"className":16472},[259,4895],[128,16474,2486],{"className":16475},[1928],"。则对任意 ",[128,16478,16480,16499],{"className":16479,"translate":218},[217],[128,16481,16483],{"className":16482},[222],[224,16484,16485],{"xmlns":226},[228,16486,16487,16496],{},[231,16488,16489,16491,16493],{},[1795,16490,2801],{},[1832,16492,1845],{"separator":246},[1795,16494,16495],{},"j",[238,16497,16498],{"encoding":240},"i, j",[128,16500,16502],{"className":16501,"ariaHidden":246},[245],[128,16503,16505,16509,16512,16515,16518],{"className":16504},[250],[128,16506],{"className":16507,"style":16508},[254],"height:0.854em;vertical-align:-0.1944em;",[128,16510,2801],{"className":16511},[259,1873],[128,16513,1845],{"className":16514},[1903],[128,16516],{"className":16517,"style":1907},[269],[128,16519,16495],{"className":16520,"style":16521},[259,1873],"margin-right:0.0572em;",[128,16523,16525,16724],{"className":16524,"translate":218},[217],[128,16526,16528],{"className":16527},[222],[224,16529,16530],{"xmlns":226},[228,16531,16532,16721],{},[231,16533,16534,16536,16539,16545,16548,16550,16564,16566,16568,16571,16573,16575,16581,16583,16585,16637,16639,16641,16644,16646,16648,16654,16656,16662,16664,16666,16708,16710,16712,16714,16717,16719],{},[1795,16535,342],{"mathvariant":2008},[1832,16537,16538],{"stretchy":1837},"[",[2016,16540,16541,16543],{},[1795,16542,2760],{},[1795,16544,2801],{},[1832,16546,16547],{"stretchy":1837},"]",[1832,16549,1994],{},[5451,16551,16552,16558],{},[2016,16553,16554,16556],{},[1795,16555,4835],{},[1795,16557,2801],{},[2016,16559,16560,16562],{},[1795,16561,4835],{},[1840,16563,2028],{},[1832,16565,1845],{"separator":246},[269,16567],{"width":11568},[1795,16569,16570],{"mathvariant":1981},"Var",[1832,16572,3278],{},[1832,16574,2477],{"stretchy":1837},[2016,16576,16577,16579],{},[1795,16578,2760],{},[1795,16580,2801],{},[1832,16582,2486],{"stretchy":1837},[1832,16584,1994],{},[5451,16586,16587,16613],{},[231,16588,16589,16595,16597,16603,16605,16611],{},[2016,16590,16591,16593],{},[1795,16592,4835],{},[1795,16594,2801],{},[1832,16596,2477],{"stretchy":1837},[2016,16598,16599,16601],{},[1795,16600,4835],{},[1840,16602,2028],{},[1832,16604,1989],{},[2016,16606,16607,16609],{},[1795,16608,4835],{},[1795,16610,2801],{},[1832,16612,2486],{"stretchy":1837},[231,16614,16615,16623,16625,16631,16633,16635],{},[2038,16616,16617,16619,16621],{},[1795,16618,4835],{},[1840,16620,2028],{},[1840,16622,2639],{},[1832,16624,2477],{"stretchy":1837},[2016,16626,16627,16629],{},[1795,16628,4835],{},[1840,16630,2028],{},[1832,16632,9486],{},[1840,16634,1842],{},[1832,16636,2486],{"stretchy":1837},[1832,16638,1845],{"separator":246},[269,16640],{"width":11568},[1795,16642,16643],{"mathvariant":1981},"Cov",[1832,16645,3278],{},[1832,16647,2477],{"stretchy":1837},[2016,16649,16650,16652],{},[1795,16651,2760],{},[1795,16653,2801],{},[1832,16655,1845],{"separator":246},[2016,16657,16658,16660],{},[1795,16659,2760],{},[1795,16661,16495],{},[1832,16663,2486],{"stretchy":1837},[1832,16665,1994],{},[5451,16667,16668,16684],{},[231,16669,16670,16672,16678],{},[1832,16671,1989],{},[2016,16673,16674,16676],{},[1795,16675,4835],{},[1795,16677,2801],{},[2016,16679,16680,16682],{},[1795,16681,4835],{},[1795,16683,16495],{},[231,16685,16686,16694,16696,16702,16704,16706],{},[2038,16687,16688,16690,16692],{},[1795,16689,4835],{},[1840,16691,2028],{},[1840,16693,2639],{},[1832,16695,2477],{"stretchy":1837},[2016,16697,16698,16700],{},[1795,16699,4835],{},[1840,16701,2028],{},[1832,16703,9486],{},[1840,16705,1842],{},[1832,16707,2486],{"stretchy":1837},[269,16709],{"width":8176},[1832,16711,2477],{"stretchy":1837},[1795,16713,2801],{},[1832,16715,16716],{"mathvariant":1981},"≠",[1795,16718,16495],{},[1832,16720,2486],{"stretchy":1837},[238,16722,16723],{"encoding":240},"\\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)",[128,16725,16727,16791,17013,17439,17756],{"className":16726,"ariaHidden":246},[245],[128,16728,16730,16733,16736,16739,16779,16782,16785,16788],{"className":16729},[250],[128,16731],{"className":16732,"style":1892},[254],[128,16734,342],{"className":16735},[259,2167],[128,16737,16538],{"className":16738},[1896],[128,16740,16742,16745],{"className":16741},[259],[128,16743,2760],{"className":16744},[259,1873],[128,16746,16748],{"className":16747},[2087],[128,16749,16751,16771],{"className":16750},[274,321],[128,16752,16754,16768],{"className":16753},[278],[128,16755,16757],{"className":16756,"style":3095},[282],[128,16758,16759,16762],{"style":2221},[128,16760],{"className":16761,"style":291},[290],[128,16763,16765],{"className":16764},[299,300,301,298],[128,16766,2801],{"className":16767},[259,1873,298],[128,16769,347],{"className":16770},[346],[128,16772,16774],{"className":16773},[278],[128,16775,16777],{"className":16776,"style":2241},[282],[128,16778],{},[128,16780,16547],{"className":16781},[1928],[128,16783],{"className":16784,"style":1878},[269],[128,16786,1994],{"className":16787},[1882],[128,16789],{"className":16790,"style":1878},[269],[128,16792,16794,16798,16943,16946,16949,16952,16958,16961,17001,17004,17007,17010],{"className":16793},[250],[128,16795],{"className":16796,"style":16797},[254],"height:1.1951em;vertical-align:-0.4451em;",[128,16799,16801,16804,16940],{"className":16800},[259],[128,16802],{"className":16803},[1896,5570],[128,16805,16807],{"className":16806},[5451],[128,16808,16810,16931],{"className":16809},[274,321],[128,16811,16813,16928],{"className":16812},[278],[128,16814,16817,16868,16876],{"className":16815,"style":16816},[282],"height:0.7115em;",[128,16818,16819,16822],{"style":5586},[128,16820],{"className":16821,"style":335},[290],[128,16823,16825],{"className":16824},[299,300,301,298],[128,16826,16828],{"className":16827},[259,298],[128,16829,16831,16834],{"className":16830},[259,298],[128,16832,4835],{"className":16833,"style":4920},[259,1873,298],[128,16835,16837],{"className":16836},[2087],[128,16838,16840,16860],{"className":16839},[274,321],[128,16841,16843,16857],{"className":16842},[278],[128,16844,16846],{"className":16845,"style":6153},[282],[128,16847,16848,16851],{"style":5786},[128,16849],{"className":16850,"style":5790},[290],[128,16852,16854],{"className":16853},[299,5794,5795,298],[128,16855,2028],{"className":16856},[259,298],[128,16858,347],{"className":16859},[346],[128,16861,16863],{"className":16862},[278],[128,16864,16866],{"className":16865,"style":5808},[282],[128,16867],{},[128,16869,16870,16873],{"style":5617},[128,16871],{"className":16872,"style":335},[290],[128,16874],{"className":16875,"style":5625},[5624],[128,16877,16879,16882],{"style":16878},"top:-3.4101em;",[128,16880],{"className":16881,"style":335},[290],[128,16883,16885],{"className":16884},[299,300,301,298],[128,16886,16888],{"className":16887},[259,298],[128,16889,16891,16894],{"className":16890},[259,298],[128,16892,4835],{"className":16893,"style":4920},[259,1873,298],[128,16895,16897],{"className":16896},[2087],[128,16898,16900,16920],{"className":16899},[274,321],[128,16901,16903,16917],{"className":16902},[278],[128,16904,16906],{"className":16905,"style":5783},[282],[128,16907,16908,16911],{"style":5786},[128,16909],{"className":16910,"style":5790},[290],[128,16912,16914],{"className":16913},[299,5794,5795,298],[128,16915,2801],{"className":16916},[259,1873,298],[128,16918,347],{"className":16919},[346],[128,16921,16923],{"className":16922},[278],[128,16924,16926],{"className":16925,"style":5808},[282],[128,16927],{},[128,16929,347],{"className":16930},[346],[128,16932,16934],{"className":16933},[278],[128,16935,16938],{"className":16936,"style":16937},[282],"height:0.4451em;",[128,16939],{},[128,16941],{"className":16942},[1928,5570],[128,16944,1845],{"className":16945},[1903],[128,16947],{"className":16948,"style":11756},[269],[128,16950],{"className":16951,"style":1907},[269],[128,16953,16955],{"className":16954},[2268],[128,16956,16570],{"className":16957},[259,3353],[128,16959,2477],{"className":16960},[1896],[128,16962,16964,16967],{"className":16963},[259],[128,16965,2760],{"className":16966},[259,1873],[128,16968,16970],{"className":16969},[2087],[128,16971,16973,16993],{"className":16972},[274,321],[128,16974,16976,16990],{"className":16975},[278],[128,16977,16979],{"className":16978,"style":3095},[282],[128,16980,16981,16984],{"style":2221},[128,16982],{"className":16983,"style":291},[290],[128,16985,16987],{"className":16986},[299,300,301,298],[128,16988,2801],{"className":16989},[259,1873,298],[128,16991,347],{"className":16992},[346],[128,16994,16996],{"className":16995},[278],[128,16997,16999],{"className":16998,"style":2241},[282],[128,17000],{},[128,17002,2486],{"className":17003},[1928],[128,17005],{"className":17006,"style":1878},[269],[128,17008,1994],{"className":17009},[1882],[128,17011],{"className":17012,"style":1878},[269],[128,17014,17016,17020,173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由命题 1.4，",[128,17774,17776,17806],{"className":17775,"translate":218},[217],[128,17777,17779],{"className":17778},[222],[224,17780,17781],{"xmlns":226},[228,17782,17783,17803],{},[231,17784,17785,17791,17793,17799,17801],{},[2016,17786,17787,17789],{},[1795,17788,2760],{},[1795,17790,2801],{},[1832,17792,1994],{},[2016,17794,17795,17797],{},[1795,17796,11131],{},[1795,17798,2801],{},[1795,17800,4751],{"mathvariant":1981},[1795,17802,7590],{},[238,17804,17805],{"encoding":240},"x_i = \\gamma_i \u002F s",[128,17807,17809,17864],{"className":17808,"ariaHidden":246},[245],[128,17810,17812,17815,17855,17858,17861],{"className":17811},[250],[128,17813],{"className":17814,"style":4242},[254],[128,17816,17818,17821],{"className":17817},[259],[128,17819,2760],{"className":17820},[259,1873],[128,17822,17824],{"className":17823},[2087],[128,17825,17827,17847],{"className":17826},[274,321],[128,17828,17830,17844],{"className":17829},[278],[128,17831,17833],{"className":17832,"style":3095},[282],[128,17834,17835,17838],{"style":2221},[128,17836],{"className":17837,"style":291},[290],[128,17839,17841],{"className":17840},[299,300,301,298],[128,17842,2801],{"className":17843},[259,1873,298],[128,17845,347],{"className":17846},[346],[128,17848,17850],{"className":17849},[278],[128,17851,17853],{"className":17852,"style":2241},[282],[128,17854],{},[128,17856],{"className":17857,"style":1878},[269],[128,17859,1994],{"className":17860},[1882],[128,17862],{"className":17863,"style":1878},[269],[128,17865,17867,17870,17910,17913],{"className":17866},[250],[128,17868],{"className":17869,"style":1892},[254],[128,17871,17873,17876],{"className":17872},[259],[128,17874,11131],{"className":17875,"style":11165},[259,1873],[128,17877,17879],{"className":17878},[2087],[128,17880,17882,17902],{"className":17881},[274,321],[128,17883,17885,17899],{"className":17884},[278],[128,17886,17888],{"className":17887,"style":3095},[282],[128,17889,17890,17893],{"style":11180},[128,17891],{"className":17892,"style":291},[290],[128,17894,17896],{"className":17895},[299,300,301,298],[128,17897,2801],{"className":17898},[259,1873,298],[128,17900,347],{"className":17901},[346],[128,17903,17905],{"className":17904},[278],[128,17906,17908],{"className":17907,"style":2241},[282],[128,17909],{},[128,17911,4751],{"className":17912},[259],[128,17914,7590],{"className":17915},[259,1873]," 且 ",[128,17918,17920,17942],{"className":17919,"translate":218},[217],[128,17921,17923],{"className":17922},[222],[224,17924,17925],{"xmlns":226},[228,17926,17927,17939],{},[231,17928,17929,17935,17937],{},[2016,17930,17931,17933],{},[1795,17932,11131],{},[1795,17934,2801],{},[1832,17936,12150],{},[1795,17938,7590],{},[238,17940,17941],{"encoding":240},"\\gamma_i \\perp s",[128,17943,17945,18000],{"className":17944,"ariaHidden":246},[245],[128,17946,17948,17951,17991,17994,17997],{"className":17947},[250],[128,17949],{"className":17950,"style":16030},[254],[128,17952,17954,17957],{"className":17953},[259],[128,17955,11131],{"className":17956,"style":11165},[259,1873],[128,17958,17960],{"className":17959},[2087],[128,17961,17963,17983],{"className":17962},[274,321],[128,17964,17966,17980],{"className":17965},[278],[128,17967,17969],{"className":17968,"style":3095},[282],[128,17970,17971,17974],{"style":11180},[128,17972],{"className":17973,"style":291},[290],[128,17975,17977],{"className":17976},[299,300,301,298],[128,17978,2801],{"className":17979},[259,1873,298],[128,17981,347],{"className":17982},[346],[128,17984,17986],{"className":17985},[278],[128,17987,17989],{"className":17988,"style":2241},[282],[128,17990],{},[128,17992],{"className":17993,"style":1878},[269],[128,17995,12150],{"className":17996},[1882],[128,17998],{"className":17999,"style":1878},[269],[128,18001,18003,18006],{"className":18002},[250],[128,18004],{"className":18005,"style":7758},[254],[128,18007,7590],{"className":18008},[259,1873],[128,18010,18012,18084],{"className":18011,"translate":218},[217],[128,18013,18015],{"className":18014},[222],[224,18016,18017],{"xmlns":226},[228,18018,18019,18081],{},[231,18020,18021,18023,18025,18031,18033,18035,18037,18039,18045,18047,18049,18051,18053,18055,18057,18059,18061,18063,18069,18071],{},[1795,18022,342],{"mathvariant":2008},[1832,18024,16538],{"stretchy":1837},[2016,18026,18027,18029],{},[1795,18028,2760],{},[1795,18030,2801],{},[1832,18032,16547],{"stretchy":1837},[1832,18034,1994],{},[1795,18036,342],{"mathvariant":2008},[1832,18038,16538],{"stretchy":1837},[2016,18040,18041,18043],{},[1795,18042,11131],{},[1795,18044,2801],{},[1832,18046,16547],{"stretchy":1837},[234,18048,6528],{},[1795,18050,342],{"mathvariant":2008},[1832,18052,16538],{"stretchy":1837},[1840,18054,1842],{},[1795,18056,4751],{"mathvariant":1981},[1795,18058,7590],{},[1832,18060,16547],{"stretchy":1837},[1832,18062,1994],{},[2016,18064,18065,18067],{},[1795,18066,4835],{},[1795,18068,2801],{},[1832,18070,12935],{},[5451,18072,18073,18075],{},[1840,18074,1842],{},[2016,18076,18077,18079],{},[1795,18078,4835],{},[1840,18080,2028],{},[238,18082,18083],{"encoding":240},"\\mathbb{E}[x_i] = \\mathbb{E}[\\gamma_i]\\,\\mathbb{E}[1\u002Fs] = \\alpha_i \\cdot \\frac{1}{\\alpha_0}",[128,18085,18087,18151,18233,18289],{"className":18086,"ariaHidden":246},[245],[128,18088,18090,18093,18096,18099,18139,18142,18145,18148],{"className":18089},[250],[128,18091],{"className":18092,"style":1892},[254],[128,18094,342],{"className":18095},[259,2167],[128,18097,16538],{"className":18098},[1896],[128,18100,18102,18105],{"className":18101},[259],[128,18103,2760],{"className":18104},[259,1873],[128,18106,18108],{"className":18107},[2087],[128,18109,18111,18131],{"className":18110},[274,321],[128,18112,18114,18128],{"className":18113},[278],[128,18115,18117],{"className":18116,"style":3095},[282],[128,18118,18119,18122],{"style":2221},[128,18120],{"className":18121,"style":291},[290],[128,18123,18125],{"className":18124},[299,300,301,298],[128,18126,2801],{"className":18127},[259,1873,298],[128,18129,347],{"className":18130},[346],[128,18132,18134],{"className":18133},[278],[128,18135,18137],{"className":18136,"style":2241},[282],[128,18138],{},[128,18140,16547],{"className":18141},[1928],[128,18143],{"className":18144,"style":1878},[269],[128,18146,1994],{"className":18147},[1882],[128,18149],{"className":18150,"style":1878},[269],[128,18152,18154,18157,18160,18163,18203,18206,18209,18212,18215,18218,18221,18224,18227,18230],{"className":18153},[250],[128,18155],{"className":18156,"style":1892},[254],[128,18158,342],{"className":18159},[259,2167],[128,18161,16538],{"className":18162},[1896],[128,18164,18166,18169],{"className":18165},[259],[128,18167,11131],{"className":18168,"style":11165},[259,1873],[128,18170,18172],{"className":18171},[2087],[128,18173,18175,18195],{"className":18174},[274,321],[128,18176,18178,18192],{"className":18177},[278],[128,18179,18181],{"className":18180,"style":3095},[282],[128,18182,18183,18186],{"style":11180},[128,18184],{"className":18185,"style":291},[290],[128,18187,18189],{"className":18188},[299,300,301,298],[128,18190,2801],{"className":18191},[259,1873,298],[128,18193,347],{"className":18194},[346],[128,18196,18198],{"className":18197},[278],[128,18199,18201],{"className":18200,"style":2241},[282],[128,18202],{},[128,18204,16547],{"className":18205},[1928],[128,18207],{"className":18208,"style":1907},[269],[128,18210,342],{"className":18211},[259,2167],[128,18213,16538],{"className":18214},[1896],[128,18216,4780],{"className":18217},[259],[128,18219,7590],{"className":18220},[259,1873],[128,18222,16547],{"className":18223},[1928],[128,18225],{"className":18226,"style":1878},[269],[128,18228,1994],{"className":18229},[1882],[128,18231],{"className":18232,"style":1878},[269],[128,18234,18236,18240,18280,18283,18286],{"className":18235},[250],[128,18237],{"className":18238,"style":18239},[254],"height:0.5945em;vertical-align:-0.15em;",[128,18241,18243,18246],{"className":18242},[259],[128,18244,4835],{"className":18245,"style":4920},[259,1873],[128,18247,18249],{"className":18248},[2087],[128,18250,18252,18272],{"className":18251},[274,321],[128,18253,18255,18269],{"className":18254},[278],[128,18256,18258],{"className":18257,"style":3095},[282],[128,18259,18260,18263],{"style":4935},[128,18261],{"className":18262,"style":291},[290],[128,18264,18266],{"className":18265},[299,300,301,298],[128,18267,2801],{"className":18268},[259,1873,298],[128,18270,347],{"className":18271},[346],[128,18273,18275],{"className":18274},[278],[128,18276,18278],{"className":18277,"style":2241},[282],[128,18279],{},[128,18281],{"className":18282,"style":2508},[269],[128,18284,12935],{"className":18285},[2115],[128,18287],{"className":18288,"style":2508},[269],[128,18290,18292,18296],{"className":18291},[250],[128,18293],{"className":18294,"style":18295},[254],"height:1.2902em;vertical-align:-0.4451em;",[128,18297,18299,18302,18398],{"className":18298},[259],[128,18300],{"className":18301},[1896,5570],[128,18303,18305],{"className":18304},[5451],[128,18306,18308,18390],{"className":18307},[274,321],[128,18309,18311,18387],{"className":18310},[278],[128,18312,18314,18365,18373],{"className":18313,"style":5583},[282],[128,18315,18316,18319],{"style":5586},[128,18317],{"className":18318,"style":335},[290],[128,18320,18322],{"className":18321},[299,300,301,298],[128,18323,18325],{"className":18324},[259,298],[128,18326,18328,18331],{"className":18327},[259,298],[128,18329,4835],{"className":18330,"style":4920},[259,1873,298],[128,18332,18334],{"className":18333},[2087],[128,18335,18337,18357],{"className":18336},[274,321],[128,18338,18340,18354],{"className":18339},[278],[128,18341,18343],{"className":18342,"style":6153},[282],[128,18344,18345,18348],{"style":5786},[128,18346],{"className":18347,"style":5790},[290],[128,18349,18351],{"className":18350},[299,5794,5795,298],[128,18352,2028],{"className":18353},[259,298],[128,18355,347],{"className":18356},[346],[128,18358,18360],{"className":18359},[278],[128,18361,18363],{"className":18362,"style":5808},[282],[128,18364],{},[128,18366,18367,18370],{"style":5617},[128,18368],{"className":18369,"style":335},[290],[128,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",[128,18403,18405,18435],{"className":18404,"translate":218},[217],[128,18406,18408],{"className":18407},[222],[224,18409,18410],{"xmlns":226},[228,18411,18412,18432],{},[231,18413,18414,18416,18418,18420,18426,18428,18430],{},[1795,18415,11282],{"mathvariant":1981},[1832,18417,3278],{},[1832,18419,2477],{"stretchy":1837},[2016,18421,18422,18424],{},[1795,18423,4835],{},[1840,18425,2028],{},[1832,18427,1845],{"separator":246},[1840,18429,1842],{},[1832,18431,2486],{"stretchy":1837},[238,18433,18434],{"encoding":240},"\\operatorname{Gamma}(\\alpha_0,1)",[128,18436,18438],{"className":18437,"ariaHidden":246},[245],[128,18439,18441,18444,18450,18453,18493,18496,18499,18502],{"className":18440},[250],[128,18442],{"className":18443,"style":1892},[254],[128,18445,18447],{"className":18446},[2268],[128,18448,11282],{"className":18449},[259,3353],[128,18451,2477],{"className":18452},[1896],[128,18454,18456,18459],{"className":18455},[259],[128,18457,4835],{"className":18458,"style":4920},[259,1873],[128,18460,18462],{"className":18461},[2087],[128,18463,18465,18485],{"className":18464},[274,321],[128,18466,18468,18482],{"className":18467},[278],[128,18469,18471],{"className":18470,"style":2945},[282],[128,18472,18473,18476],{"style":4935},[128,18474],{"className":18475,"style":291},[290],[128,18477,18479],{"className":18478},[299,300,301,298],[128,18480,2028],{"className":18481},[259,298],[128,18483,347],{"className":18484},[346],[128,18486,18488],{"className":18487},[278],[128,18489,18491],{"className":18490,"style":2241},[282],[128,18492],{},[128,18494,1845],{"className":18495},[1903],[128,18497],{"className":18498,"style":1907},[269],[128,18500,1842],{"className":18501},[259],[128,18503,2486],{"className":18504},[1928]," 的倒数的期望 ",[128,18507,18509,18553],{"className":18508,"translate":218},[217],[128,18510,18512],{"className":18511},[222],[224,18513,18514],{"xmlns":226},[228,18515,18516,18550],{},[231,18517,18518,18520,18522,18524,18526,18528,18530,18532,18534,18536,18538,18544,18546,18548],{},[1795,18519,342],{"mathvariant":2008},[1832,18521,16538],{"stretchy":1837},[1840,18523,1842],{},[1795,18525,4751],{"mathvariant":1981},[1795,18527,7590],{},[1832,18529,16547],{"stretchy":1837},[1832,18531,1994],{},[1840,18533,1842],{},[1795,18535,4751],{"mathvariant":1981},[1832,18537,2477],{"stretchy":1837},[2016,18539,18540,18542],{},[1795,18541,4835],{},[1840,18543,2028],{},[1832,18545,1989],{},[1840,18547,1842],{},[1832,18549,2486],{"stretchy":1837},[238,18551,18552],{"encoding":240},"\\mathbb{E}[1\u002Fs] = 1\u002F(\\alpha_0 - 1)",[128,18554,18556,18586,18647],{"className":18555,"ariaHidden":246},[245],[128,18557,18559,18562,18565,18568,18571,18574,18577,18580,18583],{"className":18558},[250],[128,18560],{"className":18561,"style":1892},[254],[128,18563,342],{"className":18564},[259,2167],[128,18566,16538],{"className":18567},[1896],[128,18569,4780],{"className":18570},[259],[128,18572,7590],{"className":18573},[259,1873],[128,18575,16547],{"className":18576},[1928],[128,18578],{"className":18579,"style":1878},[269],[128,18581,1994],{"className":18582},[1882],[128,18584],{"className":18585,"style":1878},[269],[128,18587,18589,18592,18595,18598,18638,18641,18644],{"className":18588},[250],[128,18590],{"className":18591,"style":1892},[254],[128,18593,4780],{"className":18594},[259],[128,18596,2477],{"className":18597},[1896],[128,18599,18601,18604],{"className":18600},[259],[128,18602,4835],{"className":18603,"style":4920},[259,1873],[128,18605,18607],{"className":18606},[2087],[128,18608,18610,18630],{"className":18609},[274,321],[128,18611,18613,18627],{"className":18612},[278],[128,18614,18616],{"className":18615,"style":2945},[282],[128,18617,18618,18621],{"style":4935},[128,18619],{"className":18620,"style":291},[290],[128,18622,18624],{"className":18623},[299,300,301,298],[128,18625,2028],{"className":18626},[259,298],[128,18628,347],{"className":18629},[346],[128,18631,18633],{"className":18632},[278],[128,18634,18636],{"className":18635,"style":2241},[282],[128,18637],{},[128,18639],{"className":18640,"style":2508},[269],[128,18642,1989],{"className":18643},[2115],[128,18645],{"className":18646,"style":2508},[269],[128,18648,18650,18653,18656],{"className":18649},[250],[128,18651],{"className":18652,"style":1892},[254],[128,18654,1842],{"className":18655},[259],[128,18657,2486],{"className":18658},[1928],[128,18660,18662,18692],{"className":18661,"translate":218},[217],[128,18663,18665],{"className":18664},[222],[224,18666,18667],{"xmlns":226},[228,18668,18669,18689],{},[231,18670,18671,18677,18679,18685,18687],{},[2016,18672,18673,18675],{},[1795,18674,4835],{},[1840,18676,2028],{},[1832,18678,16313],{},[2016,18680,18681,18683],{},[1795,18682,4835],{},[1840,18684,2028],{},[1832,18686,1989],{},[1840,18688,1842],{},[238,18690,18691],{"encoding":240},"\\alpha_0 \\mapsto \\alpha_0 - 1",[128,18693,18695,18751,18806],{"className":18694,"ariaHidden":246},[245],[128,18696,18698,18702,18742,18745,18748],{"className":18697},[250],[128,18699],{"className":18700,"style":18701},[254],"height:0.661em;vertical-align:-0.15em;",[128,18703,18705,18708],{"className":18704},[259],[128,18706,4835],{"className":18707,"style":4920},[259,1873],[128,18709,18711],{"className":18710},[2087],[128,18712,18714,18734],{"className":18713},[274,321],[128,18715,18717,18731],{"className":18716},[278],[128,18718,18720],{"className":18719,"style":2945},[282],[128,18721,18722,18725],{"style":4935},[128,18723],{"className":18724,"style":291},[290],[128,18726,18728],{"className":18727},[299,300,301,298],[128,18729,2028],{"className":18730},[259,298],[128,18732,347],{"className":18733},[346],[128,18735,18737],{"className":18736},[278],[128,18738,18740],{"className":18739,"style":2241},[282],[128,18741],{},[128,18743],{"className":18744,"style":1878},[269],[128,18746,16313],{"className":18747},[1882],[128,18749],{"className":18750,"style":1878},[269],[128,18752,18754,18757,18797,18800,18803],{"className":18753},[250],[128,18755],{"className":18756,"style":14338},[254],[128,18758,18760,18763],{"className":18759},[259],[128,18761,4835],{"className":18762,"style":4920},[259,1873],[128,18764,18766],{"className":18765},[2087],[128,18767,18769,18789],{"className":18768},[274,321],[128,18770,18772,18786],{"className":18771},[278],[128,18773,18775],{"className":18774,"style":2945},[282],[128,18776,18777,18780],{"style":4935},[128,18778],{"className":18779,"style":291},[290],[128,18781,18783],{"className":18782},[299,300,301,298],[128,18784,2028],{"className":18785},[259,298],[128,18787,347],{"className":18788},[346],[128,18790,18792],{"className":18791},[278],[128,18793,18795],{"className":18794,"style":2241},[282],[128,18796],{},[128,18798],{"className":18799,"style":2508},[269],[128,18801,1989],{"className":18802},[2115],[128,18804],{"className":18805,"style":2508},[269],[128,18807,18809,18812],{"className":18808},[250],[128,18810],{"className":18811,"style":2594},[254],[128,18813,1842],{"className":18814},[259]," 的平移技巧，或直接由命题 1.3 的矩恒等式 ",[128,18817,18819,18880],{"className":18818,"translate":218},[217],[128,18820,18822],{"className":18821},[222],[224,18823,18824],{"xmlns":226},[228,18825,18826,18877],{},[231,18827,18828,18830,18832,18838,18851,18853,18855,18857,18859,18861,18863,18865,18867,18869,18871,18873,18875],{},[1795,18829,342],{"mathvariant":2008},[1832,18831,16538],{"stretchy":1837},[2016,18833,18834,18836],{},[1832,18835,5470],{},[1795,18837,2801],{},[2038,18839,18840,18842,18844],{},[1795,18841,2760],{},[1795,18843,2801],{},[2016,18845,18846,18849],{},[1795,18847,18848],{},"β",[1795,18850,2801],{},[1832,18852,16547],{"stretchy":1837},[1832,18854,1994],{},[1795,18856,5459],{},[1832,18858,2477],{"stretchy":1837},[1795,18860,4835],{"mathvariant":4834},[1832,18862,9486],{},[1795,18864,18848],{"mathvariant":4834},[1832,18866,2486],{"stretchy":1837},[1795,18868,4751],{"mathvariant":1981},[1795,18870,5459],{},[1832,18872,2477],{"stretchy":1837},[1795,18874,4835],{"mathvariant":4834},[1832,18876,2486],{"stretchy":1837},[238,18878,18879],{"encoding":240},"\\mathbb{E}[\\prod_i x_i^{\\beta_i}] = B(\\boldsymbol{\\alpha} + \\boldsymbol{\\beta})\u002FB(\\boldsymbol{\\alpha})",[128,18881,18883,19046,19076],{"className":18882,"ariaHidden":246},[245],[128,18884,18886,18890,18893,18896,18936,18939,19034,19037,19040,19043],{"className":18885},[250],[128,18887],{"className":18888,"style":18889},[254],"height:1.2667em;vertical-align:-0.2997em;",[128,18891,342],{"className":18892},[259,2167],[128,18894,16538],{"className":18895},[1896],[128,18897,18899,18902],{"className":18898},[2268],[128,18900,5470],{"className":18901,"style":2274},[2268,2272,2273],[128,18903,18905],{"className":18904},[2087],[128,18906,18908,18928],{"className":18907},[274,321],[128,18909,18911,18925],{"className":18910},[278],[128,18912,18914],{"className":18913,"style":7796},[282],[128,18915,18916,18919],{"style":2290},[128,18917],{"className":18918,"style":291},[290],[128,18920,18922],{"className":18921},[299,300,301,298],[128,18923,2801],{"className":18924},[259,1873,298],[128,18926,347],{"className":18927},[346],[128,18929,18931],{"className":18930},[278],[128,18932,18934],{"className":18933,"style":2330},[282],[128,18935],{},[128,18937],{"className":18938,"style":1907},[269],[128,18940,18942,18945],{"className":18941},[259],[128,18943,2760],{"className":18944},[259,1873],[128,18946,18948],{"className":18947},[2087],[128,18949,18951,19026],{"className":18950},[274,321],[128,18952,18954,19023],{"className":18953},[278],[128,18955,18958,18969],{"className":18956,"style":18957},[282],"height:0.967em;",[128,18959,18960,18963],{"style":5743},[128,18961],{"className":18962,"style":291},[290],[128,18964,18966],{"className":18965},[299,300,301,298],[128,18967,2801],{"className":18968},[259,1873,298],[128,18970,18972,18975],{"style":18971},"top:-3.1809em;margin-right:0.05em;",[128,18973],{"className":18974,"style":291},[290],[128,18976,18978],{"className":18977},[299,300,301,298],[128,18979,18981],{"className":18980},[259,298],[128,18982,18984,18988],{"className":18983},[259,298],[128,18985,18848],{"className":18986,"style":18987},[259,1873,298],"margin-right:0.0528em;",[128,18989,18991],{"className":18990},[2087],[128,18992,18994,19015],{"className":18993},[274,321],[128,18995,18997,19012],{"className":18996},[278],[128,18998,19000],{"className":18999,"style":5783},[282],[128,19001,19003,19006],{"style":19002},"top:-2.357em;margin-left:-0.0528em;margin-right:0.0714em;",[128,19004],{"className":19005,"style":5790},[290],[128,19007,19009],{"className":19008},[299,5794,5795,298],[128,19010,2801],{"className":19011},[259,1873,298],[128,19013,347],{"className":19014},[346],[128,19016,19018],{"className":19017},[278],[128,19019,19021],{"className":19020,"style":5808},[282],[128,19022],{},[128,19024,347],{"className":19025},[346],[128,19027,19029],{"className":19028},[278],[128,19030,19032],{"className":19031,"style":5826},[282],[128,19033],{},[128,19035,16547],{"className":19036},[1928],[128,19038],{"className":19039,"style":1878},[269],[128,19041,1994],{"className":19042},[1882],[128,19044],{"className":19045,"style":1878},[269],[128,19047,19049,19052,19055,19058,19067,19070,19073],{"className":19048},[250],[128,19050],{"className":19051,"style":1892},[254],[128,19053,5459],{"className":19054,"style":5599},[259,1873],[128,19056,2477],{"className":19057},[1896],[128,19059,19061],{"className":19060},[259],[128,19062,19064],{"className":19063},[259],[128,19065,4835],{"className":19066},[259,4895],[128,19068],{"className":19069,"style":2508},[269],[128,19071,9486],{"className":19072},[2115],[128,19074],{"className":19075,"style":2508},[269],[128,19077,19079,19082,19092,19095,19098,19101,19104,19113],{"className":19078},[250],[128,19080],{"className":19081,"style":1892},[254],[128,19083,19085],{"className":19084},[259],[128,19086,19088],{"className":19087},[259],[128,19089,18848],{"className":19090,"style":19091},[259,4895],"margin-right:0.034em;",[128,19093,2486],{"className":19094},[1928],[128,19096,4751],{"className":19097},[259],[128,19099,5459],{"className":19100,"style":5599},[259,1873],[128,19102,2477],{"className":19103},[1896],[128,19105,19107],{"className":19106},[259],[128,19108,19110],{"className":19109},[259],[128,19111,4835],{"className":19112},[259,4895],[128,19114,2486],{"className":19115},[1928]," 取 ",[128,19118,19120,19142],{"className":19119,"translate":218},[217],[128,19121,19123],{"className":19122},[222],[224,19124,19125],{"xmlns":226},[228,19126,19127,19139],{},[231,19128,19129,19135,19137],{},[2016,19130,19131,19133],{},[1795,19132,18848],{},[1795,19134,2801],{},[1832,19136,1994],{},[1840,19138,1842],{},[238,19140,19141],{"encoding":240},"\\beta_i = 1",[128,19143,19145,19201],{"className":19144,"ariaHidden":246},[245],[128,19146,19148,19151,19192,19195,19198],{"className":19147},[250],[128,19149],{"className":19150,"style":16030},[254],[128,19152,19154,19157],{"className":19153},[259],[128,19155,18848],{"className":19156,"style":18987},[259,1873],[128,19158,19160],{"className":19159},[2087],[128,19161,19163,19184],{"className":19162},[274,321],[128,19164,19166,19181],{"className":19165},[278],[128,19167,19169],{"className":19168,"style":3095},[282],[128,19170,19172,19175],{"style":19171},"top:-2.55em;margin-left:-0.0528em;margin-right:0.05em;",[128,19173],{"className":19174,"style":291},[290],[128,19176,19178],{"className":19177},[299,300,301,298],[128,19179,2801],{"className":19180},[259,1873,298],[128,19182,347],{"className":19183},[346],[128,19185,19187],{"className":19186},[278],[128,19188,19190],{"className":19189,"style":2241},[282],[128,19191],{},[128,19193],{"className":19194,"style":1878},[269],[128,19196,1994],{"className":19197},[1882],[128,19199],{"className":19200,"style":1878},[269],[128,19202,19204,19207],{"className":19203},[250],[128,19205],{"className":19206,"style":2594},[254],[128,19208,1842],{"className":19209},[259]," 得到。二阶矩由 ",[128,19212,19214,19288],{"className":19213,"translate":218},[217],[128,19215,19217],{"className":19216},[222],[224,19218,19219],{"xmlns":226},[228,19220,19221,19285],{},[231,19222,19223,19225,19227,19235,19237,19239],{},[1795,19224,342],{"mathvariant":2008},[1832,19226,16538],{"stretchy":1837},[2038,19228,19229,19231,19233],{},[1795,19230,2760],{},[1795,19232,2801],{},[1840,19234,2639],{},[1832,19236,16547],{"stretchy":1837},[1832,19238,1994],{},[5451,19240,19241,19263],{},[231,19242,19243,19249,19251,19257,19259,19261],{},[2016,19244,19245,19247],{},[1795,19246,4835],{},[1795,19248,2801],{},[1832,19250,2477],{"stretchy":1837},[2016,19252,19253,19255],{},[1795,19254,4835],{},[1795,19256,2801],{},[1832,19258,9486],{},[1840,19260,1842],{},[1832,19262,2486],{"stretchy":1837},[231,19264,19265,19271,19273,19279,19281,19283],{},[2016,19266,19267,19269],{},[1795,19268,4835],{},[1840,19270,2028],{},[1832,19272,2477],{"stretchy":1837},[2016,19274,19275,19277],{},[1795,19276,4835],{},[1840,19278,2028],{},[1832,19280,9486],{},[1840,19282,1842],{},[1832,19284,2486],{"stretchy":1837},[238,19286,19287],{"encoding":240},"\\mathbb{E}[x_i^2] = \\frac{\\alpha_i(\\alpha_i+1)}{\\alpha_0(\\alpha_0+1)}",[128,19289,19291,19369],{"className":19290,"ariaHidden":246},[245],[128,19292,19294,19298,19301,19304,19357,19360,19363,19366],{"className":19293},[250],[128,19295],{"className":19296,"style":19297},[254],"height:1.0728em;vertical-align:-0.2587em;",[128,19299,342],{"className":19300},[259,2167],[128,19302,16538],{"className":19303},[1896],[128,19305,19307,19310],{"className":19306},[259],[128,19308,2760],{"className":19309},[259,1873],[128,19311,19313],{"className":19312},[2087],[128,19314,19316,19348],{"className":19315},[274,321],[128,19317,19319,19345],{"className":19318},[278],[128,19320,19322,19334],{"className":19321,"style":9629},[282],[128,19323,19325,19328],{"style":19324},"top:-2.4413em;margin-left:0em;margin-right:0.05em;",[128,19326],{"className":19327,"style":291},[290],[128,19329,19331],{"className":19330},[299,300,301,298],[128,19332,2801],{"className":19333},[259,1873,298],[128,19335,19336,19339],{"style":2452},[128,19337],{"className":19338,"style":291},[290],[128,19340,19342],{"className":19341},[299,300,301,298],[128,19343,2639],{"className":19344},[259,298],[128,19346,347],{"className":19347},[346],[128,19349,19351],{"className":19350},[278],[128,19352,19355],{"className":19353,"style":19354},[282],"height:0.2587em;",[128,19356],{},[128,19358,16547],{"className":19359},[1928],[128,19361],{"className":19362,"style":1878},[269],[128,19364,1994],{"className":19365},[1882],[128,19367],{"className":19368,"style":1878},[269],[128,19370,19372,19376],{"className":19371},[250],[128,19373],{"className":19374,"style":19375},[254],"height:1.53em;vertical-align:-0.52em;",[128,19377,19379,19382,19619],{"className":19378},[259],[128,19380],{"className":19381},[1896,5570],[128,19383,19385],{"className":19384},[5451],[128,19386,19388,19611],{"className":19387},[274,321],[128,19389,19391,19608],{"className":19390},[278],[128,19392,19394,19497,19505],{"className":19393,"style":17038},[282],[128,19395,19396,19399],{"style":5586},[128,19397],{"className":19398,"style":335},[290],[128,19400,19402],{"className":19401},[299,300,301,298],[128,19403,19405,19445,19448,19488,19491,19494],{"className":19404},[259,298],[128,19406,19408,19411],{"className":19407},[259,298],[128,19409,4835],{"className":19410,"style":4920},[259,1873,298],[128,19412,19414],{"className":19413},[2087],[128,19415,19417,19437],{"className":19416},[274,321],[128,19418,19420,19434],{"className":19419},[278],[128,19421,19423],{"className":19422,"style":6153},[282],[128,19424,19425,19428],{"style":5786},[128,19426],{"className":19427,"style":5790},[290],[128,19429,19431],{"className":19430},[299,5794,5795,298],[128,19432,2028],{"className":19433},[259,298],[128,19435,347],{"className":19436},[346],[128,19438,19440],{"className":19439},[278],[128,19441,19443],{"className":19442,"style":5808},[282],[128,19444],{},[128,19446,2477],{"className":19447},[1896,298],[128,19449,19451,19454],{"className":19450},[259,298],[128,19452,4835],{"className":19453,"style":4920},[259,1873,298],[128,19455,19457],{"className":19456},[2087],[128,19458,19460,19480],{"className":19459},[274,321],[128,19461,19463,19477],{"className":19462},[278],[128,19464,19466],{"className":19465,"style":6153},[282],[128,19467,19468,19471],{"style":5786},[128,19469],{"className":19470,"style":5790},[290],[128,19472,19474],{"className":19473},[299,5794,5795,298],[128,19475,2028],{"className":19476},[259,298],[128,19478,347],{"className":19479},[346],[128,19481,19483],{"className":19482},[278],[128,19484,19486],{"className":19485,"style":5808},[282],[128,19487],{},[128,19489,9486],{"className":19490},[2115,298],[128,19492,1842],{"className":19493},[259,298],[128,19495,2486],{"className":19496},[1928,298],[128,19498,19499,19502],{"style":5617},[128,19500],{"className":19501,"style":335},[290],[128,19503],{"className":19504,"style":5625},[5624],[128,19506,19507,19510],{"style":17167},[128,19508],{"className":19509,"style":335},[290],[128,19511,19513],{"className":19512},[299,300,301,298],[128,19514,19516,19556,19559,19599,19602,19605],{"className":19515},[259,298],[128,19517,19519,19522],{"className":19518},[259,298],[128,19520,4835],{"className":19521,"style":4920},[259,1873,298],[128,19523,19525],{"className":19524},[2087],[128,19526,19528,19548],{"className":19527},[274,321],[128,19529,19531,19545],{"className":19530},[278],[128,19532,19534],{"className":19533,"style":5783},[282],[128,19535,19536,19539],{"style":5786},[128,19537],{"className":19538,"style":5790},[290],[128,19540,19542],{"className":19541},[299,5794,5795,298],[128,19543,2801],{"className":19544},[259,1873,298],[128,19546,347],{"className":19547},[346],[128,19549,19551],{"className":19550},[278],[128,19552,19554],{"className":19553,"style":5808},[282],[128,19555],{},[128,19557,2477],{"className":19558},[1896,298],[128,19560,19562,19565],{"className":19561},[259,298],[128,19563,4835],{"className":19564,"style":4920},[259,1873,298],[128,19566,19568],{"className":1956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x_j] = \\frac{\\alpha_i \\alpha_j}{\\alpha_0(\\alpha_0+1)}",[128,19696,19698,19803],{"className":19697,"ariaHidden":246},[245],[128,19699,19701,19705,19708,19711,19751,19791,19794,19797,19800],{"className":19700},[250],[128,19702],{"className":19703,"style":19704},[254],"height:1.0361em;vertical-align:-0.2861em;",[128,19706,342],{"className":19707},[259,2167],[128,19709,16538],{"className":19710},[1896],[128,19712,19714,19717],{"className":19713},[259],[128,19715,2760],{"className":19716},[259,1873],[128,19718,19720],{"className":19719},[2087],[128,19721,19723,19743],{"className":19722},[274,321],[128,19724,19726,19740],{"className":19725},[278],[128,19727,19729],{"className":19728,"style":3095},[282],[128,19730,19731,19734],{"style":2221},[128,19732],{"className":19733,"style":291},[290],[128,19735,19737],{"className":19736},[299,300,301,298],[128,19738,2801],{"className":19739},[259,1873,298],[128,19741,347],{"className":19742},[346],[128,19744,19746],{"className":19745},[278],[128,19747,19749],{"className":19748,"style":2241},[282],[128,19750],{},[128,19752,19754,19757],{"className":19753},[259],[128,19755,2760],{"className":19756},[259,1873],[128,19758,19760],{"className":19759},[2087],[128,19761,19763,19783],{"className":19762},[274,321],[128,19764,19766,19780],{"className":19765},[278],[128,19767,19769],{"className":19768,"style":3095},[282],[128,19770,19771,19774],{"style":2221},[128,19772],{"className":19773,"style":291},[290],[128,19775,19777],{"className":19776},[299,300,301,298],[128,19778,16495],{"className":19779,"style":16521},[259,1873,298],[128,19781,347],{"className":19782},[346],[128,19784,19786],{"className":19785},[278],[128,19787,19789],{"className":19788,"style":17424},[282],[128,19790],{},[128,19792,16547],{"className":19793},[1928],[128,19795],{"className":19796,"style":1878},[269],[128,19798,1994],{"className":19799},[1882],[128,19801],{"className":19802,"style":1878},[269],[128,19804,19806,19810],{"className":19805},[250],[128,19807],{"className":19808,"style":19809},[254],"height:1.3287em;vertical-align:-0.52em;",[128,19811,19813,19816,20042],{"className":19812},[259],[128,19814],{"className":19815},[1896,5570],[128,19817,19819],{"className":19818},[5451],[128,19820,19822,20034],{"className":19821},[274,321],[128,19823,19825,20031],{"className":19824},[278],[128,19826,19829,19932,19940],{"className":19827,"style":19828},[282],"height:0.8087em;",[128,19830,19831,19834],{"style":5586},[128,19832],{"className":19833,"style":335},[290],[128,19835,19837],{"className":19836},[299,300,301,298],[128,19838,19840,19880,19883,19923,19926,19929],{"className":19839},[259,298],[128,19841,19843,19846],{"className":19842},[259,298],[128,19844,4835],{"className":19845,"style":4920},[259,1873,298],[128,19847,19849],{"className":19848},[2087],[128,19850,19852,19872],{"className":19851},[274,321],[128,19853,19855,19869],{"className":19854},[278],[128,19856,19858],{"className":19857,"style":6153},[282],[128,19859,19860,19863],{"style":5786},[128,19861],{"className":19862,"style":5790},[290],[128,19864,19866],{"className":19865},[299,5794,5795,298],[128,19867,2028],{"className":19868},[259,298],[128,19870,347],{"className":19871},[346],[128,19873,19875],{"className":19874},[278],[128,19876,19878],{"className":19877,"style":5808},[282],[128,19879],{},[128,19881,2477],{"className":19882},[1896,298],[128,19884,19886,19889],{"className":19885},[259,298],[128,19887,4835],{"className":19888,"style":4920},[259,1873,298],[128,19890,19892],{"className":19891},[2087],[128,19893,19895,19915],{"className":19894},[274,321],[128,19896,19898,19912],{"className":19897},[278],[128,19899,19901],{"className":19900,"style":6153},[282],[128,19902,19903,19906],{"style":5786},[128,19904],{"className":19905,"style":5790},[290],[128,19907,19909],{"className":19908},[299,5794,5795,298],[128,19910,2028],{"className":19911},[259,298],[128,19913,347],{"className":19914},[346],[128,19916,19918],{"className":19917},[278],[128,19919,19921],{"className":19920,"style":5808},[282],[128,19922],{},[128,19924,9486],{"className":19925},[2115,298],[128,19927,1842],{"className":19928},[259,298],[128,19930,2486],{"className":19931},[1928,298],[128,19933,19934,19937],{"style":5617},[128,19935],{"className":19936,"style":335},[290],[128,19938],{"className":19939,"style":5625},[5624],[128,19941,19942,19945],{"style":17589},[128,19943],{"className":19944,"style":335},[290],[128,19946,19948],{"className":19947},[299,300,301,298],[128,19949,19951,19991],{"className":19950},[259,298],[128,19952,19954,19957],{"className":19953},[259,298],[128,19955,4835],{"className":19956,"style":4920},[259,1873,298],[128,19958,19960],{"className":19959},[2087],[128,19961,19963,19983],{"className":19962},[274,321],[128,19964,19966,19980],{"className":19965},[278],[128,19967,19969],{"className":19968,"style":5783},[282],[128,19970,19971,19974],{"style":5786},[128,19972],{"className":19973,"style":5790},[290],[128,19975,19977],{"className":19976},[299,5794,5795,298],[128,19978,2801],{"className":19979},[259,1873,298],[128,19981,347],{"className":19982},[346],[128,19984,19986],{"className":19985},[278],[128,19987,19989],{"className":19988,"style":5808},[282],[128,19990],{},[128,19992,19994,19997],{"className":19993},[259,298],[128,19995,4835],{"className":19996,"style":4920},[259,1873,298],[128,19998,20000],{"className":19999},[2087],[128,20001,20003,20023],{"className":20002},[274,321],[128,20004,20006,20020],{"className":20005},[278],[128,20007,20009],{"className":20008,"style":5783},[282],[128,20010,20011,20014],{"style":5786},[128,20012],{"className":20013,"style":5790},[290],[128,20015,20017],{"className":20016},[299,5794,5795,298],[128,20018,16495],{"className":20019,"style":16521},[259,1873,298],[128,20021,347],{"className":20022},[346],[128,20024,20026],{"className":20025},[278],[128,20027,20029],{"className":20028,"style":17680},[282],[128,20030],{},[128,20032,347],{"className":20033},[346],[128,20035,20037],{"className":20036},[278],[128,20038,20040],{"className":20039,"style":5650},[282],[128,20041],{},[128,20043],{"className":20044},[1928,5570]," 相减即得。",[11,20047,20048,20049,20244],{},"上述结果可写成更紧凑的矩阵形式。记 ",[128,20050,20052,20097],{"className":20051,"translate":218},[217],[128,20053,20055],{"className":20054},[222],[224,20056,20057],{"xmlns":226},[228,20058,20059,20094],{},[231,20060,20061,20064,20066,20068,20070,20076,20078,20080,20082],{},[1795,20062,20063],{"mathvariant":4834},"μ",[1832,20065,1994],{},[1795,20067,4835],{"mathvariant":4834},[1795,20069,4751],{"mathvariant":1981},[2016,20071,20072,20074],{},[1795,20073,4835],{},[1840,20075,2028],{},[1832,20077,1834],{},[1795,20079,3275],{"mathvariant":1981},[1832,20081,3278],{},[1977,20083,20084,20086],{},[1795,20085,1982],{"mathvariant":1981},[231,20087,20088,20090,20092],{},[1795,20089,1853],{},[1832,20091,1989],{},[1840,20093,1842],{},[238,20095,20096],{"encoding":240},"\\boldsymbol{\\mu} = \\boldsymbol{\\alpha}\u002F\\alpha_0 \\in \\operatorname{int}\\Delta^{K-1}",[128,20098,20100,20124,20191],{"className":20099,"ariaHidden":246},[245],[128,20101,20103,20106,20115,20118,20121],{"className":20102},[250],[128,20104],{"className":20105,"style":2564},[254],[128,20107,20109],{"className":20108},[259],[128,20110,20112],{"className":20111},[259],[128,20113,20063],{"className":20114},[259,4895],[128,20116],{"className":20117,"style":1878},[269],[128,20119,1994],{"className":20120},[1882],[128,20122],{"className":20123,"style":1878},[269],[128,20125,20127,20130,20139,20142,20182,20185,20188],{"className":20126},[250],[128,20128],{"className":20129,"style":1892},[254],[128,20131,20133],{"className":20132},[259],[128,20134,20136],{"className":20135},[259],[128,20137,4835],{"className":20138},[259,4895],[128,20140,4751],{"className":20141},[259],[128,20143,20145,20148],{"className":20144},[259],[128,20146,4835],{"className":20147,"style":4920},[259,1873],[128,20149,20151],{"className":20150},[2087],[128,20152,20154,20174],{"className":20153},[274,321],[128,20155,20157,20171],{"className":20156},[278],[128,20158,20160],{"className":20159,"style":2945},[282],[128,20161,20162,20165],{"style":4935},[128,20163],{"className":20164,"style":291},[290],[128,20166,20168],{"className":20167},[299,300,301,298],[128,20169,2028],{"className":20170},[259,298],[128,20172,347],{"className":20173},[346],[128,20175,20177],{"className":20176},[278],[128,20178,20180],{"className":20179,"style":2241},[282],[128,20181],{},[128,20183],{"className":20184,"style":1878},[269],[128,20186,1834],{"className":20187},[1882],[128,20189],{"className":20190,"style":1878},[269],[128,20192,20194,20197,20203,20206],{"className":20193},[250],[128,20195],{"className":20196,"style":2431},[254],[128,20198,20200],{"className":20199},[2268],[128,20201,3275],{"className":20202},[259,3353],[128,20204],{"className":20205,"style":1907},[269],[128,20207,20209,20212],{"className":20208},[259],[128,20210,1982],{"className":20211},[259],[128,20213,20215],{"className":20214},[2087],[128,20216,20218],{"className":20217},[274],[128,20219,20221],{"className":20220},[278],[128,20222,20224],{"className":20223,"style":2431},[282],[128,20225,20226,20229],{"style":2452},[128,20227],{"className":20228,"style":291},[290],[128,20230,20232],{"className":20231},[299,300,301,298],[128,20233,20235,20238,20241],{"className":20234},[259,298],[128,20236,1853],{"className":20237,"style":1924},[259,1873,298],[128,20239,1989],{"className":20240},[2115,298],[128,20242,1842],{"className":20243},[259,298]," 为均值向量，则",[128,20246,20248],{"className":20247,"translate":218},[1962],[128,20249,20251,20324],{"className":20250,"translate":218},[217],[128,20252,20254],{"className":20253},[222],[224,20255,20256],{"xmlns":226,"display":1971},[228,20257,20258,20321],{},[231,20259,20260,20263,20265,20267,20269,20271,20273,20275,20277,20293],{},[1795,20261,20262],{"mathvariant":2001},"Σ",[1832,20264,1994],{},[1795,20266,16643],{"mathvariant":1981},[1832,20268,3278],{},[1832,20270,2477],{"stretchy":1837},[1795,20272,2760],{"mathvariant":2001},[1832,20274,2486],{"stretchy":1837},[1832,20276,1994],{},[5451,20278,20279,20281],{},[1840,20280,1842],{},[231,20282,20283,20289,20291],{},[2016,20284,20285,20287],{},[1795,20286,4835],{},[1840,20288,2028],{},[1832,20290,9486],{},[1840,20292,1842],{},[231,20294,20295,20297,20300,20302,20304,20306,20308,20310,20312,20319],{},[1832,20296,2477],{"fence":246},[1795,20298,20299],{"mathvariant":1981},"diag",[1832,20301,3278],{},[1832,20303,2477],{"stretchy":1837},[1795,20305,20063],{"mathvariant":4834},[1832,20307,2486],{"stretchy":1837},[1832,20309,1989],{},[1795,20311,20063],{"mathvariant":4834},[1977,20313,20314,20316],{},[1795,20315,20063],{"mathvariant":4834},[1795,20317,20318],{"mathvariant":1981},"⊤",[1832,20320,2486],{"fence":246},[238,20322,20323],{"encoding":240},"\\boldsymbol{\\Sigma} = \\operatorname{Cov}(\\mathbf{x}) = \\frac{1}{\\alpha_0 + 1}\\left(\\operatorname{diag}(\\boldsymbol{\\mu}) - \\boldsymbol{\\mu}\\boldsymbol{\\mu}^\\top\\right)",[128,20325,20327,20352,20382],{"className":20326,"ariaHidden":246},[245],[128,20328,20330,20334,20343,20346,20349],{"className":20329},[250],[128,20331],{"className":20332,"style":20333},[254],"height:0.6861em;",[128,20335,20337],{"className":20336},[259],[128,20338,20340],{"className":20339},[259],[128,20341,20262],{"className":20342},[259,2151],[128,20344],{"className":20345,"style":1878},[269],[128,20347,1994],{"className":20348},[1882],[128,20350],{"className":20351,"style":1878},[269],[128,20353,20355,20358,20364,20367,20370,20373,20376,20379],{"className":20354},[250],[128,20356],{"className":20357,"style":1892},[254],[128,20359,20361],{"className":20360},[2268],[128,20362,16643],{"className":20363,"style":17336},[259,3353],[128,20365,2477],{"className":20366},[1896],[128,20368,2760],{"className":20369},[259,2151],[128,20371,2486],{"className":20372},[1928],[128,20374],{"className":20375,"style":1878},[269],[128,20377,1994],{"className":20378},[1882],[128,20380],{"className":20381,"style":1878},[269],[128,20383,20385,20389,20502,20505],{"className":20384},[250],[128,20386],{"className":20387,"style":20388},[254],"height:2.1574em;vertical-align:-0.836em;",[128,20390,20392,20395,20499],{"className":20391},[259],[128,20393],{"className":20394},[1896,5570],[128,20396,20398],{"className":20397},[5451],[128,20399,20401,20490],{"className":20400},[274,321],[128,20402,20404,20487],{"className":20403},[278],[128,20405,20408,20468,20476],{"className":20406,"style":20407},[282],"height:1.3214em;",[128,20409,20410,20413],{"style":13123},[128,20411],{"className":20412,"style":335},[290],[128,20414,20416,20456,20459,20462,20465],{"className":20415},[259],[128,20417,20419,20422],{"className":20418},[259],[128,20420,4835],{"className":20421,"style":4920},[259,1873],[128,20423,20425],{"className":20424},[2087],[128,20426,20428,20448],{"className":20427},[274,321],[128,20429,20431,20445],{"className":20430},[278],[128,20432,20434],{"className":20433,"style":2945},[282],[128,20435,20436,20439],{"style":4935},[128,20437],{"className":20438,"style":291},[290],[128,20440,20442],{"className":20441},[299,300,301,298],[128,20443,2028],{"className":20444},[259,298],[128,20446,347],{"className":20447},[346],[128,20449,20451],{"className":20450},[278],[128,20452,20454],{"className":20453,"style":2241},[282],[128,20455],{},[128,20457],{"className":20458,"style":2508},[269],[128,20460,9486],{"className":20461},[2115],[128,20463],{"className":20464,"style":2508},[269],[128,20466,1842],{"className":20467},[259],[128,20469,20470,20473],{"style":5617},[128,20471],{"className":20472,"style":335},[290],[128,20474],{"className":20475,"style":5625},[5624],[128,20477,20478,20481],{"style":13189},[128,20479],{"className":20480,"style":335},[290],[128,20482,20484],{"className":20483},[259],[128,20485,1842],{"className":20486},[259],[128,20488,347],{"className":20489},[346],[128,20491,20493],{"className":20492},[278],[128,20494,20497],{"className":20495,"style":20496},[282],"height:0.836em;",[128,20498],{},[128,20500],{"className":20501},[1928,5570],[128,20503],{"className":20504,"style":1907},[269],[128,20506,20508,20514,20520,20523,20532,20535,20538,20541,20544,20553,20589],{"className":20507},[1911],[128,20509,20511],{"className":20510,"style":2142},[1896,2141],[128,20512,2477],{"className":20513},[2146,5795],[128,20515,20517],{"className":20516},[2268],[128,20518,20299],{"className":20519,"style":17336},[259,3353],[128,20521,2477],{"className":20522},[1896],[128,20524,20526],{"className":20525},[259],[128,20527,20529],{"className":20528},[259],[128,20530,20063],{"className":20531},[259,4895],[128,20533,2486],{"className":20534},[1928],[128,20536],{"className":20537,"style":2508},[269],[128,20539,1989],{"className":20540},[2115],[128,20542],{"className":20543,"style":2508},[269],[128,20545,20547],{"className":20546},[259],[128,20548,20550],{"className":20549},[259],[128,20551,20063],{"className":20552},[259,4895],[128,20554,20556,20565],{"className":20555},[259],[128,20557,20559],{"className":20558},[259],[128,20560,20562],{"className":20561},[259],[128,20563,20063],{"className":20564},[259,4895],[128,20566,20568],{"className":20567},[2087],[128,20569,20571],{"className":20570},[274],[128,20572,20574],{"className":20573},[278],[128,20575,20578],{"className":20576,"style":20577},[282],"height:0.8991em;",[128,20579,20580,20583],{"style":2099},[128,20581],{"className":20582,"style":291},[290],[128,20584,20586],{"className":20585},[299,300,301,298],[128,20587,20318],{"className":20588},[259,298],[128,20590,20592],{"className":20591,"style":2142},[1928,2141],[128,20593,2486],{"className":20594},[2146,5795],[11,20596,20597,20598,20648,20649,2674,20747,20782,20783,20812,20813,20873,20874,21115,21116,21144],{},"这一形式揭示了两个结构性事实。第一，协方差矩阵的秩为 ",[128,20599,20601,20618],{"className":20600,"translate":218},[217],[128,20602,20604],{"className":20603},[222],[224,20605,20606],{"xmlns":226},[228,20607,20608,20616],{},[231,20609,20610,20612,20614],{},[1795,20611,1853],{},[1832,20613,1989],{},[1840,20615,1842],{},[238,20617,2695],{"encoding":240},[128,20619,20621,20639],{"className":20620,"ariaHidden":246},[245],[128,20622,20624,20627,20630,20633,20636],{"className":20623},[250],[128,20625],{"className":20626,"style":2705},[254],[128,20628,1853],{"className":20629,"style":1924},[259,1873],[128,20631],{"className":20632,"style":2508},[269],[128,20634,1989],{"className":20635},[2115],[128,20637],{"className":20638,"style":2508},[269],[128,20640,20642,20645],{"className":20641},[250],[128,20643],{"className":20644,"style":2594},[254],[128,20646,1842],{"className":20647},[259],"：由于 ",[128,20650,20652,20678],{"className":20651,"translate":218},[217],[128,20653,20655],{"className":20654},[222],[224,20656,20657],{"xmlns":226},[228,20658,20659,20675],{},[231,20660,20661,20667,20669,20671,20673],{},[1977,20662,20663,20665],{},[1840,20664,1842],{"mathvariant":2001},[1795,20666,20318],{"mathvariant":1981},[1795,20668,20262],{"mathvariant":2001},[1840,20670,1842],{"mathvariant":2001},[1832,20672,1994],{},[1840,20674,2028],{},[238,20676,20677],{"encoding":240},"\\mathbf{1}^\\top \\boldsymbol{\\Sigma} \\mathbf{1} = 0",[128,20679,20681,20738],{"className":20680,"ariaHidden":246},[245],[128,20682,20684,20688,20717,20726,20729,20732,20735],{"className":20683},[250],[128,20685],{"className":20686,"style":20687},[254],"height:0.8491em;",[128,20689,20691,20694],{"className":20690},[259],[128,20692,1842],{"className":20693},[259,2151],[128,20695,20697],{"className":20696},[2087],[128,20698,20700],{"className":20699},[274],[128,20701,20703],{"className":20702},[278],[128,20704,20706],{"className":20705,"style":20687},[282],[128,20707,20708,20711],{"style":2452},[128,20709],{"className":20710,"style":291},[290],[128,20712,20714],{"className":20713},[299,300,301,298],[128,20715,20318],{"className":20716},[259,298],[128,20718,20720],{"className":20719},[259],[128,20721,20723],{"className":20722},[259],[128,20724,20262],{"className":20725},[259,2151],[128,20727,1842],{"className":20728},[259,2151],[128,20730],{"className":20731,"style":1878},[269],[128,20733,1994],{"className":20734},[1882],[128,20736],{"className":20737,"style":1878},[269],[128,20739,20741,20744],{"className":20740},[250],[128,20742],{"className":20743,"style":2594},[254],[128,20745,2028],{"className":20746},[259],[128,20748,20750,20764],{"className":20749,"translate":218},[217],[128,20751,20753],{"className":20752},[222],[224,20754,20755],{"xmlns":226},[228,20756,20757,20761],{},[231,20758,20759],{},[1795,20760,20262],{"mathvariant":2001},[238,20762,20763],{"encoding":240},"\\boldsymbol{\\Sigma}",[128,20765,20767],{"className":20766,"ariaHidden":246},[245],[128,20768,20770,20773],{"className":20769},[250],[128,20771],{"className":20772,"style":20333},[254],[128,20774,20776],{"className":20775},[259],[128,20777,20779],{"className":20778},[259],[128,20780,20262],{"className":20781},[259,2151]," 必然奇异，其零空间由 ",[128,20784,20786,20800],{"className":20785,"translate":218},[217],[128,20787,20789],{"className":20788},[222],[224,20790,20791],{"xmlns":226},[228,20792,20793,20797],{},[231,20794,20795],{},[1840,20796,1842],{"mathvariant":2001},[238,20798,20799],{"encoding":240},"\\mathbf{1}",[128,20801,20803],{"className":20802,"ariaHidden":246},[245],[128,20804,20806,20809],{"className":20805},[250],[128,20807],{"className":20808,"style":2594},[254],[128,20810,1842],{"className":20811},[259,2151]," 张成——这正是「分布在 ",[128,20814,20816,20837],{"className":20815,"translate":218},[217],[128,20817,20819],{"className":20818},[222],[224,20820,20821],{"xmlns":226},[228,20822,20823,20835],{},[231,20824,20825,20827,20829,20831,20833],{},[1832,20826,2477],{"stretchy":1837},[1795,20828,1853],{},[1832,20830,1989],{},[1840,20832,1842],{},[1832,20834,2486],{"stretchy":1837},[238,20836,2489],{"encoding":240},[128,20838,20840,20861],{"className":20839,"ariaHidden":246},[245],[128,20841,20843,20846,20849,20852,20855,20858],{"className":20842},[250],[128,20844],{"className":20845,"style":1892},[254],[128,20847,2477],{"className":20848},[1896],[128,20850,1853],{"className":20851,"style":1924},[259,1873],[128,20853],{"className":20854,"style":2508},[269],[128,20856,1989],{"className":20857},[2115],[128,20859],{"className":20860,"style":2508},[269],[128,20862,20864,20867,20870],{"className":20863},[250],[128,20865],{"className":20866,"style":1892},[254],[128,20868,1842],{"className":20869},[259],[128,20871,2486],{"className":20872},[1928]," 维对象上」的代数痕迹。第二，全部协方差为负：",[128,20875,20877,20927],{"className":20876,"translate":218},[217],[128,20878,20880],{"className":20879},[222],[224,20881,20882],{"xmlns":226},[228,20883,20884,20924],{},[231,20885,20886,20888,20890,20892,20898,20900,20906,20908,20910,20912,20914,20916,20918,20920,20922],{},[1795,20887,16643],{"mathvariant":1981},[1832,20889,3278],{},[1832,20891,2477],{"stretchy":1837},[2016,20893,20894,20896],{},[1795,20895,2760],{},[1795,20897,2801],{},[1832,20899,1845],{"separator":246},[2016,20901,20902,20904],{},[1795,20903,2760],{},[1795,20905,16495],{},[1832,20907,2486],{"stretchy":1837},[1832,20909,4221],{},[1840,20911,2028],{},[234,20913,2033],{},[1832,20915,2477],{"stretchy":1837},[1795,20917,2801],{},[1832,20919,16716],{"mathvariant":1981},[1795,20921,16495],{},[1832,20923,2486],{"stretchy":1837},[238,20925,20926],{"encoding":240},"\\operatorname{Cov}(x_i, x_j) \u003C 0\\ (i \\ne j)",[128,20928,20930,21043,21103],{"className":20929,"ariaHidden":246},[245],[128,20931,20933,20936,20942,20945,20985,20988,20991,21031,21034,21037,21040],{"className":20932},[250],[128,20934],{"className":20935,"style":19704},[254],[128,20937,20939],{"className":20938},[2268],[128,20940,16643],{"className":20941,"style":17336},[259,3353],[128,20943,2477],{"className":20944},[1896],[128,20946,20948,20951],{"className":20947},[259],[128,20949,2760],{"className":20950},[259,1873],[128,20952,20954],{"className":20953},[2087],[128,20955,20957,20977],{"className":20956},[274,321],[128,20958,20960,20974],{"className":20959},[278],[128,20961,20963],{"className":20962,"style":3095},[282],[128,20964,20965,20968],{"style":2221},[128,20966],{"className":20967,"style":291},[290],[128,20969,20971],{"className":20970},[299,300,301,298],[128,20972,2801],{"className":20973},[259,1873,298],[128,20975,347],{"className":20976},[346],[128,20978,20980],{"className":20979},[278],[128,20981,20983],{"className":20982,"style":2241},[282],[128,20984],{},[128,20986,1845],{"className":20987},[1903],[128,20989],{"className":20990,"style":1907},[269],[128,20992,20994,20997],{"className":20993},[259],[128,20995,2760],{"className":20996},[259,1873],[128,20998,21000],{"className":20999},[2087],[128,21001,21003,21023],{"className":21002},[274,321],[128,21004,21006,21020],{"className":21005},[278],[128,21007,21009],{"className":21008,"style":3095},[282],[128,21010,21011,21014],{"style":2221},[128,21012],{"className":21013,"style":291},[290],[128,21015,21017],{"className":21016},[299,300,301,298],[128,21018,16495],{"className":21019,"style":16521},[259,1873,298],[128,21021,347],{"className":21022},[346],[128,21024,21026],{"className":21025},[278],[128,21027,21029],{"className":21028,"style":17424},[282],[128,21030],{},[128,21032,2486],{"className":21033},[1928],[128,21035],{"className":21036,"style":1878},[269],[128,21038,4221],{"className":21039},[1882],[128,21041],{"className":21042,"style":1878},[269],[128,21044,21046,21049,21052,21055,21058,21061,21064,21100],{"className":21045},[250],[128,21047],{"className":21048,"style":1892},[254],[128,21050,2028],{"className":21051},[259],[128,21053,2033],{"className":21054},[269],[128,21056,2477],{"className":21057},[1896],[128,21059,2801],{"className":21060},[259,1873],[128,21062],{"className":21063,"style":1878},[269],[128,21065,21067,21094,21097],{"className":21066},[1882],[128,21068,21070],{"className":21069},[1882],[128,21071,21073],{"className":21072},[259,17719],[128,21074,21076],{"className":21075},[17723],[128,21077,21079,21082,21091],{"className":21078},[17727],[128,21080],{"className":21081,"style":16030},[254],[128,21083,21085],{"className":21084},[17734],[128,21086,21088],{"className":21087},[259],[128,21089,17741],{"className":21090},[1882],[128,21092],{"className":21093},[17745],[128,21095],{"className":21096},[269,17749],[128,21098,1994],{"className":21099},[1882],[128,21101],{"className":21102,"style":1878},[269],[128,21104,21106,21109,21112],{"className":21105},[250],[128,21107],{"className":21108,"style":1892},[254],[128,21110,16495],{"className":21111,"style":16521},[259,1873],[128,21113,2486],{"className":21114},[1928],"，因为分量之间必须通过和为 ",[128,21117,21119,21132],{"className":21118,"translate":218},[217],[128,21120,21122],{"className":21121},[222],[224,21123,21124],{"xmlns":226},[228,21125,21126,21130],{},[231,21127,21128],{},[1840,21129,1842],{},[238,21131,1842],{"encoding":240},[128,21133,21135],{"className":21134,"ariaHidden":246},[245],[128,21136,21138,21141],{"className":21137},[250],[128,21139],{"className":21140,"style":2594},[254],[128,21142,1842],{"className":21143},[259]," 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。",[2610,21146,21148],{"id":21147},"_22-均值精度重参数化","2.2 均值—精度重参数化",[11,21150,21151,21152,11072,21187,21257],{},"命题 2.1 中的 ",[128,21153,21155,21169],{"className":21154,"translate":218},[217],[128,21156,21158],{"className":21157},[222],[224,21159,21160],{"xmlns":226},[228,21161,21162,21166],{},[231,21163,21164],{},[1795,21165,20063],{"mathvariant":4834},[238,21167,21168],{"encoding":240},"\\boldsymbol{\\mu}",[128,21170,21172],{"className":21171,"ariaHidden":246},[245],[128,21173,21175,21178],{"className":21174},[250],[128,21176],{"className":21177,"style":2564},[254],[128,21179,21181],{"className":21180},[259],[128,21182,21184],{"className":21183},[259],[128,21185,20063],{"className":21186},[259,4895],[128,21188,21190,21208],{"className":21189,"translate":218},[217],[128,21191,21193],{"className":21192},[222],[224,21194,21195],{"xmlns":226},[228,21196,21197,21205],{},[231,21198,21199],{},[2016,21200,21201,21203],{},[1795,21202,4835],{},[1840,21204,2028],{},[238,21206,21207],{"encoding":240},"\\alpha_0",[128,21209,21211],{"className":21210,"ariaHidden":246},[245],[128,21212,21214,21217],{"className":21213},[250],[128,21215],{"className":21216,"style":4242},[254],[128,21218,21220,21223],{"className":21219},[259],[128,21221,4835],{"className":21222,"style":4920},[259,1873],[128,21224,21226],{"className":21225},[2087],[128,21227,21229,21249],{"className":21228},[274,321],[128,21230,21232,21246],{"className":21231},[278],[128,21233,21235],{"className":21234,"style":2945},[282],[128,21236,21237,21240],{"style":4935},[128,21238],{"className":21239,"style":291},[290],[128,21241,21243],{"className":21242},[299,300,301,298],[128,21244,2028],{"className":21245},[259,298],[128,21247,347],{"className":21248},[346],[128,21250,21252],{"className":21251},[278],[128,21253,21255],{"className":21254,"style":2241},[282],[128,21256],{}," 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",[128,21259,21261],{"className":21260,"translate":218},[1962],[128,21262,21264,21326],{"className":21263,"translate":218},[217],[128,21265,21267],{"className":21266},[222],[224,21268,21269],{"xmlns":226,"display":1971},[228,21270,21271,21323],{},[231,21272,21273,21275,21277,21283,21285,21287,21289,21295,21297,21299,21301,21303,21305,21307,21309,21311],{},[1795,21274,4835],{"mathvariant":4834},[1832,21276,1994],{},[2016,21278,21279,21281],{},[1795,21280,4835],{},[1840,21282,2028],{},[1795,21284,20063],{"mathvariant":4834},[1832,21286,1845],{"separator":246},[269,21288],{"width":11568},[2016,21290,21291,21293],{},[1795,21292,4835],{},[1840,21294,2028],{},[1832,21296,3321],{},[1840,21298,2028],{},[1832,21300,1845],{"separator":246},[234,21302,2033],{},[1795,21304,20063],{"mathvariant":4834},[1832,21306,1834],{},[1795,21308,3275],{"mathvariant":1981},[1832,21310,3278],{},[1977,21312,21313,21315],{},[1795,21314,1982],{"mathvariant":1981},[231,21316,21317,21319,21321],{},[1795,21318,1853],{},[1832,21320,1989],{},[1840,21322,1842],{},[238,21324,21325],{"encoding":240},"\\boldsymbol{\\alpha} = \\alpha_0 \\boldsymbol{\\mu}, \\qquad \\alpha_0 > 0,\\ \\boldsymbol{\\mu} \\in \\operatorname{int}\\Delta^{K-1}",[128,21327,21329,21353,21466,21503],{"className":21328,"ariaHidden":246},[245],[128,21330,21332,21335,21344,21347,21350],{"className":21331},[250],[128,21333],{"className":21334,"style":4439},[254],[128,21336,21338],{"className":21337},[259],[128,21339,21341],{"className":21340},[259],[128,21342,4835],{"className":21343},[259,4895],[128,21345],{"className":21346,"style":1878},[269],[128,21348,1994],{"className":21349},[1882],[128,21351],{"className":21352,"style":1878},[269],[128,21354,21356,21359,21399,21408,21411,21414,21417,21457,21460,21463],{"className":21355},[250],[128,21357],{"className":21358,"style":1869},[254],[128,21360,21362,21365],{"className":21361},[259],[128,21363,4835],{"className":21364,"style":4920},[259,1873],[128,21366,21368],{"className":21367},[2087],[128,21369,21371,21391],{"className":21370},[274,321],[128,21372,21374,21388],{"className":21373},[278],[128,21375,21377],{"className":21376,"style":2945},[282],[128,21378,21379,21382],{"style":4935},[128,21380],{"className":21381,"style":291},[290],[128,21383,21385],{"className":21384},[299,300,301,298],[128,21386,2028],{"className":21387},[259,298],[128,21389,347],{"className":21390},[346],[128,21392,21394],{"className":21393},[278],[128,21395,21397],{"className":21396,"style":2241},[282],[128,21398],{},[128,21400,21402],{"className":21401},[259],[128,21403,21405],{"className":21404},[259],[128,21406,20063],{"className":21407},[259,4895],[128,21409,1845],{"className":21410},[1903],[128,21412],{"className":21413,"style":11756},[269],[128,21415],{"className":21416,"style":1907},[269],[128,21418,21420,21423],{"className":21419},[259],[128,21421,4835],{"className":21422,"style":4920},[259,1873],[128,21424,21426],{"className":21425},[2087],[128,21427,21429,21449],{"className":21428},[274,321],[128,21430,21432,21446],{"className":21431},[278],[128,21433,21435],{"className":21434,"style":2945},[282],[128,21436,21437,21440],{"style":4935},[128,21438],{"className":21439,"style":291},[290],[128,21441,21443],{"className":21442},[299,300,301,298],[128,21444,2028],{"className":21445},[259,298],[128,21447,347],{"className":21448},[346],[128,21450,21452],{"className":21451},[278],[128,21453,21455],{"className":21454,"style":2241},[282],[128,21456],{},[128,21458],{"className":21459,"style":1878},[269],[128,21461,3321],{"className":21462},[1882],[128,21464],{"className":21465,"style":1878},[269],[128,21467,21469,21473,21476,21479,21482,21485,21494,21497,21500],{"className":21468},[250],[128,21470],{"className":21471,"style":21472},[254],"height:0.8389em;vertical-align:-0.1944em;",[128,21474,2028],{"className":21475},[259],[128,21477,1845],{"className":21478},[1903],[128,21480,2033],{"className":21481},[269],[128,21483],{"className":21484,"style":1907},[269],[128,21486,21488],{"className":21487},[259],[128,21489,21491],{"className":21490},[259],[128,21492,20063],{"className":21493},[259,4895],[128,21495],{"className":21496,"style":1878},[269],[128,21498,1834],{"className":21499},[1882],[128,21501],{"className":21502,"style":1878},[269],[128,21504,21506,21509,21515,21518],{"className":21505},[250],[128,21507],{"className":21508,"style":2077},[254],[128,21510,21512],{"className":21511},[2268],[128,21513,3275],{"className":21514},[259,3353],[128,21516],{"className":21517,"style":1907},[269],[128,21519,21521,21524],{"className":21520},[259],[128,21522,1982],{"className":21523},[259],[128,21525,21527],{"className":21526},[2087],[128,21528,21530],{"className":21529},[274],[128,21531,21533],{"className":21532},[278],[128,21534,21536],{"className":21535,"style":2077},[282],[128,21537,21538,21541],{"style":2099},[128,21539],{"className":21540,"style":291},[290],[128,21542,21544],{"className":21543},[299,300,301,298],[128,21545,21547,21550,21553],{"className":21546},[259,298],[128,21548,1853],{"className":21549,"style":1924},[259,1873,298],[128,21551,1989],{"className":21552},[2115,298],[128,21554,1842],{"className":21555},[259,298],[11,21557,21558,21559,21562,21563,21613,21614,21617,21618,2674,21901,22009,22010,22079],{},"它把参数空间分解为一个",[35,21560,21561],{},"方向","（",[128,21564,21566,21583],{"className":21565,"translate":218},[217],[128,21567,21569],{"className":21568},[222],[224,21570,21571],{"xmlns":226},[228,21572,21573,21581],{},[231,21574,21575,21577,21579],{},[1795,21576,1853],{},[1832,21578,1989],{},[1840,21580,1842],{},[238,21582,2695],{"encoding":240},[128,21584,21586,21604],{"className":21585,"ariaHidden":246},[245],[128,21587,21589,21592,21595,21598,21601],{"className":21588},[250],[128,21590],{"className":21591,"style":2705},[254],[128,21593,1853],{"className":21594,"style":1924},[259,1873],[128,21596],{"className":21597,"style":2508},[269],[128,21599,1989],{"className":21600},[2115],[128,21602],{"className":21603,"style":2508},[269],[128,21605,21607,21610],{"className":21606},[250],[128,21608],{"className":21609,"style":2594},[254],[128,21611,1842],{"className":21612},[259]," 维单纯形）与一个",[35,21615,21616],{},"尺度","（正实数）。在此参数化下，协方差为 ",[128,21619,21621,21673],{"className":21620,"translate":218},[217],[128,21622,21624],{"className":21623},[222],[224,21625,21626],{"xmlns":226},[228,21627,21628,21670],{},[231,21629,21630,21632,21634,21650,21652,21654,21656,21658,21660,21662,21668],{},[1795,21631,20262],{"mathvariant":2001},[1832,21633,1994],{},[5451,21635,21636,21638],{},[1840,21637,1842],{},[231,21639,21640,21646,21648],{},[2016,21641,21642,21644],{},[1795,21643,4835],{},[1840,21645,2028],{},[1832,21647,9486],{},[1840,21649,1842],{},[1832,21651,2477],{"stretchy":1837},[1795,21653,20299],{"mathvariant":1981},[1832,21655,3278],{},[1795,21657,20063],{"mathvariant":4834},[1832,21659,1989],{},[1795,21661,20063],{"mathvariant":4834},[1977,21663,21664,21666],{},[1795,21665,20063],{"mathvariant":4834},[1795,21667,20318],{"mathvariant":1981},[1832,21669,2486],{"stretchy":1837},[238,21671,21672],{"encoding":240},"\\boldsymbol{\\Sigma} = \\frac{1}{\\alpha_0+1}(\\operatorname{diag}\\boldsymbol{\\mu} - \\boldsymbol{\\mu}\\boldsymbol{\\mu}^\\top)",[128,21674,21676,21700,21847],{"className":21675,"ariaHidden":246},[245],[128,21677,21679,21682,21691,21694,21697],{"className":21678},[250],[128,21680],{"className":21681,"style":20333},[254],[128,21683,21685],{"className":21684},[259],[128,21686,21688],{"className":21687},[259],[128,21689,20262],{"className":21690},[259,2151],[128,21692],{"className":21693,"style":1878},[269],[128,21695,1994],{"className":21696},[1882],[128,21698],{"className":21699,"style":1878},[269],[128,21701,21703,21706,21817,21820,21826,21829,21838,21841,21844],{"className":21702},[250],[128,21704],{"className":21705,"style":18295},[254],[128,21707,21709,21712,21814],{"className":21708},[259],[128,21710],{"className":21711},[1896,5570],[128,21713,21715],{"className":21714},[5451],[128,21716,21718,21806],{"className":21717},[274,321],[128,21719,21721,21803],{"className":21720},[278],[128,21722,21724,21781,21789],{"className":21723,"style":5583},[282],[128,21725,21726,21729],{"style":5586},[128,21727],{"className":21728,"style":335},[290],[128,21730,21732],{"className":21731},[299,300,301,298],[128,21733,21735,21775,21778],{"className":21734},[259,298],[128,21736,21738,21741],{"className":21737},[259,298],[128,21739,4835],{"className":21740,"style":4920},[259,1873,298],[128,21742,21744],{"className":21743},[2087],[128,21745,21747,21767],{"className":21746},[274,321],[128,21748,21750,21764],{"className":21749},[278],[128,21751,21753],{"className":21752,"style":6153},[282],[128,21754,21755,21758],{"style":5786},[128,21756],{"className":21757,"style":5790},[290],[128,21759,21761],{"className":21760},[299,5794,5795,298],[128,21762,2028],{"className":21763},[259,298],[128,21765,347],{"className":21766},[346],[128,21768,21770],{"className":21769},[278],[128,21771,21773],{"className":21772,"style":5808},[282],[128,21774],{},[128,21776,9486],{"className":21777},[2115,298],[128,21779,1842],{"className":21780},[259,298],[128,21782,21783,21786],{"style":5617},[128,21784],{"className":21785,"style":335},[290],[128,21787],{"className":21788,"style":5625},[5624],[128,21790,21791,21794],{"style":5628},[128,21792],{"className":21793,"style":335},[290],[128,21795,21797],{"className":21796},[299,300,301,298],[128,21798,21800],{"className":21799},[259,298],[128,21801,1842],{"className":21802},[259,298],[128,21804,347],{"className":21805},[346],[128,21807,21809],{"className":21808},[278],[128,21810,21812],{"className":21811,"style":16937},[282],[128,21813],{},[128,21815],{"className":21816},[1928,5570],[128,21818,2477],{"className":21819},[1896],[128,21821,21823],{"className":21822},[2268],[128,21824,20299],{"className":21825,"style":17336},[259,3353],[128,21827],{"className":21828,"style":1907},[269],[128,21830,21832],{"className":21831},[259],[128,21833,21835],{"className":21834},[259],[128,21836,20063],{"className":21837},[259,4895],[128,21839],{"className":21840,"style":2508},[269],[128,21842,1989],{"className":21843},[2115],[128,21845],{"className":21846,"style":2508},[269],[128,21848,21850,21854,21863,21898],{"className":21849},[250],[128,21851],{"className":21852,"style":21853},[254],"height:1.0991em;vertical-align:-0.25em;",[128,21855,21857],{"className":21856},[259],[128,21858,21860],{"className":21859},[259],[128,21861,20063],{"className":21862},[259,4895],[128,21864,21866,21875],{"className":21865},[259],[128,21867,21869],{"className":21868},[259],[128,21870,21872],{"className":21871},[259],[128,21873,20063],{"className":21874},[259,4895],[128,21876,21878],{"className":21877},[2087],[128,21879,21881],{"className":21880},[274],[128,21882,21884],{"className":21883},[278],[128,21885,21887],{"className":21886,"style":20687},[282],[128,21888,21889,21892],{"style":2452},[128,21890],{"className":21891,"style":291},[290],[128,21893,21895],{"className":21894},[299,300,301,298],[128,21896,20318],{"className":21897},[259,298],[128,21899,2486],{"className":21900},[1928],[35,21902,21903,21904,21938,21939,22008],{},"与 ",[128,21905,21907,21920],{"className":21906,"translate":218},[217],[128,21908,21910],{"className":21909},[222],[224,21911,21912],{"xmlns":226},[228,21913,21914,21918],{},[231,21915,21916],{},[1795,21917,20063],{"mathvariant":4834},[238,21919,21168],{"encoding":240},[128,21921,21923],{"className":21922,"ariaHidden":246},[245],[128,21924,21926,21929],{"className":21925},[250],[128,21927],{"className":21928,"style":2564},[254],[128,21930,21932],{"className":21931},[259],[128,21933,21935],{"className":21934},[259],[128,21936,20063],{"className":21937},[259,4895]," 的取值无关、只随 ",[128,21940,21942,21959],{"className":21941,"translate":218},[217],[128,21943,21945],{"className":21944},[222],[224,21946,21947],{"xmlns":226},[228,21948,21949,21957],{},[231,21950,21951],{},[2016,21952,21953,21955],{},[1795,21954,4835],{},[1840,21956,2028],{},[238,21958,21207],{"encoding":240},[128,21960,21962],{"className":21961,"ariaHidden":246},[245],[128,21963,21965,21968],{"className":21964},[250],[128,21966],{"className":21967,"style":4242},[254],[128,21969,21971,21974],{"className":21970},[259],[128,21972,4835],{"className":21973,"style":4920},[259,1873],[128,21975,21977],{"className":21976},[2087],[128,21978,21980,22000],{"className":21979},[274,321],[128,21981,21983,21997],{"className":21982},[278],[128,21984,21986],{"className":21985,"style":2945},[282],[128,21987,21988,21991],{"style":4935},[128,21989],{"className":21990,"style":291},[290],[128,21992,21994],{"className":21993},[299,300,301,298],[128,21995,2028],{"className":21996},[259,298],[128,21998,347],{"className":21999},[346],[128,22001,22003],{"className":22002},[278],[128,22004,22006],{"className":22005,"style":2241},[282],[128,22007],{}," 单调收缩","。因此 ",[128,22011,22013,22030],{"className":22012,"translate":218},[217],[128,22014,22016],{"className":22015},[222],[224,22017,22018],{"xmlns":226},[228,22019,22020,22028],{},[231,22021,22022],{},[2016,22023,22024,22026],{},[1795,22025,4835],{},[1840,22027,2028],{},[238,22029,21207],{"encoding":240},[128,22031,22033],{"className":22032,"ariaHidden":246},[245],[128,22034,22036,22039],{"className":22035},[250],[128,22037],{"className":22038,"style":4242},[254],[128,22040,22042,22045],{"className":22041},[259],[128,22043,4835],{"className":22044,"style":4920},[259,1873],[128,22046,22048],{"className":22047},[2087],[128,22049,22051,22071],{"className":22050},[274,321],[128,22052,22054,22068],{"className":22053},[278],[128,22055,22057],{"className":22056,"style":2945},[282],[128,22058,22059,22062],{"style":4935},[128,22060],{"className":22061,"style":291},[290],[128,22063,22065],{"className":22064},[299,300,301,298],[128,22066,2028],{"className":22067},[259,298],[128,22069,347],{"className":22070},[346],[128,22072,22074],{"className":22073},[278],[128,22075,22077],{"className":22076,"style":2241},[282],[128,22078],{}," 是一个纯粹的集中度（或称精度、强度）参数：",[2615,22081,22083],{"title":22082},"命题 2.2（集中性极限）",[11,22084,22085,22086,22201,22202,22398,22399,22492,22493,22594,22595,22629,22630,893],{},"固定 ",[128,22087,22089,22121],{"className":22088,"translate":218},[217],[128,22090,22092],{"className":22091},[222],[224,22093,22094],{"xmlns":226},[228,22095,22096,22118],{},[231,22097,22098,22100,22102,22104,22106],{},[1795,22099,20063],{"mathvariant":4834},[1832,22101,1834],{},[1795,22103,3275],{"mathvariant":1981},[1832,22105,3278],{},[1977,22107,22108,22110],{},[1795,22109,1982],{"mathvariant":1981},[231,22111,22112,22114,22116],{},[1795,22113,1853],{},[1832,22115,1989],{},[1840,22117,1842],{},[238,22119,22120],{"encoding":240},"\\boldsymbol{\\mu} \\in \\operatorname{int}\\Delta^{K-1}",[128,22122,22124,22148],{"className":22123,"ariaHidden":246},[245],[128,22125,22127,22130,22139,22142,22145],{"className":22126},[250],[128,22128],{"className":22129,"style":1869},[254],[128,22131,22133],{"className":22132},[259],[128,22134,22136],{"className":22135},[259],[128,22137,20063],{"className":22138},[259,4895],[128,22140],{"className":22141,"style":1878},[269],[128,22143,1834],{"className":22144},[1882],[128,22146],{"className":22147,"style":1878},[269],[128,22149,22151,22154,22160,22163],{"className":22150},[250],[128,22152],{"className":22153,"style":2431},[254],[128,22155,22157],{"className":22156},[2268],[128,22158,3275],{"className":22159},[259,3353],[128,22161],{"className":22162,"style":1907},[269],[128,22164,22166,22169],{"className":22165},[259],[128,22167,1982],{"className":22168},[259],[128,22170,22172],{"className":22171},[2087],[128,22173,22175],{"className":22174},[274],[128,22176,22178],{"className":22177},[278],[128,22179,22181],{"className":22180,"style":2431},[282],[128,22182,22183,22186],{"style":2452},[128,22184],{"className":22185,"style":291},[290],[128,22187,22189],{"className":22188},[299,300,301,298],[128,22190,22192,22195,22198],{"className":22191},[259,298],[128,22193,1853],{"className":22194,"style":1924},[259,1873,298],[128,22196,1989],{"className":22197},[2115,298],[128,22199,1842],{"className":22200},[259,298],"，令 ",[128,22203,22205,22243],{"className":22204,"translate":218},[217],[128,22206,22208],{"className":22207},[222],[224,22209,22210],{"xmlns":226},[228,22211,22212,22240],{},[231,22213,22214,22230,22232,22238],{},[1977,22215,22216,22218],{},[1795,22217,4835],{"mathvariant":4834},[231,22219,22220,22222,22228],{},[1832,22221,2477],{"stretchy":1837},[2016,22223,22224,22226],{},[1795,22225,4835],{},[1840,22227,2028],{},[1832,22229,2486],{"stretchy":1837},[1832,22231,1994],{},[2016,22233,22234,22236],{},[1795,22235,4835],{},[1840,22237,2028],{},[1795,22239,20063],{"mathvariant":4834},[238,22241,22242],{"encoding":240},"\\boldsymbol{\\alpha}^{(\\alpha_0)} = \\alpha_0 \\boldsymbol{\\mu}",[128,22244,22246,22343],{"className":22245,"ariaHidden":246},[245],[128,22247,22249,22253,22334,22337,22340],{"className":22248},[250],[128,22250],{"className":22251,"style":22252},[254],"height:0.888em;",[128,22254,22256,22265],{"className":22255},[259],[128,22257,22259],{"className":22258},[259],[128,22260,22262],{"className":22261},[259],[128,22263,4835],{"className":22264},[259,4895],[128,22266,22268],{"className":22267},[2087],[128,22269,22271],{"className":22270},[274],[128,22272,22274],{"className":22273},[278],[128,22275,22277],{"className":22276,"style":22252},[282],[128,22278,22279,22282],{"style":2452},[128,22280],{"className":22281,"style":291},[290],[128,22283,22285],{"className":22284},[299,300,301,298],[128,22286,22288,22291,22331],{"className":22287},[259,298],[128,22289,2477],{"className":22290},[1896,298],[128,22292,22294,22297],{"className":22293},[259,298],[128,22295,4835],{"className":22296,"style":4920},[259,1873,298],[128,22298,22300],{"className":22299},[2087],[128,22301,22303,22323],{"className":22302},[274,321],[128,22304,22306,22320],{"className":22305},[278],[128,22307,22309],{"className":22308,"style":6153},[282],[128,22310,22311,22314],{"style":5786},[128,22312],{"className":22313,"style":5790},[290],[128,22315,22317],{"className":22316},[299,5794,5795,298],[128,22318,2028],{"className":22319},[259,298],[128,22321,347],{"className":22322},[346],[128,22324,22326],{"className":22325},[278],[128,22327,22329],{"className":22328,"style":5808},[282],[128,22330],{},[128,22332,2486],{"className":22333},[1928,298],[128,22335],{"className":22336,"style":1878},[269],[128,22338,1994],{"className":22339},[1882],[128,22341],{"className":22342,"style":1878},[269],[128,22344,22346,22349,22389],{"className":22345},[250],[128,22347],{"className":22348,"style":2564},[254],[128,22350,22352,22355],{"className":22351},[259],[128,22353,4835],{"className":22354,"style":4920},[259,1873],[128,22356,22358],{"className":22357},[2087],[128,22359,22361,22381],{"className":22360},[274,321],[128,22362,22364,22378],{"className":22363},[278],[128,22365,22367],{"className":22366,"style":2945},[282],[128,22368,22369,22372],{"style":4935},[128,22370],{"className":22371,"style":291},[290],[128,22373,22375],{"className":22374},[299,300,301,298],[128,22376,2028],{"className":22377},[259,298],[128,22379,347],{"className":22380},[346],[128,22382,22384],{"className":22383},[278],[128,22385,22387],{"className":22386,"style":2241},[282],[128,22388],{},[128,22390,22392],{"className":22391},[259],[128,22393,22395],{"className":22394},[259],[128,22396,20063],{"className":22397},[259,4895],"。则当 ",[128,22400,22402,22425],{"className":22401,"translate":218},[217],[128,22403,22405],{"className":22404},[222],[224,22406,22407],{"xmlns":226},[228,22408,22409,22422],{},[231,22410,22411,22417,22420],{},[2016,22412,22413,22415],{},[1795,22414,4835],{},[1840,22416,2028],{},[1832,22418,22419],{},"→",[1795,22421,8521],{"mathvariant":1981},[238,22423,22424],{"encoding":240},"\\alpha_0 \\to \\infty",[128,22426,22428,22483],{"className":22427,"ariaHidden":246},[245],[128,22429,22431,22434,22474,22477,22480],{"className":22430},[250],[128,22432],{"className":22433,"style":4242},[254],[128,22435,22437,22440],{"className":22436},[259],[128,22438,4835],{"className":22439,"style":4920},[259,1873],[128,22441,22443],{"className":22442},[2087],[128,22444,22446,22466],{"className":22445},[274,321],[128,22447,22449,22463],{"className":22448},[278],[128,22450,22452],{"className":22451,"style":2945},[282],[128,22453,22454,22457],{"style":4935},[128,22455],{"className":22456,"style":291},[290],[128,22458,22460],{"className":22459},[299,300,301,298],[128,22461,2028],{"className":22462},[259,298],[128,22464,347],{"className":22465},[346],[128,22467,22469],{"className":22468},[278],[128,22470,22472],{"className":22471,"style":2241},[282],[128,22473],{},[128,22475],{"className":22476,"style":1878},[269],[128,22478,22419],{"className":22479},[1882],[128,22481],{"className":22482,"style":1878},[269],[128,22484,22486,22489],{"className":22485},[250],[128,22487],{"className":22488,"style":7758},[254],[128,22490,8521],{"className":22491},[259]," 时，",[128,22494,22496,22524],{"className":22495,"translate":218},[217],[128,22497,22499],{"className":22498},[222],[224,22500,22501],{"xmlns":226},[228,22502,22503,22521],{},[231,22504,22505,22507,22509,22511,22517,22519],{},[1795,22506,5914],{"mathvariant":1981},[1832,22508,3278],{},[1832,22510,2477],{"stretchy":1837},[2016,22512,22513,22515],{},[1795,22514,4835],{},[1840,22516,2028],{},[1795,22518,20063],{"mathvariant":4834},[1832,22520,2486],{"stretchy":1837},[238,22522,22523],{"encoding":240},"\\operatorname{Dir}(\\alpha_0 \\boldsymbol{\\mu})",[128,22525,22527],{"className":22526,"ariaHidden":246},[245],[128,22528,22530,22533,22539,22542,22582,22591],{"className":22529},[250],[128,22531],{"className":22532,"style":1892},[254],[128,22534,22536],{"className":22535},[2268],[128,22537,5914],{"className":22538},[259,3353],[128,22540,2477],{"className":22541},[1896],[128,22543,22545,22548],{"className":22544},[259],[128,22546,4835],{"className":22547,"style":4920},[259,1873],[128,22549,22551],{"className":22550},[2087],[128,22552,22554,22574],{"className":22553},[274,321],[128,22555,22557,22571],{"className":22556},[278],[128,22558,22560],{"className":22559,"style":2945},[282],[128,22561,22562,22565],{"style":4935},[128,22563],{"className":22564,"style":291},[290],[128,22566,22568],{"className":22567},[299,300,301,298],[128,22569,2028],{"className":22570},[259,298],[128,22572,347],{"className":22573},[346],[128,22575,22577],{"className":22576},[278],[128,22578,22580],{"className":22579,"style":2241},[282],[128,22581],{},[128,22583,22585],{"className":22584},[259],[128,22586,22588],{"className":22587},[259],[128,22589,20063],{"className":22590},[259,4895],[128,22592,2486],{"className":22593},[1928]," 弱收敛于位于 ",[128,22596,22598,22611],{"className":22597,"translate":218},[217],[128,22599,22601],{"className":22600},[222],[224,22602,22603],{"xmlns":226},[228,22604,22605,22609],{},[231,22606,22607],{},[1795,22608,20063],{"mathvariant":4834},[238,22610,21168],{"encoding":240},[128,22612,22614],{"className":22613,"ariaHidden":246},[245],[128,22615,22617,22620],{"className":22616},[250],[128,22618],{"className":22619,"style":2564},[254],[128,22621,22623],{"className":22622},[259],[128,22624,22626],{"className":22625},[259],[128,22627,20063],{"className":22628},[259,4895]," 的退化测度 ",[128,22631,22633,22652],{"className":22632,"translate":218},[217],[128,22634,22636],{"className":22635},[222],[224,22637,22638],{"xmlns":226},[228,22639,22640,22649],{},[231,22641,22642],{},[2016,22643,22644,22647],{},[1795,22645,22646],{},"δ",[1795,22648,20063],{"mathvariant":4834},[238,22650,22651],{"encoding":240},"\\delta_{\\boldsymbol{\\mu}}",[128,22653,22655],{"className":22654,"ariaHidden":246},[245],[128,22656,22658,22662],{"className":22657},[250],[128,22659],{"className":22660,"style":22661},[254],"height:0.9805em;vertical-align:-0.2861em;",[128,22663,22665,22669],{"className":22664},[259],[128,22666,22646],{"className":22667,"style":22668},[259,1873],"margin-right:0.0379em;",[128,22670,22672],{"className":22671},[2087],[128,22673,22675,22706],{"className":22674},[274,321],[128,22676,22678,22703],{"className":22677},[278],[128,22679,22682],{"className":22680,"style":22681},[282],"height:0.1611em;",[128,22683,22685,22688],{"style":22684},"top:-2.55em;margin-left:-0.0379em;margin-right:0.05em;",[128,22686],{"className":22687,"style":291},[290],[128,22689,22691],{"className":22690},[299,300,301,298],[128,22692,22694],{"className":22693},[259,298],[128,22695,22697],{"className":22696},[259,298],[128,22698,22700],{"className":22699},[259,298],[128,22701,20063],{"className":22702},[259,4895,298],[128,22704,347],{"className":22705},[346],[128,22707,22709],{"className":22708},[278],[128,22710,22712],{"className":22711,"style":17424},[282],[128,22713],{},[11,22715,22716,22718,22719,17916,22791,22933,22934,22986,22987,23199,23200,893],{},[35,22717,6849],{}," 由命题 2.1，",[128,22720,22722,22746],{"className":22721,"translate":218},[217],[128,22723,22725],{"className":22724},[222],[224,22726,22727],{"xmlns":226},[228,22728,22729,22743],{},[231,22730,22731,22733,22735,22737,22739,22741],{},[1795,22732,342],{"mathvariant":2008},[1832,22734,16538],{"stretchy":1837},[1795,22736,2760],{"mathvariant":2001},[1832,22738,16547],{"stretchy":1837},[1832,22740,1994],{},[1795,22742,20063],{"mathvariant":4834},[238,22744,22745],{"encoding":240},"\\mathbb{E}[\\mathbf{x}] = \\boldsymbol{\\mu}",[128,22747,22749,22776],{"className":22748,"ariaHidden":246},[245],[128,22750,22752,22755,22758,22761,22764,22767,22770,22773],{"className":22751},[250],[128,22753],{"className":22754,"style":1892},[254],[128,22756,342],{"className":22757},[259,2167],[128,22759,16538],{"className":22760},[1896],[128,22762,2760],{"className":22763},[259,2151],[128,22765,16547],{"className":22766},[1928],[128,22768],{"className":22769,"style":1878},[269],[128,22771,1994],{"className":22772},[1882],[128,22774],{"className":22775,"style":1878},[269],[128,22777,22779,22782],{"className":22778},[250],[128,22780],{"className":22781,"style":2564},[254],[128,22783,22785],{"className":22784},[259],[128,22786,22788],{"className":22787},[259],[128,22789,20063],{"className":22790},[259,4895],[128,22792,22794,22830],{"className":22793,"translate":218},[217],[128,22795,22797],{"className":22796},[222],[224,22798,22799],{"xmlns":226},[228,22800,22801,22827],{},[231,22802,22803,22805,22807,22809,22811,22813,22815,22821,22823,22825],{},[1795,22804,20262],{"mathvariant":2001},[1832,22806,1994],{},[1795,22808,13986],{},[1832,22810,2477],{"stretchy":1837},[1840,22812,1842],{},[1795,22814,4751],{"mathvariant":1981},[2016,22816,22817,22819],{},[1795,22818,4835],{},[1840,22820,2028],{},[1832,22822,2486],{"stretchy":1837},[1832,22824,22419],{},[1840,22826,2028],{"mathvariant":2001},[238,22828,22829],{"encoding":240},"\\boldsymbol{\\Sigma} = O(1\u002F\\alpha_0) \\to \\mathbf{0}",[128,22831,22833,22857,22924],{"className":22832,"ariaHidden":246},[245],[128,22834,22836,22839,22848,22851,22854],{"className":22835},[250],[128,22837],{"className":22838,"style":20333},[254],[128,22840,22842],{"className":22841},[259],[128,22843,22845],{"className":22844},[259],[128,22846,20262],{"className":22847},[259,2151],[128,22849],{"className":22850,"style":1878},[269],[128,22852,1994],{"className":22853},[1882],[128,22855],{"className":22856,"style":1878},[269],[128,22858,22860,22863,22866,22869,22872,22912,22915,22918,22921],{"className":22859},[250],[128,22861],{"className":22862,"style":1892},[254],[128,22864,13986],{"className":22865,"style":14008},[259,1873],[128,22867,2477],{"className":22868},[1896],[128,22870,4780],{"className":22871},[259],[128,22873,22875,22878],{"className":22874},[259],[128,22876,4835],{"className":22877,"style":4920},[259,1873],[128,22879,22881],{"className":22880},[2087],[128,22882,22884,22904],{"className":22883},[274,321],[128,22885,22887,22901],{"className":22886},[278],[128,22888,22890],{"className":22889,"style":2945},[282],[128,22891,22892,22895],{"style":4935},[128,22893],{"className":22894,"style":291},[290],[128,22896,22898],{"className":22897},[299,300,301,298],[128,22899,2028],{"className":22900},[259,298],[128,22902,347],{"className":22903},[346],[128,22905,22907],{"className":22906},[278],[128,22908,22910],{"className":22909,"style":2241},[282],[128,22911],{},[128,22913,2486],{"className":22914},[1928],[128,22916],{"className":22917,"style":1878},[269],[128,22919,22419],{"className":22920},[1882],[128,22922],{"className":22923,"style":1878},[269],[128,22925,22927,22930],{"className":22926},[250],[128,22928],{"className":22929,"style":2594},[254],[128,22931,2028],{"className":22932},[259,2151],"。对任意 ",[128,22935,22937,22956],{"className":22936,"translate":218},[217],[128,22938,22940],{"className":22939},[222],[224,22941,22942],{"xmlns":226},[228,22943,22944,22953],{},[231,22945,22946,22949,22951],{},[1795,22947,22948],{},"ε",[1832,22950,3321],{},[1840,22952,2028],{},[238,22954,22955],{"encoding":240},"\\varepsilon > 0",[128,22957,22959,22977],{"className":22958,"ariaHidden":246},[245],[128,22960,22962,22965,22968,22971,22974],{"className":22961},[250],[128,22963],{"className":22964,"style":6382},[254],[128,22966,22948],{"className":22967},[259,1873],[128,22969],{"className":22970,"style":1878},[269],[128,22972,3321],{"className":22973},[1882],[128,22975],{"className":22976,"style":1878},[269],[128,22978,22980,22983],{"className":22979},[250],[128,22981],{"className":22982,"style":2594},[254],[128,22984,2028],{"className":22985},[259],"，由 Chebyshev 不等式 ",[128,22988,22990,23046],{"className":22989,"translate":218},[217],[128,22991,22993],{"className":22992},[222],[224,22994,22995],{"xmlns":226},[228,22996,22997,23043],{},[231,22998,22999,23002,23004,23007,23009,23011,23013,23015,23017,23019,23021,23024,23027,23029,23031,23033,23039,23041],{},[1795,23000,23001],{"mathvariant":2008},"P",[1832,23003,2477],{"stretchy":1837},[1795,23005,23006],{"mathvariant":1981},"∥",[1795,23008,2760],{"mathvariant":2001},[1832,23010,1989],{},[1795,23012,20063],{"mathvariant":4834},[1795,23014,23006],{"mathvariant":1981},[1832,23016,3321],{},[1795,23018,22948],{},[1832,23020,2486],{"stretchy":1837},[1832,23022,23023],{},"≤",[1795,23025,23026],{"mathvariant":1981},"tr",[1832,23028,3278],{},[1795,23030,20262],{"mathvariant":2001},[1795,23032,4751],{"mathvariant":1981},[1977,23034,23035,23037],{},[1795,23036,22948],{},[1840,23038,2639],{},[1832,23040,22419],{},[1840,23042,2028],{},[238,23044,23045],{"encoding":240},"\\mathbb{P}(\\|\\mathbf{x} - \\boldsymbol{\\mu}\\| > \\varepsilon) \\le \\operatorname{tr}\\boldsymbol{\\Sigma}\u002F\\varepsilon^2 \\to 0",[128,23047,23049,23076,23103,23124,23190],{"className":23048,"ariaHidden":246},[245],[128,23050,23052,23055,23058,23061,23064,23067,23070,23073],{"className":23051},[250],[128,23053],{"className":23054,"style":1892},[254],[128,23056,23001],{"className":23057},[259,2167],[128,23059,2477],{"className":23060},[1896],[128,23062,23006],{"className":23063},[259],[128,23065,2760],{"className":23066},[259,2151],[128,23068],{"className":23069,"style":2508},[269],[128,23071,1989],{"className":23072},[2115],[128,23074],{"className":23075,"style":2508},[269],[128,23077,23079,23082,23091,23094,23097,23100],{"className":23078},[250],[128,23080],{"className":23081,"style":1892},[254],[128,23083,23085],{"className":23084},[259],[128,23086,23088],{"className":23087},[259],[128,23089,20063],{"className":23090},[259,4895],[128,23092,23006],{"className":23093},[259],[128,23095],{"className":23096,"style":1878},[269],[128,23098,3321],{"className":23099},[1882],[128,23101],{"className":23102,"style":1878},[269],[128,23104,23106,23109,23112,23115,23118,23121],{"className":23105},[250],[128,23107],{"className":23108,"style":1892},[254],[128,23110,22948],{"className":23111},[259,1873],[128,23113,2486],{"className":23114},[1928],[128,23116],{"className":23117,"style":1878},[269],[128,23119,23023],{"className":23120},[1882],[128,23122],{"className":23123,"style":1878},[269],[128,23125,23127,23131,23137,23140,23149,23152,23181,23184,23187],{"className":23126},[250],[128,23128],{"className":23129,"style":23130},[254],"height:1.0641em;vertical-align:-0.25em;",[128,23132,23134],{"className":23133},[2268],[128,23135,23026],{"className":23136},[259,3353],[128,23138],{"className":23139,"style":1907},[269],[128,23141,23143],{"className":23142},[259],[128,23144,23146],{"className":23145},[259],[128,23147,20262],{"className":23148},[259,2151],[128,23150,4751],{"className":23151},[259],[128,23153,23155,23158],{"className":23154},[259],[128,23156,22948],{"className":23157},[259,1873],[128,23159,23161],{"className":23160},[2087],[128,23162,23164],{"className":23163},[274],[128,23165,23167],{"className":23166},[278],[128,23168,23170],{"className":23169,"style":9629},[282],[128,23171,23172,23175],{"style":2452},[128,23173],{"className":23174,"style":291},[290],[128,23176,23178],{"className":23177},[299,300,301,298],[128,23179,2639],{"className":23180},[259,298],[128,23182],{"className":23183,"style":1878},[269],[128,23185,22419],{"className":23186},[1882],[128,23188],{"className":23189,"style":1878},[269],[128,23191,23193,23196],{"className":23192},[250],[128,23194],{"className":23195,"style":2594},[254],[128,23197,2028],{"className":23198},[259],"，故依概率收敛，进而弱收敛于 ",[128,23201,23203,23221],{"className":23202,"translate":218},[217],[128,23204,23206],{"className":23205},[222],[224,23207,23208],{"xmlns":226},[228,23209,23210,23218],{},[231,23211,23212],{},[2016,23213,23214,23216],{},[1795,23215,22646],{},[1795,23217,20063],{"mathvariant":4834},[238,23219,23220],{"encoding":240},"\\delta_{\\boldsymbol\\mu}",[128,23222,23224],{"className":23223,"ariaHidden":246},[245],[128,23225,23227,23230],{"className":23226},[250],[128,23228],{"className":23229,"style":22661},[254],[128,23231,23233,23236],{"className":23232},[259],[128,23234,22646],{"className":23235,"style":22668},[259,1873],[128,23237,23239],{"className":23238},[2087],[128,23240,23242,23271],{"className":23241},[274,321],[128,23243,23245,23268],{"className":23244},[278],[128,23246,23248],{"className":23247,"style":22681},[282],[128,23249,23250,23253],{"style":22684},[128,23251],{"className":23252,"style":291},[290],[128,23254,23256],{"className":23255},[299,300,301,298],[128,23257,23259],{"className":23258},[259,298],[128,23260,23262],{"className":23261},[259,298],[128,23263,23265],{"className":23264},[259,298],[128,23266,20063],{"className":23267},[259,4895,298],[128,23269,347],{"className":23270},[346],[128,23272,23274],{"className":23273},[278],[128,23275,23277],{"className":23276,"style":17424},[282],[128,23278],{},[11,23280,23281,23282,23398],{},"这一命题给出了本文后续所有「不确定性」语汇的几何基础：",[35,23283,23284,23285,23362,23363,23397],{},"迪利克雷分布的「模糊程度」等于 ",[128,23286,23288,23310],{"className":23287,"translate":218},[217],[128,23289,23291],{"className":23290},[222],[224,23292,23293],{"xmlns":226},[228,23294,23295,23307],{},[231,23296,23297,23299,23301],{},[1840,23298,1842],{},[1795,23300,4751],{"mathvariant":1981},[2016,23302,23303,23305],{},[1795,23304,4835],{},[1840,23306,2028],{},[238,23308,23309],{"encoding":240},"1\u002F\\alpha_0",[128,23311,23313],{"className":23312,"ariaHidden":246},[245],[128,23314,23316,23319,23322],{"className":23315},[250],[128,23317],{"className":23318,"style":1892},[254],[128,23320,4780],{"className":23321},[259],[128,23323,23325,23328],{"className":23324},[259],[128,23326,4835],{"className":23327,"style":4920},[259,1873],[128,23329,23331],{"className":23330},[2087],[128,23332,23334,23354],{"className":23333},[274,321],[128,23335,23337,23351],{"className":23336},[278],[128,23338,23340],{"className":23339,"style":2945},[282],[128,23341,23342,23345],{"style":4935},[128,23343],{"className":23344,"style":291},[290],[128,23346,23348],{"className":23347},[299,300,301,298],[128,23349,2028],{"className":23350},[259,298],[128,23352,347],{"className":23353},[346],[128,23355,23357],{"className":23356},[278],[128,23358,23360],{"className":23359,"style":2241},[282],[128,23361],{}," 的量级，而它的「中心」由 ",[128,23364,23366,23379],{"className":23365,"translate":218},[217],[128,23367,23369],{"className":23368},[222],[224,23370,23371],{"xmlns":226},[228,23372,23373,23377],{},[231,23374,23375],{},[1795,23376,20063],{"mathvariant":4834},[238,23378,21168],{"encoding":240},[128,23380,23382],{"className":23381,"ariaHidden":246},[245],[128,23383,23385,23388],{"className":23384},[250],[128,23386],{"className":23387,"style":2564},[254],[128,23389,23391],{"className":23390},[259],[128,23392,23394],{"className":23393},[259],[128,23395,20063],{"className":23396},[259,4895]," 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。",[2610,23400,23402],{"id":23401},"_23-众数与熵","2.3 众数与熵",[2615,23404,23406],{"title":23405},"命题 2.3（众数）",[11,23407,23408,23409,23501,23502,23531,23532,23604,23605,23678,23679],{},"若 ",[128,23410,23412,23434],{"className":23411,"translate":218},[217],[128,23413,23415],{"className":23414},[222],[224,23416,23417],{"xmlns":226},[228,23418,23419,23431],{},[231,23420,23421,23427,23429],{},[2016,23422,23423,23425],{},[1795,23424,4835],{},[1795,23426,2801],{},[1832,23428,3321],{},[1840,23430,1842],{},[238,23432,23433],{"encoding":240},"\\alpha_i > 1",[128,23435,23437,23492],{"className":23436,"ariaHidden":246},[245],[128,23438,23440,23443,23483,23486,23489],{"className":23439},[250],[128,23441],{"className":23442,"style":3484},[254],[128,23444,23446,23449],{"className":23445},[259],[128,23447,4835],{"className":23448,"style":4920},[259,1873],[128,23450,23452],{"className":23451},[2087],[128,23453,23455,23475],{"className":23454},[274,321],[128,23456,23458,23472],{"className":23457},[278],[128,23459,23461],{"className":23460,"style":3095},[282],[128,23462,23463,23466],{"style":4935},[128,23464],{"className":23465,"style":291},[290],[128,23467,23469],{"className":23468},[299,300,301,298],[128,23470,2801],{"className":23471},[259,1873,298],[128,23473,347],{"className":23474},[346],[128,23476,23478],{"className":23477},[278],[128,23479,23481],{"className":23480,"style":2241},[282],[128,23482],{},[128,23484],{"className":23485,"style":1878},[269],[128,23487,3321],{"className":23488},[1882],[128,23490],{"className":23491,"style":1878},[269],[128,23493,23495,23498],{"className":23494},[250],[128,23496],{"className":23497,"style":2594},[254],[128,23499,1842],{"className":23500},[259]," 对一切 ",[128,23503,23505,23518],{"className":23504,"translate":218},[217],[128,23506,23508],{"className":23507},[222],[224,23509,23510],{"xmlns":226},[228,23511,23512,23516],{},[231,23513,23514],{},[1795,23515,2801],{},[238,23517,2801],{"encoding":240},[128,23519,23521],{"className":23520,"ariaHidden":246},[245],[128,23522,23524,23528],{"className":23523},[250],[128,23525],{"className":23526,"style":23527},[254],"height:0.6595em;",[128,23529,2801],{"className":23530},[259,1873]," 成立，则 ",[128,23533,23535,23559],{"className":23534,"translate":218},[217],[128,23536,23538],{"className":23537},[222],[224,23539,23540],{"xmlns":226},[228,23541,23542,23556],{},[231,23543,23544,23546,23548,23550,23552,23554],{},[1795,23545,5436],{},[1832,23547,2477],{"stretchy":1837},[1795,23549,2760],{"mathvariant":2001},[1832,23551,5443],{},[1795,23553,4835],{"mathvariant":4834},[1832,23555,2486],{"stretchy":1837},[238,23557,23558],{"encoding":240},"f(\\mathbf{x} \\mid \\boldsymbol{\\alpha})",[128,23560,23562,23586],{"className":23561,"ariaHidden":246},[245],[128,23563,23565,23568,23571,23574,23577,23580,23583],{"className":23564},[250],[128,23566],{"className":23567,"style":1892},[254],[128,23569,5436],{"className":23570,"style":5514},[259,1873],[128,23572,2477],{"className":23573},[1896],[128,23575,2760],{"className":23576},[259,2151],[128,23578],{"className":23579,"style":1878},[269],[128,23581,5443],{"className":23582},[1882],[128,23584],{"className":23585,"style":1878},[269],[128,23587,23589,23592,23601],{"className":23588},[250],[128,23590],{"className":23591,"style":1892},[254],[128,23593,23595],{"className":23594},[259],[128,23596,23598],{"className":23597},[259],[128,23599,4835],{"className":23600},[259,4895],[128,23602,2486],{"className":23603},[1928]," 在 ",[128,23606,23608,23631],{"className":23607,"translate":218},[217],[128,23609,23611],{"className":23610},[222],[224,23612,23613],{"xmlns":226},[228,23614,23615,23629],{},[231,23616,23617],{},[1977,23618,23619,23621],{},[1795,23620,1982],{"mathvariant":1981},[231,23622,23623,23625,23627],{},[1795,23624,1853],{},[1832,23626,1989],{},[1840,23628,1842],{},[238,23630,3589],{"encoding":240},[128,23632,23634],{"className":23633,"ariaHidden":246},[245],[128,23635,23637,23640],{"className":23636},[250],[128,23638],{"className":23639,"style":2431},[254],[128,23641,23643,23646],{"className":23642},[259],[128,23644,1982],{"className":23645},[259],[128,23647,23649],{"className":23648},[2087],[128,23650,23652],{"className":23651},[274],[128,23653,23655],{"className":23654},[278],[128,23656,23658],{"className":23657,"style":2431},[282],[128,23659,23660,23663],{"style":2452},[128,23661],{"className":23662,"style":291},[290],[128,23664,23666],{"className":23665},[299,300,301,298],[128,23667,23669,23672,23675],{"className":23668},[259,298],[128,23670,1853],{"className":23671,"style":1924},[259,1873,298],[128,23673,1989],{"className":23674},[2115,298],[128,23676,1842],{"className":23677},[259,298]," 的内部有唯一众数\n",[128,23680,23682,23767],{"className":23681,"translate":218},[217],[128,23683,23685],{"className":23684},[222],[224,23686,23687],{"xmlns":226},[228,23688,23689,23764],{},[231,23690,23691,23698,23700],{},[1977,23692,23693,23695],{},[1795,23694,2760],{"mathvariant":2001},[1832,23696,23697],{},"⋆",[1832,23699,1994],{},[231,23701,23702,23704,23730,23732,23734,23736,23762],{},[1832,23703,2477],{"fence":246},[5451,23705,23706,23718],{},[231,23707,23708,23714,23716],{},[2016,23709,23710,23712],{},[1795,23711,4835],{},[1840,23713,1842],{},[1832,23715,1989],{},[1840,23717,1842],{},[231,23719,23720,23726,23728],{},[2016,23721,23722,23724],{},[1795,23723,4835],{},[1840,23725,2028],{},[1832,23727,1989],{},[1795,23729,1853],{},[1832,23731,1845],{"separator":246},[1832,23733,1848],{},[1832,23735,1845],{"separator":246},[5451,23737,23738,23750],{},[231,23739,23740,23746,23748],{},[2016,23741,23742,23744],{},[1795,23743,4835],{},[1795,23745,1853],{},[1832,23747,1989],{},[1840,23749,1842],{},[231,23751,23752,23758,23760],{},[2016,23753,23754,23756],{},[1795,23755,4835],{},[1840,23757,2028],{},[1832,23759,1989],{},[1795,23761,1853],{},[1832,23763,2486],{"fence":246},[238,23765,23766],{"encoding":240},"\\mathbf{x}^\\star = \\left( \\frac{\\alpha_1 - 1}{\\alpha_0 - K}, \\dots, \\frac{\\alpha_K - 1}{\\alpha_0 - K} \\right)",[128,23768,23770,23815],{"className":23769,"ariaHidden":246},[245],[128,23771,23773,23777,23806,23809,23812],{"className":23772},[250],[128,23774],{"className":23775,"style":23776},[254],"height:0.6887em;",[128,23778,23780,23783],{"className":23779},[259],[128,23781,2760],{"className":23782},[259,2151],[128,23784,23786],{"className":23785},[2087],[128,23787,23789],{"className":23788},[274],[128,23790,23792],{"className":23791},[278],[128,23793,23795],{"className":23794,"style":23776},[282],[128,23796,23797,23800],{"style":2452},[128,23798],{"className":23799,"style":291},[290],[128,23801,23803],{"className":23802},[299,300,301,298],[128,23804,23697],{"className":23805},[2115,298],[128,23807],{"className":23808,"style":1878},[269],[128,23810,1994],{"className":23811},[1882],[128,23813],{"className":23814,"style":1878},[269],[128,23816,23818,23821],{"className":23817},[250],[128,23819],{"className":23820,"style":2134},[254],[128,23822,23824,23830,23985,23988,23991,23994,23997,24000,24003,24162],{"className":23823},[1911],[128,23825,23827],{"className":23826,"style":2142},[1896,2141],[128,23828,2477],{"className":23829},[2146,2147],[128,23831,23833,23836,23982],{"className":23832},[259],[128,23834],{"className":23835},[1896,5570],[128,23837,23839],{"className":23838},[5451],[128,23840,23842,23974],{"className":23841},[274,321],[128,23843,23845,23971],{"className":23844},[278],[128,23846,23849,23906,23914],{"className":23847,"style":23848},[282],"height:0.8612em;",[128,23850,23851,23854],{"style":5586},[128,23852],{"className":23853,"style":335},[290],[128,23855,23857],{"className":23856},[299,300,301,298],[128,23858,23860,23900,23903],{"className":23859},[259,298],[128,23861,23863,23866],{"className":23862},[259,298],[128,23864,4835],{"className":23865,"style":4920},[259,1873,298],[128,23867,23869],{"className":23868},[2087],[128,23870,23872,23892],{"className":23871},[274,321],[128,23873,23875,23889],{"className":23874},[278],[128,23876,23878],{"className":23877,"style":6153},[282],[128,23879,23880,23883],{"style":5786},[128,23881],{"className":23882,"style":5790},[290],[128,23884,23886],{"className":23885},[299,5794,5795,298],[128,23887,2028],{"className":23888},[259,298],[128,23890,347],{"className":23891},[346],[128,23893,23895],{"className":23894},[278],[128,23896,23898],{"className":23897,"style":5808},[282],[128,23899],{},[128,23901,1989],{"className":23902},[2115,298],[128,23904,1853],{"className":23905,"style":1924},[259,1873,298],[128,23907,23908,23911],{"style":5617},[128,23909],{"className":23910,"style":335},[290],[128,23912],{"className":23913,"style":5625},[5624],[128,23915,23916,23919],{"style":16878},[128,23917],{"className":23918,"style":335},[290],[128,23920,23922],{"className":23921},[299,300,301,298],[128,23923,23925,23965,23968],{"className":23924},[259,298],[128,23926,23928,23931],{"className":23927},[259,298],[128,23929,4835],{"className":23930,"style":4920},[259,1873,298],[128,23932,23934],{"className":23933},[2087],[128,23935,23937,23957],{"className":23936},[274,321],[128,23938,23940,23954],{"className":23939},[278],[128,23941,23943],{"className":23942,"style":6153},[282],[128,23944,23945,23948],{"style":5786},[128,23946],{"className":23947,"style":5790},[290],[128,23949,23951],{"className":23950},[299,5794,5795,298],[128,23952,1842],{"className":23953},[259,298],[128,23955,347],{"className":23956},[346],[128,23958,23960],{"className":23959},[278],[128,23961,23963],{"className":23962,"style":5808},[282],[128,23964],{},[128,23966,1989],{"className":23967},[2115,298],[128,23969,1842],{"className":23970},[259,298],[128,23972,347],{"className":23973},[346],[128,23975,23977],{"className":23976},[278],[128,23978,23980],{"className":23979,"style":16937},[282],[128,23981],{},[128,23983],{"className":23984},[1928,5570],[128,23986,1845],{"className":23987},[1903],[128,23989],{"className":23990,"style":1907},[269],[128,23992,1848],{"className":23993},[1911],[128,23995],{"className":23996,"style":1907},[269],[128,23998,1845],{"className":23999},[1903],[128,24001],{"className":24002,"style":1907},[269],[128,24004,24006,24009,24159],{"className":24005},[259],[128,24007],{"className":24008},[1896,5570],[128,24010,24012],{"className":24011},[5451],[128,24013,24015,24151],{"className":24014},[274,321],[128,24016,24018,24148],{"className":24017},[278],[128,24019,24022,24079,24087],{"className":24020,"style":24021},[282],"height:0.8614em;",[128,24023,24024,24027],{"style":5586},[128,24025],{"className":24026,"style":335},[290],[128,24028,24030],{"className":24029},[299,300,301,298],[128,24031,24033,24073,24076],{"className":24032},[259,298],[128,24034,24036,24039],{"className":24035},[259,298],[128,24037,4835],{"className":24038,"style":4920},[259,1873,298],[128,24040,24042],{"className":24041},[2087],[128,24043,24045,24065],{"className":24044},[274,321],[128,24046,24048,24062],{"className":24047},[278],[128,24049,24051],{"className":24050,"style":6153},[282],[128,24052,24053,24056],{"style":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",[128,24172,24174,24196],{"className":24173,"translate":218},[217],[128,24175,24177],{"className":24176},[222],[224,24178,24179],{"xmlns":226},[228,24180,24181,24193],{},[231,24182,24183,24189,24191],{},[2016,24184,24185,24187],{},[1795,24186,4835],{},[1795,24188,2801],{},[1832,24190,23023],{},[1840,24192,1842],{},[238,24194,24195],{"encoding":240},"\\alpha_i \\le 1",[128,24197,24199,24255],{"className":24198,"ariaHidden":246},[245],[128,24200,24202,24206,24246,24249,24252],{"className":24201},[250],[128,24203],{"className":24204,"style":24205},[254],"height:0.786em;vertical-align:-0.15em;",[128,24207,24209,24212],{"className":24208},[259],[128,24210,4835],{"className":24211,"style":4920},[259,1873],[128,24213,24215],{"className":24214},[2087],[128,24216,24218,24238],{"className":24217},[274,321],[128,24219,24221,24235],{"className":24220},[278],[128,24222,24224],{"className":24223,"style":3095},[282],[128,24225,24226,24229],{"style":4935},[128,24227],{"className":24228,"style":291},[290],[128,24230,24232],{"className":24231},[299,300,301,298],[128,24233,2801],{"className":24234},[259,1873,298],[128,24236,347],{"className":24237},[346],[128,24239,24241],{"className":24240},[278],[128,24242,24244],{"className":24243,"style":2241},[282],[128,24245],{},[128,24247],{"className":24248,"style":1878},[269],[128,24250,23023],{"className":24251},[1882],[128,24253],{"className":24254,"style":1878},[269],[128,24256,24258,24261],{"className":24257},[250],[128,24259],{"className":24260,"style":2594},[254],[128,24262,1842],{"className":24263},[259]," 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。",[2615,24266,24268],{"title":24267},"命题 2.4（微分熵）",[11,24269,24270,24271,24347,24348,24849,24850,24945],{},"在 1.1 节的测度约定下，",[128,24272,24274,24299],{"className":24273,"translate":218},[217],[128,24275,24277],{"className":24276},[222],[224,24278,24279],{"xmlns":226},[228,24280,24281,24297],{},[231,24282,24283,24285,24287,24289,24291,24293,24295],{},[1795,24284,2760],{"mathvariant":2001},[1832,24286,5911],{},[1795,24288,5914],{"mathvariant":1981},[1832,24290,3278],{},[1832,24292,2477],{"stretchy":1837},[1795,24294,4835],{"mathvariant":4834},[1832,24296,2486],{"stretchy":1837},[238,24298,5925],{"encoding":240},[128,24300,24302,24320],{"className":24301,"ariaHidden":246},[245],[128,24303,24305,24308,24311,24314,24317],{"className":24304},[250],[128,24306],{"className":24307,"style":4439},[254],[128,24309,2760],{"className":24310},[259,2151],[128,24312],{"className":24313,"style":1878},[269],[128,24315,5911],{"className":24316},[1882],[128,24318],{"className":24319,"style":1878},[269],[128,24321,24323,24326,24332,24335,24344],{"className":24322},[250],[128,24324],{"className":24325,"style":1892},[254],[128,24327,24329],{"className":24328},[2268],[128,24330,5914],{"className":24331},[259,3353],[128,24333,2477],{"className":24334},[1896],[128,24336,24338],{"className":24337},[259],[128,24339,24341],{"className":24340},[259],[128,24342,4835],{"className":24343},[259,4895],[128,24345,2486],{"className":24346},[1928]," 的微分熵为\n",[128,24349,24351,24462],{"className":24350,"translate":218},[217],[128,24352,24354],{"className":24353},[222],[224,24355,24356],{"xmlns":226},[228,24357,24358,24459],{},[231,24359,24360,24363,24365,24367,24369,24371,24374,24376,24378,24380,24382,24384,24386,24388,24394,24396,24398,24400,24402,24405,24407,24413,24415,24417,24431,24433,24439,24441,24443,24445,24447,24449,24451,24457],{},[1795,24361,24362],{},"H",[1832,24364,2477],{"stretchy":1837},[1795,24366,2760],{"mathvariant":2001},[1832,24368,2486],{"stretchy":1837},[1832,24370,1994],{},[1795,24372,24373],{},"log",[1832,24375,3278],{},[1795,24377,5459],{},[1832,24379,2477],{"stretchy":1837},[1795,24381,4835],{"mathvariant":4834},[1832,24383,2486],{"stretchy":1837},[1832,24385,9486],{},[1832,24387,2477],{"stretchy":1837},[2016,24389,24390,24392],{},[1795,24391,4835],{},[1840,24393,2028],{},[1832,24395,1989],{},[1795,24397,1853],{},[1832,24399,2486],{"stretchy":1837},[234,24401,6528],{},[1795,24403,24404],{},"ψ",[1832,24406,2477],{"stretchy":1837},[2016,24408,24409,24411],{},[1795,24410,4835],{},[1840,24412,2028],{},[1832,24414,2486],{"stretchy":1837},[1832,24416,1989],{},[2038,24418,24419,24421,24429],{},[1832,24420,2042],{},[231,24422,24423,24425,24427],{},[1795,24424,2801],{},[1832,24426,1994],{},[1840,24428,1842],{},[1795,24430,1853],{},[1832,24432,2477],{"stretchy":1837},[2016,24434,24435,24437],{},[1795,24436,4835],{},[1795,24438,2801],{},[1832,24440,1989],{},[1840,24442,1842],{},[1832,24444,2486],{"stretchy":1837},[234,24446,6528],{},[1795,24448,24404],{},[1832,24450,2477],{"stretchy":1837},[2016,24452,24453,24455],{},[1795,24454,4835],{},[1795,24456,2801],{},[1832,24458,2486],{"stretchy":1837},[238,24460,24461],{"encoding":240},"H(\\mathbf{x}) = \\log B(\\boldsymbol{\\alpha}) + (\\alpha_0 - K)\\,\\psi(\\alpha_0) - \\sum_{i=1}^K (\\alpha_i - 1)\\,\\psi(\\alpha_i)",[128,24463,24465,24493,24536,24594,24667,24785],{"className":24464,"ariaHidden":246},[245],[128,24466,24468,24471,24475,24478,24481,24484,24487,24490],{"className":24467},[250],[128,24469],{"className":24470,"style":1892},[254],[128,24472,24362],{"className":24473,"style":24474},[259,1873],"margin-right:0.0813em;",[128,24476,2477],{"className":24477},[1896],[128,24479,2760],{"className":24480},[259,2151],[128,24482,2486],{"className":24483},[1928],[128,24485],{"className":24486,"style":1878},[269],[128,24488,1994],{"className":24489},[1882],[128,24491],{"className":24492,"style":1878},[269],[128,24494,24496,24499,24506,24509,24512,24515,24524,24527,24530,24533],{"className":24495},[250],[128,24497],{"className":24498,"style":1892},[254],[128,24500,24502,24503],{"className":24501},[2268],"lo",[128,24504,24505],{"style":17336},"g",[128,24507],{"className":24508,"style":1907},[269],[128,24510,5459],{"className":24511,"style":5599},[259,1873],[128,24513,2477],{"className":24514},[1896],[128,24516,24518],{"className":24517},[259],[128,24519,24521],{"className":24520},[259],[128,24522,4835],{"className":24523},[259,4895],[128,24525,2486],{"className":24526},[1928],[128,24528],{"className":24529,"style":2508},[269],[128,24531,9486],{"className":24532},[2115],[128,24534],{"className":24535,"style":2508},[269],[128,24537,24539,24542,24545,24585,24588,24591],{"className":24538},[250],[128,24540],{"className":24541,"style":1892},[254],[128,24543,2477],{"className":24544},[1896],[128,24546,24548,24551],{"className":24547},[259],[128,24549,4835],{"className":24550,"style":4920},[259,1873],[128,24552,24554],{"className":24553},[2087],[128,24555,24557,24577],{"className":24556},[274,321],[128,24558,24560,24574],{"className":24559},[278],[128,24561,24563],{"className":24562,"style":2945},[282],[128,24564,24565,24568],{"style":4935},[128,24566],{"className":24567,"style":291},[290],[128,24569,24571],{"className":24570},[299,300,301,298],[128,24572,2028],{"className":24573},[259,298],[128,24575,347],{"className":24576},[346],[128,24578,24580],{"className":24579},[278],[128,24581,24583],{"className":24582,"style":2241},[282],[128,24584],{},[128,24586],{"className":24587,"style":2508},[269],[128,24589,1989],{"className":24590},[2115],[128,24592],{"className":24593,"style":2508},[269],[128,24595,24597,24600,24603,24606,24609,24612,24615,24655,24658,24661,24664],{"className":24596},[250],[128,24598],{"className":24599,"style":1892},[254],[128,24601,1853],{"className":24602,"style":1924},[259,1873],[128,24604,2486],{"className":24605},[1928],[128,24607],{"className":24608,"style":1907},[269],[128,24610,24404],{"className":24611,"style":1874},[259,1873],[128,24613,2477],{"className":24614},[1896],[128,24616,24618,24621],{"className":24617},[259],[128,24619,4835],{"className":24620,"style":4920},[259,1873],[128,24622,24624],{"className":24623},[2087],[128,24625,24627,24647],{"className":24626},[274,321],[128,24628,24630,24644],{"className":24629},[278],[128,24631,24633],{"className":24632,"style":2945},[282],[128,24634,24635,24638],{"style":4935},[128,24636],{"className":24637,"style":291},[290],[128,24639,24641],{"className":24640},[299,300,301,298],[128,24642,2028],{"className":24643},[259,298],[128,24645,347],{"className":24646},[346],[128,24648,24650],{"className":24649},[278],[128,24651,24653],{"className":24652,"style":2241},[282],[128,24654],{},[128,24656,2486],{"className":24657},[1928],[128,24659],{"className":24660,"style":2508},[269],[128,24662,1989],{"className":24663},[2115],[128,24665],{"className":24666,"style":2508},[269],[128,24668,24670,24673,24733,24736,24776,24779,24782],{"className":24669},[250],[128,24671],{"className":24672,"style":5200},[254],[128,24674,24676,24679],{"className":24675},[2268],[128,24677,2042],{"className":24678,"style":2274},[2268,2272,2273],[128,24680,24682],{"className":24681},[2087],[128,24683,24685,24725],{"className":24684},[274,321],[128,24686,24688,24722],{"className":24687},[278],[128,24689,24691,24711],{"className":24690,"style":2287},[282],[128,24692,24693,24696],{"style":2290},[128,24694],{"className":24695,"style":291},[290],[128,24697,24699],{"className":24698},[299,300,301,298],[128,24700,24702,24705,24708],{"className":24701},[259,298],[128,24703,2801],{"className":24704},[259,1873,298],[128,24706,1994],{"className":24707},[1882,298],[128,24709,1842],{"className":24710},[259,298],[128,24712,24713,24716],{"style":2311},[128,24714],{"className":24715,"style":291},[290],[128,24717,24719],{"className":24718},[299,300,301,298],[128,24720,1853],{"className":24721,"style":1924},[259,1873,298],[128,24723,347],{"className":24724},[346],[128,24726,24728],{"className":24727},[278],[128,24729,24731],{"className":24730,"style":2330},[282],[128,24732],{},[128,24734,2477],{"className":24735},[1896],[128,24737,24739,24742],{"className":24738},[259],[128,24740,4835],{"className":24741,"style":4920},[259,1873],[128,24743,24745],{"className":24744},[2087],[128,24746,24748,24768],{"className":24747},[274,321],[128,24749,24751,24765],{"className":24750},[278],[128,24752,24754],{"className":24753,"style":3095},[282],[128,24755,24756,24759],{"style":4935},[128,24757],{"className":24758,"style":291},[290],[128,24760,24762],{"className":24761},[299,300,301,298],[128,24763,2801],{"className":24764},[259,1873,298],[128,24766,347],{"className":24767},[346],[128,24769,24771],{"className":24770},[278],[128,24772,24774],{"className":24773,"style":2241},[282],[128,24775],{},[128,24777],{"className":24778,"style":2508},[269],[128,24780,1989],{"className":24781},[2115],[128,24783],{"className":24784,"style":2508},[269],[128,24786,24788,24791,24794,24797,24800,24803,24806,24846],{"className":24787},[250],[128,24789],{"className":24790,"style":1892},[254],[128,24792,1842],{"className":24793},[259],[128,24795,2486],{"className":24796},[1928],[128,24798],{"className":24799,"style":1907},[269],[128,24801,24404],{"className":24802,"style":1874},[259,1873],[128,24804,2477],{"className":24805},[1896],[128,24807,24809,24812],{"className":24808},[259],[128,24810,4835],{"className":24811,"style":4920},[259,1873],[128,24813,24815],{"className":24814},[2087],[128,24816,24818,24838],{"className":24817},[274,321],[128,24819,24821,24835],{"className":24820},[278],[128,24822,24824],{"className":24823,"style":3095},[282],[128,24825,24826,24829],{"style":4935},[128,24827],{"className":24828,"style":291},[290],[128,24830,24832],{"className":24831},[299,300,301,298],[128,24833,2801],{"className":24834},[259,1873,298],[128,24836,347],{"className":24837},[346],[128,24839,24841],{"className":24840},[278],[128,24842,24844],{"className":24843,"style":2241},[282],[128,24845],{},[128,24847,2486],{"className":24848},[1928],"\n其中 ",[128,24851,24853,24881],{"className":24852,"translate":218},[217],[128,24854,24856],{"className":24855},[222],[224,24857,24858],{"xmlns":226},[228,24859,24860,24878],{},[231,24861,24862,24864,24866,24874,24876],{},[1795,24863,24404],{},[1832,24865,1994],{},[1977,24867,24868,24870],{},[1795,24869,6020],{"mathvariant":1981},[1832,24871,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},"0em","′",[1795,24875,4751],{"mathvariant":1981},[1795,24877,6020],{"mathvariant":1981},[238,24879,24880],{"encoding":240},"\\psi = \\Gamma'\u002F\\Gamma",[128,24882,24884,24902],{"className":24883,"ariaHidden":246},[245],[128,24885,24887,24890,24893,24896,24899],{"className":24886},[250],[128,24888],{"className":24889,"style":16030},[254],[128,24891,24404],{"className":24892,"style":1874},[259,1873],[128,24894],{"className":24895,"style":1878},[269],[128,24897,1994],{"className":24898},[1882],[128,24900],{"className":24901,"style":1878},[269],[128,24903,24905,24909,24942],{"className":24904},[250],[128,24906],{"className":24907,"style":24908},[254],"height:1.0019em;vertical-align:-0.25em;",[128,24910,24912,24915],{"className":24911},[259],[128,24913,6020],{"className":24914},[259],[128,24916,24918],{"className":24917},[2087],[128,24919,24921],{"className":24920},[274],[128,24922,24924],{"className":24923},[278],[128,24925,24928],{"className":24926,"style":24927},[282],"height:0.7519em;",[128,24929,24930,24933],{"style":2452},[128,24931],{"className":24932,"style":291},[290],[128,24934,24936],{"className":24935},[299,300,301,298],[128,24937,24939],{"className":24938},[259,298],[128,24940,24873],{"className":24941},[259,298],[128,24943,12673],{"className":24944},[259]," 为 digamma 函数。",[11,24947,24948,24950,24951,25039,25040,11072,25346,25599,25600,25670],{},[35,24949,6849],{}," 直接计算 ",[128,24952,24954,24982],{"className":24953,"translate":218},[217],[128,24955,24957],{"className":24956},[222],[224,24958,24959],{"xmlns":226},[228,24960,24961,24979],{},[231,24962,24963,24965,24967,24969,24971,24973,24975,24977],{},[1795,24964,24362],{},[1832,24966,1994],{},[1832,24968,1989],{},[1832,24970,6481],{},[1795,24972,5436],{},[1795,24974,24373],{},[1832,24976,3278],{},[1795,24978,5436],{},[238,24980,24981],{"encoding":240},"H = -\\int f \\log f",[128,24983,24985,25003],{"className":24984,"ariaHidden":246},[245],[128,24986,24988,24991,24994,24997,25000],{"className":24987},[250],[128,24989],{"className":24990,"style":283},[254],[128,24992,24362],{"className":24993,"style":24474},[259,1873],[128,24995],{"className":24996,"style":1878},[269],[128,24998,1994],{"className":24999},[1882],[128,25001],{"className":25002,"style":1878},[269],[128,25004,25006,25010,25013,25016,25019,25022,25025,25028,25033,25036],{"className":25005},[250],[128,25007],{"className":25008,"style":25009},[254],"height:1.1111em;vertical-align:-0.3061em;",[128,25011,1989],{"className":25012},[259],[128,25014],{"className":25015,"style":1907},[269],[128,25017,6481],{"className":25018,"style":6562},[2268,2272,2273],[128,25020],{"className":25021,"style":1907},[269],[128,25023,5436],{"className":25024,"style":5514},[259,1873],[128,25026],{"className":25027,"style":1907},[269],[128,25029,24502,25031],{"className":25030},[2268],[128,25032,24505],{"style":17336},[128,25034],{"className":25035,"style":1907},[269],[128,25037,5436],{"className":25038,"style":5514},[259,1873],"，代入 ",[128,25041,25043,25109],{"className":25042,"translate":218},[217],[128,25044,25046],{"className":25045},[222],[224,25047,25048],{"xmlns":226},[228,25049,25050,25106],{},[231,25051,25052,25054,25056,25058,25060,25062,25064,25066,25068,25070,25072,25074,25076,25082,25084,25090,25092,25094,25096,25098,25100],{},[1832,25053,1989],{},[1795,25055,24373],{},[1832,25057,3278],{},[1795,25059,5436],{},[1832,25061,1994],{},[1795,25063,24373],{},[1832,25065,3278],{},[1795,25067,5459],{},[1832,25069,2477],{"stretchy":1837},[1795,25071,4835],{"mathvariant":4834},[1832,25073,2486],{"stretchy":1837},[1832,25075,1989],{},[2016,25077,25078,25080],{},[1832,25079,2042],{},[1795,25081,2801],{},[1832,25083,2477],{"stretchy":1837},[2016,25085,25086,25088],{},[1795,25087,4835],{},[1795,25089,2801],{},[1832,25091,1989],{},[1840,25093,1842],{},[1832,25095,2486],{"stretchy":1837},[1795,25097,24373],{},[1832,25099,3278],{},[2016,25101,25102,25104],{},[1795,25103,2760],{},[1795,25105,2801],{},[238,25107,25108],{"encoding":240},"-\\log f = \\log B(\\boldsymbol{\\alpha}) - \\sum_i (\\alpha_i - 1)\\log x_i",[128,25110,25112,25144,25185,25283],{"className":25111,"ariaHidden":246},[245],[128,25113,25115,25118,25121,25124,25129,25132,25135,25138,25141],{"className":25114},[250],[128,25116],{"className":25117,"style":16030},[254],[128,25119,1989],{"className":25120},[259],[128,25122],{"className":25123,"style":1907},[269],[128,25125,24502,25127],{"className":25126},[2268],[128,25128,24505],{"style":17336},[128,25130],{"className":25131,"style":1907},[269],[128,25133,5436],{"className":25134,"style":5514},[259,1873],[128,25136],{"className":25137,"style":1878},[269],[128,25139,1994],{"className":25140},[1882],[128,25142],{"className":25143,"style":1878},[269],[128,25145,25147,25150,25155,25158,25161,25164,25173,25176,25179,25182],{"className":25146},[250],[128,25148],{"className":25149,"style":1892},[254],[128,25151,24502,25153],{"className":25152},[2268],[128,25154,24505],{"style":17336},[128,25156],{"className":25157,"style":1907},[269],[128,25159,5459],{"className":25160,"style":5599},[259,1873],[128,25162,2477],{"className":25163},[1896],[128,25165,25167],{"className":25166},[259],[128,25168,25170],{"className":25169},[259],[128,25171,4835],{"className":25172},[259,4895],[128,25174,2486],{"className":25175},[1928],[128,25177],{"className":25178,"style":2508},[269],[128,25180,1989],{"className":25181},[2115],[128,25183],{"className":25184,"style":2508},[269],[128,25186,25188,25191,25231,25234,25274,25277,25280],{"className":25187},[250],[128,25189],{"className":25190,"style":7777},[254],[128,25192,25194,25197],{"className":25193},[2268],[128,25195,2042],{"className":25196,"style":2274},[2268,2272,2273],[128,25198,25200],{"className":25199},[2087],[128,25201,25203,25223],{"className":25202},[274,321],[128,25204,25206,25220],{"className":25205},[278],[128,25207,25209],{"className":25208,"style":7796},[282],[128,25210,25211,25214],{"style":2290},[128,25212],{"className":25213,"style":291},[290],[128,25215,25217],{"className":25216},[299,300,301,298],[128,25218,2801],{"className":25219},[259,1873,298],[128,25221,347],{"className":25222},[346],[128,25224,25226],{"className":25225},[278],[128,25227,25229],{"className":25228,"style":2330},[282],[128,25230],{},[128,25232,2477],{"className":25233},[1896],[128,25235,25237,25240],{"className":25236},[259],[128,25238,4835],{"className":25239,"style":4920},[259,1873],[128,25241,25243],{"className":25242},[2087],[128,25244,25246,25266],{"className":25245},[274,321],[128,25247,25249,25263],{"className":25248},[278],[128,25250,25252],{"className":25251,"style":3095},[282],[128,25253,25254,25257],{"style":4935},[128,25255],{"className":25256,"style":291},[290],[128,25258,25260],{"className":25259},[299,300,301,298],[128,25261,2801],{"className":25262},[259,1873,298],[128,25264,347],{"className":25265},[346],[128,25267,25269],{"className":25268},[278],[128,25270,25272],{"className":25271,"style":2241},[282],[128,25273],{},[128,25275],{"className":25276,"style":2508},[269],[128,25278,1989],{"className":25279},[2115],[128,25281],{"className":25282,"style":2508},[269],[128,25284,25286,25289,25292,25295,25298,25303,25306],{"className":25285},[250],[128,25287],{"className":25288,"style":1892},[254],[128,25290,1842],{"className":25291},[259],[128,25293,2486],{"className":25294},[1928],[128,25296],{"className":25297,"style":1907},[269],[128,25299,24502,25301],{"className":25300},[2268],[128,25302,24505],{"style":17336},[128,25304],{"className":25305,"style":1907},[269],[128,25307,25309,25312],{"className":25308},[259],[128,25310,2760],{"className":25311},[259,1873],[128,25313,25315],{"className":25314},[2087],[128,25316,25318,25338],{"className":25317},[274,321],[128,25319,25321,25335],{"className":25320},[278],[128,25322,25324],{"className":25323,"style":3095},[282],[128,25325,25326,25329],{"style":2221},[128,25327],{"className":25328,"style":291},[290],[128,25330,25332],{"className":25331},[299,300,301,298],[128,25333,2801],{"className":25334},[259,1873,298],[128,25336,347],{"className":25337},[346],[128,25339,25341],{"className":25340},[278],[128,25342,25344],{"className":25343,"style":2241},[282],[128,25345],{},[128,25347,25349,25405],{"className":25348,"translate":218},[217],[128,25350,25352],{"className":25351},[222],[224,25353,25354],{"xmlns":226},[228,25355,25356,25402],{},[231,25357,25358,25360,25362,25364,25366,25372,25374,25376,25378,25380,25386,25388,25390,25392,25394,25400],{},[1795,25359,342],{"mathvariant":2008},[1832,25361,16538],{"stretchy":1837},[1795,25363,24373],{},[1832,25365,3278],{},[2016,25367,25368,25370],{},[1795,25369,2760],{},[1795,25371,2801],{},[1832,25373,16547],{"stretchy":1837},[1832,25375,1994],{},[1795,25377,24404],{},[1832,25379,2477],{"stretchy":1837},[2016,25381,25382,25384],{},[1795,25383,4835],{},[1795,25385,2801],{},[1832,25387,2486],{"stretchy":1837},[1832,25389,1989],{},[1795,25391,24404],{},[1832,25393,2477],{"stretchy":1837},[2016,25395,25396,25398],{},[1795,25397,4835],{},[1840,25399,2028],{},[1832,25401,2486],{"stretchy":1837},[238,25403,25404],{"encoding":240},"\\mathbb{E}[\\log x_i] = \\psi(\\alpha_i) - \\psi(\\alpha_0)",[128,25406,25408,25480,25544],{"className":25407,"ariaHidden":246},[245],[128,25409,25411,25414,25417,25420,25425,25428,25468,25471,25474,25477],{"className":25410},[250],[128,25412],{"className":25413,"style":1892},[254],[128,25415,342],{"className":25416},[259,2167],[128,25418,16538],{"className":25419},[1896],[128,25421,24502,25423],{"className":25422},[2268],[128,25424,24505],{"style":17336},[128,25426],{"className":25427,"style":1907},[269],[128,25429,25431,25434],{"className":25430},[259],[128,25432,2760],{"className":25433},[259,1873],[128,25435,25437],{"className":25436},[2087],[128,25438,25440,25460],{"className":25439},[274,321],[128,25441,25443,25457],{"className":25442},[278],[128,25444,25446],{"className":25445,"style":3095},[282],[128,25447,25448,25451],{"style":2221},[128,25449],{"className":25450,"style":291},[290],[128,25452,25454],{"className":25453},[299,300,301,298],[128,25455,2801],{"className":25456},[259,1873,298],[128,25458,347],{"className":25459},[346],[128,25461,25463],{"className":25462},[278],[128,25464,25466],{"className":25465,"style":2241},[282],[128,25467],{},[128,25469,16547],{"className":25470},[1928],[128,25472],{"className":25473,"style":1878},[269],[128,25475,1994],{"className":25476},[1882],[128,25478],{"className":25479,"style":1878},[269],[128,25481,25483,25486,25489,25492,25532,25535,25538,25541],{"className":25482},[250],[128,25484],{"className":25485,"style":1892},[254],[128,25487,24404],{"className":25488,"style":1874},[259,1873],[128,25490,2477],{"className":25491},[1896],[128,25493,25495,25498],{"className":25494},[259],[128,25496,4835],{"className":25497,"style":4920},[259,1873],[128,25499,25501],{"className":25500},[2087],[128,25502,25504,25524],{"className":25503},[274,321],[128,25505,25507,25521],{"className":25506},[278],[128,25508,25510],{"className":25509,"style":3095},[282],[128,25511,25512,25515],{"style":4935},[128,25513],{"className":25514,"style":291},[290],[128,25516,25518],{"className":25517},[299,300,301,298],[128,25519,2801],{"className":25520},[259,1873,298],[128,25522,347],{"className":25523},[346],[128,25525,25527],{"className":25526},[278],[128,25528,25530],{"className":25529,"style":2241},[282],[128,25531],{},[128,25533,2486],{"className":25534},[1928],[128,25536],{"className":25537,"style":2508},[269],[128,25539,1989],{"className":25540},[2115],[128,25542],{"className":25543,"style":2508},[269],[128,25545,25547,25550,25553,25556,25596],{"className":25546},[250],[128,25548],{"className":25549,"style":1892},[254],[128,25551,24404],{"className":25552,"style":1874},[259,1873],[128,25554,2477],{"className":25555},[1896],[128,25557,25559,25562],{"className":25558},[259],[128,25560,4835],{"className":25561,"style":4920},[259,1873],[128,25563,25565],{"className":25564},[2087],[128,25566,25568,25588],{"className":25567},[274,321],[128,25569,25571,25585],{"className":25570},[278],[128,25572,25574],{"className":25573,"style":2945},[282],[128,25575,25576,25579],{"style":4935},[128,25577],{"className":25578,"style":291},[290],[128,25580,25582],{"className":25581},[299,300,301,298],[128,25583,2028],{"className":25584},[259,298],[128,25586,347],{"className":25587},[346],[128,25589,25591],{"className":25590},[278],[128,25592,25594],{"className":25593,"style":2241},[282],[128,25595],{},[128,25597,2486],{"className":25598},[1928],"（由命题 1.3 的矩恒等式对 ",[128,25601,25603,25621],{"className":25602,"translate":218},[217],[128,25604,25606],{"className":25605},[222],[224,25607,25608],{"xmlns":226},[228,25609,25610,25618],{},[231,25611,25612],{},[2016,25613,25614,25616],{},[1795,25615,18848],{},[1795,25617,2801],{},[238,25619,25620],{"encoding":240},"\\beta_i",[128,25622,25624],{"className":25623,"ariaHidden":246},[245],[128,25625,25627,25630],{"className":25626},[250],[128,25628],{"className":25629,"style":16030},[254],[128,25631,25633,25636],{"className":25632},[259],[128,25634,18848],{"className":25635,"style":18987},[259,1873],[128,25637,25639],{"className":25638},[2087],[128,25640,25642,25662],{"className":25641},[274,321],[128,25643,25645,25659],{"className":25644},[278],[128,25646,25648],{"className":25647,"style":3095},[282],[128,25649,25650,25653],{"style":19171},[128,25651],{"className":25652,"style":291},[290],[128,25654,25656],{"className":25655},[299,300,301,298],[128,25657,2801],{"className":25658},[259,1873,298],[128,25660,347],{"className":25661},[346],[128,25663,25665],{"className":25664},[278],[128,25666,25668],{"className":25667,"style":2241},[282],[128,25669],{}," 求导得到），整理即得。",[11,25672,25673,25674,25736,25737,23604,25765,25816,25817,25954,25955,26047,26048,26098,26099,26102,26103,26176],{},"在对称情形 ",[128,25675,25677,25697],{"className":25676,"translate":218},[217],[128,25678,25680],{"className":25679},[222],[224,25681,25682],{"xmlns":226},[228,25683,25684,25694],{},[231,25685,25686,25688,25690,25692],{},[1795,25687,4835],{"mathvariant":4834},[1832,25689,1994],{},[1795,25691,4835],{},[1840,25693,1842],{"mathvariant":2001},[238,25695,25696],{"encoding":240},"\\boldsymbol{\\alpha} = \\alpha \\mathbf{1}",[128,25698,25700,25724],{"className":25699,"ariaHidden":246},[245],[128,25701,25703,25706,25715,25718,25721],{"className":25702},[250],[128,25704],{"className":25705,"style":4439},[254],[128,25707,25709],{"className":25708},[259],[128,25710,25712],{"className":25711},[259],[128,25713,4835],{"className":25714},[259,4895],[128,25716],{"className":25717,"style":1878},[269],[128,25719,1994],{"className":25720},[1882],[128,25722],{"className":25723,"style":1878},[269],[128,25725,25727,25730,25733],{"className":25726},[250],[128,25728],{"className":25729,"style":2594},[254],[128,25731,4835],{"className":25732,"style":4920},[259,1873],[128,25734,1842],{"className":25735},[259,2151]," 下，",[128,25738,25740,25753],{"className":25739,"translate":218},[217],[128,25741,25743],{"className":25742},[222],[224,25744,25745],{"xmlns":226},[228,25746,25747,25751],{},[231,25748,25749],{},[1795,25750,24362],{},[238,25752,24362],{"encoding":240},[128,25754,25756],{"className":25755,"ariaHidden":246},[245],[128,25757,25759,25762],{"className":25758},[250],[128,25760],{"className":25761,"style":283},[254],[128,25763,24362],{"className":25764,"style":24474},[259,1873],[128,25766,25768,25786],{"className":25767,"translate":218},[217],[128,25769,25771],{"className":25770},[222],[224,25772,25773],{"xmlns":226},[228,25774,25775,25783],{},[231,25776,25777,25779,25781],{},[1795,25778,4835],{},[1832,25780,1994],{},[1840,25782,1842],{},[238,25784,25785],{"encoding":240},"\\alpha = 1",[128,25787,25789,25807],{"className":25788,"ariaHidden":246},[245],[128,25790,25792,25795,25798,25801,25804],{"className":25791},[250],[128,25793],{"className":25794,"style":7758},[254],[128,25796,4835],{"className":25797,"style":4920},[259,1873],[128,25799],{"className":25800,"style":1878},[269],[128,25802,1994],{"className":25803},[1882],[128,25805],{"className":25806,"style":1878},[269],[128,25808,25810,25813],{"className":25809},[250],[128,25811],{"className":25812,"style":2594},[254],[128,25814,1842],{"className":25815},[259]," 处取最大值 ",[128,25818,25820,25866],{"className":25819,"translate":218},[217],[128,25821,25823],{"className":25822},[222],[224,25824,25825],{"xmlns":226},[228,25826,25827,25863],{},[231,25828,25829,25831,25833,25835,25837,25839,25841,25843,25845,25847,25849,25851,25853,25855,25857,25859,25861],{},[1832,25830,1989],{},[1795,25832,24373],{},[1832,25834,3278],{},[1795,25836,6020],{"mathvariant":1981},[1832,25838,2477],{"stretchy":1837},[1795,25840,1853],{},[1832,25842,2486],{"stretchy":1837},[1832,25844,1994],{},[1832,25846,1989],{},[1795,25848,24373],{},[1832,25850,3278],{},[1832,25852,2477],{"stretchy":1837},[1795,25854,1853],{},[1832,25856,1989],{},[1840,25858,1842],{},[1832,25860,2486],{"stretchy":1837},[1832,25862,4764],{"stretchy":1837},[238,25864,25865],{"encoding":240},"-\\log \\Gamma(K) = -\\log (K-1)!",[128,25867,25869,25910,25942],{"className":25868,"ariaHidden":246},[245],[128,25870,25872,25875,25878,25881,25886,25889,25892,25895,25898,25901,25904,25907],{"className":25871},[250],[128,25873],{"className":25874,"style":1892},[254],[128,25876,1989],{"className":25877},[259],[128,25879],{"className":25880,"style":1907},[269],[128,25882,24502,25884],{"className":25883},[2268],[128,25885,24505],{"style":17336},[128,25887],{"className":25888,"style":1907},[269],[128,25890,6020],{"className":25891},[259],[128,25893,2477],{"className":25894},[1896],[128,25896,1853],{"className":25897,"style":1924},[259,1873],[128,25899,2486],{"className":25900},[1928],[128,25902],{"className":25903,"style":1878},[269],[128,25905,1994],{"className":25906},[1882],[128,25908],{"className":25909,"style":1878},[269],[128,25911,25913,25916,25919,25922,25927,25930,25933,25936,25939],{"className":25912},[250],[128,25914],{"className":25915,"style":1892},[254],[128,25917,1989],{"className":25918},[259],[128,25920],{"className":25921,"style":1907},[269],[128,25923,24502,25925],{"className":25924},[2268],[128,25926,24505],{"style":17336},[128,25928,2477],{"className":25929},[1896],[128,25931,1853],{"className":25932,"style":1924},[259,1873],[128,25934],{"className":25935,"style":2508},[269],[128,25937,1989],{"className":25938},[2115],[128,25940],{"className":25941,"style":2508},[269],[128,25943,25945,25948,25951],{"className":25944},[250],[128,25946],{"className":25947,"style":1892},[254],[128,25949,1842],{"className":25950},[259],[128,25952,4808],{"className":25953},[1928],"。该值为负，并不矛盾：它是相对于体积为 ",[128,25956,25958,25990],{"className":25957,"translate":218},[217],[128,25959,25961],{"className":25960},[222],[224,25962,25963],{"xmlns":226},[228,25964,25965,25987],{},[231,25966,25967,25969,25971,25973,25975,25977,25979,25981,25983,25985],{},[1840,25968,1842],{},[1795,25970,4751],{"mathvariant":1981},[1832,25972,2477],{"stretchy":1837},[1795,25974,1853],{},[1832,25976,1989],{},[1840,25978,1842],{},[1832,25980,2486],{"stretchy":1837},[1832,25982,4764],{"stretchy":1837},[1832,25984,4221],{},[1840,25986,1842],{},[238,25988,25989],{"encoding":240},"1\u002F(K-1)! \u003C 1",[128,25991,25993,26017,26038],{"className":25992,"ariaHidden":246},[245],[128,25994,25996,25999,26002,26005,26008,26011,26014],{"className":25995},[250],[128,25997],{"className":25998,"style":1892},[254],[128,26000,4780],{"className":26001},[259],[128,26003,2477],{"className":26004},[1896],[128,26006,1853],{"className":26007,"style":1924},[259,1873],[128,26009],{"className":26010,"style":2508},[269],[128,26012,1989],{"className":26013},[2115],[128,26015],{"className":26016,"style":2508},[269],[128,26018,26020,26023,26026,26029,26032,26035],{"className":26019},[250],[128,26021],{"className":26022,"style":1892},[254],[128,26024,1842],{"className":26025},[259],[128,26027,4808],{"className":26028},[1928],[128,26030],{"className":26031,"style":1878},[269],[128,26033,4221],{"className":26034},[1882],[128,26036],{"className":26037,"style":1878},[269],[128,26039,26041,26044],{"className":26040},[250],[128,26042],{"className":26043,"style":2594},[254],[128,26045,1842],{"className":26046},[259]," 的支撑集而言的。",[128,26049,26051,26068],{"className":26050,"translate":218},[217],[128,26052,26054],{"className":26053},[222],[224,26055,26056],{"xmlns":226},[228,26057,26058,26066],{},[231,26059,26060,26062,26064],{},[1795,26061,4835],{},[1832,26063,1994],{},[1840,26065,1842],{},[238,26067,25785],{"encoding":240},[128,26069,26071,26089],{"className":26070,"ariaHidden":246},[245],[128,26072,26074,26077,26080,26083,26086],{"className":26073},[250],[128,26075],{"className":26076,"style":7758},[254],[128,26078,4835],{"className":26079,"style":4920},[259,1873],[128,26081],{"className":26082,"style":1878},[269],[128,26084,1994],{"className":26085},[1882],[128,26087],{"className":26088,"style":1878},[269],[128,26090,26092,26095],{"className":26091},[250],[128,26093],{"className":26094,"style":2594},[254],[128,26096,1842],{"className":26097},[259]," 对应单纯形上的",[35,26100,26101],{},"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 ",[128,26104,26106,26129],{"className":26105,"translate":218},[217],[128,26107,26109],{"className":26108},[222],[224,26110,26111],{"xmlns":226},[228,26112,26113,26127],{},[231,26114,26115],{},[1977,26116,26117,26119],{},[1795,26118,1982],{"mathvariant":1981},[231,26120,26121,26123,26125],{},[1795,26122,1853],{},[1832,26124,1989],{},[1840,26126,1842],{},[238,26128,3589],{"encoding":240},[128,26130,26132],{"className":26131,"ariaHidden":246},[245],[128,26133,26135,26138],{"className":26134},[250],[128,26136],{"className":26137,"style":2431},[254],[128,26139,26141,26144],{"className":26140},[259],[128,26142,1982],{"className":26143},[259],[128,26145,26147],{"className":26146},[2087],[128,26148,26150],{"className":26149},[274],[128,26151,26153],{"className":26152},[278],[128,26154,26156],{"className":26155,"style":2431},[282],[128,26157,26158,26161],{"style":2452},[128,26159],{"className":26160,"style":291},[290],[128,26162,26164],{"className":26163},[299,300,301,298],[128,26165,26167,26170,26173],{"className":26166},[259,298],[128,26168,1853],{"className":26169,"style":1924},[259,1873,298],[128,26171,1989],{"className":26172},[2115,298],[128,26174,1842],{"className":26175},[259,298]," 紧且测度有限，均匀分布是最大熵分布，故",[128,26178,26180],{"className":26179,"translate":218},[1962],[128,26181,26183,26240],{"className":26182,"translate":218},[217],[128,26184,26186],{"className":26185},[222],[224,26187,26188],{"xmlns":226,"display":1971},[228,26189,26190,26237],{},[231,26191,26192,26194,26196,26198,26200,26202,26204,26206,26208,26210,26212,26214,26216,26218,26220,26223,26226,26229,26231,26233,26235],{},[1795,26193,24362],{},[1832,26195,2477],{"stretchy":1837},[1795,26197,2760],{"mathvariant":2001},[1832,26199,2486],{"stretchy":1837},[1832,26201,23023],{},[1832,26203,1989],{},[1795,26205,24373],{},[1832,26207,3278],{},[1795,26209,6020],{"mathvariant":1981},[1832,26211,2477],{"stretchy":1837},[1795,26213,1853],{},[1832,26215,2486],{"stretchy":1837},[1832,26217,1845],{"separator":246},[269,26219],{"width":11568},[234,26221,26222],{},"等号成立",[234,26224,26225],{},"  ",[1832,26227,26228],{},"⟺",[234,26230,26225],{},[1795,26232,4835],{"mathvariant":4834},[1832,26234,1994],{},[1840,26236,1842],{"mathvariant":2001},[238,26238,26239],{"encoding":240},"H(\\mathbf{x}) \\le -\\log \\Gamma(K), \\qquad \\text{等号成立} \\iff \\boldsymbol{\\alpha} = \\mathbf{1}",[128,26241,26243,26270,26332,26356],{"className":26242,"ariaHidden":246},[245],[128,26244,26246,26249,26252,26255,26258,26261,26264,26267],{"className":26245},[250],[128,26247],{"className":26248,"style":1892},[254],[128,26250,24362],{"className":26251,"style":24474},[259,1873],[128,26253,2477],{"className":26254},[1896],[128,26256,2760],{"className":26257},[259,2151],[128,26259,2486],{"className":26260},[1928],[128,26262],{"className":26263,"style":1878},[269],[128,26265,23023],{"className":26266},[1882],[128,26268],{"className":26269,"style":1878},[269],[128,26271,26273,26276,26279,26282,26287,26290,26293,26296,26299,26302,26305,26308,26311,26317,26320,26323,26326,26329],{"className":26272},[250],[128,26274],{"className":26275,"style":1892},[254],[128,26277,1989],{"className":26278},[259],[128,26280],{"className":26281,"style":1907},[269],[128,26283,24502,26285],{"className":26284},[2268],[128,26286,24505],{"style":17336},[128,26288],{"className":26289,"style":1907},[269],[128,26291,6020],{"className":26292},[259],[128,26294,2477],{"className":26295},[1896],[128,26297,1853],{"className":26298,"style":1924},[259,1873],[128,26300,2486],{"className":26301},[1928],[128,26303,1845],{"className":26304},[1903],[128,26306],{"className":26307,"style":11756},[269],[128,26309],{"className":26310,"style":1907},[269],[128,26312,26314],{"className":26313},[259,260],[128,26315,26222],{"className":26316},[259,15272],[128,26318],{"className":26319,"style":1878},[269],[128,26321],{"className":26322,"style":1878},[269],[128,26324,26228],{"className":26325},[1882],[128,26327],{"className":26328,"style":1878},[269],[128,26330],{"className":26331,"style":1878},[269],[128,26333,26335,26338,26347,26350,26353],{"className":26334},[250],[128,26336],{"className":26337,"style":4439},[254],[128,26339,26341],{"className":26340},[259],[128,26342,26344],{"className":26343},[259],[128,26345,4835],{"className":26346},[259,4895],[128,26348],{"className":26349,"style":1878},[269],[128,26351,1994],{"className":26352},[1882],[128,26354],{"className":26355,"style":1878},[269],[128,26357,26359,26362],{"className":26358},[250],[128,26360],{"className":26361,"style":2594},[254],[128,26363,1842],{"className":26364},[259,2151],[2610,26366,26368],{"id":26367},"_24-共轭性与贝叶斯更新","2.4 共轭性与贝叶斯更新",[2615,26370,26372],{"title":26371},"命题 2.5（Dirichlet–Multinomial 共轭）",[11,26373,26374,26375,26460,26461,26496,26497,21562,26669,2674,26763,26905,26906],{},"设先验 ",[128,26376,26378,26405],{"className":26377,"translate":218},[217],[128,26379,26381],{"className":26380},[222],[224,26382,26383],{"xmlns":226},[228,26384,26385,26402],{},[231,26386,26387,26390,26392,26394,26396,26398,26400],{},[1795,26388,26389],{"mathvariant":4834},"π",[1832,26391,5911],{},[1795,26393,5914],{"mathvariant":1981},[1832,26395,3278],{},[1832,26397,2477],{"stretchy":1837},[1795,26399,4835],{"mathvariant":4834},[1832,26401,2486],{"stretchy":1837},[238,26403,26404],{"encoding":240},"\\boldsymbol{\\pi} \\sim \\operatorname{Dir}(\\boldsymbol{\\alpha})",[128,26406,26408,26433],{"className":26407,"ariaHidden":246},[245],[128,26409,26411,26414,26424,26427,26430],{"className":26410},[250],[128,26412],{"className":26413,"style":4439},[254],[128,26415,26417],{"className":26416},[259],[128,26418,26420],{"className":26419},[259],[128,26421,26389],{"className":26422,"style":26423},[259,4895],"margin-right:0.037em;",[128,26425],{"className":26426,"style":1878},[269],[128,26428,5911],{"className":26429},[1882],[128,26431],{"className":26432,"style":1878},[269],[128,26434,26436,26439,26445,26448,26457],{"className":26435},[250],[128,26437],{"className":26438,"style":1892},[254],[128,26440,26442],{"className":26441},[2268],[128,26443,5914],{"className":26444},[259,3353],[128,26446,2477],{"className":26447},[1896],[128,26449,26451],{"className":26450},[259],[128,26452,26454],{"className":26453},[259],[128,26455,4835],{"className":26456},[259,4895],[128,26458,2486],{"className":26459},[1928],"，给定 ",[128,26462,26464,26478],{"className":26463,"translate":218},[217],[128,26465,26467],{"className":26466},[222],[224,26468,26469],{"xmlns":226},[228,26470,26471,26475],{},[231,26472,26473],{},[1795,26474,26389],{"mathvariant":4834},[238,26476,26477],{"encoding":240},"\\boldsymbol{\\pi}",[128,26479,26481],{"className":26480,"ariaHidden":246},[245],[128,26482,26484,26487],{"className":26483},[250],[128,26485],{"className":26486,"style":4439},[254],[128,26488,26490],{"className":26489},[259],[128,26491,26493],{"className":26492},[259],[128,26494,26389],{"className":26495,"style":26423},[259,4895]," 观测到计数向量 ",[128,26498,26500,26538],{"className":26499,"translate":218},[217],[128,26501,26503],{"className":26502},[222],[224,26504,26505],{"xmlns":226},[228,26506,26507,26535],{},[231,26508,26509,26511,26513,26515,26521,26523,26525,26527,26533],{},[1795,26510,16280],{"mathvariant":2001},[1832,26512,1994],{},[1832,26514,2477],{"stretchy":1837},[2016,26516,26517,26519],{},[1795,26518,16280],{},[1840,26520,1842],{},[1832,26522,1845],{"separator":246},[1832,26524,1848],{},[1832,26526,1845],{"separator":246},[2016,26528,26529,26531],{},[1795,26530,16280],{},[1795,26532,1853],{},[1832,26534,2486],{"stretchy":1837},[238,26536,26537],{"encoding":240},"\\mathbf{n} = (n_1, \\dots, n_K)",[128,26539,26541,26559],{"className":26540,"ariaHidden":246},[245],[128,26542,26544,26547,26550,26553,26556],{"className":26543},[250],[128,26545],{"className":26546,"style":4439},[254],[128,26548,16280],{"className":26549},[259,2151],[128,26551],{"className":26552,"style":1878},[269],[128,26554,1994],{"className":26555},[1882],[128,26557],{"className":26558,"style":1878},[269],[128,26560,26562,26565,26568,26608,26611,26614,26617,26620,26623,26626,26666],{"className":26561},[250],[128,26563],{"className":26564,"style":1892},[254],[128,26566,2477],{"className":26567},[1896],[128,26569,26571,26574],{"className":26570},[259],[128,26572,16280],{"className":26573},[259,1873],[128,26575,26577],{"className":26576},[2087],[128,26578,26580,26600],{"className":26579},[274,321],[128,26581,26583,26597],{"className":26582},[278],[128,26584,26586],{"className":26585,"style":2945},[282],[128,26587,26588,26591],{"style":2221},[128,26589],{"className":26590,"style":291},[290],[128,26592,26594],{"className":26593},[299,300,301,298],[128,26595,1842],{"className":26596},[259,298],[128,26598,347],{"className":26599},[346],[128,26601,26603],{"className":26602},[278],[128,26604,26606],{"className":26605,"style":2241},[282],[128,26607],{},[128,26609,1845],{"className":26610},[1903],[128,26612],{"className":26613,"style":1907},[269],[128,26615,1848],{"className":26616},[1911],[128,26618],{"className":26619,"style":1907},[269],[128,26621,1845],{"className":26622},[1903],[128,26624],{"className":26625,"style":1907},[269],[128,26627,26629,26632],{"className":26628},[259],[128,26630,16280],{"className":26631},[259,1873],[128,26633,26635],{"className":26634},[2087],[128,26636,26638,26658],{"className":26637},[274,321],[128,26639,26641,26655],{"className":26640},[278],[128,26642,26644],{"className":26643,"style":3004},[282],[128,26645,26646,26649],{"style":2221},[128,26647],{"className":26648,"style":291},[290],[128,26650,26652],{"className":26651},[299,300,301,298],[128,26653,1853],{"className":26654,"style":1924},[259,1873,298],[128,26656,347],{"className":26657},[346],[128,26659,26661],{"className":26660},[278],[128,26662,26664],{"className":26663,"style":2241},[282],[128,26665],{},[128,26667,2486],{"className":26668},[1928],[128,26670,26672,26695],{"className":26671,"translate":218},[217],[128,26673,26675],{"className":26674},[222],[224,26676,26677],{"xmlns":226},[228,26678,26679,26692],{},[231,26680,26681,26687,26689],{},[2016,26682,26683,26685],{},[1795,26684,16280],{},[1795,26686,2801],{},[1832,26688,1834],{},[1795,26690,26691],{"mathvariant":2008},"N",[238,26693,26694],{"encoding":240},"n_i \\in \\mathbb{N}",[128,26696,26698,26753],{"className":26697,"ariaHidden":246},[245],[128,26699,26701,26704,26744,26747,26750],{"className":26700},[250],[128,26702],{"className":26703,"style":3484},[254],[128,26705,26707,26710],{"className":26706},[259],[128,26708,16280],{"className":26709},[259,1873],[128,26711,26713],{"className":26712},[2087],[128,26714,26716,26736],{"className":26715},[274,321],[128,26717,26719,26733],{"className":26718},[278],[128,26720,26722],{"className":26721,"style":3095},[282],[128,26723,26724,26727],{"style":2221},[128,26725],{"className":26726,"style":291},[290],[128,26728,26730],{"className":26729},[299,300,301,298],[128,26731,2801],{"className":26732},[259,1873,298],[128,26734,347],{"className":26735},[346],[128,26737,26739],{"className":26738},[278],[128,26740,26742],{"className":26741,"style":2241},[282],[128,26743],{},[128,26745],{"className":26746,"style":1878},[269],[128,26748,1834],{"className":26749},[1882],[128,26751],{"className":26752,"style":1878},[269],[128,26754,26756,26760],{"className":26755},[250],[128,26757],{"className":26758,"style":26759},[254],"height:0.6889em;",[128,26761,26691],{"className":26762},[259,2167],[128,26764,26766,26794],{"className":26765,"translate":218},[217],[128,26767,26769],{"className":26768},[222],[224,26770,26771],{"xmlns":226},[228,26772,26773,26791],{},[231,26774,26775,26777,26779,26785],{},[1795,26776,26691],{},[1832,26778,1994],{},[2016,26780,26781,26783],{},[1832,26782,2042],{},[1795,26784,2801],{},[2016,26786,26787,26789],{},[1795,26788,16280],{},[1795,26790,2801],{},[238,26792,26793],{"encoding":240},"N = \\sum_i n_i",[128,26795,26797,26816],{"className":26796,"ariaHidden":246},[245],[128,26798,26800,26803,26807,26810,26813],{"className":26799},[250],[128,26801],{"className":26802,"style":283},[254],[128,26804,26691],{"className":26805,"style":26806},[259,1873],"margin-right:0.109em;",[128,26808],{"className":26809,"style":1878},[269],[128,26811,1994],{"className":26812},[1882],[128,26814],{"className":26815,"style":1878},[269],[128,26817,26819,26822,26862,26865],{"className":26818},[250],[128,26820],{"className":26821,"style":7777},[254],[128,26823,26825,26828],{"className":26824},[2268],[128,26826,2042],{"className":26827,"style":2274},[2268,2272,2273],[128,26829,26831],{"className":26830},[2087],[128,26832,26834,26854],{"className":26833},[274,321],[128,26835,26837,26851],{"className":26836},[278],[128,26838,26840],{"className":26839,"style":7796},[282],[128,26841,26842,26845],{"style":2290},[128,26843],{"className":26844,"style":291},[290],[128,26846,26848],{"className":26847},[299,300,301,298],[128,26849,2801],{"className":26850},[259,1873,298],[128,26852,347],{"className":26853},[346],[128,26855,26857],{"className":26856},[278],[128,26858,26860],{"className":26859,"style":2330},[282],[128,26861],{},[128,26863],{"className":26864,"style":1907},[269],[128,26866,26868,26871],{"className":26867},[259],[128,26869,16280],{"className":26870},[259,1873],[128,26872,26874],{"className":26873},[2087],[128,26875,26877,26897],{"className":26876},[274,321],[128,26878,26880,26894],{"className":26879},[278],[128,26881,26883],{"className":26882,"style":3095},[282],[128,26884,26885,26888],{"style":2221},[128,26886],{"className":26887,"style":291},[290],[128,26889,26891],{"className":26890},[299,300,301,298],[128,26892,2801],{"className":26893},[259,1873,298],[128,26895,347],{"className":26896},[346],[128,26898,26900],{"className":26899},[278],[128,26901,26903],{"className":26902,"style":2241},[282],[128,26904],{},"），则后验为\n",[128,26907,26909,26943],{"className":26908,"translate":218},[217],[128,26910,26912],{"className":26911},[222],[224,26913,26914],{"xmlns":226},[228,26915,26916,26940],{},[231,26917,26918,26920,26922,26924,26926,26928,26930,26932,26934,26936,26938],{},[1795,26919,26389],{"mathvariant":4834},[1832,26921,5443],{},[1795,26923,16280],{"mathvariant":2001},[1832,26925,5911],{},[1795,26927,5914],{"mathvariant":1981},[1832,26929,3278],{},[1832,26931,2477],{"stretchy":1837},[1795,26933,4835],{"mathvariant":4834},[1832,26935,9486],{},[1795,26937,16280],{"mathvariant":2001},[1832,26939,2486],{"stretchy":1837},[238,26941,26942],{"encoding":240},"\\boldsymbol{\\pi} \\mid \\mathbf{n} \\sim \\operatorname{Dir}(\\boldsymbol{\\alpha} + \\mathbf{n})",[128,26944,26946,26970,26988,27021],{"className":26945,"ariaHidden":246},[245],[128,26947,26949,26952,26961,26964,26967],{"className":26948},[250],[128,26950],{"className":26951,"style":1892},[254],[128,26953,26955],{"className":26954},[259],[128,26956,26958],{"className":26957},[259],[128,26959,26389],{"className":26960,"style":26423},[259,4895],[128,26962],{"className":26963,"style":1878},[269],[128,26965,5443],{"className":26966},[1882],[128,26968],{"className":26969,"style":1878},[269],[128,26971,26973,26976,26979,26982,26985],{"className":26972},[250],[128,26974],{"className":26975,"style":4439},[254],[128,26977,16280],{"className":26978},[259,2151],[128,26980],{"className":26981,"style":1878},[269],[128,26983,5911],{"className":26984},[1882],[128,26986],{"className":26987,"style":1878},[269],[128,26989,26991,26994,27000,27003,27012,27015,27018],{"className":26990},[250],[128,26992],{"className":26993,"style":1892},[254],[128,26995,26997],{"className":26996},[2268],[128,26998,5914],{"className":26999},[259,3353],[128,27001,2477],{"className":27002},[1896],[128,27004,27006],{"className":27005},[259],[128,27007,27009],{"className":27008},[259],[128,27010,4835],{"className":27011},[259,4895],[128,27013],{"className":27014,"style":2508},[269],[128,27016,9486],{"className":27017},[2115],[128,27019],{"className":27020,"style":2508},[269],[128,27022,27024,27027,27030],{"className":27023},[250],[128,27025],{"className":27026,"style":1892},[254],[128,27028,16280],{"className":27029},[259,2151],[128,27031,2486],{"className":27032},[1928],[11,27034,27035,27037,27038,27216],{},[35,27036,6849],{}," 多项似然正比于 ",[128,27039,27041,27071],{"className":27040,"translate":218},[217],[128,27042,27044],{"className":27043},[222],[224,27045,27046],{"xmlns":226},[228,27047,27048,27068],{},[231,27049,27050,27056],{},[2016,27051,27052,27054],{},[1832,27053,5470],{},[1795,27055,2801],{},[2038,27057,27058,27060,27062],{},[1795,27059,26389],{},[1795,27061,2801],{},[2016,27063,27064,27066],{},[1795,27065,16280],{},[1795,27067,2801],{},[238,27069,27070],{"encoding":240},"\\prod_i \\pi_i^{n_i}",[128,27072,27074],{"className":27073,"ariaHidden":246},[245],[128,27075,27077,27080,27120,27123],{"className":27076},[250],[128,27078],{"className":27079,"style":7777},[254],[128,27081,27083,27086],{"className":27082},[2268],[128,27084,5470],{"className":27085,"style":2274},[2268,2272,2273],[128,27087,27089],{"className":27088},[2087],[128,27090,27092,27112],{"className":27091},[274,321],[128,27093,27095,27109],{"className":27094},[278],[128,27096,27098],{"className":27097,"style":7796},[282],[128,27099,27100,27103],{"style":2290},[128,27101],{"className":27102,"style":291},[290],[128,27104,27106],{"className":27105},[299,300,301,298],[128,27107,2801],{"className":27108},[259,1873,298],[128,27110,347],{"className":27111},[346],[128,27113,27115],{"className":27114},[278],[128,27116,27118],{"className":27117,"style":2330},[282],[128,27119],{},[128,27121],{"className":27122,"style":1907},[269],[128,27124,27126,27129],{"className":27125},[259],[128,27127,26389],{"className":27128,"style":1874},[259,1873],[128,27130,27132],{"className":27131},[2087],[128,27133,27135,27208],{"className":27134},[274,321],[128,27136,27138,27205],{"className":27137},[278],[128,27139,27142,27154],{"className":27140,"style":27141},[282],"height:0.7463em;",[128,27143,27145,27148],{"style":27144},"top:-2.4231em;margin-left:-0.0359em;margin-right:0.05em;",[128,27146],{"className":27147,"style":291},[290],[128,27149,27151],{"className":27150},[299,300,301,298],[128,27152,2801],{"className":27153},[259,1873,298],[128,27155,27156,27159],{"style":5755},[128,27157],{"className":27158,"style":291},[290],[128,27160,27162],{"className":27161},[299,300,301,298],[128,27163,27165],{"className":27164},[259,298],[128,27166,27168,27171],{"className":27167},[259,298],[128,27169,16280],{"className":27170},[259,1873,298],[128,27172,27174],{"className":27173},[2087],[128,27175,27177,27197],{"className":27176},[274,321],[128,27178,27180,27194],{"className":27179},[278],[128,27181,27183],{"className":27182,"style":5783},[282],[128,27184,27185,27188],{"style":7535},[128,27186],{"className":27187,"style":5790},[290],[128,27189,27191],{"className":27190},[299,5794,5795,298],[128,27192,2801],{"className":27193},[259,1873,298],[128,27195,347],{"className":27196},[346],[128,27198,27200],{"className":27199},[278],[128,27201,27203],{"className":27202,"style":5808},[282],[128,27204],{},[128,27206,347],{"className":27207},[346],[128,27209,27211],{"className":27210},[278],[128,27212,27214],{"className":27213,"style":5826},[282],[128,27215],{},"，与先验密度相乘得",[128,27218,27220],{"className":27219,"translate":218},[1962],[128,27221,27223,27290],{"className":27222,"translate":218},[217],[128,27224,27226],{"className":27225},[222],[224,27227,27228],{"xmlns":226,"display":1971},[228,27229,27230,27287],{},[231,27231,27232,27234,27236,27238,27240,27242,27244,27247,27261],{},[1795,27233,11],{},[1832,27235,2477],{"stretchy":1837},[1795,27237,26389],{"mathvariant":4834},[1832,27239,5443],{},[1795,27241,16280],{"mathvariant":2001},[1832,27243,2486],{"stretchy":1837},[1832,27245,27246],{},"∝",[6961,27248,27249,27251,27259],{},[1832,27250,5470],{},[231,27252,27253,27255,27257],{},[1795,27254,2801],{},[1832,27256,1994],{},[1840,27258,1842],{},[1795,27260,1853],{},[2038,27262,27263,27265,27267],{},[1795,27264,26389],{},[1795,27266,2801],{},[231,27268,27269,27275,27277,27283,27285],{},[2016,27270,27271,27273],{},[1795,27272,4835],{},[1795,27274,2801],{},[1832,27276,9486],{},[2016,27278,27279,27281],{},[1795,27280,16280],{},[1795,27282,2801],{},[1832,27284,1989],{},[1840,27286,1842],{},[238,27288,27289],{"encoding":240},"p(\\boldsymbol{\\pi} \\mid \\mathbf{n}) \\propto \\prod_{i=1}^K \\pi_i^{\\alpha_i + n_i - 1}",[128,27291,27293,27323,27344],{"className":27292,"ariaHidden":246},[245],[128,27294,27296,27299,27302,27305,27314,27317,27320],{"className":27295},[250],[128,27297],{"className":27298,"style":1892},[254],[128,27300,11],{"className":27301},[259,1873],[128,27303,2477],{"className":27304},[1896],[128,27306,27308],{"className":27307},[259],[128,27309,27311],{"className":27310},[259],[128,27312,26389],{"className":27313,"style":26423},[259,4895],[128,27315],{"className":27316,"style":1878},[269],[128,27318,5443],{"className":27319},[1882],[128,27321],{"className":27322,"style":1878},[269],[128,27324,27326,27329,27332,27335,27338,27341],{"className":27325},[250],[128,27327],{"className":27328,"style":1892},[254],[128,27330,16280],{"className":27331},[259,2151],[128,27333,2486],{"className":27334},[1928],[128,27336],{"className":27337,"style":1878},[269],[128,27339,27246],{"className":27340},[1882],[128,27342],{"className":27343,"style":1878},[269],[128,27345,27347,27350,27414,27417],{"className":27346},[250],[128,27348],{"className":27349,"style":7070},[254],[128,27351,27353],{"className":27352},[2268,7074],[128,27354,27356,27406],{"className":27355},[274,321],[128,27357,27359,27403],{"className":27358},[278],[128,27360,27362,27382,27392],{"className":27361,"style":7084},[282],[128,27363,27364,27367],{"style":7087},[128,27365],{"className":27366,"style":7091},[290],[128,27368,27370],{"className":27369},[299,300,301,298],[128,27371,27373,27376,27379],{"className":27372},[259,298],[128,27374,2801],{"className":27375},[259,1873,298],[128,27377,1994],{"className":27378},[1882,298],[128,27380,1842],{"className":27381},[259,298],[128,27383,27384,27387],{"style":7109},[128,27385],{"className":27386,"style":7091},[290],[128,27388,27389],{},[128,27390,5470],{"className":27391},[2268,2272,7118],[128,27393,27394,27397],{"style":7121},[128,27395],{"className":27396,"style":7091},[290],[128,27398,27400],{"className":27399},[299,300,301,298],[128,27401,1853],{"className":27402,"style":1924},[259,1873,298],[128,27404,347],{"className":27405},[346],[128,27407,27409],{"className":27408},[278],[128,27410,27412],{"className":27411,"style":7140},[282],[128,27413],{},[128,27415],{"className":27416,"style":1907},[269],[128,27418,27420,27423],{"className":27419},[259],[128,27421,26389],{"className":27422,"style":1874},[259,1873],[128,27424,27426],{"className":27425},[2087],[128,27427,27429,27549],{"className":27428},[274,321],[128,27430,27432,27546],{"className":27431},[278],[128,27433,27435,27446],{"className":27434,"style":5740},[282],[128,27436,27437,27440],{"style":27144},[128,27438],{"className":27439,"style":291},[290],[128,27441,27443],{"className":27442},[299,300,301,298],[128,27444,2801],{"className":27445},[259,1873,298],[128,27447,27448,27451],{"style":5755},[128,27449],{"className":27450,"style":291},[290],[128,27452,27454],{"className":27453},[299,300,301,298],[128,27455,27457,27497,27500,27540,27543],{"className":27456},[259,298],[128,27458,27460,27463],{"className":27459},[259,298],[128,27461,4835],{"className":27462,"style":4920},[259,1873,298],[128,27464,27466],{"className":27465},[2087],[128,27467,27469,27489],{"className":27468},[274,321],[128,27470,27472,27486],{"className":27471},[278],[128,27473,27475],{"className":27474,"style":5783},[282],[128,27476,27477,27480],{"style":5786},[128,27478],{"className":27479,"style":5790},[290],[128,27481,27483],{"className":27482},[299,5794,5795,298],[128,27484,2801],{"className":27485},[259,1873,298],[128,27487,347],{"className":27488},[346],[128,27490,27492],{"className":27491},[278],[128,27493,27495],{"className":27494,"style":5808},[282],[128,27496],{},[128,27498,9486],{"className":27499},[2115,298],[128,27501,27503,27506],{"className":27502},[259,298],[128,27504,16280],{"className":27505},[259,1873,298],[128,27507,27509],{"className":27508},[2087],[128,27510,27512,27532],{"className":27511},[274,321],[128,27513,27515,27529],{"className":27514},[278],[128,27516,27518],{"className":27517,"style":5783},[282],[128,27519,27520,27523],{"style":7535},[128,27521],{"className":27522,"style":5790},[290],[128,27524,27526],{"className":27525},[299,5794,5795,298],[128,27527,2801],{"className":27528},[259,1873,298],[128,27530,347],{"className":27531},[346],[128,27533,27535],{"className":27534},[278],[128,27536,27538],{"className":27537,"style":5808},[282],[128,27539],{},[128,27541,1989],{"className":27542},[2115,298],[128,27544,1842],{"className":27545},[259,298],[128,27547,347],{"className":27548},[346],[128,27550,27552],{"className":27551},[278],[128,27553,27555],{"className":27554,"style":5826},[282],[128,27556],{},[11,27558,27559,27560,27637],{},"该核与 ",[128,27561,27563,27589],{"className":27562,"translate":218},[217],[128,27564,27566],{"className":27565},[222],[224,27567,27568],{"xmlns":226},[228,27569,27570,27586],{},[231,27571,27572,27574,27576,27578,27580,27582,27584],{},[1795,27573,5914],{"mathvariant":1981},[1832,27575,3278],{},[1832,27577,2477],{"stretchy":1837},[1795,27579,4835],{"mathvariant":4834},[1832,27581,9486],{},[1795,27583,16280],{"mathvariant":2001},[1832,27585,2486],{"stretchy":1837},[238,27587,27588],{"encoding":240},"\\operatorname{Dir}(\\boldsymbol{\\alpha} + \\mathbf{n})",[128,27590,27592,27625],{"className":27591,"ariaHidden":246},[245],[128,27593,27595,27598,27604,27607,27616,27619,27622],{"className":27594},[250],[128,27596],{"className":27597,"style":1892},[254],[128,27599,27601],{"className":27600},[2268],[128,27602,5914],{"className":27603},[259,3353],[128,27605,2477],{"className":27606},[1896],[128,27608,27610],{"className":27609},[259],[128,27611,27613],{"className":27612},[259],[128,27614,4835],{"className":27615},[259,4895],[128,27617],{"className":27618,"style":2508},[269],[128,27620,9486],{"className":27621},[2115],[128,27623],{"className":27624,"style":2508},[269],[128,27626,27628,27631,27634],{"className":27627},[250],[128,27629],{"className":27630,"style":1892},[254],[128,27632,16280],{"className":27633},[259,2151],[128,27635,2486],{"className":27636},[1928]," 的核成比例，归一化即得。",[11,27639,27640],{},"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。",[2615,27642,27644],{"title":27643},"推论 2.6（Dirichlet–Multinomial 分布）",[11,27645,27646,27647,27675,27676],{},"计数向量 ",[128,27648,27650,27663],{"className":27649,"translate":218},[217],[128,27651,27653],{"className":27652},[222],[224,27654,27655],{"xmlns":226},[228,27656,27657,27661],{},[231,27658,27659],{},[1795,27660,16280],{"mathvariant":2001},[238,27662,16283],{"encoding":240},[128,27664,27666],{"className":27665,"ariaHidden":246},[245],[128,27667,27669,27672],{"className":27668},[250],[128,27670],{"className":27671,"style":4439},[254],[128,27673,16280],{"className":27674},[259,2151]," 的边缘似然为\n",[128,27677,27679,27845],{"className":27678,"translate":218},[217],[128,27680,27682],{"className":27681},[222],[224,27683,27684],{"xmlns":226},[228,27685,27686,27842],{},[231,27687,27688,27690,27692,27694,27696,27698,27700,27702,27726,27728,27754,27756,27790,27804],{},[1795,27689,11],{},[1832,27691,2477],{"stretchy":1837},[1795,27693,16280],{"mathvariant":2001},[1832,27695,5443],{},[1795,27697,4835],{"mathvariant":4834},[1832,27699,2486],{"stretchy":1837},[1832,27701,1994],{},[5451,27703,27704,27710],{},[231,27705,27706,27708],{},[1795,27707,26691],{},[1832,27709,4764],{"stretchy":1837},[231,27711,27712,27718,27724],{},[2016,27713,27714,27716],{},[1832,27715,5470],{},[1795,27717,2801],{},[2016,27719,27720,27722],{},[1795,27721,16280],{},[1795,27723,2801],{},[1832,27725,4764],{"stretchy":1837},[1832,27727,12935],{},[5451,27729,27730,27744],{},[231,27731,27732,27734,27736,27738,27740,27742],{},[1795,27733,5459],{},[1832,27735,2477],{"stretchy":1837},[1795,27737,4835],{"mathvariant":4834},[1832,27739,9486],{},[1795,27741,16280],{"mathvariant":2001},[1832,27743,2486],{"stretchy":1837},[231,27745,27746,27748,27750,27752],{},[1795,27747,5459],{},[1832,27749,2477],{"stretchy":1837},[1795,27751,4835],{"mathvariant":4834},[1832,27753,2486],{"stretchy":1837},[1832,27755,1994],{},[5451,27757,27758,27772],{},[231,27759,27760,27762,27764,27770],{},[1795,27761,6020],{"mathvariant":1981},[1832,27763,2477],{"stretchy":1837},[2016,27765,27766,27768],{},[1795,27767,4835],{},[1840,27769,2028],{},[1832,27771,2486],{"stretchy":1837},[231,27773,27774,27776,27778,27784,27786,27788],{},[1795,27775,6020],{"mathvariant":1981},[1832,27777,2477],{"stretchy":1837},[2016,27779,27780,27782],{},[1795,27781,4835],{},[1840,27783,2028],{},[1832,27785,9486],{},[1795,27787,26691],{},[1832,27789,2486],{"stretchy":1837},[2038,27791,27792,27794,27802],{},[1832,27793,5470],{},[231,27795,27796,27798,27800],{},[1795,27797,2801],{},[1832,27799,1994],{},[1840,27801,1842],{},[1795,27803,1853],{},[5451,27805,27806,27828],{},[231,27807,27808,27810,27812,27818,27820,27826],{},[1795,27809,6020],{"mathvariant":1981},[1832,27811,2477],{"stretchy":1837},[2016,27813,27814,27816],{},[1795,27815,4835],{},[1795,27817,2801],{},[1832,27819,9486],{},[2016,27821,27822,27824],{},[1795,27823,16280],{},[1795,27825,2801],{},[1832,27827,2486],{"stretchy":1837},[231,27829,27830,27832,27834,27840],{},[1795,27831,6020],{"mathvariant":1981},[1832,27833,2477],{"stretchy":1837},[2016,27835,27836,27838],{},[1795,27837,4835],{},[1795,27839,2801],{},[1832,27841,2486],{"stretchy":1837},[238,27843,27844],{"encoding":240},"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)}",[128,27846,27848,27872,27899,28071,28190],{"className":27847,"ariaHidden":246},[245],[128,27849,27851,27854,27857,27860,27863,27866,27869],{"className":27850},[250],[128,27852],{"className":27853,"style":1892},[254],[128,27855,11],{"className":27856},[259,1873],[128,27858,2477],{"className":27859},[1896],[128,27861,16280],{"className":27862},[259,2151],[128,27864],{"className":27865,"style":1878},[269],[128,27867,5443],{"className":27868},[1882],[128,27870],{"className":27871,"style":1878},[269],[128,27873,27875,27878,27887,27890,27893,27896],{"className":27874},[250],[128,27876],{"className":27877,"style":1892},[254],[128,27879,27881],{"className":27880},[259],[128,27882,27884],{"className":27883},[259],[128,27885,4835],{"className":27886},[259,4895],[128,27888,2486],{"className":27889},[1928],[128,27891],{"className":27892,"style":1878},[269],[128,27894,1994],{"className":27895},[1882],[128,27897],{"className":27898,"style":1878},[269],[128,27900,27902,27906,28062,28065,28068],{"className":27901},[250],[128,27903],{"className":27904,"style":27905},[254],"height:1.4501em;vertical-align:-0.57em;",[128,27907,27909,27912,28059],{"className":27908},[259],[128,27910],{"className":27911},[1896,5570],[128,27913,27915],{"className":27914},[5451],[128,27916,27918,28050],{"className":27917},[274,321],[128,27919,27921,28047],{"className":27920},[278],[128,27922,27925,28022,28030],{"className":27923,"style":27924},[282],"height:0.8801em;",[128,27926,27927,27930],{"style":5586},[128,27928],{"className":27929,"style":335},[290],[128,27931,27933],{"className":27932},[299,300,301,298],[128,27934,27936,27976,27979,28019],{"className":27935},[259,298],[128,27937,27939,27942],{"className":27938},[2268,298],[128,27940,5470],{"className":27941,"style":2274},[2268,2272,2273,298],[128,27943,27945],{"className":27944},[2087],[128,27946,27948,27968],{"className":27947},[274,321],[128,27949,27951,27965],{"className":27950},[278],[128,27952,27954],{"className":27953,"style":9202},[282],[128,27955,27956,27959],{"style":6223},[128,27957],{"className":27958,"style":5790},[290],[128,27960,27962],{"className":27961},[299,5794,5795,298],[128,27963,2801],{"className":27964},[259,1873,298],[128,27966,347],{"className":27967},[346],[128,27969,27971],{"className":27970},[278],[128,27972,27974],{"className":27973,"style":6263},[282],[128,27975],{},[128,27977],{"className":27978,"style":6269},[269,298],[128,27980,27982,27985],{"className":27981},[259,298],[128,27983,16280],{"className":27984},[259,1873,298],[128,27986,27988],{"className":27987},[2087],[128,27989,27991,28011],{"className":27990},[274,321],[128,27992,27994,28008],{"className":27993},[278],[128,27995,27997],{"className":27996,"style":5783},[282],[128,27998,27999,28002],{"style":7535},[128,28000],{"className":28001,"style":5790},[290],[128,28003,28005],{"className":28004},[299,5794,5795,298],[128,28006,2801],{"className":28007},[259,1873,298],[128,28009,347],{"className":28010},[346],[128,28012,28014],{"className":28013},[278],[128,28015,28017],{"className":28016,"style":5808},[282],[128,28018],{},[128,28020,4764],{"className":28021},[1928,298],[128,28023,28024,28027],{"style":5617},[128,28025],{"className":28026,"style":335},[290],[128,28028],{"className":28029,"style":5625},[5624],[128,28031,28032,28035],{"style":5628},[128,28033],{"className":28034,"style":335},[290],[128,28036,28038],{"className":28037},[299,300,301,298],[128,28039,28041,28044],{"className":28040},[259,298],[128,28042,26691],{"className":28043,"style":26806},[259,1873,298],[128,28045,4764],{"className":28046},[1928,298],[128,28048,347],{"className":28049},[346],[128,28051,28053],{"className":28052},[278],[128,28054,28057],{"className":28055,"style":28056},[282],"height:0.57em;",[128,28058],{},[128,28060],{"className":28061},[1928,5570],[128,28063],{"className":28064,"style":2508},[269],[128,28066,12935],{"className":28067},[2115],[128,28069],{"className":28070,"style":2508},[269],[128,28072,28074,28077,28181,28184,28187],{"className":28073},[250],[128,28075],{"className":28076,"style":19375},[254],[128,28078,28080,28083,28178],{"className":28079},[259],[128,28081],{"className":28082},[1896,5570],[128,28084,28086],{"className":28085},[5451],[128,28087,28089,28170],{"className":28088},[274,321],[128,28090,28092,28167],{"className":28091},[278],[128,28093,28095,28124,28132],{"className":28094,"style":17038},[282],[128,28096,28097,28100],{"style":5586},[128,28098],{"className":28099,"style":335},[290],[128,28101,28103],{"className":28102},[299,300,301,298],[128,28104,28106,28109,28112,28121],{"className":28105},[259,298],[128,28107,5459],{"className":28108,"style":5599},[259,1873,298],[128,28110,2477],{"className":28111},[1896,298],[128,28113,28115],{"className":28114},[259,298],[128,28116,28118],{"className":28117},[259,298],[128,28119,4835],{"className":28120},[259,4895,298],[128,28122,2486],{"className":28123},[1928,298],[128,28125,28126,28129],{"style":5617},[128,28127],{"className":28128,"style":335},[290],[128,28130],{"className":28131,"style":5625},[5624],[128,28133,28134,28137],{"style":17167},[128,28135],{"className":28136,"style":335},[290],[128,28138,28140],{"className":28139},[299,300,301,298],[128,28141,28143,28146,28149,28158,28161,28164],{"className":28142},[259,298],[128,28144,5459],{"className":28145,"style":5599},[259,1873,298],[128,28147,2477],{"className":28148},[1896,298],[128,28150,28152],{"className":28151},[259,298],[128,28153,28155],{"className":28154},[259,298],[128,28156,4835],{"className":28157},[259,4895,298],[128,28159,9486],{"className":28160},[2115,298],[128,28162,16280],{"className":28163},[259,2151,298],[128,28165,2486],{"className":28166},[1928,298],[128,28168,347],{"className":28169},[346],[128,28171,28173],{"className":28172},[278],[128,28174,28176],{"className":28175,"style":5650},[282],[128,28177],{},[128,28179],{"className":28180},[1928,5570],[128,28182],{"className":28183,"style":1878},[269],[128,28185,1994],{"className":28186},[1882],[128,28188],{"className":28189,"style":1878},[269],[128,28191,28193,28196,28362,28365,28425,28428],{"className":28192},[250],[128,28194],{"className":28195,"style":19375},[254],[128,28197,28199,28202,28359],{"className":28198},[259],[128,28200],{"className":28201},[1896,5570],[128,28203,28205],{"className":28204},[5451],[128,28206,28208,28351],{"className":28207},[274,321],[128,28209,28211,28348],{"className":28210},[278],[128,28212,28214,28280,28288],{"className":28213,"style":17038},[282],[128,28215,28216,28219],{"style":5586},[128,28217],{"className":28218,"style":335},[290],[128,28220,28222],{"className":28221},[299,300,301,298],[128,28223,28225,28228,28231,28271,28274,28277],{"className":28224},[259,298],[128,28226,6020],{"className":28227},[259,298],[128,28229,2477],{"className":28230},[1896,298],[128,28232,28234,28237],{"className":28233},[259,298],[128,28235,4835],{"className":28236,"style":4920},[259,1873,298],[128,28238,28240],{"className":28239},[2087],[128,28241,28243,28263],{"className":28242},[274,321],[128,28244,28246,28260],{"className":28245},[278],[128,28247,28249],{"className":28248,"style":6153},[282],[128,28250,28251,28254],{"style":5786},[128,28252],{"className":28253,"style":5790},[290],[128,28255,28257],{"className":28256},[299,5794,5795,298],[128,28258,2028],{"className":28259},[259,298],[128,28261,347],{"className":28262},[346],[128,28264,28266],{"className":28265},[278],[128,28267,28269],{"className":28268,"style":5808},[282],[128,28270],{},[128,28272,9486],{"className":28273},[2115,298],[128,28275,26691],{"className":28276,"style":26806},[259,1873,298],[128,28278,2486],{"className":28279},[1928,298],[128,28281,28282,28285],{"style":5617},[128,28283],{"className":28284,"style":335},[290],[128,28286],{"className":28287,"style":5625},[5624],[128,28289,28290,28293],{"style":17167},[128,28291],{"className":28292,"style":335},[290],[128,28294,28296],{"className":28295},[299,300,301,298],[128,28297,28299,28302,28305,28345],{"className":28298},[259,298],[128,28300,6020],{"className":28301},[259,298],[128,28303,2477],{"className":28304},[1896,298],[128,28306,28308,28311],{"className":28307},[259,298],[128,28309,4835],{"className":28310,"style":4920},[259,1873,298],[128,28312,28314],{"className":28313},[2087],[128,28315,28317,28337],{"className":28316},[274,321],[128,28318,28320,28334],{"className":28319},[278],[128,28321,28323],{"className":28322,"style":6153},[282],[128,28324,28325,28328],{"style":5786},[128,28326],{"className":28327,"style":5790},[290],[128,28329,28331],{"className":28330},[299,5794,5795,298],[128,28332,2028],{"className":28333},[259,298],[128,28335,347],{"className":28336},[346],[128,28338,28340],{"className":28339},[278],[128,28341,28343],{"className":28342,"style":5808},[282],[128,28344],{},[128,28346,2486],{"className":28347},[1928,298],[128,28349,347],{"className":28350},[346],[128,28352,28354],{"className":28353},[278],[128,28355,28357],{"className":28356,"style":5650},[282],[128,28358],{},[128,28360],{"className":28361},[1928,5570],[128,28363],{"className":28364,"style":1907},[269],[128,28366,28368,28371],{"className":28367},[2268],[128,28369,5470],{"className":28370,"style":2274},[2268,2272,2273],[128,28372,28374],{"className":28373},[2087],[128,28375,28377,28417],{"className":28376},[274,321],[128,28378,28380,28414],{"className":28379},[278],[128,28381,28383,28403],{"className":28382,"style":2287},[282],[128,28384,28385,28388],{"style":2290},[128,28386],{"className":28387,"style":291},[290],[128,28389,28391],{"className":28390},[299,300,301,298],[128,28392,28394,28397,28400],{"className":28393},[259,298],[128,28395,2801],{"className":28396},[259,1873,298],[128,28398,1994],{"className":28399},[1882,298],[128,28401,1842],{"className":28402},[259,298],[128,28404,28405,28408],{"style":2311},[128,28406],{"className":28407,"style":291},[290],[128,28409,28411],{"className":28410},[299,300,301,298],[128,28412,1853],{"className":28413,"style":1924},[259,1873,298],[128,28415,347],{"className":28416},[346],[128,28418,28420],{"className":28419},[278],[128,28421,28423],{"className":28422,"style":2330},[282],[128,28424],{},[128,28426],{"className":28427,"style":1907},[269],[128,28429,28431,28434,28628],{"className":28430},[259],[128,28432],{"className":28433},[1896,5570],[128,28435,28437],{"className":28436},[5451],[128,28438,28440,28620],{"className":28439},[274,321],[128,28441,28443,28617],{"className":28442},[278],[128,28444,28446,28506,28514],{"className":28445,"style":17038},[282],[128,28447,28448,28451],{"style":5586},[128,28449],{"className":28450,"style":335},[290],[128,28452,28454],{"className":28453},[299,300,301,298],[128,28455,28457,28460,28463,28503],{"className":28456},[259,298],[128,28458,6020],{"className":28459},[259,298],[128,28461,2477],{"className":28462},[1896,298],[128,28464,28466,28469],{"className":28465},[259,298],[128,28467,4835],{"className":28468,"style":4920},[259,1873,298],[128,28470,28472],{"className":28471},[2087],[128,28473,28475,28495],{"className":28474},[274,321],[128,28476,28478,28492],{"className":28477},[278],[128,28479,28481],{"className":28480,"style":5783},[282],[128,28482,28483,28486],{"style":5786},[128,28484],{"className":28485,"style":5790},[290],[128,28487,28489],{"className":28488},[299,5794,5795,298],[128,28490,2801],{"className":28491},[259,1873,298],[128,28493,347],{"className":28494},[346],[128,28496,28498],{"className":28497},[278],[128,28499,28501],{"className":28500,"style":5808},[282],[128,28502],{},[128,28504,2486],{"className":28505},[1928,298],[128,28507,28508,28511],{"style":5617},[128,28509],{"className":28510,"style":335},[290],[128,28512],{"className":28513,"style":5625},[5624],[128,28515,28516,28519],{"style":17167},[128,28517],{"className":28518,"style":335},[290],[128,28520,28522],{"className":28521},[299,300,301,298],[128,28523,28525,28528,28531,28571,28574,28614],{"className":28524},[259,298],[128,28526,6020],{"className":28527},[259,298],[128,28529,2477],{"className":28530},[1896,298],[128,28532,28534,28537],{"className":28533},[259,298],[128,28535,4835],{"className":28536,"style":4920},[259,1873,298],[128,28538,28540],{"className":28539},[2087],[128,28541,28543,28563],{"className":28542},[274,321],[128,28544,28546,28560],{"className":28545},[278],[128,28547,28549],{"className":28548,"style":5783},[282],[128,28550,28551,28554],{"style":5786},[128,28552],{"className":28553,"style":5790},[290],[128,28555,28557],{"className":28556},[299,5794,5795,298],[128,28558,2801],{"className":28559},[259,1873,298],[128,28561,347],{"className":28562},[346],[128,28564,28566],{"className":28565},[278],[128,28567,28569],{"className":28568,"style":5808},[282],[128,28570],{},[128,28572,9486],{"className":28573},[2115,298],[128,28575,28577,28580],{"className":28576},[259,298],[128,28578,16280],{"className":28579},[259,1873,298],[128,28581,28583],{"className":28582},[2087],[128,28584,28586,28606],{"className":28585},[274,321],[128,28587,28589,28603],{"className":28588},[278],[128,28590,28592],{"className":28591,"style":5783},[282],[128,28593,28594,28597],{"style":7535},[128,28595],{"className":28596,"style":5790},[290],[128,28598,28600],{"className":28599},[299,5794,5795,298],[128,28601,2801],{"className":28602},[259,1873,298],[128,28604,347],{"className":28605},[346],[128,28607,28609],{"className":28608},[278],[128,28610,28612],{"className":28611,"style":5808},[282],[128,28613],{},[128,28615,2486],{"className":28616},[1928,298],[128,28618,347],{"className":28619},[346],[128,28621,28623],{"className":28622},[278],[128,28624,28626],{"className":28625,"style":5650},[282],[128,28627],{},[128,28629],{"className":28630},[1928,5570],[2615,28632,28634],{"title":28633},"推论 2.7（后验预测与收缩）",[11,28635,28636,28637,29019,29020,29127,29128,29131,29132],{},"对未见样本，\n",[128,28638,28640,28705],{"className":28639,"translate":218},[217],[128,28641,28643],{"className":28642},[222],[224,28644,28645],{"xmlns":226},[228,28646,28647,28702],{},[231,28648,28649,28651,28653,28660,28662,28664,28666,28668,28670,28672],{},[1795,28650,23001],{"mathvariant":2008},[1832,28652,2477],{"stretchy":1837},[2016,28654,28655,28657],{},[1795,28656,1830],{},[234,28658,28659],{},"new",[1832,28661,1994],{},[1795,28663,2022],{},[1832,28665,5443],{},[1795,28667,16280],{"mathvariant":2001},[1832,28669,2486],{"stretchy":1837},[1832,28671,1994],{},[5451,28673,28674,28690],{},[231,28675,28676,28682,28684],{},[2016,28677,28678,28680],{},[1795,28679,4835],{},[1795,28681,2022],{},[1832,28683,9486],{},[2016,28685,28686,28688],{},[1795,28687,16280],{},[1795,28689,2022],{},[231,28691,28692,28698,28700],{},[2016,28693,28694,28696],{},[1795,28695,4835],{},[1840,28697,2028],{},[1832,28699,9486],{},[1795,28701,26691],{},[238,28703,28704],{"encoding":240},"\\mathbb{P}(y_{\\text{new}} = k \\mid \\mathbf{n}) = \\frac{\\alpha_k + n_k}{\\alpha_0 + N}",[128,28706,28708,28777,28795,28816],{"className":28707,"ariaHidden":246},[245],[128,28709,28711,28714,28717,28720,28768,28771,28774],{"className":28710},[250],[128,28712],{"className":28713,"style":1892},[254],[128,28715,23001],{"className":28716},[259,2167],[128,28718,2477],{"className":28719},[1896],[128,28721,28723,28726],{"className":28722},[259],[128,28724,1830],{"className":28725,"style":1874},[259,1873],[128,28727,28729],{"className":28728},[2087],[128,28730,28732,28760],{"className":28731},[274,321],[128,28733,28735,28757],{"className":28734},[278],[128,28736,28739],{"className":28737,"style":28738},[282],"height:0.1514em;",[128,28740,28742,28745],{"style":28741},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[128,28743],{"className":28744,"style":291},[290],[128,28746,28748],{"className":28747},[299,300,301,298],[128,28749,28751],{"className":28750},[259,298],[128,28752,28754],{"className":28753},[259,260,298],[128,28755,28659],{"className":28756},[259,298],[128,28758,347],{"className":28759},[346],[128,28761,28763],{"className":28762},[278],[128,28764,28766],{"className":28765,"style":2241},[282],[128,28767],{},[128,28769],{"className":28770,"style":1878},[269],[128,28772,1994],{"className":28773},[1882],[128,28775],{"className":28776,"style":1878},[269],[128,28778,28780,28783,28786,28789,28792],{"className":28779},[250],[128,28781],{"className":28782,"style":1892},[254],[128,28784,2022],{"className":28785,"style":2231},[259,1873],[128,28787],{"className":28788,"style":1878},[269],[128,28790,5443],{"className":28791},[1882],[128,28793],{"className":28794,"style":1878},[269],[128,28796,28798,28801,28804,28807,28810,28813],{"className":28797},[250],[128,28799],{"className":28800,"style":1892},[254],[128,28802,16280],{"className":28803},[259,2151],[128,28805,2486],{"className":28806},[1928],[128,28808],{"className":28809,"style":1878},[269],[128,28811,1994],{"className":28812},[1882],[128,28814],{"className":28815,"style":1878},[269],[128,28817,28819,28823],{"className":28818},[250],[128,28820],{"className":28821,"style":28822},[254],"height:1.2693em;vertical-align:-0.4451em;",[128,28824,28826,28829,29016],{"className":28825},[259],[128,28827],{"className":28828},[1896,5570],[128,28830,28832],{"className":28831},[5451],[128,28833,28835,29008],{"className":28834},[274,321],[128,28836,28838,29005],{"className":28837},[278],[128,28839,28842,28899,28907],{"className":28840,"style":28841},[282],"height:0.8242em;",[128,28843,28844,28847],{"style":5586},[128,28845],{"className":28846,"style":335},[290],[128,28848,28850],{"className":28849},[299,300,301,298],[128,28851,28853,28893,28896],{"className":28852},[259,298],[128,28854,28856,28859],{"className":28855},[259,298],[128,28857,4835],{"className":28858,"style":4920},[259,1873,298],[128,28860,28862],{"className":28861},[2087],[128,28863,28865,28885],{"className":28864},[274,321],[128,28866,28868,28882],{"className":28867},[278],[128,28869,28871],{"className":28870,"style":6153},[282],[128,28872,28873,28876],{"style":5786},[128,28874],{"className":28875,"style":5790},[290],[128,28877,28879],{"className":28878},[299,5794,5795,298],[128,28880,2028],{"className":28881},[259,298],[128,28883,347],{"className":28884},[346],[128,28886,28888],{"className":28887},[278],[128,28889,28891],{"className":28890,"style":5808},[282],[128,28892],{},[128,28894,9486],{"className":28895},[2115,298],[128,28897,26691],{"className":28898,"style":26806},[259,1873,298],[128,28900,28901,28904],{"style":5617},[128,28902],{"className":28903,"style":335},[290],[128,28905],{"className":28906,"style":5625},[5624],[128,28908,28910,28913],{"style":28909},"top:-3.4159em;",[128,28911],{"className":28912,"style":335},[290],[128,28914,28916],{"className":28915},[299,300,301,298],[128,28917,28919,28961,28964],{"className":28918},[259,298],[128,28920,28922,28925],{"className":28921},[259,298],[128,28923,4835],{"className":28924,"style":4920},[259,1873,298],[128,28926,28928],{"className":28927},[2087],[128,28929,28931,28952],{"className":28930},[274,321],[128,28932,28934,28949],{"className":28933},[278],[128,28935,28937],{"className":28936,"style":24117},[282],[128,28938,28940,28943],{"style":28939},"top:-2.3488em;margin-left:-0.0037em;margin-right:0.0714em;",[128,28941],{"className":28942,"style":5790},[290],[128,28944,28946],{"className":28945},[299,5794,5795,298],[128,28947,2022],{"className":28948,"style":2231},[259,1873,298],[128,28950,347],{"className":28951},[346],[128,28953,28955],{"className":28954},[278],[128,28956,28959],{"className":28957,"style":28958},[282],"height:0.1512em;",[128,28960],{},[128,28962,9486],{"className":28963},[2115,298],[128,28965,28967,28970],{"className":28966},[259,298],[128,28968,16280],{"className":28969},[259,1873,298],[128,28971,28973],{"className":28972},[2087],[128,28974,28976,28997],{"className":28975},[274,321],[128,28977,28979,28994],{"className":28978},[278],[128,28980,28982],{"className":28981,"style":24117},[282],[128,28983,28985,28988],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\\mathbf{n}]",[128,29052,29054,29115],{"className":29053,"ariaHidden":246},[245],[128,29055,29057,29060,29063,29066,29106,29109,29112],{"className":29056},[250],[128,29058],{"className":29059,"style":1892},[254],[128,29061,342],{"className":29062},[259,2167],[128,29064,16538],{"className":29065},[1896],[128,29067,29069,29072],{"className":29068},[259],[128,29070,26389],{"className":29071,"style":1874},[259,1873],[128,29073,29075],{"className":29074},[2087],[128,29076,29078,29098],{"className":29077},[274,321],[128,29079,29081,29095],{"className":29080},[278],[128,29082,29084],{"className":29083,"style":2218},[282],[128,29085,29086,29089],{"style":28741},[128,29087],{"className":29088,"style":291},[290],[128,29090,29092],{"className":29091},[299,300,301,298],[128,29093,2022],{"className":29094,"style":2231},[259,1873,298],[128,29096,347],{"className":29097},[346],[128,29099,29101],{"className":29100},[278],[128,29102,29104],{"className":29103,"style":2241},[282],[128,29105],{},[128,29107],{"className":29108,"style":1878},[269],[128,29110,5443],{"className":29111},[1882],[128,29113],{"className":29114,"style":1878},[269],[128,29116,29118,29121,29124],{"className":29117},[250],[128,29119],{"className":29120,"style":1892},[254],[128,29122,16280],{"className":29123},[259,2151],[128,29125,16547],{"className":29126},[1928]," 是",[35,29129,29130],{},"先验均值与经验频率的凸组合","：\n",[128,29133,29135,29250],{"className":29134,"translate":218},[217],[128,29136,29138],{"className":29137},[222],[224,29139,29140],{"xmlns":226},[228,29141,29142,29247],{},[231,29143,29144,29146,29148,29154,29156,29158,29160,29162,29192,29194,29208,29210,29235,29237],{},[1795,29145,342],{"mathvariant":2008},[1832,29147,16538],{"stretchy":1837},[2016,29149,29150,29152],{},[1795,29151,26389],{},[1795,29153,2022],{},[1832,29155,5443],{},[1795,29157,16280],{"mathvariant":2001},[1832,29159,16547],{"stretchy":1837},[1832,29161,1994],{},[8606,29163,29164,29189],{},[8606,29165,29166,29186],{},[5451,29167,29168,29174],{},[2016,29169,29170,29172],{},[1795,29171,4835],{},[1840,29173,2028],{},[231,29175,29176,29182,29184],{},[2016,29177,29178,29180],{},[1795,29179,4835],{},[1840,29181,2028],{},[1832,29183,9486],{},[1795,29185,26691],{},[1832,29187,29188],{"stretchy":246},"⏟",[234,29190,29191],{},"收缩权重",[1832,29193,12935],{},[5451,29195,29196,29202],{},[2016,29197,29198,29200],{},[1795,29199,4835],{},[1795,29201,2022],{},[2016,29203,29204,29206],{},[1795,29205,4835],{},[1840,29207,2028],{},[1832,29209,9486],{},[8606,29211,29212,29232],{},[8606,29213,29214,29230],{},[5451,29215,29216,29218],{},[1795,29217,26691],{},[231,29219,29220,29226,29228],{},[2016,29221,29222,29224],{},[1795,29223,4835],{},[1840,29225,2028],{},[1832,29227,9486],{},[1795,29229,26691],{},[1832,29231,29188],{"stretchy":246},[234,29233,29234],{},"数据权重",[1832,29236,12935],{},[5451,29238,29239,29245],{},[2016,29240,29241,29243],{},[1795,29242,16280],{},[1795,29244,2022],{},[1795,29246,26691],{},[238,29248,29249],{"encoding":240},"\\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 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0 400000 548","xMinYMin slice",[29419,29420],"path",{"d":29421},"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",[128,29423,29426],{"className":29424,"style":29409},[29425],"brace-center",[29411,29427,29429],{"xmlns":29413,"width":29414,"height":29415,"viewBox":29416,"preserveAspectRatio":29428},"xMidYMin slice",[29419,29430],{"d":29431},"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",[128,29433,29436],{"className":29434,"style":29409},[29435],"brace-right",[29411,29437,29439],{"xmlns":29413,"width":29414,"height":29415,"viewBox":29416,"preserveAspectRatio":29438},"xMaxYMin slice",[29419,29440],{"d":29441},"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",[128,29443,29444,29447],{"style":29376},[128,29445],{"className":29446,"style":29361},[290],[128,29448,29450],{"className":29449},[259],[128,29451,29453,29456,29595],{"className":29452},[259],[128,29454],{"className":29455},[1896,5570],[128,29457,29459],{"className":29458},[5451],[128,29460,29462,29587],{"className":29461},[274,321],[128,29463,29465,29584],{"className":29464},[278],[128,29466,29468,29528,29536],{"className":29467,"style":29354},[282],[128,29469,29470,29473],{"style":13123},[128,29471],{"className":29472,"style":335},[290],[128,29474,29476,29516,29519,29522,29525],{"className":29475},[259],[128,29477,29479,29482],{"className":29478},[259],[128,29480,4835],{"className":29481,"style":4920},[259,1873],[128,29483,29485],{"className":29484},[2087],[128,29486,29488,29508],{"className":29487},[274,321],[128,29489,29491,29505],{"className":29490},[278],[128,29492,29494],{"className":29493,"style":2945},[282],[128,29495,29496,29499],{"style":4935},[128,29497],{"className":29498,"style":291},[290],[128,29500,29502],{"className":29501},[299,300,301,298],[128,29503,2028],{"className":29504},[259,298],[128,29506,347],{"className":29507},[346],[128,29509,29511],{"className":29510},[278],[128,29512,29514],{"className":29513,"style":2241},[282],[128,29515],{},[128,29517],{"className":29518,"style":2508},[269],[128,29520,9486],{"className":29521},[2115],[128,29523],{"className":29524,"style":2508},[269],[128,29526,26691],{"className":29527,"style":26806},[259,1873],[128,29529,29530,29533],{"style":5617},[128,29531],{"className":29532,"style":335},[290],[128,29534],{"className":29535,"style":5625},[5624],[128,29537,29538,29541],{"style":13189},[128,29539],{"className":29540,"style":335},[290],[128,29542,29544],{"className":29543},[259],[128,29545,29547,29550],{"className":29546},[259],[128,29548,4835],{"className":29549,"style":4920},[259,1873],[128,29551,29553],{"className":29552},[2087],[128,29554,29556,29576],{"className":29555},[274,321],[128,29557,29559,29573],{"className":29558},[278],[128,29560,29562],{"className":29561,"style":2945},[282],[128,29563,29564,29567],{"style":4935},[128,29565],{"className":29566,"style":291},[290],[128,29568,29570],{"className":29569},[299,300,301,298],[128,29571,2028],{"className":29572},[259,298],[128,29574,347],{"className":29575},[346],[128,29577,29579],{"className":29578},[278],[128,29580,29582],{"className":29581,"style":2241},[282],[128,29583],{},[128,29585,347],{"className":29586},[346],[128,29588,29590],{"className":29589},[278],[128,29591,29593],{"className":29592,"style":20496},[282],[128,29594],{},[128,29596],{"className":29597},[1928,5570],[128,29599,347],{"className":29600},[346],[128,29602,29604],{"className":29603},[278],[128,29605,29608],{"className":29606,"style":29607},[282],"height:1.484em;",[128,29609],{},[128,29611,347],{"className":29612},[346],[128,29614,29616],{"className":29615},[278],[128,29617,29620],{"className":29618,"style":29619},[282],"height:2.1623em;",[128,29621],{},[128,29623],{"className":29624,"style":2508},[269],[128,29626,12935],{"className":29627},[2115],[128,29629],{"className":29630,"style":2508},[269],[128,29632,29634,29638,29781,29784,29787],{"className":29633},[250],[128,29635],{"className":29636,"style":29637},[254],"height:1.1624em;vertical-align:-0.4451em;",[128,29639,29641,29644,29778],{"className":29640},[259],[128,29642],{"className":29643},[1896,5570],[128,29645,29647],{"className":29646},[5451],[128,29648,29650,29770],{"className":29649},[274,321],[128,29651,29653,29767],{"className":29652},[278],[128,29654,29657,29708,29716],{"className":29655,"style":29656},[282],"height:0.7173em;",[128,29658,29659,29662],{"style":5586},[128,29660],{"className":29661,"style":335},[290],[128,29663,29665],{"className":29664},[299,300,301,298],[128,29666,29668],{"className":29667},[259,298],[128,29669,29671,29674],{"className":29670},[259,298],[128,29672,4835],{"className":29673,"style":4920},[259,1873,298],[128,29675,29677],{"className":29676},[2087],[128,29678,29680,29700],{"className":29679},[274,321],[128,29681,29683,29697],{"className":29682},[278],[128,29684,29686],{"className":29685,"style":6153},[282],[128,29687,29688,29691],{"style":5786},[128,29689],{"className":29690,"style":5790},[290],[128,29692,29694],{"className":29693},[299,5794,5795,298],[128,29695,2028],{"className":29696},[259,298],[128,29698,347],{"className":29699},[346],[128,29701,29703],{"className":29702},[278],[128,29704,29706],{"className":29705,"style":5808},[282],[128,29707],{},[128,29709,29710,29713],{"style":5617},[128,29711],{"className":29712,"style":335},[290],[128,29714],{"className":29715,"style":5625},[5624],[128,29717,29718,29721],{"style":28909},[128,29719],{"className":29720,"style":335},[290],[128,29722,29724],{"className":29723},[299,300,301,298],[128,29725,29727],{"className":29726},[259,298],[128,29728,29730,29733],{"className":29729},[259,298],[128,29731,4835],{"className":29732,"style":4920},[259,1873,298],[128,29734,29736],{"className":29735},[2087],[128,29737,29739,29759],{"className":29738},[274,321],[128,29740,29742,29756],{"className":29741},[278],[128,29743,29745],{"className":29744,"style":24117},[282],[128,29746,29747,29750],{"style":28939},[128,29748],{"className":29749,"style":5790},[290],[128,29751,29753],{"className":29752},[299,5794,5795,298],[128,29754,2022],{"className":29755,"style":2231},[259,1873,298],[128,29757,347],{"className":29758},[346],[128,29760,29762],{"className":29761},[278],[128,29763,29765],{"className":29764,"style":28958},[282],[128,29766],{},[128,29768,347],{"className":29769},[346],[128,29771,29773],{"className":29772},[278],[128,29774,29776],{"className":29775,"style":16937},[282],[128,29777],{},[128,29779],{"className":29780},[1928,5570],[128,29782],{"className":29783,"style":2508},[269],[128,29785,9486],{"className":29786},[2115],[128,29788],{"className":29789,"style":2508},[269],[128,29791,29793,29797,30019,30022,30025],{"className":29792},[250],[128,29794],{"className":29795,"style":29796},[254],"height:3.5227em;vertical-align:-2.1623em;",[128,29798,29800],{"className":29799},[1911,8606],[128,29801,29803,30011],{"className":29802},[274,321],[128,29804,29806,30008],{"className":29805},[278],[128,29807,29810,29829],{"className":29808,"style":29809},[282],"height:1.3603em;",[128,29811,29813,29817],{"style":29812},"top:-1.198em;",[128,29814],{"className":29815,"style":29816},[290],"height:3.3603em;",[128,29818,29820],{"className":29819},[299,300,301,298],[128,29821,29823],{"className":29822},[259,298],[128,29824,29826],{"className":29825},[259,260,298],[128,29827,29234],{"className":29828},[259,15272,298],[128,29830,29832,29835],{"style":29831},"top:-3.3603em;",[128,29833],{"className":29834,"style":29816},[290],[128,29836,29838],{"className":29837},[1911,8606],[128,29839,29841,30000],{"className":29840},[274,321],[128,29842,29844,29997],{"className":29843},[278],[128,29845,29847,29878],{"className":29846,"style":29809},[282],[128,29848,29851,29854],{"className":29849,"style":29850},[29395],"top:-1.8763em;",[128,29852],{"className":29853,"style":29816},[290],[128,29855,29857,29864,29871],{"className":29856,"style":29404},[29403],[128,29858,29860],{"className":29859,"style":29409},[29408],[29411,29861,29862],{"xmlns":29413,"width":29414,"height":29415,"viewBox":29416,"preserveAspectRatio":29417},[29419,29863],{"d":29421},[128,29865,29867],{"className":29866,"style":29409},[29425],[29411,29868,29869],{"xmlns":29413,"width":29414,"height":29415,"viewBox":29416,"preserveAspectRatio":29428},[29419,29870],{"d":29431},[128,29872,29874],{"className":29873,"style":29409},[29435],[29411,29875,29876],{"xmlns":29413,"width":29414,"height":29415,"viewBox":29416,"preserveAspectRatio":29438},[29419,29877],{"d":29441},[128,29879,29880,29883],{"style":29831},[128,29881],{"className":29882,"style":29816},[290],[128,29884,29886],{"className":29885},[259],[128,29887,29889,29892,29994],{"className":29888},[259],[128,29890],{"className":29891},[1896,5570],[128,29893,29895],{"className":29894},[5451],[128,29896,29898,29986],{"className":29897},[274,321],[128,29899,29901,29983],{"className":29900},[278],[128,29902,29904,29964,29972],{"className":29903,"style":29809},[282],[128,29905,29906,29909],{"style":13123},[128,29907],{"className":29908,"style":335},[290],[128,29910,29912,29952,29955,29958,29961],{"className":29911},[259],[128,29913,29915,29918],{"className":29914},[259],[128,29916,4835],{"className":29917,"style":4920},[259,1873],[128,29919,29921],{"className":29920},[2087],[128,29922,29924,29944],{"className":29923},[274,321],[128,29925,29927,29941],{"className":29926},[278],[128,29928,29930],{"className":29929,"style":2945},[282],[128,29931,29932,29935],{"style":4935},[128,29933],{"className":29934,"style":291},[290],[128,29936,29938],{"className":29937},[299,300,301,298],[128,29939,2028],{"className":29940},[259,298],[128,29942,347],{"className":29943},[346],[128,29945,29947],{"className":29946},[278],[128,29948,29950],{"className":29949,"style":2241},[282],[128,29951],{},[128,29953],{"className":29954,"style":2508},[269],[128,29956,9486],{"className":29957},[2115],[128,29959],{"className":29960,"style":2508},[269],[128,29962,26691],{"className":29963,"style":26806},[259,1873],[128,29965,29966,29969],{"style":5617},[128,29967],{"className":29968,"style":335},[290],[128,29970],{"className":29971,"style":5625},[5624],[128,29973,29974,29977],{"style":13189},[128,29975],{"className":29976,"style":335},[290],[128,29978,29980],{"className":29979},[259],[128,29981,26691],{"className":29982,"style":26806},[259,1873],[128,29984,347],{"className":29985},[346],[128,29987,29989],{"className":29988},[278],[128,29990,29992],{"className":29991,"style":20496},[282],[128,29993],{},[128,29995],{"className":29996},[1928,5570],[128,29998,347],{"className":29999},[346],[128,30001,30003],{"className":30002},[278],[128,30004,30006],{"className":30005,"style":29607},[282],[128,30007],{},[128,30009,347],{"className":30010},[346],[128,30012,30014],{"className":30013},[278],[128,30015,30017],{"className":30016,"style":29619},[282],[128,30018],{},[128,30020],{"className":30021,"style":2508},[269],[128,30023,12935],{"className":30024},[2115],[128,30026],{"className":30027,"style":2508},[269],[128,30029,30031,30035],{"className":30030},[250],[128,30032],{"className":30033,"style":30034},[254],"height:1.0623em;vertical-align:-0.345em;",[128,30036,30038,30041,30137],{"className":30037},[259],[128,30039],{"className":30040},[1896,5570],[128,30042,30044],{"className":30043},[5451],[128,30045,30047,30129],{"className":30046},[274,321],[128,30048,30050,30126],{"className":30049},[278],[128,30051,30053,30067,30075],{"className":30052,"style":29656},[282],[128,30054,30055,30058],{"style":5586},[128,30056],{"className":30057,"style":335},[290],[128,30059,30061],{"className":30060},[299,300,301,298],[128,30062,30064],{"className":30063},[259,298],[128,30065,26691],{"className":30066,"style":26806},[259,1873,298],[128,30068,30069,30072],{"style":5617},[128,30070],{"className":30071,"style":335},[290],[128,30073],{"className":30074,"style":5625},[5624],[128,30076,30077,30080],{"style":28909},[128,30078],{"className":30079,"style":335},[290],[128,30081,30083],{"className":30082},[299,300,301,298],[128,30084,30086],{"className":30085},[259,298],[128,30087,30089,30092],{"className":30088},[259,298],[128,30090,16280],{"className":30091},[259,1873,298],[128,30093,30095],{"className":30094},[2087],[128,30096,30098,30118],{"className":30097},[274,321],[128,30099,30101,30115],{"className":30100},[278],[128,30102,30104],{"className":30103,"style":24117},[282],[128,30105,30106,30109],{"style":28984},[128,30107],{"className":30108,"style":5790},[290],[128,30110,30112],{"className":30111},[299,5794,5795,298],[128,30113,2022],{"className":30114,"style":2231},[259,1873,298],[128,30116,347],{"className":30117},[346],[128,30119,30121],{"className":30120},[278],[128,30122,30124],{"className":30123,"style":28958},[282],[128,30125],{},[128,30127,347],{"className":30128},[346],[128,30130,30132],{"className":30131},[278],[128,30133,30135],{"className":30134,"style":11919},[282],[128,30136],{},[128,30138],{"className":30139},[1928,5570],[11,30141,30142,30143,19116,30245,30337,30338,30429,30430,30522],{},"推论 2.7 用一句话概括了加法平滑的全部含义：",[35,30144,30145,30146,30215,30216,30244],{},"先验强度的倒数 ",[128,30147,30149,30166],{"className":30148,"translate":218},[217],[128,30150,30152],{"className":30151},[222],[224,30153,30154],{"xmlns":226},[228,30155,30156,30164],{},[231,30157,30158],{},[2016,30159,30160,30162],{},[1795,30161,4835],{},[1840,30163,2028],{},[238,30165,21207],{"encoding":240},[128,30167,30169],{"className":30168,"ariaHidden":246},[245],[128,30170,30172,30175],{"className":30171},[250],[128,30173],{"className":30174,"style":4242},[254],[128,30176,30178,30181],{"className":30177},[259],[128,30179,4835],{"className":30180,"style":4920},[259,1873],[128,30182,30184],{"className":30183},[2087],[128,30185,30187,30207],{"className":30186},[274,321],[128,30188,30190,30204],{"className":30189},[278],[128,30191,30193],{"className":30192,"style":2945},[282],[128,30194,30195,30198],{"style":4935},[128,30196],{"className":30197,"style":291},[290],[128,30199,30201],{"className":30200},[299,300,301,298],[128,30202,2028],{"className":30203},[259,298],[128,30205,347],{"className":30206},[346],[128,30208,30210],{"className":30209},[278],[128,30211,30213],{"className":30212,"style":2241},[282],[128,30214],{}," 相对于样本量 ",[128,30217,30219,30232],{"className":30218,"translate":218},[217],[128,30220,30222],{"className":30221},[222],[224,30223,30224],{"xmlns":226},[228,30225,30226,30230],{},[231,30227,30228],{},[1795,30229,26691],{},[238,30231,26691],{"encoding":240},[128,30233,30235],{"className":30234,"ariaHidden":246},[245],[128,30236,30238,30241],{"className":30237},[250],[128,30239],{"className":30240,"style":283},[254],[128,30242,26691],{"className":30243,"style":26806},[259,1873]," 的大小，就是数据与先验的信任分配比例。",[128,30246,30248,30270],{"className":30247,"translate":218},[217],[128,30249,30251],{"className":30250},[222],[224,30252,30253],{"xmlns":226},[228,30254,30255,30267],{},[231,30256,30257,30263,30265],{},[2016,30258,30259,30261],{},[1795,30260,4835],{},[1795,30262,2801],{},[1832,30264,1994],{},[1840,30266,1842],{},[238,30268,30269],{"encoding":240},"\\alpha_i = 1",[128,30271,30273,30328],{"className":30272,"ariaHidden":246},[245],[128,30274,30276,30279,30319,30322,30325],{"className":30275},[250],[128,30277],{"className":30278,"style":4242},[254],[128,30280,30282,30285],{"className":30281},[259],[128,30283,4835],{"className":30284,"style":4920},[259,1873],[128,30286,30288],{"className":30287},[2087],[128,30289,30291,30311],{"className":30290},[274,321],[128,30292,30294,30308],{"className":30293},[278],[128,30295,30297],{"className":30296,"style":3095},[282],[128,30298,30299,30302],{"style":4935},[128,30300],{"className":30301,"style":291},[290],[128,30303,30305],{"className":30304},[299,300,301,298],[128,30306,2801],{"className":30307},[259,1873,298],[128,30309,347],{"className":30310},[346],[128,30312,30314],{"className":30313},[278],[128,30315,30317],{"className":30316,"style":2241},[282],[128,30318],{},[128,30320],{"className":30321,"style":1878},[269],[128,30323,1994],{"className":30324},[1882],[128,30326],{"className":30327,"style":1878},[269],[128,30329,30331,30334],{"className":30330},[250],[128,30332],{"className":30333,"style":2594},[254],[128,30335,1842],{"className":30336},[259]," 得 Laplace 平滑，取 ",[128,30339,30341,30362],{"className":30340,"translate":218},[217],[128,30342,30344],{"className":30343},[222],[224,30345,30346],{"xmlns":226},[228,30347,30348,30360],{},[231,30349,30350,30356,30358],{},[2016,30351,30352,30354],{},[1795,30353,4835],{},[1795,30355,2801],{},[1832,30357,3321],{},[1840,30359,1842],{},[238,30361,23433],{"encoding":240},[128,30363,30365,30420],{"className":30364,"ariaHidden":246},[245],[128,30366,30368,30371,30411,30414,30417],{"className":30367},[250],[128,30369],{"className":30370,"style":3484},[254],[128,30372,30374,30377],{"className":30373},[259],[128,30375,4835],{"className":30376,"style":4920},[259,1873],[128,30378,30380],{"className":30379},[2087],[128,30381,30383,30403],{"className":30382},[274,321],[128,30384,30386,30400],{"className":30385},[278],[128,30387,30389],{"className":30388,"style":3095},[282],[128,30390,30391,30394],{"style":4935},[128,30392],{"className":30393,"style":291},[290],[128,30395,30397],{"className":30396},[299,300,301,298],[128,30398,2801],{"className":30399},[259,1873,298],[128,30401,347],{"className":30402},[346],[128,30404,30406],{"className":30405},[278],[128,30407,30409],{"className":30408,"style":2241},[282],[128,30410],{},[128,30412],{"className":30413,"style":1878},[269],[128,30415,3321],{"className":30416},[1882],[128,30418],{"className":30419,"style":1878},[269],[128,30421,30423,30426],{"className":30422},[250],[128,30424],{"className":30425,"style":2594},[254],[128,30427,1842],{"className":30428},[259]," 得 Lidstone 平滑，取 ",[128,30431,30433,30455],{"className":30432,"translate":218},[217],[128,30434,30436],{"className":30435},[222],[224,30437,30438],{"xmlns":226},[228,30439,30440,30452],{},[231,30441,30442,30448,30450],{},[2016,30443,30444,30446],{},[1795,30445,4835],{},[1795,30447,2801],{},[1832,30449,22419],{},[1840,30451,2028],{},[238,30453,30454],{"encoding":240},"\\alpha_i \\to 0",[128,30456,30458,30513],{"className":30457,"ariaHidden":246},[245],[128,30459,30461,30464,30504,30507,30510],{"className":30460},[250],[128,30462],{"className":30463,"style":4242},[254],[128,30465,30467,30470],{"className":30466},[259],[128,30468,4835],{"className":30469,"style":4920},[259,1873],[128,30471,30473],{"className":30472},[2087],[128,30474,30476,30496],{"className":30475},[274,321],[128,30477,30479,30493],{"className":30478},[278],[128,30480,30482],{"className":30481,"style":3095},[282],[128,30483,30484,30487],{"style":4935},[128,30485],{"className":30486,"style":291},[290],[128,30488,30490],{"className":30489},[299,300,301,298],[128,30491,2801],{"className":30492},[259,1873,298],[128,30494,347],{"className":30495},[346],[128,30497,30499],{"className":30498},[278],[128,30500,30502],{"className":30501,"style":2241},[282],[128,30503],{},[128,30505],{"className":30506,"style":1878},[269],[128,30508,22419],{"className":30509},[1882],[128,30511],{"className":30512,"style":1878},[269],[128,30514,30516,30519],{"className":30515},[250],[128,30517],{"className":30518,"style":2594},[254],[128,30520,2028],{"className":30521},[259]," 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。",[2610,30524,30526],{"id":30525},"_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",[2615,30528,30530],{"title":30529},"命题 2.8（聚合性）",[11,30531,1781,30532,2674,30608,3637,30762,30830,30831,31074,31075,7713,31153,893],{},[128,30533,30535,30560],{"className":30534,"translate":218},[217],[128,30536,30538],{"className":30537},[222],[224,30539,30540],{"xmlns":226},[228,30541,30542,30558],{},[231,30543,30544,30546,30548,30550,30552,30554,30556],{},[1795,30545,2760],{"mathvariant":2001},[1832,30547,5911],{},[1795,30549,5914],{"mathvariant":1981},[1832,30551,3278],{},[1832,30553,2477],{"stretchy":1837},[1795,30555,4835],{"mathvariant":4834},[1832,30557,2486],{"stretchy":1837},[238,30559,5925],{"encoding":240},[128,30561,30563,30581],{"className":30562,"ariaHidden":246},[245],[128,30564,30566,30569,30572,30575,30578],{"className":30565},[250],[128,30567],{"className":30568,"style":4439},[254],[128,30570,2760],{"className":30571},[259,2151],[128,30573],{"className":30574,"style":1878},[269],[128,30576,5911],{"className":30577},[1882],[128,30579],{"className":30580,"style":1878},[269],[128,30582,30584,30587,30593,30596,30605],{"className":30583},[250],[128,30585],{"className":30586,"style":1892},[254],[128,30588,30590],{"className":30589},[2268],[128,30591,5914],{"className":30592},[259,3353],[128,30594,2477],{"className":30595},[1896],[128,30597,30599],{"className":30598},[259],[128,30600,30602],{"className":30601},[259],[128,30603,4835],{"className":30604},[259,4895],[128,30606,2486],{"className":30607},[1928],[128,30609,30611,30647],{"className":30610,"translate":218},[217],[128,30612,30614],{"className":30613},[222],[224,30615,30616],{"xmlns":226},[228,30617,30618,30644],{},[231,30619,30620,30622,30629,30631,30633,30635,30642],{},[1832,30621,1838],{"stretchy":1837},[2016,30623,30624,30627],{},[1795,30625,30626],{},"I",[1840,30628,1842],{},[1832,30630,1845],{"separator":246},[1832,30632,1848],{},[1832,30634,1845],{"separator":246},[2016,30636,30637,30639],{},[1795,30638,30626],{},[1795,30640,30641],{},"M",[1832,30643,1856],{"stretchy":1837},[238,30645,30646],{"encoding":240},"\\{I_1, \\dots, I_M\\}",[128,30648,30650],{"className":30649,"ariaHidden":246},[245],[128,30651,30653,30656,30659,30701,30704,30707,30710,30713,30716,30719,30759],{"className":30652},[250],[128,30654],{"className":30655,"style":1892},[254],[128,30657,1838],{"className":30658},[1896],[128,30660,30662,30666],{"className":30661},[259],[128,30663,30626],{"className":30664,"style":30665},[259,1873],"margin-right:0.0785em;",[128,30667,30669],{"className":30668},[2087],[128,30670,30672,30693],{"className":30671},[274,321],[128,30673,30675,30690],{"className":30674},[278],[128,30676,30678],{"className":30677,"style":2945},[282],[128,30679,30681,30684],{"style":30680},"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;",[128,30682],{"className":30683,"style":291},[290],[128,30685,30687],{"className":30686},[299,300,301,298],[128,30688,1842],{"className":30689},[259,298],[128,30691,347],{"className":30692},[346],[128,30694,30696],{"className":30695},[278],[128,30697,30699],{"className":30698,"style":2241},[282],[128,30700],{},[128,30702,1845],{"className":30703},[1903],[128,30705],{"className":30706,"style":1907},[269],[128,30708,1848],{"className":30709},[1911],[128,30711],{"className":30712,"style":1907},[269],[128,30714,1845],{"className":30715},[1903],[128,30717],{"className":30718,"style":1907},[269],[128,30720,30722,30725],{"className":30721},[259],[128,30723,30626],{"className":30724,"style":30665},[259,1873],[128,30726,30728],{"className":30727},[2087],[128,30729,30731,30751],{"className":30730},[274,321],[128,30732,30734,30748],{"className":30733},[278],[128,30735,30737],{"className":30736,"style":3004},[282],[128,30738,30739,30742],{"style":30680},[128,30740],{"className":30741,"style":291},[290],[128,30743,30745],{"className":30744},[299,300,301,298],[128,30746,30641],{"className":30747,"style":26806},[259,1873,298],[128,30749,347],{"className":30750},[346],[128,30752,30754],{"className":30753},[278],[128,30755,30757],{"className":30756,"style":2241},[282],[128,30758],{},[128,30760,1856],{"className":30761},[1928],[128,30763,30765,30791],{"className":30764,"translate":218},[217],[128,30766,30768],{"className":30767},[222],[224,30769,30770],{"xmlns":226},[228,30771,30772,30788],{},[231,30773,30774,30776,30778,30780,30782,30784,30786],{},[1832,30775,1838],{"stretchy":1837},[1840,30777,1842],{},[1832,30779,1845],{"separator":246},[1832,30781,1848],{},[1832,30783,1845],{"separator":246},[1795,30785,1853],{},[1832,30787,1856],{"stretchy":1837},[238,30789,30790],{"encoding":240},"\\{1, \\dots, K\\}",[128,30792,30794],{"className":30793,"ariaHidden":246},[245],[128,30795,30797,30800,30803,30806,30809,30812,30815,30818,30821,30824,30827],{"className":30796},[250],[128,30798],{"className":30799,"style":1892},[254],[128,30801,1838],{"className":30802},[1896],[128,30804,1842],{"className":30805},[259],[128,30807,1845],{"className":30808},[1903],[128,30810],{"className":30811,"style":1907},[269],[128,30813,1848],{"className":30814},[1911],[128,30816],{"className":30817,"style":1907},[269],[128,30819,1845],{"className":30820},[1903],[128,30822],{"className":30823,"style":1907},[269],[128,30825,1853],{"className":30826,"style":1924},[259,1873],[128,30828,1856],{"className":30829},[1928]," 的一个划分。令 ",[128,30832,30834,30877],{"className":30833,"translate":218},[217],[128,30835,30837],{"className":30836},[222],[224,30838,30839],{"xmlns":226},[228,30840,30841,30874],{},[231,30842,30843,30850,30852,30868],{},[2016,30844,30845,30847],{},[1795,30846,1830],{},[1795,30848,30849],{},"m",[1832,30851,1994],{},[2016,30853,30854,30856],{},[1832,30855,2042],{},[231,30857,30858,30860,30862],{},[1795,30859,2801],{},[1832,30861,1834],{},[2016,30863,30864,30866],{},[1795,30865,30626],{},[1795,30867,30849],{},[2016,30869,30870,30872],{},[1795,30871,2760],{},[1795,30873,2801],{},[238,30875,30876],{"encoding":240},"y_m = \\sum_{i \\in I_m} x_i",[128,30878,30880,30935],{"className":30879,"ariaHidden":246},[245],[128,30881,30883,30886,30926,30929,30932],{"className":30882},[250],[128,30884],{"className":30885,"style":11158},[254],[128,30887,30889,30892],{"className":30888},[259],[128,30890,1830],{"className":30891,"style":1874},[259,1873],[128,30893,30895],{"className":30894},[2087],[128,30896,30898,30918],{"className":30897},[274,321],[128,30899,30901,30915],{"className":30900},[278],[128,30902,30904],{"className":30903,"style":28738},[282],[128,30905,30906,30909],{"style":28741},[128,30907],{"className":30908,"style":291},[290],[128,30910,30912],{"className":30911},[299,300,301,298],[128,30913,30849],{"className":30914},[259,1873,298],[128,30916,347],{"className":30917},[346],[128,30919,30921],{"className":30920},[278],[128,30922,30924],{"className":30923,"style":2241},[282],[128,30925],{},[128,30927],{"className":30928,"style":1878},[269],[128,30930,1994],{"className":30931},[1882],[128,30933],{"className":30934,"style":1878},[269],[128,30936,30938,30942,31031,31034],{"className":30937},[250],[128,30939],{"className":30940,"style":30941},[254],"height:1.1498em;vertical-align:-0.3998em;",[128,30943,30945,30948],{"className":30944},[2268],[128,30946,2042],{"className":30947,"style":2274},[2268,2272,2273],[128,30949,30951],{"className":30950},[2087],[128,30952,30954,31022],{"className":30953},[274,321],[128,30955,30957,31019],{"className":30956},[278],[128,30958,30960],{"className":30959,"style":4336},[282],[128,30961,30962,30965],{"style":2290},[128,30963],{"className":30964,"style":291},[290],[128,30966,30968],{"className":30967},[299,300,301,298],[128,30969,30971,30974,30977],{"className":30970},[259,298],[128,30972,2801],{"className":30973},[259,1873,298],[128,30975,1834],{"className":30976},[1882,298],[128,30978,30980,30983],{"className":30979},[259,298],[128,30981,30626],{"className":30982,"style":30665},[259,1873,298],[128,30984,30986],{"className":30985},[2087],[128,30987,30989,31011],{"className":30988},[274,321],[128,30990,30992,31008],{"className":30991},[278],[128,30993,30996],{"className":30994,"style":30995},[282],"height:0.1645em;",[128,30997,30999,31002],{"style":30998},"top:-2.357em;margin-left:-0.0785em;margin-right:0.0714em;",[128,31000],{"className":31001,"style":5790},[290],[128,31003,31005],{"className":31004},[299,5794,5795,298],[128,31006,30849],{"className":31007},[259,1873,298],[128,31009,347],{"className":31010},[346],[128,31012,31014],{"className":31013},[278],[128,31015,31017],{"className":31016,"style":5808},[282],[128,31018],{},[128,31020,347],{"className":31021},[346],[128,31023,31025],{"className":31024},[278],[128,31026,31029],{"className":31027,"style":31028},[282],"height:0.3998em;",[128,31030],{},[128,31032],{"className":31033,"style":1907},[269],[128,31035,31037,31040],{"className":31036},[259],[128,31038,2760],{"className":31039},[259,1873],[128,31041,31043],{"className":31042},[2087],[128,31044,31046,31066],{"className":31045},[274,321],[128,31047,31049,31063],{"className":31048},[278],[128,31050,31052],{"className":31051,"style":3095},[282],[128,31053,31054,31057],{"style":2221},[128,31055],{"className":31056,"style":291},[290],[128,31058,31060],{"className":31059},[299,300,301,298],[128,31061,2801],{"className":31062},[259,1873,298],[128,31064,347],{"className":31065},[346],[128,31067,31069],{"className":31068},[278],[128,31070,31072],{"className":31071,"style":2241},[282],[128,31073],{},"，则 ",[128,31076,31078,31104],{"className":31077,"translate":218},[217],[128,31079,31081],{"className":31080},[222],[224,31082,31083],{"xmlns":226},[228,31084,31085,31101],{},[231,31086,31087,31089,31091,31093,31095,31097,31099],{},[1795,31088,1830],{"mathvariant":2001},[1832,31090,5911],{},[1795,31092,5914],{"mathvariant":1981},[1832,31094,3278],{},[1832,31096,2477],{"stretchy":1837},[1795,31098,18848],{"mathvariant":4834},[1832,31100,2486],{"stretchy":1837},[238,31102,31103],{"encoding":240},"\\mathbf{y} \\sim \\operatorname{Dir}(\\boldsymbol{\\beta})",[128,31105,31107,31126],{"className":31106,"ariaHidden":246},[245],[128,31108,31110,31113,31117,31120,31123],{"className":31109},[250],[128,31111],{"className":31112,"style":2564},[254],[128,31114,1830],{"className":31115,"style":31116},[259,2151],"margin-right:0.016em;",[128,31118],{"className":31119,"style":1878},[269],[128,31121,5911],{"className":31122},[1882],[128,31124],{"className":31125,"style":1878},[269],[128,31127,31129,31132,31138,31141,31150],{"className":31128},[250],[128,31130],{"className":31131,"style":1892},[254],[128,31133,31135],{"className":31134},[2268],[128,31136,5914],{"className":31137},[259,3353],[128,31139,2477],{"className":31140},[1896],[128,31142,31144],{"className":31143},[259],[128,31145,31147],{"className":31146},[259],[128,31148,18848],{"className":31149,"style":19091},[259,4895],[128,31151,2486],{"className":31152},[1928],[128,31154,31156,31198],{"className":31155,"translate":218},[217],[128,31157,31159],{"className":31158},[222],[224,31160,31161],{"xmlns":226},[228,31162,31163,31195],{},[231,31164,31165,31171,31173,31189],{},[2016,31166,31167,31169],{},[1795,31168,18848],{},[1795,31170,30849],{},[1832,31172,1994],{},[2016,31174,31175,31177],{},[1832,31176,2042],{},[231,31178,31179,31181,31183],{},[1795,31180,2801],{},[1832,31182,1834],{},[2016,31184,31185,31187],{},[1795,31186,30626],{},[1795,31188,30849],{},[2016,31190,31191,31193],{},[1795,31192,4835],{},[1795,31194,2801],{},[238,31196,31197],{"encoding":240},"\\beta_m = \\sum_{i \\in I_m} \\alpha_i",[128,31199,31201,31256],{"className":31200,"ariaHidden":246},[245],[128,31202,31204,31207,31247,31250,31253],{"className":31203},[250],[128,31205],{"className":31206,"style":16030},[254],[128,31208,31210,31213],{"className":31209},[259],[128,31211,18848],{"className":31212,"style":18987},[259,1873],[128,31214,31216],{"className":31215},[2087],[128,31217,31219,31239],{"className":31218},[274,321],[128,31220,31222,31236],{"className":31221},[278],[128,31223,31225],{"className":31224,"style":28738},[282],[128,31226,31227,31230],{"style":19171},[128,31228],{"className":31229,"style":291},[290],[128,31231,31233],{"className":31232},[299,300,301,298],[128,31234,30849],{"className":31235},[259,1873,298],[128,31237,347],{"className":31238},[346],[128,31240,31242],{"className":31241},[278],[128,31243,31245],{"className":31244,"style":2241},[282],[128,31246],{},[128,31248],{"className":31249,"style":1878},[269],[128,31251,1994],{"className":31252},[1882],[128,31254],{"className":31255,"style":1878},[269],[128,31257,31259,31262,31348,31351],{"className":31258},[250],[128,31260],{"className":31261,"style":30941},[254],[128,31263,31265,31268],{"className":31264},[2268],[128,31266,2042],{"className":31267,"style":2274},[2268,2272,2273],[128,31269,31271],{"className":31270},[2087],[128,31272,31274,31340],{"className":31273},[274,321],[128,31275,31277,31337],{"className":31276},[278],[128,31278,31280],{"className":31279,"style":4336},[282],[128,31281,31282,31285],{"style":2290},[128,31283],{"className":31284,"style":291},[290],[128,31286,31288],{"className":31287},[299,300,301,298],[128,31289,31291,31294,31297],{"className":31290},[259,298],[128,31292,2801],{"className":31293},[259,1873,298],[128,31295,1834],{"className":31296},[1882,298],[128,31298,31300,31303],{"className":31299},[259,298],[128,31301,30626],{"className":31302,"style":30665},[259,1873,298],[128,31304,31306],{"className":31305},[2087],[128,31307,31309,31329],{"className":31308},[274,321],[128,31310,31312,31326],{"className":31311},[278],[128,31313,31315],{"className":31314,"style":30995},[282],[128,31316,31317,31320],{"style":30998},[128,31318],{"className":31319,"style":5790},[290],[128,31321,31323],{"className":31322},[299,5794,5795,298],[128,31324,30849],{"className":31325},[259,1873,298],[128,31327,347],{"className":31328},[346],[128,31330,31332],{"className":31331},[278],[128,31333,31335],{"className":31334,"style":5808},[282],[128,31336],{},[128,31338,347],{"className":31339},[346],[128,31341,31343],{"className":31342},[278],[128,31344,31346],{"className":31345,"style":31028},[282],[128,31347],{},[128,31349],{"className":31350,"style":1907},[269],[128,31352,31354,31357],{"className":31353},[259],[128,31355,4835],{"className":31356,"style":4920},[259,1873],[128,31358,31360],{"className":31359},[2087],[128,31361,31363,31383],{"className":31362},[274,321],[128,31364,31366,31380],{"className":31365},[278],[128,31367,31369],{"className":31368,"style":3095},[282],[128,31370,31371,31374],{"style":4935},[128,31372],{"className":31373,"style":291},[290],[128,31375,31377],{"className":31376},[299,300,301,298],[128,31378,2801],{"className":31379},[259,1873,298],[128,31381,347],{"className":31382},[346],[128,31384,31386],{"className":31385},[278],[128,31387,31389],{"className":31388,"style":2241},[282],[128,31390],{},[11,31392,31393,31394,31397],{},"聚合性说明迪利克雷族在",[35,31395,31396],{},"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。",[11,31399,31400,31401,31404,31405,2674,31433,31503,31504,31759,31760,31867,31868,32138],{},"由聚合性可导出",[35,31402,31403],{},"中立性（neutrality）","：对任意 ",[128,31406,31408,31421],{"className":31407,"translate":218},[217],[128,31409,31411],{"className":31410},[222],[224,31412,31413],{"xmlns":226},[228,31414,31415,31419],{},[231,31416,31417],{},[1795,31418,2022],{},[238,31420,2022],{"encoding":240},[128,31422,31424],{"className":31423,"ariaHidden":246},[245],[128,31425,31427,31430],{"className":31426},[250],[128,31428],{"className":31429,"style":12173},[254],[128,31431,2022],{"className":31432,"style":2231},[259,1873],[128,31434,31436,31454],{"className":31435,"translate":218},[217],[128,31437,31439],{"className":31438},[222],[224,31440,31441],{"xmlns":226},[228,31442,31443,31451],{},[231,31444,31445],{},[2016,31446,31447,31449],{},[1795,31448,2760],{},[1795,31450,2022],{},[238,31452,31453],{"encoding":240},"x_k",[128,31455,31457],{"className":31456,"ariaHidden":246},[245],[128,31458,31460,31463],{"className":31459},[250],[128,31461],{"className":31462,"style":4242},[254],[128,31464,31466,31469],{"className":31465},[259],[128,31467,2760],{"className":31468},[259,1873],[128,31470,31472],{"className":31471},[2087],[128,31473,31475,31495],{"className":31474},[274,321],[128,31476,31478,31492],{"className":31477},[278],[128,31479,31481],{"className":31480,"style":2218},[282],[128,31482,31483,31486],{"style":2221},[128,31484],{"className":31485,"style":291},[290],[128,31487,31489],{"className":31488},[299,300,301,298],[128,31490,2022],{"className":31491,"style":2231},[259,1873,298],[128,31493,347],{"className":31494},[346],[128,31496,31498],{"className":31497},[278],[128,31499,31501],{"className":31500,"style":2241},[282],[128,31502],{}," 与其余分量的归一化版本 ",[128,31505,31507,31557],{"className":31506,"translate":218},[217],[128,31508,31510],{"className":31509},[222],[224,31511,31512],{"xmlns":226},[228,31513,31514,31554],{},[231,31515,31516],{},[2016,31517,31518,31546],{},[231,31519,31520,31522,31528,31530,31532,31534,31536,31542,31544],{},[1832,31521,2477],{"fence":246},[2016,31523,31524,31526],{},[1795,31525,2760],{},[1795,31527,2801],{},[1795,31529,4751],{"mathvariant":1981},[1832,31531,2477],{"stretchy":1837},[1840,31533,1842],{},[1832,31535,1989],{},[2016,31537,31538,31540],{},[1795,31539,2760],{},[1795,31541,2022],{},[1832,31543,2486],{"stretchy":1837},[1832,31545,2486],{"fence":246},[231,31547,31548,31550,31552],{},[1795,31549,2801],{},[1832,31551,16716],{"mathvariant":1981},[1795,31553,2022],{},[238,31555,31556],{"encoding":240},"\\left(x_i\u002F(1-x_k)\\right)_{i \\ne k}",[128,31558,31560],{"className":31559,"ariaHidden":246},[245],[128,31561,31563,31567],{"className":31562},[250],[128,31564],{"className":31565,"style":31566},[254],"height:1.1858em;vertical-align:-0.4358em;",[128,31568,31570,31680],{"className":31569},[1911],[128,31571,31573,31576,31616,31619,31622,31625,31628,31631,31634,31674,31677],{"className":31572},[1911],[128,31574,2477],{"className":31575,"style":2142},[1896,2141],[128,31577,31579,31582],{"className":31578},[259],[128,31580,2760],{"className":31581},[259,1873],[128,31583,31585],{"className":31584},[2087],[128,31586,31588,31608],{"className":31587},[274,321],[128,31589,31591,31605],{"className":31590},[278],[128,31592,31594],{"className":31593,"style":3095},[282],[128,31595,31596,31599],{"style":2221},[128,31597],{"className":31598,"style":291},[290],[128,31600,31602],{"className":31601},[299,300,301,298],[128,31603,2801],{"className":31604},[259,1873,298],[128,31606,347],{"className":31607},[346],[128,31609,31611],{"className":31610},[278],[128,31612,31614],{"className":31613,"style":2241},[282],[128,31615],{},[128,31617,4751],{"className":31618},[259],[128,31620,2477],{"className":31621},[1896],[128,31623,1842],{"className":31624},[259],[128,31626],{"className":31627,"style":2508},[269],[128,31629,1989],{"className":31630},[2115],[128,31632],{"className":31633,"style":2508},[269],[128,31635,31637,31640],{"className":31636},[259],[128,31638,2760],{"className":31639},[259,1873],[128,31641,31643],{"className":31642},[2087],[128,31644,31646,31666],{"className":31645},[274,321],[128,31647,31649,31663],{"className":31648},[278],[128,31650,31652],{"className":31651,"style":2218},[282],[128,31653,31654,31657],{"style":2221},[128,31655],{"className":31656,"style":291},[290],[128,31658,31660],{"className":31659},[299,300,301,298],[128,31661,2022],{"className":31662,"style":2231},[259,1873,298],[128,31664,347],{"className":31665},[346],[128,31667,31669],{"className":31668},[278],[128,31670,31672],{"className":31671,"style":2241},[282],[128,31673],{},[128,31675,2486],{"className":31676},[1928],[128,31678,2486],{"className":31679,"style":2142},[1928,2141],[128,31681,31683],{"className":31682},[2087],[128,31684,31686,31750],{"className":31685},[274,321],[128,31687,31689,31747],{"className":31688},[278],[128,31690,31693],{"className":31691,"style":31692},[282],"height:0.1864em;",[128,31694,31696,31699],{"style":31695},"top:-2.4003em;margin-right:0.05em;",[128,31697],{"className":31698,"style":291},[290],[128,31700,31702],{"className":31701},[299,300,301,298],[128,31703,31705,31708,31744],{"className":31704},[259,298],[128,31706,2801],{"className":31707},[259,1873,298],[128,31709,31711,31738,31741],{"className":31710},[1882,298],[128,31712,31714],{"className":31713},[1882,298],[128,31715,31717],{"className":31716},[259,17719,298],[128,31718,31720],{"className":31719},[17723,298],[128,31721,31723,31726,31735],{"className":31722},[17727,298],[128,31724],{"className":31725,"style":16030},[254],[128,31727,31729],{"className":31728},[17734],[128,31730,31732],{"className":31731},[259,298],[128,31733,17741],{"className":31734},[1882,298],[128,31736],{"className":31737},[17745],[128,31739],{"className":31740},[269,17749,298],[128,31742,1994],{"className":31743},[1882,298],[128,31745,2022],{"className":31746,"style":2231},[259,1873,298],[128,31748,347],{"className":31749},[346],[128,31751,31753],{"className":31752},[278],[128,31754,31757],{"className":31755,"style":31756},[282],"height:0.4358em;",[128,31758],{}," 相互独立，且后者服从 ",[128,31761,31763,31793],{"className":31762,"translate":218},[217],[128,31764,31766],{"className":31765},[222],[224,31767,31768],{"xmlns":226},[228,31769,31770,31790],{},[231,31771,31772,31774,31776,31778,31788],{},[1795,31773,5914],{"mathvariant":1981},[1832,31775,3278],{},[1832,31777,2477],{"stretchy":1837},[2016,31779,31780,31782],{},[1795,31781,4835],{"mathvariant":4834},[231,31783,31784,31786],{},[1832,31785,1989],{},[1795,31787,2022],{},[1832,31789,2486],{"stretchy":1837},[238,31791,31792],{"encoding":240},"\\operatorname{Dir}(\\boldsymbol{\\alpha}_{-k})",[128,31794,31796],{"className":31795,"ariaHidden":246},[245],[128,31797,31799,31802,31808,31811,31864],{"className":31798},[250],[128,31800],{"className":31801,"style":1892},[254],[128,31803,31805],{"className":31804},[2268],[128,31806,5914],{"className":31807},[259,3353],[128,31809,2477],{"className":31810},[1896],[128,31812,31814,31823],{"className":31813},[259],[128,31815,31817],{"className":31816},[259],[128,31818,31820],{"className":31819},[259],[128,31821,4835],{"className":31822},[259,4895],[128,31824,31826],{"className":31825},[2087],[128,31827,31829,31856],{"className":31828},[274,321],[128,31830,31832,31853],{"className":31831},[278],[128,31833,31835],{"className":31834,"style":2218},[282],[128,31836,31838,31841],{"style":31837},"top:-2.55em;margin-right:0.05em;",[128,31839],{"className":31840,"style":291},[290],[128,31842,31844],{"className":31843},[299,300,301,298],[128,31845,31847,31850],{"className":31846},[259,298],[128,31848,1989],{"className":31849},[259,298],[128,31851,2022],{"className":31852,"style":2231},[259,1873,298],[128,31854,347],{"className":31855},[346],[128,31857,31859],{"className":31858},[278],[128,31860,31862],{"className":31861,"style":4183},[282],[128,31863],{},[128,31865,2486],{"className":31866},[1928]," 而 ",[128,31869,31871,31921],{"className":31870,"translate":218},[217],[128,31872,31874],{"className":31873},[222],[224,31875,31876],{"xmlns":226},[228,31877,31878,31918],{},[231,31879,31880,31886,31888,31890,31892,31894,31900,31902,31908,31910,31916],{},[2016,31881,31882,31884],{},[1795,31883,2760],{},[1795,31885,2022],{},[1832,31887,5911],{},[1795,31889,14677],{"mathvariant":1981},[1832,31891,3278],{},[1832,31893,2477],{"stretchy":1837},[2016,31895,31896,31898],{},[1795,31897,4835],{},[1795,31899,2022],{},[1832,31901,1845],{"separator":246},[2016,31903,31904,31906],{},[1795,31905,4835],{},[1840,31907,2028],{},[1832,31909,1989],{},[2016,31911,31912,31914],{},[1795,31913,4835],{},[1795,31915,2022],{},[1832,31917,2486],{"stretchy":1837},[238,31919,31920],{"encoding":240},"x_k \\sim \\operatorname{Beta}(\\alpha_k, \\alpha_0 - \\alpha_k)",[128,31922,31924,31979,32089],{"className":31923,"ariaHidden":246},[245],[128,31925,31927,31930,31970,31973,31976],{"className":31926},[250],[128,31928],{"className":31929,"style":4242},[254],[128,31931,31933,31936],{"className":31932},[259],[128,31934,2760],{"className":31935},[259,1873],[128,31937,31939],{"className":31938},[2087],[128,31940,31942,31962],{"className":31941},[274,321],[128,31943,31945,31959],{"className":31944},[278],[128,31946,31948],{"className":31947,"style":2218},[282],[128,31949,31950,31953],{"style":2221},[128,31951],{"className":31952,"style":291},[290],[128,31954,31956],{"className":31955},[299,300,301,298],[128,31957,2022],{"className":31958,"style":2231},[259,1873,298],[128,31960,347],{"className":31961},[346],[128,31963,31965],{"className":31964},[278],[128,31966,31968],{"className":31967,"style":2241},[282],[128,31969],{},[128,31971],{"className":31972,"style":1878},[269],[128,31974,5911],{"className":31975},[1882],[128,31977],{"className":31978,"style":1878},[269],[128,31980,31982,31985,31991,31994,32034,32037,32040,32080,32083,32086],{"className":31981},[250],[128,31983],{"className":31984,"style":1892},[254],[128,31986,31988],{"className":31987},[2268],[128,31989,14677],{"className":31990},[259,3353],[128,31992,2477],{"className":31993},[1896],[128,31995,31997,32000],{"className":31996},[259],[128,31998,4835],{"className":31999,"style":4920},[259,1873],[128,32001,32003],{"className":32002},[2087],[128,32004,32006,32026],{"className":32005},[274,321],[128,32007,32009,32023],{"className":32008},[278],[128,32010,32012],{"className":32011,"style":2218},[282],[128,32013,32014,32017],{"style":4935},[128,32015],{"className":32016,"style":291},[290],[128,32018,32020],{"className":32019},[299,300,301,298],[128,32021,2022],{"className":32022,"style":2231},[259,1873,298],[128,32024,347],{"className":32025},[346],[128,32027,32029],{"className":32028},[278],[128,32030,32032],{"className":32031,"style":2241},[282],[128,32033],{},[128,32035,1845],{"className":32036},[1903],[128,32038],{"className":32039,"style":1907},[269],[128,32041,32043,32046],{"className":32042},[259],[128,32044,4835],{"className":32045,"style":4920},[259,1873],[128,32047,32049],{"className":32048},[2087],[128,32050,32052,32072],{"className":32051},[274,321],[128,32053,32055,32069],{"className":32054},[278],[128,32056,32058],{"className":32057,"style":2945},[282],[128,32059,32060,32063],{"style":4935},[128,32061],{"className":32062,"style":291},[290],[128,32064,32066],{"className":32065},[299,300,301,298],[128,32067,2028],{"className":32068},[259,298],[128,32070,347],{"className":32071},[346],[128,32073,32075],{"className":32074},[278],[128,32076,32078],{"className":32077,"style":2241},[282],[128,32079],{},[128,32081],{"className":32082,"style":2508},[269],[128,32084,1989],{"className":32085},[2115],[128,32087],{"className":32088,"style":2508},[269],[128,32090,32092,32095,32135],{"className":32091},[250],[128,32093],{"className":32094,"style":1892},[254],[128,32096,32098,32101],{"className":32097},[259],[128,32099,4835],{"className":32100,"style":4920},[259,1873],[128,32102,32104],{"className":32103},[2087],[128,32105,32107,32127],{"className":32106},[274,321],[128,32108,32110,32124],{"className":32109},[278],[128,32111,32113],{"className":32112,"style":2218},[282],[128,32114,32115,32118],{"style":4935},[128,32116],{"className":32117,"style":291},[290],[128,32119,32121],{"className":32120},[299,300,301,298],[128,32122,2022],{"className":32123,"style":2231},[259,1873,298],[128,32125,347],{"className":32126},[346],[128,32128,32130],{"className":32129},[278],[128,32131,32133],{"className":32132,"style":2241},[282],[128,32134],{},[128,32136,2486],{"className":32137},[1928],"。反复施用中立性，得到如下构造性表示：",[2615,32140,32142],{"title":32141},"命题 2.9（stick-breaking 表示）",[11,32143,1781,32144,32435,32436,12056,32904,893],{},[128,32145,32147,32206],{"className":32146,"translate":218},[217],[128,32148,32150],{"className":32149},[222],[224,32151,32152],{"xmlns":226},[228,32153,32154,32203],{},[231,32155,32156,32163,32165,32167,32169,32171],{},[2016,32157,32158,32161],{},[1795,32159,32160],{},"v",[1795,32162,2022],{},[1832,32164,5911],{},[1795,32166,14677],{"mathvariant":1981},[1832,32168,3278],{},[234,32170,8524],{},[231,32172,32173,32175,32181,32183,32195,32201],{},[1832,32174,2477],{"fence":246},[2016,32176,32177,32179],{},[1795,32178,4835],{},[1795,32180,2022],{},[1832,32182,1845],{"separator":246},[2016,32184,32185,32187],{},[1832,32186,2042],{},[231,32188,32189,32191,32193],{},[1795,32190,16495],{},[1832,32192,3321],{},[1795,32194,2022],{},[2016,32196,32197,32199],{},[1795,32198,4835],{},[1795,32200,16495],{},[1832,32202,2486],{"fence":246},[238,32204,32205],{"encoding":240},"v_k \\sim \\operatorname{Beta}\\!\\left(\\alpha_k, \\sum_{j>k} 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相互独立。令\n",[128,32437,32439,32529],{"className":32438,"translate":218},[217],[128,32440,32442],{"className":32441},[222],[224,32443,32444],{"xmlns":226},[228,32445,32446,32526],{},[231,32447,32448,32454,32456,32462,32464,32466,32472,32474,32480,32492,32494,32496,32498,32504,32506,32508,32510,32512,32514,32516,32518,32520,32522,32524],{},[2016,32449,32450,32452],{},[1795,32451,2760],{},[1840,32453,1842],{},[1832,32455,1994],{},[2016,32457,32458,32460],{},[1795,32459,32160],{},[1840,32461,1842],{},[1832,32463,1845],{"separator":246},[269,32465],{"width":11568},[2016,32467,32468,32470],{},[1795,32469,2760],{},[1795,32471,2022],{},[1832,32473,1994],{},[2016,32475,32476,32478],{},[1795,32477,32160],{},[1795,32479,2022],{},[2016,32481,32482,32484],{},[1832,32483,5470],{},[231,32485,32486,32488,32490],{},[1795,32487,16495],{},[1832,32489,4221],{},[1795,32491,2022],{},[1832,32493,2477],{"stretchy":1837},[1840,32495,1842],{},[1832,32497,1989],{},[2016,32499,32500,32502],{},[1795,32501,32160],{},[1795,32503,16495],{},[1832,32505,2486],{"stretchy":1837},[269,32507],{"width":8176},[1832,32509,2477],{"stretchy":1837},[1795,32511,2022],{},[1832,32513,1994],{},[1840,32515,2639],{},[1832,32517,1845],{"separator":246},[1832,32519,1848],{},[1832,32521,1845],{"separator":246},[1795,32523,1853],{},[1832,32525,2486],{"stretchy":1837},[238,32527,32528],{"encoding":240},"x_1 = v_1, \\qquad x_k = v_k \\prod_{j \u003C k}(1 - v_j) \\quad (k = 2, \\dots, K)",[128,32530,32532,32587,32691,32804,32871],{"className":32531,"ariaHidden":246},[245],[128,32533,32535,32538,32578,32581,32584],{"className":32534},[250],[128,32536],{"className":32537,"style":4242},[254],[128,32539,32541,32544],{"className":32540},[259],[128,32542,2760],{"className":32543},[259,1873],[128,32545,32547],{"className":32546},[2087],[128,32548,32550,32570],{"className":32549},[274,321],[128,32551,32553,32567],{"className":32552},[278],[128,32554,32556],{"className":32555,"style":2945},[282],[128,32557,32558,32561],{"style":2221},[128,32559],{"className":32560,"style":291},[290],[128,32562,32564],{"className":32563},[299,300,301,298],[128,32565,1842],{"className":32566},[259,298],[128,32568,347],{"className":32569},[346],[128,32571,32573],{"className":32572},[278],[128,32574,32576],{"className":32575,"style":2241},[282],[128,32577],{},[128,32579],{"className":32580,"style":1878},[269],[128,32582,1994],{"className":32583},[1882],[128,32585],{"className":32586,"style":1878},[269],[128,32588,32590,32593,32633,32636,32639,32642,32682,32685,32688],{"className":32589},[250],[128,32591],{"className":32592,"style":11158},[254],[128,32594,32596,32599],{"className":32595},[259],[128,32597,32160],{"className":32598,"style":1874},[259,1873],[128,32600,32602],{"className":32601},[2087],[128,32603,32605,32625],{"className":32604},[274,321],[128,32606,32608,32622],{"className":32607},[278],[128,32609,32611],{"className":32610,"style":2945},[282],[128,32612,32613,32616],{"style":28741},[128,32614],{"className":32615,"style":291},[290],[128,32617,32619],{"className":32618},[299,300,301,298],[128,32620,1842],{"className":32621},[259,298],[128,32623,347],{"className":32624},[346],[128,32626,32628],{"className":32627},[278],[128,32629,32631],{"className":32630,"style":2241},[282],[128,32632],{},[128,32634,1845],{"className":32635},[1903],[128,32637],{"className":32638,"style":11756},[269],[128,32640],{"className":32641,"style":1907},[269],[128,32643,32645,32648],{"className":32644},[259],[128,32646,2760],{"className":32647},[259,1873],[128,32649,32651],{"className":32650},[2087],[128,32652,32654,32674],{"className":32653},[274,321],[128,32655,32657,32671],{"className":32656},[278],[128,32658,32660],{"className":32659,"style":2218},[282],[128,32661,32662,32665],{"style":2221},[128,32663],{"className":32664,"style":291},[290],[128,32666,32668],{"className":32667},[299,300,301,298],[128,32669,2022],{"className":32670,"style":2231},[259,1873,298],[128,32672,347],{"className":32673},[346],[128,32675,32677],{"className":32676},[278],[128,32678,32680],{"className":32679,"style":2241},[282],[128,32681],{},[128,32683],{"className":32684,"style":1878},[269],[128,32686,1994],{"className":32687},[1882],[128,32689],{"className":32690,"style":1878},[269],[128,32692,32694,32697,32737,32740,32789,32792,32795,32798,32801],{"className":32693},[250],[128,32695],{"className":32696,"style":31566},[254],[128,32698,32700,32703],{"className":32699},[259],[128,32701,32160],{"className":32702,"style":1874},[259,1873],[128,32704,32706],{"className":32705},[2087],[128,32707,32709,32729],{"className":32708},[274,321],[128,32710,32712,32726],{"className":32711},[278],[128,32713,32715],{"className":32714,"style":2218},[282],[128,32716,32717,32720],{"style":28741},[128,32718],{"className":32719,"style":291},[290],[128,32721,32723],{"className":32722},[299,300,301,298],[128,32724,2022],{"className":32725,"style":2231},[259,1873,298],[128,32727,347],{"className":32728},[346],[128,32730,32732],{"className":32731},[278],[128,32733,32735],{"className":32734,"style":2241},[282],[128,32736],{},[128,32738],{"className":32739,"style":1907},[269],[128,32741,32743,32746],{"className":32742},[2268],[128,32744,5470],{"className":32745,"style":2274},[2268,2272,2273],[128,32747,32749],{"className":32748},[2087],[128,32750,32752,32781],{"className":32751},[274,321],[128,32753,32755,32778],{"className":32754},[278],[128,32756,32758],{"className":32757,"style":31692},[282],[128,32759,32760,32763],{"style":2290},[128,32761],{"className":32762,"style":291},[290],[128,32764,32766],{"className":32765},[299,300,301,298],[128,32767,32769,32772,32775],{"className":32768},[259,298],[128,32770,16495],{"className":32771,"style":16521},[259,1873,298],[128,32773,4221],{"className":32774},[1882,298],[128,32776,2022],{"className":32777,"style":2231},[259,1873,298],[128,32779,347],{"className":32780},[346],[128,32782,32784],{"className":32783},[278],[128,32785,32787],{"className":32786,"style":31756},[282],[128,32788],{},[128,32790,2477],{"className":32791},[1896],[128,32793,1842],{"className":32794},[259],[128,32796],{"className":32797,"style":2508},[269],[128,32799,1989],{"className":32800},[2115],[128,32802],{"className":32803,"style":2508},[269],[128,32805,32807,32810,32850,32853,32856,32859,32862,32865,32868],{"className":32806},[250],[128,32808],{"className":32809,"style":19704},[254],[128,32811,32813,32816],{"className":32812},[259],[128,32814,32160],{"className":32815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\\dots, x_K) \\sim \\operatorname{Dir}(\\boldsymbol{\\alpha})",[128,32954,32956,33075],{"className":32955,"ariaHidden":246},[245],[128,32957,32959,32962,32965,33005,33008,33011,33014,33017,33020,33023,33063,33066,33069,33072],{"className":32958},[250],[128,32960],{"className":32961,"style":1892},[254],[128,32963,2477],{"className":32964},[1896],[128,32966,32968,32971],{"className":32967},[259],[128,32969,2760],{"className":32970},[259,1873],[128,32972,32974],{"className":32973},[2087],[128,32975,32977,32997],{"className":32976},[274,321],[128,32978,32980,32994],{"className":32979},[278],[128,32981,32983],{"className":32982,"style":2945},[282],[128,32984,32985,32988],{"style":2221},[128,32986],{"className":32987,"style":291},[290],[128,32989,32991],{"className":32990},[299,300,301,298],[128,32992,1842],{"className":32993},[259,298],[128,32995,347],{"className":32996},[346],[128,32998,33000],{"className":32999},[278],[128,33001,33003],{"className":33002,"style":2241},[282],[128,33004],{},[128,33006,1845],{"className":33007},[1903],[128,33009],{"className":33010,"style":1907},[269],[128,33012,1848],{"className":33013},[1911],[128,33015],{"className":33016,"style":1907},[269],[128,33018,1845],{"className":33019},[1903],[128,33021],{"className":33022,"style":1907},[269],[128,33024,33026,33029],{"className":33025},[259],[128,33027,2760],{"className":33028},[259,1873],[128,33030,33032],{"className":33031},[2087],[128,33033,33035,33055],{"className":33034},[274,321],[128,33036,33038,33052],{"className":33037},[278],[128,33039,33041],{"className":33040,"style":3004},[282],[128,33042,33043,33046],{"style":2221},[128,33044],{"className":33045,"style":291},[290],[128,33047,33049],{"className":33048},[299,300,301,298],[128,33050,1853],{"className":33051,"style":1924},[259,1873,298],[128,33053,347],{"className":33054},[346],[128,33056,33058],{"className":33057},[278],[128,33059,33061],{"className":33060,"style":2241},[282],[128,33062],{},[128,33064,2486],{"className":33065},[1928],[128,33067],{"className":33068,"style":1878},[269],[128,33070,5911],{"className":33071},[1882],[128,33073],{"className":33074,"style":1878},[269],[128,33076,33078,33081,33087,33090,33099],{"className":33077},[250],[128,33079],{"className":33080,"style":1892},[254],[128,33082,33084],{"className":33083},[2268],[128,33085,5914],{"className":33086},[259,3353],[128,33088,2477],{"className":33089},[1896],[128,33091,33093],{"className":33092},[259],[128,33094,33096],{"className":33095},[259],[128,33097,4835],{"className":33098},[259,4895],[128,33100,2486],{"className":33101},[1928],[11,33103,33104,33105,33133,33134,33204],{},"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 ",[128,33106,33108,33121],{"className":33107,"translate":218},[217],[128,33109,33111],{"className":33110},[222],[224,33112,33113],{"xmlns":226},[228,33114,33115,33119],{},[231,33116,33117],{},[1840,33118,1842],{},[238,33120,1842],{"encoding":240},[128,33122,33124],{"className":33123,"ariaHidden":246},[245],[128,33125,33127,33130],{"className":33126},[250],[128,33128],{"className":33129,"style":2594},[254],[128,33131,1842],{"className":33132},[259]," 的木棍中依次折断出比例 ",[128,33135,33137,33155],{"className":33136,"translate":218},[217],[128,33138,33140],{"className":33139},[222],[224,33141,33142],{"xmlns":226},[228,33143,33144,33152],{},[231,33145,33146],{},[2016,33147,33148,33150],{},[1795,33149,32160],{},[1795,33151,2022],{},[238,33153,33154],{"encoding":240},"v_k",[128,33156,33158],{"className":33157,"ariaHidden":246},[245],[128,33159,33161,33164],{"className":33160},[250],[128,33162],{"className":33163,"style":4242},[254],[128,33165,33167,33170],{"className":33166},[259],[128,33168,32160],{"className":33169,"style":1874},[259,1873],[128,33171,33173],{"className":33172},[2087],[128,33174,33176,33196],{"className":33175},[274,321],[128,33177,33179,33193],{"className":33178},[278],[128,33180,33182],{"className":33181,"style":2218},[282],[128,33183,33184,33187],{"style":28741},[128,33185],{"className":33186,"style":291},[290],[128,33188,33190],{"className":33189},[299,300,301,298],[128,33191,2022],{"className":33192,"style":2231},[259,1873,298],[128,33194,347],{"className":33195},[346],[128,33197,33199],{"className":33198},[278],[128,33200,33202],{"className":33201,"style":2241},[282],[128,33203],{}," 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。",[2610,33206,33208],{"id":33207},"_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",[11,33210,33211,33212,33246],{},"综合 2.1 至 2.5 节，可以把形状参数 ",[128,33213,33215,33228],{"className":33214,"translate":218},[217],[128,33216,33218],{"className":33217},[222],[224,33219,33220],{"xmlns":226},[228,33221,33222,33226],{},[231,33223,33224],{},[1795,33225,4835],{"mathvariant":4834},[238,33227,5875],{"encoding":240},[128,33229,33231],{"className":33230,"ariaHidden":246},[245],[128,33232,33234,33237],{"className":33233},[250],[128,33235],{"className":33236,"style":4439},[254],[128,33238,33240],{"className":33239},[259],[128,33241,33243],{"className":33242},[259],[128,33244,4835],{"className":33245},[259,4895]," 的语义概括为三点：",[33248,33249,33250,33362,33538],"ol",{},[33251,33252,33253,33291,33292,33361],"li",{},[35,33254,33255,33256,33290],{},"在共轭更新中，",[128,33257,33259,33272],{"className":33258,"translate":218},[217],[128,33260,33262],{"className":33261},[222],[224,33263,33264],{"xmlns":226},[228,33265,33266,33270],{},[231,33267,33268],{},[1795,33269,4835],{"mathvariant":4834},[238,33271,5875],{"encoding":240},[128,33273,33275],{"className":33274,"ariaHidden":246},[245],[128,33276,33278,33281],{"className":33277},[250],[128,33279],{"className":33280,"style":4439},[254],[128,33282,33284],{"className":33283},[259],[128,33285,33287],{"className":33286},[259],[128,33288,4835],{"className":33289},[259,4895]," 起先验样本计数的角色","（命题 2.5），其总强度 ",[128,33293,33295,33312],{"className":33294,"translate":218},[217],[128,33296,33298],{"className":33297},[222],[224,33299,33300],{"xmlns":226},[228,33301,33302,33310],{},[231,33303,33304],{},[2016,33305,33306,33308],{},[1795,33307,4835],{},[1840,33309,2028],{},[238,33311,21207],{"encoding":240},[128,33313,33315],{"className":33314,"ariaHidden":246},[245],[128,33316,33318,33321],{"className":33317},[250],[128,33319],{"className":33320,"style":4242},[254],[128,33322,33324,33327],{"className":33323},[259],[128,33325,4835],{"className":33326,"style":4920},[259,1873],[128,33328,33330],{"className":33329},[2087],[128,33331,33333,33353],{"className":33332},[274,321],[128,33334,33336,33350],{"className":33335},[278],[128,33337,33339],{"className":33338,"style":2945},[282],[128,33340,33341,33344],{"style":4935},[128,33342],{"className":33343,"style":291},[290],[128,33345,33347],{"className":33346},[299,300,301,298],[128,33348,2028],{"className":33349},[259,298],[128,33351,347],{"className":33352},[346],[128,33354,33356],{"className":33355},[278],[128,33357,33359],{"className":33358,"style":2241},[282],[128,33360],{}," 是「先验等价样本量」（推论 2.7）。",[33251,33363,33364,33502,33503,33537],{},[35,33365,33366,33367,33396,33397,33431,33432,33501],{},"在几何上，",[128,33368,33370,33384],{"className":33369,"translate":218},[217],[128,33371,33373],{"className":33372},[222],[224,33374,33375],{"xmlns":226},[228,33376,33377,33381],{},[231,33378,33379],{},[1795,33380,4835],{},[238,33382,33383],{"encoding":240},"\\alpha",[128,33385,33387],{"className":33386,"ariaHidden":246},[245],[128,33388,33390,33393],{"className":33389},[250],[128,33391],{"className":33392,"style":7758},[254],[128,33394,4835],{"className":33395,"style":4920},[259,1873]," 由方向 ",[128,33398,33400,33413],{"className":33399,"translate":218},[217],[128,33401,33403],{"className":33402},[222],[224,33404,33405],{"xmlns":226},[228,33406,33407,33411],{},[231,33408,33409],{},[1795,33410,20063],{"mathvariant":4834},[238,33412,21168],{"encoding":240},[128,33414,33416],{"className":33415,"ariaHidden":246},[245],[128,33417,33419,33422],{"className":33418},[250],[128,33420],{"className":33421,"style":2564},[254],[128,33423,33425],{"className":33424},[259],[128,33426,33428],{"className":33427},[259],[128,33429,20063],{"className":33430},[259,4895]," 与精度 ",[128,33433,33435,33452],{"className":33434,"translate":218},[217],[128,33436,33438],{"className":33437},[222],[224,33439,33440],{"xmlns":226},[228,33441,33442,33450],{},[231,33443,33444],{},[2016,33445,33446,33448],{},[1795,33447,4835],{},[1840,33449,2028],{},[238,33451,21207],{"encoding":240},[128,33453,33455],{"className":33454,"ariaHidden":246},[245],[128,33456,33458,33461],{"className":33457},[250],[128,33459],{"className":33460,"style":4242},[254],[128,33462,33464,33467],{"className":33463},[259],[128,33465,4835],{"className":33466,"style":4920},[259,1873],[128,33468,33470],{"className":33469},[2087],[128,33471,33473,33493],{"className":33472},[274,321],[128,33474,33476,33490],{"className":33475},[278],[128,33477,33479],{"className":33478,"style":2945},[282],[128,33480,33481,33484],{"style":4935},[128,33482],{"className":33483,"style":291},[290],[128,33485,33487],{"className":33486},[299,300,301,298],[128,33488,2028],{"className":33489},[259,298],[128,33491,347],{"className":33492},[346],[128,33494,33496],{"className":33495},[278],[128,33497,33499],{"className":33498,"style":2241},[282],[128,33500],{}," 两个正交分量构成","（2.2 节），精度决定围绕 ",[128,33504,33506,33519],{"className":33505,"translate":218},[217],[128,33507,33509],{"className":33508},[222],[224,33510,33511],{"xmlns":226},[228,33512,33513,33517],{},[231,33514,33515],{},[1795,33516,20063],{"mathvariant":4834},[238,33518,21168],{"encoding":240},[128,33520,33522],{"className":33521,"ariaHidden":246},[245],[128,33523,33525,33528],{"className":33524},[250],[128,33526],{"className":33527,"style":2564},[254],[128,33529,33531],{"className":33530},[259],[128,33532,33534],{"className":33533},[259],[128,33535,20063],{"className":33536},[259,4895]," 的收缩程度。",[33251,33539,33540,16150,33706,33798,33799,33891],{},[35,33541,33542,33543,33635,33636,33705],{},"在似然意义上，",[128,33544,33546,33568],{"className":33545,"translate":218},[217],[128,33547,33549],{"className":33548},[222],[224,33550,33551],{"xmlns":226},[228,33552,33553,33565],{},[231,33554,33555,33561,33563],{},[2016,33556,33557,33559],{},[1795,33558,4835],{},[1795,33560,2801],{},[1832,33562,1989],{},[1840,33564,1842],{},[238,33566,33567],{"encoding":240},"\\alpha_i - 1",[128,33569,33571,33626],{"className":33570,"ariaHidden":246},[245],[128,33572,33574,33577,33617,33620,33623],{"className":33573},[250],[128,33575],{"className":33576,"style":14338},[254],[128,33578,33580,33583],{"className":33579},[259],[128,33581,4835],{"className":33582,"style":4920},[259,1873],[128,33584,33586],{"className":33585},[2087],[128,33587,33589,33609],{"className":33588},[274,321],[128,33590,33592,33606],{"className":33591},[278],[128,33593,33595],{"className":33594,"style":3095},[282],[128,33596,33597,33600],{"style":4935},[128,33598],{"className":33599,"style":291},[290],[128,33601,33603],{"className":33602},[299,300,301,298],[128,33604,2801],{"className":33605},[259,1873,298],[128,33607,347],{"className":33608},[346],[128,33610,33612],{"className":33611},[278],[128,33613,33615],{"className":33614,"style":2241},[282],[128,33616],{},[128,33618],{"className":33619,"style":2508},[269],[128,33621,1989],{"className":33622},[2115],[128,33624],{"className":33625,"style":2508},[269],[128,33627,33629,33632],{"className":33628},[250],[128,33630],{"className":33631,"style":2594},[254],[128,33633,1842],{"className":33634},[259]," 是对数密度中 ",[128,33637,33639,33656],{"className":33638,"translate":218},[217],[128,33640,33642],{"className":33641},[222],[224,33643,33644],{"xmlns":226},[228,33645,33646,33654],{},[231,33647,33648],{},[2016,33649,33650,33652],{},[1795,33651,2760],{},[1795,33653,2801],{},[238,33655,15571],{"encoding":240},[128,33657,33659],{"className":33658,"ariaHidden":246},[245],[128,33660,33662,33665],{"className":33661},[250],[128,33663],{"className":33664,"style":4242},[254],[128,33666,33668,33671],{"className":33667},[259],[128,33669,2760],{"className":33670},[259,1873],[128,33672,33674],{"className":33673},[2087],[128,33675,33677,33697],{"className":33676},[274,321],[128,33678,33680,33694],{"className":33679},[278],[128,33681,33683],{"className":33682,"style":3095},[282],[128,33684,33685,33688],{"style":2221},[128,33686],{"className":33687,"style":291},[290],[128,33689,33691],{"className":33690},[299,300,301,298],[128,33692,2801],{"className":33693},[259,1873,298],[128,33695,347],{"className":33696},[346],[128,33698,33700],{"className":33699},[278],[128,33701,33703],{"className":33702,"style":2241},[282],[128,33704],{}," 的指数",[128,33707,33709,33731],{"className":33708,"translate":218},[217],[128,33710,33712],{"className":33711},[222],[224,33713,33714],{"xmlns":226},[228,33715,33716,33728],{},[231,33717,33718,33724,33726],{},[2016,33719,33720,33722],{},[1795,33721,4835],{},[1795,33723,2801],{},[1832,33725,4221],{},[1840,33727,1842],{},[238,33729,33730],{"encoding":240},"\\alpha_i \u003C 1",[128,33732,33734,33789],{"className":33733,"ariaHidden":246},[245],[128,33735,33737,33740,33780,33783,33786],{"className":33736},[250],[128,33738],{"className":33739,"style":3484},[254],[128,33741,33743,33746],{"className":33742},[259],[128,33744,4835],{"className":33745,"style":4920},[259,1873],[128,33747,33749],{"className":33748},[2087],[128,33750,33752,33772],{"className":33751},[274,321],[128,33753,33755,33769],{"className":33754},[278],[128,33756,33758],{"className":33757,"style":3095},[282],[128,33759,33760,33763],{"style":4935},[128,33761],{"className":33762,"style":291},[290],[128,33764,33766],{"className":33765},[299,300,301,298],[128,33767,2801],{"className":33768},[259,1873,298],[128,33770,347],{"className":33771},[346],[128,33773,33775],{"className":33774},[278],[128,33776,33778],{"className":33777,"style":2241},[282],[128,33779],{},[128,33781],{"className":33782,"style":1878},[269],[128,33784,4221],{"className":33785},[1882],[128,33787],{"className":33788,"style":1878},[269],[128,33790,33792,33795],{"className":33791},[250],[128,33793],{"className":33794,"style":2594},[254],[128,33796,1842],{"className":33797},[259]," 意味着密度在 ",[128,33800,33802,33824],{"className":33801,"translate":218},[217],[128,33803,33805],{"className":33804},[222],[224,33806,33807],{"xmlns":226},[228,33808,33809,33821],{},[231,33810,33811,33817,33819],{},[2016,33812,33813,33815],{},[1795,33814,2760],{},[1795,33816,2801],{},[1832,33818,22419],{},[1840,33820,2028],{},[238,33822,33823],{"encoding":240},"x_i \\to 0",[128,33825,33827,33882],{"className":33826,"ariaHidden":246},[245],[128,33828,33830,33833,33873,33876,33879],{"className":33829},[250],[128,33831],{"className":33832,"style":4242},[254],[128,33834,33836,33839],{"className":33835},[259],[128,33837,2760],{"className":33838},[259,1873],[128,33840,33842],{"className":33841},[2087],[128,33843,33845,33865],{"className":33844},[274,321],[128,33846,33848,33862],{"className":33847},[278],[128,33849,33851],{"className":33850,"style":3095},[282],[128,33852,33853,33856],{"style":2221},[128,33854],{"className":33855,"style":291},[290],[128,33857,33859],{"className":33858},[299,300,301,298],[128,33860,2801],{"className":33861},[259,1873,298],[128,33863,347],{"className":33864},[346],[128,33866,33868],{"className":33867},[278],[128,33869,33871],{"className":33870,"style":2241},[282],[128,33872],{},[128,33874],{"className":33875,"style":1878},[269],[128,33877,22419],{"className":33878},[1882],[128,33880],{"className":33881,"style":1878},[269],[128,33883,33885,33888],{"className":33884},[250],[128,33886],{"className":33887,"style":2594},[254],[128,33889,2028],{"className":33890},[259]," 处发散。",[11,33893,33894,33895,33898,33899,33960],{},"对于",[35,33896,33897],{},"对称","情形 ",[128,33900,33902,33921],{"className":33901,"translate":218},[217],[128,33903,33905],{"className":33904},[222],[224,33906,33907],{"xmlns":226},[228,33908,33909,33919],{},[231,33910,33911,33913,33915,33917],{},[1795,33912,4835],{"mathvariant":4834},[1832,33914,1994],{},[1795,33916,4835],{},[1840,33918,1842],{"mathvariant":2001},[238,33920,25696],{"encoding":240},[128,33922,33924,33948],{"className":33923,"ariaHidden":246},[245],[128,33925,33927,33930,33939,33942,33945],{"className":33926},[250],[128,33928],{"className":33929,"style":4439},[254],[128,33931,33933],{"className":33932},[259],[128,33934,33936],{"className":33935},[259],[128,33937,4835],{"className":33938},[259,4895],[128,33940],{"className":33941,"style":1878},[269],[128,33943,1994],{"className":33944},[1882],[128,33946],{"className":33947,"style":1878},[269],[128,33949,33951,33954,33957],{"className":33950},[250],[128,33952],{"className":33953,"style":2594},[254],[128,33955,4835],{"className":33956,"style":4920},[259,1873],[128,33958,1842],{"className":33959},[259,2151],"，这三重语义给出一条完整的形态谱：",[33962,33963,33964,33983],"table",{},[33965,33966,33967],"thead",{},[23026,33968,33969,33974,33977,33980],{},[33970,33971,33973],"th",{"align":33972},"left","参数区间",[33970,33975,33976],{"align":33972},"分布的形态",[33970,33978,33979],{"align":33972},"采样的典型特征",[33970,33981,33982],{"align":33972},"典型用途",[33984,33985,33986,34160,34223],"tbody",{},[23026,33987,33988,34042,34126,34157],{},[33989,33990,33991],"td",{"align":33972},[128,33992,33994,34012],{"className":33993,"translate":218},[217],[128,33995,33997],{"className":33996},[222],[224,33998,33999],{"xmlns":226},[228,34000,34001,34009],{},[231,34002,34003,34005,34007],{},[1795,34004,4835],{},[1832,34006,22419],{},[1840,34008,2028],{},[238,34010,34011],{"encoding":240},"\\alpha \\to 0",[128,34013,34015,34033],{"className":34014,"ariaHidden":246},[245],[128,34016,34018,34021,34024,34027,34030],{"className":34017},[250],[128,34019],{"className":34020,"style":7758},[254],[128,34022,4835],{"className":34023,"style":4920},[259,1873],[128,34025],{"className":34026,"style":1878},[269],[128,34028,22419],{"className":34029},[1882],[128,34031],{"className":34032,"style":1878},[269],[128,34034,34036,34039],{"className":34035},[250],[128,34037],{"className":34038,"style":2594},[254],[128,34040,2028],{"className":34041},[259],[33989,34043,34044,34045,34125],{"align":33972},"质量集中于顶点 ",[128,34046,34048,34070],{"className":34047,"translate":218},[217],[128,34049,34051],{"className":34050},[222],[224,34052,34053],{"xmlns":226},[228,34054,34055,34067],{},[231,34056,34057,34059,34065],{},[1832,34058,1838],{"stretchy":1837},[2016,34060,34061,34063],{},[1795,34062,3713],{"mathvariant":2001},[1795,34064,2801],{},[1832,34066,1856],{"stretchy":1837},[238,34068,34069],{"encoding":240},"\\{\\mathbf{e}_i\\}",[128,34071,34073],{"className":34072,"ariaHidden":246},[245],[128,34074,34076,34079,34082,34122],{"className":34075},[250],[128,34077],{"className":34078,"style":1892},[254],[128,34080,1838],{"className":34081},[1896],[128,34083,34085,34088],{"className":34084},[259],[128,34086,3713],{"className":34087},[259,2151],[128,34089,34091],{"className":34090},[2087],[128,34092,34094,34114],{"className":34093},[274,321],[128,34095,34097,34111],{"className":34096},[278],[128,34098,34100],{"className":34099,"style":3095},[282],[128,34101,34102,34105],{"style":2221},[128,34103],{"className":34104,"style":291},[290],[128,34106,34108],{"className":34107},[299,300,301,298],[128,34109,2801],{"className":34110},[259,1873,298],[128,34112,347],{"className":34113},[346],[128,34115,34117],{"className":34116},[278],[128,34118,34120],{"className":34119,"style":2241},[282],[128,34121],{},[128,34123,1856],{"className":34124},[1928]," 邻域",[33989,34127,34128,34129],{"align":33972},"极端稀疏，单个分量接近 ",[128,34130,34132,34145],{"className":34131,"translate":218},[217],[128,34133,34135],{"className":34134},[222],[224,34136,34137],{"xmlns":226},[228,34138,34139,34143],{},[231,34140,34141],{},[1840,34142,1842],{},[238,34144,1842],{"encoding":240},[128,34146,34148],{"className":34147,"ariaHidden":246},[245],[128,34149,34151,34154],{"className":34150},[250],[128,34152],{"className":34153,"style":2594},[254],[128,34155,1842],{"className":34156},[259],[33989,34158,34159],{"align":33972},"LDA 文档—主题混合（文档只涉少数主题）",[23026,34161,34162,34214,34217,34220],{},[33989,34163,34164],{"align":33972},[128,34165,34167,34184],{"className":34166,"translate":218},[217],[128,34168,34170],{"className":34169},[222],[224,34171,34172],{"xmlns":226},[228,34173,34174,34182],{},[231,34175,34176,34178,34180],{},[1795,34177,4835],{},[1832,34179,1994],{},[1840,34181,1842],{},[238,34183,25785],{"encoding":240},[128,34185,34187,34205],{"className":34186,"ariaHidden":246},[245],[128,34188,34190,34193,34196,34199,34202],{"className":34189},[250],[128,34191],{"className":34192,"style":7758},[254],[128,34194,4835],{"className":34195,"style":4920},[259,1873],[128,34197],{"className":34198,"style":1878},[269],[128,34200,1994],{"className":34201},[1882],[128,34203],{"className":34204,"style":1878},[269],[128,34206,34208,34211],{"className":34207},[250],[128,34209],{"className":34210,"style":2594},[254],[128,34212,1842],{"className":34213},[259],[33989,34215,34216],{"align":33972},"单纯形上的均匀分布",[33989,34218,34219],{"align":33972},"各分量量级相当，无偏好",[33989,34221,34222],{"align":33972},"无信息先验",[23026,34224,34225,34278,34350,34390],{},[33989,34226,34227],{"align":33972},[128,34228,34230,34248],{"className":34229,"translate":218},[217],[128,34231,34233],{"className":34232},[222],[224,34234,34235],{"xmlns":226},[228,34236,34237,34245],{},[231,34238,34239,34241,34243],{},[1795,34240,4835],{},[1832,34242,3321],{},[1840,34244,1842],{},[238,34246,34247],{"encoding":240},"\\alpha > 1",[128,34249,34251,34269],{"className":34250,"ariaHidden":246},[245],[128,34252,34254,34257,34260,34263,34266],{"className":34253},[250],[128,34255],{"className":34256,"style":6382},[254],[128,34258,4835],{"className":34259,"style":4920},[259,1873],[128,34261],{"className":34262,"style":1878},[269],[128,34264,3321],{"className":34265},[1882],[128,34267],{"className":34268,"style":1878},[269],[128,34270,34272,34275],{"className":34271},[250],[128,34273],{"className":34274,"style":2594},[254],[128,34276,1842],{"className":34277},[259],[33989,34279,34280,34281,34320,34321,34349],{"align":33972},"集中于中心 ",[128,34282,34284,34302],{"className":34283,"translate":218},[217],[128,34285,34287],{"className":34286},[222],[224,34288,34289],{"xmlns":226},[228,34290,34291,34299],{},[231,34292,34293,34295,34297],{},[1840,34294,1842],{"mathvariant":2001},[1795,34296,4751],{"mathvariant":1981},[1795,34298,1853],{},[238,34300,34301],{"encoding":240},"\\mathbf{1}\u002FK",[128,34303,34305],{"className":34304,"ariaHidden":246},[245],[128,34306,34308,34311,34314,34317],{"className":34307},[250],[128,34309],{"className":34310,"style":1892},[254],[128,34312,1842],{"className":34313},[259,2151],[128,34315,4751],{"className":34316},[259],[128,34318,1853],{"className":34319,"style":1924},[259,1873],"，随 ",[128,34322,34324,34337],{"className":34323,"translate":218},[217],[128,34325,34327],{"className":34326},[222],[224,34328,34329],{"xmlns":226},[228,34330,34331,34335],{},[231,34332,34333],{},[1795,34334,4835],{},[238,34336,33383],{"encoding":240},[128,34338,34340],{"className":34339,"ariaHidden":246},[245],[128,34341,34343,34346],{"className":34342},[250],[128,34344],{"className":34345,"style":7758},[254],[128,34347,4835],{"className":34348,"style":4920},[259,1873]," 增大而收缩",[33989,34351,34352,34353,34389],{"align":33972},"各分量接近 ",[128,34354,34356,34374],{"className":34355,"translate":218},[217],[128,34357,34359],{"className":34358},[222],[224,34360,34361],{"xmlns":226},[228,34362,34363,34371],{},[231,34364,34365,34367,34369],{},[1840,34366,1842],{},[1795,34368,4751],{"mathvariant":1981},[1795,34370,1853],{},[238,34372,34373],{"encoding":240},"1\u002FK",[128,34375,34377],{"className":34376,"ariaHidden":246},[245],[128,34378,34380,34383,34386],{"className":34379},[250],[128,34381],{"className":34382,"style":1892},[254],[128,34384,4780],{"className":34385},[259],[128,34387,1853],{"className":34388,"style":1924},[259,1873]," 的平滑向量",[33989,34391,34392],{"align":33972},"强正则化、收缩估计",[11,34394,34395,34396,34465,34466,34558,34559,22492,34650,34765,34766,34987],{},"此处必须澄清一个常见但过强的说法：把 ",[128,34397,34399,34416],{"className":34398,"translate":218},[217],[128,34400,34402],{"className":34401},[222],[224,34403,34404],{"xmlns":226},[228,34405,34406,34414],{},[231,34407,34408],{},[2016,34409,34410,34412],{},[1795,34411,4835],{},[1795,34413,2801],{},[238,34415,11448],{"encoding":240},[128,34417,34419],{"className":34418,"ariaHidden":246},[245],[128,34420,34422,34425],{"className":34421},[250],[128,34423],{"className":34424,"style":4242},[254],[128,34426,34428,34431],{"className":34427},[259],[128,34429,4835],{"className":34430,"style":4920},[259,1873],[128,34432,34434],{"className":34433},[2087],[128,34435,34437,34457],{"className":34436},[274,321],[128,34438,34440,34454],{"className":34439},[278],[128,34441,34443],{"className":34442,"style":3095},[282],[128,34444,34445,34448],{"style":4935},[128,34446],{"className":34447,"style":291},[290],[128,34449,34451],{"className":34450},[299,300,301,298],[128,34452,2801],{"className":34453},[259,1873,298],[128,34455,347],{"className":34456},[346],[128,34458,34460],{"className":34459},[278],[128,34461,34463],{"className":34462,"style":2241},[282],[128,34464],{}," 直接称为「观测到的次数」只在 ",[128,34467,34469,34491],{"className":34468,"translate":218},[217],[128,34470,34472],{"className":34471},[222],[224,34473,34474],{"xmlns":226},[228,34475,34476,34488],{},[231,34477,34478,34484,34486],{},[2016,34479,34480,34482],{},[1795,34481,4835],{},[1795,34483,2801],{},[1832,34485,2025],{},[1840,34487,1842],{},[238,34489,34490],{"encoding":240},"\\alpha_i \\ge 1",[128,34492,34494,34549],{"className":34493,"ariaHidden":246},[245],[128,34495,34497,34500,34540,34543,34546],{"className":34496},[250],[128,34498],{"className":34499,"style":24205},[254],[128,34501,34503,34506],{"className":34502},[259],[128,34504,4835],{"className":34505,"style":4920},[259,1873],[128,34507,34509],{"className":34508},[2087],[128,34510,34512,34532],{"className":34511},[274,321],[128,34513,34515,34529],{"className":34514},[278],[128,34516,34518],{"className":34517,"style":3095},[282],[128,34519,34520,34523],{"style":4935},[128,34521],{"className":34522,"style":291},[290],[128,34524,34526],{"className":34525},[299,300,301,298],[128,34527,2801],{"className":34528},[259,1873,298],[128,34530,347],{"className":34531},[346],[128,34533,34535],{"className":34534},[278],[128,34536,34538],{"className":34537,"style":2241},[282],[128,34539],{},[128,34541],{"className":34542,"style":1878},[269],[128,34544,2025],{"className":34545},[1882],[128,34547],{"className":34548,"style":1878},[269],[128,34550,34552,34555],{"className":34551},[250],[128,34553],{"className":34554,"style":2594},[254],[128,34556,1842],{"className":34557},[259]," 时在字面上成立。当 ",[128,34560,34562,34583],{"className":34561,"translate":218},[217],[128,34563,34565],{"className":34564},[222],[224,34566,34567],{"xmlns":226},[228,34568,34569,34581],{},[231,34570,34571,34577,34579],{},[2016,34572,34573,34575],{},[1795,34574,4835],{},[1795,34576,2801],{},[1832,34578,4221],{},[1840,34580,1842],{},[238,34582,33730],{"encoding":240},[128,34584,34586,34641],{"className":34585,"ariaHidden":246},[245],[128,34587,34589,34592,34632,34635,34638],{"className":34588},[250],[128,34590],{"className":34591,"style":3484},[254],[128,34593,34595,34598],{"className":34594},[259],[128,34596,4835],{"className":34597,"style":4920},[259,1873],[128,34599,34601],{"className":34600},[2087],[128,34602,34604,34624],{"className":34603},[274,321],[128,34605,34607,34621],{"className":34606},[278],[128,34608,34610],{"className":34609,"style":3095},[282],[128,34611,34612,34615],{"style":4935},[128,34613],{"className":34614,"style":291},[290],[128,34616,34618],{"className":34617},[299,300,301,298],[128,34619,2801],{"className":34620},[259,1873,298],[128,34622,347],{"className":34623},[346],[128,34625,34627],{"className":34626},[278],[128,34628,34630],{"className":34629,"style":2241},[282],[128,34631],{},[128,34633],{"className":34634,"style":1878},[269],[128,34636,4221],{"className":34637},[1882],[128,34639],{"className":34640,"style":1878},[269],[128,34642,34644,34647],{"className":34643},[250],[128,34645],{"className":34646,"style":2594},[254],[128,34648,1842],{"className":34649},[259],[128,34651,34653,34679],{"className":34652,"translate":218},[217],[128,34654,34656],{"className":34655},[222],[224,34657,34658],{"xmlns":226},[228,34659,34660,34676],{},[231,34661,34662,34668,34670,34672,34674],{},[2016,34663,34664,34666],{},[1795,34665,4835],{},[1795,34667,2801],{},[1832,34669,1989],{},[1840,34671,1842],{},[1832,34673,4221],{},[1840,34675,2028],{},[238,34677,34678],{"encoding":240},"\\alpha_i - 1 \u003C 0",[128,34680,34682,34737,34756],{"className":34681,"ariaHidden":246},[245],[128,34683,34685,34688,34728,34731,34734],{"className":34684},[250],[128,34686],{"className":34687,"style":14338},[254],[128,34689,34691,34694],{"className":34690},[259],[128,34692,4835],{"className":34693,"style":4920},[259,1873],[128,34695,34697],{"className":34696},[2087],[128,34698,34700,34720],{"className":34699},[274,321],[128,34701,34703,34717],{"className":34702},[278],[128,34704,34706],{"className":34705,"style":3095},[282],[128,34707,34708,34711],{"style":4935},[128,34709],{"className":34710,"style":291},[290],[128,34712,34714],{"className":34713},[299,300,301,298],[128,34715,2801],{"className":34716},[259,1873,298],[128,34718,347],{"className":34719},[346],[128,34721,34723],{"className":34722},[278],[128,34724,34726],{"className":34725,"style":2241},[282],[128,34727],{},[128,34729],{"className":34730,"style":2508},[269],[128,34732,1989],{"className":34733},[2115],[128,34735],{"className":34736,"style":2508},[269],[128,34738,34740,34744,34747,34750,34753],{"className":34739},[250],[128,34741],{"className":34742,"style":34743},[254],"height:0.6835em;vertical-align:-0.0391em;",[128,34745,1842],{"className":34746},[259],[128,34748],{"className":34749,"style":1878},[269],[128,34751,4221],{"className":34752},[1882],[128,34754],{"className":34755,"style":1878},[269],[128,34757,34759,34762],{"className":34758},[250],[128,34760],{"className":34761,"style":2594},[254],[128,34763,2028],{"className":34764},[259],"，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：",[35,34767,34768,34802,34803,34894,34895,34986],{},[128,34769,34771,34784],{"className":34770,"translate":218},[217],[128,34772,34774],{"className":34773},[222],[224,34775,34776],{"xmlns":226},[228,34777,34778,34782],{},[231,34779,34780],{},[1795,34781,4835],{"mathvariant":4834},[238,34783,5875],{"encoding":240},[128,34785,34787],{"className":34786,"ariaHidden":246},[245],[128,34788,34790,34793],{"className":34789},[250],[128,34791],{"className":34792,"style":4439},[254],[128,34794,34796],{"className":34795},[259],[128,34797,34799],{"className":34798},[259],[128,34800,4835],{"className":34801},[259,4895]," 是伪计数概念的连续化，其在 ",[128,34804,34806,34827],{"className":34805,"translate":218},[217],[128,34807,34809],{"className":34808},[222],[224,34810,34811],{"xmlns":226},[228,34812,34813,34825],{},[231,34814,34815,34821,34823],{},[2016,34816,34817,34819],{},[1795,34818,4835],{},[1795,34820,2801],{},[1832,34822,2025],{},[1840,34824,1842],{},[238,34826,34490],{"encoding":240},[128,34828,34830,34885],{"className":34829,"ariaHidden":246},[245],[128,34831,34833,34836,34876,34879,34882],{"className":34832},[250],[128,34834],{"className":34835,"style":24205},[254],[128,34837,34839,34842],{"className":34838},[259],[128,34840,4835],{"className":34841,"style":4920},[259,1873],[128,34843,34845],{"className":34844},[2087],[128,34846,34848,34868],{"className":34847},[274,321],[128,34849,34851,34865],{"className":34850},[278],[128,34852,34854],{"className":34853,"style":3095},[282],[128,34855,34856,34859],{"style":4935},[128,34857],{"className":34858,"style":291},[290],[128,34860,34862],{"className":34861},[299,300,301,298],[128,34863,2801],{"className":34864},[259,1873,298],[128,34866,347],{"className":34867},[346],[128,34869,34871],{"className":34870},[278],[128,34872,34874],{"className":34873,"style":2241},[282],[128,34875],{},[128,34877],{"className":34878,"style":1878},[269],[128,34880,2025],{"className":34881},[1882],[128,34883],{"className":34884,"style":1878},[269],[128,34886,34888,34891],{"className":34887},[250],[128,34889],{"className":34890,"style":2594},[254],[128,34892,1842],{"className":34893},[259]," 区域退化回字面意义上的计数解释，而在 ",[128,34896,34898,34919],{"className":34897,"translate":218},[217],[128,34899,34901],{"className":34900},[222],[224,34902,34903],{"xmlns":226},[228,34904,34905,34917],{},[231,34906,34907,34913,34915],{},[2016,34908,34909,34911],{},[1795,34910,4835],{},[1795,34912,2801],{},[1832,34914,4221],{},[1840,34916,1842],{},[238,34918,33730],{"encoding":240},[128,34920,34922,34977],{"className":34921,"ariaHidden":246},[245],[128,34923,34925,34928,34968,34971,34974],{"className":34924},[250],[128,34926],{"className":34927,"style":3484},[254],[128,34929,34931,34934],{"className":34930},[259],[128,34932,4835],{"className":34933,"style":4920},[259,1873],[128,34935,34937],{"className":34936},[2087],[128,34938,34940,34960],{"className":34939},[274,321],[128,34941,34943,34957],{"className":34942},[278],[128,34944,34946],{"className":34945,"style":3095},[282],[128,34947,34948,34951],{"style":4935},[128,34949],{"className":34950,"style":291},[290],[128,34952,34954],{"className":34953},[299,300,301,298],[128,34955,2801],{"className":34956},[259,1873,298],[128,34958,347],{"className":34959},[346],[128,34961,34963],{"className":34962},[278],[128,34964,34966],{"className":34965,"style":2241},[282],[128,34967],{},[128,34969],{"className":34970,"style":1878},[269],[128,34972,4221],{"className":34973},[1882],[128,34975],{"className":34976,"style":1878},[269],[128,34978,34980,34983],{"className":34979},[250],[128,34981],{"className":34982,"style":2594},[254],[128,34984,1842],{"className":34985},[259]," 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。",[51,34989,34991],{"id":34990},"三主观逻辑到证据深度学习","三、主观逻辑到证据深度学习",[2610,34993,34995],{"id":34994},"_31-主观逻辑的-opinion-表示","3.1 主观逻辑的 opinion 表示",[11,34997,34998,34999,35002],{},"证据深度学习的直接理论前身是 Josang 的",[35,35000,35001],{},"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。",[2615,35004,35006,35194,35781],{"title":35005},"定义 3.1（opinion）",[11,35007,35008,35009,35102,35103,35193],{},"在有限域 ",[128,35010,35012,35043],{"className":35011,"translate":218},[217],[128,35013,35015],{"className":35014},[222],[224,35016,35017],{"xmlns":226},[228,35018,35019,35040],{},[231,35020,35021,35024,35026,35028,35030,35032,35034,35036,35038],{},[1795,35022,35023],{"mathvariant":1797},"Y",[1832,35025,1994],{},[1832,35027,1838],{"stretchy":1837},[1840,35029,1842],{},[1832,35031,1845],{"separator":246},[1832,35033,1848],{},[1832,35035,1845],{"separator":246},[1795,35037,1853],{},[1832,35039,1856],{"stretchy":1837},[238,35041,35042],{"encoding":240},"\\mathcal{Y} = \\{1, \\dots, K\\}",[128,35044,35046,35066],{"className":35045,"ariaHidden":246},[245],[128,35047,35049,35053,35057,35060,35063],{"className":35048},[250],[128,35050],{"className":35051,"style":35052},[254],"height:0.7805em;vertical-align:-0.0972em;",[128,35054,35023],{"className":35055,"style":35056},[259,1813],"margin-right:0.0822em;",[128,35058],{"className":35059,"style":1878},[269],[128,35061,1994],{"className":35062},[1882],[128,35064],{"className":35065,"style":1878},[269],[128,35067,35069,35072,35075,35078,35081,35084,35087,35090,35093,35096,35099],{"className":35068},[250],[128,35070],{"className":35071,"style":1892},[254],[128,35073,1838],{"className":35074},[1896],[128,35076,1842],{"className":35077},[259],[128,35079,1845],{"className":35080},[1903],[128,35082],{"className":35083,"style":1907},[269],[128,35085,1848],{"className":35086},[1911],[128,35088],{"className":35089,"style":1907},[269],[128,35091,1845],{"className":35092},[1903],[128,35094],{"className":35095,"style":1907},[269],[128,35097,1853],{"className":35098,"style":1924},[259,1873],[128,35100,1856],{"className":35101},[1928]," 上的一个 opinion 是三元组 ",[128,35104,35106,35139],{"className":35105,"translate":218},[217],[128,35107,35109],{"className":35108},[222],[224,35110,35111],{"xmlns":226},[228,35112,35113,35136],{},[231,35114,35115,35118,35120,35122,35125,35127,35130,35132,35134],{},[1795,35116,35117],{},"ω",[1832,35119,1994],{},[1832,35121,2477],{"stretchy":1837},[1795,35123,35124],{"mathvariant":2001},"b",[1832,35126,1845],{"separator":246},[1795,35128,35129],{},"u",[1832,35131,1845],{"separator":246},[1795,35133,21],{"mathvariant":2001},[1832,35135,2486],{"stretchy":1837},[238,35137,35138],{"encoding":240},"\\omega = (\\mathbf{b}, u, \\mathbf{a})",[128,35140,35142,35160],{"className":35141,"ariaHidden":246},[245],[128,35143,35145,35148,35151,35154,35157],{"className":35144},[250],[128,35146],{"className":35147,"style":7758},[254],[128,35149,35117],{"className":35150,"style":1874},[259,1873],[128,35152],{"className":35153,"style":1878},[269],[128,35155,1994],{"className":35156},[1882],[128,35158],{"className":35159,"style":1878},[269],[128,35161,35163,35166,35169,35172,35175,35178,35181,35184,35187,35190],{"className":35162},[250],[128,35164],{"className":35165,"style":1892},[254],[128,35167,2477],{"className":35168},[1896],[128,35170,35124],{"className":35171},[259,2151],[128,35173,1845],{"className":35174},[1903],[128,35176],{"className":35177,"style":1907},[269],[128,35179,35129],{"className":35180},[259,1873],[128,35182,1845],{"className":35183},[1903],[128,35185],{"className":35186,"style":1907},[269],[128,35188,21],{"className":35189},[259,2151],[128,35191,2486],{"className":35192},[1928],"，其中",[35195,35196,35197,35451,35530],"ul",{},[33251,35198,35199,35447,35448,893],{},[128,35200,35202,35256],{"className":35201,"translate":218},[217],[128,35203,35205],{"className":35204},[222],[224,35206,35207],{"xmlns":226},[228,35208,35209,35253],{},[231,35210,35211,35213,35215,35217,35223,35225,35227,35229,35235,35237,35239,35241,35243,35245,35247],{},[1795,35212,35124],{"mathvariant":2001},[1832,35214,1994],{},[1832,35216,2477],{"stretchy":1837},[2016,35218,35219,35221],{},[1795,35220,35124],{},[1840,35222,1842],{},[1832,35224,1845],{"separator":246},[1832,35226,1848],{},[1832,35228,1845],{"separator":246},[2016,35230,35231,35233],{},[1795,35232,35124],{},[1795,35234,1853],{},[1832,35236,2486],{"stretchy":1837},[1832,35238,1834],{},[1832,35240,16538],{"stretchy":1837},[1840,35242,2028],{},[1832,35244,1845],{"separator":246},[1840,35246,1842],{},[1977,35248,35249,35251],{},[1832,35250,16547],{"stretchy":1837},[1795,35252,1853],{},[238,35254,35255],{"encoding":240},"\\mathbf{b} = (b_1, \\dots, b_K) \\in [0,1]^K",[128,35257,35259,35277,35396],{"className":35258,"ariaHidden":246},[245],[128,35260,35262,35265,35268,35271,35274],{"className":35261},[250],[128,35263],{"className":35264,"style":12173},[254],[128,35266,35124],{"className":35267},[259,2151],[128,35269],{"className":35270,"style":1878},[269],[128,35272,1994],{"className":35273},[1882],[128,35275],{"className":35276,"style":1878},[269],[128,35278,35280,35283,35286,35326,35329,35332,35335,35338,35341,35344,35384,35387,35390,35393],{"className":35279},[250],[128,35281],{"className":35282,"style":1892},[254],[128,35284,2477],{"className":35285},[1896],[128,35287,35289,35292],{"className":35288},[259],[128,35290,35124],{"className":35291},[259,1873],[128,35293,35295],{"className":35294},[2087],[128,35296,35298,35318],{"className":35297},[274,321],[128,35299,35301,35315],{"className":35300},[278],[128,35302,35304],{"className":35303,"style":2945},[282],[128,35305,35306,35309],{"style":2221},[128,35307],{"className":35308,"style":291},[290],[128,35310,35312],{"className":35311},[299,300,301,298],[128,35313,1842],{"className":35314},[259,298],[128,35316,347],{"className":35317},[346],[128,35319,35321],{"className":35320},[278],[128,35322,35324],{"className":35323,"style":2241},[282],[128,35325],{},[128,35327,1845],{"className":35328},[1903],[128,35330],{"className":35331,"style":1907},[269],[128,35333,1848],{"className":35334},[1911],[128,35336],{"className":35337,"style":1907},[269],[128,35339,1845],{"className":35340},[1903],[128,35342],{"className":35343,"style":1907},[269],[128,35345,35347,35350],{"className":35346},[259],[128,35348,35124],{"className":35349},[259,1873],[128,35351,35353],{"className":35352},[2087],[128,35354,35356,35376],{"className":35355},[274,321],[128,35357,35359,35373],{"className":35358},[278],[128,35360,35362],{"className":35361,"style":3004},[282],[128,35363,35364,35367],{"style":2221},[128,35365],{"className":35366,"style":291},[290],[128,35368,35370],{"className":35369},[299,300,301,298],[128,35371,1853],{"className":35372,"style":1924},[259,1873,298],[128,35374,347],{"className":35375},[346],[128,35377,35379],{"className":35378},[278],[128,35380,35382],{"className":35381,"style":2241},[282],[128,35383],{},[128,35385,2486],{"className":35386},[1928],[128,35388],{"className":35389,"style":1878},[269],[128,35391,1834],{"className":35392},[1882],[128,35394],{"className":35395,"style":1878},[269],[128,35397,35399,35403,35406,35409,35412,35415,35418],{"className":35398},[250],[128,35400],{"className":35401,"style":35402},[254],"height:1.0913em;vertical-align:-0.25em;",[128,35404,16538],{"className":35405},[1896],[128,35407,2028],{"className":35408},[259],[128,35410,1845],{"className":35411},[1903],[128,35413],{"className":35414,"style":1907},[269],[128,35416,1842],{"className":35417},[259],[128,35419,35421,35424],{"className":35420},[1928],[128,35422,16547],{"className":35423},[1928],[128,35425,35427],{"className":35426},[2087],[128,35428,35430],{"className":35429},[274],[128,35431,35433],{"className":35432},[278],[128,35434,35436],{"className":35435,"style":2431},[282],[128,35437,35438,35441],{"style":2452},[128,35439],{"className":35440,"style":291},[290],[128,35442,35444],{"className":35443},[299,300,301,298],[128,35445,1853],{"className":35446,"style":1924},[259,1873,298]," 为",[35,35449,35450],{},"信念质量（belief mass）",[33251,35452,35453,35447,35527,893],{},[128,35454,35456,35482],{"className":35455,"translate":218},[217],[128,35457,35459],{"className":35458},[222],[224,35460,35461],{"xmlns":226},[228,35462,35463,35479],{},[231,35464,35465,35467,35469,35471,35473,35475,35477],{},[1795,35466,35129],{},[1832,35468,1834],{},[1832,35470,16538],{"stretchy":1837},[1840,35472,2028],{},[1832,35474,1845],{"separator":246},[1840,35476,1842],{},[1832,35478,16547],{"stretchy":1837},[238,35480,35481],{"encoding":240},"u \\in [0,1]",[128,35483,35485,35503],{"className":35484,"ariaHidden":246},[245],[128,35486,35488,35491,35494,35497,35500],{"className":35487},[250],[128,35489],{"className":35490,"style":6382},[254],[128,35492,35129],{"className":35493},[259,1873],[128,35495],{"className":35496,"style":1878},[269],[128,35498,1834],{"className":35499},[1882],[128,35501],{"className":35502,"style":1878},[269],[128,35504,35506,35509,35512,35515,35518,35521,35524],{"className":35505},[250],[128,35507],{"className":35508,"style":1892},[254],[128,35510,16538],{"className":35511},[1896],[128,35513,2028],{"className":35514},[259],[128,35516,1845],{"className":35517},[1903],[128,35519],{"className":35520,"style":1907},[269],[128,35522,1842],{"className":35523},[259],[128,35525,16547],{"className":35526},[1928],[35,35528,35529],{},"不确定性质量（uncertainty mass）",[33251,35531,35532,2674,35636,35777,35778,893],{},[128,35533,35535,35565],{"className":35534,"translate":218},[217],[128,35536,35538],{"className":35537},[222],[224,35539,35540],{"xmlns":226},[228,35541,35542,35562],{},[231,35543,35544,35546,35548,35550,35552,35554,35556],{},[1795,35545,21],{"mathvariant":2001},[1832,35547,1834],{},[1832,35549,16538],{"stretchy":1837},[1840,35551,2028],{},[1832,35553,1845],{"separator":246},[1840,35555,1842],{},[1977,35557,35558,35560],{},[1832,35559,16547],{"stretchy":1837},[1795,35561,1853],{},[238,35563,35564],{"encoding":240},"\\mathbf{a} \\in [0,1]^K",[128,35566,35568,35586],{"className":35567,"ariaHidden":246},[245],[128,35569,35571,35574,35577,35580,35583],{"className":35570},[250],[128,35572],{"className":35573,"style":6382},[254],[128,35575,21],{"className":35576},[259,2151],[128,35578],{"className":35579,"style":1878},[269],[128,35581,1834],{"className":35582},[1882],[128,35584],{"className":35585,"style":1878},[269],[128,35587,35589,35592,35595,35598,35601,35604,35607],{"className":35588},[250],[128,35590],{"className":35591,"style":35402},[254],[128,35593,16538],{"className":35594},[1896],[128,35596,2028],{"className":35597},[259],[128,35599,1845],{"className":35600},[1903],[128,35602],{"className":35603,"style":1907},[269],[128,35605,1842],{"className":35606},[259],[128,35608,35610,35613],{"className":35609},[1928],[128,35611,16547],{"className":35612},[1928],[128,35614,35616],{"className":35615},[2087],[128,35617,35619],{"className":35618},[274],[128,35620,35622],{"className":35621},[278],[128,35623,35625],{"className":35624,"style":2431},[282],[128,35626,35627,35630],{"style":2452},[128,35628],{"className":35629,"style":291},[290],[128,35631,35633],{"className":35632},[299,300,301,298],[128,35634,1853],{"className":35635,"style":1924},[259,1873,298],[128,35637,35639,35667],{"className":35638,"translate":218},[217],[128,35640,35642],{"className":35641},[222],[224,35643,35644],{"xmlns":226},[228,35645,35646,35664],{},[231,35647,35648,35654,35660,35662],{},[2016,35649,35650,35652],{},[1832,35651,2042],{},[1795,35653,2022],{},[2016,35655,35656,35658],{},[1795,35657,21],{},[1795,35659,2022],{},[1832,35661,1994],{},[1840,35663,1842],{},[238,35665,35666],{"encoding":240},"\\sum_k a_k = 1",[128,35668,35670,35768],{"className":35669,"ariaHidden":246},[245],[128,35671,35673,35676,35716,35719,35759,35762,35765],{"className":35672},[250],[128,35674],{"className":35675,"style":7777},[254],[128,35677,35679,35682],{"className":35678},[2268],[128,35680,2042],{"className":35681,"style":2274},[2268,2272,2273],[128,35683,35685],{"className":35684},[2087],[128,35686,35688,35708],{"className":35687},[274,321],[128,35689,35691,35705],{"className":35690},[278],[128,35692,35694],{"className":35693,"style":31692},[282],[128,35695,35696,35699],{"style":2290},[128,35697],{"className":35698,"style":291},[290],[128,35700,35702],{"className":35701},[299,300,301,298],[128,35703,2022],{"className":35704,"style":2231},[259,1873,298],[128,35706,347],{"className":35707},[346],[128,35709,35711],{"className":35710},[278],[128,35712,35714],{"className":35713,"style":2330},[282],[128,35715],{},[128,35717],{"className":35718,"style":1907},[269],[128,35720,35722,35725],{"className":35721},[259],[128,35723,21],{"className":35724},[259,1873],[128,35726,35728],{"className":35727},[2087],[128,35729,35731,35751],{"className":35730},[274,321],[128,35732,35734,35748],{"className":35733},[278],[128,35735,35737],{"className":35736,"style":2218},[282],[128,35738,35739,35742],{"style":2221},[128,35740],{"className":35741,"style":291},[290],[128,35743,35745],{"className":35744},[299,300,301,298],[128,35746,2022],{"className":35747,"style":2231},[259,1873,298],[128,35749,347],{"className":35750},[346],[128,35752,35754],{"className":35753},[278],[128,35755,35757],{"className":35756,"style":2241},[282],[128,35758],{},[128,35760],{"className":35761,"style":1878},[269],[128,35763,1994],{"className":35764},[1882],[128,35766],{"className":35767,"style":1878},[269],[128,35769,35771,35774],{"className":35770},[250],[128,35772],{"className":35773,"style":2594},[254],[128,35775,1842],{"className":35776},[259],"，为",[35,35779,35780],{},"基准率（base rate）",[11,35782,35783,35784,893],{},"并满足单纯形约束 ",[128,35785,35787,35827],{"className":35786,"translate":218},[217],[128,35788,35790],{"className":35789},[222],[224,35791,35792],{"xmlns":226},[228,35793,35794,35824],{},[231,35795,35796,35810,35816,35818,35820,35822],{},[2038,35797,35798,35800,35808],{},[1832,35799,2042],{},[231,35801,35802,35804,35806],{},[1795,35803,2022],{},[1832,35805,1994],{},[1840,35807,1842],{},[1795,35809,1853],{},[2016,35811,35812,35814],{},[1795,35813,35124],{},[1795,35815,2022],{},[1832,35817,9486],{},[1795,35819,35129],{},[1832,35821,1994],{},[1840,35823,1842],{},[238,35825,35826],{"encoding":240},"\\sum_{k=1}^K b_k + u = 1",[128,35828,35830,35948,35966],{"className":35829,"ariaHidden":246},[245],[128,35831,35833,35836,35896,35899,35939,35942,35945],{"className":35832},[250],[128,35834],{"className":35835,"style":5200},[254],[128,35837,35839,35842],{"className":35838},[2268],[128,35840,2042],{"className":35841,"style":2274},[2268,2272,2273],[128,35843,35845],{"className":35844},[2087],[128,35846,35848,35888],{"className":35847},[274,321],[128,35849,35851,35885],{"className":35850},[278],[128,35852,35854,35874],{"className":35853,"style":2287},[282],[128,35855,35856,35859],{"style":2290},[128,35857],{"className":35858,"style":291},[290],[128,35860,35862],{"className":35861},[299,300,301,298],[128,35863,35865,35868,35871],{"className":35864},[259,298],[128,35866,2022],{"className":35867,"style":2231},[259,1873,298],[128,35869,1994],{"className":35870},[1882,298],[128,35872,1842],{"className":35873},[259,298],[128,35875,35876,35879],{"style":2311},[128,35877],{"className":35878,"style":291},[290],[128,35880,35882],{"className":35881},[299,300,301,298],[128,35883,1853],{"className":35884,"style":1924},[259,1873,298],[128,35886,347],{"className":35887},[346],[128,35889,35891],{"className":35890},[278],[128,35892,35894],{"className":35893,"style":2330},[282],[128,35895],{},[128,35897],{"className":35898,"style":1907},[269],[128,35900,35902,35905],{"className":35901},[259],[128,35903,35124],{"className":35904},[259,1873],[128,35906,35908],{"className":35907},[2087],[128,35909,35911,35931],{"className":35910},[274,321],[128,35912,35914,35928],{"className":35913},[278],[128,35915,35917],{"className":35916,"style":2218},[282],[128,35918,35919,35922],{"style":2221},[128,35920],{"className":35921,"style":291},[290],[128,35923,35925],{"className":35924},[299,300,301,298],[128,35926,2022],{"className":35927,"style":2231},[259,1873,298],[128,35929,347],{"className":35930},[346],[128,35932,35934],{"className":35933},[278],[128,35935,35937],{"className":35936,"style":2241},[282],[128,35938],{},[128,35940],{"className":35941,"style":2508},[269],[128,35943,9486],{"className":35944},[2115],[128,35946],{"className":35947,"style":2508},[269],[128,35949,35951,35954,35957,35960,35963],{"className":35950},[250],[128,35952],{"className":35953,"style":7758},[254],[128,35955,35129],{"className":35956},[259,1873],[128,35958],{"className":35959,"style":1878},[269],[128,35961,1994],{"className":35962},[1882],[128,35964],{"className":35965,"style":1878},[269],[128,35967,35969,35972],{"className":35968},[250],[128,35970],{"className":35971,"style":2594},[254],[128,35973,1842],{"className":35974},[259],[11,35976,35977,11101,36006,36009,36010,36215,36216,22492,36315,893],{},[128,35978,35980,35994],{"className":35979,"translate":218},[217],[128,35981,35983],{"className":35982},[222],[224,35984,35985],{"xmlns":226},[228,35986,35987,35991],{},[231,35988,35989],{},[1795,35990,35117],{},[238,35992,35993],{"encoding":240},"\\omega",[128,35995,35997],{"className":35996,"ariaHidden":246},[245],[128,35998,36000,36003],{"className":35999},[250],[128,36001],{"className":36002,"style":7758},[254],[128,36004,35117],{"className":36005,"style":1874},[259,1873],[35,36007,36008],{},"概率投影（probability projection）"," 定义为 ",[128,36011,36013,36049],{"className":36012,"translate":218},[217],[128,36014,36016],{"className":36015},[222],[224,36017,36018],{"xmlns":226},[228,36019,36020,36046],{},[231,36021,36022,36028,36030,36036,36038,36044],{},[2016,36023,36024,36026],{},[1795,36025,23001],{},[1795,36027,2022],{},[1832,36029,1994],{},[2016,36031,36032,36034],{},[1795,36033,35124],{},[1795,36035,2022],{},[1832,36037,9486],{},[2016,36039,36040,36042],{},[1795,36041,21],{},[1795,36043,2022],{},[1795,36045,35129],{},[238,36047,36048],{"encoding":240},"P_k = b_k + a_k u",[128,36050,36052,36110,36166],{"className":36051,"ariaHidden":246},[245],[128,36053,36055,36059,36101,36104,36107],{"className":36054},[250],[128,36056],{"className":36057,"style":36058},[254],"height:0.8333em;vertical-align:-0.15em;",[128,36060,36062,36066],{"className":36061},[259],[128,36063,23001],{"className":36064,"style":36065},[259,1873],"margin-right:0.1389em;",[128,36067,36069],{"className":36068},[2087],[128,36070,36072,36093],{"className":36071},[274,321],[128,36073,36075,36090],{"className":36074},[278],[128,36076,36078],{"className":36077,"style":2218},[282],[128,36079,36081,36084],{"style":36080},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[128,36082],{"className":36083,"style":291},[290],[128,36085,36087],{"className":36086},[299,300,301,298],[128,36088,2022],{"className":36089,"style":2231},[259,1873,298],[128,36091,347],{"className":36092},[346],[128,36094,36096],{"className":36095},[278],[128,36097,36099],{"className":36098,"style":2241},[282],[128,36100],{},[128,36102],{"className":36103,"style":1878},[269],[128,36105,1994],{"className":36106},[1882],[128,36108],{"className":36109,"style":1878},[269],[128,36111,36113,36117,36157,36160,36163],{"className":36112},[250],[128,36114],{"className":36115,"style":36116},[254],"height:0.8444em;vertical-align:-0.15em;",[128,36118,36120,36123],{"className":36119},[259],[128,36121,35124],{"className":36122},[259,1873],[128,36124,36126],{"className":36125},[2087],[128,36127,36129,36149],{"className":36128},[274,321],[128,36130,36132,36146],{"className":36131},[278],[128,36133,36135],{"className":36134,"style":2218},[282],[128,36136,36137,36140],{"style":2221},[128,36138],{"className":36139,"style":291},[290],[128,36141,36143],{"className":36142},[299,300,301,298],[128,36144,2022],{"className":36145,"style":2231},[259,1873,298],[128,36147,347],{"className":36148},[346],[128,36150,36152],{"className":36151},[278],[128,36153,36155],{"className":36154,"style":2241},[282],[128,36156],{},[128,36158],{"className":36159,"style":2508},[269],[128,36161,9486],{"className":36162},[2115],[128,36164],{"className":36165,"style":2508},[269],[128,36167,36169,36172,36212],{"className":36168},[250],[128,36170],{"className":36171,"style":4242},[254],[128,36173,36175,36178],{"className":36174},[259],[128,36176,21],{"className":36177},[259,1873],[128,36179,36181],{"className":36180},[2087],[128,36182,36184,36204],{"className":36183},[274,321],[128,36185,36187,36201],{"className":36186},[278],[128,36188,36190],{"className":36189,"style":2218},[282],[128,36191,36192,36195],{"style":2221},[128,36193],{"className":36194,"style":291},[290],[128,36196,36198],{"className":36197},[299,300,301,298],[128,36199,2022],{"className":36200,"style":2231},[259,1873,298],[128,36202,347],{"className":36203},[346],[128,36205,36207],{"className":36206},[278],[128,36208,36210],{"className":36209,"style":2241},[282],[128,36211],{},[128,36213,35129],{"className":36214},[259,1873],"：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 ",[128,36217,36219,36245],{"className":36218,"translate":218},[217],[128,36220,36222],{"className":36221},[222],[224,36223,36224],{"xmlns":226},[228,36225,36226,36242],{},[231,36227,36228,36234,36236,36238,36240],{},[2016,36229,36230,36232],{},[1795,36231,21],{},[1795,36233,2022],{},[1832,36235,1994],{},[1840,36237,1842],{},[1795,36239,4751],{"mathvariant":1981},[1795,36241,1853],{},[238,36243,36244],{"encoding":240},"a_k = 1\u002FK",[128,36246,36248,36303],{"className":36247,"ariaHidden":246},[245],[128,36249,36251,36254,36294,36297,36300],{"className":36250},[250],[128,36252],{"className":36253,"style":4242},[254],[128,36255,36257,36260],{"className":36256},[259],[128,36258,21],{"className":36259},[259,1873],[128,36261,36263],{"className":36262},[2087],[128,36264,36266,36286],{"className":36265},[274,321],[128,36267,36269,36283],{"className":36268},[278],[128,36270,36272],{"className":36271,"style":2218},[282],[128,36273,36274,36277],{"style":2221},[128,36275],{"className":36276,"style":291},[290],[128,36278,36280],{"className":36279},[299,300,301,298],[128,36281,2022],{"className":36282,"style":2231},[259,1873,298],[128,36284,347],{"className":36285},[346],[128,36287,36289],{"className":36288},[278],[128,36290,36292],{"className":36291,"style":2241},[282],[128,36293],{},[128,36295],{"className":36296,"style":1878},[269],[128,36298,1994],{"className":36299},[1882],[128,36301],{"className":36302,"style":1878},[269],[128,36304,36306,36309,36312],{"className":36305},[250],[128,36307],{"className":36308,"style":1892},[254],[128,36310,4780],{"className":36311},[259],[128,36313,1853],{"className":36314,"style":1924},[259,1873],[128,36316,36318,36352],{"className":36317,"translate":218},[217],[128,36319,36321],{"className":36320},[222],[224,36322,36323],{"xmlns":226},[228,36324,36325,36349],{},[231,36326,36327,36333,36335,36341,36343,36345,36347],{},[2016,36328,36329,36331],{},[1795,36330,23001],{},[1795,36332,2022],{},[1832,36334,1994],{},[2016,36336,36337,36339],{},[1795,36338,35124],{},[1795,36340,2022],{},[1832,36342,9486],{},[1795,36344,35129],{},[1795,36346,4751],{"mathvariant":1981},[1795,36348,1853],{},[238,36350,36351],{"encoding":240},"P_k = b_k + u\u002FK",[128,36353,36355,36410,36465],{"className":36354,"ariaHidden":246},[245],[128,36356,36358,36361,36401,36404,36407],{"className":36357},[250],[128,36359],{"className":36360,"style":36058},[254],[128,36362,36364,36367],{"className":36363},[259],[128,36365,23001],{"className":36366,"style":36065},[259,1873],[128,36368,36370],{"className":36369},[2087],[128,36371,36373,36393],{"className":36372},[274,321],[128,36374,36376,36390],{"className":36375},[278],[128,36377,36379],{"className":36378,"style":2218},[282],[128,36380,36381,36384],{"style":36080},[128,36382],{"className":36383,"style":291},[290],[128,36385,36387],{"className":36386},[299,300,301,298],[128,36388,2022],{"className":36389,"style":2231},[259,1873,298],[128,36391,347],{"className":36392},[346],[128,36394,36396],{"className":36395},[278],[128,36397,36399],{"className":36398,"style":2241},[282],[128,36400],{},[128,36402],{"className":36403,"style":1878},[269],[128,36405,1994],{"className":36406},[1882],[128,36408],{"className":36409,"style":1878},[269],[128,36411,36413,36416,36456,36459,36462],{"className":36412},[250],[128,36414],{"className":36415,"style":36116},[254],[128,36417,36419,36422],{"className":36418},[259],[128,36420,35124],{"className":36421},[259,1873],[128,36423,36425],{"className":36424},[2087],[128,36426,36428,36448],{"className":36427},[274,321],[128,36429,36431,36445],{"className":36430},[278],[128,36432,36434],{"className":36433,"style":2218},[282],[128,36435,36436,36439],{"style":2221},[128,36437],{"className":36438,"style":291},[290],[128,36440,36442],{"className":36441},[299,300,301,298],[128,36443,2022],{"className":36444,"style":2231},[259,1873,298],[128,36446,347],{"className":36447},[346],[128,36449,36451],{"className":36450},[278],[128,36452,36454],{"className":36453,"style":2241},[282],[128,36455],{},[128,36457],{"className":36458,"style":2508},[269],[128,36460,9486],{"className":36461},[2115],[128,36463],{"className":36464,"style":2508},[269],[128,36466,36468,36471,36474,36477],{"className":36467},[250],[128,36469],{"className":36470,"style":1892},[254],[128,36472,35129],{"className":36473},[259,1873],[128,36475,4751],{"className":36476},[259],[128,36478,1853],{"className":36479,"style":1924},[259,1873],[11,36481,36482,36483,36545,36546,36574,36575,36648],{},"定义 3.1 的关键在于：opinion 所栖居的空间是 ",[128,36484,36486,36504],{"className":36485,"translate":218},[217],[128,36487,36489],{"className":36488},[222],[224,36490,36491],{"xmlns":226},[228,36492,36493,36501],{},[231,36494,36495],{},[1977,36496,36497,36499],{},[1795,36498,1982],{"mathvariant":1981},[1795,36500,1853],{},[238,36502,36503],{"encoding":240},"\\Delta^{K}",[128,36505,36507],{"className":36506,"ariaHidden":246},[245],[128,36508,36510,36513],{"className":36509},[250],[128,36511],{"className":36512,"style":2431},[254],[128,36514,36516,36519],{"className":36515},[259],[128,36517,1982],{"className":36518},[259],[128,36520,36522],{"className":36521},[2087],[128,36523,36525],{"className":36524},[274],[128,36526,36528],{"className":36527},[278],[128,36529,36531],{"className":36530,"style":2431},[282],[128,36532,36533,36536],{"style":2452},[128,36534],{"className":36535,"style":291},[290],[128,36537,36539],{"className":36538},[299,300,301,298],[128,36540,36542],{"className":36541},[259,298],[128,36543,1853],{"className":36544,"style":1924},[259,1873,298],"——一个 ",[128,36547,36549,36562],{"className":36548,"translate":218},[217],[128,36550,36552],{"className":36551},[222],[224,36553,36554],{"xmlns":226},[228,36555,36556,36560],{},[231,36557,36558],{},[1795,36559,1853],{},[238,36561,1853],{"encoding":240},[128,36563,36565],{"className":36564,"ariaHidden":246},[245],[128,36566,36568,36571],{"className":36567},[250],[128,36569],{"className":36570,"style":283},[254],[128,36572,1853],{"className":36573,"style":1924},[259,1873]," 维单纯形，比 ",[128,36576,36578,36601],{"className":36577,"translate":218},[217],[128,36579,36581],{"className":36580},[222],[224,36582,36583],{"xmlns":226},[228,36584,36585,36599],{},[231,36586,36587],{},[1977,36588,36589,36591],{},[1795,36590,1982],{"mathvariant":1981},[231,36592,36593,36595,36597],{},[1795,36594,1853],{},[1832,36596,1989],{},[1840,36598,1842],{},[238,36600,3589],{"encoding":240},[128,36602,36604],{"className":36603,"ariaHidden":246},[245],[128,36605,36607,36610],{"className":36606},[250],[128,36608],{"className":36609,"style":2431},[254],[128,36611,36613,36616],{"className":36612},[259],[128,36614,1982],{"className":36615},[259],[128,36617,36619],{"className":36618},[2087],[128,36620,36622],{"className":36621},[274],[128,36623,36625],{"className":36624},[278],[128,36626,36628],{"className":36627,"style":2431},[282],[128,36629,36630,36633],{"style":2452},[128,36631],{"className":36632,"style":291},[290],[128,36634,36636],{"className":36635},[299,300,301,298],[128,36637,36639,36642,36645],{"className":36638},[259,298],[128,36640,1853],{"className":36641,"style":1924},[259,1873,298],[128,36643,1989],{"className":36644},[2115,298],[128,36646,1842],{"className":36647},[259,298]," 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。",[2610,36650,36652],{"id":36651},"_32-dirichlet-与-opinion-的双射","3.2 Dirichlet 与 opinion 的双射",[11,36654,36655,36656,893],{},"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",[35,36657,36658],{},"双射",[2615,36660,36662],{"title":36661},"命题 3.2（双射）",[11,36663,36664,36665,36717,36718,36816,36817],{},"设先验权重 ",[128,36666,36668,36687],{"className":36667,"translate":218},[217],[128,36669,36671],{"className":36670},[222],[224,36672,36673],{"xmlns":226},[228,36674,36675,36684],{},[231,36676,36677,36680,36682],{},[1795,36678,36679],{},"W",[1832,36681,1994],{},[1795,36683,1853],{},[238,36685,36686],{"encoding":240},"W = K",[128,36688,36690,36708],{"className":36689,"ariaHidden":246},[245],[128,36691,36693,36696,36699,36702,36705],{"className":36692},[250],[128,36694],{"className":36695,"style":283},[254],[128,36697,36679],{"className":36698,"style":36065},[259,1873],[128,36700],{"className":36701,"style":1878},[269],[128,36703,1994],{"className":36704},[1882],[128,36706],{"className":36707,"style":1878},[269],[128,36709,36711,36714],{"className":36710},[250],[128,36712],{"className":36713,"style":283},[254],[128,36715,1853],{"className":36716,"style":1924},[259,1873],"、基准率 ",[128,36719,36721,36746],{"className":36720,"translate":218},[217],[128,36722,36724],{"className":36723},[222],[224,36725,36726],{"xmlns":226},[228,36727,36728,36744],{},[231,36729,36730,36736,36738,36740,36742],{},[2016,36731,36732,36734],{},[1795,36733,21],{},[1795,36735,2022],{},[1832,36737,1994],{},[1840,36739,1842],{},[1795,36741,4751],{"mathvariant":1981},[1795,36743,1853],{},[238,36745,36244],{"encoding":240},[128,36747,36749,36804],{"className":36748,"ariaHidden":246},[245],[128,36750,36752,36755,36795,36798,36801],{"className":36751},[250],[128,36753],{"className":36754,"style":4242},[254],[128,36756,36758,36761],{"className":36757},[259],[128,36759,21],{"className":36760},[259,1873],[128,36762,36764],{"className":36763},[2087],[128,36765,36767,36787],{"className":36766},[274,321],[128,36768,36770,36784],{"className":36769},[278],[128,36771,36773],{"className":36772,"style":2218},[282],[128,36774,36775,36778],{"style":2221},[128,36776],{"className":36777,"style":291},[290],[128,36779,36781],{"className":36780},[299,300,301,298],[128,36782,2022],{"className":36783,"style":2231},[259,1873,298],[128,36785,347],{"className":36786},[346],[128,36788,36790],{"className":36789},[278],[128,36791,36793],{"className":36792,"style":2241},[282],[128,36794],{},[128,36796],{"className":36797,"style":1878},[269],[128,36799,1994],{"className":36800},[1882],[128,36802],{"className":36803,"style":1878},[269],[128,36805,36807,36810,36813],{"className":36806},[250],[128,36808],{"className":36809,"style":1892},[254],[128,36811,4780],{"className":36812},[259],[128,36814,1853],{"className":36815,"style":1924},[259,1873],"。则如下两个映射互逆：\n",[128,36818,36820,36922],{"className":36819,"translate":218},[217],[128,36821,36823],{"className":36822},[222],[224,36824,36825],{"xmlns":226},[228,36826,36827,36919],{},[231,36828,36829,36831,36833,36849,36851,36853,36855,36857,36867,36869,36871,36873,36879,36881,36897,36899,36901,36903,36905,36911,36913],{},[1795,36830,35124],{"mathvariant":2001},[1832,36832,1994],{},[5451,36834,36835,36843],{},[231,36836,36837,36839,36841],{},[1795,36838,4835],{"mathvariant":4834},[1832,36840,1989],{},[1840,36842,1842],{"mathvariant":2001},[2016,36844,36845,36847],{},[1795,36846,4835],{},[1840,36848,2028],{},[1832,36850,1845],{"separator":246},[269,36852],{"width":11568},[1795,36854,35129],{},[1832,36856,1994],{},[5451,36858,36859,36861],{},[1795,36860,1853],{},[2016,36862,36863,36865],{},[1795,36864,4835],{},[1840,36866,2028],{},[269,36868],{"width":11568},[1832,36870,26228],{},[269,36872],{"width":11568},[2016,36874,36875,36877],{},[1795,36876,4835],{},[1795,36878,2022],{},[1832,36880,1994],{},[5451,36882,36883,36895],{},[231,36884,36885,36887,36889],{},[1795,36886,1853],{},[234,36888,6528],{},[2016,36890,36891,36893],{},[1795,36892,35124],{},[1795,36894,2022],{},[1795,36896,35129],{},[1832,36898,9486],{},[1840,36900,1842],{},[1832,36902,1845],{"separator":246},[269,36904],{"width":11568},[2016,36906,36907,36909],{},[1795,36908,4835],{},[1840,36910,2028],{},[1832,36912,1994],{},[5451,36914,36915,36917],{},[1795,36916,1853],{},[1795,36918,35129],{},[238,36920,36921],{"encoding":240},"\\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}",[128,36923,36925,36943,37087,37215,37270,37398,37465],{"className":36924,"ariaHidden":246},[245],[128,36926,36928,36931,36934,36937,36940],{"className":36927},[250],[128,36929],{"className":36930,"style":12173},[254],[128,36932,35124],{"className":36933},[259,2151],[128,36935],{"className":36936,"style":1878},[269],[128,36938,1994],{"className":36939},[1882],[128,36941],{"className":36942,"style":1878},[269],[128,36944,36946,36949,37066,37069,37072,37075,37078,37081,37084],{"className":36945},[250],[128,36947],{"className":36948,"style":18295},[254],[128,36950,36952,36955,37063],{"className":36951},[259],[128,36953],{"className":36954},[1896,5570],[128,36956,36958],{"className":36957},[5451],[128,36959,36961,37055],{"className":36960},[274,321],[128,36962,36964,37052],{"className":36963},[278],[128,36965,36967,37018,37026],{"className":36966,"style":5583},[282],[128,36968,36969,36972],{"style":5586},[128,36970],{"className":36971,"style":335},[290],[128,36973,36975],{"className":36974},[299,300,301,298],[128,36976,36978],{"className":36977},[259,298],[128,36979,36981,36984],{"className":36980},[259,298],[128,36982,4835],{"className":36983,"style":4920},[259,1873,298],[128,36985,36987],{"className":36986},[2087],[128,36988,36990,37010],{"className":36989},[274,321],[128,36991,36993,37007],{"className":36992},[278],[128,36994,36996],{"className":36995,"style":6153},[282],[128,36997,36998,37001],{"style":5786},[128,36999],{"className":37000,"style":5790},[290],[128,37002,37004],{"className":37003},[299,5794,5795,298],[128,37005,2028],{"className":37006},[259,298],[128,37008,347],{"className":37009},[346],[128,37011,37013],{"className":37012},[278],[128,37014,37016],{"className":37015,"style":5808},[282],[128,37017],{},[128,37019,37020,37023],{"style":5617},[128,37021],{"className":37022,"style":335},[290],[128,37024],{"className":37025,"style":5625},[5624],[128,37027,37028,37031],{"style":5628},[128,37029],{"className":37030,"style":335},[290],[128,37032,37034],{"className":37033},[299,300,301,298],[128,37035,37037,37046,37049],{"className":37036},[259,298],[128,37038,37040],{"className":37039},[259,298],[128,37041,37043],{"className":37042},[259,298],[128,37044,4835],{"className":37045},[259,4895,298],[128,37047,1989],{"className":37048},[2115,298],[128,37050,1842],{"className":37051},[259,2151,298],[128,37053,347],{"className":37054},[346],[128,37056,37058],{"className":37057},[278],[128,37059,37061],{"className":37060,"style":16937},[282],[128,37062],{},[128,37064],{"className":37065},[1928,5570],[128,37067,1845],{"className":37068},[1903],[128,37070],{"className":37071,"style":11756},[269],[128,37073],{"className":37074,"style":1907},[269],[128,37076,35129],{"className":37077},[259,1873],[128,37079],{"className":37080,"style":1878},[269],[128,37082,1994],{"className":37083},[1882],[128,37085],{"className":37086,"style":1878},[269],[128,37088,37090,37094,37200,37203,37206,37209,37212],{"className":37089},[250],[128,37091],{"className":37092,"style":37093},[254],"height:1.3174em;vertical-align:-0.4451em;",[128,37095,37097,37100,37197],{"className":37096},[259],[128,37098],{"className":37099},[1896,5570],[128,37101,37103],{"className":37102},[5451],[128,37104,37106,37189],{"className":37105},[274,321],[128,37107,37109,37186],{"className":37108},[278],[128,37110,37113,37164,37172],{"className":37111,"style":37112},[282],"height:0.8723em;",[128,37114,37115,37118],{"style":5586},[128,37116],{"className":37117,"style":335},[290],[128,37119,37121],{"className":37120},[299,300,301,298],[128,37122,37124],{"className":37123},[259,298],[128,37125,37127,37130],{"className":37126},[259,298],[128,37128,4835],{"className":37129,"style":4920},[259,1873,298],[128,37131,37133],{"className":37132},[2087],[128,37134,37136,37156],{"className":37135},[274,321],[128,37137,37139,37153],{"className":37138},[278],[128,37140,37142],{"className":37141,"style":6153},[282],[128,37143,37144,37147],{"style":5786},[128,37145],{"className":37146,"style":5790},[290],[128,37148,37150],{"className":37149},[299,5794,5795,298],[128,37151,2028],{"className":37152},[259,298],[128,37154,347],{"className":37155},[346],[128,37157,37159],{"className":37158},[278],[128,37160,37162],{"className":37161,"style":5808},[282],[128,37163],{},[128,37165,37166,37169],{"style":5617},[128,37167],{"className":37168,"style":335},[290],[128,37170],{"className":37171,"style":5625},[5624],[128,37173,37174,37177],{"style":5628},[128,37175],{"className":37176,"style":335},[290],[128,37178,37180],{"className":37179},[299,300,301,298],[128,37181,37183],{"className":37182},[259,298],[128,37184,1853],{"className":37185,"style":1924},[259,1873,298],[128,37187,347],{"className":37188},[346],[128,37190,37192],{"className":37191},[278],[128,37193,37195],{"className":37194,"style":16937},[282],[128,37196],{},[128,37198],{"className":37199},[1928,5570],[128,37201],{"className":37202,"style":11756},[269],[128,37204],{"className":37205,"style":1878},[269],[128,37207,26228],{"className":37208},[1882],[128,37210],{"className":37211,"style":11756},[269],[128,37213],{"className":37214,"style":1878},[269],[128,37216,37218,37221,37261,37264,37267],{"className":37217},[250],[128,37219],{"className":37220,"style":4242},[254],[128,37222,37224,37227],{"className":37223},[259],[128,37225,4835],{"className":37226,"style":4920},[259,1873],[128,37228,37230],{"className":37229},[2087],[128,37231,37233,37253],{"className":37232},[274,321],[128,37234,37236,37250],{"className":37235},[278],[128,37237,37239],{"className":37238,"style":2218},[282],[128,37240,37241,37244],{"style":4935},[128,37242],{"className":37243,"style":291},[290],[128,37245,37247],{"className":37246},[299,300,301,298],[128,37248,2022],{"className":37249,"style":2231},[259,1873,298],[128,37251,347],{"className":37252},[346],[128,37254,37256],{"className":37255},[278],[128,37257,37259],{"className":37258,"style":2241},[282],[128,37260],{},[128,37262],{"className":37263,"style":1878},[269],[128,37265,1994],{"className":37266},[1882],[128,37268],{"className":37269,"style":1878},[269],[128,37271,37273,37277,37389,37392,37395],{"className":37272},[250],[128,37274],{"className":37275,"style":37276},[254],"height:1.247em;vertical-align:-0.345em;",[128,37278,37280,37283,37386],{"className":37279},[259],[128,37281],{"className":37282},[1896,5570],[128,37284,37286],{"className":37285},[5451],[128,37287,37289,37378],{"className":37288},[274,321],[128,37290,37292,37375],{"className":37291},[278],[128,37293,37296,37310,37318],{"className":37294,"style":37295},[282],"height:0.902em;",[128,37297,37298,37301],{"style":5586},[128,37299],{"className":37300,"style":335},[290],[128,37302,37304],{"className":37303},[299,300,301,298],[128,37305,37307],{"className":37306},[259,298],[128,37308,35129],{"className":37309},[259,1873,298],[128,37311,37312,37315],{"style":5617},[128,37313],{"className":37314,"style":335},[290],[128,37316],{"className":37317,"style":5625},[5624],[128,37319,37320,37323],{"style":28909},[128,37321],{"className":37322,"style":335},[290],[128,37324,37326],{"className":37325},[299,300,301,298],[128,37327,37329,37332,37335],{"className":37328},[259,298],[128,37330,1853],{"className":37331,"style":1924},[259,1873,298],[128,37333],{"className":37334,"style":6269},[269,298],[128,37336,37338,37341],{"className":37337},[259,298],[128,37339,35124],{"className":37340},[259,1873,298],[128,37342,37344],{"className":37343},[2087],[128,37345,37347,37367],{"className":37346},[274,321],[128,37348,37350,37364],{"className":37349},[278],[128,37351,37353],{"className":37352,"style":24117},[282],[128,37354,37355,37358],{"style":28984},[128,37356],{"className":37357,"style":5790},[290],[128,37359,37361],{"className":37360},[299,5794,5795,298],[128,37362,2022],{"className":37363,"style":2231},[259,1873,298],[128,37365,347],{"className":37366},[346],[128,37368,37370],{"className":37369},[278],[128,37371,37373],{"className":37372,"style":28958},[282],[128,37374],{},[128,37376,347],{"className":37377},[346],[128,37379,37381],{"className":37380},[278],[128,37382,37384],{"className":37383,"style":11919},[282],[128,37385],{},[128,37387],{"className":37388},[1928,5570],[128,37390],{"className":37391,"style":2508},[269],[128,37393,9486],{"className":37394},[2115],[128,37396],{"className":37397,"style":2508},[269],[128,37399,37401,37404,37407,37410,37413,37416,37456,37459,37462],{"className":37400},[250],[128,37402],{"className":37403,"style":21472},[254],[128,37405,1842],{"className":37406},[259],[128,37408,1845],{"className":37409},[1903],[128,37411],{"className":37412,"style":11756},[269],[128,37414],{"className":37415,"style":1907},[269],[128,37417,37419,37422],{"className":37418},[259],[128,37420,4835],{"className":37421,"style":4920},[259,1873],[128,37423,37425],{"className":37424},[2087],[128,37426,37428,37448],{"className":37427},[274,321],[128,37429,37431,37445],{"className":37430},[278],[128,37432,37434],{"className":37433,"style":2945},[282],[128,37435,37436,37439],{"style":4935},[128,37437],{"className":37438,"style":291},[290],[128,37440,37442],{"className":37441},[299,300,301,298],[128,37443,2028],{"className":37444},[259,298],[128,37446,347],{"className":37447},[346],[128,37449,37451],{"className":37450},[278],[128,37452,37454],{"className":37453,"style":2241},[282],[128,37455],{},[128,37457],{"className":37458,"style":1878},[269],[128,37460,1994],{"className":37461},[1882],[128,37463],{"className":37464,"style":1878},[269],[128,37466,37468,37472],{"className":37467},[250],[128,37469],{"className":37470,"style":37471},[254],"height:1.2173em;vertical-align:-0.345em;",[128,37473,37475,37478,37537],{"className":37474},[259],[128,37476],{"className":37477},[1896,5570],[128,37479,37481],{"className":37480},[5451],[128,37482,37484,37529],{"className":37483},[274,321],[128,37485,37487,37526],{"className":37486},[278],[128,37488,37490,37504,37512],{"className":37489,"style":37112},[282],[128,37491,37492,37495],{"style":5586},[128,37493],{"className":37494,"style":335},[290],[128,37496,37498],{"className":37497},[299,300,301,298],[128,37499,37501],{"className":37500},[259,298],[128,37502,35129],{"className":37503},[259,1873,298],[128,37505,37506,37509],{"style":5617},[128,37507],{"className":37508,"style":335},[290],[128,37510],{"className":37511,"style":5625},[5624],[128,37513,37514,37517],{"style":5628},[128,37515],{"className":37516,"style":335},[290],[128,37518,37520],{"className":37519},[299,300,301,298],[128,37521,37523],{"className":37522},[259,298],[128,37524,1853],{"className":37525,"style":1924},[259,1873,298],[128,37527,347],{"className":37528},[346],[128,37530,37532],{"className":37531},[278],[128,37533,37535],{"className":37534,"style":11919},[282],[128,37536],{},[128,37538],{"className":37539},[1928,5570],[11,37541,37542,37545,37546,38028],{},[35,37543,37544],{},"验证"," 正向：",[128,37547,37549,37615],{"className":37548,"translate":218},[217],[128,37550,37552],{"className":37551},[222],[224,37553,37554],{"xmlns":226},[228,37555,37556,37612],{},[231,37557,37558,37564,37570,37572,37574,37576,37596,37598,37608,37610],{},[2016,37559,37560,37562],{},[1832,37561,2042],{},[1795,37563,2022],{},[2016,37565,37566,37568],{},[1795,37567,35124],{},[1795,37569,2022],{},[1832,37571,9486],{},[1795,37573,35129],{},[1832,37575,1994],{},[5451,37577,37578,37590],{},[231,37579,37580,37586,37588],{},[2016,37581,37582,37584],{},[1795,37583,4835],{},[1840,37585,2028],{},[1832,37587,1989],{},[1795,37589,1853],{},[2016,37591,37592,37594],{},[1795,37593,4835],{},[1840,37595,2028],{},[1832,37597,9486],{},[5451,37599,37600,37602],{},[1795,37601,1853],{},[2016,37603,37604,37606],{},[1795,37605,4835],{},[1840,37607,2028],{},[1832,37609,1994],{},[1840,37611,1842],{},[238,37613,37614],{"encoding":240},"\\sum_k b_k + u = \\frac{\\alpha_0 - K}{\\alpha_0} + \\frac{K}{\\alpha_0} = 1",[128,37616,37618,37716,37734,37899,38019],{"className":37617,"ariaHidden":246},[245],[128,37619,37621,37624,37664,37667,37707,37710,37713],{"className":37620},[250],[128,37622],{"className":37623,"style":7777},[254],[128,37625,37627,37630],{"className":37626},[2268],[128,37628,2042],{"className":37629,"style":2274},[2268,2272,2273],[128,37631,37633],{"className":37632},[2087],[128,37634,37636,37656],{"className":37635},[274,321],[128,37637,37639,37653],{"className":37638},[278],[128,37640,37642],{"className":37641,"style":31692},[282],[128,37643,37644,37647],{"style":2290},[128,37645],{"className":37646,"style":291},[290],[128,37648,37650],{"className":37649},[299,300,301,298],[128,37651,2022],{"className":37652,"style":2231},[259,1873,298],[128,37654,347],{"className":37655},[346],[128,37657,37659],{"className":37658},[278],[128,37660,37662],{"className":37661,"style":2330},[282],[128,37663],{},[128,37665],{"className":37666,"style":1907},[269],[128,37668,37670,37673],{"className":37669},[259],[128,37671,35124],{"className":37672},[259,1873],[128,37674,37676],{"className":37675},[2087],[128,37677,37679,37699],{"className":37678},[274,321],[128,37680,37682,37696],{"className":37681},[278],[128,37683,37685],{"className":37684,"style":2218},[282],[128,37686,37687,37690],{"style":2221},[128,37688],{"className":37689,"style":291},[290],[128,37691,37693],{"className":37692},[299,300,301,298],[128,37694,2022],{"className":37695,"style":2231},[259,1873,298],[128,37697,347],{"className":37698},[346],[128,37700,37702],{"className":37701},[278],[128,37703,37705],{"className":37704,"style":2241},[282],[128,37706],{},[128,37708],{"className":37709,"style":2508},[269],[128,37711,9486],{"className":37712},[2115],[128,37714],{"className":37715,"style":2508},[269],[128,37717,37719,37722,37725,37728,37731],{"className":37718},[250],[128,37720],{"className":37721,"style":7758},[254],[128,37723,35129],{"className":37724},[259,1873],[128,37726],{"className":37727,"style":1878},[269],[128,37729,1994],{"className":37730},[1882],[128,37732],{"className":37733,"style":1878},[269],[128,37735,37737,37741,37890,37893,37896],{"className":37736},[250],[128,37738],{"className":37739,"style":37740},[254],"height:1.3335em;vertical-align:-0.4451em;",[128,37742,37744,37747,37887],{"className":37743},[259],[128,37745],{"className":37746},[1896,5570],[128,37748,37750],{"className":37749},[5451],[128,37751,37753,37879],{"className":37752},[274,321],[128,37754,37756,37876],{"className":37755},[278],[128,37757,37760,37811,37819],{"className":37758,"style":37759},[282],"height:0.8884em;",[128,37761,37762,37765],{"style":5586},[128,37763],{"className":37764,"style":335},[290],[128,37766,37768],{"className":37767},[299,300,301,298],[128,37769,37771],{"className":37770},[259,298],[128,37772,37774,37777],{"className":37773},[259,298],[128,37775,4835],{"className":37776,"style":4920},[259,1873,298],[128,37778,37780],{"className":37779},[2087],[128,37781,37783,37803],{"className":37782},[274,321],[128,37784,37786,37800],{"className":37785},[278],[128,37787,37789],{"className":37788,"style":6153},[282],[128,37790,37791,37794],{"style":5786},[128,37792],{"className":37793,"style":5790},[290],[128,37795,37797],{"className":37796},[299,5794,5795,298],[128,37798,2028],{"className":37799},[259,298],[128,37801,347],{"className":37802},[346],[128,37804,37806],{"className":37805},[278],[128,37807,37809],{"className":37808,"style":5808},[282],[128,37810],{},[128,37812,37813,37816],{"style":5617},[128,37814],{"className":37815,"style":335},[290],[128,37817],{"className":37818,"style":5625},[5624],[128,37820,37821,37824],{"style":16878},[128,37822],{"className":37823,"style":335},[290],[128,37825,37827],{"className":37826},[299,300,301,298],[128,37828,37830,37870,37873],{"className":37829},[259,298],[128,37831,37833,37836],{"className":37832},[259,298],[128,37834,4835],{"className":37835,"style":4920},[259,1873,298],[128,37837,37839],{"className":37838},[2087],[128,37840,37842,37862],{"className":37841},[274,321],[128,37843,37845,37859],{"className":37844},[278],[128,37846,37848],{"className":37847,"style":6153},[282],[128,37849,37850,37853],{"style":5786},[128,37851],{"className":37852,"style":5790},[290],[128,37854,37856],{"className":37855},[299,5794,5795,298],[128,37857,2028],{"className":37858},[259,298],[128,37860,347],{"className":37861},[346],[128,37863,37865],{"className":37864},[278],[128,37866,37868],{"className":37867,"style":5808},[282],[128,37869],{},[128,37871,1989],{"className":37872},[2115,298],[128,37874,1853],{"className":37875,"style":1924},[259,1873,298],[128,37877,347],{"className":37878},[346],[128,37880,37882],{"className":37881},[278],[128,37883,37885],{"className":37884,"style":16937},[282],[128,37886],{},[128,37888],{"className":37889},[1928,5570],[128,37891],{"className":37892,"style":2508},[269],[128,37894,9486],{"className":37895},[2115],[128,37897],{"className":37898,"style":2508},[269],[128,37900,37902,37905,38010,38013,38016],{"className":37901},[250],[128,37903],{"className":37904,"style":37093},[254],[128,37906,37908,37911,38007],{"className":37907},[259],[128,37909],{"className":37910},[1896,5570],[128,37912,37914],{"className":37913},[5451],[128,37915,37917,37999],{"className":37916},[274,321],[128,37918,37920,37996],{"className":37919},[278],[128,37921,37923,37974,37982],{"className":37922,"style":37112},[282],[128,37924,37925,37928],{"style":5586},[128,37926],{"className":37927,"style":335},[290],[128,37929,37931],{"className":37930},[299,300,301,298],[128,37932,37934],{"className":37933},[259,298],[128,37935,37937,37940],{"className":37936},[259,298],[128,37938,4835],{"className":37939,"style":4920},[259,1873,298],[128,37941,37943],{"className":37942},[2087],[128,37944,37946,37966],{"className":37945},[274,321],[128,37947,37949,37963],{"className":37948},[278],[128,37950,37952],{"className":37951,"style":6153},[282],[128,37953,37954,37957],{"style":5786},[128,37955],{"className":37956,"style":5790},[290],[128,37958,37960],{"className":37959},[299,5794,5795,298],[128,37961,2028],{"className":37962},[259,298],[128,37964,347],{"className":37965},[346],[128,37967,37969],{"className":37968},[278],[128,37970,37972],{"className":37971,"style":5808},[282],[128,37973],{},[128,37975,37976,37979],{"style":5617},[128,37977],{"className":37978,"style":335},[290],[128,37980],{"className":37981,"style":5625},[5624],[128,37983,37984,37987],{"style":5628},[128,37985],{"className":37986,"style":335},[290],[128,37988,37990],{"className":37989},[299,300,301,298],[128,37991,37993],{"className":37992},[259,298],[128,37994,1853],{"className":37995,"style":1924},[259,1873,298],[128,37997,347],{"className":37998},[346],[128,38000,38002],{"className":38001},[278],[128,38003,38005],{"className":38004,"style":16937},[282],[128,38006],{},[128,38008],{"className":38009},[1928,5570],[128,38011],{"className":38012,"style":1878},[269],[128,38014,1994],{"className":38015},[1882],[128,38017],{"className":38018,"style":1878},[269],[128,38020,38022,38025],{"className":38021},[250],[128,38023],{"className":38024,"style":2594},[254],[128,38026,1842],{"className":38027},[259],"，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：",[128,38030,38032],{"className":38031,"translate":218},[1962],[128,38033,38035,38133],{"className":38034,"translate":218},[217],[128,38036,38038],{"className":38037},[222],[224,38039,38040],{"xmlns":226,"display":1971},[228,38041,38042,38130],{},[231,38043,38044,38050,38052,38058,38060,38066,38068,38088,38090,38100,38102,38116,38118,38120,38122,38128],{},[2016,38045,38046,38048],{},[1795,38047,23001],{},[1795,38049,2022],{},[1832,38051,1994],{},[2016,38053,38054,38056],{},[1795,38055,35124],{},[1795,38057,2022],{},[1832,38059,9486],{},[5451,38061,38062,38064],{},[1795,38063,35129],{},[1795,38065,1853],{},[1832,38067,1994],{},[5451,38069,38070,38082],{},[231,38071,38072,38078,38080],{},[2016,38073,38074,38076],{},[1795,38075,4835],{},[1795,38077,2022],{},[1832,38079,1989],{},[1840,38081,1842],{},[2016,38083,38084,38086],{},[1795,38085,4835],{},[1840,38087,2028],{},[1832,38089,9486],{},[5451,38091,38092,38094],{},[1840,38093,1842],{},[2016,38095,38096,38098],{},[1795,38097,4835],{},[1840,38099,2028],{},[1832,38101,1994],{},[5451,38103,38104,38110],{},[2016,38105,38106,38108],{},[1795,38107,4835],{},[1795,38109,2022],{},[2016,38111,38112,38114],{},[1795,38113,4835],{},[1840,38115,2028],{},[1832,38117,1994],{},[1795,38119,342],{"mathvariant":2008},[1832,38121,16538],{"stretchy":1837},[2016,38123,38124,38126],{},[1795,38125,2760],{},[1795,38127,2022],{},[1832,38129,16547],{"stretchy":1837},[238,38131,38132],{"encoding":240},"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]",[128,38134,38136,38191,38246,38325,38488,38602,38754],{"className":38135,"ariaHidden":246},[245],[128,38137,38139,38142,38182,38185,38188],{"className":38138},[250],[128,38140],{"className":38141,"style":36058},[254],[128,38143,38145,38148],{"className":38144},[259],[128,38146,23001],{"className":38147,"style":36065},[259,1873],[128,38149,38151],{"className":38150},[2087],[128,38152,38154,38174],{"className":38153},[274,321],[128,38155,38157,38171],{"className":38156},[278],[128,38158,38160],{"className":38159,"style":2218},[282],[128,38161,38162,38165],{"style":36080},[128,38163],{"className":38164,"style":291},[290],[128,38166,38168],{"className":38167},[299,300,301,298],[128,38169,2022],{"className":38170,"style":2231},[259,1873,298],[128,38172,347],{"className":38173},[346],[128,38175,38177],{"className":38176},[278],[128,38178,38180],{"className":38179,"style":2241},[282],[128,38181],{},[128,38183],{"className":38184,"style":1878},[269],[128,38186,1994],{"className":38187},[1882],[128,38189],{"className":38190,"style":1878},[269],[128,38192,38194,38197,38237,38240,38243],{"className":38193},[250],[128,38195],{"className":38196,"style":36116},[254],[128,38198,38200,38203],{"className":38199},[259],[128,38201,35124],{"className":38202},[259,1873],[128,38204,38206],{"className":38205},[2087],[128,38207,38209,38229],{"className":38208},[274,321],[128,38210,38212,38226],{"className":38211},[278],[128,38213,38215],{"className":38214,"style":2218},[282],[128,38216,38217,38220],{"style":2221},[128,38218],{"className":38219,"style":291},[290],[128,38221,38223],{"className":38222},[299,300,301,298],[128,38224,2022],{"className":38225,"style":2231},[259,1873,298],[128,38227,347],{"className":38228},[346],[128,38230,38232],{"className":38231},[278],[128,38233,38235],{"className":38234,"style":2241},[282],[128,38236],{},[128,38238],{"className":38239,"style":2508},[269],[128,38241,9486],{"className":38242},[2115],[128,38244],{"className":38245,"style":2508},[269],[128,38247,38249,38253,38316,38319,38322],{"className":38248},[250],[128,38250],{"className":38251,"style":38252},[254],"height:1.7936em;vertical-align:-0.686em;",[128,38254,38256,38259,38313],{"className":38255},[259],[128,38257],{"className":38258},[1896,5570],[128,38260,38262],{"className":38261},[5451],[128,38263,38265,38304],{"className":38264},[274,321],[128,38266,38268,38301],{"className":38267},[278],[128,38269,38271,38282,38290],{"className":38270,"style":29354},[282],[128,38272,38273,38276],{"style":13123},[128,38274],{"className":38275,"style":335},[290],[128,38277,38279],{"className":38278},[259],[128,38280,1853],{"className":38281,"style":1924},[259,1873],[128,38283,38284,38287],{"style":5617},[128,38285],{"className":38286,"style":335},[290],[128,38288],{"className":38289,"style":5625},[5624],[128,38291,38292,38295],{"style":13189},[128,38293],{"className":38294,"style":335},[290],[128,38296,38298],{"className":38297},[259],[128,38299,35129],{"className":38300},[259,1873],[128,38302,347],{"className":38303},[346],[128,38305,38307],{"className":38306},[278],[128,38308,38311],{"className":38309,"style":38310},[282],"height:0.686em;",[128,38312],{},[128,38314],{"className":38315},[1928,5570],[128,38317],{"className":38318,"style":1878},[269],[128,38320,1994],{"className":38321},[1882],[128,38323],{"className":38324,"style":1878},[269],[128,38326,38328,38331,38479,38482,38485],{"className":38327},[250],[128,38329],{"className":38330,"style":20388},[254],[128,38332,38334,38337,38476],{"className":38333},[259],[128,38335],{"className":38336},[1896,5570],[128,38338,38340],{"className":38339},[5451],[128,38341,38343,38468],{"className":38342},[274,321],[128,38344,38346,38465],{"className":38345},[278],[128,38347,38349,38397,38405],{"className":38348,"style":20407},[282],[128,38350,38351,38354],{"style":13123},[128,38352],{"className":38353,"style":335},[290],[128,38355,38357],{"className":38356},[259],[128,38358,38360,38363],{"className":38359},[259],[128,38361,4835],{"className":38362,"style":4920},[259,1873],[128,38364,38366],{"className":38365},[2087],[128,38367,38369,38389],{"className":38368},[274,321],[128,38370,38372,38386],{"className":38371},[278],[128,38373,38375],{"className":38374,"style":2945},[282],[128,38376,38377,38380],{"style":4935},[128,38378],{"className":38379,"style":291},[290],[128,38381,38383],{"className":38382},[299,300,301,298],[128,38384,2028],{"className":38385},[259,298],[128,38387,347],{"className":38388},[346],[128,38390,38392],{"className":38391},[278],[128,38393,38395],{"className":38394,"style":2241},[282],[128,38396],{},[128,38398,38399,38402],{"style":5617},[128,38400],{"className":38401,"style":335},[290],[128,38403],{"className":38404,"style":5625},[5624],[128,38406,38407,38410],{"style":13189},[128,38408],{"className":38409,"style":335},[290],[128,38411,38413,38453,38456,38459,38462],{"className":38412},[259],[128,38414,38416,38419],{"className":38415},[259],[128,38417,4835],{"className":38418,"style":4920},[259,1873],[128,38420,38422],{"className":38421},[2087],[128,38423,38425,38445],{"className":38424},[274,321],[128,38426,38428,38442],{"className":38427},[278],[128,38429,38431],{"className":38430,"style":2218},[282],[128,38432,38433,38436],{"style":4935},[128,38434],{"className":38435,"style":291},[290],[128,38437,38439],{"className":38438},[299,300,301,298],[128,38440,2022],{"className":38441,"style":2231},[259,1873,298],[128,38443,347],{"className":38444},[346],[128,38446,38448],{"className":38447},[278],[128,38449,38451],{"className":38450,"style":2241},[282],[128,38452],{},[128,38454],{"className":38455,"style":2508},[269],[128,38457,1989],{"className":38458},[2115],[128,38460],{"className":38461,"style":2508},[269],[128,38463,1842],{"className":38464},[259],[128,38466,347],{"className":38467},[346],[128,38469,38471],{"className":38470},[278],[128,38472,38474],{"className":38473,"style":20496},[282],[128,38475],{},[128,38477],{"className":38478},[1928,5570],[128,38480],{"className":38481,"style":2508},[269],[128,38483,9486],{"className":38484},[2115],[128,38486],{"className":38487,"style":2508},[269],[128,38489,38491,38494,38593,38596,38599],{"className":38490},[250],[128,38492],{"className":38493,"style":20388},[254],[128,38495,38497,38500,38590],{"className":38496},[259],[128,38498],{"className":38499},[1896,5570],[128,38501,38503],{"className":38502},[5451],[128,38504,38506,38582],{"className":38505},[274,321],[128,38507,38509,38579],{"className":38508},[278],[128,38510,38512,38560,38568],{"className":38511,"style":20407},[282],[128,38513,38514,38517],{"style":13123},[128,38515],{"className":38516,"style":335},[290],[128,38518,38520],{"className":38519},[259],[128,38521,38523,38526],{"className":38522},[259],[128,38524,4835],{"className":38525,"style":4920},[259,1873],[128,38527,38529],{"className":38528},[2087],[128,38530,38532,38552],{"className":38531},[274,321],[128,38533,38535,38549],{"className":38534},[278],[128,38536,38538],{"className":38537,"style":2945},[282],[128,38539,38540,38543],{"style":4935},[128,38541],{"className":38542,"style":291},[290],[128,38544,38546],{"className":38545},[299,300,301,298],[128,38547,2028],{"className":38548},[259,298],[128,38550,347],{"className":38551},[346],[128,38553,38555],{"className":38554},[278],[128,38556,38558],{"className":38557,"style":2241},[282],[128,38559],{},[128,38561,38562,38565],{"style":5617},[128,38563],{"className":38564,"style":335},[290],[128,38566],{"className":38567,"style":5625},[5624],[128,38569,38570,38573],{"style":13189},[128,38571],{"className":38572,"style":335},[290],[128,38574,38576],{"className":38575},[259],[128,38577,1842],{"className":38578},[259],[128,38580,347],{"className":38581},[346],[128,38583,38585],{"className":38584},[278],[128,38586,38588],{"className":38587,"style":20496},[282],[128,38589],{},[128,38591],{"className":38592},[1928,5570],[128,38594],{"className":38595,"style":1878},[269],[128,38597,1994],{"className":38598},[1882],[128,38600],{"className":38601,"style":1878},[269],[128,38603,38605,38609,38745,38748,38751],{"className":38604},[250],[128,38606],{"className":38607,"style":38608},[254],"height:1.9436em;vertical-align:-0.836em;",[128,38610,38612,38615,38742],{"className":38611},[259],[128,38613],{"className":38614},[1896,5570],[128,38616,38618],{"className":38617},[5451],[128,38619,38621,38734],{"className":38620},[274,321],[128,38622,38624,38731],{"className":38623},[278],[128,38625,38627,38675,38683],{"className":38626,"style":29354},[282],[128,38628,38629,38632],{"style":13123},[128,38630],{"className":38631,"style":335},[290],[128,38633,38635],{"className":38634},[259],[128,38636,38638,38641],{"className":38637},[259],[128,38639,4835],{"className":38640,"style":4920},[259,1873],[128,38642,38644],{"className":38643},[2087],[128,38645,38647,38667],{"className":38646},[274,321],[128,38648,38650,38664],{"className":38649},[278],[128,38651,38653],{"className":38652,"style":2945},[282],[128,38654,38655,38658],{"style":4935},[128,38656],{"className":38657,"style":291},[290],[128,38659,38661],{"className":38660},[299,300,301,298],[128,38662,2028],{"className":38663},[259,298],[128,38665,347],{"className":38666},[346],[128,38668,38670],{"className":38669},[278],[128,38671,38673],{"className":38672,"style":2241},[282],[128,38674],{},[128,38676,38677,38680],{"style":5617},[128,38678],{"className":38679,"style":335},[290],[128,38681],{"className":38682,"style":5625},[5624],[128,38684,38685,38688],{"style":13189},[128,38686],{"className":38687,"style":335},[290],[128,38689,38691],{"className":38690},[259],[128,38692,38694,38697],{"className":38693},[259],[128,38695,4835],{"className":38696,"style":4920},[259,1873],[128,38698,38700],{"className":38699},[2087],[128,38701,38703,38723],{"className":38702},[274,321],[128,38704,38706,38720],{"className":38705},[278],[128,38707,38709],{"className":38708,"style":2218},[282],[128,38710,38711,38714],{"style":4935},[128,38712],{"className":38713,"style":291},[290],[128,38715,38717],{"className":38716},[299,300,301,298],[128,38718,2022],{"className":38719,"style":2231},[259,1873,298],[128,38721,347],{"className":38722},[346],[128,38724,38726],{"className":38725},[278],[128,38727,38729],{"className":38728,"style":2241},[282],[128,38730],{},[128,38732,347],{"className":38733},[346],[128,38735,38737],{"className":38736},[278],[128,38738,38740],{"className":38739,"style":20496},[282],[128,38741],{},[128,38743],{"className":38744},[1928,5570],[128,38746],{"className":38747,"style":1878},[269],[128,38749,1994],{"className":38750},[1882],[128,38752],{"className":38753,"style":1878},[269],[128,38755,38757,38760,38763,38766,38806],{"className":38756},[250],[128,38758],{"className":38759,"style":1892},[254],[128,38761,342],{"className":38762},[259,2167],[128,38764,16538],{"className":38765},[1896],[128,38767,38769,38772],{"className":38768},[259],[128,38770,2760],{"className":38771},[259,1873],[128,38773,38775],{"className":38774},[2087],[128,38776,38778,38798],{"className":38777},[274,321],[128,38779,38781,38795],{"className":38780},[278],[128,38782,38784],{"className":38783,"style":2218},[282],[128,38785,38786,38789],{"style":2221},[128,38787],{"className":38788,"style":291},[290],[128,38790,38792],{"className":38791},[299,300,301,298],[128,38793,2022],{"className":38794,"style":2231},[259,1873,298],[128,38796,347],{"className":38797},[346],[128,38799,38801],{"className":38800},[278],[128,38802,38804],{"className":38803,"style":2241},[282],[128,38805],{},[128,38807,16547],{"className":38808},[1928],[11,38810,38811],{},"其中最后一个等号由命题 2.1 给出。",[11,38813,38814,38815,38818],{},"命题 3.2 是整篇文章的枢纽：它说明",[35,38816,38817],{},"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。",[2610,38820,38822],{"id":38821},"_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",[11,38824,38825,38826,38982,38983,39100,39101,39173,39174,39480],{},"设神经网络 ",[128,38827,38829,38860],{"className":38828,"translate":218},[217],[128,38830,38832],{"className":38831},[222],[224,38833,38834],{"xmlns":226},[228,38835,38836,38857],{},[231,38837,38838,38845,38847,38849,38851],{},[2016,38839,38840,38842],{},[1795,38841,5436],{},[1795,38843,38844],{"mathvariant":4834},"θ",[1832,38846,2014],{},[1795,38848,364],{"mathvariant":1797},[1832,38850,22419],{},[1977,38852,38853,38855],{},[1795,38854,2009],{"mathvariant":2008},[1795,38856,1853],{},[238,38858,38859],{"encoding":240},"f_{\\boldsymbol{\\theta}}: \\mathcal{X} \\to \\mathbb{R}^K",[128,38861,38863,38929,38947],{"className":38862,"ariaHidden":246},[245],[128,38864,38866,38869,38920,38923,38926],{"className":38865},[250],[128,38867],{"className":38868,"style":16030},[254],[128,38870,38872,38875],{"className":38871},[259],[128,38873,5436],{"className":38874,"style":5514},[259,1873],[128,38876,38878],{"className":38877},[2087],[128,38879,38881,38912],{"className":38880},[274,321],[128,38882,38884,38909],{"className":38883},[278],[128,38885,38887],{"className":38886,"style":2218},[282],[128,38888,38890,38893],{"style":38889},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[128,38891],{"className":38892,"style":291},[290],[128,38894,38896],{"className":38895},[299,300,301,298],[128,38897,38899],{"className":38898},[259,298],[128,38900,38902],{"className":38901},[259,298],[128,38903,38905],{"className":38904},[259,298],[128,38906,38844],{"className":38907,"style":38908},[259,4895,298],"margin-right:0.0319em;",[128,38910,347],{"className":38911},[346],[128,38913,38915],{"className":38914},[278],[128,38916,38918],{"className":38917,"style":2241},[282],[128,38919],{},[128,38921],{"className":38922,"style":1878},[269],[128,38924,2014],{"className":38925},[1882],[128,38927],{"className":38928,"style":1878},[269],[128,38930,38932,38935,38938,38941,38944],{"className":38931},[250],[128,38933],{"className":38934,"style":283},[254],[128,38936,364],{"className":38937,"style":1814},[259,1813],[128,38939],{"className":38940,"style":1878},[269],[128,38942,22419],{"className":38943},[1882],[128,38945],{"className":38946,"style":1878},[269],[128,38948,38950,38953],{"className":38949},[250],[128,38951],{"className":38952,"style":2431},[254],[128,38954,38956,38959],{"className":38955},[259],[128,38957,2009],{"className":38958},[259,2167],[128,38960,38962],{"className":38961},[2087],[128,38963,38965],{"className":38964},[274],[128,38966,38968],{"className":38967},[278],[128,38969,38971],{"className":38970,"style":2431},[282],[128,38972,38973,38976],{"style":2452},[128,38974],{"className":38975,"style":291},[290],[128,38977,38979],{"className":38978},[299,300,301,298],[128,38980,1853],{"className":38981,"style":1924},[259,1873,298]," 输出 logits ",[128,38984,38986,39015],{"className":38985,"translate":218},[217],[128,38987,38989],{"className":38988},[222],[224,38990,38991],{"xmlns":226},[228,38992,38993,39012],{},[231,38994,38995,38998,39000,39006,39008,39010],{},[1795,38996,38997],{"mathvariant":2001},"z",[1832,38999,1994],{},[2016,39001,39002,39004],{},[1795,39003,5436],{},[1795,39005,38844],{"mathvariant":4834},[1832,39007,2477],{"stretchy":1837},[1795,39009,2760],{"mathvariant":2001},[1832,39011,2486],{"stretchy":1837},[238,39013,39014],{"encoding":240},"\\mathbf{z} = f_{\\boldsymbol{\\theta}}(\\mathbf{x})",[128,39016,39018,39036],{"className":39017,"ariaHidden":246},[245],[128,39019,39021,39024,39027,39030,39033],{"className":39020},[250],[128,39022],{"className":39023,"style":4439},[254],[128,39025,38997],{"className":39026},[259,2151],[128,39028],{"className":39029,"style":1878},[269],[128,39031,1994],{"className":39032},[1882],[128,39034],{"className":39035,"style":1878},[269],[128,39037,39039,39042,39091,39094,39097],{"className":39038},[250],[128,39040],{"className":39041,"style":1892},[254],[128,39043,39045,39048],{"className":39044},[259],[128,39046,5436],{"className":39047,"style":5514},[259,1873],[128,39049,39051],{"className":39050},[2087],[128,39052,39054,39083],{"className":39053},[274,321],[128,39055,39057,39080],{"className":39056},[278],[128,39058,39060],{"className":39059,"style":2218},[282],[128,39061,39062,39065],{"style":38889},[128,39063],{"className":39064,"style":291},[290],[128,39066,39068],{"className":39067},[299,300,301,298],[128,39069,39071],{"className":39070},[259,298],[128,39072,39074],{"className":39073},[259,298],[128,39075,39077],{"className":39076},[259,298],[128,39078,38844],{"className":39079,"style":38908},[259,4895,298],[128,39081,347],{"className":39082},[346],[128,39084,39086],{"className":39085},[278],[128,39087,39089],{"className":39088,"style":2241},[282],[128,39090],{},[128,39092,2477],{"className":39093},[1896],[128,39095,2760],{"className":39096},[259,2151],[128,39098,2486],{"className":39099},[1928],"，softmax 给出 ",[128,39102,39104,39131],{"className":39103,"translate":218},[217],[128,39105,39107],{"className":39106},[222],[224,39108,39109],{"xmlns":226},[228,39110,39111,39128],{},[231,39112,39113,39115,39117,39120,39122,39124,39126],{},[1795,39114,11],{"mathvariant":2001},[1832,39116,1994],{},[1795,39118,39119],{"mathvariant":1981},"softmax",[1832,39121,3278],{},[1832,39123,2477],{"stretchy":1837},[1795,39125,38997],{"mathvariant":2001},[1832,39127,2486],{"stretchy":1837},[238,39129,39130],{"encoding":240},"\\mathbf{p} = \\operatorname{softmax}(\\mathbf{z})",[128,39132,39134,39152],{"className":39133,"ariaHidden":246},[245],[128,39135,39137,39140,39143,39146,39149],{"className":39136},[250],[128,39138],{"className":39139,"style":2564},[254],[128,39141,11],{"className":39142},[259,2151],[128,39144],{"className":39145,"style":1878},[269],[128,39147,1994],{"className":39148},[1882],[128,39150],{"className":39151,"style":1878},[269],[128,39153,39155,39158,39164,39167,39170],{"className":39154},[250],[128,39156],{"className":39157,"style":1892},[254],[128,39159,39161],{"className":39160},[2268],[128,39162,39119],{"className":39163},[259,3353],[128,39165,2477],{"className":39166},[1896],[128,39168,38997],{"className":39169},[259,2151],[128,39171,2486],{"className":39172},[1928],"，即 ",[128,39175,39177,39225],{"className":39176,"translate":218},[217],[128,39178,39180],{"className":39179},[222],[224,39181,39182],{"xmlns":226},[228,39183,39184,39222],{},[231,39185,39186,39192,39194,39204,39206,39212],{},[2016,39187,39188,39190],{},[1795,39189,11],{},[1795,39191,2022],{},[1832,39193,1994],{},[1977,39195,39196,39198],{},[1795,39197,3713],{},[2016,39199,39200,39202],{},[1795,39201,38997],{},[1795,39203,2022],{},[1795,39205,4751],{"mathvariant":1981},[2016,39207,39208,39210],{},[1832,39209,2042],{},[1795,39211,16495],{},[1977,39213,39214,39216],{},[1795,39215,3713],{},[2016,39217,39218,39220],{},[1795,39219,38997],{},[1795,39221,16495],{},[238,39223,39224],{"encoding":240},"p_k = e^{z_k}\u002F\\sum_j e^{z_j}",[128,39226,39228,39283],{"className":39227,"ariaHidden":246},[245],[128,39229,39231,39234,39274,39277,39280],{"className":39230},[250],[128,39232],{"className":39233,"style":11158},[254],[128,39235,39237,39240],{"className":39236},[259],[128,39238,11],{"className":39239},[259,1873],[128,39241,39243],{"className":39242},[2087],[128,39244,39246,39266],{"className":39245},[274,321],[128,39247,39249,39263],{"className":39248},[278],[128,39250,39252],{"className":39251,"style":2218},[282],[128,39253,39254,39257],{"style":2221},[128,39255],{"className":39256,"style":291},[290],[128,39258,39260],{"className":39259},[299,300,301,298],[128,39261,2022],{"className":39262,"style":2231},[259,1873,298],[128,39264,347],{"className":39265},[346],[128,39267,39269],{"className":39268},[278],[128,39270,39272],{"className":39271,"style":2241},[282],[128,39273],{},[128,39275],{"className":39276,"style":1878},[269],[128,39278,1994],{"className":39279},[1882],[128,39281],{"className":39282,"style":1878},[269],[128,39284,39286,39289,39361,39364,39367,39407,39410],{"className":39285},[250],[128,39287],{"className":39288,"style":31566},[254],[128,39290,39292,39295],{"className":39291},[259],[128,39293,3713],{"className":39294},[259,1873],[128,39296,39298],{"className":39297},[2087],[128,39299,39301],{"className":39300},[274],[128,39302,39304],{"className":39303},[278],[128,39305,39308],{"className":39306,"style":39307},[282],"height:0.6644em;",[128,39309,39310,39313],{"style":2452},[128,39311],{"className":39312,"style":291},[290],[128,39314,39316],{"className":39315},[299,300,301,298],[128,39317,39319],{"className":39318},[259,298],[128,39320,39322,39326],{"className":39321},[259,298],[128,39323,38997],{"className":39324,"style":39325},[259,1873,298],"margin-right:0.044em;",[128,39327,39329],{"className":39328},[2087],[128,39330,39332,39353],{"className":39331},[274,321],[128,39333,39335,39350],{"className":39334},[278],[128,39336,39338],{"className":39337,"style":24117},[282],[128,39339,39341,39344],{"style":39340},"top:-2.3488em;margin-left:-0.044em;margin-right:0.0714em;",[128,39342],{"className":39343,"style":5790},[290],[128,39345,39347],{"className":39346},[299,5794,5795,298],[128,39348,2022],{"className":39349,"style":2231},[259,1873,298],[128,39351,347],{"className":39352},[346],[128,39354,39356],{"className":39355},[278],[128,39357,39359],{"className":39358,"style":28958},[282],[128,39360],{},[128,39362,4751],{"className":39363},[259],[128,39365],{"className":39366,"style":1907},[269],[128,39368,39370,39373],{"className":39369},[2268],[128,39371,2042],{"className":39372,"style":2274},[2268,2272,2273],[128,39374,39376],{"className":39375},[2087],[128,39377,39379,39399],{"className":39378},[274,321],[128,39380,39382,39396],{"className":39381},[278],[128,39383,39385],{"className":39384,"style":7796},[282],[128,39386,39387,39390],{"style":2290},[128,39388],{"className":39389,"style":291},[290],[128,39391,39393],{"className":39392},[299,300,301,298],[128,39394,16495],{"className":39395,"style":16521},[259,1873,298],[128,39397,347],{"className":39398},[346],[128,39400,39402],{"className":39401},[278],[128,39403,39405],{"className":39404,"style":31756},[282],[128,39406],{},[128,39408],{"className":39409,"style":1907},[269],[128,39411,39413,39416],{"className":39412},[259],[128,39414,3713],{"className":39415},[259,1873],[128,39417,39419],{"className":39418},[2087],[128,39420,39422],{"className":39421},[274],[128,39423,39425],{"className":39424},[278],[128,39426,39428],{"className":39427,"style":39307},[282],[128,39429,39430,39433],{"style":2452},[128,39431],{"className":39432,"style":291},[290],[128,39434,39436],{"className":39435},[299,300,301,298],[128,39437,39439],{"className":39438},[259,298],[128,39440,39442,39445],{"className":39441},[259,298],[128,39443,38997],{"className":39444,"style":39325},[259,1873,298],[128,39446,39448],{"className":39447},[2087],[128,39449,39451,39472],{"className":39450},[274,321],[128,39452,39454,39469],{"className":39453},[278],[128,39455,39457],{"className":39456,"style":5783},[282],[128,39458,39460,39463],{"style":39459},"top:-2.357em;margin-left:-0.044em;margin-right:0.0714em;",[128,39461],{"className":39462,"style":5790},[290],[128,39464,39466],{"className":39465},[299,5794,5795,298],[128,39467,16495],{"className":39468,"style":16521},[259,1873,298],[128,39470,347],{"className":39471},[346],[128,39473,39475],{"className":39474},[278],[128,39476,39478],{"className":39477,"style":17680},[282],[128,39479],{},"。这一映射存在两个结构性缺陷。",[11,39482,39483,39486,39487,2674,39516,39634,39635,11101,39716,39719,39720,39771,39772,39846,39847,39885],{},[35,39484,39485],{},"其一，平移不变性抹去了「无信息」这一状态。"," 对任意常数 ",[128,39488,39490,39504],{"className":39489,"translate":218},[217],[128,39491,39493],{"className":39492},[222],[224,39494,39495],{"xmlns":226},[228,39496,39497,39502],{},[231,39498,39499],{},[1795,39500,39501],{},"c",[238,39503,39501],{"encoding":240},[128,39505,39507],{"className":39506,"ariaHidden":246},[245],[128,39508,39510,39513],{"className":39509},[250],[128,39511],{"className":39512,"style":7758},[254],[128,39514,39501],{"className":39515},[259,1873],[128,39517,39519,39559],{"className":39518,"translate":218},[217],[128,39520,39522],{"className":39521},[222],[224,39523,39524],{"xmlns":226},[228,39525,39526,39556],{},[231,39527,39528,39530,39532,39534,39536,39538,39540,39542,39544,39546,39548,39550,39552,39554],{},[1795,39529,39119],{"mathvariant":1981},[1832,39531,3278],{},[1832,39533,2477],{"stretchy":1837},[1795,39535,38997],{"mathvariant":2001},[1832,39537,9486],{},[1795,39539,39501],{},[1840,39541,1842],{"mathvariant":2001},[1832,39543,2486],{"stretchy":1837},[1832,39545,1994],{},[1795,39547,39119],{"mathvariant":1981},[1832,39549,3278],{},[1832,39551,2477],{"stretchy":1837},[1795,39553,38997],{"mathvariant":2001},[1832,39555,2486],{"stretchy":1837},[238,39557,39558],{"encoding":240},"\\operatorname{softmax}(\\mathbf{z} + c\\mathbf{1}) = \\operatorname{softmax}(\\mathbf{z})",[128,39560,39562,39589,39613],{"className":39561,"ariaHidden":246},[245],[128,39563,39565,39568,39574,39577,39580,39583,39586],{"className":39564},[250],[128,39566],{"className":39567,"style":1892},[254],[128,39569,39571],{"className":39570},[2268],[128,39572,39119],{"className":39573},[259,3353],[128,39575,2477],{"className":39576},[1896],[128,39578,38997],{"className":39579},[259,2151],[128,39581],{"className":39582,"style":2508},[269],[128,39584,9486],{"className":39585},[2115],[128,39587],{"className":39588,"style":2508},[269],[128,39590,39592,39595,39598,39601,39604,39607,39610],{"className":39591},[250],[128,39593],{"className":39594,"style":1892},[254],[128,39596,39501],{"className":39597},[259,1873],[128,39599,1842],{"className":39600},[259,2151],[128,39602,2486],{"className":39603},[1928],[128,39605],{"className":39606,"style":1878},[269],[128,39608,1994],{"className":39609},[1882],[128,39611],{"className":39612,"style":1878},[269],[128,39614,39616,39619,39625,39628,39631],{"className":39615},[250],[128,39617],{"className":39618,"style":1892},[254],[128,39620,39622],{"className":39621},[2268],[128,39623,39119],{"className":39624},[259,3353],[128,39626,2477],{"className":39627},[1896],[128,39629,38997],{"className":39630},[259,2151],[128,39632,2486],{"className":39633},[1928],"。因此 logits 的绝对水平不含任何信息，网络的输出只依赖于 ",[128,39636,39638,39660],{"className":39637,"translate":218},[217],[128,39639,39641],{"className":39640},[222],[224,39642,39643],{"xmlns":226},[228,39644,39645,39657],{},[231,39646,39647,39649,39655],{},[1832,39648,1838],{"stretchy":1837},[2016,39650,39651,39653],{},[1795,39652,38997],{},[1795,39654,2022],{},[1832,39656,1856],{"stretchy":1837},[238,39658,39659],{"encoding":240},"\\{z_k\\}",[128,39661,39663],{"className":39662,"ariaHidden":246},[245],[128,39664,39666,39669,39672,39713],{"className":39665},[250],[128,39667],{"className":39668,"style":1892},[254],[128,39670,1838],{"className":39671},[1896],[128,39673,39675,39678],{"className":39674},[259],[128,39676,38997],{"className":39677,"style":39325},[259,1873],[128,39679,39681],{"className":39680},[2087],[128,39682,39684,39705],{"className":39683},[274,321],[128,39685,39687,39702],{"className":39686},[278],[128,39688,39690],{"className":39689,"style":2218},[282],[128,39691,39693,39696],{"style":39692},"top:-2.55em;margin-left:-0.044em;margin-right:0.05em;",[128,39694],{"className":39695,"style":291},[290],[128,39697,39699],{"className":39698},[299,300,301,298],[128,39700,2022],{"className":39701,"style":2231},[259,1873,298],[128,39703,347],{"className":39704},[346],[128,39706,39708],{"className":39707},[278],[128,39709,39711],{"className":39710,"style":2241},[282],[128,39712],{},[128,39714,1856],{"className":39715},[1928],[35,39717,39718],{},"相对差","。后果是：",[128,39721,39723,39741],{"className":39722,"translate":218},[217],[128,39724,39726],{"className":39725},[222],[224,39727,39728],{"xmlns":226},[228,39729,39730,39738],{},[231,39731,39732,39734,39736],{},[1795,39733,38997],{"mathvariant":2001},[1832,39735,1994],{},[1840,39737,2028],{"mathvariant":2001},[238,39739,39740],{"encoding":240},"\\mathbf{z} = \\mathbf{0}",[128,39742,39744,39762],{"className":39743,"ariaHidden":246},[245],[128,39745,39747,39750,39753,39756,39759],{"className":39746},[250],[128,39748],{"className":39749,"style":4439},[254],[128,39751,38997],{"className":39752},[259,2151],[128,39754],{"className":39755,"style":1878},[269],[128,39757,1994],{"className":39758},[1882],[128,39760],{"className":39761,"style":1878},[269],[128,39763,39765,39768],{"className":39764},[250],[128,39766],{"className":39767,"style":2594},[254],[128,39769,2028],{"className":39770},[259,2151],"（「全零 logits」）与 ",[128,39773,39775,39798],{"className":39774,"translate":218},[217],[128,39776,39778],{"className":39777},[222],[224,39779,39780],{"xmlns":226},[228,39781,39782,39795],{},[231,39783,39784,39786,39788,39791,39793],{},[1795,39785,38997],{"mathvariant":2001},[1832,39787,1994],{},[1840,39789,39790],{},"100",[1832,39792,12935],{},[1840,39794,1842],{"mathvariant":2001},[238,39796,39797],{"encoding":240},"\\mathbf{z} = 100 \\cdot \\mathbf{1}",[128,39799,39801,39819,39837],{"className":39800,"ariaHidden":246},[245],[128,39802,39804,39807,39810,39813,39816],{"className":39803},[250],[128,39805],{"className":39806,"style":4439},[254],[128,39808,38997],{"className":39809},[259,2151],[128,39811],{"className":39812,"style":1878},[269],[128,39814,1994],{"className":39815},[1882],[128,39817],{"className":39818,"style":1878},[269],[128,39820,39822,39825,39828,39831,39834],{"className":39821},[250],[128,39823],{"className":39824,"style":2594},[254],[128,39826,39790],{"className":39827},[259],[128,39829],{"className":39830,"style":2508},[269],[128,39832,12935],{"className":39833},[2115],[128,39835],{"className":39836,"style":2508},[269],[128,39838,39840,39843],{"className":39839},[250],[128,39841],{"className":39842,"style":2594},[254],[128,39844,1842],{"className":39845},[259,2151]," 不可区分，二者都对应均匀分布 ",[128,39848,39850,39867],{"className":39849,"translate":218},[217],[128,39851,39853],{"className":39852},[222],[224,39854,39855],{"xmlns":226},[228,39856,39857,39865],{},[231,39858,39859,39861,39863],{},[1840,39860,1842],{"mathvariant":2001},[1795,39862,4751],{"mathvariant":1981},[1795,39864,1853],{},[238,39866,34301],{"encoding":240},[128,39868,39870],{"className":39869,"ariaHidden":246},[245],[128,39871,39873,39876,39879,39882],{"className":39872},[250],[128,39874],{"className":39875,"style":1892},[254],[128,39877,1842],{"className":39878},[259,2151],[128,39880,4751],{"className":39881},[259],[128,39883,1853],{"className":39884,"style":1924},[259,1873],"。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。",[11,39887,39888,39891,39892,40024,40025,40028,40029,893],{},[35,39889,39890],{},"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 ",[128,39893,39895,39931],{"className":39894,"translate":218},[217],[128,39896,39898],{"className":39897},[222],[224,39899,39900],{"xmlns":226},[228,39901,39902,39928],{},[231,39903,39904,39906,39908,39910,39912,39918,39920,39922,39924,39926],{},[1795,39905,38997],{"mathvariant":2001},[1832,39907,22419],{},[1795,39909,39501],{},[234,39911,6528],{},[1977,39913,39914,39916],{},[1795,39915,38997],{"mathvariant":2001},[1832,39917,23697],{},[1832,39919,1845],{"separator":246},[234,39921,2033],{},[1795,39923,39501],{},[1832,39925,22419],{},[1795,39927,8521],{"mathvariant":1981},[238,39929,39930],{"encoding":240},"\\mathbf{z} \\to c\\,\\mathbf{z}^\\star,\\ c \\to \\infty",[128,39932,39934,39952,40015],{"className":39933,"ariaHidden":246},[245],[128,39935,39937,39940,39943,39946,39949],{"className":39936},[250],[128,39938],{"className":39939,"style":4439},[254],[128,39941,38997],{"className":39942},[259,2151],[128,39944],{"className":39945,"style":1878},[269],[128,39947,22419],{"className":39948},[1882],[128,39950],{"className":39951,"style":1878},[269],[128,39953,39955,39959,39962,39965,39994,39997,40000,40003,40006,40009,40012],{"className":39954},[250],[128,39956],{"className":39957,"style":39958},[254],"height:0.8831em;vertical-align:-0.1944em;",[128,39960,39501],{"className":39961},[259,1873],[128,39963],{"className":39964,"style":1907},[269],[128,39966,39968,39971],{"className":39967},[259],[128,39969,38997],{"className":39970},[259,2151],[128,39972,39974],{"className":39973},[2087],[128,39975,39977],{"className":39976},[274],[128,39978,39980],{"className":39979},[278],[128,39981,39983],{"className":39982,"style":23776},[282],[128,39984,39985,39988],{"style":2452},[128,39986],{"className":39987,"style":291},[290],[128,39989,39991],{"className":39990},[299,300,301,298],[128,39992,23697],{"className":39993},[2115,298],[128,39995,1845],{"className":39996},[1903],[128,39998,2033],{"className":39999},[269],[128,40001],{"className":40002,"style":1907},[269],[128,40004,39501],{"className":40005},[259,1873],[128,40007],{"className":40008,"style":1878},[269],[128,40010,22419],{"className":40011},[1882],[128,40013],{"className":40014,"style":1878},[269],[128,40016,40018,40021],{"className":40017},[250],[128,40019],{"className":40020,"style":7758},[254],[128,40022,8521],{"className":40023},[259]," 可将损失单调压向零。换言之，",[35,40026,40027],{},"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",[35,40030,40031],{},"完全不受输入是否为分布内样本的约束",[11,40033,40034],{},"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」。",[2610,40036,40038],{"id":40037},"_34-证据参数化","3.4 证据参数化",[11,40040,40041,40042],{},"证据深度学习对上述缺陷的回应是：",[35,40043,40044],{},"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。",[2615,40046,40048],{"title":40047},"定义 3.3（证据网络）",[11,40049,1781,40050,40239,40240,40243,40244,40503,40504,40741,40742,893],{},[128,40051,40053,40089],{"className":40052,"translate":218},[217],[128,40054,40056],{"className":40055},[222],[224,40057,40058],{"xmlns":226},[228,40059,40060,40086],{},[231,40061,40062,40068,40070,40072,40074],{},[2016,40063,40064,40066],{},[1795,40065,24505],{},[1795,40067,38844],{"mathvariant":4834},[1832,40069,2014],{},[1795,40071,364],{"mathvariant":1797},[1832,40073,22419],{},[2038,40075,40076,40078,40084],{},[1795,40077,2009],{"mathvariant":2008},[231,40079,40080,40082],{},[1832,40081,2025],{},[1840,40083,2028],{},[1795,40085,1853],{},[238,40087,40088],{"encoding":240},"g_{\\boldsymbol{\\theta}}: \\mathcal{X} \\to \\mathbb{R}_{\\ge 0}^K",[128,40090,40092,40156,40174],{"className":40091,"ariaHidden":246},[245],[128,40093,40095,40098,40147,40150,40153],{"className":40094},[250],[128,40096],{"className":40097,"style":11158},[254],[128,40099,40101,40104],{"className":40100},[259],[128,40102,24505],{"className":40103,"style":1874},[259,1873],[128,40105,40107],{"className":40106},[2087],[128,40108,40110,40139],{"className":40109},[274,321],[128,40111,40113,40136],{"className":40112},[278],[128,40114,40116],{"className":40115,"style":2218},[282],[128,40117,40118,40121],{"style":28741},[128,40119],{"className":40120,"style":291},[290],[128,40122,40124],{"className":40123},[299,300,301,298],[128,40125,40127],{"className":40126},[259,298],[128,40128,40130],{"className":40129},[259,298],[128,40131,40133],{"className":40132},[259,298],[128,40134,38844],{"className":40135,"style":38908},[259,4895,298],[128,40137,347],{"className":40138},[346],[128,40140,40142],{"className":40141},[278],[128,40143,40145],{"className":40144,"style":2241},[282],[128,40146],{},[128,40148],{"className":40149,"style":1878},[269],[128,40151,2014],{"className":40152},[1882],[128,40154],{"className":40155,"style":1878},[269],[128,40157,40159,40162,40165,40168,40171],{"className":40158},[250],[128,40160],{"className":40161,"style":283},[254],[128,40163,364],{"className":40164,"style":1814},[259,1813],[128,40166],{"className":40167,"style":1878},[269],[128,40169,22419],{"className":40170},[1882],[128,40172],{"className":40173,"style":1878},[269],[128,40175,40177,40181],{"className":40176},[250],[128,40178],{"className":40179,"style":40180},[254],"height:1.1846em;vertical-align:-0.3433em;",[128,40182,40184,40187],{"className":40183},[259],[128,40185,2009],{"className":40186},[259,2167],[128,40188,40190],{"className":40189},[2087],[128,40191,40193,40230],{"className":40192},[274,321],[128,40194,40196,40227],{"className":40195},[278],[128,40197,40199,40216],{"className":40198,"style":2431},[282],[128,40200,40201,40204],{"style":5053},[128,40202],{"className":40203,"style":291},[290],[128,40205,40207],{"className":40206},[299,300,301,298],[128,40208,40210,40213],{"className":40209},[259,298],[128,40211,2025],{"className":40212},[1882,298],[128,40214,2028],{"className":40215},[259,298],[128,40217,40218,40221],{"style":2452},[128,40219],{"className":40220,"style":291},[290],[128,40222,40224],{"className":40223},[299,300,301,298],[128,40225,1853],{"className":40226,"style":1924},[259,1873,298],[128,40228,347],{"className":40229},[346],[128,40231,40233],{"className":40232},[278],[128,40234,40237],{"className":40235,"style":40236},[282],"height:0.3433em;",[128,40238],{}," 是由主干网络与",[35,40241,40242],{},"非负激活函数","复合而成的证据函数，输出 ",[128,40245,40247,40299],{"className":40246,"translate":218},[217],[128,40248,40250],{"className":40249},[222],[224,40251,40252],{"xmlns":226},[228,40253,40254,40296],{},[231,40255,40256,40258,40260,40266,40268,40270,40272,40274,40276,40282,40284,40286,40288,40294],{},[1795,40257,3713],{"mathvariant":2001},[1832,40259,1994],{},[2016,40261,40262,40264],{},[1795,40263,24505],{},[1795,40265,38844],{"mathvariant":4834},[1832,40267,2477],{"stretchy":1837},[1795,40269,2760],{"mathvariant":2001},[1832,40271,2486],{"stretchy":1837},[1832,40273,1994],{},[1832,40275,2477],{"stretchy":1837},[2016,40277,40278,40280],{},[1795,40279,3713],{},[1840,40281,1842],{},[1832,40283,1845],{"separator":246},[1832,40285,1848],{},[1832,40287,1845],{"separator":246},[2016,40289,40290,40292],{},[1795,40291,3713],{},[1795,40293,1853],{},[1832,40295,2486],{"stretchy":1837},[238,40297,40298],{"encoding":240},"\\mathbf{e} = g_{\\boldsymbol{\\theta}}(\\mathbf{x}) = (e_1, \\dots, e_K)",[128,40300,40302,40320,40393],{"className":40301,"ariaHidden":246},[245],[128,40303,40305,40308,40311,40314,40317],{"className":40304},[250],[128,40306],{"className":40307,"style":4439},[254],[128,40309,3713],{"className":40310},[259,2151],[128,40312],{"className":40313,"style":1878},[269],[128,40315,1994],{"className":40316},[1882],[128,40318],{"className":40319,"style":1878},[269],[128,40321,40323,40326,40375,40378,40381,40384,40387,40390],{"className":40322},[250],[128,40324],{"className":40325,"style":1892},[254],[128,40327,40329,40332],{"className":40328},[259],[128,40330,24505],{"className":40331,"style":1874},[259,1873],[128,40333,40335],{"className":40334},[2087],[128,40336,40338,40367],{"className":40337},[274,321],[128,40339,40341,40364],{"className":40340},[278],[128,40342,40344],{"className":40343,"style":2218},[282],[128,40345,40346,40349],{"style":28741},[128,40347],{"className":40348,"style":291},[290],[128,40350,40352],{"className":40351},[299,300,301,298],[128,40353,40355],{"className":40354},[259,298],[128,40356,40358],{"className":40357},[259,298],[128,40359,40361],{"className":40360},[259,298],[128,40362,38844],{"className":40363,"style":38908},[259,4895,298],[128,40365,347],{"className":40366},[346],[128,40368,40370],{"className":40369},[278],[128,40371,40373],{"className":40372,"style":2241},[282],[128,40374],{},[128,40376,2477],{"className":40377},[1896],[128,40379,2760],{"className":40380},[259,2151],[128,40382,2486],{"className":40383},[1928],[128,40385],{"className":40386,"style":1878},[269],[128,40388,1994],{"className":40389},[1882],[128,40391],{"className":40392,"style":1878},[269],[128,40394,40396,40399,40402,40442,40445,40448,40451,40454,40457,40460,40500],{"className":40395},[250],[128,40397],{"className":40398,"style":1892},[254],[128,40400,2477],{"className":40401},[1896],[128,40403,40405,40408],{"className":40404},[259],[128,40406,3713],{"className":40407},[259,1873],[128,40409,40411],{"className":40410},[2087],[128,40412,40414,40434],{"className":40413},[274,321],[128,40415,40417,40431],{"className":40416},[278],[128,40418,40420],{"className":40419,"style":2945},[282],[128,40421,40422,40425],{"style":2221},[128,40423],{"className":40424,"style":291},[290],[128,40426,40428],{"className":40427},[299,300,301,298],[128,40429,1842],{"className":40430},[259,298],[128,40432,347],{"className":40433},[346],[128,40435,40437],{"className":40436},[278],[128,40438,40440],{"className":40439,"style":2241},[282],[128,40441],{},[128,40443,1845],{"className":40444},[1903],[128,40446],{"className":40447,"style":1907},[269],[128,40449,1848],{"className":40450},[1911],[128,40452],{"className":40453,"style":1907},[269],[128,40455,1845],{"className":40456},[1903],[128,40458],{"className":40459,"style":1907},[269],[128,40461,40463,40466],{"className":40462},[259],[128,40464,3713],{"className":40465},[259,1873],[128,40467,40469],{"className":40468},[2087],[128,40470,40472,40492],{"className":40471},[274,321],[128,40473,40475,40489],{"className":40474},[278],[128,40476,40478],{"className":40477,"style":3004},[282],[128,40479,40480,40483],{"style":2221},[128,40481],{"className":40482,"style":291},[290],[128,40484,40486],{"className":40485},[299,300,301,298],[128,40487,1853],{"className":40488,"style":1924},[259,1873,298],[128,40490,347],{"className":40491},[346],[128,40493,40495],{"className":40494},[278],[128,40496,40498],{"className":40497,"style":2241},[282],[128,40499],{},[128,40501,2486],{"className":40502},[1928],"。迪利克雷参数取为\n",[128,40505,40507,40555],{"className":40506,"translate":218},[217],[128,40508,40510],{"className":40509},[222],[224,40511,40512],{"xmlns":226},[228,40513,40514,40552],{},[231,40515,40516,40522,40524,40530,40532,40534,40536,40538,40540,40542,40544,40546,40548,40550],{},[2016,40517,40518,40520],{},[1795,40519,4835],{},[1795,40521,2022],{},[1832,40523,1994],{},[2016,40525,40526,40528],{},[1795,40527,3713],{},[1795,40529,2022],{},[1832,40531,9486],{},[1840,40533,1842],{},[1832,40535,1845],{"separator":246},[269,40537],{"width":11568},[234,40539,14647],{},[269,40541],{"width":11568},[1795,40543,4835],{"mathvariant":4834},[1832,40545,1994],{},[1795,40547,3713],{"mathvariant":2001},[1832,40549,9486],{},[1840,40551,1842],{"mathvariant":2001},[238,40553,40554],{"encoding":240},"\\alpha_k = e_k + 1, \\qquad \\text{即} \\qquad \\boldsymbol{\\alpha} = \\mathbf{e} + \\mathbf{1}",[128,40556,40558,40613,40668,40714,40732],{"className":40557,"ariaHidden":246},[245],[128,40559,40561,40564,40604,40607,40610],{"className":40560},[250],[128,40562],{"className":40563,"style":4242},[254],[128,40565,40567,40570],{"className":40566},[259],[128,40568,4835],{"className":40569,"style":4920},[259,1873],[128,40571,40573],{"className":40572},[2087],[128,40574,40576,40596],{"className":40575},[274,321],[128,40577,40579,40593],{"className":40578},[278],[128,40580,40582],{"className":40581,"style":2218},[282],[128,40583,40584,40587],{"style":4935},[128,40585],{"className":40586,"style":291},[290],[128,40588,40590],{"className":40589},[299,300,301,298],[128,40591,2022],{"className":40592,"style":2231},[259,1873,298],[128,40594,347],{"className":40595},[346],[128,40597,40599],{"className":40598},[278],[128,40600,40602],{"className":40601,"style":2241},[282],[128,40603],{},[128,40605],{"className":40606,"style":1878},[269],[128,40608,1994],{"className":40609},[1882],[128,40611],{"className":40612,"style":1878},[269],[128,40614,40616,40619,40659,40662,40665],{"className":40615},[250],[128,40617],{"className":40618,"style":14338},[254],[128,40620,40622,40625],{"className":40621},[259],[128,40623,3713],{"className":40624},[259,1873],[128,40626,40628],{"className":40627},[2087],[128,40629,40631,40651],{"className":40630},[274,321],[128,40632,40634,40648],{"className":40633},[278],[128,40635,40637],{"className":40636,"style":2218},[282],[128,40638,40639,40642],{"style":2221},[128,40640],{"className":40641,"style":291},[290],[128,40643,40645],{"className":40644},[299,300,301,298],[128,40646,2022],{"className":40647,"style":2231},[259,1873,298],[128,40649,347],{"className":40650},[346],[128,40652,40654],{"className":40653},[278],[128,40655,40657],{"className":40656,"style":2241},[282],[128,40658],{},[128,40660],{"className":40661,"style":2508},[269],[128,40663,9486],{"className":40664},[2115],[128,40666],{"className":40667,"style":2508},[269],[128,40669,40671,40675,40678,40681,40684,40687,40693,40696,40705,40708,40711],{"className":40670},[250],[128,40672],{"className":40673,"style":40674},[254],"height:0.8778em;vertical-align:-0.1944em;",[128,40676,1842],{"className":40677},[259],[128,40679,1845],{"className":40680},[1903],[128,40682],{"className":40683,"style":11756},[269],[128,40685],{"className":40686,"style":1907},[269],[128,40688,40690],{"className":40689},[259,260],[128,40691,14647],{"className":40692},[259,15272],[128,40694],{"className":40695,"style":11756},[269],[128,40697,40699],{"className":40698},[259],[128,40700,40702],{"className":40701},[259],[128,40703,4835],{"className":40704},[259,4895],[128,40706],{"className":40707,"style":1878},[269],[128,40709,1994],{"className":40710},[1882],[128,40712],{"className":40713,"style":1878},[269],[128,40715,40717,40720,40723,40726,40729],{"className":40716},[250],[128,40718],{"className":40719,"style":8462},[254],[128,40721,3713],{"className":40722},[259,2151],[128,40724],{"className":40725,"style":2508},[269],[128,40727,9486],{"className":40728},[2115],[128,40730],{"className":40731,"style":2508},[269],[128,40733,40735,40738],{"className":40734},[250],[128,40736],{"className":40737,"style":2594},[254],[128,40739,1842],{"className":40740},[259,2151],"\n网络对输入的预测由此被定义为 ",[128,40743,40745,40767],{"className":40744,"translate":218},[217],[128,40746,40748],{"className":40747},[222],[224,40749,40750],{"xmlns":226},[228,40751,40752,40764],{},[231,40753,40754,40756,40758,40760,40762],{},[1795,40755,5914],{"mathvariant":1981},[1832,40757,3278],{},[1832,40759,2477],{"stretchy":1837},[1795,40761,4835],{"mathvariant":4834},[1832,40763,2486],{"stretchy":1837},[238,40765,40766],{"encoding":240},"\\operatorname{Dir}(\\boldsymbol{\\alpha})",[128,40768,40770],{"className":40769,"ariaHidden":246},[245],[128,40771,40773,40776,40782,40785,40794],{"className":40772},[250],[128,40774],{"className":40775,"style":1892},[254],[128,40777,40779],{"className":40778},[2268],[128,40780,5914],{"className":40781},[259,3353],[128,40783,2477],{"className":40784},[1896],[128,40786,40788],{"className":40787},[259],[128,40789,40791],{"className":40790},[259],[128,40792,4835],{"className":40793},[259,4895],[128,40795,2486],{"className":40796},[1928],[11,40798,40799,40800,40879,40880,40981,40982,41052,41053,41081],{},"参数化的语义可直接由命题 3.2 读出：",[128,40801,40803,40825],{"className":40802,"translate":218},[217],[128,40804,40806],{"className":40805},[222],[224,40807,40808],{"xmlns":226},[228,40809,40810,40822],{},[231,40811,40812,40814,40816,40818,40820],{},[1795,40813,3713],{"mathvariant":2001},[1832,40815,1994],{},[1795,40817,4835],{"mathvariant":4834},[1832,40819,1989],{},[1840,40821,1842],{"mathvariant":2001},[238,40823,40824],{"encoding":240},"\\mathbf{e} = \\boldsymbol{\\alpha} - \\mathbf{1}",[128,40826,40828,40846,40870],{"className":40827,"ariaHidden":246},[245],[128,40829,40831,40834,40837,40840,40843],{"className":40830},[250],[128,40832],{"className":40833,"style":4439},[254],[128,40835,3713],{"className":40836},[259,2151],[128,40838],{"className":40839,"style":1878},[269],[128,40841,1994],{"className":40842},[1882],[128,40844],{"className":40845,"style":1878},[269],[128,40847,40849,40852,40861,40864,40867],{"className":40848},[250],[128,40850],{"className":40851,"style":8462},[254],[128,40853,40855],{"className":40854},[259],[128,40856,40858],{"className":40857},[259],[128,40859,4835],{"className":40860},[259,4895],[128,40862],{"className":40863,"style":2508},[269],[128,40865,1989],{"className":40866},[2115],[128,40868],{"className":40869,"style":2508},[269],[128,40871,40873,40876],{"className":40872},[250],[128,40874],{"className":40875,"style":2594},[254],[128,40877,1842],{"className":40878},[259,2151]," 正是",[35,40881,40882,40883,40980],{},"超出均匀先验 ",[128,40884,40886,40910],{"className":40885,"translate":218},[217],[128,40887,40889],{"className":40888},[222],[224,40890,40891],{"xmlns":226},[228,40892,40893,40907],{},[231,40894,40895,40901,40903,40905],{},[2016,40896,40897,40899],{},[1795,40898,21],{},[1795,40900,2022],{},[1795,40902,36679],{},[1832,40904,1994],{},[1840,40906,1842],{},[238,40908,40909],{"encoding":240},"a_k W = 1",[128,40911,40913,40971],{"className":40912,"ariaHidden":246},[245],[128,40914,40916,40919,40959,40962,40965,40968],{"className":40915},[250],[128,40917],{"className":40918,"style":36058},[254],[128,40920,40922,40925],{"className":40921},[259],[128,40923,21],{"className":40924},[259,1873],[128,40926,40928],{"className":40927},[2087],[128,40929,40931,40951],{"className":40930},[274,321],[128,40932,40934,40948],{"className":40933},[278],[128,40935,40937],{"className":40936,"style":2218},[282],[128,40938,40939,40942],{"style":2221},[128,40940],{"className":40941,"style":291},[290],[128,40943,40945],{"className":40944},[299,300,301,298],[128,40946,2022],{"className":40947,"style":2231},[259,1873,298],[128,40949,347],{"className":40950},[346],[128,40952,40954],{"className":40953},[278],[128,40955,40957],{"className":40956,"style":2241},[282],[128,40958],{},[128,40960,36679],{"className":40961,"style":36065},[259,1873],[128,40963],{"className":40964,"style":1878},[269],[128,40966,1994],{"className":40967},[1882],[128,40969],{"className":40970,"style":1878},[269],[128,40972,40974,40977],{"className":40973},[250],[128,40975],{"className":40976,"style":2594},[254],[128,40978,1842],{"className":40979},[259]," 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：",[128,40983,40985,41003],{"className":40984,"translate":218},[217],[128,40986,40988],{"className":40987},[222],[224,40989,40990],{"xmlns":226},[228,40991,40992,41000],{},[231,40993,40994],{},[2016,40995,40996,40998],{},[1795,40997,3713],{},[1795,40999,2022],{},[238,41001,41002],{"encoding":240},"e_k",[128,41004,41006],{"className":41005,"ariaHidden":246},[245],[128,41007,41009,41012],{"className":41008},[250],[128,41010],{"className":41011,"style":4242},[254],[128,41013,41015,41018],{"className":41014},[259],[128,41016,3713],{"className":41017},[259,1873],[128,41019,41021],{"className":41020},[2087],[128,41022,41024,41044],{"className":41023},[274,321],[128,41025,41027,41041],{"className":41026},[278],[128,41028,41030],{"className":41029,"style":2218},[282],[128,41031,41032,41035],{"style":2221},[128,41033],{"className":41034,"style":291},[290],[128,41036,41038],{"className":41037},[299,300,301,298],[128,41039,2022],{"className":41040,"style":2231},[259,1873,298],[128,41042,347],{"className":41043},[346],[128,41045,41047],{"className":41046},[278],[128,41048,41050],{"className":41049,"style":2241},[282],[128,41051],{}," 是与类别 ",[128,41054,41056,41069],{"className":41055,"translate":218},[217],[128,41057,41059],{"className":41058},[222],[224,41060,41061],{"xmlns":226},[228,41062,41063,41067],{},[231,41064,41065],{},[1795,41066,2022],{},[238,41068,2022],{"encoding":240},[128,41070,41072],{"className":41071,"ariaHidden":246},[245],[128,41073,41075,41078],{"className":41074},[250],[128,41076],{"className":41077,"style":12173},[254],[128,41079,2022],{"className":41080,"style":2231},[259,1873]," 相关的、由网络从输入中提取出的支持性观测。",[11,41083,41084],{},"非负激活函数的选择影响显著，值得逐一说明：",[35195,41086,41087,41407,41527,41829],{},[33251,41088,41089,41232,41233,41289,41290,41349,41350,41406],{},[128,41090,41092,41135],{"className":41091,"translate":218},[217],[128,41093,41095],{"className":41094},[222],[224,41096,41097],{"xmlns":226},[228,41098,41099,41132],{},[231,41100,41101,41104,41106,41108,41110,41112,41114,41116,41118,41120,41122,41124,41130],{},[1795,41102,41103],{"mathvariant":1981},"softplus",[1832,41105,3278],{},[1832,41107,2477],{"stretchy":1837},[1795,41109,38997],{},[1832,41111,2486],{"stretchy":1837},[1832,41113,1994],{},[1795,41115,24373],{},[1832,41117,3278],{},[1832,41119,2477],{"stretchy":1837},[1840,41121,1842],{},[1832,41123,9486],{},[1977,41125,41126,41128],{},[1795,41127,3713],{},[1795,41129,38997],{},[1832,41131,2486],{"stretchy":1837},[238,41133,41134],{"encoding":240},"\\operatorname{softplus}(z) = \\log(1 + e^z)",[128,41136,41138,41168,41194],{"className":41137,"ariaHidden":246},[245],[128,41139,41141,41144,41150,41153,41156,41159,41162,41165],{"className":41140},[250],[128,41142],{"className":41143,"style":1892},[254],[128,41145,41147],{"className":41146},[2268],[128,41148,41103],{"className":41149},[259,3353],[128,41151,2477],{"className":41152},[1896],[128,41154,38997],{"className":41155,"style":39325},[259,1873],[128,41157,2486],{"className":41158},[1928],[128,41160],{"className":41161,"style":1878},[269],[128,41163,1994],{"className":41164},[1882],[128,41166],{"className":41167,"style":1878},[269],[128,41169,41171,41174,41179,41182,41185,41188,41191],{"className":41170},[250],[128,41172],{"className":41173,"style":1892},[254],[128,41175,24502,41177],{"className":41176},[2268],[128,41178,24505],{"style":17336},[128,41180,2477],{"className":41181},[1896],[128,41183,1842],{"className":41184},[259],[128,41186],{"className":41187,"style":2508},[269],[128,41189,9486],{"className":41190},[2115],[128,41192],{"className":41193,"style":2508},[269],[128,41195,41197,41200,41229],{"className":41196},[250],[128,41198],{"className":41199,"style":1892},[254],[128,41201,41203,41206],{"className":41202},[259],[128,41204,3713],{"className":41205},[259,1873],[128,41207,41209],{"className":41208},[2087],[128,41210,41212],{"className":41211},[274],[128,41213,41215],{"className":41214},[278],[128,41216,41218],{"className":41217,"style":39307},[282],[128,41219,41220,41223],{"style":2452},[128,41221],{"className":41222,"style":291},[290],[128,41224,41226],{"className":41225},[299,300,301,298],[128,41227,38997],{"className":41228,"style":39325},[259,1873,298],[128,41230,2486],{"className":41231},[1928],"：恒正、处处可微、在 ",[128,41234,41236,41256],{"className":41235,"translate":218},[217],[128,41237,41239],{"className":41238},[222],[224,41240,41241],{"xmlns":226},[228,41242,41243,41253],{},[231,41244,41245,41247,41249,41251],{},[1795,41246,38997],{},[1832,41248,22419],{},[1832,41250,1989],{},[1795,41252,8521],{"mathvariant":1981},[238,41254,41255],{"encoding":240},"z \\to -\\infty",[128,41257,41259,41277],{"className":41258,"ariaHidden":246},[245],[128,41260,41262,41265,41268,41271,41274],{"className":41261},[250],[128,41263],{"className":41264,"style":7758},[254],[128,41266,38997],{"className":41267,"style":39325},[259,1873],[128,41269],{"className":41270,"style":1878},[269],[128,41272,22419],{"className":41273},[1882],[128,41275],{"className":41276,"style":1878},[269],[128,41278,41280,41283,41286],{"className":41279},[250],[128,41281],{"className":41282,"style":8462},[254],[128,41284,1989],{"className":41285},[259],[128,41287,8521],{"className":41288},[259]," 时以 ",[128,41291,41293,41311],{"className":41292,"translate":218},[217],[128,41294,41296],{"className":41295},[222],[224,41297,41298],{"xmlns":226},[228,41299,41300,41308],{},[231,41301,41302],{},[1977,41303,41304,41306],{},[1795,41305,3713],{},[1795,41307,38997],{},[238,41309,41310],{"encoding":240},"e^z",[128,41312,41314],{"className":41313,"ariaHidden":246},[245],[128,41315,41317,41320],{"className":41316},[250],[128,41318],{"className":41319,"style":39307},[254],[128,41321,41323,41326],{"className":41322},[259],[128,41324,3713],{"className":41325},[259,1873],[128,41327,41329],{"className":41328},[2087],[128,41330,41332],{"className":41331},[274],[128,41333,41335],{"className":41334},[278],[128,41336,41338],{"className":41337,"style":39307},[282],[128,41339,41340,41343],{"style":2452},[128,41341],{"className":41342,"style":291},[290],[128,41344,41346],{"className":41345},[299,300,301,298],[128,41347,38997],{"className":41348,"style":39325},[259,1873,298]," 的速度趋零、在 ",[128,41351,41353,41373],{"className":41352,"translate":218},[217],[128,41354,41356],{"className":41355},[222],[224,41357,41358],{"xmlns":226},[228,41359,41360,41370],{},[231,41361,41362,41364,41366,41368],{},[1795,41363,38997],{},[1832,41365,22419],{},[1832,41367,9486],{},[1795,41369,8521],{"mathvariant":1981},[238,41371,41372],{"encoding":240},"z \\to +\\infty",[128,41374,41376,41394],{"className":41375,"ariaHidden":246},[245],[128,41377,41379,41382,41385,41388,41391],{"className":41378},[250],[128,41380],{"className":41381,"style":7758},[254],[128,41383,38997],{"className":41384,"style":39325},[259,1873],[128,41386],{"className":41387,"style":1878},[269],[128,41389,22419],{"className":41390},[1882],[128,41392],{"className":41393,"style":1878},[269],[128,41395,41397,41400,41403],{"className":41396},[250],[128,41398],{"className":41399,"style":8462},[254],[128,41401,9486],{"className":41402},[259],[128,41404,8521],{"className":41405},[259]," 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。",[33251,41408,41409,41456,41457,41526],{},[128,41410,41412,41435],{"className":41411,"translate":218},[217],[128,41413,41415],{"className":41414},[222],[224,41416,41417],{"xmlns":226},[228,41418,41419,41432],{},[231,41420,41421,41424,41426,41428,41430],{},[1795,41422,41423],{},"exp",[1832,41425,3278],{},[1832,41427,2477],{"stretchy":1837},[1795,41429,38997],{},[1832,41431,2486],{"stretchy":1837},[238,41433,41434],{"encoding":240},"\\exp(z)",[128,41436,41438],{"className":41437,"ariaHidden":246},[245],[128,41439,41441,41444,41447,41450,41453],{"className":41440},[250],[128,41442],{"className":41443,"style":1892},[254],[128,41445,41423],{"className":41446},[2268],[128,41448,2477],{"className":41449},[1896],[128,41451,38997],{"className":41452,"style":39325},[259,1873],[128,41454,2486],{"className":41455},[1928],"：严格正、光滑，但无上界，使 ",[128,41458,41460,41477],{"className":41459,"translate":218},[217],[128,41461,41463],{"className":41462},[222],[224,41464,41465],{"xmlns":226},[228,41466,41467,41475],{},[231,41468,41469],{},[2016,41470,41471,41473],{},[1795,41472,4835],{},[1840,41474,2028],{},[238,41476,21207],{"encoding":240},[128,41478,41480],{"className":41479,"ariaHidden":246},[245],[128,41481,41483,41486],{"className":41482},[250],[128,41484],{"className":41485,"style":4242},[254],[128,41487,41489,41492],{"className":41488},[259],[128,41490,4835],{"className":41491,"style":4920},[259,1873],[128,41493,41495],{"className":41494},[2087],[128,41496,41498,41518],{"className":41497},[274,321],[128,41499,41501,41515],{"className":41500},[278],[128,41502,41504],{"className":41503,"style":2945},[282],[128,41505,41506,41509],{"style":4935},[128,41507],{"className":41508,"style":291},[290],[128,41510,41512],{"className":41511},[299,300,301,298],[128,41513,2028],{"className":41514},[259,298],[128,41516,347],{"className":41517},[346],[128,41519,41521],{"className":41520},[278],[128,41522,41524],{"className":41523,"style":2241},[282],[128,41525],{}," 可任意大，易造成数值溢出与损失对证据的不稳定响应。",[33251,41528,41529,41579,41580,41631,41632,41724,41725,41728,41729,41799,41800,41828],{},[128,41530,41532,41555],{"className":41531,"translate":218},[217],[128,41533,41535],{"className":41534},[222],[224,41536,41537],{"xmlns":226},[228,41538,41539,41552],{},[231,41540,41541,41544,41546,41548,41550],{},[1795,41542,41543],{"mathvariant":1981},"ReLU",[1832,41545,3278],{},[1832,41547,2477],{"stretchy":1837},[1795,41549,38997],{},[1832,41551,2486],{"stretchy":1837},[238,41553,41554],{"encoding":240},"\\operatorname{ReLU}(z)",[128,41556,41558],{"className":41557,"ariaHidden":246},[245],[128,41559,41561,41564,41570,41573,41576],{"className":41560},[250],[128,41562],{"className":41563,"style":1892},[254],[128,41565,41567],{"className":41566},[2268],[128,41568,41543],{"className":41569},[259,3353],[128,41571,2477],{"className":41572},[1896],[128,41574,38997],{"className":41575,"style":39325},[259,1873],[128,41577,2486],{"className":41578},[1928],"：计算廉价，但在 ",[128,41581,41583,41601],{"className":41582,"translate":218},[217],[128,41584,41586],{"className":41585},[222],[224,41587,41588],{"xmlns":226},[228,41589,41590,41598],{},[231,41591,41592,41594,41596],{},[1795,41593,38997],{},[1832,41595,4221],{},[1840,41597,2028],{},[238,41599,41600],{"encoding":240},"z \u003C 0",[128,41602,41604,41622],{"className":41603,"ariaHidden":246},[245],[128,41605,41607,41610,41613,41616,41619],{"className":41606},[250],[128,41608],{"className":41609,"style":6382},[254],[128,41611,38997],{"className":41612,"style":39325},[259,1873],[128,41614],{"className":41615,"style":1878},[269],[128,41617,4221],{"className":41618},[1882],[128,41620],{"className":41621,"style":1878},[269],[128,41623,41625,41628],{"className":41624},[250],[128,41626],{"className":41627,"style":2594},[254],[128,41629,2028],{"className":41630},[259]," 处梯度恒为零。处于该区域的单元输出证据 ",[128,41633,41635,41657],{"className":41634,"translate":218},[217],[128,41636,41638],{"className":41637},[222],[224,41639,41640],{"xmlns":226},[228,41641,41642,41654],{},[231,41643,41644,41650,41652],{},[2016,41645,41646,41648],{},[1795,41647,3713],{},[1795,41649,2022],{},[1832,41651,1994],{},[1840,41653,2028],{},[238,41655,41656],{"encoding":240},"e_k = 0",[128,41658,41660,41715],{"className":41659,"ariaHidden":246},[245],[128,41661,41663,41666,41706,41709,41712],{"className":41662},[250],[128,41664],{"className":41665,"style":4242},[254],[128,41667,41669,41672],{"className":41668},[259],[128,41670,3713],{"className":41671},[259,1873],[128,41673,41675],{"className":41674},[2087],[128,41676,41678,41698],{"className":41677},[274,321],[128,41679,41681,41695],{"className":41680},[278],[128,41682,41684],{"className":41683,"style":2218},[282],[128,41685,41686,41689],{"style":2221},[128,41687],{"className":41688,"style":291},[290],[128,41690,41692],{"className":41691},[299,300,301,298],[128,41693,2022],{"className":41694,"style":2231},[259,1873,298],[128,41696,347],{"className":41697},[346],[128,41699,41701],{"className":41700},[278],[128,41702,41704],{"className":41703,"style":2241},[282],[128,41705],{},[128,41707],{"className":41708,"style":1878},[269],[128,41710,1994],{"className":41711},[1882],[128,41713],{"className":41714,"style":1878},[269],[128,41716,41718,41721],{"className":41717},[250],[128,41719],{"className":41720,"style":2594},[254],[128,41722,2028],{"className":41723},[259]," 且",[35,41726,41727],{},"永远无法通过梯度逃离","——",[128,41730,41732,41750],{"className":41731,"translate":218},[217],[128,41733,41735],{"className":41734},[222],[224,41736,41737],{"xmlns":226},[228,41738,41739,41747],{},[231,41740,41741],{},[2016,41742,41743,41745],{},[1795,41744,4835],{},[1795,41746,2022],{},[238,41748,41749],{"encoding":240},"\\alpha_k",[128,41751,41753],{"className":41752,"ariaHidden":246},[245],[128,41754,41756,41759],{"className":41755},[250],[128,41757],{"className":41758,"style":4242},[254],[128,41760,41762,41765],{"className":41761},[259],[128,41763,4835],{"className":41764,"style":4920},[259,1873],[128,41766,41768],{"className":41767},[2087],[128,41769,41771,41791],{"className":41770},[274,321],[128,41772,41774,41788],{"className":41773},[278],[128,41775,41777],{"className":41776,"style":2218},[282],[128,41778,41779,41782],{"style":4935},[128,41780],{"className":41781,"style":291},[290],[128,41783,41785],{"className":41784},[299,300,301,298],[128,41786,2022],{"className":41787,"style":2231},[259,1873,298],[128,41789,347],{"className":41790},[346],[128,41792,41794],{"className":41793},[278],[128,41795,41797],{"className":41796,"style":2241},[282],[128,41798],{}," 被锁在 ",[128,41801,41803,41816],{"className":41802,"translate":218},[217],[128,41804,41806],{"className":41805},[222],[224,41807,41808],{"xmlns":226},[228,41809,41810,41814],{},[231,41811,41812],{},[1840,41813,1842],{},[238,41815,1842],{"encoding":240},[128,41817,41819],{"className":41818,"ariaHidden":246},[245],[128,41820,41822,41825],{"className":41821},[250],[128,41823],{"className":41824,"style":2594},[254],[128,41826,1842],{"className":41827},[259],"，形成死区。这使 ReLU 在证据函数中通常劣于 softplus。",[33251,41830,41831,41903,41904,41932],{},[128,41832,41834,41861],{"className":41833,"translate":218},[217],[128,41835,41837],{"className":41836},[222],[224,41838,41839],{"xmlns":226},[228,41840,41841,41858],{},[231,41842,41843,41846,41848,41850,41852,41854,41856],{},[1795,41844,41845],{"mathvariant":1981},"ELU",[1832,41847,3278],{},[1832,41849,2477],{"stretchy":1837},[1795,41851,38997],{},[1832,41853,2486],{"stretchy":1837},[1832,41855,9486],{},[1840,41857,1842],{},[238,41859,41860],{"encoding":240},"\\operatorname{ELU}(z) + 1",[128,41862,41864,41894],{"className":41863,"ariaHidden":246},[245],[128,41865,41867,41870,41876,41879,41882,41885,41888,41891],{"className":41866},[250],[128,41868],{"className":41869,"style":1892},[254],[128,41871,41873],{"className":41872},[2268],[128,41874,41845],{"className":41875},[259,3353],[128,41877,2477],{"className":41878},[1896],[128,41880,38997],{"className":41881,"style":39325},[259,1873],[128,41883,2486],{"className":41884},[1928],[128,41886],{"className":41887,"style":2508},[269],[128,41889,9486],{"className":41890},[2115],[128,41892],{"className":41893,"style":2508},[269],[128,41895,41897,41900],{"className":41896},[250],[128,41898],{"className":41899,"style":2594},[254],[128,41901,1842],{"className":41902},[259],"：具有负饱和下界 ",[128,41905,41907,41920],{"className":41906,"translate":218},[217],[128,41908,41910],{"className":41909},[222],[224,41911,41912],{"xmlns":226},[228,41913,41914,41918],{},[231,41915,41916],{},[1840,41917,2028],{},[238,41919,2028],{"encoding":240},[128,41921,41923],{"className":41922,"ariaHidden":246},[245],[128,41924,41926,41929],{"className":41925},[250],[128,41927],{"className":41928,"style":2594},[254],[128,41930,2028],{"className":41931},[259],"，梯度在负半轴非零，是介于二者之间的折中。",[2610,41934,41936],{"id":41935},"_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",[2615,41938,41940],{"title":41939},"命题 3.4（EDL 的预测与不确定性）",[11,41941,41942,41943,42339,42340],{},"在定义 3.3 的参数化下，记总强度 ",[128,41944,41946,42017],{"className":41945,"translate":218},[217],[128,41947,41949],{"className":41948},[222],[224,41950,41951],{"xmlns":226},[228,41952,41953,42014],{},[231,41954,41955,41958,41960,41966,41968,41982,41988,41990,41992,41994,42008],{},[1795,41956,41957],{},"S",[1832,41959,1994],{},[2016,41961,41962,41964],{},[1795,41963,4835],{},[1840,41965,2028],{},[1832,41967,1994],{},[2038,41969,41970,41972,41980],{},[1832,41971,2042],{},[231,41973,41974,41976,41978],{},[1795,41975,2022],{},[1832,41977,1994],{},[1840,41979,1842],{},[1795,41981,1853],{},[2016,41983,41984,41986],{},[1795,41985,4835],{},[1795,41987,2022],{},[1832,41989,1994],{},[1795,41991,1853],{},[1832,41993,9486],{},[2038,41995,41996,41998,42006],{},[1832,41997,2042],{},[231,41999,42000,42002,42004],{},[1795,42001,2022],{},[1832,42003,1994],{},[1840,42005,1842],{},[1795,42007,1853],{},[2016,42009,42010,42012],{},[1795,42011,3713],{},[1795,42013,2022],{},[238,42015,42016],{"encoding":240},"S = \\alpha_0 = \\sum_{k=1}^K \\alpha_k = K + \\sum_{k=1}^K e_k",[128,42018,42020,42039,42094,42212,42230],{"className":42019,"ariaHidden":246},[245],[128,42021,42023,42026,42030,42033,42036],{"className":42022},[250],[128,42024],{"className":42025,"style":283},[254],[128,42027,41957],{"className":42028,"style":42029},[259,1873],"margin-right:0.0576em;",[128,42031],{"className":42032,"style":1878},[269],[128,42034,1994],{"className":42035},[1882],[128,42037],{"className":42038,"style":1878},[269],[128,42040,42042,42045,42085,42088,42091],{"className":42041},[250],[128,42043],{"className":42044,"style":4242},[254],[128,42046,42048,42051],{"className":42047},[259],[128,42049,4835],{"className":42050,"style":4920},[259,1873],[128,42052,42054],{"className":42053},[2087],[128,42055,42057,42077],{"className":42056},[274,321],[128,42058,42060,42074],{"className":42059},[278],[128,42061,42063],{"className":42062,"style":2945},[282],[128,42064,42065,42068],{"style":4935},[128,42066],{"className":42067,"style":291},[290],[128,42069,42071],{"className":42070},[299,300,301,298],[128,42072,2028],{"className":42073},[259,298],[128,42075,347],{"className":42076},[346],[128,42078,42080],{"className":42079},[278],[128,42081,42083],{"className":42082,"style":2241},[282],[128,42084],{},[128,42086],{"className":42087,"style":1878},[269],[128,42089,1994],{"className":42090},[1882],[128,42092],{"className":42093,"style":1878},[269],[128,42095,42097,42100,42160,42163,42203,42206,42209],{"className":42096},[250],[128,42098],{"className":42099,"style":5200},[254],[128,42101,42103,42106],{"className":42102},[2268],[128,42104,2042],{"className":42105,"style":2274},[2268,2272,2273],[128,42107,42109],{"className":42108},[2087],[128,42110,42112,42152],{"className":42111},[274,321],[128,42113,42115,42149],{"className":42114},[278],[128,42116,42118,42138],{"className":42117,"style":2287},[282],[128,42119,42120,42123],{"style":2290},[128,42121],{"className":42122,"style":291},[290],[128,42124,42126],{"className":42125},[299,300,301,298],[128,42127,42129,42132,42135],{"className":42128},[259,298],[128,42130,2022],{"className":42131,"style":2231},[259,1873,298],[128,42133,1994],{"className":42134},[1882,298],[128,42136,1842],{"className":42137},[259,298],[128,42139,42140,42143],{"style":2311},[128,42141],{"className":42142,"style":291},[290],[128,42144,42146],{"className":42145},[299,300,301,298],[128,42147,1853],{"className":42148,"style":1924},[259,1873,298],[128,42150,347],{"className":42151},[346],[128,42153,42155],{"className":42154},[278],[128,42156,42158],{"className":42157,"style":2330},[282],[128,42159],{},[128,42161],{"className":42162,"style":1907},[269],[128,42164,42166,42169],{"className":42165},[259],[128,42167,4835],{"className":42168,"style":4920},[259,1873],[128,42170,42172],{"className":42171},[2087],[128,42173,42175,42195],{"className":42174},[274,321],[128,42176,42178,42192],{"className":42177},[278],[128,42179,42181],{"className":42180,"style":2218},[282],[128,42182,42183,42186],{"style":4935},[128,42184],{"className":42185,"style":291},[290],[128,42187,42189],{"className":42188},[299,300,301,298],[128,42190,2022],{"className":42191,"style":2231},[259,1873,298],[128,42193,347],{"className":42194},[346],[128,42196,42198],{"className":42197},[278],[128,42199,42201],{"className":42200,"style":2241},[282],[128,42202],{},[128,42204],{"className":42205,"style":1878},[269],[128,42207,1994],{"className":42208},[1882],[128,42210],{"className":42211,"style":1878},[269],[128,42213,42215,42218,42221,42224,42227],{"className":42214},[250],[128,42216],{"className":42217,"style":2705},[254],[128,42219,1853],{"className":42220,"style":1924},[259,1873],[128,42222],{"className":42223,"style":2508},[269],[128,42225,9486],{"className":42226},[2115],[128,42228],{"className":42229,"style":2508},[269],[128,42231,42233,42236,42296,42299],{"className":42232},[250],[128,42234],{"className":42235,"style":5200},[254],[128,42237,42239,42242],{"className":42238},[2268],[128,42240,2042],{"className":42241,"style":2274},[2268,2272,2273],[128,42243,42245],{"className":42244},[2087],[128,42246,42248,42288],{"className":42247},[274,321],[128,42249,42251,42285],{"className":42250},[278],[128,42252,42254,42274],{"className":42253,"style":2287},[282],[128,42255,42256,42259],{"style":2290},[128,42257],{"className":42258,"style":291},[290],[128,42260,42262],{"className":42261},[299,300,301,298],[128,42263,42265,42268,42271],{"className":42264},[259,298],[128,42266,2022],{"className":42267,"style":2231},[259,1873,298],[128,42269,1994],{"className":42270},[1882,298],[128,42272,1842],{"className":42273},[259,298],[128,42275,42276,42279],{"style":2311},[128,42277],{"className":42278,"style":291},[290],[128,42280,42282],{"className":42281},[299,300,301,298],[128,42283,1853],{"className":42284,"style":1924},[259,1873,298],[128,42286,347],{"className":42287},[346],[128,42289,42291],{"className":42290},[278],[128,42292,42294],{"className":42293,"style":2330},[282],[128,42295],{},[128,42297],{"className":42298,"style":1907},[269],[128,42300,42302,42305],{"className":42301},[259],[128,42303,3713],{"className":42304},[259,1873],[128,42306,42308],{"className":42307},[2087],[128,42309,42311,42331],{"className":42310},[274,321],[128,42312,42314,42328],{"className":42313},[278],[128,42315,42317],{"className":42316,"style":2218},[282],[128,42318,42319,42322],{"style":2221},[128,42320],{"className":42321,"style":291},[290],[128,42323,42325],{"className":42324},[299,300,301,298],[128,42326,2022],{"className":42327,"style":2231},[259,1873,298],[128,42329,347],{"className":42330},[346],[128,42332,42334],{"className":42333},[278],[128,42335,42337],{"className":42336,"style":2241},[282],[128,42338],{},"。则\n",[128,42341,42343,42401],{"className":42342,"translate":218},[217],[128,42344,42346],{"className":42345},[222],[224,42347,42348],{"xmlns":226},[228,42349,42350,42398],{},[231,42351,42352,42358,42360,42362,42364,42370,42372,42374,42384,42386,42388,42390,42392],{},[2016,42353,42354,42356],{},[1795,42355,11],{},[1795,42357,2022],{},[1832,42359,1994],{},[1795,42361,342],{"mathvariant":2008},[1832,42363,16538],{"stretchy":1837},[2016,42365,42366,42368],{},[1795,42367,2760],{},[1795,42369,2022],{},[1832,42371,16547],{"stretchy":1837},[1832,42373,1994],{},[5451,42375,42376,42382],{},[2016,42377,42378,42380],{},[1795,42379,4835],{},[1795,42381,2022],{},[1795,42383,41957],{},[1832,42385,1845],{"separator":246},[269,42387],{"width":11568},[1795,42389,35129],{},[1832,42391,1994],{},[5451,42393,42394,42396],{},[1795,42395,1853],{},[1795,42397,41957],{},[238,42399,42400],{"encoding":240},"p_k = \\mathbb{E}[x_k] = \\frac{\\alpha_k}{S}, \\qquad u = \\frac{K}{S}",[128,42402,42404,42459,42523,42655],{"className":42403,"ariaHidden":246},[245],[128,42405,42407,42410,42450,42453,42456],{"className":42406},[250],[128,42408],{"className":42409,"style":11158},[254],[128,42411,42413,42416],{"className":42412},[259],[128,42414,11],{"className":42415},[259,1873],[128,42417,42419],{"className":42418},[2087],[128,42420,42422,42442],{"className":42421},[274,321],[128,42423,42425,42439],{"className":42424},[278],[128,42426,42428],{"className":42427,"style":2218},[282],[128,42429,42430,42433],{"style":2221},[128,42431],{"className":42432,"style":291},[290],[128,42434,42436],{"className":42435},[299,300,301,298],[128,42437,2022],{"className":42438,"style":2231},[259,1873,298],[128,42440,347],{"className":42441},[346],[128,42443,42445],{"className":42444},[278],[128,42446,42448],{"className":42447,"style":2241},[282],[128,42449],{},[128,42451],{"className":42452,"style":1878},[269],[128,42454,1994],{"className":42455},[1882],[128,42457],{"className":42458,"style":1878},[269],[128,42460,42462,42465,42468,42471,42511,42514,42517,42520],{"className":42461},[250],[128,42463],{"className":42464,"style":1892},[254],[128,42466,342],{"className":42467},[259,2167],[128,42469,16538],{"className":42470},[1896],[128,42472,42474,42477],{"className":42473},[259],[128,42475,2760],{"className":42476},[259,1873],[128,42478,42480],{"className":42479},[2087],[128,42481,42483,42503],{"className":42482},[274,321],[128,42484,42486,42500],{"className":42485},[278],[128,42487,42489],{"className":42488,"style":2218},[282],[128,42490,42491,42494],{"style":2221},[128,42492],{"className":42493,"style":291},[290],[128,42495,42497],{"className":42496},[299,300,301,298],[128,42498,2022],{"className":42499,"style":2231},[259,1873,298],[128,42501,347],{"className":42502},[346],[128,42504,42506],{"className":42505},[278],[128,42507,42509],{"className":42508,"style":2241},[282],[128,42510],{},[128,42512,16547],{"className":42513},[1928],[128,42515],{"className":42516,"style":1878},[269],[128,42518,1994],{"className":42519},[1882],[128,42521],{"className":42522,"style":1878},[269],[128,42524,42526,42529,42634,42637,42640,42643,42646,42649,42652],{"className":42525},[250],[128,42527],{"className":42528,"style":30034},[254],[128,42530,42532,42535,42631],{"className":42531},[259],[128,42533],{"className":42534},[1896,5570],[128,42536,42538],{"className":42537},[5451],[128,42539,42541,42623],{"className":42540},[274,321],[128,42542,42544,42620],{"className":42543},[278],[128,42545,42547,42561,42569],{"className":42546,"style":29656},[282],[128,42548,42549,42552],{"style":5586},[128,42550],{"className":42551,"style":335},[290],[128,42553,42555],{"className":42554},[299,300,301,298],[128,42556,42558],{"className":42557},[259,298],[128,42559,41957],{"className":42560,"style":42029},[259,1873,298],[128,42562,42563,42566],{"style":5617},[128,42564],{"className":42565,"style":335},[290],[128,42567],{"className":42568,"style":5625},[5624],[128,42570,42571,42574],{"style":28909},[128,42572],{"className":42573,"style":335},[290],[128,42575,42577],{"className":42576},[299,300,301,298],[128,42578,42580],{"className":42579},[259,298],[128,42581,42583,42586],{"className":42582},[259,298],[128,42584,4835],{"className":42585,"style":4920},[259,1873,298],[128,42587,42589],{"className":42588},[2087],[128,42590,42592,42612],{"className":42591},[274,321],[128,42593,42595,42609],{"className":42594},[278],[128,42596,42598],{"className":42597,"style":24117},[282],[128,42599,42600,42603],{"style":28939},[128,42601],{"className":42602,"style":5790},[290],[128,42604,42606],{"className":42605},[299,5794,5795,298],[128,42607,2022],{"className":42608,"style":2231},[259,1873,298],[128,42610,347],{"className":42611},[346],[128,42613,42615],{"className":42614},[278],[128,42616,42618],{"className":42617,"style":28958},[282],[128,42619],{},[128,42621,347],{"className":42622},[346],[128,42624,42626],{"className":42625},[278],[128,42627,42629],{"className":42628,"style":11919},[282],[128,42630],{},[128,42632],{"className":42633},[1928,5570],[128,42635,1845],{"className":42636},[1903],[128,42638],{"className":42639,"style":11756},[269],[128,42641],{"className":42642,"style":1907},[269],[128,42644,35129],{"className":42645},[259,1873],[128,42647],{"className":42648,"style":1878},[269],[128,42650,1994],{"className":42651},[1882],[128,42653],{"className":42654,"style":1878},[269],[128,42656,42658,42661],{"className":42657},[250],[128,42659],{"className":42660,"style":37471},[254],[128,42662,42664,42667,42726],{"className":42663},[259],[128,42665],{"className":42666},[1896,5570],[128,42668,42670],{"className":42669},[5451],[128,42671,42673,42718],{"className":42672},[274,321],[128,42674,42676,42715],{"className":42675},[278],[128,42677,42679,42693,42701],{"className":42678,"style":37112},[282],[128,42680,42681,42684],{"style":5586},[128,42682],{"className":42683,"style":335},[290],[128,42685,42687],{"className":42686},[299,300,301,298],[128,42688,42690],{"className":42689},[259,298],[128,42691,41957],{"className":42692,"style":42029},[259,1873,298],[128,42694,42695,42698],{"style":5617},[128,42696],{"className":42697,"style":335},[290],[128,42699],{"className":42700,"style":5625},[5624],[128,42702,42703,42706],{"style":5628},[128,42704],{"className":42705,"style":335},[290],[128,42707,42709],{"className":42708},[299,300,301,298],[128,42710,42712],{"className":42711},[259,298],[128,42713,1853],{"className":42714,"style":1924},[259,1873,298],[128,42716,347],{"className":42717},[346],[128,42719,42721],{"className":42720},[278],[128,42722,42724],{"className":42723,"style":11919},[282],[128,42725],{},[128,42727],{"className":42728},[1928,5570],[11,42730,42731,42733,42734,42762,42763,42832,42833,893],{},[35,42732,6849],{}," 第一式即命题 2.1。第二式即命题 3.2。对 ",[128,42735,42737,42750],{"className":42736,"translate":218},[217],[128,42738,42740],{"className":42739},[222],[224,42741,42742],{"xmlns":226},[228,42743,42744,42748],{},[231,42745,42746],{},[1795,42747,35129],{},[238,42749,35129],{"encoding":240},[128,42751,42753],{"className":42752,"ariaHidden":246},[245],[128,42754,42756,42759],{"className":42755},[250],[128,42757],{"className":42758,"style":7758},[254],[128,42760,35129],{"className":42761},[259,1873]," 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 ",[128,42764,42766,42783],{"className":42765,"translate":218},[217],[128,42767,42769],{"className":42768},[222],[224,42770,42771],{"xmlns":226},[228,42772,42773,42781],{},[231,42774,42775],{},[2016,42776,42777,42779],{},[1795,42778,4835],{},[1840,42780,2028],{},[238,42782,21207],{"encoding":240},[128,42784,42786],{"className":42785,"ariaHidden":246},[245],[128,42787,42789,42792],{"className":42788},[250],[128,42790],{"className":42791,"style":4242},[254],[128,42793,42795,42798],{"className":42794},[259],[128,42796,4835],{"className":42797,"style":4920},[259,1873],[128,42799,42801],{"className":42800},[2087],[128,42802,42804,42824],{"className":42803},[274,321],[128,42805,42807,42821],{"className":42806},[278],[128,42808,42810],{"className":42809,"style":2945},[282],[128,42811,42812,42815],{"style":4935},[128,42813],{"className":42814,"style":291},[290],[128,42816,42818],{"className":42817},[299,300,301,298],[128,42819,2028],{"className":42820},[259,298],[128,42822,347],{"className":42823},[346],[128,42825,42827],{"className":42826},[278],[128,42828,42830],{"className":42829,"style":2241},[282],[128,42831],{},"，不确定性质量即为 ",[128,42834,42836,42858],{"className":42835,"translate":218},[217],[128,42837,42839],{"className":42838},[222],[224,42840,42841],{"xmlns":226},[228,42842,42843,42855],{},[231,42844,42845,42847,42849],{},[1795,42846,1853],{},[1795,42848,4751],{"mathvariant":1981},[2016,42850,42851,42853],{},[1795,42852,4835],{},[1840,42854,2028],{},[238,42856,42857],{"encoding":240},"K\u002F\\alpha_0",[128,42859,42861],{"className":42860,"ariaHidden":246},[245],[128,42862,42864,42867,42870,42873],{"className":42863},[250],[128,42865],{"className":42866,"style":1892},[254],[128,42868,1853],{"className":42869,"style":1924},[259,1873],[128,42871,4751],{"className":42872},[259],[128,42874,42876,42879],{"className":42875},[259],[128,42877,4835],{"className":42878,"style":4920},[259,1873],[128,42880,42882],{"className":42881},[2087],[128,42883,42885,42905],{"className":42884},[274,321],[128,42886,42888,42902],{"className":42887},[278],[128,42889,42891],{"className":42890,"style":2945},[282],[128,42892,42893,42896],{"style":4935},[128,42894],{"className":42895,"style":291},[290],[128,42897,42899],{"className":42898},[299,300,301,298],[128,42900,2028],{"className":42901},[259,298],[128,42903,347],{"className":42904},[346],[128,42906,42908],{"className":42907},[278],[128,42909,42911],{"className":42910,"style":2241},[282],[128,42912],{},[11,42914,42915,42916,42944],{},"在 ",[128,42917,42919,42932],{"className":42918,"translate":218},[217],[128,42920,42922],{"className":42921},[222],[224,42923,42924],{"xmlns":226},[228,42925,42926,42930],{},[231,42927,42928],{},[1795,42929,35129],{},[238,42931,35129],{"encoding":240},[128,42933,42935],{"className":42934,"ariaHidden":246},[245],[128,42936,42938,42941],{"className":42937},[250],[128,42939],{"className":42940,"style":7758},[254],[128,42942,35129],{"className":42943},[259,1873]," 的定义下，预测概率具有一个在解释上极有用的分解：",[128,42946,42948],{"className":42947,"translate":218},[1962],[128,42949,42951,43065],{"className":42950,"translate":218},[217],[128,42952,42954],{"className":42953},[222],[224,42955,42956],{"xmlns":226,"display":1971},[228,42957,42958,43062],{},[231,42959,42960,42966,42968,42993,42995,43010,43012,43014,43016,43018,43020,43022,43024,43050,43052,43054,43056],{},[2016,42961,42962,42964],{},[1795,42963,11],{},[1795,42965,2022],{},[1832,42967,1994],{},[8606,42969,42970,42990],{},[8606,42971,42972,42988],{},[5451,42973,42974,42986],{},[231,42975,42976,42982,42984],{},[2016,42977,42978,42980],{},[1795,42979,4835],{},[1795,42981,2022],{},[1832,42983,1989],{},[1840,42985,1842],{},[1795,42987,41957],{},[1832,42989,29188],{"stretchy":246},[234,42991,42992],{},"证据部分",[1832,42994,9486],{},[8606,42996,42997,43007],{},[8606,42998,42999,43005],{},[5451,43000,43001,43003],{},[1840,43002,1842],{},[1795,43004,41957],{},[1832,43006,29188],{"stretchy":246},[234,43008,43009],{},"先验部分",[1832,43011,1994],{},[1832,43013,2477],{"stretchy":1837},[1840,43015,1842],{},[1832,43017,1989],{},[1795,43019,35129],{},[1832,43021,2486],{"stretchy":1837},[234,43023,6528],{},[5451,43025,43026,43038],{},[231,43027,43028,43034,43036],{},[2016,43029,43030,43032],{},[1795,43031,4835],{},[1795,43033,2022],{},[1832,43035,1989],{},[1840,43037,1842],{},[231,43039,43040,43046,43048],{},[2016,43041,43042,43044],{},[1795,43043,4835],{},[1840,43045,2028],{},[1832,43047,1989],{},[1795,43049,1853],{},[1832,43051,9486],{},[1795,43053,35129],{},[1832,43055,12935],{},[5451,43057,43058,43060],{},[1840,43059,1842],{},[1795,43061,1853],{},[238,43063,43064],{"encoding":240},"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}",[128,43066,43068,43123,43362,43545,43566,43750,43769],{"className":43067,"ariaHidden":246},[245],[128,43069,43071,43074,43114,43117,43120],{"className":43070},[250],[128,43072],{"className":43073,"style":11158},[254],[128,43075,43077,43080],{"className":43076},[259],[128,43078,11],{"className":43079},[259,1873],[128,43081,43083],{"className":43082},[2087],[128,43084,43086,43106],{"className":43085},[274,321],[128,43087,43089,43103],{"className":43088},[278],[128,43090,43092],{"className":43091,"style":2218},[282],[128,43093,43094,43097],{"style":2221},[128,43095],{"className":43096,"style":291},[290],[128,43098,43100],{"className":43099},[299,300,301,298],[128,43101,2022],{"className":43102,"style":2231},[259,1873,298],[128,43104,347],{"className":43105},[346],[128,43107,43109],{"className":43108},[278],[128,43110,43112],{"className":43111,"style":2241},[282],[128,43113],{},[128,43115],{"className":43116,"style":1878},[269],[128,43118,1994],{"className":43119},[1882],[128,43121],{"className":43122,"style":1878},[269],[128,43124,43126,43130,43353,43356,43359],{"className":43125},[250],[128,43127],{"className":43128,"style":43129},[254],"height:3.3338em;vertical-align:-2.0123em;",[128,43131,43133],{"className":43132},[1911,8606],[128,43134,43136,43344],{"className":43135},[274,321],[128,43137,43139,43341],{"className":43138},[278],[128,43140,43142,43161],{"className":43141,"style":20407},[282],[128,43143,43145,43149],{"style":43144},"top:-1.3091em;",[128,43146],{"className":43147,"style":43148},[290],"height:3.3214em;",[128,43150,43152],{"className":43151},[299,300,301,298],[128,43153,43155],{"className":43154},[259,298],[128,43156,43158],{"className":43157},[259,260,298],[128,43159,42992],{"className":43160},[259,15272,298],[128,43162,43164,43167],{"style":43163},"top:-3.3214em;",[128,43165],{"className":43166,"style":43148},[290],[128,43168,43170],{"className":43169},[1911,8606],[128,43171,43173,43332],{"className":43172},[274,321],[128,43174,43176,43329],{"className":43175},[278],[128,43177,43179,43210],{"className":43178,"style":20407},[282],[128,43180,43183,43186],{"className":43181,"style":43182},[29395],"top:-1.9874em;",[128,43184],{"className":43185,"style":43148},[290],[128,43187,43189,43196,43203],{"className":43188,"style":29404},[29403],[128,43190,43192],{"className":43191,"style":29409},[29408],[29411,43193,43194],{"xmlns":29413,"width":29414,"height":29415,"viewBox":29416,"preserveAspectRatio":29417},[29419,43195],{"d":29421},[128,43197,43199],{"className":43198,"style":29409},[29425],[29411,43200,43201],{"xmlns":29413,"width":29414,"height":29415,"viewBox":29416,"preserveAspectRatio":29428},[29419,43202],{"d":29431},[128,43204,43206],{"className":43205,"style":29409},[29435],[29411,43207,43208],{"xmlns":29413,"width":29414,"height":29415,"viewBox":29416,"preserveAspectRatio":29438},[29419,43209],{"d":29441},[128,43211,43212,43215],{"style":43163},[128,43213],{"className":43214,"style":43148},[290],[128,43216,43218],{"className":43217},[259],[128,43219,43221,43224,43326],{"className":43220},[259],[128,43222],{"className":43223},[1896,5570],[128,43225,43227],{"className":43226},[5451],[128,43228,43230,43318],{"className":43229},[274,321],[128,43231,43233,43315],{"className":43232},[278],[128,43234,43236,43247,43255],{"className":43235,"style":20407},[282],[128,43237,43238,43241],{"style":13123},[128,43239],{"className":43240,"style":335},[290],[128,43242,43244],{"className":43243},[259],[128,43245,41957],{"className":43246,"style":42029},[259,1873],[128,43248,43249,43252],{"style":5617},[128,43250],{"className":43251,"style":335},[290],[128,43253],{"className":43254,"style":5625},[5624],[128,43256,43257,43260],{"style":13189},[128,43258],{"className":43259,"style":335},[290],[128,43261,43263,43303,43306,43309,43312],{"className":43262},[259],[128,43264,43266,43269],{"className":43265},[259],[128,43267,4835],{"className":43268,"style":4920},[259,1873],[128,43270,43272],{"className":43271},[2087],[128,43273,43275,43295],{"className":43274},[274,321],[128,43276,43278,43292],{"className":43277},[278],[128,43279,43281],{"className":43280,"style":2218},[282],[128,43282,43283,43286],{"style":4935},[128,43284],{"className":43285,"style":291},[290],[128,43287,43289],{"className":43288},[299,300,301,298],[128,43290,2022],{"className":43291,"style":2231},[259,1873,298],[128,43293,347],{"className":43294},[346],[128,43296,43298],{"className":43297},[278],[128,43299,43301],{"className":43300,"style":2241},[282],[128,43302],{},[128,43304],{"className":43305,"style":2508},[269],[128,43307,1989],{"className":43308},[2115],[128,43310],{"className":43311,"style":2508},[269],[128,43313,1842],{"className":43314},[259],[128,43316,347],{"className":43317},[346],[128,43319,43321],{"className":43320},[278],[128,43322,43324],{"className":43323,"style":38310},[282],[128,43325],{},[128,43327],{"className":43328},[1928,5570],[128,43330,347],{"className":43331},[346],[128,43333,43335],{"className":43334},[278],[128,43336,43339],{"className":43337,"style":43338},[282],"height:1.334em;",[128,43340],{},[128,43342,347],{"className":43343},[346],[128,43345,43347],{"className":43346},[278],[128,43348,43351],{"className":43349,"style":43350},[282],"height:2.0123em;",[128,43352],{},[128,43354],{"className":43355,"style":2508},[269],[128,43357,9486],{"className":43358},[2115],[128,43360],{"className":43361,"style":2508},[269],[128,43363,43365,43368,43536,43539,43542],{"className":43364},[250],[128,43366],{"className":43367,"style":43129},[254],[128,43369,43371],{"className":43370},[1911,8606],[128,43372,43374,43528],{"className":43373},[274,321],[128,43375,43377,43525],{"className":43376},[278],[128,43378,43380,43397],{"className":43379,"style":20407},[282],[128,43381,43382,43385],{"style":43144},[128,43383],{"className":43384,"style":43148},[290],[128,43386,43388],{"className":43387},[299,300,301,298],[128,43389,43391],{"className":43390},[259,298],[128,43392,43394],{"className":43393},[259,260,298],[128,43395,43009],{"className":43396},[259,15272,298],[128,43398,43399,43402],{"style":43163},[128,43400],{"className":43401,"style":43148},[290],[128,43403,43405],{"className":43404},[1911,8606],[128,43406,43408,43517],{"className":43407},[274,321],[128,43409,43411,43514],{"className":43410},[278],[128,43412,43414,43444],{"className":43413,"style":20407},[282],[128,43415,43417,43420],{"className":43416,"style":43182},[29395],[128,43418],{"className":43419,"style":43148},[290],[128,43421,43423,43430,43437],{"className":43422,"style":29404},[29403],[128,43424,43426],{"className":43425,"style":29409},[29408],[29411,43427,43428],{"xmlns":29413,"width":29414,"height":29415,"viewBox":29416,"preserveAspectRatio":29417},[29419,43429],{"d":29421},[128,43431,43433],{"className":43432,"style":29409},[29425],[29411,43434,43435],{"xmlns":29413,"width":29414,"height":29415,"viewBox":29416,"preserveAspectRatio":29428},[29419,43436],{"d":29431},[128,43438,43440],{"className":43439,"style":29409},[29435],[29411,43441,43442],{"xmlns":29413,"width":29414,"height":29415,"viewBox":29416,"preserveAspectRatio":29438},[29419,43443],{"d":29441},[128,43445,43446,43449],{"style":43163},[128,43447],{"className":43448,"style":43148},[290],[128,43450,43452],{"className":43451},[259],[128,43453,43455,43458,43511],{"className":43454},[259],[128,43456],{"className":43457},[1896,5570],[128,43459,43461],{"className":43460},[5451],[128,43462,43464,43503],{"className":43463},[274,321],[128,43465,43467,43500],{"className":43466},[278],[128,43468,43470,43481,43489],{"className":43469,"style":20407},[282],[128,43471,43472,43475],{"style":13123},[128,43473],{"className":43474,"style":335},[290],[128,43476,43478],{"className":43477},[259],[128,43479,41957],{"className":43480,"style":42029},[259,1873],[128,43482,43483,43486],{"style":5617},[128,43484],{"className":43485,"style":335},[290],[128,43487],{"className":43488,"style":5625},[5624],[128,43490,43491,43494],{"style":13189},[128,43492],{"className":43493,"style":335},[290],[128,43495,43497],{"className":43496},[259],[128,43498,1842],{"className":43499},[259],[128,43501,347],{"className":43502},[346],[128,43504,43506],{"className":43505},[278],[128,43507,43509],{"className":43508,"style":38310},[282],[128,43510],{},[128,43512],{"className":43513},[1928,5570],[128,43515,347],{"className":43516},[346],[128,43518,43520],{"className":43519},[278],[128,43521,43523],{"className":43522,"style":43338},[282],[128,43524],{},[128,43526,347],{"className":43527},[346],[128,43529,43531],{"className":43530},[278],[128,43532,43534],{"className":43533,"style":43350},[282],[128,43535],{},[128,43537],{"className":43538,"style":1878},[269],[128,43540,1994],{"className":43541},[1882],[128,43543],{"className":43544,"style":1878},[269],[128,43546,43548,43551,43554,43557,43560,43563],{"className":43547},[250],[128,43549],{"className":43550,"style":1892},[254],[128,43552,2477],{"className":43553},[1896],[128,43555,1842],{"className":43556},[259],[128,43558],{"className":43559,"style":2508},[269],[128,43561,1989],{"className":43562},[2115],[128,43564],{"className":43565,"style":2508},[269],[128,43567,43569,43572,43575,43578,43581,43741,43744,43747],{"className":43568},[250],[128,43570],{"className":43571,"style":20388},[254],[128,43573,35129],{"className":43574},[259,1873],[128,43576,2486],{"className":43577},[1928],[128,43579],{"className":43580,"style":1907},[269],[128,43582,43584,43587,43738],{"className":43583},[259],[128,43585],{"className":43586},[1896,5570],[128,43588,43590],{"className":43589},[5451],[128,43591,43593,43730],{"className":43592},[274,321],[128,43594,43596,43727],{"className":43595},[278],[128,43597,43599,43659,43667],{"className":43598,"style":20407},[282],[128,43600,43601,43604],{"style":13123},[128,43602],{"className":43603,"style":335},[290],[128,43605,43607,43647,43650,43653,43656],{"className":43606},[259],[128,43608,43610,43613],{"className":43609},[259],[128,43611,4835],{"className":43612,"style":4920},[259,1873],[128,43614,43616],{"className":43615},[2087],[128,43617,43619,43639],{"className":43618},[274,321],[128,43620,43622,43636],{"className":43621},[278],[128,43623,43625],{"className":43624,"style":2945},[282],[128,43626,43627,43630],{"style":4935},[128,43628],{"className":43629,"style":291},[290],[128,43631,43633],{"className":43632},[299,300,301,298],[128,43634,2028],{"className":43635},[259,298],[128,43637,347],{"className":43638},[346],[128,43640,43642],{"className":43641},[278],[128,43643,43645],{"className":43644,"style":2241},[282],[128,43646],{},[128,43648],{"className":43649,"style":2508},[269],[128,43651,1989],{"className":43652},[2115],[128,43654],{"className":43655,"style":2508},[269],[128,43657,1853],{"className":43658,"style":1924},[259,1873],[128,43660,43661,43664],{"style":5617},[128,43662],{"className":43663,"style":335},[290],[128,43665],{"className":43666,"style":5625},[5624],[128,43668,43669,43672],{"style":13189},[128,43670],{"className":43671,"style":335},[290],[128,43673,43675,43715,43718,43721,43724],{"className":43674},[259],[128,43676,43678,43681],{"className":43677},[259],[128,43679,4835],{"className":43680,"style":4920},[259,1873],[128,43682,43684],{"className":43683},[2087],[128,43685,43687,43707],{"className":43686},[274,321],[128,43688,43690,43704],{"className":43689},[278],[128,43691,43693],{"className":43692,"style":2218},[282],[128,43694,43695,43698],{"style":4935},[128,43696],{"className":43697,"style":291},[290],[128,43699,43701],{"className":43700},[299,300,301,298],[128,43702,2022],{"className":43703,"style":2231},[259,1873,298],[128,43705,347],{"className":43706},[346],[128,43708,43710],{"className":43709},[278],[128,43711,43713],{"className":43712,"style":2241},[282],[128,43714],{},[128,43716],{"className":43717,"style":2508},[269],[128,43719,1989],{"className":43720},[2115],[128,43722],{"className":43723,"style":2508},[269],[128,43725,1842],{"className":43726},[259],[128,43728,347],{"className":43729},[346],[128,43731,43733],{"className":43732},[278],[128,43734,43736],{"className":43735,"style":20496},[282],[128,43737],{},[128,43739],{"className":43740},[1928,5570],[128,43742],{"className":43743,"style":2508},[269],[128,43745,9486],{"className":43746},[2115],[128,43748],{"className":43749,"style":2508},[269],[128,43751,43753,43757,43760,43763,43766],{"className":43752},[250],[128,43754],{"className":43755,"style":43756},[254],"height:0.4445em;",[128,43758,35129],{"className":43759},[259,1873],[128,43761],{"className":43762,"style":2508},[269],[128,43764,12935],{"className":43765},[2115],[128,43767],{"className":43768,"style":2508},[269],[128,43770,43772,43776],{"className":43771},[250],[128,43773],{"className":43774,"style":43775},[254],"height:2.0074em;vertical-align:-0.686em;",[128,43777,43779,43782,43835],{"className":43778},[259],[128,43780],{"className":43781},[1896,5570],[128,43783,43785],{"className":43784},[5451],[128,43786,43788,43827],{"className":43787},[274,321],[128,43789,43791,43824],{"className":43790},[278],[128,43792,43794,43805,43813],{"className":43793,"style":20407},[282],[128,43795,43796,43799],{"style":13123},[128,43797],{"className":43798,"style":335},[290],[128,43800,43802],{"className":43801},[259],[128,43803,1853],{"className":43804,"style":1924},[259,1873],[128,43806,43807,43810],{"style":5617},[128,43808],{"className":43809,"style":335},[290],[128,43811],{"className":43812,"style":5625},[5624],[128,43814,43815,43818],{"style":13189},[128,43816],{"className":43817,"style":335},[290],[128,43819,43821],{"className":43820},[259],[128,43822,1842],{"className":43823},[259],[128,43825,347],{"className":43826},[346],[128,43828,43830],{"className":43829},[278],[128,43831,43833],{"className":43832,"style":38310},[282],[128,43834],{},[128,43836],{"className":43837},[1928,5570],[11,43839,14647,43840,43918,43919,43970,43971,44022],{},[35,43841,43842,43843,43917],{},"预测概率是「证据归一化的类比例」与「均匀分布」按 ",[128,43844,43846,43872],{"className":43845,"translate":218},[217],[128,43847,43849],{"className":43848},[222],[224,43850,43851],{"xmlns":226},[228,43852,43853,43869],{},[231,43854,43855,43857,43859,43861,43863,43865,43867],{},[1832,43856,2477],{"stretchy":1837},[1840,43858,1842],{},[1832,43860,1989],{},[1795,43862,35129],{},[1832,43864,1845],{"separator":246},[1795,43866,35129],{},[1832,43868,2486],{"stretchy":1837},[238,43870,43871],{"encoding":240},"(1-u, u)",[128,43873,43875,43896],{"className":43874,"ariaHidden":246},[245],[128,43876,43878,43881,43884,43887,43890,43893],{"className":43877},[250],[128,43879],{"className":43880,"style":1892},[254],[128,43882,2477],{"className":43883},[1896],[128,43885,1842],{"className":43886},[259],[128,43888],{"className":43889,"style":2508},[269],[128,43891,1989],{"className":43892},[2115],[128,43894],{"className":43895,"style":2508},[269],[128,43897,43899,43902,43905,43908,43911,43914],{"className":43898},[250],[128,43900],{"className":43901,"style":1892},[254],[128,43903,35129],{"className":43904},[259,1873],[128,43906,1845],{"className":43907},[1903],[128,43909],{"className":43910,"style":1907},[269],[128,43912,35129],{"className":43913},[259,1873],[128,43915,2486],{"className":43916},[1928]," 的凸组合","。当证据充分时（",[128,43920,43922,43940],{"className":43921,"translate":218},[217],[128,43923,43925],{"className":43924},[222],[224,43926,43927],{"xmlns":226},[228,43928,43929,43937],{},[231,43930,43931,43933,43935],{},[1795,43932,35129],{},[1832,43934,22419],{},[1840,43936,2028],{},[238,43938,43939],{"encoding":240},"u \\to 0",[128,43941,43943,43961],{"className":43942,"ariaHidden":246},[245],[128,43944,43946,43949,43952,43955,43958],{"className":43945},[250],[128,43947],{"className":43948,"style":7758},[254],[128,43950,35129],{"className":43951},[259,1873],[128,43953],{"className":43954,"style":1878},[269],[128,43956,22419],{"className":43957},[1882],[128,43959],{"className":43960,"style":1878},[269],[128,43962,43964,43967],{"className":43963},[250],[128,43965],{"className":43966,"style":2594},[254],[128,43968,2028],{"className":43969},[259],"），预测趋于证据的方向。当证据消失时（",[128,43972,43974,43992],{"className":43973,"translate":218},[217],[128,43975,43977],{"className":43976},[222],[224,43978,43979],{"xmlns":226},[228,43980,43981,43989],{},[231,43982,43983,43985,43987],{},[1795,43984,35129],{},[1832,43986,22419],{},[1840,43988,1842],{},[238,43990,43991],{"encoding":240},"u \\to 1",[128,43993,43995,44013],{"className":43994,"ariaHidden":246},[245],[128,43996,43998,44001,44004,44007,44010],{"className":43997},[250],[128,43999],{"className":44000,"style":7758},[254],[128,44002,35129],{"className":44003},[259,1873],[128,44005],{"className":44006,"style":1878},[269],[128,44008,22419],{"className":44009},[1882],[128,44011],{"className":44012,"style":1878},[269],[128,44014,44016,44019],{"className":44015},[250],[128,44017],{"className":44018,"style":2594},[254],[128,44020,1842],{"className":44021},[259],"），预测退回均匀分布。极限行为因此完全符合直觉：",[128,44024,44026],{"className":44025,"translate":218},[1962],[128,44027,44029,44134],{"className":44028,"translate":218},[217],[128,44030,44032],{"className":44031},[222],[224,44033,44034],{"xmlns":226,"display":1971},[228,44035,44036,44131],{},[231,44037,44038,44040,44042,44044,44046,44048,44050,44052,44054,44056,44058,44060,44062,44064,44066,44068,44071,44073,44075,44083,44085,44087,44089,44091,44093,44095,44097,44099,44101,44103,44105,44107,44109,44111,44113],{},[1795,44039,41957],{},[1832,44041,22419],{},[1795,44043,1853],{},[234,44045,2033],{},[1832,44047,2477],{"stretchy":1837},[1795,44049,3713],{"mathvariant":2001},[1832,44051,22419],{},[1840,44053,2028],{"mathvariant":2001},[1832,44055,2486],{"stretchy":1837},[1832,44057,2014],{},[269,44059],{"width":8176},[1795,44061,35129],{},[1832,44063,22419],{},[1840,44065,1842],{},[1832,44067,1845],{"separator":246},[234,44069,44070],{},"  ",[1795,44072,11],{"mathvariant":2001},[1832,44074,22419],{},[2035,44076,44077],{"scriptlevel":2028,"displaystyle":1837},[5451,44078,44079,44081],{},[1840,44080,1842],{},[1795,44082,1853],{},[1840,44084,1842],{"mathvariant":2001},[269,44086],{"width":11568},[269,44088],{"width":11568},[1795,44090,41957],{},[1832,44092,22419],{},[1795,44094,8521],{"mathvariant":1981},[1832,44096,2014],{},[269,44098],{"width":8176},[1795,44100,35129],{},[1832,44102,22419],{},[1840,44104,2028],{},[1832,44106,1845],{"separator":246},[234,44108,44070],{},[1795,44110,11],{"mathvariant":2001},[1832,44112,22419],{},[5451,44114,44115,44117],{},[1795,44116,3713],{"mathvariant":2001},[231,44118,44119,44125],{},[8606,44120,44121,44123],{},[1832,44122,2042],{},[1795,44124,16495],{},[2016,44126,44127,44129],{},[1795,44128,3713],{},[1795,44130,16495],{},[238,44132,44133],{"encoding":240},"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}",[128,44135,44137,44155,44182,44206,44224,44257,44353,44374,44392,44425],{"className":44136,"ariaHidden":246},[245],[128,44138,44140,44143,44146,44149,44152],{"className":44139},[250],[128,44141],{"className":44142,"style":283},[254],[128,44144,41957],{"className":44145,"style":42029},[259,1873],[128,44147],{"className":44148,"style":1878},[269],[128,44150,22419],{"className":44151},[1882],[128,44153],{"className":44154,"style":1878},[269],[128,44156,44158,44161,44164,44167,44170,44173,44176,44179],{"className":44157},[250],[128,44159],{"className":44160,"style":1892},[254],[128,44162,1853],{"className":44163,"style":1924},[259,1873],[128,44165,2033],{"className":44166},[269],[128,44168,2477],{"className":44169},[1896],[128,44171,3713],{"className":44172},[259,2151],[128,44174],{"className":44175,"style":1878},[269],[128,44177,22419],{"className":44178},[1882],[128,44180],{"className":44181,"style":1878},[269],[128,44183,44185,44188,44191,44194,44197,44200,44203],{"className":44184},[250],[128,44186],{"className":44187,"style":1892},[254],[128,44189,2028],{"className":44190},[259,2151],[128,44192,2486],{"className":44193},[1928],[128,44195],{"className":44196,"style":1878},[269],[128,44198,2014],{"className":44199},[1882],[128,44201],{"className":44202,"style":17700},[269],[128,44204],{"className":44205,"style":1878},[269],[128,44207,44209,44212,44215,44218,44221],{"className":44208},[250],[128,44210],{"className":44211,"style":7758},[254],[128,44213,35129],{"className":44214},[259,1873],[128,44216],{"className":44217,"style":1878},[269],[128,44219,22419],{"className":44220},[1882],[128,44222],{"className":44223,"style":1878},[269],[128,44225,44227,44230,44233,44236,44239,44242,44245,44248,44251,44254],{"className":44226},[250],[128,44228],{"className":44229,"style":21472},[254],[128,44231,1842],{"className":44232},[259],[128,44234,1845],{"className":44235},[1903],[128,44237,2033],{"className":44238},[269],[128,44240,2033],{"className":44241},[269],[128,44243],{"className":44244,"style":1907},[269],[128,44246,11],{"className":44247},[259,2151],[128,44249],{"className":44250,"style":1878},[269],[128,44252,22419],{"className":44253},[1882],[128,44255],{"className":44256,"style":1878},[269],[128,44258,44260,44264,44332,44335,44338,44341,44344,44347,44350],{"className":44259},[250],[128,44261],{"className":44262,"style":44263},[254],"height:1.1901em;vertical-align:-0.345em;",[128,44265,44267,44270,44329],{"className":44266},[259],[128,44268],{"className":44269},[1896,5570],[128,44271,44273],{"className":44272},[5451],[128,44274,44276,44321],{"className":44275},[274,321],[128,44277,44279,44318],{"className":44278},[278],[128,44280,44282,44296,44304],{"className":44281,"style":5583},[282],[128,44283,44284,44287],{"style":5586},[128,44285],{"className":44286,"style":335},[290],[128,44288,44290],{"className":44289},[299,300,301,298],[128,44291,44293],{"className":44292},[259,298],[128,44294,1853],{"className":44295,"style":1924},[259,1873,298],[128,44297,44298,44301],{"style":5617},[128,44299],{"className":44300,"style":335},[290],[128,44302],{"className":44303,"style":5625},[5624],[128,44305,44306,44309],{"style":5628},[128,44307],{"className":44308,"style":335},[290],[128,44310,44312],{"className":44311},[299,300,301,298],[128,44313,44315],{"className":44314},[259,298],[128,44316,1842],{"className":44317},[259,298],[128,44319,347],{"className":44320},[346],[128,44322,44324],{"className":44323},[278],[128,44325,44327],{"className":44326,"style":11919},[282],[128,44328],{},[128,44330],{"className":44331},[1928,5570],[128,44333,1842],{"className":44334},[259,2151],[128,44336],{"className":44337,"style":11756},[269],[128,44339],{"className":44340,"style":11756},[269],[128,44342,41957],{"className":44343,"style":42029},[259,1873],[128,44345],{"className":44346,"style":1878},[269],[128,44348,22419],{"className":44349},[1882],[128,44351],{"className":44352,"style":1878},[269],[128,44354,44356,44359,44362,44365,44368,44371],{"className":44355},[250],[128,44357],{"className":44358,"style":7758},[254],[128,44360,8521],{"className":44361},[259],[128,44363],{"className":44364,"style":1878},[269],[128,44366,2014],{"className":44367},[1882],[128,44369],{"className":44370,"style":17700},[269],[128,44372],{"className":44373,"style":1878},[269],[128,44375,44377,44380,44383,44386,44389],{"className":44376},[250],[128,44378],{"className":44379,"style":7758},[254],[128,44381,35129],{"className":44382},[259,1873],[128,44384],{"className":44385,"style":1878},[269],[128,44387,22419],{"className":44388},[1882],[128,44390],{"className":44391,"style":1878},[269],[128,44393,44395,44398,44401,44404,44407,44410,44413,44416,44419,44422],{"className":44394},[250],[128,44396],{"className":44397,"style":21472},[254],[128,44399,2028],{"className":44400},[259],[128,44402,1845],{"className":44403},[1903],[128,44405,2033],{"className":44406},[269],[128,44408,2033],{"className":44409},[269],[128,44411],{"className":44412,"style":1907},[269],[128,44414,11],{"className":44415},[259,2151],[128,44417],{"className":44418,"style":1878},[269],[128,44420,22419],{"className":44421},[1882],[128,44423],{"className":44424,"style":1878},[269],[128,44426,44428,44432],{"className":44427},[250],[128,44429],{"className":44430,"style":44431},[254],"height:2.2433em;vertical-align:-1.1218em;",[128,44433,44435,44438,44573],{"className":44434},[259],[128,44436],{"className":44437},[1896,5570],[128,44439,44441],{"className":44440},[5451],[128,44442,44444,44564],{"className":44443},[274,321],[128,44445,44447,44561],{"className":44446},[278],[128,44448,44451,44542,44550],{"className":44449,"style":44450},[282],"height:1.1214em;",[128,44452,44453,44456],{"style":13123},[128,44454],{"className":44455,"style":335},[290],[128,44457,44459,44499,44502],{"className":44458},[259],[128,44460,44462,44465],{"className":44461},[2268],[128,44463,2042],{"className":44464,"style":2274},[2268,2272,2273],[128,44466,44468],{"className":44467},[2087],[128,44469,44471,44491],{"className":44470},[274,321],[128,44472,44474,44488],{"className":44473},[278],[128,44475,44477],{"className":44476,"style":7796},[282],[128,44478,44479,44482],{"style":2290},[128,44480],{"className":44481,"style":291},[290],[128,44483,44485],{"className":44484},[299,300,301,298],[128,44486,16495],{"className":44487,"style":16521},[259,1873,298],[128,44489,347],{"className":44490},[346],[128,44492,44494],{"className":44493},[278],[128,44495,44497],{"className":44496,"style":31756},[282],[128,44498],{},[128,44500],{"className":44501,"style":1907},[269],[128,44503,44505,44508],{"className":44504},[259],[128,44506,3713],{"className":44507},[259,1873],[128,44509,44511],{"className":44510},[2087],[128,44512,44514,44534],{"className":44513},[274,321],[128,44515,44517,44531],{"className":44516},[278],[128,44518,44520],{"className":44519,"style":3095},[282],[128,44521,44522,44525],{"style":2221},[128,44523],{"className":44524,"style":291},[290],[128,44526,44528],{"className":44527},[299,300,301,298],[128,44529,16495],{"className":44530,"style":16521},[259,1873,298],[128,44532,347],{"className":44533},[346],[128,44535,44537],{"className":44536},[278],[128,44538,44540],{"className":44539,"style":17424},[282],[128,44541],{},[128,44543,44544,44547],{"style":5617},[128,44545],{"className":44546,"style":335},[290],[128,44548],{"className":44549,"style":5625},[5624],[128,44551,44552,44555],{"style":13189},[128,44553],{"className":44554,"style":335},[290],[128,44556,44558],{"className":44557},[259],[128,44559,3713],{"className":44560},[259,2151],[128,44562,347],{"className":44563},[346],[128,44565,44567],{"className":44566},[278],[128,44568,44571],{"className":44569,"style":44570},[282],"height:1.1218em;",[128,44572],{},[128,44574],{"className":44575},[1928,5570],[11,44577,44578,44579,44582,44583,44611,44612,44640,44641,44644],{},"命题 3.4 同时也暴露了该参数化的一个",[35,44580,44581],{},"结构性局限","：",[128,44584,44586,44599],{"className":44585,"translate":218},[217],[128,44587,44589],{"className":44588},[222],[224,44590,44591],{"xmlns":226},[228,44592,44593,44597],{},[231,44594,44595],{},[1795,44596,35129],{},[238,44598,35129],{"encoding":240},[128,44600,44602],{"className":44601,"ariaHidden":246},[245],[128,44603,44605,44608],{"className":44604},[250],[128,44606],{"className":44607,"style":7758},[254],[128,44609,35129],{"className":44610},[259,1873]," 只是总强度 ",[128,44613,44615,44628],{"className":44614,"translate":218},[217],[128,44616,44618],{"className":44617},[222],[224,44619,44620],{"xmlns":226},[228,44621,44622,44626],{},[231,44623,44624],{},[1795,44625,41957],{},[238,44627,41957],{"encoding":240},[128,44629,44631],{"className":44630,"ariaHidden":246},[245],[128,44632,44634,44637],{"className":44633},[250],[128,44635],{"className":44636,"style":283},[254],[128,44638,41957],{"className":44639,"style":42029},[259,1873]," 的函数，与证据在各类别之间的",[35,44642,44643],{},"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。",[2610,44646,44648],{"id":44647},"_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",[11,44650,44651,44652,44713,44714,44717],{},"命题 3.4 给出的 ",[128,44653,44655,44677],{"className":44654,"translate":218},[217],[128,44656,44658],{"className":44657},[222],[224,44659,44660],{"xmlns":226},[228,44661,44662,44674],{},[231,44663,44664,44666,44668,44670,44672],{},[1795,44665,35129],{},[1832,44667,1994],{},[1795,44669,1853],{},[1795,44671,4751],{"mathvariant":1981},[1795,44673,41957],{},[238,44675,44676],{"encoding":240},"u = K\u002FS",[128,44678,44680,44698],{"className":44679,"ariaHidden":246},[245],[128,44681,44683,44686,44689,44692,44695],{"className":44682},[250],[128,44684],{"className":44685,"style":7758},[254],[128,44687,35129],{"className":44688},[259,1873],[128,44690],{"className":44691,"style":1878},[269],[128,44693,1994],{"className":44694},[1882],[128,44696],{"className":44697,"style":1878},[269],[128,44699,44701,44704,44707,44710],{"className":44700},[250],[128,44702],{"className":44703,"style":1892},[254],[128,44705,1853],{"className":44706,"style":1924},[259,1873],[128,44708,4751],{"className":44709},[259],[128,44711,41957],{"className":44712,"style":42029},[259,1873]," 是一个",[35,44715,44716],{},"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。",[11,44719,1781,44720,17916,44802,44908],{},[128,44721,44723,44748],{"className":44722,"translate":218},[217],[128,44724,44726],{"className":44725},[222],[224,44727,44728],{"xmlns":226},[228,44729,44730,44746],{},[231,44731,44732,44734,44736,44738,44740,44742,44744],{},[1795,44733,26389],{"mathvariant":4834},[1832,44735,5911],{},[1795,44737,5914],{"mathvariant":1981},[1832,44739,3278],{},[1832,44741,2477],{"stretchy":1837},[1795,44743,4835],{"mathvariant":4834},[1832,44745,2486],{"stretchy":1837},[238,44747,26404],{"encoding":240},[128,44749,44751,44775],{"className":44750,"ariaHidden":246},[245],[128,44752,44754,44757,44766,44769,44772],{"className":44753},[250],[128,44755],{"className":44756,"style":4439},[254],[128,44758,44760],{"className":44759},[259],[128,44761,44763],{"className":44762},[259],[128,44764,26389],{"className":44765,"style":26423},[259,4895],[128,44767],{"className":44768,"style":1878},[269],[128,44770,5911],{"className":44771},[1882],[128,44773],{"className":44774,"style":1878},[269],[128,44776,44778,44781,44787,44790,44799],{"className":44777},[250],[128,44779],{"className":44780,"style":1892},[254],[128,44782,44784],{"className":44783},[2268],[128,44785,5914],{"className":44786},[259,3353],[128,44788,2477],{"className":44789},[1896],[128,44791,44793],{"className":44792},[259],[128,44794,44796],{"className":44795},[259],[128,44797,4835],{"className":44798},[259,4895],[128,44800,2486],{"className":44801},[1928],[128,44803,44805,44836],{"className":44804,"translate":218},[217],[128,44806,44808],{"className":44807},[222],[224,44809,44810],{"xmlns":226},[228,44811,44812,44833],{},[231,44813,44814,44816,44818,44820,44822,44825,44827,44829,44831],{},[1795,44815,1830],{},[1832,44817,5443],{},[1795,44819,26389],{"mathvariant":4834},[1832,44821,5911],{},[1795,44823,44824],{"mathvariant":1981},"Cat",[1832,44826,3278],{},[1832,44828,2477],{"stretchy":1837},[1795,44830,26389],{"mathvariant":4834},[1832,44832,2486],{"stretchy":1837},[238,44834,44835],{"encoding":240},"y \\mid \\boldsymbol{\\pi} \\sim \\operatorname{Cat}(\\boldsymbol{\\pi})",[128,44837,44839,44857,44881],{"className":44838,"ariaHidden":246},[245],[128,44840,44842,44845,44848,44851,44854],{"className":44841},[250],[128,44843],{"className":44844,"style":1892},[254],[128,44846,1830],{"className":44847,"style":1874},[259,1873],[128,44849],{"className":44850,"style":1878},[269],[128,44852,5443],{"className":44853},[1882],[128,44855],{"className":44856,"style":1878},[269],[128,44858,44860,44863,44872,44875,44878],{"className":44859},[250],[128,44861],{"className":44862,"style":4439},[254],[128,44864,44866],{"className":44865},[259],[128,44867,44869],{"className":44868},[259],[128,44870,26389],{"className":44871,"style":26423},[259,4895],[128,44873],{"className":44874,"style":1878},[269],[128,44876,5911],{"className":44877},[1882],[128,44879],{"className":44880,"style":1878},[269],[128,44882,44884,44887,44893,44896,44905],{"className":44883},[250],[128,44885],{"className":44886,"style":1892},[254],[128,44888,44890],{"className":44889},[2268],[128,44891,44824],{"className":44892},[259,3353],[128,44894,2477],{"className":44895},[1896],[128,44897,44899],{"className":44898},[259],[128,44900,44902],{"className":44901},[259],[128,44903,26389],{"className":44904,"style":26423},[259,4895],[128,44906,2486],{"className":44907},[1928],"。考虑三个量：",[33248,44910,44911,45261,45414],{},[33251,44912,44913,44916,44917,7713,44996,893],{},[35,44914,44915],{},"总不确定性（total uncertainty）","：预测分布的熵 ",[128,44918,44920,44950],{"className":44919,"translate":218},[217],[128,44921,44923],{"className":44922},[222],[224,44924,44925],{"xmlns":226},[228,44926,44927,44947],{},[231,44928,44929,44931,44933,44935,44937,44939,44941,44943,44945],{},[1795,44930,24362],{},[1832,44932,16538],{"stretchy":1837},[1795,44934,23001],{"mathvariant":2008},[1832,44936,2477],{"stretchy":1837},[1795,44938,1830],{},[1832,44940,5443],{},[1795,44942,2760],{"mathvariant":2001},[1832,44944,2486],{"stretchy":1837},[1832,44946,16547],{"stretchy":1837},[238,44948,44949],{"encoding":240},"H[\\mathbb{P}(y \\mid \\mathbf{x})]",[128,44951,44953,44983],{"className":44952,"ariaHidden":246},[245],[128,44954,44956,44959,44962,44965,44968,44971,44974,44977,44980],{"className":44955},[250],[128,44957],{"className":44958,"style":1892},[254],[128,44960,24362],{"className":44961,"style":24474},[259,1873],[128,44963,16538],{"className":44964},[1896],[128,44966,23001],{"className":44967},[259,2167],[128,44969,2477],{"className":44970},[1896],[128,44972,1830],{"className":44973,"style":1874},[259,1873],[128,44975],{"className":44976,"style":1878},[269],[128,44978,5443],{"className":44979},[1882],[128,44981],{"className":44982,"style":1878},[269],[128,44984,44986,44989,44992],{"className":44985},[250],[128,44987],{"className":44988,"style":1892},[254],[128,44990,2760],{"className":44991},[259,2151],[128,44993,44995],{"className":44994},[1928],")]",[128,44997,44999,45051],{"className":44998,"translate":218},[217],[128,45000,45002],{"className":45001},[222],[224,45003,45004],{"xmlns":226},[228,45005,45006,45048],{},[231,45007,45008,45010,45012,45014,45016,45018,45020,45022,45024,45026,45032,45034,45040,45042],{},[1795,45009,23001],{"mathvariant":2008},[1832,45011,2477],{"stretchy":1837},[1795,45013,1830],{},[1832,45015,1994],{},[1795,45017,2022],{},[1832,45019,5443],{},[1795,45021,2760],{"mathvariant":2001},[1832,45023,2486],{"stretchy":1837},[1832,45025,1994],{},[2016,45027,45028,45030],{},[1795,45029,11],{},[1795,45031,2022],{},[1832,45033,1994],{},[2016,45035,45036,45038],{},[1795,45037,4835],{},[1795,45039,2022],{},[1795,45041,4751],{"mathvariant":1981},[2016,45043,45044,45046],{},[1795,45045,4835],{},[1840,45047,2028],{},[238,45049,45050],{"encoding":240},"\\mathbb{P}(y = k \\mid \\mathbf{x}) = p_k = \\alpha_k\u002F\\alpha_0",[128,45052,45054,45078,45096,45117,45172],{"className":45053,"ariaHidden":246},[245],[128,45055,45057,45060,45063,45066,45069,45072,45075],{"className":45056},[250],[128,45058],{"className":45059,"style":1892},[254],[128,45061,23001],{"className":45062},[259,2167],[128,45064,2477],{"className":45065},[1896],[128,45067,1830],{"className":45068,"style":1874},[259,1873],[128,45070],{"className":45071,"style":1878},[269],[128,45073,1994],{"className":45074},[1882],[128,45076],{"className":45077,"style":1878},[269],[128,45079,45081,45084,45087,45090,45093],{"className":45080},[250],[128,45082],{"className":45083,"style":1892},[254],[128,45085,2022],{"className":45086,"style":2231},[259,1873],[128,45088],{"className":45089,"style":1878},[269],[128,45091,5443],{"className":45092},[1882],[128,45094],{"className":45095,"style":1878},[269],[128,45097,45099,45102,45105,45108,45111,45114],{"className":45098},[250],[128,45100],{"className":45101,"style":1892},[254],[128,45103,2760],{"className":45104},[259,2151],[128,45106,2486],{"className":45107},[1928],[128,45109],{"className":45110,"style":1878},[269],[128,45112,1994],{"className":45113},[1882],[128,45115],{"className":45116,"style":1878},[269],[128,45118,45120,45123,45163,45166,45169],{"className":45119},[250],[128,45121],{"className":45122,"style":11158},[254],[128,45124,45126,45129],{"className":45125},[259],[128,45127,11],{"className":45128},[259,1873],[128,45130,45132],{"className":45131},[2087],[128,45133,45135,45155],{"className":45134},[274,321],[128,45136,45138,45152],{"className":45137},[278],[128,45139,45141],{"className":45140,"style":2218},[282],[128,45142,45143,45146],{"style":2221},[128,45144],{"className":45145,"style":291},[290],[128,45147,45149],{"className":45148},[299,300,301,298],[128,45150,2022],{"className":45151,"style":2231},[259,1873,298],[128,45153,347],{"className":45154},[346],[128,45156,45158],{"className":45157},[278],[128,45159,45161],{"className":45160,"style":2241},[282],[128,45162],{},[128,45164],{"className":45165,"style":1878},[269],[128,45167,1994],{"className":45168},[1882],[128,45170],{"className":45171,"style":1878},[269],[128,45173,45175,45178,45218,45221],{"className":45174},[250],[128,45176],{"className":45177,"style":1892},[254],[128,45179,45181,45184],{"className":45180},[259],[128,45182,4835],{"className":45183,"style":4920},[259,1873],[128,45185,45187],{"className":45186},[2087],[128,45188,45190,45210],{"className":45189},[274,321],[128,45191,45193,45207],{"className":45192},[278],[128,45194,45196],{"className":45195,"style":2218},[282],[128,45197,45198,45201],{"style":4935},[128,45199],{"className":45200,"style":291},[290],[128,45202,45204],{"className":45203},[299,300,301,298],[128,45205,2022],{"className":45206,"style":2231},[259,1873,298],[128,45208,347],{"className":45209},[346],[128,45211,45213],{"className":45212},[278],[128,45214,45216],{"className":45215,"style":2241},[282],[128,45217],{},[128,45219,4751],{"className":45220},[259],[128,45222,45224,45227],{"className":45223},[259],[128,45225,4835],{"className":45226,"style":4920},[259,1873],[128,45228,45230],{"className":45229},[2087],[128,45231,45233,45253],{"className":45232},[274,321],[128,45234,45236,45250],{"className":45235},[278],[128,45237,45239],{"className":45238,"style":2945},[282],[128,45240,45241,45244],{"style":4935},[128,45242],{"className":45243,"style":291},[290],[128,45245,45247],{"className":45246},[299,300,301,298],[128,45248,2028],{"className":45249},[259,298],[128,45251,347],{"className":45252},[346],[128,45254,45256],{"className":45255},[278],[128,45257,45259],{"className":45258,"style":2241},[282],[128,45260],{},[33251,45262,45263,45266,45267,45301,45302,893],{},[35,45264,45265],{},"偶然不确定性（aleatoric uncertainty）","：给定 ",[128,45268,45270,45283],{"className":45269,"translate":218},[217],[128,45271,45273],{"className":45272},[222],[224,45274,45275],{"xmlns":226},[228,45276,45277,45281],{},[231,45278,45279],{},[1795,45280,26389],{"mathvariant":4834},[238,45282,26477],{"encoding":240},[128,45284,45286],{"className":45285,"ariaHidden":246},[245],[128,45287,45289,45292],{"className":45288},[250],[128,45290],{"className":45291,"style":4439},[254],[128,45293,45295],{"className":45294},[259],[128,45296,45298],{"className":45297},[259],[128,45299,26389],{"className":45300,"style":26423},[259,4895]," 后仍存在的熵的期望 ",[128,45303,45305,45335],{"className":45304,"translate":218},[217],[128,45306,45308],{"className":45307},[222],[224,45309,45310],{"xmlns":226},[228,45311,45312,45332],{},[231,45313,45314,45320,45322,45324,45326,45328,45330],{},[2016,45315,45316,45318],{},[1795,45317,342],{"mathvariant":2008},[1795,45319,26389],{"mathvariant":4834},[1832,45321,16538],{"stretchy":1837},[1795,45323,24362],{},[1832,45325,2477],{"stretchy":1837},[1795,45327,26389],{"mathvariant":4834},[1832,45329,2486],{"stretchy":1837},[1832,45331,16547],{"stretchy":1837},[238,45333,45334],{"encoding":240},"\\mathbb{E}_{\\boldsymbol{\\pi}}[H(\\boldsymbol{\\pi})]",[128,45336,45338],{"className":45337,"ariaHidden":246},[245],[128,45339,45341,45344,45393,45396,45399,45402,45411],{"className":45340},[250],[128,45342],{"className":45343,"style":1892},[254],[128,45345,45347,45350],{"className":45346},[259],[128,45348,342],{"className":45349},[259,2167],[128,45351,45353],{"className":45352},[2087],[128,45354,45356,45385],{"className":45355},[274,321],[128,45357,45359,45382],{"className":45358},[278],[128,45360,45362],{"className":45361,"style":22681},[282],[128,45363,45364,45367],{"style":2221},[128,45365],{"className":45366,"style":291},[290],[128,45368,45370],{"className":45369},[299,300,301,298],[128,45371,45373],{"className":45372},[259,298],[128,45374,45376],{"className":45375},[259,298],[128,45377,45379],{"className":45378},[259,298],[128,45380,26389],{"className":45381,"style":26423},[259,4895,298],[128,45383,347],{"className":45384},[346],[128,45386,45388],{"className":45387},[278],[128,45389,45391],{"className":45390,"style":2241},[282],[128,45392],{},[128,45394,16538],{"className":45395},[1896],[128,45397,24362],{"className":45398,"style":24474},[259,1873],[128,45400,2477],{"className":45401},[1896],[128,45403,45405],{"className":45404},[259],[128,45406,45408],{"className":45407},[259],[128,45409,26389],{"className":45410,"style":26423},[259,4895],[128,45412,44995],{"className":45413},[1928],[33251,45415,45416,45419,45420,11072,45448,45482],{},[35,45417,45418],{},"认知不确定性（epistemic uncertainty）","：二者的差，即 ",[128,45421,45423,45436],{"className":45422,"translate":218},[217],[128,45424,45426],{"className":45425},[222],[224,45427,45428],{"xmlns":226},[228,45429,45430,45434],{},[231,45431,45432],{},[1795,45433,1830],{},[238,45435,1830],{"encoding":240},[128,45437,45439],{"className":45438,"ariaHidden":246},[245],[128,45440,45442,45445],{"className":45441},[250],[128,45443],{"className":45444,"style":11158},[254],[128,45446,1830],{"className":45447,"style":1874},[259,1873],[128,45449,45451,45464],{"className":45450,"translate":218},[217],[128,45452,45454],{"className":45453},[222],[224,45455,45456],{"xmlns":226},[228,45457,45458,45462],{},[231,45459,45460],{},[1795,45461,26389],{"mathvariant":4834},[238,45463,26477],{"encoding":240},[128,45465,45467],{"className":45466,"ariaHidden":246},[245],[128,45468,45470,45473],{"className":45469},[250],[128,45471],{"className":45472,"style":4439},[254],[128,45474,45476],{"className":45475},[259],[128,45477,45479],{"className":45478},[259],[128,45480,26389],{"className":45481,"style":26423},[259,4895]," 之间的互信息。",[2615,45484,45486],{"title":45485},"命题 3.5（Dirichlet 族内的不确定性分解）",[11,45487,45488,45489,2674,45673,42339,45765,46052,46451],{},"记 ",[128,45490,45492,45526],{"className":45491,"translate":218},[217],[128,45493,45495],{"className":45494},[222],[224,45496,45497],{"xmlns":226},[228,45498,45499,45523],{},[231,45500,45501,45507,45509,45515,45517],{},[2016,45502,45503,45505],{},[1795,45504,11],{},[1795,45506,2022],{},[1832,45508,1994],{},[2016,45510,45511,45513],{},[1795,45512,4835],{},[1795,45514,2022],{},[1795,45516,4751],{"mathvariant":1981},[2016,45518,45519,45521],{},[1795,45520,4835],{},[1840,45522,2028],{},[238,45524,45525],{"encoding":240},"p_k = \\alpha_k\u002F\\alpha_0",[128,45527,45529,45584],{"className":45528,"ariaHidden":246},[245],[128,45530,45532,45535,45575,45578,45581],{"className":45531},[250],[128,45533],{"className":45534,"style":11158},[254],[128,45536,45538,45541],{"className":45537},[259],[128,45539,11],{"className":45540},[259,1873],[128,45542,45544],{"className":45543},[2087],[128,45545,45547,45567],{"className":45546},[274,321],[128,45548,45550,45564],{"className":45549},[278],[128,45551,45553],{"className":45552,"style":2218},[282],[128,45554,45555,45558],{"style":2221},[128,45556],{"className":45557,"style":291},[290],[128,45559,45561],{"className":45560},[299,300,301,298],[128,45562,2022],{"className":45563,"style":2231},[259,1873,298],[128,45565,347],{"className":45566},[346],[128,45568,45570],{"className":45569},[278],[128,45571,45573],{"className":45572,"style":2241},[282],[128,45574],{},[128,45576],{"className":45577,"style":1878},[269],[128,45579,1994],{"className":45580},[1882],[128,45582],{"className":45583,"style":1878},[269],[128,45585,45587,45590,45630,45633],{"className":45586},[250],[128,45588],{"className":45589,"style":1892},[254],[128,45591,45593,45596],{"className":45592},[259],[128,45594,4835],{"className":45595,"style":4920},[259,1873],[128,45597,45599],{"className":45598},[2087],[128,45600,45602,45622],{"className":45601},[274,321],[128,45603,45605,45619],{"className":45604},[278],[128,45606,45608],{"className":45607,"style":2218},[282],[128,45609,45610,45613],{"style":4935},[128,45611],{"className":45612,"style":291},[290],[128,45614,45616],{"className":45615},[299,300,301,298],[128,45617,2022],{"className":45618,"style":2231},[259,1873,298],[128,45620,347],{"className":45621},[346],[128,45623,45625],{"className":45624},[278],[128,45626,45628],{"className":45627,"style":2241},[282],[128,45629],{},[128,45631,4751],{"className":45632},[259],[128,45634,45636,45639],{"className":45635},[259],[128,45637,4835],{"className":45638,"style":4920},[259,1873],[128,45640,45642],{"className":45641},[2087],[128,45643,45645,45665],{"className":45644},[274,321],[128,45646,45648,45662],{"className":45647},[278],[128,45649,45651],{"className":45650,"style":2945},[282],[128,45652,45653,45656],{"style":4935},[128,45654],{"className":45655,"style":291},[290],[128,45657,45659],{"className":45658},[299,300,301,298],[128,45660,2028],{"className":45661},[259,298],[128,45663,347],{"className":45664},[346],[128,45666,45668],{"className":45667},[278],[128,45669,45671],{"className":45670,"style":2241},[282],[128,45672],{},[128,45674,45676,45698],{"className":45675,"translate":218},[217],[128,45677,45679],{"className":45678},[222],[224,45680,45681],{"xmlns":226},[228,45682,45683,45695],{},[231,45684,45685,45687,45689],{},[1795,45686,41957],{},[1832,45688,1994],{},[2016,45690,45691,45693],{},[1795,45692,4835],{},[1840,45694,2028],{},[238,45696,45697],{"encoding":240},"S = \\alpha_0",[128,45699,45701,45719],{"className":45700,"ariaHidden":246},[245],[128,45702,45704,45707,45710,45713,45716],{"className":45703},[250],[128,45705],{"className":45706,"style":283},[254],[128,45708,41957],{"className":45709,"style":42029},[259,1873],[128,45711],{"className":45712,"style":1878},[269],[128,45714,1994],{"className":45715},[1882],[128,45717],{"className":45718,"style":1878},[269],[128,45720,45722,45725],{"className":45721},[250],[128,45723],{"className":45724,"style":4242},[254],[128,45726,45728,45731],{"className":45727},[259],[128,45729,4835],{"className":45730,"style":4920},[259,1873],[128,45732,45734],{"className":45733},[2087],[128,45735,45737,45757],{"className":45736},[274,321],[128,45738,45740,45754],{"className":45739},[278],[128,45741,45743],{"className":45742,"style":2945},[282],[128,45744,45745,45748],{"style":4935},[128,45746],{"className":45747,"style":291},[290],[128,45749,45751],{"className":45750},[299,300,301,298],[128,45752,2028],{"className":45753},[259,298],[128,45755,347],{"className":45756},[346],[128,45758,45760],{"className":45759},[278],[128,45761,45763],{"className":45762,"style":2241},[282],[128,45764],{},[128,45766,45768,45832],{"className":45767,"translate":218},[217],[128,45769,45771],{"className":45770},[222],[224,45772,45773],{"xmlns":226},[228,45774,45775,45829],{},[231,45776,45777,45779,45781,45783,45785,45787,45789,45791,45793,45795,45797,45799,45813,45819,45821,45823],{},[1795,45778,24362],{},[1832,45780,16538],{"stretchy":1837},[1795,45782,23001],{"mathvariant":2008},[1832,45784,2477],{"stretchy":1837},[1795,45786,1830],{},[1832,45788,5443],{},[1795,45790,2760],{"mathvariant":2001},[1832,45792,2486],{"stretchy":1837},[1832,45794,16547],{"stretchy":1837},[1832,45796,1994],{},[1832,45798,1989],{},[2038,45800,45801,45803,45811],{},[1832,45802,2042],{},[231,45804,45805,45807,45809],{},[1795,45806,2022],{},[1832,45808,1994],{},[1840,45810,1842],{},[1795,45812,1853],{},[2016,45814,45815,45817],{},[1795,45816,11],{},[1795,45818,2022],{},[1795,45820,24373],{},[1832,45822,3278],{},[2016,45824,45825,45827],{},[1795,45826,11],{},[1795,45828,2022],{},[238,45830,45831],{"encoding":240},"H[\\mathbb{P}(y \\mid \\mathbf{x})] = -\\sum_{k=1}^K p_k \\log p_k",[128,45833,45835,45865,45886],{"className":45834,"ariaHidden":246},[245],[128,45836,45838,45841,45844,45847,45850,45853,45856,45859,45862],{"className":45837},[250],[128,45839],{"className":45840,"style":1892},[254],[128,45842,24362],{"className":45843,"style":24474},[259,1873],[128,45845,16538],{"className":45846},[1896],[128,45848,23001],{"className":45849},[259,2167],[128,45851,2477],{"className":45852},[1896],[128,45854,1830],{"className":45855,"style":1874},[259,1873],[128,45857],{"className":45858,"style":1878},[269],[128,45860,5443],{"className":45861},[1882],[128,45863],{"className":45864,"style":1878},[269],[128,45866,45868,45871,45874,45877,45880,45883],{"className":45867},[250],[128,45869],{"className":45870,"style":1892},[254],[128,45872,2760],{"className":45873},[259,2151],[128,45875,44995],{"className":45876},[1928],[128,45878],{"className":45879,"style":1878},[269],[128,45881,1994],{"className":45882},[1882],[128,45884],{"className":45885,"style":1878},[269],[128,45887,45889,45892,45895,45898,45958,45961,46001,46004,46009,46012],{"className":45888},[250],[128,45890],{"className":45891,"style":5200},[254],[128,45893,1989],{"className":45894},[259],[128,45896],{"className":45897,"style":1907},[269],[128,45899,45901,45904],{"className":45900},[2268],[128,45902,2042],{"className":45903,"style":2274},[2268,2272,2273],[128,45905,45907],{"className":45906},[2087],[128,45908,45910,45950],{"className":45909},[274,321],[128,45911,45913,45947],{"className":45912},[278],[128,45914,45916,45936],{"className":45915,"style":2287},[282],[128,45917,45918,45921],{"style":2290},[128,45919],{"className":45920,"style":291},[290],[128,45922,45924],{"className":45923},[299,300,301,298],[128,45925,45927,45930,45933],{"className":45926},[259,298],[128,45928,2022],{"className":45929,"style":2231},[259,1873,298],[128,45931,1994],{"className":45932},[1882,298],[128,45934,1842],{"className":45935},[259,298],[128,45937,45938,45941],{"style":2311},[128,45939],{"className":45940,"style":291},[290],[128,45942,45944],{"className":45943},[299,300,301,298],[128,45945,1853],{"className":45946,"style":1924},[259,1873,298],[128,45948,347],{"className":45949},[346],[128,45951,45953],{"className":45952},[278],[128,45954,45956],{"className":45955,"style":2330},[282],[128,45957],{},[128,45959],{"className":45960,"style":1907},[269],[128,45962,45964,45967],{"className":45963},[259],[128,45965,11],{"className":45966},[259,1873],[128,45968,45970],{"className":45969},[2087],[128,45971,45973,45993],{"className":45972},[274,321],[128,45974,45976,45990],{"className":45975},[278],[128,45977,45979],{"className":45978,"style":2218},[282],[128,45980,45981,45984],{"style":2221},[128,45982],{"className":45983,"style":291},[290],[128,45985,45987],{"className":45986},[299,300,301,298],[128,45988,2022],{"className":45989,"style":2231},[259,1873,298],[128,45991,347],{"className":45992},[346],[128,45994,45996],{"className":45995},[278],[128,45997,45999],{"className":45998,"style":2241},[282],[128,46000],{},[128,46002],{"className":46003,"style":1907},[269],[128,46005,24502,46007],{"className":46006},[2268],[128,46008,24505],{"style":17336},[128,46010],{"className":46011,"style":1907},[269],[128,46013,46015,46018],{"className":46014},[259],[128,46016,11],{"className":46017},[259,1873],[128,46019,46021],{"className":46020},[2087],[128,46022,46024,46044],{"className":46023},[274,321],[128,46025,46027,46041],{"className":46026},[278],[128,46028,46030],{"className":46029,"style":2218},[282],[128,46031,46032,46035],{"style":2221},[128,46033],{"className":46034,"style":291},[290],[128,46036,46038],{"className":46037},[299,300,301,298],[128,46039,2022],{"className":46040,"style":2231},[259,1873,298],[128,46042,347],{"className":46043},[346],[128,46045,46047],{"className":46046},[278],[128,46048,46050],{"className":46049,"style":2241},[282],[128,46051],{},[128,46053,46055,46139],{"className":46054,"translate":218},[217],[128,46056,46058],{"className":46057},[222],[224,46059,46060],{"xmlns":226},[228,46061,46062,46136],{},[231,46063,46064,46070,46072,46074,46076,46078,46080,46082,46084,46086,46088,46090,46092,46094,46096,46098,46112,46118,46120,46122,46124,46130,46132,46134],{},[2016,46065,46066,46068],{},[1795,46067,342],{"mathvariant":2008},[1795,46069,26389],{"mathvariant":4834},[1832,46071,16538],{"stretchy":1837},[1795,46073,24362],{},[1832,46075,2477],{"stretchy":1837},[1795,46077,26389],{"mathvariant":4834},[1832,46079,2486],{"stretchy":1837},[1832,46081,16547],{"stretchy":1837},[1832,46083,1994],{},[1795,46085,24404],{},[1832,46087,2477],{"stretchy":1837},[1795,46089,41957],{},[1832,46091,9486],{},[1840,46093,1842],{},[1832,46095,2486],{"stretchy":1837},[1832,46097,1989],{},[2038,46099,46100,46102,46110],{},[1832,46101,2042],{},[231,46103,46104,46106,46108],{},[1795,46105,2022],{},[1832,46107,1994],{},[1840,46109,1842],{},[1795,46111,1853],{},[2016,46113,46114,46116],{},[1795,46115,11],{},[1795,46117,2022],{},[234,46119,6528],{},[1795,46121,24404],{},[1832,46123,2477],{"stretchy":1837},[2016,46125,46126,46128],{},[1795,46127,4835],{},[1795,46129,2022],{},[1832,46131,9486],{},[1840,46133,1842],{},[1832,46135,2486],{"stretchy":1837},[238,46137,46138],{"encoding":240},"\\mathbb{E}_{\\boldsymbol{\\pi}}[H(\\boldsymbol{\\pi})] = \\psi(S + 1) - \\sum_{k=1}^K p_k \\,\\psi(\\alpha_k + 1)",[128,46140,46142,46227,46251,46272,46439],{"className":46141,"ariaHidden":246},[245],[128,46143,46145,46148,46197,46200,46203,46206,46215,46218,46221,46224],{"className":46144},[250],[128,46146],{"className":46147,"style":1892},[254],[128,46149,46151,46154],{"className":46150},[259],[128,46152,342],{"className":46153},[259,2167],[128,46155,46157],{"className":46156},[2087],[128,46158,46160,46189],{"className":46159},[274,321],[128,46161,46163,46186],{"className":46162},[278],[128,46164,46166],{"className":46165,"style":22681},[282],[128,46167,46168,46171],{"style":2221},[128,46169],{"className":46170,"style":291},[290],[128,46172,46174],{"className":46173},[299,300,301,298],[128,46175,46177],{"className":46176},[259,298],[128,46178,46180],{"className":46179},[259,298],[128,46181,46183],{"className":46182},[259,298],[128,46184,26389],{"className":46185,"style":26423},[259,4895,298],[128,46187,347],{"className":46188},[346],[128,46190,46192],{"className":46191},[278],[128,46193,46195],{"className":46194,"style":2241},[282],[128,46196],{},[128,46198,16538],{"className":46199},[1896],[128,46201,24362],{"className":46202,"style":24474},[259,1873],[128,46204,2477],{"className":46205},[1896],[128,46207,46209],{"className":46208},[259],[128,46210,46212],{"className":46211},[259],[128,46213,26389],{"className":46214,"style":26423},[259,4895],[128,46216,44995],{"className":46217},[1928],[128,46219],{"className":46220,"style":1878},[269],[128,46222,1994],{"className":46223},[1882],[128,46225],{"className":46226,"style":1878},[269],[128,46228,46230,46233,46236,46239,46242,46245,46248],{"className":46229},[250],[128,46231],{"className":46232,"style":1892},[254],[128,46234,24404],{"className":46235,"style":1874},[259,1873],[128,46237,2477],{"className":46238},[1896],[128,46240,41957],{"className":46241,"style":42029},[259,1873],[128,46243],{"className":46244,"style":2508},[269],[128,46246,9486],{"className":46247},[2115],[128,46249],{"className":46250,"style":2508},[269],[128,46252,46254,46257,46260,46263,46266,46269],{"className":46253},[250],[128,46255],{"className":46256,"style":1892},[254],[128,46258,1842],{"className":46259},[259],[128,46261,2486],{"className":46262},[1928],[128,46264],{"className":46265,"style":2508},[269],[128,46267,1989],{"className":46268},[2115],[128,46270],{"className":46271,"style":2508},[269],[128,46273,46275,46278,46338,46341,46381,46384,46387,46390,46430,46433,46436],{"className":46274},[250],[128,46276],{"className":46277,"style":5200},[254],[128,46279,46281,46284],{"className":46280},[2268],[128,46282,2042],{"className":46283,"style":2274},[2268,2272,2273],[128,46285,46287],{"className":46286},[2087],[128,46288,46290,46330],{"className":46289},[274,321],[128,46291,46293,46327],{"className":46292},[278],[128,46294,46296,46316],{"className":46295,"style":2287},[282],[128,46297,46298,46301],{"style":2290},[128,46299],{"className":46300,"style":291},[290],[128,46302,46304],{"className":46303},[299,300,301,298],[128,46305,46307,46310,46313],{"className":46306},[259,298],[128,46308,2022],{"className":46309,"style":2231},[259,1873,298],[128,46311,1994],{"className":46312},[1882,298],[128,46314,1842],{"className":46315},[259,298],[128,46317,46318,46321],{"style":2311},[128,46319],{"className":46320,"style":291},[290],[128,46322,46324],{"className":46323},[299,300,301,298],[128,46325,1853],{"className":46326,"style":1924},[259,1873,298],[128,46328,347],{"className":46329},[346],[128,46331,46333],{"className":46332},[278],[128,46334,46336],{"className":46335,"style":2330},[282],[128,46337],{},[128,46339],{"className":46340,"style":1907},[269],[128,46342,46344,46347],{"className":46343},[259],[128,46345,11],{"className":46346},[259,1873],[128,46348,46350],{"className":46349},[2087],[128,46351,46353,46373],{"className":46352},[274,321],[128,46354,46356,46370],{"className":46355},[278],[128,46357,46359],{"className":46358,"style":2218},[282],[128,46360,46361,46364],{"style":2221},[128,46362],{"className":46363,"style":291},[290],[128,46365,46367],{"className":46366},[299,300,301,298],[128,46368,2022],{"className":46369,"style":2231},[259,1873,298],[128,46371,347],{"className":46372},[346],[128,46374,46376],{"className":46375},[278],[128,46377,46379],{"className":46378,"style":2241},[282],[128,46380],{},[128,46382],{"className":46383,"style":1907},[269],[128,46385,24404],{"className":46386,"style":1874},[259,1873],[128,46388,2477],{"className":46389},[1896],[128,46391,46393,46396],{"className":46392},[259],[128,46394,4835],{"className":46395,"style":4920},[259,1873],[128,46397,46399],{"className":46398},[2087],[128,46400,46402,46422],{"className":46401},[274,321],[128,46403,46405,46419],{"className":46404},[278],[128,46406,46408],{"className":46407,"style":2218},[282],[128,46409,46410,46413],{"style":4935},[128,46411],{"className":46412,"style":291},[290],[128,46414,46416],{"className":46415},[299,300,301,298],[128,46417,2022],{"className":46418,"style":2231},[259,1873,298],[128,46420,347],{"className":46421},[346],[128,46423,46425],{"className":46424},[278],[128,46426,46428],{"className":46427,"style":2241},[282],[128,46429],{},[128,46431],{"className":46432,"style":2508},[269],[128,46434,9486],{"className":46435},[2115],[128,46437],{"className":46438,"style":2508},[269],[128,46440,46442,46445,46448],{"className":46441},[250],[128,46443],{"className":46444,"style":1892},[254],[128,46446,1842],{"className":46447},[259],[128,46449,2486],{"className":46450},[1928],[128,46452,46454,46587],{"className":46453,"translate":218},[217],[128,46455,46457],{"className":46456},[222],[224,46458,46459],{"xmlns":226},[228,46460,46461,46584],{},[231,46462,46463,46465,46467,46469,46471,46473,46475,46477,46479,46481,46483,46485,46487,46489,46491,46493,46495,46497,46503,46505,46507,46509,46511,46513,46515,46517,46531,46537,46540,46542,46544,46550,46552,46554,46556,46558,46560,46562,46568,46570,46572,46574,46576,46578,46580,46582],{},[1795,46464,30626],{},[1832,46466,2477],{"stretchy":1837},[1795,46468,1830],{},[1832,46470,13024],{"separator":246},[1795,46472,26389],{"mathvariant":4834},[1832,46474,2486],{"stretchy":1837},[1832,46476,1994],{},[1795,46478,24362],{},[1832,46480,16538],{"stretchy":1837},[1795,46482,23001],{"mathvariant":2008},[1832,46484,2477],{"stretchy":1837},[1795,46486,1830],{},[1832,46488,5443],{},[1795,46490,2760],{"mathvariant":2001},[1832,46492,2486],{"stretchy":1837},[1832,46494,16547],{"stretchy":1837},[1832,46496,1989],{},[2016,46498,46499,46501],{},[1795,46500,342],{"mathvariant":2008},[1795,46502,26389],{"mathvariant":4834},[1832,46504,16538],{"stretchy":1837},[1795,46506,24362],{},[1832,46508,2477],{"stretchy":1837},[1795,46510,26389],{"mathvariant":4834},[1832,46512,2486],{"stretchy":1837},[1832,46514,16547],{"stretchy":1837},[1832,46516,1994],{},[2038,46518,46519,46521,46529],{},[1832,46520,2042],{},[231,46522,46523,46525,46527],{},[1795,46524,2022],{},[1832,46526,1994],{},[1840,46528,1842],{},[1795,46530,1853],{},[2016,46532,46533,46535],{},[1795,46534,11],{},[1795,46536,2022],{},[1832,46538,2477],{"fence":1837,"stretchy":246,"minsize":46539,"maxsize":46539},"1.2em",[1795,46541,24404],{},[1832,46543,2477],{"stretchy":1837},[2016,46545,46546,46548],{},[1795,46547,4835],{},[1795,46549,2022],{},[1832,46551,9486],{},[1840,46553,1842],{},[1832,46555,2486],{"stretchy":1837},[1832,46557,1989],{},[1795,46559,24373],{},[1832,46561,3278],{},[2016,46563,46564,46566],{},[1795,46565,11],{},[1795,46567,2022],{},[1832,46569,2486],{"fence":1837,"stretchy":246,"minsize":46539,"maxsize":46539},[1832,46571,1989],{},[1795,46573,24404],{},[1832,46575,2477],{"stretchy":1837},[1795,46577,41957],{},[1832,46579,9486],{},[1840,46581,1842],{},[1832,46583,2486],{"stretchy":1837},[238,46585,46586],{"encoding":240},"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)",[128,46588,46590,46632,46662,46683,46768,46939,46960,47030,47054],{"className":46589,"ariaHidden":246},[245],[128,46591,46593,46596,46599,46602,46605,46608,46611,46620,46623,46626,46629],{"className":46592},[250],[128,46594],{"className":46595,"style":1892},[254],[128,46597,30626],{"className":46598,"style":30665},[259,1873],[128,46600,2477],{"className":46601},[1896],[128,46603,1830],{"className":46604,"style":1874},[259,1873],[128,46606,13024],{"className":46607},[1903],[128,46609],{"className":46610,"style":1907},[269],[128,46612,46614],{"className":46613},[259],[128,46615,46617],{"className":46616},[259],[128,46618,26389],{"className":46619,"style":26423},[259,4895],[128,46621,2486],{"className":46622},[1928],[128,46624],{"className":46625,"style":1878},[269],[128,46627,1994],{"className":46628},[1882],[128,46630],{"className":46631,"style":1878},[269],[128,46633,46635,46638,46641,46644,46647,46650,46653,46656,46659],{"className":46634},[250],[128,46636],{"className":46637,"style":1892},[254],[128,46639,24362],{"className":46640,"style":24474},[259,1873],[128,46642,16538],{"className":46643},[1896],[128,46645,23001],{"className":46646},[259,2167],[128,46648,2477],{"className":46649},[1896],[128,46651,1830],{"className":46652,"style":1874},[259,1873],[128,46654],{"className":46655,"style":1878},[269],[128,46657,5443],{"className":46658},[1882],[128,46660],{"className":46661,"style":1878},[269],[128,46663,46665,46668,46671,46674,46677,46680],{"className":46664},[250],[128,46666],{"className":46667,"style":1892},[254],[128,46669,2760],{"className":46670},[259,2151],[128,46672,44995],{"className":46673},[1928],[128,46675],{"className":46676,"style":2508},[269],[128,46678,1989],{"className":46679},[2115],[128,46681],{"className":46682,"style":2508},[269],[128,46684,46686,46689,46738,46741,46744,46747,46756,46759,46762,46765],{"className":46685},[250],[128,46687],{"className":46688,"style":1892},[254],[128,46690,46692,46695],{"className":46691},[259],[128,46693,342],{"className":46694},[259,2167],[128,46696,46698],{"className":46697},[2087],[128,46699,46701,46730],{"className":46700},[274,321],[128,46702,46704,46727],{"className":46703},[278],[128,46705,46707],{"className":46706,"style":22681},[282],[128,46708,46709,46712],{"style":2221},[128,46710],{"className":46711,"style":291},[290],[128,46713,46715],{"className":46714},[299,300,301,298],[128,46716,46718],{"className":46717},[259,298],[128,46719,46721],{"className":46720},[259,298],[128,46722,46724],{"className":46723},[259,298],[128,46725,26389],{"className":46726,"style":26423},[259,4895,298],[128,46728,347],{"className":46729},[346],[128,46731,46733],{"className":46732},[278],[128,46734,46736],{"className":46735,"style":2241},[282],[128,46737],{},[128,46739,16538],{"className":46740},[1896],[128,46742,24362],{"className":46743,"style":24474},[259,1873],[128,46745,2477],{"className":46746},[1896],[128,46748,46750],{"className":46749},[259],[128,46751,46753],{"className":46752},[259],[128,46754,26389],{"className":46755,"style":26423},[259,4895],[128,46757,44995],{"className":46758},[1928],[128,46760],{"className":46761,"style":1878},[269],[128,46763,1994],{"className":46764},[1882],[128,46766],{"className":46767,"style":1878},[269],[128,46769,46771,46775,46835,46838,46878,46884,46887,46890,46930,46933,46936],{"className":46770},[250],[128,46772],{"className":46773,"style":46774},[254],"height:1.3312em;vertical-align:-0.35em;",[128,46776,46778,46781],{"className":46777},[2268],[128,46779,2042],{"className":46780,"style":2274},[2268,2272,2273],[128,46782,46784],{"className":46783},[2087],[128,46785,46787,46827],{"className":46786},[274,321],[128,46788,46790,46824],{"className":46789},[278],[128,46791,46793,46813],{"className":46792,"style":2287},[282],[128,46794,46795,46798],{"style":2290},[128,46796],{"className":46797,"style":291},[290],[128,46799,46801],{"className":46800},[299,300,301,298],[128,46802,46804,46807,46810],{"className":46803},[259,298],[128,46805,2022],{"className":46806,"style":2231},[259,1873,298],[128,46808,1994],{"className":46809},[1882,298],[128,46811,1842],{"className":46812},[259,298],[128,46814,46815,46818],{"style":2311},[128,46816],{"className":46817,"style":291},[290],[128,46819,46821],{"className":46820},[299,300,301,298],[128,46822,1853],{"className":46823,"style":1924},[259,1873,298],[128,46825,347],{"className":46826},[346],[128,46828,46830],{"className":46829},[278],[128,46831,46833],{"className":46832,"style":2330},[282],[128,46834],{},[128,46836],{"className":46837,"style":1907},[269],[128,46839,46841,46844],{"className":46840},[259],[128,46842,11],{"className":46843},[259,1873],[128,46845,46847],{"className":46846},[2087],[128,46848,46850,46870],{"className":46849},[274,321],[128,46851,46853,46867],{"className":46852},[278],[128,46854,46856],{"className":46855,"style":2218},[282],[128,46857,46858,46861],{"style":2221},[128,46859],{"className":46860,"style":291},[290],[128,46862,46864],{"className":46863},[299,300,3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关键在于 ",[128,47072,47074,47120],{"className":47073,"translate":218},[217],[128,47075,47077],{"className":47076},[222],[224,47078,47079],{"xmlns":226},[228,47080,47081,47117],{},[231,47082,47083,47085,47087,47089,47091,47093,47095,47101,47107,47109,47111],{},[1795,47084,24362],{},[1832,47086,2477],{"stretchy":1837},[1795,47088,26389],{"mathvariant":4834},[1832,47090,2486],{"stretchy":1837},[1832,47092,1994],{},[1832,47094,1989],{},[2016,47096,47097,47099],{},[1832,47098,2042],{},[1795,47100,2022],{},[2016,47102,47103,47105],{},[1795,47104,26389],{},[1795,47106,2022],{},[1795,47108,24373],{},[1832,47110,3278],{},[2016,47112,47113,47115],{},[1795,47114,26389],{},[1795,47116,2022],{},[238,47118,47119],{"encoding":240},"H(\\boldsymbol{\\pi}) = -\\sum_k \\pi_k \\log 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= -\\sum_k \\mathbb{E}[\\pi_k \\log \\pi_k]",[128,47364,47366,47405],{"className":47365,"ariaHidden":246},[245],[128,47367,47369,47372,47375,47378,47381,47384,47393,47396,47399,47402],{"className":47368},[250],[128,47370],{"className":47371,"style":1892},[254],[128,47373,342],{"className":47374},[259,2167],[128,47376,16538],{"className":47377},[1896],[128,47379,24362],{"className":47380,"style":24474},[259,1873],[128,47382,2477],{"className":47383},[1896],[128,47385,47387],{"className":47386},[259],[128,47388,47390],{"className":47389},[259],[128,47391,26389],{"className":47392,"style":26423},[259,4895],[128,47394,44995],{"className":47395},[1928],[128,47397],{"className":47398,"style":1878},[269],[128,47400,1994],{"className":47401},[1882],[128,47403],{"className":47404,"style":1878},[269],[128,47406,47408,47411,47414,47417,47457,47460,47463,47466,47506,47509,47514,47517,47557],{"className":47407},[250],[128,47409],{"className":47410,"style":7777},[254],[128,47412,1989],{"className":47413},[259],[128,47415],{"className":47416,"style":1907},[269],[128,47418,47420,47423],{"className":47419},[2268],[128,47421,2042],{"className":47422,"style":2274},[2268,2272,2273],[128,47424,47426],{"className":47425},[2087],[128,47427,47429,47449],{"className":47428},[274,321],[128,47430,47432,47446],{"className":47431},[278],[128,47433,47435],{"className":47434,"style":31692},[282],[128,47436,47437,47440],{"style":2290},[128,47438],{"className":47439,"style":291},[290],[128,47441,47443],{"className":47442},[299,300,301,298],[128,47444,2022],{"className":47445,"style":2231},[259,1873,298],[128,47447,347],{"className":47448},[346],[128,47450,47452],{"className":47451},[278],[128,47453,47455],{"className":47454,"style":2330},[282],[128,47456],{},[128,47458],{"className":47459,"style":1907},[269],[128,47461,342],{"className":47462},[259,2167],[128,47464,16538],{"className":47465},[1896],[128,47467,47469,47472],{"className":47468},[259],[128,47470,26389],{"className":47471,"style":1874},[259,1873],[128,47473,47475],{"className":47474},[2087],[128,47476,47478,47498],{"className":47477},[274,321],[128,47479,47481,47495],{"className":47480},[278],[128,47482,47484],{"className":47483,"style":2218},[282],[128,47485,47486,47489],{"style":28741},[128,47487],{"className":47488,"style":291},[290],[128,47490,47492],{"className":47491},[299,300,301,298],[128,47493,2022],{"className":47494,"style":2231},[259,1873,298],[128,47496,347],{"className":47497},[346],[128,47499,47501],{"className":47500},[278],[128,47502,47504],{"className":47503,"style":2241},[282],[128,47505],{},[128,47507],{"className":47508,"style":1907},[269],[128,47510,24502,47512],{"className":47511},[2268],[128,47513,24505],{"style":17336},[128,47515],{"className":47516,"style":1907},[269],[128,47518,47520,47523],{"className":47519},[259],[128,47521,26389],{"className":47522,"style":1874},[259,1873],[128,47524,47526],{"className":47525},[2087],[128,47527,47529,47549],{"className":47528},[274,321],[128,47530,47532,47546],{"className":47531},[278],[128,47533,47535],{"className":47534,"style":2218},[282],[128,47536,47537,47540],{"style":28741},[128,47538],{"className":47539,"style":291},[290],[128,47541,47543],{"className":47542},[299,300,301,298],[128,47544,2022],{"className":47545,"style":2231},[259,1873,298],[128,47547,347],{"className":47548},[346],[128,47550,47552],{"className":47551},[278],[128,47553,47555],{"className":47554,"style":2241},[282],[128,47556],{},[128,47558,16547],{"className":47559},[1928],"。由 1.4 节的边缘 Beta 性，",[128,47562,47564,47610],{"className":47563,"translate":218},[217],[128,47565,47567],{"className":47566},[222],[224,47568,47569],{"xmlns":226},[228,47570,47571,47607],{},[231,47572,47573,47579,47581,47583,47585,47587,47593,47595,47597,47599,47605],{},[2016,47574,47575,47577],{},[1795,47576,26389],{},[1795,47578,2022],{},[1832,47580,5911],{},[1795,47582,14677],{"mathvariant":1981},[1832,47584,3278],{},[1832,47586,2477],{"stretchy":1837},[2016,47588,47589,47591],{},[1795,47590,4835],{},[1795,47592,2022],{},[1832,47594,1845],{"separator":246},[1795,47596,41957],{},[1832,47598,1989],{},[2016,47600,47601,47603],{},[1795,47602,4835],{},[1795,47604,2022],{},[1832,47606,2486],{"stretchy":1837},[238,47608,47609],{"encoding":240},"\\pi_k \\sim \\operatorname{Beta}(\\alpha_k, S - \\alpha_k)",[128,47611,47613,47668,47741],{"className":47612,"ariaHidden":246},[245],[128,47614,47616,47619,47659,47662,47665],{"className":47615},[250],[128,47617],{"className":47618,"style":4242},[254],[128,47620,47622,47625],{"className":47621},[259],[128,47623,26389],{"className":47624,"style":1874},[259,1873],[128,47626,47628],{"className":47627},[2087],[128,47629,47631,47651],{"className":47630},[274,321],[128,47632,47634,47648],{"className":47633},[278],[128,47635,47637],{"className":47636,"style":2218},[282],[128,47638,47639,47642],{"style":28741},[128,47640],{"className":47641,"style":291},[290],[128,47643,47645],{"className":47644},[299,300,301,298],[128,47646,2022],{"className":47647,"style":2231},[259,1873,298],[128,47649,347],{"className":47650},[346],[128,47652,47654],{"className":47653},[278],[128,47655,47657],{"className":47656,"style":2241},[282],[128,47658],{},[128,47660],{"className":47661,"style":1878},[269],[128,47663,5911],{"className":47664},[1882],[128,47666],{"className":47667,"style":1878},[269],[128,47669,47671,47674,47680,47683,47723,47726,47729,47732,47735,47738],{"className":47670},[250],[128,47672],{"className":47673,"style":1892},[254],[128,47675,47677],{"className":47676},[2268],[128,47678,14677],{"className":47679},[259,3353],[128,47681,2477],{"className":47682},[1896],[128,47684,47686,47689],{"className":47685},[259],[128,47687,4835],{"className":47688,"style":4920},[259,1873],[128,47690,47692],{"className":47691},[2087],[128,47693,47695,47715],{"className":47694},[274,321],[128,47696,47698,47712],{"className":47697},[278],[128,47699,47701],{"className":47700,"style":2218},[282],[128,47702,47703,47706],{"style":4935},[128,47704],{"className":47705,"style":291},[290],[128,47707,47709],{"className":47708},[299,300,301,298],[128,47710,2022],{"className":47711,"style":2231},[259,1873,298],[128,47713,347],{"className":47714},[346],[128,47716,47718],{"className":47717},[278],[128,47719,47721],{"className":47720,"style":2241},[282],[128,47722],{},[128,47724,1845],{"className":47725},[1903],[128,47727],{"className":47728,"style":1907},[269],[128,47730,41957],{"className":47731,"style":42029},[259,1873],[128,47733],{"className":47734,"style":2508},[269],[128,47736,1989],{"className":47737},[2115],[128,47739],{"className":47740,"style":2508},[269],[128,47742,47744,47747,47787],{"className":47743},[250],[128,47745],{"className":47746,"style":1892},[254],[128,47748,47750,47753],{"className":47749},[259],[128,47751,4835],{"className":47752,"style":4920},[259,1873],[128,47754,47756],{"className":47755},[2087],[128,47757,47759,47779],{"className":47758},[274,321],[128,47760,47762,47776],{"className":47761},[278],[128,47763,47765],{"className":47764,"style":2218},[282],[128,47766,47767,47770],{"style":4935},[128,47768],{"className":47769,"style":291},[290],[128,47771,47773],{"className":47772},[299,300,301,298],[128,47774,2022],{"className":47775,"style":2231},[259,1873,298],[128,47777,347],{"className":47778},[346],[128,47780,47782],{"className":47781},[278],[128,47783,47785],{"className":47784,"style":2241},[282],[128,47786],{},[128,47788,2486],{"className":47789},[1928],"，而对该 Beta 分布有恒等式 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\\log X] = \\frac{a}{a+b}\\big(\\psi(a+1) - \\psi(a+b+1)\\big)",[128,47869,47871,47912,48019,48040,48064,48083],{"className":47870,"ariaHidden":246},[245],[128,47872,47874,47877,47880,47883,47886,47889,47894,47897,47900,47903,47906,47909],{"className":47873},[250],[128,47875],{"className":47876,"style":1892},[254],[128,47878,342],{"className":47879},[259,2167],[128,47881,16538],{"className":47882},[1896],[128,47884,364],{"className":47885,"style":30665},[259,1873],[128,47887],{"className":47888,"style":1907},[269],[128,47890,24502,47892],{"className":47891},[2268],[128,47893,24505],{"style":17336},[128,47895],{"className":47896,"style":1907},[269],[128,47898,364],{"className":47899,"style":30665},[259,1873],[128,47901,16547],{"className":47902},[1928],[128,47904],{"className":47905,"style":1878},[269],[128,47907,1994],{"className":47908},[1882],[128,47910],{"className":47911,"style":1878},[269],[128,47913,47915,47919,47995,48001,48004,48007,48010,48013,48016],{"className":47914},[250],[128,47916],{"className":47917,"style":47918},[254],"height:1.2533em;vertical-align:-0.4033em;",[128,47920,47922,47925,47992],{"className":47921},[259],[128,47923],{"className":47924},[1896,5570],[128,47926,47928],{"className":47927},[5451],[128,47929,47931,47983],{"className":47930},[274,321],[128,47932,47934,47980],{"className":47933},[278],[128,47935,47938,47958,47966],{"className":47936,"style":47937},[282],"height:0.6954em;",[128,47939,47940,47943],{"style":5586},[128,47941],{"className":47942,"style":335},[290],[128,47944,47946],{"className":47945},[299,300,301,298],[128,47947,47949,47952,47955],{"className":47948},[259,298],[128,47950,21],{"className":47951},[259,1873,298],[128,47953,9486],{"className":47954},[2115,298],[128,47956,35124],{"className":47957},[259,1873,298],[128,47959,47960,47963],{"style":5617},[128,47961],{"className":47962,"style":335},[290],[128,47964],{"className":47965,"style":5625},[5624],[128,47967,47968,47971],{"style":5628},[128,47969],{"className":47970,"style":335},[290],[128,47972,47974],{"className":47973},[299,300,301,298],[128,47975,47977],{"className":47976},[259,298],[128,47978,21],{"className":47979},[259,1873,298],[128,47981,347],{"className":47982},[346],[128,47984,47986],{"className":47985},[278],[128,47987,47990],{"className":47988,"style":47989},[282],"height:0.4033em;",[128,47991],{},[128,47993],{"className":47994},[1928,5570],[128,47996,47998],{"className":47997},[259],[128,47999,2477],{"className":48000},[2146,5795],[128,48002,24404],{"className":48003,"style":1874},[259,1873],[128,48005,2477],{"className":48006},[1896],[128,48008,21],{"className":48009},[259,1873],[128,48011],{"className":48012,"style":2508},[269],[128,48014,9486],{"className":48015},[2115],[128,48017],{"className":48018,"style":2508},[269],[128,48020,48022,48025,48028,48031,48034,48037],{"className":48021},[250],[128,48023],{"className":48024,"style":1892},[254],[128,48026,1842],{"className":48027},[259],[128,48029,2486],{"className":48030},[1928],[128,48032],{"className":48033,"style":2508},[269],[128,48035,1989],{"className":48036},[2115],[128,48038],{"className":48039,"style":2508},[269],[128,48041,48043,48046,48049,48052,48055,48058,48061],{"className":48042},[250],[128,48044],{"className":48045,"style":1892},[254],[128,48047,24404],{"className":48048,"style":1874},[259,1873],[128,48050,2477],{"className":48051},[1896],[128,48053,21],{"className":48054},[259,1873],[128,48056],{"className":48057,"style":2508},[269],[128,48059,9486],{"className":48060},[2115],[128,48062],{"className":48063,"style":2508},[269],[128,48065,48067,48071,48074,48077,48080],{"className":48066},[250],[128,48068],{"className":48069,"style":48070},[254],"height:0.7778em;vertical-align:-0.0833em;",[128,48072,35124],{"className":48073},[259,1873],[128,48075],{"className":48076,"style":2508},[269],[128,48078,9486],{"className":48079},[2115],[128,48081],{"className":48082,"style":2508},[269],[128,48084,48086,48089,48092,48095],{"className":48085},[250],[128,48087],{"className":48088,"style":46966},[254],[128,48090,1842],{"className":48091},[259],[128,48093,2486],{"className":48094},[1928],[128,48096,48098],{"className":48097},[259],[128,48099,2486],{"className":48100},[2146,5795],"（此处 ",[128,48103,48105,48127],{"className":48104,"translate":218},[217],[128,48106,48108],{"className":48107},[222],[224,48109,48110],{"xmlns":226},[228,48111,48112,48124],{},[231,48113,48114,48116,48118],{},[1795,48115,21],{},[1832,48117,1994],{},[2016,48119,48120,48122],{},[1795,48121,4835],{},[1795,48123,2022],{},[238,48125,48126],{"encoding":240},"a = \\alpha_k",[128,48128,48130,48148],{"className":48129,"ariaHidden":246},[245],[128,48131,48133,48136,48139,48142,48145],{"className":48132},[250],[128,48134],{"className":48135,"style":7758},[254],[128,48137,21],{"className":48138},[259,1873],[128,48140],{"className":48141,"style":1878},[269],[128,48143,1994],{"className":48144},[1882],[128,48146],{"className":48147,"style":1878},[269],[128,48149,48151,48154],{"className":48150},[250],[128,48152],{"className":48153,"style":4242},[254],[128,48155,48157,48160],{"className":48156},[259],[128,48158,4835],{"className":48159,"style":4920},[259,1873],[128,48161,48163],{"className":48162},[2087],[128,48164,48166,48186],{"className":48165},[274,321],[128,48167,48169,48183],{"className":48168},[278],[128,48170,48172],{"className":48171,"style":2218},[282],[128,48173,48174,48177],{"style":4935},[128,48175],{"className":48176,"style":291},[290],[128,48178,48180],{"className":48179},[299,300,301,298],[128,48181,2022],{"className":48182,"style":2231},[259,1873,298],[128,48184,347],{"className":48185},[346],[128,48187,48189],{"className":48188},[278],[128,48190,48192],{"className":48191,"style":2241},[282],[128,48193],{},[128,48195,48197,48219],{"className":48196,"translate":218},[217],[128,48198,48200],{"className":48199},[222],[224,48201,48202],{"xmlns":226},[228,48203,48204,48216],{},[231,48205,48206,48208,48210,48212,48214],{},[1795,48207,21],{},[1832,48209,9486],{},[1795,48211,35124],{},[1832,48213,1994],{},[1795,48215,41957],{},[238,48217,48218],{"encoding":240},"a + b = S",[128,48220,48222,48240,48258],{"className":48221,"ariaHidden":246},[245],[128,48223,48225,48228,48231,48234,48237],{"className":48224},[250],[128,48226],{"className":48227,"style":8462},[254],[128,48229,21],{"className":48230},[259,1873],[128,48232],{"className":48233,"style":2508},[269],[128,48235,9486],{"className":48236},[2115],[128,48238],{"className":48239,"style":2508},[269],[128,48241,48243,48246,48249,48252,48255],{"className":48242},[250],[128,48244],{"className":48245,"style":12173},[254],[128,48247,35124],{"className":48248},[259,1873],[128,48250],{"className":48251,"style":1878},[269],[128,48253,1994],{"className":48254},[1882],[128,48256],{"className":48257,"style":1878},[269],[128,48259,48261,48264],{"className":48260},[250],[128,48262],{"className":48263,"style":283},[254],[128,48265,41957],{"className":48266,"style":42029},[259,1873],"）。代入 ",[128,48269,48271,48305],{"className":48270,"translate":218},[217],[128,48272,48274],{"className":48273},[222],[224,48275,48276],{"xmlns":226},[228,48277,48278,48302],{},[231,48279,48280,48282,48284,48286,48288,48290,48292,48294,48296],{},[1795,48281,21],{},[1795,48283,4751],{"mathvariant":1981},[1832,48285,2477],{"stretchy":1837},[1795,48287,21],{},[1832,48289,9486],{},[1795,48291,35124],{},[1832,48293,2486],{"stretchy":1837},[1832,48295,1994],{},[2016,48297,48298,48300],{},[1795,48299,11],{},[1795,48301,2022],{},[238,48303,48304],{"encoding":240},"a\u002F(a+b) = p_k",[128,48306,48308,48335,48356],{"className":48307,"ariaHidden":246},[245],[128,48309,48311,48314,48317,48320,48323,48326,48329,48332],{"className":48310},[250],[128,48312],{"className":48313,"style":1892},[254],[128,48315,21],{"className":48316},[259,1873],[128,48318,4751],{"className":48319},[259],[128,48321,2477],{"className":48322},[1896],[128,48324,21],{"className":48325},[259,1873],[128,48327],{"className":48328,"style":2508},[269],[128,48330,9486],{"className":48331},[2115],[128,48333],{"className":48334,"style":2508},[269],[128,48336,48338,48341,48344,48347,48350,48353],{"className":48337},[250],[128,48339],{"className":48340,"style":1892},[254],[128,48342,35124],{"className":48343},[259,1873],[128,48345,2486],{"className":48346},[1928],[128,48348],{"className":48349,"style":1878},[269],[128,48351,1994],{"className":48352},[1882],[128,48354],{"className":48355,"style":1878},[269],[128,48357,48359,48362],{"className":48358},[250],[128,48360],{"className":48361,"style":11158},[254],[128,48363,48365,48368],{"className":48364},[259],[128,48366,11],{"className":48367},[259,1873],[128,48369,48371],{"className":48370},[2087],[128,48372,48374,48394],{"className":48373},[274,321],[128,48375,48377,48391],{"className":48376},[278],[128,48378,48380],{"className":48379,"style":2218},[282],[128,48381,48382,48385],{"style":2221},[128,48383],{"className":48384,"style":291},[290],[128,48386,48388],{"className":48387},[299,300,301,298],[128,48389,2022],{"className":48390,"style":2231},[259,1873,298],[128,48392,347],{"className":48393},[346],[128,48395,48397],{"className":48396},[278],[128,48398,48400],{"className":48399,"style":2241},[282],[128,48401],{}," 即得第二式。互信息由 ",[128,48404,48406,48450],{"className":48405,"translate":218},[217],[128,48407,48409],{"className":48408},[222],[224,48410,48411],{"xmlns":226},[228,48412,48413,48447],{},[231,48414,48415,48417,48419,48421,48423,48425,48427,48429,48431,48433,48435,48437,48439,48441,48443,48445],{},[1795,48416,30626],{},[1832,48418,1994],{},[1795,48420,24362],{},[1832,48422,16538],{"stretchy":1837},[1795,48424,342],{"mathvariant":2008},[234,48426,6528],{},[1795,48428,26389],{"mathvariant":4834},[1832,48430,16547],{"stretchy":1837},[1832,48432,1989],{},[1795,48434,342],{"mathvariant":2008},[1832,48436,16538],{"stretchy":1837},[1795,48438,24362],{},[1832,48440,2477],{"stretchy":1837},[1795,48442,26389],{"mathvariant":4834},[1832,48444,2486],{"stretchy":1837},[1832,48446,16547],{"stretchy":1837},[238,48448,48449],{"encoding":240},"I = H[\\mathbb{E}\\,\\boldsymbol{\\pi}] - \\mathbb{E}[H(\\boldsymbol{\\pi})]",[128,48451,48453,48471,48510],{"className":48452,"ariaHidden":246},[245],[128,48454,48456,48459,48462,48465,48468],{"className":48455},[250],[128,48457],{"className":48458,"style":283},[254],[128,48460,30626],{"className":48461,"style":30665},[259,1873],[128,48463],{"className":48464,"style":1878},[269],[128,48466,1994],{"className":48467},[1882],[128,48469],{"className":48470,"style":1878},[269],[128,48472,48474,48477,48480,48483,48486,48489,48498,48501,48504,48507],{"className":48473},[250],[128,48475],{"className":48476,"style":1892},[254],[128,48478,24362],{"className":48479,"style":24474},[259,1873],[128,48481,16538],{"className":48482},[1896],[128,48484,342],{"className":48485},[259,2167],[128,48487],{"className":48488,"style":1907},[269],[128,48490,48492],{"className":48491},[259],[128,48493,48495],{"className":48494},[259],[128,48496,26389],{"className":48497,"style":26423},[259,4895],[128,48499,16547],{"className":48500},[1928],[128,48502],{"className":48503,"style":2508},[269],[128,48505,1989],{"className":48506},[2115],[128,48508],{"className":48509,"style":2508},[269],[128,48511,48513,48516,48519,48522,48525,48528,48537],{"className":48512},[250],[128,48514],{"className":48515,"style":1892},[254],[128,48517,342],{"className":48518},[259,2167],[128,48520,16538],{"className":48521},[1896],[128,48523,24362],{"className":48524,"style":24474},[259,1873],[128,48526,2477],{"className":48527},[1896],[128,48529,48531],{"className":48530},[259],[128,48532,48534],{"className":48533},[259],[128,48535,26389],{"className":48536,"style":26423},[259,4895],[128,48538,44995],{"className":48539},[1928]," 得到。",[11,48542,48543,48544,48547,48548,23604,48611,48662,48663,48723,48724,48753,48754,48782,48783,48786,48787,48815],{},"这一分解的意义在于：",[35,48545,48546],{},"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 ",[128,48549,48551,48575],{"className":48550,"translate":218},[217],[128,48552,48554],{"className":48553},[222],[224,48555,48556],{"xmlns":226},[228,48557,48558,48572],{},[231,48559,48560,48562,48564,48566,48568,48570],{},[1795,48561,30626],{},[1832,48563,2477],{"stretchy":1837},[1795,48565,1830],{},[1832,48567,13024],{"separator":246},[1795,48569,26389],{"mathvariant":4834},[1832,48571,2486],{"stretchy":1837},[238,48573,48574],{"encoding":240},"I(y;\\boldsymbol{\\pi})",[128,48576,48578],{"className":48577,"ariaHidden":246},[245],[128,48579,48581,48584,48587,48590,48593,48596,48599,48608],{"className":48580},[250],[128,48582],{"className":48583,"style":1892},[254],[128,48585,30626],{"className":48586,"style":30665},[259,1873],[128,48588,2477],{"className":48589},[1896],[128,48591,1830],{"className":48592,"style":1874},[259,1873],[128,48594,13024],{"className":48595},[1903],[128,48597],{"className":48598,"style":1907},[269],[128,48600,48602],{"className":48601},[259],[128,48603,48605],{"className":48604},[259],[128,48606,26389],{"className":48607,"style":26423},[259,4895],[128,48609,2486],{"className":48610},[1928],[128,48612,48614,48632],{"className":48613,"translate":218},[217],[128,48615,48617],{"className":48616},[222],[224,48618,48619],{"xmlns":226},[228,48620,48621,48629],{},[231,48622,48623,48625,48627],{},[1795,48624,41957],{},[1832,48626,22419],{},[1795,48628,8521],{"mathvariant":1981},[238,48630,48631],{"encoding":240},"S \\to \\infty",[128,48633,48635,48653],{"className":48634,"ariaHidden":246},[245],[128,48636,48638,48641,48644,48647,48650],{"className":48637},[250],[128,48639],{"className":48640,"style":283},[254],[128,48642,41957],{"className":48643,"style":42029},[259,1873],[128,48645],{"className":48646,"style":1878},[269],[128,48648,22419],{"className":48649},[1882],[128,48651],{"className":48652,"style":1878},[269],[128,48654,48656,48659],{"className":48655},[250],[128,48657],{"className":48658,"style":7758},[254],[128,48660,8521],{"className":48661},[259],"（证据充分）时趋于零，在证据缺失时增大，与 ",[128,48664,48666,48687],{"className":48665,"translate":218},[217],[128,48667,48669],{"className":48668},[222],[224,48670,48671],{"xmlns":226},[228,48672,48673,48685],{},[231,48674,48675,48677,48679,48681,48683],{},[1795,48676,35129],{},[1832,48678,1994],{},[1795,48680,1853],{},[1795,48682,4751],{"mathvariant":1981},[1795,48684,41957],{},[238,48686,44676],{"encoding":240},[128,48688,48690,48708],{"className":48689,"ariaHidden":246},[245],[128,48691,48693,48696,48699,48702,48705],{"className":48692},[250],[128,48694],{"className":48695,"style":7758},[254],[128,48697,35129],{"className":48698},[259,1873],[128,48700],{"className":48701,"style":1878},[269],[128,48703,1994],{"className":48704},[1882],[128,48706],{"className":48707,"style":1878},[269],[128,48709,48711,48714,48717,48720],{"className":48710},[250],[128,48712],{"className":48713,"style":1892},[254],[128,48715,1853],{"className":48716,"style":1924},[259,1873],[128,48718,4751],{"className":48719},[259],[128,48721,41957],{"className":48722,"style":42029},[259,1873]," 的定性行为一致。但它是通过 ",[128,48725,48727,48741],{"className":48726,"translate":218},[217],[128,48728,48730],{"className":48729},[222],[224,48731,48732],{"xmlns":226},[228,48733,48734,48738],{},[231,48735,48736],{},[1795,48737,24404],{},[238,48739,48740],{"encoding":240},"\\psi",[128,48742,48744],{"className":48743,"ariaHidden":246},[245],[128,48745,48747,48750],{"className":48746},[250],[128,48748],{"className":48749,"style":16030},[254],[128,48751,24404],{"className":48752,"style":1874},[259,1873]," 函数的差构造的，捕捉了 ",[128,48755,48757,48770],{"className":48756,"translate":218},[217],[128,48758,48760],{"className":48759},[222],[224,48761,48762],{"xmlns":226},[228,48763,48764,48768],{},[231,48765,48766],{},[1795,48767,35129],{},[238,48769,35129],{"encoding":240},[128,48771,48773],{"className":48772,"ariaHidden":246},[245],[128,48774,48776,48779],{"className":48775},[250],[128,48777],{"className":48778,"style":7758},[254],[128,48780,35129],{"className":48781},[259,1873]," 所忽略的",[35,48784,48785],{},"证据分布","信息，因而是比 ",[128,48788,48790,48803],{"className":48789,"translate":218},[217],[128,48791,48793],{"className":48792},[222],[224,48794,48795],{"xmlns":226},[228,48796,48797,48801],{},[231,48798,48799],{},[1795,48800,35129],{},[238,48802,35129],{"encoding":240},[128,48804,48806],{"className":48805,"ariaHidden":246},[245],[128,48807,48809,48812],{"className":48808},[250],[128,48810],{"className":48811,"style":7758},[254],[128,48813,35129],{"className":48814},[259,1873]," 更精细的分数。",[11,48817,48818,48819,48853,48854,48888,48889,48983,48984,22009,48987,49049,49050,49054,49055,49058],{},"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 ",[128,48820,48822,48835],{"className":48821,"translate":218},[217],[128,48823,48825],{"className":48824},[222],[224,48826,48827],{"xmlns":226},[228,48828,48829,48833],{},[231,48830,48831],{},[1795,48832,26389],{"mathvariant":4834},[238,48834,26477],{"encoding":240},[128,48836,48838],{"className":48837,"ariaHidden":246},[245],[128,48839,48841,48844],{"className":48840},[250],[128,48842],{"className":48843,"style":4439},[254],[128,48845,48847],{"className":48846},[259],[128,48848,48850],{"className":48849},[259],[128,48851,26389],{"className":48852,"style":26423},[259,4895]," 的不确定性」，而 ",[128,48855,48857,48870],{"className":48856,"translate":218},[217],[128,48858,48860],{"className":48859},[222],[224,48861,48862],{"xmlns":226},[228,48863,48864,48868],{},[231,48865,48866],{},[1795,48867,26389],{"mathvariant":4834},[238,48869,26477],{"encoding":240},[128,48871,48873],{"className":48872,"ariaHidden":246},[245],[128,48874,48876,48879],{"className":48875},[250],[128,48877],{"className":48878,"style":4439},[254],[128,48880,48882],{"className":48881},[259],[128,48883,48885],{"className":48884},[259],[128,48886,26389],{"className":48887,"style":26423},[259,4895]," 在 EDL 中是 ",[128,48890,48892,48916],{"className":48891,"translate":218},[217],[128,48893,48895],{"className":48894},[222],[224,48896,48897],{"xmlns":226},[228,48898,48899,48913],{},[231,48900,48901,48907,48909,48911],{},[2016,48902,48903,48905],{},[1795,48904,24505],{},[1795,48906,38844],{"mathvariant":4834},[1832,48908,2477],{"stretchy":1837},[1795,48910,2760],{"mathvariant":2001},[1832,48912,2486],{"stretchy":1837},[238,48914,48915],{"encoding":240},"g_{\\boldsymbol{\\theta}}(\\mathbf{x})",[128,48917,48919],{"className":48918,"ariaHidden":246},[245],[128,48920,48922,48925,48974,48977,48980],{"className":48921},[250],[128,48923],{"className":48924,"style":1892},[254],[128,48926,48928,48931],{"className":48927},[259],[128,48929,24505],{"className":48930,"style":1874},[259,1873],[128,48932,48934],{"className":48933},[2087],[128,48935,48937,48966],{"className":48936},[274,321],[128,48938,48940,48963],{"className":48939},[278],[128,48941,48943],{"className":48942,"style":2218},[282],[128,48944,48945,48948],{"style":28741},[128,48946],{"className":48947,"style":291},[290],[128,48949,48951],{"className":48950},[299,300,301,298],[128,48952,48954],{"className":48953},[259,298],[128,48955,48957],{"className":48956},[259,298],[128,48958,48960],{"className":48959},[259,298],[128,48961,38844],{"className":48962,"style":38908},[259,4895,298],[128,48964,347],{"className":48965},[346],[128,48967,48969],{"className":48968},[278],[128,48970,48972],{"className":48971,"style":2241},[282],[128,48973],{},[128,48975,2477],{"className":48976},[1896],[128,48978,2760],{"className":48979},[259,2151],[128,48981,2486],{"className":48982},[1928]," 的输出，是",[35,48985,48986],{},"网络参数的确定性函数",[128,48988,48990,49013],{"className":48989,"translate":218},[217],[128,48991,48993],{"className":48992},[222],[224,48994,48995],{"xmlns":226},[228,48996,48997,49011],{},[231,48998,48999,49001,49003,49005,49007,49009],{},[1795,49000,30626],{},[1832,49002,2477],{"stretchy":1837},[1795,49004,1830],{},[1832,49006,13024],{"separator":246},[1795,49008,26389],{"mathvariant":4834},[1832,49010,2486],{"stretchy":1837},[238,49012,48574],{"encoding":240},[128,49014,49016],{"className":49015,"ariaHidden":246},[245],[128,49017,49019,49022,49025,49028,49031,49034,49037,49046],{"className":49018},[250],[128,49020],{"className":49021,"style":1892},[254],[128,49023,30626],{"className":49024,"style":30665},[259,1873],[128,49026,2477],{"className":49027},[1896],[128,49029,1830],{"className":49030,"style":1874},[259,1873],[128,49032,13024],{"className":49033},[1903],[128,49035],{"className":49036,"style":1907},[269],[128,49038,49040],{"className":49039},[259],[128,49041,49043],{"className":49042},[259],[128,49044,26389],{"className":49045,"style":26423},[259,4895],[128,49047,2486],{"className":49048},[1928]," 度量的是",[49051,49052,49053],"em",{},"类概率向量","的不确定，而不是",[49051,49056,49057],{},"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。",[51,49060,49062],{"id":49061},"四证据深度学习的损失函数","四、证据深度学习的损失函数",[11,49064,49065,49066,49094,49095,49149],{},"EDL 的训练目标不再是「使 ",[128,49067,49069,49082],{"className":49068,"translate":218},[217],[128,49070,49072],{"className":49071},[222],[224,49073,49074],{"xmlns":226},[228,49075,49076,49080],{},[231,49077,49078],{},[1795,49079,11],{"mathvariant":2001},[238,49081,2554],{"encoding":240},[128,49083,49085],{"className":49084,"ariaHidden":246},[245],[128,49086,49088,49091],{"className":49087},[250],[128,49089],{"className":49090,"style":2564},[254],[128,49092,11],{"className":49093},[259,2151]," 逼近 one-hot 标签」，而是「使整族 ",[128,49096,49098,49119],{"className":49097,"translate":218},[217],[128,49099,49101],{"className":49100},[222],[224,49102,49103],{"xmlns":226},[228,49104,49105,49117],{},[231,49106,49107,49109,49111,49113,49115],{},[1795,49108,5914],{"mathvariant":1981},[1832,49110,3278],{},[1832,49112,2477],{"stretchy":1837},[1795,49114,4835],{"mathvariant":4834},[1832,49116,2486],{"stretchy":1837},[238,49118,40766],{"encoding":240},[128,49120,49122],{"className":49121,"ariaHidden":246},[245],[128,49123,49125,49128,49134,49137,49146],{"className":49124},[250],[128,49126],{"className":49127,"style":1892},[254],[128,49129,49131],{"className":49130},[2268],[128,49132,5914],{"className":49133},[259,3353],[128,49135,2477],{"className":49136},[1896],[128,49138,49140],{"className":49139},[259],[128,49141,49143],{"className":49142},[259],[128,49144,4835],{"className":49145},[259,4895],[128,49147,2486],{"className":49148},[1928]," 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。",[2610,49151,49153],{"id":49152},"_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",[11,49155,49156,49157,49160],{},"最自然的构造是极小化对数损失在迪利克雷先验下的",[35,49158,49159],{},"贝叶斯风险","（亦称 Type-II 极大似然）：",[128,49162,49164],{"className":49163,"translate":218},[1962],[128,49165,49167,49224],{"className":49166,"translate":218},[217],[128,49168,49170],{"className":49169},[222],[224,49171,49172],{"xmlns":226,"display":1971},[228,49173,49174,49221],{},[231,49175,49176,49183,49185,49205,49207,49209,49211,49213,49219],{},[1977,49177,49178,49180],{},[1795,49179,265],{"mathvariant":1797},[234,49181,49182],{},"NLL",[1832,49184,1994],{},[2016,49186,49187,49189],{},[1795,49188,342],{"mathvariant":2008},[231,49190,49191,49193,49195,49197,49199,49201,49203],{},[1795,49192,26389],{"mathvariant":4834},[1832,49194,5911],{},[1795,49196,5914],{"mathvariant":1981},[1832,49198,3278],{},[1832,49200,2477],{"stretchy":1837},[1795,49202,4835],{"mathvariant":4834},[1832,49204,2486],{"stretchy":1837},[1832,49206,16538],{"fence":1837,"stretchy":246,"minsize":46539,"maxsize":46539},[1832,49208,1989],{},[1795,49210,24373],{},[1832,49212,3278],{},[2016,49214,49215,49217],{},[1795,49216,26389],{},[1795,49218,1830],{},[1832,49220,16547],{"fence":1837,"stretchy":246,"minsize":46539,"maxsize":46539},[238,49222,49223],{"encoding":240},"\\mathcal{L}^{\\text{NLL}} = \\mathbb{E}_{\\boldsymbol{\\pi} \\sim \\operatorname{Dir}(\\boldsymbol{\\alpha})}\\big[-\\log \\pi_y\\big]",[128,49225,49227,49277,49374],{"className":49226,"ariaHidden":246},[245],[128,49228,49230,49233,49268,49271,49274],{"className":49229},[250],[128,49231],{"className":49232,"style":2077},[254],[128,49234,49236,49239],{"className":49235},[259],[128,49237,265],{"className":49238},[259,1813],[128,49240,49242],{"className":49241},[2087],[128,49243,49245],{"className":49244},[274],[128,49246,49248],{"className":49247},[278],[128,49249,49251],{"className":49250,"style":2077},[282],[128,49252,49253,49256],{"style":2099},[128,49254],{"className":49255,"style":291},[290],[128,49257,49259],{"className":49258},[299,300,301,298],[128,49260,49262],{"className":49261},[259,298],[128,49263,49265],{"className":49264},[259,260,298],[128,49266,49182],{"className":49267},[259,298],[128,49269],{"className":49270,"style":1878},[269],[128,49272,1994],{"className":49273},[1882],[128,49275],{"className":49276,"style":1878},[269],[128,49278,49280,49284,49359,49365,49368,49371],{"className":49279},[250],[128,49281],{"className":49282,"style":49283},[254],"height:1.2052em;vertical-align:-0.3552em;",[128,49285,49287,49290],{"className":49286},[259],[128,49288,342],{"className":49289},[259,2167],[128,49291,49293],{"className":49292},[2087],[128,49294,49296,49350],{"className":49295},[274,321],[128,49297,49299,49347],{"className":49298},[278],[128,49300,49302],{"className":49301,"style":24117},[282],[128,49303,49305,49308],{"style":49304},"top:-2.5198em;margin-left:0em;margin-right:0.05em;",[128,49306],{"className":49307,"style":291},[290],[128,49309,49311],{"className":49310},[299,300,301,298],[128,49312,49314,49323,49326,49332,49335,49344],{"className":49313},[259,298],[128,49315,49317],{"className":49316},[259,298],[128,49318,49320],{"className":49319},[259,298],[128,49321,26389],{"className":49322,"style":26423},[259,4895,298],[128,49324,5911],{"className":49325},[1882,298],[128,49327,49329],{"className":49328},[2268,298],[128,49330,5914],{"className":49331},[259,3353,298],[128,49333,2477],{"className":49334},[1896,298],[128,49336,49338],{"className":49337},[259,298],[128,49339,49341],{"className":49340},[259,298],[128,49342,4835],{"className":49343},[259,4895,298],[128,49345,2486],{"className":49346},[1928,298],[128,49348,347],{"className":49349},[346],[128,49351,49353],{"className":49352},[278],[128,49354,49357],{"className":49355,"style":49356},[282],"height:0.3552em;",[128,49358],{},[128,49360,49362],{"className":49361},[259],[128,49363,16538],{"className":49364},[2146,5795],[128,49366],{"className":49367,"style":2508},[269],[128,49369,1989],{"className":49370},[2115],[128,49372],{"className":49373,"style":2508},[269],[128,49375,49377,49380,49385,49388,49428],{"className":49376},[250],[128,49378],{"className":49379,"style":46966},[254],[128,49381,24502,49383],{"className":49382},[2268],[128,49384,24505],{"style":17336},[128,49386],{"className":49387,"style":1907},[269],[128,49389,49391,49394],{"className":49390},[259],[128,49392,26389],{"className":49393,"style":1874},[259,1873],[128,49395,49397],{"className":49396},[2087],[128,49398,49400,49420],{"className":49399},[274,321],[128,49401,49403,49417],{"className":49402},[278],[128,49404,49406],{"className":49405,"style":28738},[282],[128,49407,49408,49411],{"style":28741},[128,49409],{"className":49410,"style":291},[290],[128,49412,49414],{"className":49413},[299,300,301,298],[128,49415,1830],{"className":49416,"style":1874},[259,1873,298],[128,49418,347],{"className":49419},[346],[128,49421,49423],{"className":49422},[278],[128,49424,49426],{"className":49425,"style":17424},[282],[128,49427],{},[128,49429,49431],{"className":49430},[259],[128,49432,16547],{"className":49433},[2146,5795],[2615,49435,49437],{"title":49436},"命题 4.1（对数风险的闭式）",[11,49438,49439,49440,49468,49469],{},"设真实标签为 ",[128,49441,49443,49456],{"className":49442,"translate":218},[217],[128,49444,49446],{"className":49445},[222],[224,49447,49448],{"xmlns":226},[228,49449,49450,49454],{},[231,49451,49452],{},[1795,49453,1830],{},[238,49455,1830],{"encoding":240},[128,49457,49459],{"className":49458,"ariaHidden":246},[245],[128,49460,49462,49465],{"className":49461},[250],[128,49463],{"className":49464,"style":11158},[254],[128,49466,1830],{"className":49467,"style":1874},[259,1873],"，则\n",[128,49470,49472,49514],{"className":49471,"translate":218},[217],[128,49473,49475],{"className":49474},[222],[224,49476,49477],{"xmlns":226},[228,49478,49479,49511],{},[231,49480,49481,49487,49489,49491,49493,49495,49497,49499,49501,49503,49509],{},[1977,49482,49483,49485],{},[1795,49484,265],{"mathvariant":1797},[234,49486,49182],{},[1832,49488,1994],{},[1795,49490,24404],{},[1832,49492,2477],{"stretchy":1837},[1795,49494,41957],{},[1832,49496,2486],{"stretchy":1837},[1832,49498,1989],{},[1795,49500,24404],{},[1832,49502,2477],{"stretchy":1837},[2016,49504,49505,49507],{},[1795,49506,4835],{},[1795,49508,1830],{},[1832,49510,2486],{"stretchy":1837},[238,49512,49513],{"encoding":240},"\\mathcal{L}^{\\text{NLL}} = \\psi(S) - \\psi(\\alpha_y)",[128,49515,49517,49567,49594],{"className":49516,"ariaHidden":246},[245],[128,49518,49520,49523,49558,49561,49564],{"className":49519},[250],[128,49521],{"className":49522,"style":2431},[254],[128,49524,49526,49529],{"className":49525},[259],[128,49527,265],{"className":49528},[259,1813],[128,49530,49532],{"className":49531},[2087],[128,49533,49535],{"className":49534},[274],[128,49536,49538],{"className":49537},[278],[128,49539,49541],{"className":49540,"style":2431},[282],[128,49542,49543,49546],{"style":2452},[128,49544],{"className":49545,"style":291},[290],[128,49547,49549],{"className":49548},[299,300,301,298],[128,49550,49552],{"className":49551},[259,298],[128,49553,49555],{"className":49554},[259,260,298],[128,49556,49182],{"className":49557},[259,298],[128,49559],{"className":49560,"style":1878},[269],[128,49562,1994],{"className":49563},[1882],[128,49565],{"className":49566,"style":1878},[269],[128,49568,49570,49573,49576,49579,49582,49585,49588,49591],{"className":49569},[250],[128,49571],{"className":49572,"style":1892},[254],[128,49574,24404],{"className":49575,"style":1874},[259,1873],[128,49577,2477],{"className":49578},[1896],[128,49580,41957],{"className":49581,"style":42029},[259,1873],[128,49583,2486],{"className":49584},[1928],[128,49586],{"className":49587,"style":2508},[269],[128,49589,1989],{"className":49590},[2115],[128,49592],{"className":49593,"style":2508},[269],[128,49595,49597,49600,49603,49606,49646],{"className":49596},[250],[128,49598],{"className":49599,"style":19704},[254],[128,49601,24404],{"className":49602,"style":1874},[259,1873],[128,49604,2477],{"className":49605},[1896],[128,49607,49609,49612],{"className":49608},[259],[128,49610,4835],{"className":49611,"style":4920},[259,1873],[128,49613,49615],{"className":49614},[2087],[128,49616,49618,49638],{"className":49617},[274,321],[128,49619,49621,49635],{"className":49620},[278],[128,49622,49624],{"className":49623,"style":28738},[282],[128,49625,49626,49629],{"style":4935},[128,49627],{"className":49628,"style":291},[290],[128,49630,49632],{"className":49631},[299,300,301,298],[128,49633,1830],{"className":49634,"style":1874},[259,1873,298],[128,49636,347],{"className":49637},[346],[128,49639,49641],{"className":49640},[278],[128,49642,49644],{"className":49643,"style":17424},[282],[128,49645],{},[128,49647,2486],{"className":49648},[1928],[11,49650,49651,49653,49654,49907,49908,49959,49960,49994],{},[35,49652,6849],{}," 由 ",[128,49655,49657,49713],{"className":49656,"translate":218},[217],[128,49658,49660],{"className":49659},[222],[224,49661,49662],{"xmlns":226},[228,49663,49664,49710],{},[231,49665,49666,49668,49670,49672,49674,49680,49682,49684,49686,49688,49694,49696,49698,49700,49702,49708],{},[1795,49667,342],{"mathvariant":2008},[1832,49669,16538],{"stretchy":1837},[1795,49671,24373],{},[1832,49673,3278],{},[2016,49675,49676,49678],{},[1795,49677,2760],{},[1795,49679,2022],{},[1832,49681,16547],{"stretchy":1837},[1832,49683,1994],{},[1795,49685,24404],{},[1832,49687,2477],{"stretchy":1837},[2016,49689,49690,49692],{},[1795,49691,4835],{},[1795,49693,2022],{},[1832,49695,2486],{"stretchy":1837},[1832,49697,1989],{},[1795,49699,24404],{},[1832,49701,2477],{"stretchy":1837},[2016,49703,49704,49706],{},[1795,49705,4835],{},[1840,49707,2028],{},[1832,49709,2486],{"stretchy":1837},[238,49711,49712],{"encoding":240},"\\mathbb{E}[\\log x_k] = \\psi(\\alpha_k) - \\psi(\\alpha_0)",[128,49714,49716,49788,49852],{"className":49715,"ariaHidden":246},[245],[128,49717,49719,49722,49725,49728,49733,49736,49776,49779,49782,49785],{"className":49718},[250],[128,49720],{"className":49721,"style":1892},[254],[128,49723,342],{"className":49724},[259,2167],[128,49726,16538],{"className":49727},[1896],[128,49729,24502,49731],{"className":49730},[2268],[128,49732,24505],{"style":17336},[128,49734],{"className":49735,"style":1907},[269],[128,49737,49739,49742],{"className":49738},[259],[128,49740,2760],{"className":49741},[259,1873],[128,49743,49745],{"className":49744},[2087],[128,49746,49748,49768],{"className":49747},[274,321],[128,49749,49751,49765],{"className":49750},[278],[128,49752,49754],{"className":49753,"style":2218},[282],[128,49755,49756,49759],{"style":2221},[128,49757],{"className":49758,"style":291},[290],[128,49760,49762],{"className":49761},[299,300,301,298],[128,49763,2022],{"className":49764,"style":2231},[259,1873,298],[128,49766,347],{"className":49767},[346],[128,49769,49771],{"className":49770},[278],[128,49772,49774],{"className":49773,"style":2241},[282],[128,49775],{},[128,49777,16547],{"className":49778},[1928],[128,49780],{"className":49781,"style":1878},[269],[128,49783,1994],{"className":49784},[1882],[128,49786],{"className":49787,"style":1878},[269],[128,49789,49791,49794,49797,49800,49840,49843,49846,49849],{"className":49790},[250],[128,49792],{"className":49793,"style":1892},[254],[128,49795,24404],{"className":49796,"style":1874},[259,1873],[128,49798,2477],{"className":49799},[1896],[128,49801,49803,49806],{"className":49802},[259],[128,49804,4835],{"className":49805,"style":4920},[259,1873],[128,49807,49809],{"className":49808},[2087],[128,49810,49812,49832],{"className":49811},[274,321],[128,49813,49815,49829],{"className":49814},[278],[128,49816,49818],{"className":49817,"style":2218},[282],[128,49819,49820,49823],{"style":4935},[128,49821],{"className":49822,"style":291},[290],[128,49824,49826],{"className":49825},[299,300,301,298],[128,49827,2022],{"className":49828,"style":2231},[259,1873,298],[128,49830,347],{"className":49831},[346],[128,49833,49835],{"className":49834},[278],[128,49836,49838],{"className":49837,"style":2241},[282],[128,49839],{},[128,49841,2486],{"className":49842},[1928],[128,49844],{"className":49845,"style":2508},[269],[128,49847,1989],{"className":49848},[2115],[128,49850],{"className":49851,"style":2508},[269],[128,49853,49855,49858,49861,49864,49904],{"className":49854},[250],[128,49856],{"className":49857,"style":1892},[254],[128,49859,24404],{"className":49860,"style":1874},[259,1873],[128,49862,2477],{"className":49863},[1896],[128,49865,49867,49870],{"className":49866},[259],[128,49868,4835],{"className":49869,"style":4920},[259,1873],[128,49871,49873],{"className":49872},[2087],[128,49874,49876,49896],{"className":49875},[274,321],[128,49877,49879,49893],{"className":49878},[278],[128,49880,49882],{"className":49881,"style":2945},[282],[128,49883,49884,49887],{"style":4935},[128,49885],{"className":49886,"style":291},[290],[128,49888,49890],{"className":49889},[299,300,301,298],[128,49891,2028],{"className":49892},[259,298],[128,49894,347],{"className":49895},[346],[128,49897,49899],{"className":49898},[278],[128,49900,49902],{"className":49901,"style":2241},[282],[128,49903],{},[128,49905,2486],{"className":49906},[1928],"（命题 2.4 的证明中已给出），取 ",[128,49909,49911,49929],{"className":49910,"translate":218},[217],[128,49912,49914],{"className":49913},[222],[224,49915,49916],{"xmlns":226},[228,49917,49918,49926],{},[231,49919,49920,49922,49924],{},[1795,49921,2022],{},[1832,49923,1994],{},[1795,49925,1830],{},[238,49927,49928],{"encoding":240},"k = y",[128,49930,49932,49950],{"className":49931,"ariaHidden":246},[245],[128,49933,49935,49938,49941,49944,49947],{"className":49934},[250],[128,49936],{"className":49937,"style":12173},[254],[128,49939,2022],{"className":49940,"style":2231},[259,1873],[128,49942],{"className":49943,"style":1878},[269],[128,49945,1994],{"className":49946},[1882],[128,49948],{"className":49949,"style":1878},[269],[128,49951,49953,49956],{"className":49952},[250],[128,49954],{"className":49955,"style":11158},[254],[128,49957,1830],{"className":49958,"style":1874},[259,1873]," 并乘以 ",[128,49961,49963,49979],{"className":49962,"translate":218},[217],[128,49964,49966],{"className":49965},[222],[224,49967,49968],{"xmlns":226},[228,49969,49970,49976],{},[231,49971,49972,49974],{},[1832,49973,1989],{},[1840,49975,1842],{},[238,49977,49978],{"encoding":240},"-1",[128,49980,49982],{"className":49981,"ariaHidden":246},[245],[128,49983,49985,49988,49991],{"className":49984},[250],[128,49986],{"className":49987,"style":4298},[254],[128,49989,1989],{"className":49990},[259],[128,49992,1842],{"className":49993},[259]," 即得。",[11,49996,49997],{},"该损失的梯度结构值得注意：",[128,49999,50001],{"className":50000,"translate":218},[1962],[128,50002,50004,50131],{"className":50003,"translate":218},[217],[128,50005,50007],{"className":50006},[222],[224,50008,50009],{"xmlns":226,"display":1971},[228,50010,50011,50128],{},[231,50012,50013,50036,50038,50044,50046,50048,50050,50052,50058,50060,50066,50068,50070,50072,50074,50076,50098,50100,50106,50108,50110,50112,50114,50116,50118,50120,50122,50124,50126],{},[5451,50014,50015,50026],{},[231,50016,50017,50020],{},[1795,50018,50019],{"mathvariant":1981},"∂",[1977,50021,50022,50024],{},[1795,50023,265],{"mathvariant":1797},[234,50025,49182],{},[231,50027,50028,50030],{},[1795,50029,50019],{"mathvariant":1981},[2016,50031,50032,50034],{},[1795,50033,4835],{},[1795,50035,1830],{},[1832,50037,1994],{},[1977,50039,50040,50042],{},[1795,50041,24404],{},[1832,50043,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},[1832,50045,2477],{"stretchy":1837},[1795,50047,41957],{},[1832,50049,2486],{"stretchy":1837},[1832,50051,1989],{},[1977,50053,50054,50056],{},[1795,50055,24404],{},[1832,50057,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},[1832,50059,2477],{"stretchy":1837},[2016,50061,50062,50064],{},[1795,50063,4835],{},[1795,50065,1830],{},[1832,50067,2486],{"stretchy":1837},[1832,50069,23023],{},[1840,50071,2028],{},[1832,50073,1845],{"separator":246},[269,50075],{"width":11568},[5451,50077,50078,50088],{},[231,50079,50080,50082],{},[1795,50081,50019],{"mathvariant":1981},[1977,50083,50084,50086],{},[1795,50085,265],{"mathvariant":1797},[234,50087,49182],{},[231,50089,50090,50092],{},[1795,50091,50019],{"mathvariant":1981},[2016,50093,50094,50096],{},[1795,50095,4835],{},[1795,50097,16495],{},[1832,50099,1994],{},[1977,50101,50102,50104],{},[1795,50103,24404],{},[1832,50105,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},[1832,50107,2477],{"stretchy":1837},[1795,50109,41957],{},[1832,50111,2486],{"stretchy":1837},[1832,50113,3321],{},[1840,50115,2028],{},[269,50117],{"width":8176},[1832,50119,2477],{"stretchy":1837},[1795,50121,16495],{},[1832,50123,16716],{"mathvariant":1981},[1795,50125,1830],{},[1832,50127,2486],{"stretchy":1837},[238,50129,50130],{"encoding":240},"\\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)",[128,50132,50134,50289,50347,50441,50605,50661,50721],{"className":50133,"ariaHidden":246},[245],[128,50135,50137,50141,50280,50283,50286],{"className":50136},[250],[128,50138],{"className":50139,"style":50140},[254],"height:2.4904em;vertical-align:-0.9721em;",[128,50142,50144,50147,50277],{"className":50143},[259],[128,50145],{"className":50146},[1896,5570],[128,50148,50150],{"className":50149},[5451],[128,50151,50153,50268],{"className":50152},[274,321],[128,50154,50156,50265],{"className":50155},[278],[128,50157,50160,50211,50219],{"className":50158,"style":50159},[282],"height:1.5183em;",[128,50161,50162,50165],{"style":13123},[128,50163],{"className":50164,"style":335},[290],[128,50166,50168,50171],{"className":50167},[259],[128,50169,50019],{"className":50170,"style":11165},[259],[128,50172,50174,50177],{"className":50173},[259],[128,50175,4835],{"className":50176,"style":4920},[259,1873],[128,50178,50180],{"className":50179},[2087],[128,50181,50183,50203],{"className":50182},[274,321],[128,50184,50186,50200],{"className":50185},[278],[128,50187,50189],{"className":50188,"style":28738},[282],[128,50190,50191,50194],{"style":4935},[128,50192],{"className":50193,"style":291},[290],[128,50195,50197],{"className":50196},[299,300,301,298],[128,50198,1830],{"className":50199,"style":1874},[259,1873,298],[128,50201,347],{"className":50202},[346],[128,50204,50206],{"className":50205},[278],[128,50207,50209],{"className":50208,"style":17424},[282],[128,50210],{},[128,50212,50213,50216],{"style":5617},[128,50214],{"className":50215,"style":335},[290],[128,50217],{"className":50218,"style":5625},[5624],[128,50220,50221,50224],{"style":13189},[128,50222],{"className":50223,"style":335},[290],[128,50225,50227,50230],{"className":50226},[259],[128,50228,50019],{"className":50229,"style":11165},[259],[128,50231,50233,50236],{"className":50232},[259],[128,50234,265],{"className":50235},[259,1813],[128,50237,50239],{"className":50238},[2087],[128,50240,50242],{"className":50241},[274],[128,50243,50245],{"className":50244},[278],[128,50246,50248],{"className":50247,"style":2431},[282],[128,50249,50250,50253],{"style":2452},[128,50251],{"className":50252,"style":291},[290],[128,50254,50256],{"className":50255},[299,300,301,298],[128,50257,50259],{"className":50258},[259,298],[128,50260,50262],{"className":50261},[259,260,298],[128,50263,49182],{"className":50264},[259,298],[128,50266,347],{"className":50267},[346],[128,50269,50271],{"className":50270},[278],[128,50272,50275],{"className":50273,"style":50274},[282],"height:0.9721em;",[128,50276],{},[128,50278],{"className":50279},[1928,5570],[128,50281],{"className":50282,"style":1878},[269],[128,50284,1994],{"className":50285},[1882],[128,50287],{"className":50288,"style":1878},[269],[128,50290,50292,50296,50329,50332,50335,50338,50341,50344],{"className":50291},[250],[128,50293],{"className":50294,"style":50295},[254],"height:1.0519em;vertical-align:-0.25em;",[128,50297,50299,50302],{"className":50298},[259],[128,50300,24404],{"className":50301,"style":1874},[259,1873],[128,50303,50305],{"className":50304},[2087],[128,50306,50308],{"className":50307},[274],[128,50309,50311],{"className":50310},[278],[128,50312,50315],{"className":50313,"style":50314},[282],"height:0.8019em;",[128,50316,50317,50320],{"style":2099},[128,50318],{"className":50319,"style":291},[290],[128,50321,50323],{"className":50322},[299,300,301,298],[128,50324,50326],{"className":50325},[259,298],[128,50327,24873],{"className":50328},[259,298],[128,50330,2477],{"className":50331},[1896],[128,50333,41957],{"className":50334,"style":42029},[259,1873],[128,50336,2486],{"className":50337},[1928],[128,50339],{"className":50340,"style":2508},[269],[128,50342,1989],{"className":50343},[2115],[128,50345],{"className":50346,"style":2508},[269],[128,50348,50350,50354,50386,50389,50429,50432,50435,50438],{"className":50349},[250],[128,50351],{"className":50352,"style":50353},[254],"height:1.088em;vertical-align:-0.2861em;",[128,50355,50357,50360],{"className":50356},[259],[128,50358,24404],{"className":50359,"style":1874},[259,1873],[128,50361,50363],{"className":50362},[2087],[128,50364,50366],{"className":50365},[274],[128,50367,50369],{"className":50368},[278],[128,50370,50372],{"className":50371,"style":50314},[282],[128,50373,50374,50377],{"style":2099},[128,50375],{"className":50376,"style":291},[290],[128,50378,50380],{"className":50379},[299,300,301,298],[128,50381,50383],{"className":50382},[259,298],[128,50384,24873],{"className":50385},[259,298],[128,50387,2477],{"className":50388},[1896],[128,50390,50392,50395],{"className":50391},[259],[128,50393,4835],{"className":50394,"style":4920},[259,1873],[128,50396,50398],{"className":50397},[2087],[128,50399,50401,50421],{"className":50400},[274,321],[128,50402,50404,50418],{"className":50403},[278],[128,50405,50407],{"className":50406,"style":28738},[282],[128,50408,50409,50412],{"style":4935},[128,50410],{"className":50411,"style":291},[290],[128,5041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04,50706],{"className":50705},[259],[128,50707,17741],{"className":50708},[1882],[128,50710],{"className":50711},[17745],[128,50713],{"className":50714},[269,17749],[128,50716,1994],{"className":50717},[1882],[128,50719],{"className":50720,"style":1878},[269],[128,50722,50724,50727,50730],{"className":50723},[250],[128,50725],{"className":50726,"style":1892},[254],[128,50728,1830],{"className":50729,"style":1874},[259,1873],[128,50731,2486],{"className":50732},[1928],[11,50734,50735,50736,50799,50800,21562,50803,50874,50875,21562,50878,50948,50949,51018,51019,51047,51048,51076],{},"其中 ",[128,50737,50739,50757],{"className":50738,"translate":218},[217],[128,50740,50742],{"className":50741},[222],[224,50743,50744],{"xmlns":226},[228,50745,50746,50754],{},[231,50747,50748],{},[1977,50749,50750,50752],{},[1795,50751,24404],{},[1832,50753,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},[238,50755,50756],{"encoding":240},"\\psi'",[128,50758,50760],{"className":50759,"ariaHidden":246},[245],[128,50761,50763,50767],{"className":50762},[250],[128,50764],{"className":50765,"style":50766},[254],"height:0.9463em;vertical-align:-0.1944em;",[128,50768,50770,50773],{"className":50769},[259],[128,50771,24404],{"className":50772,"style":1874},[259,1873],[128,50774,50776],{"className":50775},[2087],[128,50777,50779],{"className":50778},[274],[128,50780,50782],{"className":50781},[278],[128,50783,50785],{"className":50784,"style":24927},[282],[128,50786,50787,50790],{"style":2452},[128,50788],{"className":50789,"style":291},[290],[128,50791,50793],{"className":50792},[299,300,301,298],[128,50794,50796],{"className":50795},[259,298],[128,50797,24873],{"className":50798},[259,298]," 为 trigamma 函数（恒正、单调递减）。因此梯度沿两个方向作用：",[35,50801,50802],{},"提升真实类别的证据",[128,50804,50806,50824],{"className":50805,"translate":218},[217],[128,50807,50809],{"className":50808},[222],[224,50810,50811],{"xmlns":226},[228,50812,50813,50821],{},[231,50814,50815],{},[2016,50816,50817,50819],{},[1795,50818,4835],{},[1795,50820,1830],{},[238,50822,50823],{"encoding":240},"\\alpha_y",[128,50825,50827],{"className":50826,"ariaHidden":246},[245],[128,50828,50830,50834],{"className":50829},[250],[128,50831],{"className":50832,"style":50833},[254],"height:0.7167em;vertical-align:-0.2861em;",[128,50835,50837,50840],{"className":50836},[259],[128,50838,4835],{"className":50839,"style":4920},[259,1873],[128,50841,50843],{"className":50842},[2087],[128,50844,50846,50866],{"className":50845},[274,321],[128,50847,50849,50863],{"className":50848},[278],[128,50850,50852],{"className":50851,"style":28738},[282],[128,50853,50854,50857],{"style":4935},[128,50855],{"className":50856,"style":291},[290],[128,50858,50860],{"className":50859},[299,300,301,298],[128,50861,1830],{"className":50862,"style":1874},[259,1873,298],[128,50864,347],{"className":50865},[346],[128,50867,50869],{"className":50868},[278],[128,50870,50872],{"className":50871,"style":17424},[282],[128,50873],{}," 增大），",[35,50876,50877],{},"压低其余类别的证据",[128,50879,50881,50899],{"className":50880,"translate":218},[217],[128,50882,50884],{"className":50883},[222],[224,50885,50886],{"xmlns":226},[228,50887,50888,50896],{},[231,50889,50890],{},[2016,50891,50892,50894],{},[1795,50893,4835],{},[1795,50895,16495],{},[238,50897,50898],{"encoding":240},"\\alpha_j",[128,50900,50902],{"className":50901,"ariaHidden":246},[245],[128,50903,50905,50908],{"className":50904},[250],[128,50906],{"className":50907,"style":50833},[254],[128,50909,50911,50914],{"className":50910},[259],[128,50912,4835],{"className":50913,"style":4920},[259,1873],[128,50915,50917],{"className":50916},[2087],[128,50918,50920,50940],{"className":50919},[274,321],[128,50921,50923,50937],{"className":50922},[278],[128,50924,50926],{"className":50925,"style":3095},[282],[128,50927,50928,50931],{"style":4935},[128,50929],{"className":50930,"style":291},[290],[128,50932,50934],{"className":50933},[299,300,301,298],[128,50935,16495],{"className":50936,"style":16521},[259,1873,298],[128,50938,347],{"className":50939},[346],[128,50941,50943],{"className":50942},[278],[128,50944,50946],{"className":50945,"style":17424},[282],[128,50947],{}," 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 ",[128,50950,50952,50969],{"className":50951,"translate":218},[217],[128,50953,50955],{"className":50954},[222],[224,50956,50957],{"xmlns":226},[228,50958,50959,50967],{},[231,50960,50961],{},[2016,50962,50963,50965],{},[1795,50964,4835],{},[1795,50966,16495],{},[238,50968,50898],{"encoding":240},[128,50970,50972],{"className":50971,"ariaHidden":246},[245],[128,50973,50975,50978],{"className":50974},[250],[128,50976],{"className":50977,"style":50833},[254],[128,50979,50981,50984],{"className":50980},[259],[128,50982,4835],{"className":50983,"style":4920},[259,1873],[128,50985,50987],{"className":50986},[2087],[128,50988,50990,51010],{"className":50989},[274,321],[128,50991,50993,51007],{"className":50992},[278],[128,50994,50996],{"className":50995,"style":3095},[282],[128,50997,50998,51001],{"style":4935},[128,50999],{"className":51000,"style":291},[290],[128,51002,51004],{"className":51003},[299,300,301,298],[128,51005,16495],{"className":51006,"style":16521},[259,1873,298],[128,51008,347],{"className":51009},[346],[128,51011,51013],{"className":51012},[278],[128,51014,51016],{"className":51015,"style":17424},[282],[128,51017],{}," 全部驱向 ",[128,51020,51022,51035],{"className":51021,"translate":218},[217],[128,51023,51025],{"className":51024},[222],[224,51026,51027],{"xmlns":226},[228,51028,51029,51033],{},[231,51030,51031],{},[1840,51032,1842],{},[238,51034,1842],{"encoding":240},[128,51036,51038],{"className":51037,"ariaHidden":246},[245],[128,51039,51041,51044],{"className":51040},[250],[128,51042],{"className":51043,"style":2594},[254],[128,51045,1842],{"className":51046},[259],"，从而收缩总证据 ",[128,51049,51051,51064],{"className":51050,"translate":218},[217],[128,51052,51054],{"className":51053},[222],[224,51055,51056],{"xmlns":226},[228,51057,51058,51062],{},[231,51059,51060],{},[1795,51061,41957],{},[238,51063,41957],{"encoding":240},[128,51065,51067],{"className":51066,"ariaHidden":246},[245],[128,51068,51070,51073],{"className":51069},[250],[128,51071],{"className":51072,"style":283},[254],[128,51074,41957],{"className":51075,"style":42029},[259,1873],"——这正是 4.3 节引入正则项的直接原因。",[2615,51078,51080],{"title":51079},"推论 4.2（与插值交叉熵的关系）",[11,51081,51082,51147,51148],{},[128,51083,51085,51103],{"className":51084,"translate":218},[217],[128,51086,51088],{"className":51087},[222],[224,51089,51090],{"xmlns":226},[228,51091,51092,51100],{},[231,51093,51094],{},[1977,51095,51096,51098],{},[1795,51097,265],{"mathvariant":1797},[234,51099,49182],{},[238,51101,51102],{"encoding":240},"\\mathcal{L}^{\\text{NLL}}",[128,51104,51106],{"className":51105,"ariaHidden":246},[245],[128,51107,51109,51112],{"className":51108},[250],[128,51110],{"className":51111,"style":2431},[254],[128,51113,51115,51118],{"className":51114},[259],[128,51116,265],{"className":51117},[259,1813],[128,51119,51121],{"className":51120},[2087],[128,51122,51124],{"className":51123},[274],[128,51125,51127],{"className":51126},[278],[128,51128,51130],{"className":51129,"style":2431},[282],[128,51131,51132,51135],{"style":2452},[128,51133],{"className":51134,"style":291},[290],[128,51136,51138],{"className":51137},[299,300,301,298],[128,51139,51141],{"className":51140},[259,298],[128,51142,51144],{"className":51143},[259,260,298],[128,51145,49182],{"className":51146},[259,298]," 是 one-hot 标签下插值交叉熵的 Jensen 上界：\n",[128,51149,51151,51255],{"className":51150,"translate":218},[217],[128,51152,51154],{"className":51153},[222],[224,51155,51156],{"xmlns":226},[228,51157,51158,51252],{},[231,51159,51160,51166,51168,51170,51172,51174,51180,51182,51188,51212,51214,51216,51218,51234,51236,51238,51240,51242,51244,51246],{},[1977,51161,51162,51164],{},[1795,51163,265],{"mathvariant":1797},[234,51165,49182],{},[1832,51167,1994],{},[1832,51169,1989],{},[1795,51171,24373],{},[1832,51173,3278],{},[2016,51175,51176,51178],{},[1795,51177,11],{},[1795,51179,1830],{},[1832,51181,9486],{},[5451,51183,51184,51186],{},[1840,51185,1842],{},[1840,51187,2639],{},[231,51189,51190,51192,51202,51204,51210],{},[1832,51191,2477],{"fence":246},[5451,51193,51194,51196],{},[1840,51195,1842],{},[2016,51197,51198,51200],{},[1795,51199,4835],{},[1795,51201,1830],{},[1832,51203,1989],{},[5451,51205,51206,51208],{},[1840,51207,1842],{},[1795,51209,41957],{},[1832,51211,2486],{"fence":246},[1832,51213,9486],{},[1795,51215,13986],{},[234,51217,8524],{},[231,51219,51220,51222,51232],{},[1832,51221,2477],{"fence":246},[1977,51223,51224,51226],{},[1795,51225,41957],{},[231,51227,51228,51230],{},[1832,51229,1989],{},[1840,51231,2639],{},[1832,51233,2486],{"fence":246},[234,51235,2033],{},[1832,51237,2025],{},[234,51239,2033],{},[1832,51241,1989],{},[1795,51243,24373],{},[1832,51245,3278],{},[2016,51247,51248,51250],{},[1795,51249,11],{},[1795,51251,1830],{},[238,51253,51254],{"encoding":240},"\\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",[128,51256,51258,51308,51377,51661,51741],{"className":51257,"ariaHidden":246},[245],[128,51259,51261,51264,51299,51302,51305],{"className":51260},[250],[128,51262],{"className":51263,"style":2431},[254],[128,51265,51267,51270],{"className":51266},[259],[128,51268,265],{"className":51269},[259,1813],[128,51271,51273],{"className":51272},[2087],[128,51274,51276],{"className":51275},[274],[128,51277,51279],{"className":51278},[278],[128,51280,51282],{"className":51281,"style":2431},[282],[128,51283,51284,51287],{"style":2452},[128,51285],{"className":51286,"style":291},[290],[128,51288,51290],{"className":51289},[299,300,301,298],[128,51291,51293],{"className":51292},[259,298],[128,51294,51296],{"className":51295},[259,260,298],[128,51297,49182],{"className":51298},[259,298],[128,51300],{"className":51301,"style":1878},[269],[128,51303,1994],{"className":51304},[1882],[128,51306],{"className":51307,"style":1878},[269],[128,51309,51311,51314,51317,51320,51325,51328,51368,51371,51374],{"className":51310},[250],[128,51312],{"className":51313,"style":22661},[254],[128,51315,1989],{"className":51316},[259],[128,51318],{"className":51319,"style":1907},[269],[128,51321,24502,51323],{"className":51322},[2268],[128,51324,24505],{"style":17336},[128,51326],{"className":51327,"style":1907},[269],[128,51329,51331,51334],{"className":51330},[259],[128,51332,11],{"className":51333},[259,1873],[128,51335,51337],{"className":51336},[2087],[128,51338,51340,51360],{"className":51339},[274,321],[128,51341,51343,51357],{"className":51342},[278],[128,51344,51346],{"className":51345,"style":28738},[282],[128,51347,51348,51351],{"style":2221},[128,51349],{"className":51350,"style":291},[290],[128,51352,51354],{"className":51353},[299,300,301,298],[128,51355,1830],{"className":51356,"style":1874},[259,1873,298],[128,51358,347],{"className":51359},[346],[128,51361,51363],{"className":51362},[278],[128,51364,51366],{"className":51365,"style":17424},[282],[128,51367],{},[128,51369],{"className":51370,"style":2508},[269],[128,51372,9486],{"className":51373},[2115],[128,51375],{"className":51376,"style":2508},[269],[128,51378,51380,51383,51451,51454,51652,51655,51658],{"className":51379},[250],[128,51381],{"className":51382,"style":2134},[254],[128,51384,51386,51389,51448],{"className":51385},[259],[128,51387],{"className":51388},[1896,5570],[128,51390,51392],{"className":51391},[5451],[128,51393,51395,51440],{"className":51394},[274,321],[128,51396,51398,51437],{"className":51397},[278],[128,51399,51401,51415,51423],{"className":51400,"style":5583},[282],[128,51402,51403,51406],{"style":5586},[128,51404],{"className":51405,"style":335},[290],[128,51407,51409],{"className":51408},[299,300,301,298],[128,51410,51412],{"className":51411},[259,298],[128,51413,2639],{"className":51414},[259,298],[128,51416,51417,51420],{"style":5617},[128,51418],{"className":51419,"style":335},[290],[128,51421],{"className":51422,"style":5625},[5624],[128,51424,51425,51428],{"style":5628},[128,51426],{"className":51427,"style":335},[290],[128,51429,51431],{"className":51430},[299,300,301,298],[128,51432,51434],{"className":51433},[259,298],[128,51435,1842],{"className":51436},[259,298],[128,51438,347],{"className":51439},[346],[128,51441,51443],{"className":51442},[278],[128,51444,51446],{"className":51445,"style":11919},[282],[128,51447],{},[128,51449],{"className":51450},[1928,5570],[128,51452],{"className":51453,"style":1907},[269],[128,51455,51457,51463,51569,51572,51575,51578,51646],{"className":51456},[1911],[128,51458,51460],{"className":51459,"style":2142},[1896,2141],[128,51461,2477],{"className":51462},[2146,2147],[128,51464,51466,51469,51566],{"className":51465},[259],[128,51467],{"className":51468},[1896,5570],[128,51470,51472],{"className":51471},[5451],[128,51473,51475,51557],{"className":51474},[274,321],[128,51476,51478,51554],{"className":51477},[278],[128,51479,51481,51532,51540],{"className":51480,"style":5583},[282],[128,51482,51483,51486],{"style":5586},[128,51484],{"className":51485,"style":335},[290],[128,51487,51489],{"className":51488},[299,300,301,298],[128,51490,51492],{"className":51491},[259,298],[128,51493,51495,51498],{"className":51494},[259,298],[128,51496,4835],{"className":51497,"style":4920},[259,1873,298],[128,51499,51501],{"className":51500},[2087],[128,51502,51504,51524],{"className":51503},[274,321],[128,51505,51507,51521],{"className":51506},[278],[128,51508,51510],{"className":51509,"style":30995},[282],[128,51511,51512,51515],{"style":5786},[128,51513],{"className":51514,"style":5790},[290],[128,51516,51518],{"className":51517},[299,5794,5795,298],[128,51519,1830],{"className":51520,"style":1874},[259,1873,298],[128,51522,347],{"className":51523},[346],[128,51525,51527],{"className":51526},[278],[128,51528,51530],{"className":51529,"style":17680},[282],[128,51531],{},[128,51533,51534,51537],{"style":5617},[128,51535],{"className":51536,"style":335},[290],[128,51538],{"className":51539,"style":5625},[5624],[128,51541,51542,51545],{"style":5628},[128,51543],{"className":51544,"style":335},[290],[128,51546,51548],{"className":51547},[299,300,301,298],[128,51549,51551],{"className":51550},[259,298],[128,51552,1842],{"className":51553},[259,298],[128,51555,347],{"className":51556},[346],[128,51558,51560],{"className":51559},[278],[128,51561,51564],{"className":51562,"style":51563},[282],"height:0.5423em;",[128,51565],{},[128,51567],{"className":51568},[1928,5570],[128,51570],{"className":51571,"style":2508},[269],[128,51573,1989],{"className":51574},[2115],[128,51576],{"className":51577,"style":2508},[269],[128,51579,51581,51584,51643],{"className":51580},[259],[128,51582],{"className":51583},[1896,5570],[128,51585,51587],{"className":51586},[5451],[128,51588,51590,51635],{"className":51589},[274,321],[128,51591,51593,51632],{"className":51592},[278],[128,51594,51596,51610,51618],{"className":51595,"style":5583},[282],[128,51597,51598,51601],{"style":5586},[128,51599],{"className":51600,"style":335},[290],[128,51602,51604],{"className":51603},[299,300,301,298],[128,51605,51607],{"className":51606},[259,298],[128,51608,41957],{"className":51609,"style":42029},[259,1873,298],[128,51611,51612,51615],{"style":5617},[128,51613],{"className":51614,"style":335},[290],[128,51616],{"className":51617,"style":5625},[5624],[128,51619,51620,51623],{"style":5628},[128,51621],{"className":51622,"style":335},[290],[128,51624,51626],{"className":51625},[299,300,301,298],[128,51627,51629],{"className":51628},[259,298],[128,51630,1842],{"className":51631},[259,298],[128,51633,347],{"className":51634},[346],[128,51636,51638],{"className":51637},[278],[128,51639,51641],{"className":51640,"style":11919},[282],[128,51642],{},[128,51644],{"className":51645},[1928,5570],[128,51647,51649],{"className":51648,"style":2142},[1928,2141],[128,51650,2486],{"className":51651},[2146,2147],[128,51653],{"className":51654,"style":2508},[269],[128,51656,9486],{"className":51657},[2115],[128,51659],{"className":51660,"style":2508},[269],[128,51662,51664,51667,51670,51673,51676,51726,51729,51732,51735,51738],{"className":51663},[250],[128,51665],{"className":51666,"style":46966},[254],[128,51668,13986],{"className":51669,"style":14008},[259,1873],[128,51671],{"className":51672,"style":317},[269],[128,51674],{"className":51675,"style":1907},[269],[128,51677,51679,51685,51720],{"className":51678},[1911],[128,51680,51682],{"className":51681,"style":2142},[1896,2141],[128,51683,2477],{"className":51684},[2146,5795],[128,51686,51688,51691],{"className":51687},[259],[128,51689,41957],{"className":51690,"style":42029},[259,1873],[128,51692,51694],{"className":51693},[2087],[128,51695,51697],{"className":51696},[274],[128,51698,51700],{"className":51699},[278],[128,51701,51703],{"className":51702,"style":9629},[282],[128,51704,51705,51708],{"style":2452},[128,51706],{"className":51707,"style":291},[290],[128,51709,51711],{"className":51710},[299,300,301,298],[128,51712,51714,51717],{"className":51713},[259,298],[128,51715,1989],{"className":51716},[259,298],[128,51718,2639],{"className":51719},[259,298],[128,51721,51723],{"className":51722,"style":2142},[1928,2141],[128,51724,2486],{"className":51725},[2146,5795],[128,51727,2033],{"className":51728},[269],[128,51730],{"className":51731,"style":1878},[269],[128,51733,2025],{"className":51734},[1882],[128,51736,2033],{"className":51737},[269],[128,51739],{"className":51740,"style":1878},[269],[128,51742,51744,51747,51750,51753,51758,51761],{"className":51743},[250],[128,51745],{"className":51746,"style":22661},[254],[128,51748,1989],{"className":51749},[259],[128,51751],{"className":51752,"style":1907},[269],[128,51754,24502,51756],{"className":51755},[2268],[128,51757,24505],{"style":17336},[128,51759],{"className":51760,"style":1907},[269],[128,51762,51764,51767],{"className":51763},[259],[128,51765,11],{"className":51766},[259,1873],[128,51768,51770],{"className":51769},[2087],[128,51771,51773,51793],{"className":51772},[274,321],[128,51774,51776,51790],{"className":51775},[278],[128,51777,51779],{"className":51778,"style":28738},[282],[128,51780,51781,51784],{"style":2221},[128,51782],{"className":51783,"style":291},[290],[128,51785,51787],{"className":51786},[299,300,301,298],[128,51788,1830],{"className":51789,"style":1874},[259,1873,298],[128,51791,347],{"className":51792},[346],[128,51794,51796],{"className":51795},[278],[128,51797,51799],{"className":51798,"style":17424},[282],[128,51800],{},[11,51802,51803,51805,51806,16150,52068,52217,52218,52471,52472,52565],{},[35,51804,6849],{}," 由 Jensen 不等式 ",[128,51807,51809,51867],{"className":51808,"translate":218},[217],[128,51810,51812],{"className":51811},[222],[224,51813,51814],{"xmlns":226},[228,51815,51816,51864],{},[231,51817,51818,51820,51822,51824,51826,51832,51834,51836,51838,51840,51842,51844,51850,51852,51854,51856,51858],{},[1795,51819,342],{"mathvariant":2008},[1832,51821,16538],{"stretchy":1837},[1795,51823,24373],{},[1832,51825,3278],{},[2016,51827,51828,51830],{},[1795,51829,26389],{},[1795,51831,1830],{},[1832,51833,16547],{"stretchy":1837},[1832,51835,23023],{},[1795,51837,24373],{},[1832,51839,3278],{},[1795,51841,342],{"mathvariant":2008},[1832,51843,16538],{"stretchy":1837},[2016,51845,51846,51848],{},[1795,51847,26389],{},[1795,51849,1830],{},[1832,51851,16547],{"stretchy":1837},[1832,51853,1994],{},[1795,51855,24373],{},[1832,51857,3278],{},[2016,51859,51860,51862],{},[1795,51861,11],{},[1795,51863,1830],{},[238,51865,51866],{"encoding":240},"\\mathbb{E}[\\log \\pi_y] \\le \\log \\mathbb{E}[\\pi_y] = \\log p_y",[128,51868,51870,51942,52014],{"className":51869,"ariaHidden":246},[245],[128,51871,51873,51876,51879,51882,51887,51890,51930,51933,51936,51939],{"className":51872},[250],[128,51874],{"className":51875,"style":19704},[254],[128,51877,342],{"className":51878},[259,2167],[128,51880,16538],{"className":51881},[1896],[128,51883,24502,51885],{"className":51884},[2268],[128,51886,24505],{"style":17336},[128,51888],{"className":51889,"style":1907},[269],[128,51891,51893,51896],{"className":51892},[259],[128,51894,26389],{"className":51895,"style":1874},[259,1873],[128,51897,51899],{"className":51898},[2087],[128,51900,51902,51922],{"className":51901},[274,321],[128,51903,51905,51919],{"className":51904},[278],[128,51906,51908],{"className":51907,"style":28738},[282],[128,51909,51910,51913],{"style":28741},[128,51911],{"className":51912,"style":291},[290],[128,51914,51916],{"className":51915},[299,300,301,298],[128,51917,1830],{"className":51918,"style":1874},[259,1873,298],[128,51920,347],{"className":51921},[346],[128,51923,51925],{"className":51924},[278],[128,51926,51928],{"className":51927,"style":17424},[282],[128,51929],{},[128,51931,16547],{"className":51932},[1928],[128,51934],{"className":51935,"style":1878},[269],[128,51937,23023],{"className":51938},[1882],[128,51940],{"className":51941,"style":1878},[269],[128,51943,51945,51948,51953,51956,51959,51962,52002,52005,52008,52011],{"className":51944},[250],[128,51946],{"className":51947,"style":19704},[254],[128,51949,24502,51951],{"className":51950},[2268],[128,51952,24505],{"style":17336},[128,51954],{"className":51955,"style":1907},[269],[128,51957,342],{"className":51958},[259,2167],[128,51960,16538],{"className":51961},[1896],[128,51963,51965,51968],{"className":51964},[259],[128,51966,26389],{"className":51967,"style":1874},[259,1873],[128,51969,51971],{"className":51970},[2087],[128,51972,51974,51994],{"className":51973},[274,321],[128,51975,51977,51991],{"className":51976},[278],[128,51978,51980],{"className":51979,"style":28738},[282],[128,51981,51982,51985],{"style":28741},[128,51983],{"className":51984,"style":291},[290],[128,51986,51988],{"className":51987},[299,300,301,298],[128,51989,1830],{"className":51990,"style":1874},[259,1873,298],[128,51992,347],{"className":51993},[346],[128,51995,51997],{"className":51996},[278],[128,51998,52000],{"className":51999,"style":17424},[282],[128,52001],{},[128,52003,16547],{"className":52004},[1928],[128,52006],{"className":52007,"style":1878},[269],[128,52009,1994],{"className":52010},[1882],[128,52012],{"className":52013,"style":1878},[269],[128,52015,52017,52020,52025,52028],{"className":52016},[250],[128,52018],{"className":52019,"style":22661},[254],[128,52021,24502,52023],{"className":52022},[2268],[128,52024,24505],{"style":17336},[128,52026],{"className":52027,"style":1907},[269],[128,52029,52031,52034],{"className":52030},[259],[128,52032,11],{"className":52033},[259,1873],[128,52035,52037],{"className":52036},[2087],[128,52038,52040,52060],{"className":52039},[274,321],[128,52041,52043,52057],{"className":52042},[278],[128,52044,52046],{"className":52045,"style":28738},[282],[128,52047,52048,52051],{"style":2221},[128,52049],{"className":52050,"style":291},[290],[128,52052,52054],{"className":52053},[299,300,301,298],[128,52055,1830],{"className":52056,"style":1874},[259,1873,298],[128,52058,347],{"className":52059},[346],[128,52061,52063],{"className":52062},[278],[128,52064,52066],{"className":52065,"style":17424},[282],[128,52067],{},[128,52069,52071,52103],{"className":52070,"translate":218},[217],[128,52072,52074],{"className":52073},[222],[224,52075,52076],{"xmlns":226},[228,52077,52078,52100],{},[231,52079,52080,52086,52088,52090,52092,52094],{},[1977,52081,52082,52084],{},[1795,52083,265],{"mathvariant":1797},[234,52085,49182],{},[1832,52087,2025],{},[1832,52089,1989],{},[1795,52091,24373],{},[1832,52093,3278],{},[2016,52095,52096,52098],{},[1795,52097,11],{},[1795,52099,1830],{},[238,52101,52102],{"encoding":240},"\\mathcal{L}^{\\text{NLL}} \\ge -\\log p_y",[128,52104,52106,52157],{"className":52105,"ariaHidden":246},[245],[128,52107,52109,52113,52148,52151,52154],{"className":52108},[250],[128,52110],{"className":52111,"style":52112},[254],"height:0.9773em;vertical-align:-0.136em;",[128,52114,52116,52119],{"className":52115},[259],[128,52117,265],{"className":52118},[259,1813],[128,52120,52122],{"className":52121},[2087],[128,52123,52125],{"className":52124},[274],[128,52126,52128],{"className":52127},[278],[128,52129,52131],{"className":52130,"style":2431},[282],[128,52132,52133,52136],{"style":2452},[128,52134],{"className":52135,"style":291},[290],[128,52137,52139],{"className":52138},[299,300,301,298],[128,52140,52142],{"className":52141},[259,298],[128,52143,52145],{"className":52144},[259,260,298],[128,52146,49182],{"className":52147},[259,298],[128,52149],{"className":52150,"style":1878},[269],[128,52152,2025],{"className":52153},[1882],[128,52155],{"className":52156,"style":1878},[269],[128,52158,52160,52163,52166,52169,52174,52177],{"className":52159},[250],[128,52161],{"className":52162,"style":22661},[254],[128,52164,1989],{"className":52165},[259],[128,52167],{"className":52168,"style":1907},[269],[128,52170,24502,52172],{"className":52171},[2268],[128,52173,24505],{"style":17336},[128,52175],{"className":52176,"style":1907},[269],[128,52178,52180,52183],{"className":52179},[259],[128,52181,11],{"className":52182},[259,1873],[128,52184,52186],{"className":52185},[2087],[128,52187,52189,52209],{"className":52188},[274,321],[128,52190,52192,52206],{"className":52191},[278],[128,52193,52195],{"className":52194,"style":28738},[282],[128,52196,52197,52200],{"style":2221},[128,52198],{"className":52199,"style":291},[290],[128,52201,52203],{"className":52202},[299,300,301,298],[128,52204,1830],{"className":52205,"style":1874},[259,1873,298],[128,52207,347],{"className":52208},[346],[128,52210,52212],{"className":52211},[278],[128,52213,52215],{"className":52214,"style":17424},[282],[128,52216],{},"。渐近展开由 ",[128,52219,52221,52279],{"className":52220,"translate":218},[217],[128,52222,52224],{"className":52223},[222],[224,52225,52226],{"xmlns":226},[228,52227,52228,52276],{},[231,52229,52230,52232,52234,52236,52238,52240,52242,52244,52246,52248,52258,52260,52262,52264,52274],{},[1795,52231,24404],{},[1832,52233,2477],{"stretchy":1837},[1795,52235,21],{},[1832,52237,2486],{"stretchy":1837},[1832,52239,1994],{},[1795,52241,24373],{},[1832,52243,3278],{},[1795,52245,21],{},[1832,52247,1989],{},[5451,52249,52250,52252],{},[1840,52251,1842],{},[231,52253,52254,52256],{},[1840,52255,2639],{},[1795,52257,21],{},[1832,52259,9486],{},[1795,52261,13986],{},[1832,52263,2477],{"stretchy":1837},[1977,52265,52266,52268],{},[1795,52267,21],{},[231,52269,52270,52272],{},[1832,52271,1989],{},[1840,52273,2639],{},[1832,52275,2486],{"stretchy":1837},[238,52277,52278],{"encoding":240},"\\psi(a) = \\log a - \\frac{1}{2a} + O(a^{-2})",[128,52280,52282,52309,52335,52421],{"className":52281,"ariaHidden":246},[245],[128,52283,52285,52288,52291,52294,52297,52300,52303,52306],{"className":52284},[250],[128,52286],{"className":52287,"style":1892},[254],[128,52289,24404],{"className":52290,"style":1874},[259,1873],[128,52292,2477],{"className":52293},[1896],[128,52295,21],{"className":52296},[259,1873],[128,52298,2486],{"className":52299},[1928],[128,52301],{"className":52302,"style":1878},[269],[128,52304,1994],{"className":52305},[1882],[128,52307],{"className":52308,"style":1878},[269],[128,52310,52312,52315,52320,52323,52326,52329,52332],{"className":52311},[250],[128,52313],{"className":52314,"style":16030},[254],[128,52316,24502,52318],{"className":52317},[2268],[128,52319,24505],{"style":17336},[128,52321],{"className":52322,"style":1907},[269],[128,52324,21],{"className":52325},[259,1873],[128,52327],{"className":52328,"style":2508},[269],[128,52330,1989],{"className":52331},[2115],[128,52333],{"className":52334,"style":2508},[269],[128,52336,52338,52341,52412,52415,52418],{"className":52337},[250],[128,52339],{"className":52340,"style":44263},[254],[128,52342,52344,52347,52409],{"className":52343},[259],[128,52345],{"className":52346},[1896,5570],[128,52348,52350],{"className":52349},[5451],[128,52351,52353,52401],{"className":52352},[274,321],[128,52354,52356,52398],{"className":52355},[278],[128,52357,52359,52376,52384],{"className":52358,"style":5583},[282],[128,52360,52361,52364],{"style":5586},[128,52362],{"className":52363,"style":335},[290],[128,52365,52367],{"className":52366},[299,300,301,298],[128,52368,52370,52373],{"className":52369},[259,298],[128,52371,2639],{"className":52372},[259,298],[128,52374,21],{"className":52375},[259,1873,298],[128,52377,52378,52381],{"style":5617},[128,52379],{"className":52380,"style":335},[290],[128,52382],{"className":52383,"style":5625},[5624],[128,52385,52386,52389],{"style":5628},[128,52387],{"className":52388,"style":335},[290],[128,52390,52392],{"className":52391},[299,300,301,298],[128,52393,52395],{"className":52394},[259,298],[128,52396,1842],{"className":52397},[259,298],[128,52399,347],{"className":52400},[346],[128,52402,52404],{"className":52403},[278],[128,52405,52407],{"className":52406,"style":11919},[282],[128,52408],{},[128,52410],{"className":52411},[1928,5570],[128,52413],{"className":52414,"style":2508},[269],[128,52416,9486],{"className":52417},[2115],[128,52419],{"className":52420,"style":2508},[269],[128,52422,52424,52427,52430,52433,52468],{"className":52423},[250],[128,52425],{"className":52426,"style":23130},[254],[128,52428,13986],{"className":52429,"style":14008},[259,1873],[128,52431,2477],{"className":52432},[1896],[128,52434,52436,52439],{"className":52435},[259],[128,52437,21],{"className":52438},[259,1873],[128,52440,52442],{"className":52441},[2087],[128,52443,52445],{"className":52444},[274],[128,52446,52448],{"className":52447},[278],[128,52449,52451],{"className":52450,"style":9629},[282],[128,52452,52453,52456],{"style":2452},[128,52454],{"className":52455,"style":291},[290],[128,52457,52459],{"className":52458},[299,300,301,298],[128,52460,52462,52465],{"className":52461},[259,298],[128,52463,1989],{"className":52464},[259,298],[128,52466,2639],{"className":52467},[259,298],[128,52469,2486],{"className":52470},[1928]," 给出，而 ",[128,52473,52475,52497],{"className":52474,"translate":218},[217],[128,52476,52478],{"className":52477},[222],[224,52479,52480],{"xmlns":226},[228,52481,52482,52494],{},[231,52483,52484,52490,52492],{},[2016,52485,52486,52488],{},[1795,52487,4835],{},[1795,52489,1830],{},[1832,52491,23023],{},[1795,52493,41957],{},[238,52495,52496],{"encoding":240},"\\alpha_y \\le S",[128,52498,52500,52556],{"className":52499,"ariaHidden":246},[245],[128,52501,52503,52507,52547,52550,52553],{"className":52502},[250],[128,52504],{"className":52505,"style":52506},[254],"height:0.9221em;vertical-align:-0.2861em;",[128,52508,52510,52513],{"className":52509},[259],[128,52511,4835],{"className":52512,"style":4920},[259,1873],[128,52514,52516],{"className":52515},[2087],[128,52517,52519,52539],{"className":52518},[274,321],[128,52520,52522,52536],{"className":52521},[278],[128,52523,52525],{"className":52524,"style":28738},[282],[128,52526,52527,52530],{"style":4935},[128,52528],{"className":52529,"style":291},[290],[128,52531,52533],{"className":52532},[299,300,301,298],[128,52534,1830],{"className":52535,"style":1874},[259,1873,298],[128,52537,347],{"className":52538},[346],[128,52540,52542],{"className":52541},[278],[128,52543,52545],{"className":52544,"style":17424},[282],[128,52546],{},[128,52548],{"className":52549,"style":1878},[269],[128,52551,23023],{"className":52552},[1882],[128,52554],{"className":52555,"style":1878},[269],[128,52557,52559,52562],{"className":52558},[250],[128,52560],{"className":52561,"style":283},[254],[128,52563,41957],{"className":52564,"style":42029},[259,1873]," 保证修正项非负。",[11,52567,52568,52569,52572,52573,52601],{},"推论 4.2 揭示了一个在文献中常被忽略的事实：",[35,52570,52571],{},"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 ",[128,52574,52576,52589],{"className":52575,"translate":218},[217],[128,52577,52579],{"className":52578},[222],[224,52580,52581],{"xmlns":226},[228,52582,52583,52587],{},[231,52584,52585],{},[1795,52586,41957],{},[238,52588,41957],{"encoding":240},[128,52590,52592],{"className":52591,"ariaHidden":246},[245],[128,52593,52595,52598],{"className":52594},[250],[128,52596],{"className":52597,"style":283},[254],[128,52599,41957],{"className":52600,"style":42029},[259,1873]," 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。",[2610,52603,52605],{"id":52604},"_42-平方损失的贝叶斯风险","4.2 平方损失的贝叶斯风险",[11,52607,52608],{},"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。",[2615,52610,52612],{"title":52611},"命题 4.3（平方风险的闭式）",[11,52613,1781,52614,52643,52644],{},[128,52615,52617,52631],{"className":52616,"translate":218},[217],[128,52618,52620],{"className":52619},[222],[224,52621,52622],{"xmlns":226},[228,52623,52624,52628],{},[231,52625,52626],{},[1795,52627,1830],{"mathvariant":2001},[238,52629,52630],{"encoding":240},"\\mathbf{y}",[128,52632,52634],{"className":52633,"ariaHidden":246},[245],[128,52635,52637,52640],{"className":52636},[250],[128,52638],{"className":52639,"style":2564},[254],[128,52641,1830],{"className":52642,"style":31116},[259,2151]," 为 one-hot 标签，则\n",[128,52645,52647,52772],{"className":52646,"translate":218},[217],[128,52648,52650],{"className":52649},[222],[224,52651,52652],{"xmlns":226},[228,52653,52654,52769],{},[231,52655,52656,52663,52665,52671,52691,52693,52707],{},[1977,52657,52658,52660],{},[1795,52659,265],{"mathvariant":1797},[234,52661,52662],{},"MSE",[1832,52664,1994],{},[2016,52666,52667,52669],{},[1795,52668,342],{"mathvariant":2008},[1795,52670,26389],{"mathvariant":4834},[231,52672,52673,52675,52677,52679,52681,52683,52689],{},[1832,52674,16538],{"fence":246},[1795,52676,23006],{"mathvariant":1981},[1795,52678,1830],{"mathvariant":2001},[1832,52680,1989],{},[1795,52682,26389],{"mathvariant":4834},[1977,52684,52685,52687],{},[1795,52686,23006],{"mathvariant":1981},[1840,52688,2639],{},[1832,52690,16547],{"fence":246},[1832,52692,1994],{},[2038,52694,52695,52697,52705],{},[1832,52696,2042],{},[231,52698,52699,52701,52703],{},[1795,52700,2022],{},[1832,52702,1994],{},[1840,52704,1842],{},[1795,52706,1853],{},[231,52708,52709,52711,52713,52719,52721,52727,52733,52735,52767],{},[1832,52710,16538],{"fence":246},[1832,52712,2477],{"stretchy":1837},[2016,52714,52715,52717],{},[1795,52716,1830],{},[1795,52718,2022],{},[1832,52720,1989],{},[2016,52722,52723,52725],{},[1795,52724,11],{},[1795,52726,2022],{},[1977,52728,52729,52731],{},[1832,52730,2486],{"stretchy":1837},[1840,52732,2639],{},[1832,52734,9486],{},[5451,52736,52737,52759],{},[231,52738,52739,52745,52747,52749,52751,52757],{},[2016,52740,52741,52743],{},[1795,52742,11],{},[1795,52744,2022],{},[1832,52746,2477],{"stretchy":1837},[1840,52748,1842],{},[1832,52750,1989],{},[2016,52752,52753,52755],{},[1795,52754,11],{},[1795,52756,2022],{},[1832,52758,2486],{"stretchy":1837},[231,52760,52761,52763,52765],{},[1795,52762,41957],{},[1832,52764,9486],{},[1840,52766,1842],{},[1832,52768,16547],{"fence":246},[238,52770,52771],{"encoding":240},"\\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]",[128,52773,52775,52825,52960],{"className":52774,"ariaHidden":246},[245],[128,52776,52778,52781,52816,52819,52822],{"className":52777},[250],[128,52779],{"className":52780,"style":2431},[254],[128,52782,52784,52787],{"className":52783},[259],[128,52785,265],{"className":52786},[259,1813],[128,52788,52790],{"className":52789},[2087],[128,52791,52793],{"className":52792},[274],[128,52794,52796],{"className":52795},[278],[128,52797,52799],{"className":52798,"style":2431},[282],[128,52800,52801,52804],{"style":2452},[128,52802],{"className":52803,"style":291},[290],[128,52805,52807],{"className":52806},[299,300,301,298],[128,52808,52810],{"className":52809},[259,298],[128,52811,52813],{"className":52812},[259,260,298],[128,52814,52662],{"className":52815},[259,298],[128,52817],{"className":52818,"style":1878},[269],[128,52820,1994],{"className":52821},[1882],[128,52823],{"className":52824,"style":1878},[269],[128,52826,52828,52831,52880,52883,52951,52954,52957],{"className":52827},[250],[128,52829],{"className":52830,"style":46966},[254],[128,52832,52834,52837],{"className":52833},[259],[128,52835,342],{"className":52836},[259,2167],[128,52838,52840],{"className":52839},[2087],[128,52841,52843,52872],{"className":52842},[274,321],[128,52844,52846,52869],{"className":52845},[278],[128,52847,52849],{"className":52848,"style":22681},[282],[128,52850,52851,52854],{"style":2221},[128,52852],{"className":52853,"style":291},[290],[128,52855,52857],{"className":52856},[299,300,301,298],[128,52858,52860],{"className":52859},[259,298],[128,52861,52863],{"className":52862},[259,298],[128,52864,52866],{"className":52865},[259,298],[128,52867,26389],{"className":52868,"style":26423},[259,4895,298],[128,52870,347],{"className":52871},[346],[128,52873,52875],{"className":52874},[278],[128,52876,52878],{"className":52877,"style":2241},[282],[128,52879],{},[128,52881],{"className":52882,"style":1907},[269],[128,52884,52886,52892,52895,52898,52901,52904,52907,52916,52945],{"className":52885},[1911],[128,52887,52889],{"className":52888,"style":2142},[1896,2141],[128,52890,16538],{"className":52891},[2146,5795],[128,52893,23006],{"className":52894},[259],[128,52896,1830],{"className":52897,"style":31116},[259,2151],[128,52899],{"className":52900,"style":2508},[269],[128,52902,1989],{"className":52903},[2115],[128,52905],{"className":52906,"style":2508},[269],[128,52908,52910],{"className":52909},[259],[128,52911,52913],{"className":52912},[259],[128,52914,26389],{"className":52915,"style":26423},[259,4895],[128,52917,52919,52922],{"className":52918},[259],[128,52920,23006],{"className":52921},[259],[128,52923,52925],{"className":52924},[2087],[128,52926,52928],{"className":52927},[274],[128,52929,52931],{"className":52930},[278],[128,52932,52934],{"className":52933,"style":9629},[282],[128,52935,52936,52939],{"style":2452},[128,52937],{"className":52938,"style":291},[290],[128,52940,52942],{"className":52941},[299,300,301,298],[128,52943,2639],{"className":52944},[259,298],[128,52946,52948],{"className":52947,"style":2142},[1928,2141],[128,52949,16547],{"className":52950},[2146,5795],[128,52952],{"className":52953,"style":1878},[269],[128,52955,1994],{"className":52956},[1882],[128,52958],{"className":52959,"style":1878},[269],[128,52961,52963,52966,53026,53029],{"className":52962},[250],[128,52964],{"className":52965,"style":2134},[254],[128,52967,52969,52972],{"className":52968},[2268],[128,52970,2042],{"className":52971,"style":2274},[2268,2272,2273],[128,52973,52975],{"className":52974},[2087],[128,52976,52978,53018],{"className":52977},[274,321],[128,52979,52981,53015],{"className":52980},[278],[128,52982,52984,53004],{"className":52983,"style":2287},[282],[128,52985,52986,52989],{"style":2290},[128,52987],{"className":52988,"style":291},[290],[128,52990,52992],{"className":52991},[299,300,301,298],[128,52993,52995,52998,53001],{"className":52994},[259,298],[128,52996,2022],{"className":52997,"style":2231},[259,1873,298],[128,52999,1994],{"className":53000},[1882,298],[128,53002,1842],{"className":53003},[259,298],[128,53005,53006,53009],{"style":2311},[128,53007],{"className":53008,"style":291},[290],[128,53010,53012],{"className":53011},[299,300,301,298],[128,53013,1853],{"className":53014,"style":1924},[259,1873,298],[128,53016,347],{"className":53017},[346],[128,53019,53021],{"className":53020},[278],[128,53022,53024],{"className":53023,"style":2330},[282],[128,53025],{},[128,53027],{"className":53028,"style":1907},[269],[128,53030,53032,53038,53041,53081,53084,53087,53090,53130,53159,53162,53165,53168,53331],{"className":53031},[1911],[128,53033,53035],{"className":53034,"style":2142},[1896,2141],[128,53036,16538],{"className":53037},[2146,2147],[128,53039,2477],{"className":53040},[1896],[128,53042,53044,53047],{"className":53043},[259],[128,53045,1830],{"className":53046,"style":1874},[259,1873],[128,53048,53050],{"className":53049},[2087],[128,53051,53053,53073],{"className":53052},[274,321],[128,53054,530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逐项展开：",[128,53343,53345,53425],{"className":53344,"translate":218},[217],[128,53346,53348],{"className":53347},[222],[224,53349,53350],{"xmlns":226},[228,53351,53352,53422],{},[231,53353,53354,53356,53358,53360,53366,53368,53374,53380,53382,53384,53386,53392,53394,53400,53406,53408,53410,53412,53414,53420],{},[1795,53355,342],{"mathvariant":2008},[1832,53357,16538],{"stretchy":1837},[1832,53359,2477],{"stretchy":1837},[2016,53361,53362,53364],{},[1795,53363,1830],{},[1795,53365,2022],{},[1832,53367,1989],{},[2016,53369,53370,53372],{},[1795,53371,26389],{},[1795,53373,2022],{},[1977,53375,53376,53378],{},[1832,53377,2486],{"stretchy":1837},[1840,53379,2639],{},[1832,53381,16547],{"stretchy":1837},[1832,53383,1994],{},[1832,53385,2477],{"stretchy":1837},[2016,53387,53388,53390],{},[1795,53389,1830],{},[1795,53391,2022],{},[1832,53393,1989],{},[2016,53395,53396,53398],{},[1795,53397,11],{},[1795,53399,2022],{},[1977,53401,53402,53404],{},[1832,53403,2486],{"stretchy":1837},[1840,53405,2639],{},[1832,53407,9486],{},[1795,53409,16570],{"mathvariant":1981},[1832,53411,3278],{},[1832,53413,2477],{"stretchy":1837},[2016,53415,53416,53418],{},[1795,53417,26389],{},[1795,53419,2022],{},[1832,53421,2486],{"stretchy":1837},[238,53423,53424],{"encoding":240},"\\mathbb{E}[(y_k - \\pi_k)^2] = (y_k - p_k)^2 + \\operatorname{Var}(\\pi_k)",[128,53426,53428,53490,53577,53635,53719],{"className":53427,"ariaHidden":246},[245],[128,53429,53431,53434,53437,53441,53481,53484,53487],{"className":53430},[250],[128,53432],{"className":53433,"style":1892},[254],[128,53435,342],{"className":53436},[259,2167],[128,53438,53440],{"className":53439},[1896],"[(",[128,53442,53444,53447],{"className":53443},[259],[128,53445,1830],{"className":53446,"style":1874},[259,1873],[128,53448,53450],{"className":53449},[2087],[128,53451,53453,53473],{"className":53452},[274,321],[128,53454,53456,53470],{"className":53455},[278],[128,53457,53459],{"className":53458,"style":2218},[282],[128,53460,53461,53464],{"style":28741},[128,53462],{"className":53463,"style":291},[290],[128,53465,53467],{"className":53466},[299,300,301,298],[128,53468,2022],{"className":53469,"style":2231},[259,1873,298],[128,53471,347],{"className":53472},[346],[128,53474,53476],{"className":53475},[278],[128,53477,53479],{"className":53478,"style":2241},[282],[128,53480],{},[128,53482],{"className":53483,"style":2508},[269],[128,53485,1989],{"className":53486},[2115],[128,53488],{"className":53489,"style":2508},[269],[128,53491,53493,53496,53536,53565,53568,53571,53574],{"className":53492},[250],[128,53494],{"className":53495,"style":23130},[254],[128,53497,53499,53502],{"className":53498},[259],[128,53500,26389],{"className":53501,"style":1874},[259,1873],[128,53503,53505],{"className":53504},[2087],[128,53506,53508,53528],{"className":53507},[274,321],[128,53509,53511,53525],{"className":53510},[278],[128,53512,53514],{"className":53513,"style":2218},[282],[128,53515,53516,53519],{"style":28741},[128,53517],{"className":53518,"style":291},[290],[128,53520,53522],{"className":53521},[299,300,301,298],[128,53523,2022],{"className":53524,"style":2231},[259,1873,298],[128,53526,347],{"className":53527},[346],[128,53529,53531],{"className":53530},[278],[128,53532,53534],{"className":53533,"style":2241},[282],[128,53535],{},[128,53537,53539,53542],{"className":53538},[1928],[128,53540,2486],{"className":53541},[1928],[128,53543,53545],{"className":53544},[2087],[128,53546,53548],{"className":53547},[274],[128,53549,53551],{"className":53550},[278],[128,53552,53554],{"className":53553,"style":9629},[282],[128,53555,53556,53559],{"style":2452},[128,53557],{"className":53558,"style":291},[290],[128,53560,53562],{"className":53561},[299,300,301,298],[128,53563,2639],{"className":53564},[259,298],[128,53566,16547],{"className":53567},[1928],[128,53569],{"className":53570,"style":1878},[269],[128,53572,1994],{"className":53573},[1882],[128,53575],{"className":53576,"style":1878},[269],[128,53578,53580,53583,53586,53626,53629,53632],{"className":53579},[250],[128,53581],{"className":53582,"style":1892},[254],[128,53584,2477],{"className":53585},[1896],[128,53587,53589,53592],{"className":53588},[259],[128,53590,1830],{"className":53591,"style":1874},[259,1873],[128,53593,53595],{"className":53594},[2087],[128,53596,53598,53618],{"className":53597},[274,321],[128,53599,53601,53615],{"className":53600},[278],[128,53602,53604],{"className":53603,"style":2218},[282],[128,53605,53606,53609],{"style":28741},[128,53607],{"className":53608,"style":291},[290],[128,53610,53612],{"className":53611},[299,300,301,298],[128,53613,2022],{"className":53614,"style":2231},[259,1873,298],[128,53616,347],{"className":53617},[346],[128,53619,53621],{"className":53620},[278],[128,53622,53624],{"className":53623,"style":2241},[282],[128,53625],{},[128,53627],{"className":53628,"style":2508},[269],[128,53630,1989],{"className":53631},[2115],[128,53633],{"className":53634,"style":2508},[269],[128,53636,53638,53641,53681,53710,53713,53716],{"className":53637},[250],[128,53639],{"className":53640,"style":23130},[254],[128,53642,53644,53647],{"className":53643},[259],[128,53645,11],{"className":53646},[259,1873],[128,53648,53650],{"className":53649},[2087],[128,53651,53653,53673],{"className":53652},[274,321],[128,53654,53656,53670],{"className":53655},[278],[128,53657,53659],{"className":53658,"style":2218},[282],[128,53660,53661,53664],{"style":2221},[128,53662],{"className":53663,"style":291},[290],[128,53665,53667],{"className":53666},[299,300,301,298],[128,53668,2022],{"className":53669,"style":2231},[259,1873,298],[128,53671,347],{"className":53672},[346],[128,53674,53676],{"className":53675},[278],[128,53677,53679],{"className":53678,"style":2241},[282],[128,53680],{},[128,53682,53684,53687],{"className":53683},[1928],[128,53685,2486],{"className":53686},[1928],[128,53688,53690],{"className":53689},[2087],[128,53691,53693],{"className":53692},[274],[128,53694,53696],{"className":53695},[278],[128,53697,53699],{"className":53698,"style":9629},[282],[128,53700,53701,53704],{"style":2452},[128,53702],{"className":53703,"style":291},[290],[128,53705,53707],{"className":53706},[299,300,301,298],[128,53708,2639],{"className":53709},[259,298],[128,53711],{"className":53712,"style":2508},[269],[128,53714,9486],{"className":53715},[2115],[128,53717],{"className":53718,"style":2508},[269],[128,53720,53722,53725,53731,53734,53774],{"className":53721},[250],[128,53723],{"className":53724,"style":1892},[254],[128,53726,53728],{"className":53727},[2268],[128,53729,16570],{"className":53730},[259,3353],[128,53732,2477],{"className":53733},[1896],[128,53735,53737,53740],{"className":53736},[259],[128,53738,26389],{"className":53739,"style":1874},[259,1873],[128,53741,53743],{"className":53742},[2087],[128,53744,53746,53766],{"className":53745},[274,321],[128,53747,53749,53763],{"className":53748},[278],[128,53750,53752],{"className":53751,"style":2218},[282],[128,53753,53754,53757],{"style":28741},[128,53755],{"className":53756,"style":291},[290],[128,53758,53760],{"className":53759},[299,300,301,298],[128,53761,2022],{"className":53762,"style":2231},[259,1873,298],[128,53764,347],{"className":53765},[346],[128,53767,53769],{"className":53768},[278],[128,53770,53772],{"className":53771,"style":2241},[282],[128,53773],{},[128,53775,2486],{"className":53776},[1928],"。由命题 2.1，",[128,53779,53781,53885],{"className":53780,"translate":218},[217],[128,53782,53784],{"className":53783},[222],[224,53785,53786],{"xmlns":226},[228,53787,53788,53882],{},[231,53789,53790,53792,53794,53796,53802,53804,53806,53848,53850],{},[1795,53791,16570],{"mathvariant":1981},[1832,53793,3278],{},[1832,53795,2477],{"stretchy":1837},[2016,53797,53798,53800],{},[1795,53799,26389],{},[1795,53801,2022],{},[1832,53803,2486],{"stretchy":1837},[1832,53805,1994],{},[5451,53807,53808,53830],{},[231,53809,53810,53816,53818,53820,53822,53828],{},[2016,53811,53812,53814],{},[1795,53813,4835],{},[1795,53815,2022],{},[1832,53817,2477],{"stretchy":1837},[1795,53819,41957],{},[1832,53821,1989],{},[2016,53823,53824,53826],{},[1795,53825,4835],{},[1795,53827,2022],{},[1832,53829,2486],{"stretchy":1837},[231,53831,53832,53838,53840,53842,53844,53846],{},[1977,53833,53834,53836],{},[1795,53835,41957],{},[1840,53837,2639],{},[1832,53839,2477],{"stretchy":1837},[1795,53841,41957],{},[1832,53843,9486],{},[1840,53845,1842],{},[1832,53847,2486],{"stretchy":1837},[1832,53849,1994],{},[5451,53851,53852,53874],{},[231,53853,53854,53860,53862,53864,53866,53872],{},[2016,53855,53856,53858],{},[1795,53857,11],{},[1795,53859,2022],{},[1832,53861,2477],{"stretchy":1837},[1840,53863,1842],{},[1832,53865,1989],{},[2016,53867,53868,53870],{},[1795,53869,11],{},[1795,53871,2022],{},[1832,53873,2486],{"stretchy":1837},[231,53875,53876,53878,53880],{},[1795,53877,41957],{},[1832,53879,9486],{},[1840,53881,1842],{},[238,53883,53884],{"encoding":240},"\\operatorname{Var}(\\pi_k) = \\frac{\\alpha_k(S - \\alpha_k)}{S^2(S+1)} = \\frac{p_k(1-p_k)}{S+1}",[128,53886,53888,53955,54168],{"className":53887,"ariaHidden":246},[245],[128,53889,53891,53894,53900,53903,53943,53946,53949,53952],{"className":53890},[250],[128,53892],{"className":53893,"style":1892},[254],[128,53895,53897],{"className":53896},[2268],[128,53898,16570],{"className":53899},[259,3353],[128,53901,2477],{"className":53902},[1896],[128,53904,53906,53909],{"className":53905},[259],[128,53907,26389],{"className":53908,"style":1874},[259,1873],[128,53910,53912],{"className":53911},[2087],[128,53913,53915,53935],{"className":53914},[274,321],[128,53916,53918,53932],{"className":53917},[278],[128,53919,53921],{"className":53920,"style":2218},[282],[128,53922,53923,53926],{"style":28741},[128,53924],{"className":53925,"style":291},[290],[128,53927,53929],{"className":53928},[299,300,301,298],[128,53930,2022],{"className":53931,"style":2231},[259,1873,298],[128,53933,347],{"className":53934},[346],[128,53936,53938],{"className":53937},[278],[128,53939,53941],{"className":53940,"style":2241},[282],[128,53942],{},[128,53944,2486],{"className":53945},[1928],[128,53947],{"className":53948,"style":1878},[269],[128,53950,1994],{"className":53951},[1882],[128,53953],{"className":53954,"style":1878},[269],[128,53956,53958,53961,54159,54162,54165],{"className":53957},[250],[128,53959],{"className":53960,"style":19375},[254],[128,53962,53964,53967,54156],{"className":53963},[259],[128,53965],{"className":53966},[1896,5570],[128,53968,53970],{"className":53969},[5451],[128,53971,53973,54148],{"className":53972},[274,321],[128,53974,53976,54145],{"className":53975},[278],[128,53977,53979,54034,54042],{"className":53978,"style":17038},[282],[128,53980,53981,53984],{"style":5586},[128,53982],{"className":53983,"style":335},[290],[128,53985,53987],{"className":53986},[299,300,301,298],[128,53988,53990,54019,54022,54025,54028,54031],{"className":53989},[259,298],[128,53991,53993,53996],{"className":53992},[259,298],[128,53994,41957],{"className":53995,"style":42029},[259,1873,298],[128,53997,53999],{"className":53998},[2087],[128,54000,54002],{"className":54001},[274],[128,54003,54005],{"className":54004},[278],[128,54006,54008],{"className":54007,"style":27141},[282],[128,54009,54010,54013],{"style":6609},[128,54011],{"className":54012,"style":5790},[290],[128,54014,54016],{"className":54015},[299,5794,5795,298],[128,54017,2639],{"className":54018},[259,298],[128,54020,2477],{"className":54021},[1896,298],[128,54023,41957],{"className":54024,"style":42029},[259,1873,298],[128,54026,9486],{"className":54027},[2115,298],[128,54029,1842],{"className":54030},[259,298],[128,54032,2486],{"className":54033},[1928,298],[128,54035,54036,54039],{"style":5617},[128,54037],{"className":54038,"style":335},[290],[128,54040],{"className":54041,"style":5625},[5624],[128,54043,54044,54047],{"style":17167},[128,54045],{"className":54046,"style":335},[290],[128,54048,54050],{"className":54049},[299,300,301,298],[128,54051,54053,54093,54096,54099,54102,54142],{"className":54052},[259,298],[128,54054,54056,54059],{"className":54055},[259,298],[128,54057,4835],{"className":54058,"style":4920},[259,1873,298],[128,54060,54062],{"className":54061},[2087],[128,54063,54065,54085],{"className":54064},[274,321],[128,54066,54068,54082],{"className":54067},[278],[128,54069,54071],{"className":54070,"style":24117},[282],[128,54072,54073,54076],{"style":28939},[128,54074],{"className":54075,"style":5790},[290],[128,54077,54079],{"className":54078},[299,5794,5795,298],[128,54080,2022],{"className":54081,"style":2231},[259,1873,298],[128,54083,347],{"className":54084},[346],[128,54086,54088],{"className":54087},[278],[128,54089,54091],{"className":54090,"style":28958},[282],[128,54092],{},[128,54094,2477],{"className":54095},[1896,298],[128,54097,41957],{"className":54098,"style":42029},[259,1873,298],[128,54100,1989],{"className":54101},[2115,298],[128,54103,54105,54108],{"className":54104},[259,298],[128,54106,4835],{"className":54107,"style":4920},[259,1873,298],[128,54109,54111],{"className":54110},[2087],[128,54112,54114,54134],{"className":54113},[274,321],[128,54115,54117,54131],{"className":54116},[278],[128,54118,54120],{"className":54119,"style":24117},[282],[128,54121,54122,54125],{"style":28939},[128,54123],{"className":54124,"style":5790},[290],[128,54126,54128],{"className":54127},[299,5794,5795,298],[128,54129,2022],{"className":54130,"style":2231},[259,1873,298],[128,54132,347],{"className":54133},[346],[128,54135,54137],{"className":54136},[278],[128,54138,54140],{"className":54139,"style":28958},[282],[128,54141],{},[128,54143,2486],{"className":54144},[1928,298],[128,54146,347],{"className":54147},[346],[128,54149,54151],{"className":54150},[278],[128,54152,54154],{"className":54153,"style":5650},[282],[128,54155],{},[128,54157],{"className":54158},[1928,5570],[128,54160],{"className":54161,"style":1878},[269],[128,54163,1994],{"className":54164},[1882],[128,54166],{"className":54167,"style":1878},[269],[128,54169,54171,54175],{"className":54170},[250],[128,54172],{"className":54173,"style":54174},[254],"height:1.4133em;vertical-align:-0.4033em;",[128,54176,54178,54181,54335],{"className":54177},[259],[128,54179],{"className":54180},[1896,5570],[128,54182,54184],{"className":54183},[5451],[128,54185,54187,54327],{"className":54186},[274,321],[128,54188,54190,54324],{"className":54189},[278],[128,54191,54193,54213,54221],{"className":54192,"style":17038},[282],[128,54194,54195,54198],{"style":5586},[128,54196],{"className":54197,"style":335},[290],[128,54199,54201],{"className":54200},[299,300,301,298],[128,54202,54204,54207,54210],{"className":54203},[259,298],[128,54205,41957],{"className":54206,"style":42029},[259,1873,298],[128,54208,9486],{"className":54209},[2115,298],[128,54211,1842],{"className":54212},[259,298],[128,54214,54215,54218],{"style":5617},[128,54216],{"className":54217,"style":335},[290],[128,54219],{"className":54220,"style":5625},[5624],[128,54222,54223,54226],{"style":17167},[128,54224],{"className":54225,"style":335},[290],[128,54227,54229],{"className":54228},[299,300,301,298],[128,54230,54232,54272,54275,54278,54281,54321],{"className":54231},[259,298],[128,54233,54235,54238],{"className":54234},[259,298],[128,54236,11],{"className":54237},[259,1873,298],[128,54239,54241],{"className":54240},[2087],[128,54242,54244,54264],{"className":54243},[274,321],[128,54245,54247,54261],{"className":54246},[278],[128,54248,54250],{"className":54249,"style":24117},[282],[128,54251,54252,54255],{"style":28984},[128,54253],{"className":54254,"style":5790},[290],[128,54256,54258],{"className":54257},[299,5794,5795,298],[128,54259,2022],{"className":54260,"style":2231},[259,1873,298],[128,54262,347],{"className":54263},[346],[128,54265,54267],{"className":54266},[278],[128,54268,54270],{"className":54269,"style":28958},[282],[128,54271],{},[128,54273,2477],{"className":54274},[1896,298],[128,54276,1842],{"className":54277},[259,298],[128,54279,1989],{"className":54280},[2115,298],[128,54282,54284,54287],{"className":54283},[259,298],[128,54285,11],{"className":54286},[259,1873,298],[128,54288,54290],{"className":54289},[2087],[128,54291,54293,54313],{"className":54292},[274,321],[128,54294,54296,54310],{"className":54295},[278],[128,54297,54299],{"className":54298,"style":24117},[282],[128,54300,54301,54304],{"style":28984},[128,54302],{"className":54303,"style":5790},[290],[128,54305,54307],{"className":54306},[299,5794,5795,298],[128,54308,2022],{"className":54309,"style":2231},[259,1873,298],[128,54311,347],{"className":54312},[346],[128,54314,54316],{"className":54315},[278],[128,54317,54319],{"className":54318,"style":28958},[282],[128,54320],{},[128,54322,2486],{"className":54323},[1928,298],[128,54325,347],{"className":54326},[346],[128,54328,54330],{"className":54329},[278],[128,54331,54333],{"className":54332,"style":47989},[282],[128,54334],{},[128,54336],{"className":54337},[1928,5570],"。求和即得。",[11,54340,54341,54342,54345,54346,54416,54417,54420,54421,54569,54570,54621],{},"该损失的两项具有不同的角色。",[35,54343,54344],{},"第一项是拟合项","：在 ",[128,54347,54349,54367],{"className":54348,"translate":218},[217],[128,54350,54352],{"className":54351},[222],[224,54353,54354],{"xmlns":226},[228,54355,54356,54364],{},[231,54357,54358],{},[2016,54359,54360,54362],{},[1795,54361,11],{},[1795,54363,2022],{},[238,54365,54366],{"encoding":240},"p_k",[128,54368,54370],{"className":54369,"ariaHidden":246},[245],[128,54371,54373,54376],{"className":54372},[250],[128,54374],{"className":54375,"style":11158},[254],[128,54377,54379,54382],{"className":54378},[259],[128,54380,11],{"className":54381},[259,1873],[128,54383,54385],{"className":54384},[2087],[128,54386,54388,54408],{"className":54387},[274,321],[128,54389,54391,54405],{"className":54390},[278],[128,54392,54394],{"className":54393,"style":2218},[282],[128,54395,54396,54399],{"style":2221},[128,54397],{"className":54398,"style":291},[290],[128,54400,54402],{"className":54401},[299,300,301,298],[128,54403,2022],{"className":54404,"style":2231},[259,1873,298],[128,54406,347],{"className":54407},[346],[128,54409,54411],{"className":54410},[278],[128,54412,54414],{"className":54413,"style":2241},[282],[128,54415],{}," 退化为确定性预测时，它退化为 one-hot 编码下的均方误差。",[35,54418,54419],{},"第二项是方差惩罚项","：它正比于每个分量的伯努利方差 ",[128,54422,54424,54456],{"className":54423,"translate":218},[217],[128,54425,54427],{"className":54426},[222],[224,54428,54429],{"xmlns":226},[228,54430,54431,54453],{},[231,54432,54433,54439,54441,54443,54445,54451],{},[2016,54434,54435,54437],{},[1795,54436,11],{},[1795,54438,2022],{},[1832,54440,2477],{"stretchy":1837},[1840,54442,1842],{},[1832,54444,1989],{},[2016,54446,54447,54449],{},[1795,54448,11],{},[1795,54450,2022],{},[1832,54452,2486],{"stretchy":1837},[238,54454,54455],{"encoding":240},"p_k(1-p_k)",[128,54457,54459,54520],{"className":54458,"ariaHidden":246},[245],[128,54460,54462,54465,54505,54508,54511,54514,54517],{"className":54461},[250],[128,54463],{"className":54464,"style":1892},[254],[128,54466,54468,54471],{"className":54467},[259],[128,54469,11],{"className":54470},[259,1873],[128,54472,54474],{"className":54473},[2087],[128,54475,54477,54497],{"className":54476},[274,321],[128,54478,54480,54494],{"className":54479},[278],[128,54481,54483],{"className":54482,"style":2218},[282],[128,54484,54485,54488],{"style":2221},[128,54486],{"className":54487,"style":291},[290],[128,54489,54491],{"className":54490},[299,300,301,298],[128,54492,2022],{"className":54493,"style":2231},[259,1873,298],[128,54495,347],{"className":54496},[346],[128,54498,54500],{"className":54499},[278],[128,54501,54503],{"className":54502,"style":2241},[282],[128,54504],{},[128,54506,2477],{"className":54507},[1896],[128,54509,1842],{"className":54510},[259],[128,54512],{"className":54513,"style":2508},[269],[128,54515,1989],{"className":54516},[2115],[128,54518],{"className":54519,"style":2508},[269],[128,54521,54523,54526,54566],{"className":54522},[250],[128,54524],{"className":54525,"style":1892},[254],[128,54527,54529,54532],{"className":54528},[259],[128,54530,11],{"className":54531},[259,1873],[128,54533,54535],{"className":54534},[2087],[128,54536,54538,54558],{"className":54537},[274,321],[128,54539,54541,54555],{"className":54540},[278],[128,54542,54544],{"className":54543,"style":2218},[282],[128,54545,54546,54549],{"style":2221},[128,54547],{"className":54548,"style":291},[290],[128,54550,54552],{"className":54551},[299,300,301,298],[128,54553,2022],{"className":54554,"style":2231},[259,1873,298],[128,54556,347],{"className":54557},[346],[128,54559,54561],{"className":54560},[278],[128,54562,54564],{"className":54563,"style":2241},[282],[128,54565],{},[128,54567,2486],{"className":54568},[1928],"，反比于总证据 ",[128,54571,54573,54591],{"className":54572,"translate":218},[217],[128,54574,54576],{"className":54575},[222],[224,54577,54578],{"xmlns":226},[228,54579,54580,54588],{},[231,54581,54582,54584,54586],{},[1795,54583,41957],{},[1832,54585,9486],{},[1840,54587,1842],{},[238,54589,54590],{"encoding":240},"S + 1",[128,54592,54594,54612],{"className":54593,"ariaHidden":246},[245],[128,54595,54597,54600,54603,54606,54609],{"className":54596},[250],[128,54598],{"className":54599,"style":2705},[254],[128,54601,41957],{"className":54602,"style":42029},[259,1873],[128,54604],{"className":54605,"style":2508},[269],[128,54607,9486],{"className":54608},[2115],[128,54610],{"className":54611,"style":2508},[269],[128,54613,54615,54618],{"className":54614},[250],[128,54616],{"className":54617,"style":2594},[254],[128,54619,1842],{"className":54620},[259],"。其作用是双重的：",[33248,54623,54624,54660],{},[33251,54625,54626,54627,54655,54656,54659],{},"当证据稀缺（",[128,54628,54630,54643],{"className":54629,"translate":218},[217],[128,54631,54633],{"className":54632},[222],[224,54634,54635],{"xmlns":226},[228,54636,54637,54641],{},[231,54638,54639],{},[1795,54640,41957],{},[238,54642,41957],{"encoding":240},[128,54644,54646],{"className":54645,"ariaHidden":246},[245],[128,54647,54649,54652],{"className":54648},[250],[128,54650],{"className":54651,"style":283},[254],[128,54653,41957],{"className":54654,"style":42029},[259,1873]," 小）时，方差项较大，迫使模型",[35,54657,54658],{},"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。",[33251,54661,54662,54663,11072,54691,54760,54761,54789],{},"当证据变化时，",[128,54664,54666,54679],{"className":54665,"translate":218},[217],[128,54667,54669],{"className":54668},[222],[224,54670,54671],{"xmlns":226},[228,54672,54673,54677],{},[231,54674,54675],{},[1795,54676,41957],{},[238,54678,41957],{"encoding":240},[128,54680,54682],{"className":54681,"ariaHidden":246},[245],[128,54683,54685,54688],{"className":54684},[250],[128,54686],{"className":54687,"style":283},[254],[128,54689,41957],{"className":54690,"style":42029},[259,1873],[128,54692,54694,54711],{"className":54693,"translate":218},[217],[128,54695,54697],{"className":54696},[222],[224,54698,54699],{"xmlns":226},[228,54700,54701,54709],{},[231,54702,54703],{},[2016,54704,54705,54707],{},[1795,54706,11],{},[1795,54708,2022],{},[238,54710,54366],{"encoding":240},[128,54712,54714],{"className":54713,"ariaHidden":246},[245],[128,54715,54717,54720],{"className":54716},[250],[128,54718],{"className":54719,"style":11158},[254],[128,54721,54723,54726],{"className":54722},[259],[128,54724,11],{"className":54725},[259,1873],[128,54727,54729],{"className":54728},[2087],[128,54730,54732,54752],{"className":54731},[274,321],[128,54733,54735,54749],{"className":54734},[278],[128,54736,54738],{"className":54737,"style":2218},[282],[128,54739,54740,54743],{"style":2221},[128,54741],{"className":54742,"style":291},[290],[128,54744,54746],{"className":54745},[299,300,301,298],[128,54747,2022],{"className":54748,"style":2231},[259,1873,298],[128,54750,347],{"className":54751},[346],[128,54753,54755],{"className":54754},[278],[128,54756,54758],{"className":54757,"style":2241},[282],[128,54759],{}," 同时进入两项，形成张力：增大 ",[128,54762,54764,54777],{"className":54763,"translate":218},[217],[128,54765,54767],{"className":54766},[222],[224,54768,54769],{"xmlns":226},[228,54770,54771,54775],{},[231,54772,54773],{},[1795,54774,41957],{},[238,54776,41957],{"encoding":240},[128,54778,54780],{"className":54779,"ariaHidden":246},[245],[128,54781,54783,54786],{"className":54782},[250],[128,54784],{"className":54785,"style":283},[254],[128,54787,41957],{"className":54788,"style":42029},[259,1873]," 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。",[2610,54791,54793],{"id":54792},"_43-证据正则化与退火-kl","4.3 证据正则化与退火 KL",[11,54795,54796,54797,54800,54801,54878,54879,54882],{},"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",[35,54798,54799],{},"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 ",[128,54802,54804,54828],{"className":54803,"translate":218},[217],[128,54805,54807],{"className":54806},[222],[224,54808,54809],{"xmlns":226},[228,54810,54811,54825],{},[231,54812,54813,54819,54821,54823],{},[1977,54814,54815,54817],{},[1795,54816,24404],{},[1832,54818,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},[1832,54820,2477],{"stretchy":1837},[1795,54822,41957],{},[1832,54824,2486],{"stretchy":1837},[238,54826,54827],{"encoding":240},"\\psi'(S)",[128,54829,54831],{"className":54830,"ariaHidden":246},[245],[128,54832,54834,54837,54869,54872,54875],{"className":54833},[250],[128,54835],{"className":54836,"style":24908},[254],[128,54838,54840,54843],{"className":54839},[259],[128,54841,24404],{"className":54842,"style":1874},[259,1873],[128,54844,54846],{"className":54845},[2087],[128,54847,54849],{"className":54848},[274],[128,54850,54852],{"className":54851},[278],[128,54853,54855],{"className":54854,"style":24927},[282],[128,54856,54857,54860],{"style":2452},[128,54858],{"className":54859,"style":291},[290],[128,54861,54863],{"className":54862},[299,300,301,298],[128,54864,54866],{"className":54865},[259,298],[128,54867,24873],{"className":54868},[259,298],[128,54870,2477],{"className":54871},[1896],[128,54873,41957],{"className":54874,"style":42029},[259,1873],[128,54876,2486],{"className":54877},[1928]," 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：",[35,54880,54881],{},"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。",[11,54884,54885],{},"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。",[2615,54887,54889],{"title":54888},"定义 4.4（反事实参数与证据正则）",[11,54890,54891,54892,55073,55074,55102,55103],{},"令 ",[128,54893,54895,54936],{"className":54894,"translate":218},[217],[128,54896,54898],{"className":54897},[222],[224,54899,54900],{"xmlns":226},[228,54901,54902,54933],{},[231,54903,54904,54912,54914,54916,54918,54920,54922,54924,54926,54928,54931],{},[54905,54906,54907,54909],"mover",{"accent":246},[1795,54908,4835],{"mathvariant":4834},[1832,54910,54911],{},"~",[1832,54913,1994],{},[1795,54915,1830],{"mathvariant":2001},[1832,54917,9486],{},[1832,54919,2477],{"stretchy":1837},[1840,54921,1842],{"mathvariant":2001},[1832,54923,1989],{},[1795,54925,1830],{"mathvariant":2001},[1832,54927,2486],{"stretchy":1837},[1832,54929,54930],{},"⊙",[1795,54932,4835],{"mathvariant":4834},[238,54934,54935],{"encoding":240},"\\tilde{\\boldsymbol{\\alpha}} = \\mathbf{y} + (\\mathbf{1} - \\mathbf{y}) \\odot \\boldsymbol{\\alpha}",[128,54937,54939,54997,55016,55037,55058],{"className":54938,"ariaHidden":246},[245],[128,54940,54942,54946,54988,54991,54994],{"className":54941},[250],[128,54943],{"className":54944,"style":54945},[254],"height:0.6813em;",[128,54947,54950],{"className":54948},[259,54949],"accent",[128,54951,54953],{"className":54952},[274],[128,54954,54956],{"className":54955},[278],[128,54957,54959,54974],{"className":54958,"style":54945},[282],[128,54960,54962,54965],{"style":54961},"top:-3em;",[128,54963],{"className":54964,"style":335},[290],[128,54966,54968],{"className":54967},[259],[128,54969,54971],{"className":54970},[259],[128,54972,4835],{"className":54973},[259,4895],[128,54975,54977,54980],{"style":54976},"top:-3.3634em;",[128,54978],{"className":54979,"style":335},[290],[128,54981,54985],{"className":54982,"style":54984},[54983],"accent-body","left:-0.25em;",[128,54986,54911],{"className":54987},[259],[128,54989],{"className":54990,"style":1878},[269],[128,54992,1994],{"className":54993},[1882],[128,54995],{"className":54996,"style":1878},[269],[128,54998,55000,55004,55007,55010,55013],{"className":54999},[250],[128,55001],{"className":55002,"style":55003},[254],"height:0.7778em;vertical-align:-0.1944em;",[128,55005,1830],{"className":55006,"style":31116},[259,2151],[128,55008],{"className":55009,"style":2508},[269],[128,55011,9486],{"className":55012},[2115],[128,55014],{"className":55015,"style":2508},[269],[128,55017,55019,55022,55025,55028,55031,55034],{"className":55018},[250],[128,55020],{"className":55021,"style":1892},[254],[128,55023,2477],{"className":55024},[1896],[128,55026,1842],{"className":55027},[259,2151],[128,55029],{"className":55030,"style":2508},[269],[128,55032,1989],{"className":55033},[2115],[128,55035],{"className":55036,"style":2508},[269],[128,55038,55040,55043,55046,55049,55052,55055],{"className":55039},[250],[128,55041],{"className":55042,"style":1892},[254],[128,55044,1830],{"className":55045,"style":31116},[259,2151],[128,55047,2486],{"className":55048},[1928],[128,55050],{"className":55051,"style":2508},[269],[128,55053,54930],{"className":55054},[2115],[128,55056],{"className":55057,"style":2508},[269],[128,55059,55061,55064],{"className":55060},[250],[128,55062],{"className":55063,"style":4439},[254],[128,55065,55067],{"className":55066},[259],[128,55068,55070],{"className":55069},[259],[128,55071,4835],{"className":55072},[259,4895],"，即把真实类别处的参数置为 ",[128,55075,55077,55090],{"className":55076,"translate":218},[217],[128,55078,55080],{"className":55079},[222],[224,55081,55082],{"xmlns":226},[228,55083,55084,55088],{},[231,55085,55086],{},[1840,55087,1842],{},[238,55089,1842],{"encoding":240},[128,55091,55093],{"className":55092,"ariaHidden":246},[245],[128,55094,55096,55099],{"className":55095},[250],[128,55097],{"className":55098,"style":2594},[254],[128,55100,1842],{"className":55101},[259],"、其余保持不变。证据正则项定义为\n",[128,55104,55106,55168],{"className":55105,"translate":218},[217],[128,55107,55109],{"className":55108},[222],[224,55110,55111],{"xmlns":226},[228,55112,55113,55165],{},[231,55114,55115,55122,55124,55127,55129],{},[1977,55116,55117,55119],{},[1795,55118,265],{"mathvariant":1797},[234,55120,55121],{},"reg",[1832,55123,1994],{},[1795,55125,55126],{"mathvariant":1981},"KL",[1832,55128,3278],{},[231,55130,55131,55133,55135,55137,55139,55145,55147,55149,55151,55153,55155,55157,55159,55161,55163],{},[1832,55132,16538],{"fence":246},[1795,55134,5914],{"mathvariant":1981},[1832,55136,3278],{},[1832,55138,2477],{"stretchy":1837},[54905,55140,55141,55143],{"accent":246},[1795,55142,4835],{"mathvariant":4834},[1832,55144,54911],{},[1832,55146,2486],{"stretchy":1837},[234,55148,6528],{},[1832,55150,23006],{"fence":1837,"stretchy":246,"minsize":46539,"maxsize":46539},[234,55152,6528],{},[1795,55154,5914],{"mathvariant":1981},[1832,55156,3278],{},[1832,55158,2477],{"stretchy":1837},[1840,55160,1842],{"mathvariant":2001},[1832,55162,2486],{"stretchy":1837},[1832,55164,16547],{"fence":246},[238,55166,55167],{"encoding":240},"\\mathcal{L}^{\\text{reg}} = \\operatorname{KL}\\left[\\operatorname{Dir}(\\tilde{\\boldsymbol{\\alpha}}) \\,\\big\\|\\, \\operatorname{Dir}(\\mathbf{1})\\right]",[128,55169,55171,55221],{"className":55170,"ariaHidden":246},[245],[128,55172,55174,55177,55212,55215,55218],{"className":55173},[250],[128,55175],{"className":55176,"style":283},[254],[128,55178,55180,55183],{"className":55179},[259],[128,55181,265],{"className":55182},[259,1813],[128,55184,55186],{"className":55185},[2087],[128,55187,55189],{"className":55188},[274],[128,55190,55192],{"className":55191},[278],[128,55193,55195],{"className":55194,"style":39307},[282],[128,55196,55197,55200],{"style":2452},[128,55198],{"className":55199,"style":291},[290],[128,55201,55203],{"className":55202},[299,300,301,298],[128,55204,55206],{"className":55205},[259,298],[128,55207,55209],{"className":55208},[259,260,298],[128,55210,55121],{"className":55211},[259,298],[128,55213],{"className":55214,"style":1878},[269],[128,55216,1994],{"className":55217},[1882],[128,55219],{"className":55220,"style":1878},[269],[128,55222,55224,55227,55233,55236],{"className":55223},[250],[128,55225],{"className":55226,"style":46966},[254],[128,55228,55230],{"className":55229},[2268],[128,55231,55126],{"className":55232},[259,3353],[128,55234],{"className":55235,"style":1907},[269],[128,55237,55239,55245,55251,55254,55291,55294,55297,55343,55346,55349,55355,55358,55361,55364],{"className":55238},[1911],[128,55240,55242],{"className":55241,"style":2142},[1896,2141],[128,55243,16538],{"className":55244},[2146,5795],[128,55246,55248],{"className":55247},[2268],[128,55249,5914],{"className":55250},[259,3353],[128,55252,2477],{"className":55253},[1896],[128,55255,55257],{"className":55256},[259,54949],[128,55258,55260],{"className":55259},[274],[128,55261,55263],{"className":55262},[278],[128,55264,55266,55280],{"className":55265,"style":54945},[282],[128,55267,55268,55271],{"style":54961},[128,55269],{"className":55270,"style":335},[290],[128,55272,55274],{"className":55273},[259],[128,55275,55277],{"className":55276},[259],[128,55278,4835],{"className":55279},[259,4895],[128,55281,55282,55285],{"style":54976},[128,55283],{"className":55284,"style":335},[290],[128,55286,55288],{"className":55287,"style":54984},[54983],[128,55289,54911],{"className":55290},[259],[128,55292,2486],{"className":55293},[1928],[128,55295],{"className":55296,"style":1907},[269],[128,55298,55300],{"className":55299},[259],[128,55301,55304],{"className":55302},[2146,55303],"mult",[128,55305,55307,55334],{"className":55306},[274,321],[128,55308,55310,55331],{"className":55309},[278],[128,55311,55314],{"className":55312,"style":55313},[282],"height:0.85em;",[128,55315,55317,55321],{"style":55316},"top:-2.85em;",[128,55318],{"className":55319,"style":55320},[290],"height:3.2em;",[128,55322,55324],{"style":55323},"width:0.556em;height:1.2em;",[29411,55325,55328],{"xmlns":29413,"width":55326,"height":46539,"viewBox":55327},"0.556em","0 0 556 1200",[29419,55329],{"d":55330},"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",[128,55332,347],{"className":55333},[346],[128,55335,55337],{"className":55336},[278],[128,55338,55341],{"className":55339,"style":55340},[282],"height:0.35em;",[128,55342],{},[128,55344],{"className":55345,"style":1907},[269],[128,55347],{"className":55348,"style":1907},[269],[128,55350,55352],{"className":55351},[2268],[128,55353,5914],{"className":55354},[259,3353],[128,55356,2477],{"className":55357},[1896],[128,55359,1842],{"className":55360},[259,2151],[128,55362,2486],{"className":55363},[1928],[128,55365,55367],{"className":55366,"style":2142},[1928,2141],[128,55368,16547],{"className":55369},[2146,5795],[11,55371,55372,55373,55422,55423,55510],{},"注意 ",[128,55374,55376,55398],{"className":55375,"translate":218},[217],[128,55377,55379],{"className":55378},[222],[224,55380,55381],{"xmlns":226},[228,55382,55383,55395],{},[231,55384,55385,55387,55389,55391,55393],{},[1795,55386,5914],{"mathvariant":1981},[1832,55388,3278],{},[1832,55390,2477],{"stretchy":1837},[1840,55392,1842],{"mathvariant":2001},[1832,55394,2486],{"stretchy":1837},[238,55396,55397],{"encoding":240},"\\operatorname{Dir}(\\mathbf{1})",[128,55399,55401],{"className":55400,"ariaHidden":246},[245],[128,55402,55404,55407,55413,55416,55419],{"className":55403},[250],[128,55405],{"className":55406,"style":1892},[254],[128,55408,55410],{"className":55409},[2268],[128,55411,5914],{"className":55412},[259,3353],[128,55414,2477],{"className":55415},[1896],[128,55417,1842],{"className":55418},[259,2151],[128,55420,2486],{"className":55421},[1928]," 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，",[128,55424,55426,55452],{"className":55425,"translate":218},[217],[128,55427,55429],{"className":55428},[222],[224,55430,55431],{"xmlns":226},[228,55432,55433,55449],{},[231,55434,55435,55437,55439,55441,55447],{},[1795,55436,5914],{"mathvariant":1981},[1832,55438,3278],{},[1832,55440,2477],{"stretchy":1837},[54905,55442,55443,55445],{"accent":246},[1795,55444,4835],{"mathvariant":4834},[1832,55446,54911],{},[1832,55448,2486],{"stretchy":1837},[238,55450,55451],{"encoding":240},"\\operatorname{Dir}(\\tilde{\\boldsymbol{\\alpha}})",[128,55453,55455],{"className":55454,"ariaHidden":246},[245],[128,55456,55458,55461,55467,55470,55507],{"className":55457},[250],[128,55459],{"className":55460,"style":1892},[254],[128,55462,55464],{"className":55463},[2268],[128,55465,5914],{"className":55466},[259,3353],[128,55468,2477],{"className":55469},[1896],[128,55471,55473],{"className":55472},[259,54949],[128,55474,55476],{"className":55475},[274],[128,55477,55479],{"className":55478},[278],[128,55480,55482,55496],{"className":55481,"style":54945},[282],[128,55483,55484,55487],{"style":54961},[128,55485],{"className":55486,"style":335},[290],[128,55488,55490],{"className":55489},[259],[128,55491,55493],{"className":55492},[259],[128,55494,4835],{"className":55495},[259,4895],[128,55497,55498,55501],{"style":54976},[128,55499],{"className":55500,"style":335},[290],[128,55502,55504],{"className":55503,"style":54984},[54983],[128,55505,54911],{"className":55506},[259],[128,55508,2486],{"className":55509},[1928]," 将显著偏离均匀分布，KL 随之增大。",[2615,55512,55514],{"title":55513},"命题 4.5（Dirichlet 的 KL 散度）",[11,55515,55516,55517,6464,55657,56343,56344,56401,56402,56488,56489],{},"对 ",[128,55518,55520,55552],{"className":55519,"translate":218},[217],[128,55521,55523],{"className":55522},[222],[224,55524,55525],{"xmlns":226},[228,55526,55527,55549],{},[231,55528,55529,55531,55533,55535,55537],{},[1795,55530,4835],{"mathvariant":4834},[1832,55532,1845],{"separator":246},[1795,55534,18848],{"mathvariant":4834},[1832,55536,1834],{},[2038,55538,55539,55541,55547],{},[1795,55540,2009],{"mathvariant":2008},[231,55542,55543,55545],{},[1832,55544,3321],{},[1840,55546,2028],{},[1795,55548,1853],{},[238,55550,55551],{"encoding":240},"\\boldsymbol{\\alpha}, \\boldsymbol{\\beta} \\in \\mathbb{R}_{>0}^K",[128,55553,55555,55594],{"className":55554,"ariaHidden":246},[245],[128,55556,55558,55561,55570,55573,55576,55585,55588,55591],{"className":55557},[250],[128,55559],{"className":55560,"style":16030},[254],[128,55562,55564],{"className":55563},[259],[128,55565,55567],{"className":55566},[259],[128,55568,4835],{"className":55569},[259,4895],[128,55571,1845],{"className":55572},[1903],[128,55574],{"className":55575,"style":1907},[269],[128,55577,55579],{"className":55578},[259],[128,55580,55582],{"className":55581},[259],[128,55583,18848],{"className":55584,"style":19091},[259,4895],[128,55586],{"className":55587,"style":1878},[269],[128,55589,1834],{"className":55590},[1882],[128,55592],{"className":55593,"style":1878},[269],[128,55595,55597,55600],{"className":55596},[250],[128,55598],{"className":55599,"style":5032},[254],[128,55601,55603,55606],{"className":55602},[259],[128,55604,2009],{"className":55605},[259,2167],[128,55607,55609],{"className":55608},[2087],[128,55610,55612,55649],{"className":55611},[274,321],[128,55613,55615,55646],{"className":55614},[278],[128,55616,55618,55635],{"className":55617,"style":2431},[282],[128,55619,55620,55623],{"style":5053},[128,55621],{"className":55622,"style":291},[290],[128,55624,55626],{"className":55625},[299,300,301,298],[128,55627,55629,55632],{"className":55628},[259,298],[128,55630,3321],{"className":55631},[1882,298],[128,55633,2028],{"className":55634},[259,298],[128,55636,55637,55640],{"style":2452},[128,55638],{"className":55639,"style":291},[290],[128,55641,55643],{"className":55642},[299,300,301,298],[128,55644,1853],{"className":55645,"style":1924},[259,1873,298],[128,55647,347],{"className":55648},[346],[128,55650,55652],{"className":55651},[278],[128,55653,55655],{"className":55654,"style":5089},[282],[128,55656],{},[128,55658,55660,55800],{"className":55659,"translate":218},[217],[128,55661,55663],{"className":55662},[222],[224,55664,55665],{"xmlns":226},[228,55666,55667,55797],{},[231,55668,55669,55671,55673,55705,55707,55709,55711,55733,55735,55749,55751,55757,55759,55765,55767,55769,55771,55773,55779,55781,55783,55785,55787,55793,55795],{},[1795,55670,55126],{"mathvariant":1981},[1832,55672,3278],{},[231,55674,55675,55677,55679,55681,55683,55685,55687,55689,55691,55693,55695,55697,55699,55701,55703],{},[1832,55676,16538],{"fence":246},[1795,55678,5914],{"mathvariant":1981},[1832,55680,3278],{},[1832,55682,2477],{"stretchy":1837},[1795,55684,4835],{"mathvariant":4834},[1832,55686,2486],{"stretchy":1837},[234,55688,6528],{},[1832,55690,23006],{"fence":1837,"stretchy":246,"minsize":46539,"maxsize":46539},[234,55692,6528],{},[1795,55694,5914],{"mathvariant":1981},[1832,55696,3278],{},[1832,55698,2477],{"stretchy":1837},[1795,55700,18848],{"mathvariant":4834},[1832,55702,2486],{"stretchy":1837},[1832,55704,16547],{"fence":246},[1832,55706,1994],{},[1795,55708,24373],{},[1832,55710,3278],{},[5451,55712,55713,55723],{},[231,55714,55715,55717,55719,55721],{},[1795,55716,5459],{},[1832,55718,2477],{"stretchy":1837},[1795,55720,18848],{"mathvariant":4834},[1832,55722,2486],{"stretchy":1837},[231,55724,55725,55727,55729,55731],{},[1795,55726,5459],{},[1832,55728,2477],{"stretchy":1837},[1795,55730,4835],{"mathvariant":4834},[1832,55732,2486],{"stretchy":1837},[1832,55734,9486],{},[2038,55736,55737,55739,55747],{},[1832,55738,2042],{},[231,55740,55741,55743,55745],{},[1795,55742,2022],{},[1832,55744,1994],{},[1840,55746,1842],{},[1795,55748,1853],{},[1832,55750,2477],{"stretchy":1837},[2016,55752,55753,55755],{},[1795,55754,4835],{},[1795,55756,2022],{},[1832,55758,1989],{},[2016,55760,55761,55763],{},[1795,55762,18848],{},[1795,55764,2022],{},[1832,55766,2486],{"stretchy":1837},[1832,55768,2477],{"fence":1837,"stretchy":246,"minsize":46539,"maxsize":46539},[1795,55770,24404],{},[1832,55772,2477],{"stretchy":1837},[2016,55774,55775,55777],{},[1795,55776,4835],{},[1795,55778,2022],{},[1832,55780,2486],{"stretchy":1837},[1832,55782,1989],{},[1795,55784,24404],{},[1832,55786,2477],{"stretchy":1837},[2016,55788,55789,55791],{},[1795,55790,4835],{},[1840,55792,2028],{},[1832,55794,2486],{"stretchy":1837},[1832,55796,2486],{"fence":1837,"stretchy":246,"minsize":46539,"maxsize":46539},[238,55798,55799],{"encoding":240},"\\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)",[128,55801,55803,55930,56051,56169,56282],{"className":55802,"ariaHidden":246},[245],[128,55804,55806,55809,55815,55818,55921,55924,55927],{"className":55805},[250],[128,55807],{"className":55808,"style":46966},[254],[128,55810,55812],{"className":55811},[2268],[128,55813,55126],{"className":55814},[259,3353],[128,55816],{"className":55817,"style":1907},[269],[128,55819,55821,55827,55833,55836,55845,55848,55851,55888,55891,55894,55900,55903,55912,55915],{"className":55820},[1911],[128,55822,55824],{"className":55823,"style":2142},[1896,2141],[128,55825,16538],{"className":55826},[2146,5795],[128,55828,55830],{"className":55829},[2268],[128,55831,5914],{"className":55832},[259,3353],[128,55834,2477],{"className":55835},[1896],[128,55837,55839],{"className":55838},[259],[128,55840,55842],{"className":55841},[259],[128,55843,4835],{"className":55844},[259,4895],[128,55846,2486],{"className":55847},[1928],[128,55849],{"className":55850,"style":1907},[269],[128,55852,55854],{"className":55853},[259],[128,55855,55857],{"className":55856},[2146,55303],[128,55858,55860,55880],{"className":55859},[274,321],[128,55861,55863,55877],{"className":55862},[278],[128,55864,55866],{"className":55865,"style":55313},[282],[128,55867,55868,55871],{"style":55316},[128,55869],{"className":55870,"style":55320},[290],[128,55872,55873],{"style":55323},[29411,55874,55875],{"xmlns":29413,"width":55326,"height":46539,"viewBox":55327},[29419,55876],{"d":55330},[128,55878,347],{"className":55879},[346],[128,55881,55883],{"className":55882},[278],[128,55884,55886],{"className":55885,"style":55340},[282],[128,55887],{},[128,55889],{"className":55890,"style":1907},[269],[128,55892],{"className":55893,"style":1907},[269],[128,55895,55897],{"className":55896},[2268],[128,55898,5914],{"className":55899},[259,3353],[128,55901,2477],{"className":55902},[1896],[128,55904,55906],{"className":55905},[259],[128,55907,55909],{"className":55908},[259],[128,55910,18848],{"className":55911,"style":19091},[259,4895],[128,55913,2486],{"className":55914},[1928],[128,55916,55918],{"className":55917,"style":2142},[1928,2141],[128,55919,16547],{"className":55920},[2146,5795],[128,55922],{"className":55923,"style":1878},[269],[128,55925,1994],{"className":55926},[1882],[128,55928],{"className":55929,"style":1878},[269],[128,55931,55933,55936,55941,55944,56042,56045,56048],{"className":55932},[250],[128,55934],{"className":55935,"style":19375},[254],[128,55937,24502,55939],{"className":55938},[2268],[128,55940,24505],{"style":17336},[128,55942],{"className":55943,"style":1907},[269],[128,55945,55947,55950,56039],{"className":55946},[259],[128,55948],{"className":55949},[1896,5570],[128,55951,55953],{"className":55952},[5451],[128,55954,55956,56031],{"className":55955},[274,321],[128,55957,55959,56028],{"className":55958},[278],[128,55960,55962,55991,55999],{"className":55961,"style":17038},[282],[128,55963,55964,55967],{"style":5586},[128,55965],{"className":55966,"style":335},[290],[128,55968,55970],{"className":55969},[299,300,301,298],[128,55971,55973,55976,55979,55988],{"className":55972},[259,298],[128,55974,5459],{"className":55975,"style":5599},[259,1873,298],[128,55977,2477],{"className":55978},[1896,298],[128,55980,55982],{"className":55981},[259,298],[128,55983,55985],{"className":55984},[259,298],[128,55986,4835],{"className":55987},[259,4895,298],[128,55989,2486],{"className":55990},[1928,298],[128,55992,55993,55996],{"style":5617},[128,55994],{"className":55995,"style":335},[290],[128,55997],{"className":55998,"style":5625},[5624],[128,56000,56001,56004],{"style":17167},[128,56002],{"className":56003,"style":335},[290],[128,56005,56007],{"className":56006},[299,300,301,298],[128,56008,56010,56013,56016,56025],{"className":56009},[259,298],[128,56011,5459],{"className":56012,"style":5599},[259,1873,298],[128,56014,2477],{"className":56015},[1896,298],[128,56017,56019],{"className":56018},[259,298],[128,56020,56022],{"className":56021},[259,298],[128,56023,18848],{"className":56024,"style":19091},[259,4895,298],[128,56026,2486],{"className":56027},[1928,298],[128,56029,347],{"className":56030},[346],[128,56032,56034],{"className":56033},[278],[128,56035,56037],{"className":56036,"style":5650},[282],[128,56038],{},[128,56040],{"className":56041},[1928,5570],[128,56043],{"className":56044,"style":2508},[269],[128,56046,9486],{"className":56047},[2115],[128,56049],{"className":56050,"style":2508},[269],[128,56052,56054,56057,56117,56120,56160,56163,56166],{"className":56053},[250],[128,56055],{"className":56056,"style":5200},[254],[128,56058,56060,56063],{"className":56059},[2268],[128,56061,2042],{"className":56062,"style":2274},[2268,2272,2273],[128,56064,56066],{"className":56065},[2087],[128,56067,56069,56109],{"className":56068},[274,321],[128,56070,56072,56106],{"className":56071},[278],[128,56073,56075,56095],{"className":56074,"style":2287},[282],[128,56076,56077,56080],{"style":2290},[128,56078],{"className":56079,"style":291},[290],[128,56081,56083],{"className":56082},[299,300,301,298],[128,56084,56086,56089,56092],{"className":56085},[259,298],[128,56087,2022],{"className":56088,"style":2231},[259,1873,298],[128,56090,1994],{"className":56091},[1882,298],[128,56093,1842],{"className":56094},[259,298],[128,56096,56097,56100],{"style":2311},[128,56098],{"className":56099,"style":291},[290],[128,56101,56103],{"className":56102},[299,300,301,298],[128,56104,1853],{"className":56105,"style":1924},[259,1873,298],[128,56107,347],{"className":56108},[346],[128,56110,56112],{"className":56111},[278],[128,56113,56115],{"className":56114,"style":2330},[282],[128,56116],{},[128,56118,2477],{"className":56119},[1896],[128,56121,56123,56126],{"className":56122},[259],[128,56124,4835],{"className":56125,"style":4920},[259,1873],[128,56127,56129],{"className":56128},[2087],[128,56130,56132,56152],{"className":56131},[274,321],[128,56133,56135,56149],{"className":56134},[278],[128,56136,56138],{"className":56137,"style":2218},[282],[128,56139,56140,56143],{"style":4935},[128,56141],{"className":56142,"style":291},[290],[128,56144,56146],{"className":56145},[299,300,301,298],[128,56147,2022],{"className":56148,"style":2231},[259,1873,298],[128,56150,347],{"className":56151},[346],[128,56153,56155],{"className":56154},[278],[128,56156,56158],{"className":56157,"style":2241},[282],[128,56159],{},[128,56161],{"className":56162,"style":2508},[269],[128,56164,1989],{"className":56165},[2115],[128,56167],{"className":56168,"style":2508},[269],[128,56170,56172,56175,56215,56218,56224,56227,56230,56270,56273,56276,56279],{"className":56171},[250],[128,56173],{"className":56174,"style":46966},[254],[128,56176,56178,56181],{"className":56177},[259],[128,56179,18848],{"className":56180,"style":18987},[259,1873],[128,56182,56184],{"className":56183},[2087],[128,56185,56187,56207],{"className":56186},[274,321],[128,56188,56190,56204],{"className":56189},[278],[128,56191,56193],{"className":56192,"style":2218},[282],[128,56194,56195,56198],{"style":19171},[128,56196],{"className":56197,"style":291},[290],[128,56199,56201],{"className":56200},[299,300,301,298],[128,56202,2022],{"className":56203,"style":2231},[259,1873,298],[128,56205,347],{"className":56206},[346],[128,56208,56210],{"className":56209},[278],[128,56211,56213],{"className":56212,"style":2241},[282],[128,56214],{},[128,56216,2486],{"className":56217},[1928],[128,56219,56221],{"className":56220},[259],[128,56222,2477],{"className":56223},[2146,5795],[128,56225,24404],{"className":56226,"style":1874},[259,1873],[128,56228,2477],{"className":56229},[1896],[128,56231,56233,56236],{"className":56232},[259],[128,56234,4835],{"className":56235,"style":4920},[259,1873],[128,56237,56239],{"className":56238},[2087],[128,56240,56242,56262],{"className":56241},[274,321],[128,56243,56245,56259],{"className":56244},[278],[128,56246,56248],{"className":56247,"style":2218},[282],[128,56249,56250,56253],{"style":4935},[128,56251],{"className":56252,"style":291},[290],[128,56254,56256],{"className":56255},[299,300,301,298],[128,56257,2022],{"className":56258,"style":2231},[259,1873,298],[128,56260,347],{"className":56261},[346],[128,56263,56265],{"className":56264},[278],[128,56266,56268],{"className":56267,"style":2241},[282],[128,56269],{},[128,56271,2486],{"className":56272},[1928],[128,56274],{"className":56275,"style":2508},[269],[128,56277,1989],{"className":56278},[2115],[128,56280],{"className":56281,"style":2508},[269],[128,56283,56285,56288,56291,56294,56334,56337],{"className":56284},[250],[128,56286],{"className":56287,"style":46966},[254],[128,56289,24404],{"className":56290,"style":1874},[259,1873],[128,56292,2477],{"className":56293},[1896],[128,56295,56297,56300],{"className":56296},[259],[128,56298,4835],{"className":56299,"style":4920},[259,1873],[128,56301,56303],{"className":56302},[2087],[128,56304,56306,56326],{"className":56305},[274,321],[128,56307,56309,56323],{"className":56308},[278],[128,56310,56312],{"className":56311,"style":2945},[282],[128,56313,56314,56317],{"style":4935},[128,56315],{"className":56316,"style":291},[290],[128,56318,56320],{"className":56319},[299,300,301,298],[128,56321,2028],{"className":56322},[259,298],[128,56324,347],{"className":56325},[346],[128,56327,56329],{"className":56328},[278],[128,56330,56332],{"className":56331,"style":2241},[282],[128,56333],{},[128,56335,2486],{"className":56336},[1928],[128,56338,56340],{"className":56339},[259],[128,56341,2486],{"className":56342},[2146,5795],"\n特别地，取 ",[128,56345,56347,56365],{"className":56346,"translate":218},[217],[128,56348,56350],{"className":56349},[222],[224,56351,56352],{"xmlns":226},[228,56353,56354,56362],{},[231,56355,56356,56358,56360],{},[1795,56357,18848],{"mathvariant":4834},[1832,56359,1994],{},[1840,56361,1842],{"mathvariant":2001},[238,56363,56364],{"encoding":240},"\\boldsymbol{\\beta} = \\mathbf{1}",[128,56366,56368,56392],{"className":56367,"ariaHidden":246},[245],[128,56369,56371,56374,56383,56386,56389],{"className":56370},[250],[128,56372],{"className":56373,"style":16030},[254],[128,56375,56377],{"className":56376},[259],[128,56378,56380],{"className":56379},[259],[128,56381,18848],{"className":56382,"style":19091},[259,4895],[128,56384],{"className":56385,"style":1878},[269],[128,56387,1994],{"className":56388},[1882],[128,56390],{"className":56391,"style":1878},[269],[128,56393,56395,56398],{"className":56394},[250],[128,56396],{"className":56397,"style":2594},[254],[128,56399,1842],{"className":56400},[259,2151],"（此时 ",[128,56403,56405,56439],{"className":56404,"translate":218},[217],[128,56406,56408],{"className":56407},[222],[224,56409,56410],{"xmlns":226},[228,56411,56412,56436],{},[231,56413,56414,56416,56418,56420,56422,56424,56426,56428,56430,56432,56434],{},[1795,56415,5459],{},[1832,56417,2477],{"stretchy":1837},[1840,56419,1842],{"mathvariant":2001},[1832,56421,2486],{"stretchy":1837},[1832,56423,1994],{},[1840,56425,1842],{},[1795,56427,4751],{"mathvariant":1981},[1795,56429,6020],{"mathvariant":1981},[1832,56431,2477],{"stretchy":1837},[1795,56433,1853],{},[1832,56435,2486],{"stretchy":1837},[238,56437,56438],{"encoding":240},"B(\\mathbf{1}) = 1\u002F\\Gamma(K)",[128,56440,56442,56469],{"className":56441,"ariaHidden":246},[245],[128,56443,56445,56448,56451,56454,56457,56460,56463,56466],{"className":56444},[250],[128,56446],{"className":56447,"style":1892},[254],[128,56449,5459],{"className":56450,"style":5599},[259,1873],[128,56452,2477],{"className":56453},[1896],[128,56455,1842],{"className":56456},[259,2151],[128,56458,2486],{"className":56459},[1928],[128,56461],{"className":56462,"style":1878},[269],[128,56464,1994],{"className":56465},[1882],[128,56467],{"className":56468,"style":1878},[269],[128,56470,56472,56475,56479,56482,56485],{"className":56471},[250],[128,56473],{"className":56474,"style":1892},[254],[128,56476,56478],{"className":56477},[259],"1\u002FΓ",[128,56480,2477],{"className":56481},[1896],[128,56483,1853],{"className":56484,"style":1924},[259,1873],[128,56486,2486],{"className":56487},[1928],"）得\n",[128,56490,56492,56654],{"className":56491,"translate":218},[217],[128,56493,56495],{"className":56494},[222],[224,56496,56497],{"xmlns":226},[228,56498,56499,56651],{},[231,56500,56501,56507,56509,56511,56513,56515,56517,56527,56529,56531,56545,56547,56549,56551,56553,56563,56565,56567,56569,56571,56573,56575,56577,56579,56581,56595,56597,56607,56609,56611,56613,56615,56617,56619,56629,56631,56633,56635,56637,56647,56649],{},[1977,56502,56503,56505],{},[1795,56504,265],{"mathvariant":1797},[234,56506,55121],{},[1832,56508,1994],{},[1795,56510,24373],{},[1832,56512,3278],{},[1795,56514,6020],{"mathvariant":1981},[1832,56516,2477],{"stretchy":1837},[2016,56518,56519,56525],{},[54905,56520,56521,56523],{"accent":246},[1795,56522,4835],{},[1832,56524,54911],{},[1840,56526,2028],{},[1832,56528,2486],{"stretchy":1837},[1832,56530,1989],{},[2038,56532,56533,56535,56543],{},[1832,56534,2042],{},[231,56536,56537,56539,56541],{},[1795,56538,2022],{},[1832,56540,1994],{},[1840,56542,1842],{},[1795,56544,1853],{},[1795,56546,24373],{},[1832,56548,3278],{},[1795,56550,6020],{"mathvariant":1981},[1832,56552,2477],{"stretchy":1837},[2016,56554,56555,56561],{},[54905,56556,56557,56559],{"accent":246},[1795,56558,4835],{},[1832,56560,54911],{},[1795,56562,2022],{},[1832,56564,2486],{"stretchy":1837},[1832,56566,1989],{},[1795,56568,24373],{},[1832,56570,3278],{},[1795,56572,6020],{"mathvariant":1981},[1832,56574,2477],{"stretchy":1837},[1795,56576,1853],{},[1832,56578,2486],{"stretchy":1837},[1832,56580,9486],{},[2038,56582,56583,56585,56593],{},[1832,56584,2042],{},[231,56586,56587,56589,56591],{},[1795,56588,2022],{},[1832,56590,1994],{},[1840,56592,1842],{},[1795,56594,1853],{},[1832,56596,2477],{"stretchy":1837},[2016,56598,56599,56605],{},[54905,56600,56601,56603],{"accent":246},[1795,56602,4835],{},[1832,56604,54911],{},[1795,56606,2022],{},[1832,56608,1989],{},[1840,56610,1842],{},[1832,56612,2486],{"stretchy":1837},[1832,56614,2477],{"fence":1837,"stretchy":246,"minsize":46539,"maxsize":46539},[1795,56616,24404],{},[1832,56618,2477],{"stretchy":1837},[2016,56620,56621,56627],{},[54905,56622,56623,56625],{"accent":246},[1795,56624,4835],{},[1832,56626,54911],{},[1795,56628,2022],{},[1832,56630,2486],{"stretchy":1837},[1832,56632,1989],{},[1795,56634,24404],{},[1832,56636,2477],{"stretchy":1837},[2016,56638,56639,56645],{},[54905,56640,56641,56643],{"accent":246},[1795,56642,4835],{},[1832,56644,54911],{},[1840,56646,2028],{},[1832,56648,2486],{"stretchy":1837},[1832,56650,2486],{"fence":1837,"stretchy":246,"minsize":46539,"maxsize":46539},[238,56652,56653],{"encoding":240},"\\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)",[128,56655,56657,56707,56810,56973,57008,57154,57258],{"className":56656,"ariaHidden":246},[245],[128,56658,56660,56663,56698,56701,56704],{"className":56659},[250],[128,56661],{"className":56662,"style":283},[254],[128,56664,56666,56669],{"className":56665},[259],[128,56667,265],{"className":56668},[259,1813],[128,56670,56672],{"className":56671},[2087],[128,56673,56675],{"className":56674},[274],[128,56676,56678],{"className":56677},[278],[128,56679,56681],{"className":56680,"style":39307},[282],[128,56682,56683,56686],{"style":2452},[128,56684],{"className":56685,"style":291},[290],[128,56687,56689],{"className":56688},[299,300,301,298],[128,56690,56692],{"className":56691},[259,298],[128,56693,56695],{"className":56694},[259,260,298],[128,56696,55121],{"className":56697},[259,298],[128,56699],{"className":56700,"style":1878},[269],[128,56702,1994],{"className":56703},[1882],[128,56705],{"className":56706,"style":1878},[269],[128,56708,56710,56713,56718,56721,56724,56727,56798,56801,56804,56807],{"className":56709},[250],[128,56711],{"className":56712,"style":1892},[254],[128,56714,24502,56716],{"className":56715},[2268],[128,56717,24505],{"style":17336},[128,56719],{"className":56720,"style":1907},[269],[128,56722,6020],{"className":56723},[259],[128,56725,2477],{"className":56726},[1896],[128,56728,56730,56764],{"className":56729},[259],[128,56731,56733],{"className":56732},[259,54949],[128,56734,56736],{"className":56735},[274],[128,56737,56739],{"className":56738},[278],[128,56740,56743,56751],{"className":56741,"style":56742},[282],"height:0.6679em;",[128,56744,56745,56748],{"style":54961},[128,56746],{"className":56747,"style":335},[290],[128,56749,4835],{"className":56750,"style":4920},[259,1873],[128,56752,56754,56757],{"style":56753},"top:-3.35em;",[128,56755],{"className":56756,"style":335},[290],[128,56758,56761],{"className":56759,"style":56760},[54983],"left:-0.2222em;",[128,56762,54911],{"className":56763},[259],[128,56765,56767],{"className":56766},[2087],[128,56768,56770,56790],{"className":56769},[274,321],[128,56771,56773,56787],{"className":56772},[278],[128,56774,56776],{"className":56775,"style":2945},[282],[128,56777,56778,56781],{"style":4935},[128,56779],{"className":56780,"style":291},[290],[128,56782,56784],{"className":56783},[299,300,301,298],[128,56785,2028],{"className":56786},[259,298],[128,56788,347],{"className":56789},[346],[128,56791,56793],{"className":56792},[278],[128,56794,56796],{"className":56795,"style":2241},[282],[128,56797],{},[128,56799,2486],{"className":56800},[1928],[128,56802],{"className":56803,"style":2508},[269],[128,56805,1989],{"className":56806},[2115],[128,56808],{"className":56809,"style":2508},[269],[128,56811,56813,56816,56876,56879,56884,56887,56890,56893,56961,56964,56967,56970],{"className":56812},[250],[128,56814],{"className":56815,"style":5200},[254],[128,56817,56819,56822],{"className":56818},[2268],[128,56820,2042],{"className":56821,"style":2274},[2268,2272,2273],[128,56823,56825],{"className":56824},[2087],[128,56826,56828,56868],{"className":56827},[274,321],[128,56829,56831,56865],{"className":56830},[278],[128,56832,56834,56854],{"className":56833,"style":2287},[282],[128,56835,56836,56839],{"style":2290},[128,56837],{"className":56838,"style":291},[290],[128,56840,56842],{"className":56841},[299,300,301,298],[128,56843,56845,56848,56851],{"className":56844},[259,298],[128,56846,2022],{"className":56847,"style":2231},[259,1873,298],[128,56849,1994],{"className":56850},[1882,298],[128,56852,1842],{"className":56853},[259,298],[128,56855,56856,56859],{"style":2311},[128,56857],{"className":56858,"style":291},[290],[128,56860,56862],{"className":56861},[299,300,301,298],[128,56863,1853],{"className":56864,"style":1924},[259,1873,298],[128,56866,347],{"className":56867},[346],[128,56869,56871],{"className":56870},[278],[128,56872,56874],{"className":56873,"style":2330},[282],[128,56875],{},[128,56877],{"className":56878,"style":1907},[269],[128,56880,24502,56882],{"className":56881},[2268],[128,56883,24505],{"style":17336},[128,56885],{"className":56886,"style":1907},[269],[128,56888,6020],{"className":56889},[259],[128,56891,2477],{"className":56892},[1896],[128,56894,56896,56927],{"className":56895},[259],[128,56897,56899],{"className":56898},[259,54949],[128,56900,56902],{"className":56901},[274],[128,56903,56905],{"className":56904},[278],[128,56906,56908,56916],{"className":56907,"style":56742},[282],[128,56909,56910,56913],{"style":54961},[128,56911],{"className":56912,"style":335},[290],[128,56914,4835],{"className":56915,"style":4920},[259,1873],[128,56917,56918,56921],{"style":56753},[128,56919],{"className":56920,"style":335},[290],[128,56922,56924],{"className":56923,"style":56760},[54983],[128,56925,54911],{"className":56926},[259],[128,56928,56930],{"className":56929},[2087],[128,56931,56933,56953],{"className":56932},[274,321],[128,56934,56936,56950],{"className":56935},[278],[128,56937,56939],{"className":56938,"style":2218},[282],[128,56940,56941,56944],{"style":4935},[128,56942],{"className":56943,"style":291},[290],[128,56945,56947],{"className":56946},[299,300,301,298],[128,56948,2022],{"className":56949,"style":2231},[259,1873,298],[128,56951,347],{"className":56952},[346],[128,56954,56956],{"className":56955},[278],[128,56957,56959],{"className":56958,"style":2241},[282],[128,56960],{},[128,56962,2486],{"className":56963},[1928],[128,56965],{"className":56966,"style":2508},[269],[128,56968,1989],{"className":56969},[2115],[128,56971],{"className":56972,"style":2508},[269],[128,56974,56976,56979,56984,56987,56990,56993,56996,56999,57002,57005],{"className":56975},[250],[128,56977],{"className":56978,"style":1892},[254],[128,56980,24502,56982],{"className":56981},[2268],[128,56983,24505],{"style":17336},[128,56985],{"className":56986,"style":1907},[269],[128,56988,6020],{"className":56989},[259],[128,56991,2477],{"className":56992},[1896],[128,56994,1853],{"className":56995,"style":1924},[259,1873],[128,56997,2486],{"className":56998},[1928],[128,57000],{"className":57001,"style":2508},[269],[128,57003,9486],{"className":57004},[2115],[128,57006],{"className":57007,"style":2508},[269],[128,57009,57011,57014,57074,57077,57145,57148,57151],{"className":57010},[250],[128,57012],{"className":57013,"style":5200},[254],[128,57015,57017,57020],{"className":57016},[2268],[128,57018,2042],{"className":57019,"style":2274},[2268,2272,2273],[128,57021,57023],{"className":57022},[2087],[128,57024,57026,57066],{"className":57025},[274,321],[128,57027,57029,57063],{"className":57028},[278],[128,57030,57032,57052],{"className":57031,"style":2287},[282],[128,57033,57034,57037],{"style":2290},[128,57035],{"className":57036,"style":291},[290],[128,57038,57040],{"className":57039},[299,300,301,298],[128,57041,57043,57046,57049],{"className":57042},[259,298],[128,57044,2022],{"className":57045,"style":2231},[259,1873,298],[128,57047,1994],{"className":57048},[1882,298],[128,57050,1842],{"className":57051},[259,298],[128,57053,57054,57057],{"style":2311},[128,57055],{"className":57056,"style":291},[290],[128,57058,57060],{"className":57059},[299,300,301,298],[128,57061,1853],{"className":57062,"style":1924},[259,1873,298],[128,57064,347],{"className":57065},[346],[128,57067,57069],{"className":57068},[278],[128,57070,57072],{"className":57071,"style":2330},[282],[128,57073],{},[128,57075,2477],{"className":57076},[1896],[128,57078,57080,57111],{"className":57079},[259],[128,57081,57083],{"className":57082},[259,54949],[128,57084,57086],{"className":57085},[274],[128,57087,57089],{"className":57088},[278],[128,57090,57092,57100],{"className":57091,"style":56742},[282],[128,57093,57094,57097],{"style":54961},[128,57095],{"className":57096,"style":335},[290],[128,57098,4835],{"className":57099,"style":4920},[259,1873],[128,57101,57102,57105],{"style":56753},[128,57103],{"className":57104,"style":335},[290],[128,57106,57108],{"className":57107,"style":56760},[54983],[128,57109,54911],{"className":57110},[259],[128,57112,57114],{"className":57113},[2087],[128,57115,57117,57137],{"className":57116},[274,321],[128,57118,57120,57134],{"className":57119},[278],[128,57121,57123],{"className":57122,"style":2218},[282],[128,57124,57125,57128],{"style":4935},[128,57126],{"className":57127,"style":291},[290],[128,57129,57131],{"className":57130},[299,300,301,298],[128,57132,2022],{"className":57133,"style":2231},[259,1873,298],[128,57135,347],{"className":57136},[346],[128,57138,57140],{"className":57139},[278],[128,57141,57143],{"className":57142,"style":2241},[282],[128,57144],{},[128,57146],{"className":57147,"style":2508},[269],[128,57149,1989],{"className":57150},[2115],[128,57152],{"className":57153,"style":2508},[269],[128,57155,57157,57160,57163,57166,57172,57175,57178,57246,57249,57252,57255],{"className":57156},[250],[128,57158],{"className":57159,"style":46966},[254],[128,57161,1842],{"className":57162},[259],[128,57164,2486],{"className":57165},[1928],[128,57167,57169],{"className":57168},[259],[128,57170,2477],{"className":57171},[2146,5795],[128,57173,24404],{"className":57174,"style":1874},[259,1873],[128,57176,2477],{"className":57177},[1896],[128,57179,57181,57212],{"className":57180},[259],[128,57182,57184],{"className":57183},[259,54949],[128,57185,57187],{"className":57186},[274],[128,57188,57190],{"className":57189},[278],[128,57191,57193,57201],{"className":57192,"style":56742},[282],[128,57194,57195,57198],{"style":54961},[128,57196],{"className":57197,"style":335},[290],[128,57199,4835],{"className":57200,"style":4920},[259,1873],[128,57202,57203,57206],{"style":56753},[128,57204],{"className":57205,"style":335},[290],[128,57207,57209],{"className":57208,"style":56760},[54983],[128,57210,54911],{"className":57211},[259],[128,57213,57215],{"className":57214},[2087],[128,57216,57218,57238],{"className":57217},[274,321],[128,57219,57221,57235],{"className":57220},[278],[128,57222,57224],{"className":57223,"style":2218},[282],[128,57225,57226,57229],{"style":4935},[128,57227],{"className":57228,"style":291},[290],[128,57230,57232],{"className":57231},[299,300,301,298],[128,57233,2022],{"className":57234,"style":2231},[259,1873,298],[128,57236,347],{"className":57237},[346],[128,57239,57241],{"className":57240},[278],[128,57242,57244],{"className":57243,"style":2241},[282],[128,57245],{},[128,57247,2486],{"className":57248},[1928],[128,57250],{"className":57251,"style":2508},[269],[128,57253,1989],{"className":57254},[2115],[128,57256],{"className":57257,"style":2508},[269],[128,57259,57261,57264,57267,57270,57338,57341],{"className":57260},[250],[128,57262],{"className":57263,"style":46966},[254],[128,57265,24404],{"className":57266,"style":1874},[259,1873],[128,57268,2477],{"className":57269},[1896],[128,57271,57273,57304],{"className":57272},[259],[128,57274,57276],{"className":57275},[259,54949],[128,57277,57279],{"className":57278},[274],[128,57280,57282],{"className":57281},[278],[128,57283,57285,57293],{"className":57284,"style":56742},[282],[128,57286,57287,57290],{"style":54961},[128,57288],{"className":57289,"style":335},[290],[128,57291,4835],{"className":57292,"style":4920},[259,1873],[128,57294,57295,57298],{"style":56753},[128,57296],{"className":57297,"style":335},[290],[128,57299,57301],{"className":57300,"style":56760},[54983],[128,57302,54911],{"className":57303},[259],[128,57305,57307],{"className":57306},[2087],[128,57308,57310,57330],{"className":57309},[274,321],[128,57311,57313,57327],{"className":57312},[278],[128,57314,57316],{"className":57315,"style":2945},[282],[128,57317,57318,57321],{"style":4935},[128,57319],{"className":57320,"style":291},[290],[128,57322,57324],{"className":57323},[299,300,301,298],[128,57325,2028],{"className":57326},[259,298],[128,57328,347],{"className":57329},[346],[128,57331,57333],{"className":57332},[278],[128,57334,57336],{"className":57335,"style":2241},[282],[128,57337],{},[128,57339,2486],{"className":57340},[1928],[128,57342,57344],{"className":57343},[259],[128,57345,2486],{"className":57346},[2146,5795],[11,57348,57349,57351,57352,57619,57620,11072,57923,58350],{},[35,57350,6849],{}," 由指数族的一般 KL 公式：",[128,57353,57355,57405],{"className":57354,"translate":218},[217],[128,57356,57358],{"className":57357},[222],[224,57359,57360],{"xmlns":226},[228,57361,57362,57402],{},[231,57363,57364,57366,57368,57370,57376,57378,57380,57382,57388,57390,57392,57394,57400],{},[1795,57365,55126],{"mathvariant":1981},[1832,57367,3278],{},[1832,57369,1994],{},[2016,57371,57372,57374],{},[1795,57373,342],{"mathvariant":2008},[1795,57375,4835],{"mathvariant":4834},[1832,57377,16538],{"stretchy":1837},[1795,57379,24373],{},[1832,57381,3278],{},[2016,57383,57384,57386],{},[1795,57385,11],{},[1795,57387,4835],{"mathvariant":4834},[1832,57389,1989],{},[1795,57391,24373],{},[1832,57393,3278],{},[2016,57395,57396,57398],{},[1795,57397,11],{},[1795,57399,18848],{"mathvariant":4834},[1832,57401,16547],{"stretchy":1837},[238,57403,57404],{"encoding":240},"\\operatorname{KL} = \\mathbb{E}_{\\boldsymbol{\\alpha}}[\\log p_{\\boldsymbol{\\alpha}} - \\log p_{\\boldsymbol{\\beta}}]",[128,57406,57408,57429,57553],{"className":57407,"ariaHidden":246},[245],[128,57409,57411,57414,57420,57423,57426],{"className":57410},[250],[128,57412],{"className":57413,"style":283},[254],[128,57415,57417],{"className":57416},[2268],[128,57418,55126],{"className":57419},[259,3353],[128,57421],{"className":57422,"style":1878},[269],[128,57424,1994],{"className":57425},[1882],[128,57427],{"className":57428,"style":1878},[269],[128,57430,57432,57435,57484,57487,57492,57495,57544,57547,57550],{"className":57431},[250],[128,57433],{"className":57434,"style":1892},[254],[128,57436,57438,57441],{"className":57437},[259],[128,57439,342],{"className":57440},[259,2167],[128,57442,57444],{"className":57443},[2087],[128,57445,57447,57476],{"className":57446},[274,321],[128,57448,57450,57473],{"className":57449},[278],[128,57451,57453],{"className":57452,"style":22681},[282],[128,57454,57455,57458],{"style":2221},[128,57456],{"className":57457,"style":291},[290],[128,57459,57461],{"className":57460},[299,300,301,298],[128,57462,57464],{"className":57463},[259,298],[128,57465,57467],{"className":57466},[259,298],[128,57468,57470],{"className":57469},[259,298],[128,57471,4835],{"className":57472},[259,4895,298],[128,57474,347],{"className":57475},[346],[128,57477,57479],{"className":57478},[278],[128,57480,57482],{"className":57481,"style":2241},[282],[128,57483],{},[128,57485,16538],{"className":57486},[1896],[128,57488,24502,57490],{"className":57489},[2268],[128,57491,24505],{"style":17336},[128,57493],{"className":57494,"style":1907},[269],[128,57496,57498,57501],{"className":57497},[259],[128,57499,11],{"className":57500},[259,1873],[128,57502,57504],{"className":57503},[2087],[128,57505,57507,57536],{"className":57506},[274,321],[128,57508,57510,57533],{"className":57509},[278],[128,57511,57513],{"className":57512,"style":22681},[282],[128,57514,57515,57518],{"style":2221},[128,57516],{"className":57517,"style":291},[290],[128,57519,57521],{"className":57520},[299,300,301,298],[128,57522,57524],{"className":57523},[259,298],[128,57525,57527],{"className":57526},[259,298],[128,57528,57530],{"className":57529},[259,298],[128,57531,4835],{"className":57532},[259,4895,298],[128,57534,347],{"className":57535},[346],[128,57537,57539],{"className":57538},[278],[128,57540,57542],{"className":57541,"style":2241},[282],[128,57543],{},[128,57545],{"className":57546,"style":2508},[269],[128,57548,1989],{"className":57549},[2115],[128,57551],{"className":57552,"style":2508},[269],[128,57554,57556,57559,57564,57567,57616],{"className":57555},[250],[128,57557],{"className":57558,"style":19704},[254],[128,57560,24502,57562],{"className":57561},[2268],[128,57563,24505],{"style":17336},[128,57565],{"className":57566,"style":1907},[269],[128,57568,57570,57573],{"className":57569},[259],[128,57571,11],{"className":57572},[259,1873],[128,57574,57576],{"className":57575},[2087],[128,57577,57579,57608],{"className":57578},[274,321],[128,57580,57582,57605],{"className":57581},[278],[128,57583,57585],{"className":57584,"style":2218},[282],[128,57586,57587,57590],{"style":2221},[128,57588],{"className":57589,"style":291},[290],[128,57591,57593],{"className":57592},[299,300,301,298],[128,57594,57596],{"className":57595},[259,298],[128,57597,57599],{"className":57598},[259,298],[128,57600,57602],{"className":57601},[259,298],[128,57603,18848],{"className":57604,"style":19091},[259,4895,298],[128,57606,347],{"className":57607},[346],[128,57609,57611],{"className":57610},[278],[128,57612,57614],{"className":57613,"style":17424},[282],[128,57615],{},[128,57617,16547],{"className":57618},[1928],"。代入 1.2 节的密度并利用 ",[128,57621,57623,57683],{"className":57622,"translate":218},[217],[128,57624,57626],{"className":57625},[222],[224,57627,57628],{"xmlns":226},[228,57629,57630,57680],{},[231,57631,57632,57638,57640,57642,57644,57650,57652,57654,57656,57658,57664,57666,57668,57670,57672,57678],{},[2016,57633,57634,57636],{},[1795,57635,342],{"mathvariant":2008},[1795,57637,4835],{"mathvariant":4834},[1832,57639,16538],{"stretchy":1837},[1795,57641,24373],{},[1832,57643,3278],{},[2016,57645,57646,57648],{},[1795,57647,2760],{},[1795,57649,2022],{},[1832,57651,16547],{"stretchy":1837},[1832,57653,1994],{},[1795,57655,24404],{},[1832,57657,2477],{"stretchy":1837},[2016,57659,57660,57662],{},[1795,57661,4835],{},[1795,57663,2022],{},[1832,57665,2486],{"stretchy":1837},[1832,57667,1989],{},[1795,57669,24404],{},[1832,57671,2477],{"stretchy":1837},[2016,57673,57674,57676],{},[1795,57675,4835],{},[1840,57677,2028],{},[1832,57679,2486],{"stretchy":1837},[238,57681,57682],{"encoding":240},"\\mathbb{E}_{\\boldsymbol{\\alpha}}[\\log x_k] = \\psi(\\alpha_k) - \\psi(\\alpha_0)",[128,57684,57686,57804,57868],{"className":57685,"ariaHidden":246},[245],[128,57687,57689,57692,57741,57744,57749,57752,57792,57795,57798,57801],{"className":57688},[250],[128,57690],{"className":57691,"style":1892},[254],[128,57693,57695,57698],{"className":57694},[259],[128,57696,342],{"className":57697},[259,2167],[128,57699,57701],{"className":57700},[2087],[128,57702,57704,57733],{"className":57703},[274,321],[128,57705,57707,57730],{"className":57706},[278],[128,57708,57710],{"className":57709,"style":22681},[282],[128,57711,57712,57715],{"style":2221},[128,57713],{"className":57714,"style":291},[290],[128,57716,57718],{"className":57717},[299,300,301,298],[128,57719,57721],{"className":57720},[259,298],[128,57722,57724],{"className":57723},[259,298],[128,57725,57727],{"className":57726},[259,298],[128,57728,4835],{"className":57729},[259,4895,298],[128,57731,347],{"className":57732},[346],[128,57734,57736],{"className":57735},[278],[128,57737,57739],{"className":57738,"style":2241},[282],[128,57740],{},[128,57742,16538],{"className":57743},[1896],[128,57745,24502,57747],{"className":57746},[2268],[128,57748,24505],{"style":17336},[128,57750],{"className":57751,"style":1907},[269],[128,57753,57755,57758],{"className":57754},[259],[128,57756,2760],{"className":57757},[259,1873],[128,57759,57761],{"className":57760},[2087],[128,57762,57764,57784],{"className":57763},[274,321],[128,57765,57767,57781],{"className":57766},[278],[128,57768,57770],{"className":57769,"style":2218},[282],[128,57771,57772,57775],{"style":2221},[128,57773],{"className":57774,"style":291},[290],[128,57776,57778],{"className":57777},[299,300,301,298],[128,57779,2022],{"className":57780,"style":2231},[259,1873,298],[128,57782,347],{"className":57783},[346],[128,57785,57787],{"className":57786},[278],[128,57788,57790],{"className":57789,"style":2241},[282],[128,57791],{},[128,57793,16547],{"className":57794},[1928],[128,57796],{"className":57797,"style":1878},[269],[128,57799,1994],{"className":57800},[1882],[128,57802],{"className":57803,"style":1878},[269],[128,57805,57807,57810,57813,57816,57856,57859,57862,57865],{"className":57806},[250],[128,57808],{"className":57809,"style":1892},[254],[128,57811,24404],{"className":57812,"style":1874},[259,1873],[128,57814,2477],{"className":57815},[1896],[128,57817,57819,57822],{"className":57818},[259],[128,57820,4835],{"className":57821,"style":4920},[259,1873],[128,57823,57825],{"className":57824},[2087],[128,57826,57828,57848],{"className":57827},[274,321],[128,57829,57831,57845],{"className":57830},[278],[128,57832,57834],{"className":57833,"style":2218},[282],[128,57835,57836,57839],{"style":4935},[128,57837],{"className":57838,"style":291},[290],[128,57840,57842],{"className":57841},[299,300,301,298],[128,57843,2022],{"className":57844,"style":2231},[259,1873,298],[128,57846,347],{"className":57847},[346],[128,57849,57851],{"className":57850},[278],[128,57852,57854],{"className":57853,"style":2241},[282],[128,57855],{},[128,57857,2486],{"className":57858},[1928],[128,57860],{"className":57861,"style":2508},[269],[128,57863,1989],{"className":57864},[2115],[128,57866],{"className":57867,"style":2508},[269],[128,57869,57871,57874,57877,57880,57920],{"className":57870},[250],[128,57872],{"className":57873,"style":1892},[254],[128,57875,24404],{"className":57876,"style":1874},[259,1873],[128,57878,2477],{"className":57879},[1896],[128,57881,57883,57886],{"className":57882},[259],[128,57884,4835],{"className":57885,"style":4920},[259,1873],[128,57887,57889],{"className":57888},[2087],[128,57890,57892,57912],{"className":57891},[274,321],[128,57893,57895,57909],{"className":57894},[278],[128,57896,57898],{"className":57897,"style":2945},[282],[128,57899,57900,57903],{"style":4935},[128,57901],{"className":57902,"style":291},[290],[128,57904,57906],{"className":57905},[299,300,301,298],[128,57907,2028],{"className":57908},[259,298],[128,57910,347],{"className":57911},[346],[128,57913,57915],{"className":57914},[278],[128,57916,57918],{"className":57917,"style":2241},[282],[128,57919],{},[128,57921,2486],{"className":57922},[1928],[128,57924,57926,58016],{"className":57925,"translate":218},[217],[128,57927,57929],{"className":57928},[222],[224,57930,57931],{"xmlns":226},[228,57932,57933,58013],{},[231,57934,57935,57941,57943,57945,57947,57949,57955,57957,57959,57961,57963,57969,57971,57973,57975,57977,57979,57985,57987,57989,57991,57993,57995,57997,57999,58001,58003,58005,58011],{},[2016,57936,57937,57939],{},[1832,57938,2042],{},[1795,57940,2022],{},[1795,57942,342],{"mathvariant":2008},[1832,57944,16538],{"stretchy":1837},[1795,57946,24373],{},[1832,57948,3278],{},[2016,57950,57951,57953],{},[1795,57952,2760],{},[1795,57954,2022],{},[1832,57956,16547],{"stretchy":1837},[1832,57958,1994],{},[1795,57960,24404],{},[1832,57962,2477],{"stretchy":1837},[2016,57964,57965,57967],{},[1795,57966,4835],{},[1840,57968,2028],{},[1832,57970,2486],{"stretchy":1837},[1832,57972,1989],{},[1795,57974,1853],{},[1795,57976,24404],{},[1832,57978,2477],{"stretchy":1837},[2016,57980,57981,57983],{},[1795,57982,4835],{},[1840,57984,2028],{},[1832,57986,2486],{"stretchy":1837},[1832,57988,1994],{},[1832,57990,1989],{},[1832,57992,2477],{"stretchy":1837},[1795,57994,1853],{},[1832,57996,1989],{},[1840,57998,1842],{},[1832,58000,2486],{"stretchy":1837},[1795,58002,24404],{},[1832,58004,2477],{"stretchy":1837},[2016,58006,58007,58009],{},[1795,58008,4835],{},[1840,58010,2028],{},[1832,58012,2486],{"stretchy":1837},[238,58014,58015],{"encoding":240},"\\sum_k \\mathbb{E}[\\log x_k] = \\psi(\\alpha_0) - K\\psi(\\alpha_0) = -(K-1)\\psi(\\alpha_0)",[128,58017,58019,58134,58198,58265,58289],{"className":58018,"ariaHidden":246},[245],[128,58020,58022,58025,58065,58068,58071,58074,58079,58082,58122,58125,58128,58131],{"className":58021},[250],[128,58023],{"className":58024,"style":7777},[254],[128,58026,58028,58031],{"className":58027},[2268],[128,58029,2042],{"className":58030,"style":2274},[2268,2272,2273],[128,58032,58034],{"className":58033},[2087],[128,58035,58037,58057],{"className":58036},[274,321],[128,58038,58040,58054],{"className":58039},[278],[128,58041,58043],{"className":58042,"style":31692},[282],[128,58044,58045,58048],{"style":2290},[128,58046],{"className":58047,"style":291},[290],[128,58049,58051],{"className":58050},[299,300,301,298],[128,58052,2022],{"className":58053,"style":2231},[259,1873,298],[128,58055,347],{"className":58056},[346],[128,58058,58060],{"className":58059},[278],[128,58061,58063],{"className":58062,"style":2330},[282],[128,58064],{},[128,58066],{"className":58067,"style":1907},[269],[128,58069,342],{"className":58070},[259,2167],[128,58072,16538],{"className":58073},[1896],[128,58075,24502,58077],{"className":58076},[2268],[128,58078,24505],{"style":17336},[128,58080],{"className":58081,"style":1907},[269],[128,58083,58085,58088],{"className":58084},[259],[128,58086,2760],{"className":58087},[259,1873],[128,58089,58091],{"className":58090},[2087],[128,58092,58094,58114],{"className":58093},[274,321],[128,58095,58097,58111],{"className":58096},[278],[128,58098,58100],{"className":58099,"style":2218},[282],[128,58101,58102,58105],{"style":2221},[128,58103],{"className":58104,"style":291},[290],[128,58106,58108],{"className":58107},[299,300,301,298],[128,58109,2022],{"className":58110,"style":2231},[259,1873,298],[128,58112,347],{"className":58113},[346],[128,58115,58117],{"className":58116},[278],[128,58118,58120],{"className":58119,"style":2241},[282],[128,58121],{},[128,58123,16547],{"className":58124},[1928],[128,58126],{"className":58127,"style":1878},[269],[128,58129,1994],{"className":58130},[1882],[128,58132],{"className":58133,"style":1878},[269],[128,58135,58137,58140,58143,58146,58186,58189,58192,58195],{"className":58136},[250],[128,58138],{"className":58139,"style":1892},[254],[128,58141,24404],{"className":58142,"style":1874},[259,1873],[128,58144,2477],{"className":58145},[1896],[128,58147,58149,58152],{"className":58148},[259],[128,58150,4835],{"className":58151,"style":4920},[259,1873],[128,58153,58155],{"className":58154},[2087],[128,58156,58158,58178],{"className":58157},[274,321],[128,58159,58161,58175],{"className":58160},[278],[128,58162,58164],{"className":58163,"style":2945},[282],[128,58165,58166,58169],{"style":4935},[128,58167],{"className":58168,"style":291},[290],[128,58170,58172],{"className":58171},[299,300,301,298],[128,58173,2028],{"className":58174},[259,298],[128,58176,347],{"className":58177},[346],[128,58179,58181],{"className":58180},[278],[128,58182,58184],{"className":58183,"style":2241},[282],[128,58185],{},[128,58187,2486],{"className":58188},[1928],[128,58190],{"className":58191,"style":2508},[269],[128,58193,1989],{"className":58194},[2115],[128,58196],{"className":58197,"style":2508},[269],[128,58199,58201,58204,58207,58210,58213,58253,58256,58259,58262],{"className":58200},[250],[128,58202],{"className":58203,"style":1892},[254],[128,58205,1853],{"className":58206,"style":1924},[259,1873],[128,58208,24404],{"className":58209,"style":1874},[259,1873],[128,58211,2477],{"className":58212},[1896],[128,58214,58216,58219],{"className":58215},[259],[128,58217,4835],{"className":58218,"style":4920},[259,1873],[128,58220,58222],{"className":58221},[2087],[128,58223,58225,58245],{"className":58224},[274,321],[128,58226,58228,58242],{"className":58227},[278],[128,58229,58231],{"className":58230,"style":2945},[282],[128,58232,58233,58236],{"style":4935},[128,58234],{"className":58235,"style":291},[290],[128,58237,58239],{"className":58238},[299,300,301,298],[128,58240,2028],{"className":58241},[259,298],[128,58243,347],{"className":58244},[346],[128,58246,58248],{"className":58247},[278],[128,58249,58251],{"className":58250,"style":2241},[282],[128,58252],{},[128,58254,2486],{"className":58255},[1928],[128,58257],{"className":58258,"style":1878},[269],[128,58260,1994],{"className":58261},[1882],[128,58263],{"className":58264,"style":1878},[269],[128,58266,58268,58271,58274,58277,58280,58283,58286],{"className":58267},[250],[128,58269],{"className":58270,"style":1892},[254],[128,58272,1989],{"className":58273},[259],[128,58275,2477],{"className":58276},[1896],[128,58278,1853],{"className":58279,"style":1924},[259,1873],[128,58281],{"className":58282,"style":2508},[269],[128,58284,1989],{"className":58285},[2115],[128,58287],{"className":58288,"style":2508},[269],[128,58290,58292,58295,58298,58301,58304,58307,58347],{"className":58291},[250],[128,58293],{"className":58294,"style":1892},[254],[128,58296,1842],{"className":58297},[259],[128,58299,2486],{"className":58300},[1928],[128,58302,24404],{"className":58303,"style":1874},[259,1873],[128,58305,2477],{"className":58306},[1896],[128,58308,58310,58313],{"className":58309},[259],[128,58311,4835],{"className":58312,"style":4920},[259,1873],[128,58314,58316],{"className":58315},[2087],[128,58317,58319,58339],{"className":58318},[274,321],[128,58320,58322,58336],{"className":58321},[278],[128,58323,58325],{"className":58324,"style":2945},[282],[128,58326,58327,58330],{"style":4935},[128,58328],{"className":58329,"style":291},[290],[128,58331,58333],{"className":58332},[299,300,301,298],[128,58334,2028],{"className":58335},[259,298],[128,58337,347],{"className":58338},[346],[128,58340,58342],{"className":58341},[278],[128,58343,58345],{"className":58344,"style":2241},[282],[128,58346],{},[128,58348,2486],{"className":58349},[1928]," 即可化简。",[11,58352,58353,58354,44582],{},"总损失为两项的加权和，其中权重按训练步",[35,58355,58356],{},"退火",[128,58358,58360],{"className":58359,"translate":218},[1962],[128,58361,58363,58443],{"className":58362,"translate":218},[217],[128,58364,58366],{"className":58365},[222],[224,58367,58368],{"xmlns":226,"display":1971},[228,58369,58370,58440],{},[231,58371,58372,58374,58376,58383,58385,58392,58394,58400,58402,58404,58410,58412,58415,58417,58419],{},[1795,58373,265],{"mathvariant":1797},[1832,58375,1994],{},[1977,58377,58378,58380],{},[1795,58379,265],{"mathvariant":1797},[234,58381,58382],{},"fit",[1832,58384,9486],{},[2016,58386,58387,58390],{},[1795,58388,58389],{},"λ",[1795,58391,7023],{},[234,58393,6528],{},[1977,58395,58396,58398],{},[1795,58397,265],{"mathvariant":1797},[234,58399,55121],{},[1832,58401,1845],{"separator":246},[269,58403],{"width":11568},[2016,58405,58406,58408],{},[1795,58407,58389],{},[1795,58409,7023],{},[1832,58411,1994],{},[1795,58413,58414],{},"min",[1832,58416,3278],{},[234,58418,8524],{},[231,58420,58421,58423,58425,58427,58438],{},[1832,58422,2477],{"fence":246},[1840,58424,1842],{},[1832,58426,1845],{"separator":246},[5451,58428,58429,58431],{},[1795,58430,7023],{},[2016,58432,58433,58435],{},[1795,58434,313],{},[234,58436,58437],{},"anneal",[1832,58439,2486],{"fence":246},[238,58441,58442],{"encoding":240},"\\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)",[128,58444,58446,58464,58515,58660],{"className":58445,"ariaHidden":246},[245],[128,58447,58449,58452,58455,58458,58461],{"className":58448},[250],[128,58450],{"className":58451,"style":283},[254],[128,58453,265],{"className":58454},[259,1813],[128,58456],{"className":58457,"style":1878},[269],[128,58459,1994],{"className":58460},[1882],[128,58462],{"className":58463,"style":1878},[269],[128,58465,58467,58471,58506,58509,58512],{"className":58466},[250],[128,58468],{"className":58469,"style":58470},[254],"height:0.9824em;vertical-align:-0.0833em;",[128,58472,58474,58477],{"className":58473},[259],[128,58475,265],{"className":58476},[259,1813],[128,58478,58480],{"className":58479},[2087],[128,58481,58483],{"className":58482},[274],[128,58484,58486],{"className":58485},[278],[128,58487,58489],{"className":58488,"style":20577},[282],[128,58490,58491,58494],{"style":2099},[128,58492],{"className":58493,"style":291},[290],[128,58495,58497],{"className":58496},[299,300,301,298],[128,58498,58500],{"className":58499},[259,298],[128,58501,58503],{"className":58502},[259,260,298],[128,58504,58382],{"className":58505},[259,298],[128,58507],{"className":58508,"style":2508},[269],[128,58510,9486],{"className":58511},[2115],[128,58513],{"className":58514,"style":2508},[269],[128,58516,58518,58522,58563,58566,58602,58605,58608,58611,58651,58654,58657],{"className":58517},[250],[128,58519],{"className":58520,"style":58521},[254],"height:0.9088em;vertical-align:-0.1944em;",[128,58523,58525,58528],{"className":58524},[259],[128,58526,58389],{"className":58527},[259,1873],[128,58529,58531],{"className":58530},[2087],[128,58532,58534,58555],{"className":58533},[274,321],[128,58535,58537,58552],{"className":58536},[278],[128,58538,58541],{"className":58539,"style":58540},[282],"height:0.2806em;",[128,58542,58543,58546],{"style":2221},[128,58544],{"className":58545,"style":291},[290],[128,58547,58549],{"className":58548},[299,300,301,298],[128,58550,7023],{"className":58551},[259,1873,298],[128,58553,347],{"className":58554},[346],[128,58556,58558],{"className":58557},[278],[128,58559,58561],{"className":58560,"style":2241},[282],[128,58562],{},[128,58564],{"className":58565,"style":1907},[269],[128,58567,58569,58572],{"className":58568},[259],[128,58570,265],{"className":58571},[259,1813],[128,58573,58575],{"className":58574},[2087],[128,58576,58578],{"className":58577},[274],[128,58579,58581],{"className":58580},[278],[128,58582,58585],{"className":58583,"style":58584},[282],"height:0.7144em;",[128,58586,58587,58590],{"style":2099},[128,58588],{"className":58589,"style":291},[290],[128,58591,58593],{"className":58592},[299,300,301,298],[128,58594,58596],{"className":58595},[259,298],[128,58597,58599],{"className":58598},[259,260,298],[128,58600,55121],{"className":58601},[259,298],[128,58603,1845],{"className":58604},[1903],[128,58606],{"className":58607,"style":11756},[269],[128,58609],{"className":58610,"style":1907},[269],[128,58612,58614,58617],{"className":58613},[259],[128,58615,58389],{"className":58616},[259,1873],[128,58618,58620],{"className":58619},[2087],[128,58621,58623,58643],{"className":58622},[274,321],[128,58624,58626,58640],{"className":58625},[278],[128,58627,58629],{"className":58628,"style":58540},[282],[128,58630,58631,58634],{"style":2221},[128,58632],{"className":58633,"style":291},[290],[128,58635,58637],{"className":58636},[299,300,301,298],[128,58638,7023],{"className":58639},[259,1873,298],[128,58641,347],{"className":58642},[346],[128,58644,58646],{"className":58645},[278],[128,58647,58649],{"className":58648,"style":2241},[282],[128,58650],{},[128,58652],{"className":58653,"style":1878},[269],[128,58655,1994],{"className":58656},[1882],[128,58658],{"className":58659,"style":1878},[269],[128,58661,58663,58666,58669,58672,58675],{"className":58662},[250],[128,58664],{"className":58665,"style":8239},[254],[128,58667,58414],{"className":58668},[2268],[128,58670],{"className":58671,"style":317},[269],[128,58673],{"className":58674,"style":1907},[269],[128,58676,58678,58684,58687,58690,58693,58799],{"className":58677},[1911],[128,58679,58681],{"className":58680,"style":2142},[1896,2141],[128,58682,2477],{"className":58683},[2146,301],[128,58685,1842],{"className":58686},[259],[128,58688,1845],{"className":58689},[1903],[128,58691],{"className":58692,"style":1907},[269],[128,58694,58696,58699,58796],{"className":58695},[259],[128,58697],{"className":58698},[1896,5570],[128,58700,58702],{"className":58701},[5451],[128,58703,58705,58788],{"className":58704},[274,321],[128,58706,58708,58785],{"className":58707},[278],[128,58709,58712,58766,58774],{"className":58710,"style":58711},[282],"height:1.2921em;",[128,58713,58714,58717],{"style":13123},[128,58715],{"className":58716,"style":335},[290],[128,58718,58720],{"className":58719},[259],[128,58721,58723,58726],{"className":58722},[259],[128,58724,313],{"className":58725,"style":36065},[259,1873],[128,58727,58729],{"className":58728},[2087],[128,58730,58732,58758],{"className":58731},[274,321],[128,58733,58735,58755],{"className":58734},[278],[128,58736,58738],{"className":58737,"style":2218},[282],[128,58739,58740,58743],{"style":36080},[128,58741],{"className":58742,"style":291},[290],[128,58744,58746],{"className":58745},[299,300,301,298],[128,58747,58749],{"className":58748},[259,298],[128,58750,58752],{"className":58751},[259,260,298],[128,58753,58437],{"className":58754},[259,298],[128,58756,347],{"className":58757},[346],[128,58759,58761],{"className":58760},[278],[128,58762,58764],{"className":58763,"style":2241},[282],[128,58765],{},[128,58767,58768,58771],{"style":5617},[128,58769],{"className":58770,"style":335},[290],[128,58772],{"className":58773,"style":5625},[5624],[128,58775,58776,58779],{"style":13189},[128,58777],{"className":58778,"style":335},[290],[128,58780,58782],{"className":58781},[259],[128,58783,7023],{"className":58784},[259,1873],[128,58786,347],{"className":58787},[346],[128,58789,58791],{"className":58790},[278],[128,58792,58794],{"className":58793,"style":20496},[282],[128,58795],{},[128,58797],{"className":58798},[1928,5570],[128,58800,58802],{"className":58801,"style":2142},[1928,2141],[128,58803,2486],{"className":58804},[2146,301],[11,58806,58807,58808,58901,58902,58994,58995,59024],{},"退火的设计意图是分工时段的划分：训练初期 ",[128,58809,58811,58834],{"className":58810,"translate":218},[217],[128,58812,58814],{"className":58813},[222],[224,58815,58816],{"xmlns":226},[228,58817,58818,58831],{},[231,58819,58820,58826,58829],{},[2016,58821,58822,58824],{},[1795,58823,58389],{},[1795,58825,7023],{},[1832,58827,58828],{},"≈",[1840,58830,2028],{},[238,58832,58833],{"encoding":240},"\\lambda_t \\approx 0",[128,58835,58837,58892],{"className":58836,"ariaHidden":246},[245],[128,58838,58840,58843,58883,58886,58889],{"className":58839},[250],[128,58841],{"className":58842,"style":36116},[254],[128,58844,58846,58849],{"className":58845},[259],[128,58847,58389],{"className":58848},[259,1873],[128,58850,58852],{"className":58851},[2087],[128,58853,58855,58875],{"className":58854},[274,321],[128,58856,58858,58872],{"className":58857},[278],[128,58859,58861],{"className":58860,"style":58540},[282],[128,58862,58863,58866],{"style":2221},[128,58864],{"className":58865,"style":291},[290],[128,58867,58869],{"className":58868},[299,300,301,298],[128,58870,7023],{"className":58871},[259,1873,298],[128,58873,347],{"className":58874},[346],[128,58876,58878],{"className":58877},[278],[128,58879,58881],{"className":58880,"style":2241},[282],[128,58882],{},[128,58884],{"className":58885,"style":1878},[269],[128,58887,58828],{"className":58888},[1882],[128,58890],{"className":58891,"style":1878},[269],[128,58893,58895,58898],{"className":58894},[250],[128,58896],{"className":58897,"style":2594},[254],[128,58899,2028],{"className":58900},[259],"，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 ",[128,58903,58905,58927],{"className":58904,"translate":218},[217],[128,58906,58908],{"className":58907},[222],[224,58909,58910],{"xmlns":226},[228,58911,58912,58924],{},[231,58913,58914,58920,58922],{},[2016,58915,58916,58918],{},[1795,58917,58389],{},[1795,58919,7023],{},[1832,58921,22419],{},[1840,58923,1842],{},[238,58925,58926],{"encoding":240},"\\lambda_t \\to 1",[128,58928,58930,58985],{"className":58929,"ariaHidden":246},[245],[128,58931,58933,58936,58976,58979,58982],{"className":58932},[250],[128,58934],{"className":58935,"style":36116},[254],[128,58937,58939,58942],{"className":58938},[259],[128,58940,58389],{"className":58941},[259,1873],[128,58943,58945],{"className":58944},[2087],[128,58946,58948,58968],{"className":58947},[274,321],[128,58949,58951,58965],{"className":58950},[278],[128,58952,58954],{"className":58953,"style":58540},[282],[128,58955,58956,58959],{"style":2221},[128,58957],{"className":58958,"style":291},[290],[128,58960,58962],{"className":58961},[299,300,301,298],[128,58963,7023],{"className":58964},[259,1873,298],[128,58966,347],{"className":58967},[346],[128,58969,58971],{"className":58970},[278],[128,58972,58974],{"className":58973,"style":2241},[282],[128,58975],{},[128,58977],{"className":58978,"style":1878},[269],[128,58980,22419],{"className":58981},[1882],[128,58983],{"className":58984,"style":1878},[269],[128,58986,58988,58991],{"className":58987},[250],[128,58989],{"className":58990,"style":2594},[254],[128,58992,1842],{"className":58993},[259],"，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 ",[128,58996,58998,59012],{"className":58997,"translate":218},[217],[128,58999,59001],{"className":59000},[222],[224,59002,59003],{"xmlns":226},[228,59004,59005,59009],{},[231,59006,59007],{},[1795,59008,58389],{},[238,59010,59011],{"encoding":240},"\\lambda",[128,59013,59015],{"className":59014,"ariaHidden":246},[245],[128,59016,59018,59021],{"className":59017},[250],[128,59019],{"className":59020,"style":12173},[254],[128,59022,58389],{"className":59023},[259,1873],"）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。",[2610,59026,59028],{"id":59027},"_44-统一视角与变体","4.4 统一视角与变体",[11,59030,59031],{},"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",[128,59033,59035],{"className":59034,"translate":218},[1962],[128,59036,59038,59097],{"className":59037,"translate":218},[217],[128,59039,59041],{"className":59040},[222],[224,59042,59043],{"xmlns":226,"display":1971},[228,59044,59045,59094],{},[231,59046,59047,59053,59055,59075],{},[1977,59048,59049,59051],{},[1795,59050,265],{"mathvariant":1797},[234,59052,58382],{},[1832,59054,1994],{},[2016,59056,59057,59059],{},[1795,59058,342],{"mathvariant":2008},[231,59060,59061,59063,59065,59067,59069,59071,59073],{},[1795,59062,26389],{"mathvariant":4834},[1832,59064,5911],{},[1795,59066,5914],{"mathvariant":1981},[1832,59068,3278],{},[1832,59070,2477],{"stretchy":1837},[1795,59072,4835],{"mathvariant":4834},[1832,59074,2486],{"stretchy":1837},[231,59076,59077,59079,59082,59084,59086,59088,59090,59092],{},[1832,59078,16538],{"fence":246},[1795,59080,59081],{"mathvariant":1981},"ℓ",[1832,59083,2477],{"stretchy":1837},[1795,59085,1830],{"mathvariant":2001},[1832,59087,1845],{"separator":246},[1795,59089,26389],{"mathvariant":4834},[1832,59091,2486],{"stretchy":1837},[1832,59093,16547],{"fence":246},[238,59095,59096],{"encoding":240},"\\mathcal{L}^{\\text{fit}} = \\mathbb{E}_{\\boldsymbol{\\pi} \\sim \\operatorname{Dir}(\\boldsymbol{\\alpha})}\\left[\\ell(\\mathbf{y}, \\boldsymbol{\\pi})\\right]",[128,59098,59100,59150],{"className":59099,"ariaHidden":246},[245],[128,59101,59103,59106,59141,59144,59147],{"className":59102},[250],[128,59104],{"className":59105,"style":20577},[254],[128,59107,59109,59112],{"className":59108},[259],[128,59110,265],{"className":59111},[259,1813],[128,59113,59115],{"className":59114},[2087],[128,59116,59118],{"className":59117},[274],[128,59119,59121],{"className":59120},[278],[128,59122,59124],{"className":59123,"style":20577},[282],[128,59125,59126,59129],{"style":2099},[128,59127],{"className":59128,"style":291},[290],[128,59130,59132],{"className":59131},[299,300,301,298],[128,59133,59135],{"className":59134},[259,298],[128,59136,59138],{"className":59137},[259,260,298],[128,59139,58382],{"className":59140},[259,298],[128,59142],{"className":59143,"style":1878},[269],[128,59145,1994],{"className":59146},[1882],[128,59148],{"className":59149,"style":1878},[269],[128,59151,59153,59157,59230,59233],{"className":59152},[250],[128,59154],{"className":59155,"style":59156},[254],"height:1.1052em;vertical-align:-0.3552em;",[128,59158,59160,59163],{"className":59159},[259],[128,59161,342],{"className":59162},[259,2167],[128,59164,59166],{"className":59165},[2087],[128,59167,59169,59222],{"className":59168},[274,321],[128,59170,59172,59219],{"className":59171},[278],[128,59173,59175],{"className":59174,"style":24117},[282],[128,59176,59177,59180],{"style":49304},[128,59178],{"className":59179,"style":291},[290],[128,59181,59183],{"className":59182},[299,300,301,298],[128,59184,59186,59195,59198,59204,59207,59216],{"className":59185},[259,298],[128,59187,59189],{"className":59188},[259,298],[128,59190,59192],{"className":59191},[259,298],[128,59193,26389],{"className":59194,"style":26423},[259,4895,298],[128,59196,5911],{"className":59197},[1882,298],[128,59199,59201],{"className":59200},[2268,298],[128,59202,5914],{"className":59203},[259,3353,298],[128,59205,2477],{"className":59206},[1896,298],[128,59208,59210],{"className":59209},[259,298],[128,59211,59213],{"className":59212},[259,298],[128,59214,4835],{"className":59215},[259,4895,298],[128,59217,2486],{"className":59218},[1928,298],[128,59220,347],{"className":59221},[346],[128,59223,59225],{"className":59224},[278],[128,59226,59228],{"className":59227,"style":49356},[282],[128,59229],{},[128,59231],{"className":59232,"style":1907},[269],[128,59234,59236,59239,59242,59245,59248,59251,59254,59263,59266],{"className":59235},[1911],[128,59237,16538],{"className":59238,"style":2142},[1896,2141],[128,59240,59081],{"className":59241},[259],[128,59243,2477],{"className":59244},[1896],[128,59246,1830],{"className":59247,"style":31116},[259,2151],[128,59249,1845],{"className":59250},[1903],[128,59252],{"className":59253,"style":1907},[269],[128,59255,59257],{"className":59256},[259],[128,59258,59260],{"className":59259},[259],[128,59261,26389],{"className":59262,"style":26423},[259,4895],[128,59264,2486],{"className":59265},[1928],[128,59267,16547],{"className":59268,"style":2142},[1928,2141],[11,59270,14647,59271,59304,59305,59417,59418,59537],{},[35,59272,59273,59274,59303],{},"对某个一阶损失 ",[128,59275,59277,59291],{"className":59276,"translate":218},[217],[128,59278,59280],{"className":59279},[222],[224,59281,59282],{"xmlns":226},[228,59283,59284,59288],{},[231,59285,59286],{},[1795,59287,59081],{"mathvariant":1981},[238,59289,59290],{"encoding":240},"\\ell",[128,59292,59294],{"className":59293,"ariaHidden":246},[245],[128,59295,59297,59300],{"className":59296},[250],[128,59298],{"className":59299,"style":12173},[254],[128,59301,59081],{"className":59302},[259]," 的先验期望","。取 ",[128,59306,59308,59336],{"className":59307,"translate":218},[217],[128,59309,59311],{"className":59310},[222],[224,59312,59313],{"xmlns":226},[228,59314,59315,59333],{},[231,59316,59317,59319,59321,59323,59325,59327],{},[1795,59318,59081],{"mathvariant":1981},[1832,59320,1994],{},[1832,59322,1989],{},[1795,59324,24373],{},[1832,59326,3278],{},[2016,59328,59329,59331],{},[1795,59330,26389],{},[1795,59332,1830],{},[238,59334,59335],{"encoding":240},"\\ell = -\\log \\pi_y",[128,59337,59339,59357],{"className":59338,"ariaHidden":246},[245],[128,59340,59342,59345,59348,59351,59354],{"className":59341},[250],[128,59343],{"className":59344,"style":12173},[254],[128,59346,59081],{"className":59347},[259],[128,59349],{"className":59350,"style":1878},[269],[128,59352,1994],{"className":59353},[1882],[128,59355],{"className":59356,"style":1878},[269],[128,59358,59360,59363,59366,59369,59374,59377],{"className":59359},[250],[128,59361],{"className":59362,"style":22661},[254],[128,59364,1989],{"className":59365},[259],[128,59367],{"className":59368,"style":1907},[269],[128,59370,24502,59372],{"className":59371},[2268],[128,59373,24505],{"style":17336},[128,59375],{"className":59376,"style":1907},[269],[128,59378,59380,59383],{"className":59379},[259],[128,59381,26389],{"className":59382,"style":1874},[259,1873],[128,59384,59386],{"className":59385},[2087],[128,59387,59389,59409],{"className":59388},[274,321],[128,59390,59392,59406],{"className":59391},[278],[128,59393,59395],{"className":59394,"style":28738},[282],[128,59396,59397,59400],{"style":28741},[128,59398],{"className":59399,"style":291},[290],[128,59401,59403],{"className":59402},[299,300,301,298],[128,59404,1830],{"className":59405,"style":1874},[259,1873,298],[128,59407,347],{"className":59408},[346],[128,59410,59412],{"className":59411},[278],[128,59413,59415],{"className":59414,"style":17424},[282],[128,59416],{}," 得命题 4.1 的 digamma 形式。取 ",[128,59419,59421,59451],{"className":59420,"translate":218},[217],[128,59422,59424],{"className":59423},[222],[224,59425,59426],{"xmlns":226},[228,59427,59428,59448],{},[231,59429,59430,59432,59434,59436,59438,59440,59442],{},[1795,59431,59081],{"mathvariant":1981},[1832,59433,1994],{},[1795,59435,23006],{"mathvariant":1981},[1795,59437,1830],{"mathvariant":2001},[1832,59439,1989],{},[1795,59441,26389],{"mathvariant":4834},[1977,59443,59444,59446],{},[1795,59445,23006],{"mathvariant":1981},[1840,59447,2639],{},[238,59449,59450],{"encoding":240},"\\ell = \\|\\mathbf{y} - \\boldsymbol{\\pi}\\|^2",[128,59452,59454,59472,59493],{"className":59453,"ariaHidden":246},[245],[128,59455,59457,59460,59463,59466,59469],{"className":59456},[250],[128,59458],{"className":59459,"style":12173},[254],[128,59461,59081],{"className":59462},[259],[128,59464],{"className":59465,"style":1878},[269],[128,59467,1994],{"className":59468},[1882],[128,59470],{"className":59471,"style":1878},[269],[128,59473,59475,59478,59481,59484,59487,59490],{"className":59474},[250],[128,59476],{"className":59477,"style":1892},[254],[128,59479,23006],{"className":59480},[259],[128,59482,1830],{"className":59483,"style":31116},[259,2151],[128,59485],{"className":59486,"style":2508},[269],[128,59488,1989],{"className":59489},[2115],[128,59491],{"className":59492,"style":2508},[269],[128,59494,59496,59499,59508],{"className":59495},[250],[128,59497],{"className":59498,"style":23130},[254],[128,59500,59502],{"className":59501},[259],[128,59503,59505],{"className":59504},[259],[128,59506,26389],{"className":59507,"style":26423},[259,4895],[128,59509,59511,59514],{"className":59510},[259],[128,59512,23006],{"className":59513},[259],[128,59515,59517],{"className":59516},[2087],[128,59518,59520],{"className":59519},[274],[128,59521,59523],{"className":59522},[278],[128,59524,59526],{"className":59525,"style":9629},[282],[128,59527,59528,59531],{"style":2452},[128,59529],{"className":59530,"style":291},[290],[128,59532,59534],{"className":59533},[299,300,301,298],[128,59535,2639],{"className":59536},[259,298]," 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。",[11,59539,59540],{},"在此基础上，文献中出现的主要变体可归入三类：",[33248,59542,59543,59649,59659],{},[33251,59544,59545,59548,59549,59619,59620,59648],{},[35,59546,59547],{},"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 ",[128,59550,59552,59570],{"className":59551,"translate":218},[217],[128,59553,59555],{"className":59554},[222],[224,59556,59557],{"xmlns":226},[228,59558,59559,59567],{},[231,59560,59561],{},[2016,59562,59563,59565],{},[1795,59564,265],{},[1840,59566,2639],{},[238,59568,59569],{"encoding":240},"L_2",[128,59571,59573],{"className":59572,"ariaHidden":246},[245],[128,59574,59576,59579],{"className":59575},[250],[128,59577],{"className":59578,"style":36058},[254],[128,59580,59582,59585],{"className":59581},[259],[128,59583,265],{"className":59584},[259,1873],[128,59586,59588],{"className":59587},[2087],[128,59589,59591,59611],{"className":59590},[274,321],[128,59592,59594,59608],{"className":59593},[278],[128,59595,59597],{"className":59596,"style":2945},[282],[128,59598,59599,59602],{"style":2221},[128,59600],{"className":59601,"style":291},[290],[128,59603,59605],{"className":59604},[299,300,301,298],[128,59606,2639],{"className":59607},[259,298],[128,59609,347],{"className":59610},[346],[128,59612,59614],{"className":59613},[278],[128,59615,59617],{"className":59616,"style":2241},[282],[128,59618],{}," 惩罚。其共同目标都是阻止 ",[128,59621,59623,59636],{"className":59622,"translate":218},[217],[128,59624,59626],{"className":59625},[222],[224,59627,59628],{"xmlns":226},[228,59629,59630,59634],{},[231,59631,59632],{},[1795,59633,41957],{},[238,59635,41957],{"encoding":240},[128,59637,59639],{"className":59638,"ariaHidden":246},[245],[128,59640,59642,59645],{"className":59641},[250],[128,59643],{"className":59644,"style":283},[254],[128,59646,41957],{"className":59647,"style":42029},[259,1873]," 的退化。",[33251,59650,59651,59654,59655,59658],{},[35,59652,59653],{},"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",[35,59656,59657],{},"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。",[33251,59660,59661,59664],{},[35,59662,59663],{},"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）。",[11,59666,59667,59668,59671,59672,59675],{},"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",[35,59669,59670],{},"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",[35,59673,59674],{},"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。",[2610,59677,59679],{"id":59678},"_45-使用边界","4.5 使用边界",[11,59681,59682],{},"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：",[33248,59684,59685,60596,60726,60992,61053],{},[33251,59686,59687,59690,59691,60001,60002,60072,60073,893,60288,60291,60292,60475,60476,11072,60504,60566,60567,60595],{},[35,59688,59689],{},"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",[128,59692,59694,59780],{"className":59693,"translate":218},[217],[128,59695,59697],{"className":59696},[222],[224,59698,59699],{"xmlns":226},[228,59700,59701,59777],{},[231,59702,59703,59705,59707,59709,59711,59713,59715,59718,59720,59722,59725,59727,59729,59731,59733,59735,59737,59739,59741,59743,59745,59747,59749,59751,59753,59755,59757,59759,59761,59763,59765,59767,59769,59771,59773,59775],{},[1795,59704,11],{},[1832,59706,2477],{"stretchy":1837},[1795,59708,1830],{},[1832,59710,5443],{},[1795,59712,2760],{"mathvariant":2001},[1832,59714,1845],{"separator":246},[1795,59716,59717],{"mathvariant":1797},"D",[1832,59719,2486],{"stretchy":1837},[1832,59721,1994],{},[1832,59723,59724],{},"∬",[1795,59726,11],{},[1832,59728,2477],{"stretchy":1837},[1795,59730,1830],{},[1832,59732,5443],{},[1795,59734,26389],{"mathvariant":4834},[1832,59736,2486],{"stretchy":1837},[234,59738,6528],{},[1795,59740,11],{},[1832,59742,2477],{"stretchy":1837},[1795,59744,26389],{"mathvariant":4834},[1832,59746,5443],{},[1795,59748,38844],{"mathvariant":4834},[1832,59750,2486],{"stretchy":1837},[234,59752,6528],{},[1795,59754,11],{},[1832,59756,2477],{"stretchy":1837},[1795,59758,38844],{"mathvariant":4834},[1832,59760,5443],{},[1795,59762,59717],{"mathvariant":1797},[1832,59764,2486],{"stretchy":1837},[234,59766,6528],{},[1795,59768,4519],{"mathvariant":1981},[1795,59770,26389],{"mathvariant":4834},[234,59772,6528],{},[1795,59774,4519],{"mathvariant":1981},[1795,59776,38844],{"mathvariant":4834},[238,59778,59779],{"encoding":240},"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}",[128,59781,59783,59807,59837,59869,59914,59959],{"className":59782,"ariaHidden":246},[245],[128,59784,59786,59789,59792,59795,59798,59801,59804],{"className":59785},[250],[128,59787],{"className":59788,"style":1892},[254],[128,59790,11],{"className":59791},[259,1873],[128,59793,2477],{"className":59794},[1896],[128,59796,1830],{"className":59797,"style":1874},[259,1873],[128,59799],{"className":59800,"style":1878},[269],[128,59802,5443],{"className":59803},[1882],[128,59805],{"className":59806,"style":1878},[269],[128,59808,59810,59813,59816,59819,59822,59825,59828,59831,59834],{"className":59809},[250],[128,59811],{"className":59812,"style":1892},[254],[128,59814,2760],{"className":59815},[259,2151],[128,59817,1845],{"className":59818},[1903],[128,59820],{"className":59821,"style":1907},[269],[128,59823,59717],{"className":59824,"style":14008},[259,1813],[128,59826,2486],{"className":59827},[1928],[128,59829],{"className":59830,"style":1878},[269],[128,59832,1994],{"className":59833},[1882],[128,59835],{"className":59836,"style":1878},[269],[128,59838,59840,59844,59848,59851,59854,59857,59860,59863,59866],{"className":59839},[250],[128,59841],{"className":59842,"style":59843},[254],"height:1.111em;vertical-align:-0.306em;",[128,59845,59724],{"className":59846,"style":59847},[2268,2272,2273],"margin-right:0.1945em;position:relative;top:-0.0005em;",[128,59849],{"className":59850,"style":1907},[269],[128,59852,11],{"className":59853},[259,1873],[128,59855,2477],{"className":59856},[1896],[128,59858,1830],{"className":59859,"style":1874},[259,1873],[128,59861],{"className":59862,"style":1878},[269],[128,59864,5443],{"className":59865},[1882],[128,59867],{"className":59868,"style":1878},[269],[128,59870,59872,59875,59884,59887,59890,59893,59896,59905,59908,59911],{"className":59871},[250],[128,59873],{"className":59874,"style":1892},[254],[128,59876,59878],{"className":59877},[259],[128,59879,59881],{"className":59880},[259],[128,59882,26389],{"className":59883,"style":26423},[259,4895],[128,59885,2486],{"className":59886},[1928],[128,59888],{"className":59889,"style":1907},[269],[128,59891,11],{"className":59892},[259,1873],[128,59894,2477],{"className":59895},[1896],[128,59897,59899],{"className":59898},[259],[128,59900,59902],{"className":59901},[259],[128,59903,26389],{"className":59904,"style":26423},[259,4895],[128,59906],{"className":59907,"style":1878},[269],[128,59909,5443],{"className":59910},[1882],[128,59912],{"className":59913,"style":1878},[269],[128,59915,59917,59920,59929,59932,59935,59938,59941,59950,59953,59956],{"className":59916},[250],[128,59918],{"className":59919,"style":1892},[254],[128,59921,59923],{"className":59922},[259],[128,59924,59926],{"className":59925},[259],[128,59927,38844],{"className":59928,"style":38908},[259,4895],[128,59930,2486],{"className":59931},[1928],[128,59933],{"className":59934,"style":1907},[269],[128,59936,11],{"className":59937},[259,1873],[128,59939,2477],{"className":59940},[1896],[128,59942,59944],{"className":59943},[259],[128,59945,59947],{"className":59946},[259],[128,59948,38844],{"className":59949,"style":38908},[259,4895],[128,59951],{"className":59952,"style":1878},[269],[128,59954,5443],{"className":59955},[1882],[128,59957],{"className":59958,"style":1878},[269],[128,59960,59962,59965,59968,59971,59974,59977,59986,59989,59992],{"className":59961},[250],[128,59963],{"className":59964,"style":1892},[254],[128,59966,59717],{"className":59967,"style":14008},[259,1813],[128,59969,2486],{"className":59970},[1928],[128,59972],{"className":59973,"style":1907},[269],[128,59975,4519],{"className":59976},[259,3353],[128,59978,59980],{"className":59979},[259],[128,59981,59983],{"className":59982},[259],[128,59984,26389],{"className":59985,"style":26423},[259,4895],[128,59987],{"className":59988,"style":1907},[269],[128,59990,4519],{"className":59991},[259,3353],[128,59993,59995],{"className":59994},[259],[128,59996,59998],{"className":59997},[259],[128,59999,38844],{"className":60000,"style":38908},[259,4895],"\n而 EDL 以点估计 ",[128,60003,60005,60024],{"className":60004,"translate":218},[217],[128,60006,60008],{"className":60007},[222],[224,60009,60010],{"xmlns":226},[228,60011,60012,60021],{},[231,60013,60014],{},[54905,60015,60016,60018],{"accent":246},[1795,60017,38844],{"mathvariant":4834},[1832,60019,60020],{},"^",[238,60022,60023],{"encoding":240},"\\hat{\\boldsymbol{\\theta}}",[128,60025,60027],{"className":60026,"ariaHidden":246},[245],[128,60028,60030,60034],{"className":60029},[250],[128,60031],{"className":60032,"style":60033},[254],"height:0.9579em;",[128,60035,60037],{"className":60036},[259,54949],[128,60038,60040],{"className":60039},[274],[128,60041,60043],{"className":60042},[278],[128,60044,60046,60060],{"className":60045,"style":60033},[282],[128,60047,60048,60051],{"style":54961},[128,60049],{"className":60050,"style":335},[290],[128,60052,60054],{"className":60053},[259],[128,60055,60057],{"className":60056},[259],[128,60058,38844],{"className":60059,"style":38908},[259,4895],[128,60061,60063,60066],{"style":60062},"top:-3.2634em;",[128,60064],{"className":60065,"style":335},[290],[128,60067,60069],{"className":60068,"style":54984},[54983],[128,60070,60020],{"className":60071},[259]," 替换外层积分，取 ",[128,60074,60076,60130],{"className":60075,"translate":218},[217],[128,60077,60079],{"className":60078},[222],[224,60080,60081],{"xmlns":226},[228,60082,60083,60127],{},[231,60084,60085,60087,60089,60091,60093,60095,60097,60099,60101,60103,60105,60107,60109,60111,60113,60115,60117,60123,60125],{},[1795,60086,11],{},[1832,60088,2477],{"stretchy":1837},[1795,60090,26389],{"mathvariant":4834},[1832,60092,5443],{},[1795,60094,2760],{"mathvariant":2001},[1832,60096,2486],{"stretchy":1837},[1832,60098,1994],{},[1795,60100,5914],{"mathvariant":1981},[1832,60102,3278],{},[1832,60104,2477],{"fence":1837,"stretchy":246,"minsize":46539,"maxsize":46539},[1795,60106,26389],{"mathvariant":4834},[1832,60108,13024],{"separator":246},[1795,60110,4835],{"mathvariant":4834},[1832,60112,2477],{"stretchy":1837},[1795,60114,2760],{"mathvariant":2001},[1832,60116,13024],{"separator":246},[54905,60118,60119,60121],{"accent":246},[1795,60120,38844],{"mathvariant":4834},[1832,60122,60020],{},[1832,60124,2486],{"stretchy":1837},[1832,60126,2486],{"fence":1837,"stretchy":246,"minsize":46539,"maxsize":46539},[238,60128,60129],{"encoding":240},"p(\\boldsymbol{\\pi} \\mid \\mathbf{x}) = \\operatorname{Dir}\\big(\\boldsymbol{\\pi}; \\boldsymbol{\\alpha}(\\mathbf{x}; \\hat{\\boldsymbol{\\theta}})\\big)",[128,60131,60133,60163,60184],{"className":60132,"ariaHidden":246},[245],[128,60134,60136,60139,60142,60145,60154,60157,60160],{"className":60135},[250],[128,60137],{"className":60138,"style":1892},[254],[128,60140,11],{"className":60141},[259,1873],[128,60143,2477],{"className":60144},[1896],[128,60146,60148],{"className":60147},[259],[128,60149,60151],{"className":60150},[259],[128,60152,26389],{"className":60153,"style":26423},[259,4895],[128,60155],{"className":60156,"style":1878},[269],[128,60158,5443],{"className":60159},[1882],[128,60161],{"className":60162,"style":1878},[269],[128,60164,60166,60169,60172,60175,60178,60181],{"className":60165},[250],[128,60167],{"className":60168,"style":1892},[254],[128,60170,2760],{"className":60171},[259,2151],[128,60173,2486],{"className":60174},[1928],[128,60176],{"className":60177,"style":1878},[269],[128,60179,1994],{"className":60180},[1882],[128,60182],{"className":60183,"style":1878},[269],[128,60185,60187,60191,60197,60200,60206,60215,60218,60221,60230,60233,60236,60239,60242,60279,60282],{"className":60186},[250],[128,60188],{"className":60189,"style":60190},[254],"height:1.3079em;vertical-align:-0.35em;",[128,60192,60194],{"className":60193},[2268],[128,60195,5914],{"className":60196},[259,3353],[128,60198],{"className":60199,"style":1907},[269],[128,60201,60203],{"className":60202},[259],[128,60204,2477],{"className":60205},[2146,5795],[128,60207,60209],{"className":60208},[259],[128,60210,60212],{"className":60211},[259],[128,60213,26389],{"className":60214,"style":26423},[259,4895],[128,60216,13024],{"className":60217},[1903],[128,60219],{"className":60220,"style":1907},[269],[128,60222,60224],{"className":60223},[259],[128,60225,60227],{"className":60226},[259],[128,60228,4835],{"className":60229},[259,4895],[128,60231,2477],{"className":60232},[1896],[128,60234,2760],{"className":60235},[259,2151],[128,60237,13024],{"className":60238},[1903],[128,60240],{"className":60241,"style":1907},[269],[128,60243,60245],{"className":60244},[259,54949],[128,60246,60248],{"className":60247},[274],[128,60249,60251],{"className":60250},[278],[128,60252,60254,60268],{"className":60253,"style":60033},[282],[128,60255,60256,60259],{"style":54961},[128,60257],{"className":60258,"style":335},[290],[128,60260,60262],{"className":60261},[259],[128,60263,60265],{"className":60264},[259],[128,60266,38844],{"className":60267,"style":38908},[259,4895],[128,60269,60270,60273],{"style":60062},[128,60271],{"className":60272,"style":335},[290],[128,60274,60276],{"className":60275,"style":54984},[54983],[128,60277,60020],{"className":60278},[259],[128,60280,2486],{"className":60281},[1928],[128,60283,60285],{"className":60284},[259],[128,60286,2486],{"className":60287},[2146,5795],[35,60289,60290],{},"结果是一个插值（plug-in）估计","，其内层积分给出 ",[128,60293,60295,60328],{"className":60294,"translate":218},[217],[128,60296,60298],{"className":60297},[222],[224,60299,60300],{"xmlns":226},[228,60301,60302,60326],{},[231,60303,60304,60310,60312,60318,60320],{},[2016,60305,60306,60308],{},[1795,60307,11],{},[1795,60309,2022],{},[1832,60311,1994],{},[2016,60313,60314,60316],{},[1795,60315,4835],{},[1795,60317,2022],{},[1795,60319,4751],{"mathvariant":1981},[2016,60321,60322,60324],{},[1795,60323,4835],{},[1840,60325,2028],{},[238,60327,45525],{"encoding":240},[128,60329,60331,60386],{"className":60330,"ariaHidden":246},[245],[128,60332,60334,60337,60377,60380,60383],{"className":60333},[250],[128,60335],{"className":60336,"style":11158},[254],[128,60338,60340,60343],{"className":60339},[259],[128,60341,11],{"className":60342},[259,1873],[128,60344,60346],{"className":60345},[2087],[128,60347,60349,60369],{"className":60348},[274,321],[128,60350,60352,60366],{"className":60351},[278],[128,60353,60355],{"className":60354,"style":2218},[282],[128,60356,60357,60360],{"style":2221},[128,60358],{"className":60359,"style":291},[290],[128,60361,60363],{"className":60362},[299,300,301,298],[128,60364,2022],{"className":60365,"style":2231},[259,1873,298],[128,60367,347],{"className":60368},[346],[128,60370,60372],{"className":60371},[278],[128,60373,60375],{"className":60374,"style":2241},[282],[128,60376],{},[128,60378],{"className":60379,"style":1878},[269],[128,60381,1994],{"className":60382},[1882],[128,60384],{"className":60385,"style":1878},[269],[128,60387,60389,60392,60432,60435],{"className":60388},[250],[128,60390],{"className":60391,"style":1892},[254],[128,60393,60395,60398],{"className":60394},[259],[128,60396,4835],{"className":60397,"style":4920},[259,1873],[128,60399,60401],{"className":60400},[2087],[128,60402,60404,60424],{"className":60403},[274,321],[128,60405,60407,60421],{"className":60406},[278],[128,60408,60410],{"className":60409,"style":2218},[282],[128,60411,60412,60415],{"style":4935},[128,60413],{"className":60414,"style":291},[290],[128,60416,60418],{"className":60417},[299,300,301,298],[128,60419,2022],{"className":60420,"style":2231},[259,1873,298],[128,60422,347],{"className":60423},[346],[128,60425,60427],{"className":60426},[278],[128,60428,60430],{"className":60429,"style":2241},[282],[128,60431],{},[128,60433,4751],{"className":60434},[259],[128,60436,60438,60441],{"className":60437},[259],[128,60439,4835],{"className":60440,"style":4920},[259,1873],[128,60442,60444],{"className":60443},[2087],[128,60445,60447,60467],{"className":60446},[274,321],[128,60448,60450,60464],{"className":60449},[278],[128,60451,60453],{"className":60452,"style":2945},[282],[128,60454,60455,60458],{"style":4935},[128,60456],{"className":60457,"style":291},[290],[128,60459,60461],{"className":60460},[299,300,301,298],[128,60462,2028],{"className":60463},[259,298],[128,60465,347],{"className":60466},[346],[128,60468,60470],{"className":60469},[278],[128,60471,60473],{"className":60472,"style":2241},[282],[128,60474],{},"（由聚合性），确实正确。但外层积分被抛弃，",[128,60477,60479,60492],{"className":60478,"translate":218},[217],[128,60480,60482],{"className":60481},[222],[224,60483,60484],{"xmlns":226},[228,60485,60486,60490],{},[231,60487,60488],{},[1795,60489,35129],{},[238,60491,35129],{"encoding":240},[128,60493,60495],{"className":60494,"ariaHidden":246},[245],[128,60496,60498,60501],{"className":60497},[250],[128,60499],{"className":60500,"style":7758},[254],[128,60502,35129],{"className":60503},[259,1873],[128,60505,60507,60530],{"className":60506,"translate":218},[217],[128,60508,60510],{"className":60509},[222],[224,60511,60512],{"xmlns":226},[228,60513,60514,60528],{},[231,60515,60516,60518,60520,60522,60524,60526],{},[1795,60517,30626],{},[1832,60519,2477],{"stretchy":1837},[1795,60521,1830],{},[1832,60523,13024],{"separator":246},[1795,60525,26389],{"mathvariant":4834},[1832,60527,2486],{"stretchy":1837},[238,60529,48574],{"encoding":240},[128,60531,60533],{"className":60532,"ariaHidden":246},[245],[128,60534,60536,60539,60542,60545,60548,60551,60554,60563],{"className":60535},[250],[128,60537],{"className":60538,"style":1892},[254],[128,60540,30626],{"className":60541,"style":30665},[259,1873],[128,60543,2477],{"className":60544},[1896],[128,60546,1830],{"className":60547,"style":1874},[259,1873],[128,60549,13024],{"className":60550},[1903],[128,60552],{"className":60553,"style":1907},[269],[128,60555,60557],{"className":60556},[259],[128,60558,60560],{"className":60559},[259],[128,60561,26389],{"className":60562,"style":26423},[259,4895],[128,60564,2486],{"className":60565},[1928]," 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 ",[128,60568,60570,60583],{"className":60569,"translate":218},[217],[128,60571,60573],{"className":60572},[222],[224,60574,60575],{"xmlns":226},[228,60576,60577,60581],{},[231,60578,60579],{},[1795,60580,35129],{},[238,60582,35129],{"encoding":240},[128,60584,60586],{"className":60585,"ariaHidden":246},[245],[128,60587,60589,60592],{"className":60588},[250],[128,60590],{"className":60591,"style":7758},[254],[128,60593,35129],{"className":60594},[259,1873]," 输出一个错误的类别。",[33251,60597,60598,60601,60602,60662,60663,60725],{},[35,60599,60600],{},"不确定性分数丢弃了证据的分布信息。"," 如 3.5 节所述，",[128,60603,60605,60626],{"className":60604,"translate":218},[217],[128,60606,60608],{"className":60607},[222],[224,60609,60610],{"xmlns":226},[228,60611,60612,60624],{},[231,60613,60614,60616,60618,60620,60622],{},[1795,60615,35129],{},[1832,60617,1994],{},[1795,60619,1853],{},[1795,60621,4751],{"mathvariant":1981},[1795,60623,41957],{},[238,60625,44676],{"encoding":240},[128,60627,60629,60647],{"className":60628,"ariaHidden":246},[245],[128,60630,60632,60635,60638,60641,60644],{"className":60631},[250],[128,60633],{"className":60634,"style":7758},[254],[128,60636,35129],{"className":60637},[259,1873],[128,60639],{"className":60640,"style":1878},[269],[128,60642,1994],{"className":60643},[1882],[128,60645],{"className":60646,"style":1878},[269],[128,60648,60650,60653,60656,60659],{"className":60649},[250],[128,60651],{"className":60652,"style":1892},[254],[128,60654,1853],{"className":60655,"style":1924},[259,1873],[128,60657,4751],{"className":60658},[259],[128,60660,41957],{"className":60661,"style":42029},[259,1873]," 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。",[128,60664,60666,60689],{"className":60665,"translate":218},[217],[128,60667,60669],{"className":60668},[222],[224,60670,60671],{"xmlns":226},[228,60672,60673,60687],{},[231,60674,60675,60677,60679,60681,60683,60685],{},[1795,60676,30626],{},[1832,60678,2477],{"stretchy":1837},[1795,60680,1830],{},[1832,60682,13024],{"separator":246},[1795,60684,26389],{"mathvariant":4834},[1832,60686,2486],{"stretchy":1837},[238,60688,48574],{"encoding":240},[128,60690,60692],{"className":60691,"ariaHidden":246},[245],[128,60693,60695,60698,60701,60704,60707,60710,60713,60722],{"className":60694},[250],[128,60696],{"className":60697,"style":1892},[254],[128,60699,30626],{"className":60700,"style":30665},[259,1873],[128,60702,2477],{"className":60703},[1896],[128,60705,1830],{"className":60706,"style":1874},[259,1873],[128,60708,13024],{"className":60709},[1903],[128,60711],{"className":60712,"style":1907},[269],[128,60714,60716],{"className":60715},[259],[128,60717,60719],{"className":60718},[259],[128,60720,26389],{"className":60721,"style":26423},[259,4895],[128,60723,2486],{"className":60724},[1928]," 缓解了这一点，但仍不引入任何关于模型参数的信息。",[33251,60727,60728,60731,60732,60987,60988,60991],{},[35,60729,60730],{},"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 ",[128,60733,60735,60777],{"className":60734,"translate":218},[217],[128,60736,60738],{"className":60737},[222],[224,60739,60740],{"xmlns":226},[228,60741,60742,60774],{},[231,60743,60744,60746,60760,60762,60772],{},[1832,60745,2477],{"stretchy":1837},[5451,60747,60748,60750],{},[1840,60749,1842],{},[231,60751,60752,60754],{},[1840,60753,2639],{},[2016,60755,60756,60758],{},[1795,60757,4835],{},[1795,60759,1830],{},[1832,60761,1989],{},[5451,60763,60764,60766],{},[1840,60765,1842],{},[231,60767,60768,60770],{},[1840,60769,2639],{},[1795,60771,41957],{},[1832,60773,2486],{"stretchy":1837},[238,60775,60776],{"encoding":240},"(\\frac{1}{2\\alpha_y} - \\frac{1}{2S})",[128,60778,60780,60907],{"className":60779,"ariaHidden":246},[245],[128,60781,60783,60787,60790,60898,60901,60904],{"className":60782},[250],[128,60784],{"className":60785,"style":60786},[254],"height:1.3874em;vertical-align:-0.5423em;",[128,60788,2477],{"className":60789},[1896],[128,60791,60793,60796,60895],{"className":60792},[259],[128,60794],{"className":60795},[1896,5570],[128,60797,60799],{"className":60798},[5451],[128,60800,60802,60887],{"className":60801},[274,321],[128,60803,60805,60884],{"className":60804},[278],[128,60806,60808,60862,60870],{"className":60807,"style":5583},[282],[128,60809,60810,60813],{"style":5586},[128,60811],{"className":60812,"style":335},[290],[128,60814,60816],{"className":60815},[299,300,301,298],[128,60817,60819,60822],{"className":60818},[259,298],[128,60820,2639],{"className":60821},[259,298],[128,60823,60825,60828],{"className":60824},[259,298],[128,60826,4835],{"className":60827,"style":4920},[259,1873,298],[128,60829,60831],{"className":60830},[2087],[128,60832,60834,60854],{"className":60833},[274,321],[128,60835,60837,60851],{"className":60836},[278],[128,60838,60840],{"className":60839,"style":30995},[282],[128,60841,60842,60845],{"style":5786},[128,60843],{"className":60844,"style":5790},[290],[128,60846,60848],{"className":60847},[299,5794,5795,298],[128,60849,1830],{"className":60850,"style":1874},[259,1873,298],[128,60852,347],{"className":60853},[346],[128,60855,60857],{"className":60856},[278],[128,60858,60860],{"className":60859,"style":17680},[282],[128,60861],{},[128,60863,60864,60867],{"style":5617},[128,60865],{"className":60866,"style":335},[290],[128,60868],{"className":60869,"style":5625},[5624],[128,60871,60872,60875],{"style":5628},[128,60873],{"className":60874,"style":335},[290],[128,60876,60878],{"className":60877},[299,300,301,298],[128,60879,60881],{"className":60880},[259,298],[128,60882,1842],{"className":60883},[259,298],[128,60885,347],{"className":60886},[346],[128,60888,60890],{"className":60889},[278],[128,60891,60893],{"className":60892,"style":51563},[282],[128,60894],{},[128,60896],{"className":60897},[1928,5570],[128,60899],{"className":60900,"style":2508},[269],[128,60902,1989],{"className":60903},[2115],[128,60905],{"className":60906,"style":2508},[269],[128,60908,60910,60913,60984],{"className":60909},[250],[128,60911],{"className":60912,"style":44263},[254],[128,60914,60916,60919,60981],{"className":60915},[259],[128,60917],{"className":60918},[1896,5570],[128,60920,60922],{"className":60921},[5451],[128,60923,60925,60973],{"className":60924},[274,321],[128,60926,60928,60970],{"className":60927},[278],[128,60929,60931,60948,60956],{"className":60930,"style":5583},[282],[128,60932,60933,60936],{"style":5586},[128,60934],{"className":60935,"style":335},[290],[128,60937,60939],{"className":60938},[299,300,301,298],[128,60940,60942,60945],{"className":60941},[259,298],[128,60943,2639],{"className":60944},[259,298],[128,60946,41957],{"className":60947,"style":42029},[259,1873,298],[128,60949,60950,60953],{"style":5617},[128,60951],{"className":60952,"style":335},[290],[128,60954],{"className":60955,"style":5625},[5624],[128,60957,60958,60961],{"style":5628},[128,60959],{"className":60960,"style":335},[290],[128,60962,60964],{"className":60963},[299,300,301,298],[128,60965,60967],{"className":60966},[259,298],[128,60968,1842],{"className":60969},[259,298],[128,60971,347],{"className":60972},[346],[128,60974,60976],{"className":60975},[278],[128,60977,60979],{"className":60978,"style":11919},[282],[128,60980],{},[128,60982],{"className":60983},[1928,5570],[128,60985,2486],{"className":60986},[1928]," 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",[35,60989,60990],{},"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。",[33251,60993,60994,60997,60998,61052],{},[35,60995,60996],{},"「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 ",[128,60999,61001,61022],{"className":61000,"translate":218},[217],[128,61002,61004],{"className":61003},[222],[224,61005,61006],{"xmlns":226},[228,61007,61008,61020],{},[231,61009,61010,61012,61014,61016,61018],{},[1795,61011,5914],{"mathvariant":1981},[1832,61013,3278],{},[1832,61015,2477],{"stretchy":1837},[1795,61017,4835],{"mathvariant":4834},[1832,61019,2486],{"stretchy":1837},[238,61021,40766],{"encoding":240},[128,61023,61025],{"className":61024,"ariaHidden":246},[245],[128,61026,61028,61031,61037,61040,61049],{"className":61027},[250],[128,61029],{"className":61030,"style":1892},[254],[128,61032,61034],{"className":61033},[2268],[128,61035,5914],{"className":61036},[259,3353],[128,61038,2477],{"className":61039},[1896],[128,61041,61043],{"className":61042},[259],[128,61044,61046],{"className":61045},[259],[128,61047,4835],{"className":61048},[259,4895],[128,61050,2486],{"className":61051},[1928]," 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。",[33251,61054,61055,61058,61059,61175,61176,61204,61205,893],{},[35,61056,61057],{},"它对主干特征的可分性有隐含依赖。"," 证据由 ",[128,61060,61062,61090],{"className":61061,"translate":218},[217],[128,61063,61065],{"className":61064},[222],[224,61066,61067],{"xmlns":226},[228,61068,61069,61087],{},[231,61070,61071,61073,61075,61081,61083,61085],{},[1795,61072,3713],{"mathvariant":2001},[1832,61074,1994],{},[2016,61076,61077,61079],{},[1795,61078,24505],{},[1795,61080,38844],{"mathvariant":4834},[1832,61082,2477],{"stretchy":1837},[1795,61084,2760],{"mathvariant":2001},[1832,61086,2486],{"stretchy":1837},[238,61088,61089],{"encoding":240},"\\mathbf{e} = g_{\\boldsymbol{\\theta}}(\\mathbf{x})",[128,61091,61093,61111],{"className":61092,"ariaHidden":246},[245],[128,61094,61096,61099,61102,61105,61108],{"className":61095},[250],[128,61097],{"className":61098,"style":4439},[254],[128,61100,3713],{"className":61101},[259,2151],[128,61103],{"className":61104,"style":1878},[269],[128,61106,1994],{"className":61107},[1882],[128,61109],{"className":61110,"style":1878},[269],[128,61112,61114,61117,61166,61169,61172],{"className":61113},[250],[128,61115],{"className":61116,"style":1892},[254],[128,61118,61120,61123],{"className":61119},[259],[128,61121,24505],{"className":61122,"style":1874},[259,1873],[128,61124,61126],{"className":61125},[2087],[128,61127,61129,61158],{"className":61128},[274,321],[128,61130,61132,61155],{"className":61131},[278],[128,61133,61135],{"className":61134,"style":2218},[282],[128,61136,61137,61140],{"style":28741},[128,61138],{"className":61139,"style":291},[290],[128,61141,61143],{"className":61142},[299,300,301,298],[128,61144,61146],{"className":61145},[259,298],[128,61147,61149],{"className":61148},[259,298],[128,61150,61152],{"className":61151},[259,298],[128,61153,38844],{"className":61154,"style":38908},[259,4895,298],[128,61156,347],{"className":61157},[346],[128,61159,61161],{"className":61160},[278],[128,61162,61164],{"className":61163,"style":2241},[282],[128,61165],{},[128,61167,2477],{"className":61168},[1896],[128,61170,2760],{"className":61171},[259,2151],[128,61173,2486],{"className":61174},[1928]," 给出，因此 ",[128,61177,61179,61192],{"className":61178,"translate":218},[217],[128,61180,61182],{"className":61181},[222],[224,61183,61184],{"xmlns":226},[228,61185,61186,61190],{},[231,61187,61188],{},[1795,61189,2760],{"mathvariant":2001},[238,61191,4429],{"encoding":240},[128,61193,61195],{"className":61194,"ariaHidden":246},[245],[128,61196,61198,61201],{"className":61197},[250],[128,61199],{"className":61200,"style":4439},[254],[128,61202,2760],{"className":61203},[259,2151]," 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——",[35,61206,61207],{},"它把 OOD 问题从输出层转移到了特征层，而非解决它",[11,61209,61210,61211,61214],{},"综合以上点，恰当的使用立场是：",[35,61212,61213],{},"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。",[51,61216,61218],{"id":61217},"五应用","五、应用",[2610,61220,61222],{"id":61221},"_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",[11,61224,61225,61226,44713,61286,61289,61290,61318,61319,61350],{},"由命题 3.4，",[128,61227,61229,61250],{"className":61228,"translate":218},[217],[128,61230,61232],{"className":61231},[222],[224,61233,61234],{"xmlns":226},[228,61235,61236,61248],{},[231,61237,61238,61240,61242,61244,61246],{},[1795,61239,35129],{},[1832,61241,1994],{},[1795,61243,1853],{},[1795,61245,4751],{"mathvariant":1981},[1795,61247,41957],{},[238,61249,44676],{"encoding":240},[128,61251,61253,61271],{"className":61252,"ariaHidden":246},[245],[128,61254,61256,61259,61262,61265,61268],{"className":61255},[250],[128,61257],{"className":61258,"style":7758},[254],[128,61260,35129],{"className":61261},[259,1873],[128,61263],{"className":61264,"style":1878},[269],[128,61266,1994],{"className":61267},[1882],[128,61269],{"className":61270,"style":1878},[269],[128,61272,61274,61277,61280,61283],{"className":61273},[250],[128,61275],{"className":61276,"style":1892},[254],[128,61278,1853],{"className":61279,"style":1924},[259,1873],[128,61281,4751],{"className":61282},[259],[128,61284,41957],{"className":61285,"style":42029},[259,1873],[35,61287,61288],{},"单调反比于总证据","的量，因此可以直接充当分布外（OOD）分数：",[128,61291,61293,61306],{"className":61292,"translate":218},[217],[128,61294,61296],{"className":61295},[222],[224,61297,61298],{"xmlns":226},[228,61299,61300,61304],{},[231,61301,61302],{},[1795,61303,35129],{},[238,61305,35129],{"encoding":240},[128,61307,61309],{"className":61308,"ariaHidden":246},[245],[128,61310,61312,61315],{"className":61311},[250],[128,61313],{"className":61314,"style":7758},[254],[128,61316,35129],{"className":61317},[259,1873]," 高意味着输入未能激活任何类别的证据。以阈值 ",[128,61320,61322,61337],{"className":61321,"translate":218},[217],[128,61323,61325],{"className":61324},[222],[224,61326,61327],{"xmlns":226},[228,61328,61329,61334],{},[231,61330,61331],{},[1795,61332,61333],{},"τ",[238,61335,61336],{"encoding":240},"\\tau",[128,61338,61340],{"className":61339,"ariaHidden":246},[245],[128,61341,61343,61346],{"className":61342},[250],[128,61344],{"className":61345,"style":7758},[254],[128,61347,61333],{"className":61348,"style":61349},[259,1873],"margin-right:0.1132em;"," 作拒识判决",[128,61352,61354],{"className":61353,"translate":218},[1962],[128,61355,61357,61472],{"className":61356,"translate":218},[217],[128,61358,61360],{"className":61359},[222],[224,61361,61362],{"xmlns":226,"display":1971},[228,61363,61364,61469],{},[231,61365,61366,61372,61374,61376,61378,61380],{},[54905,61367,61368,61370],{"accent":246},[1795,61369,1830],{},[1832,61371,60020],{},[1832,61373,2477],{"stretchy":1837},[1795,61375,2760],{"mathvariant":2001},[1832,61377,2486],{"stretchy":1837},[1832,61379,1994],{},[231,61381,61382,61384],{},[1832,61383,1838],{"fence":246},[8172,61385,61388,61438],{"rowspacing":61386,"columnalign":61387,"columnspacing":8176},"0.36em","left left",[8178,61389,61390,61420],{},[8181,61391,61392],{},[2035,61393,61394],{"scriptlevel":2028,"displaystyle":1837},[231,61395,61396,61399,61401,61412,61418],{},[1795,61397,61398],{},"arg",[1832,61400,3278],{},[2016,61402,61403,61410],{},[231,61404,61405,61408],{},[1795,61406,61407],{},"max",[1832,61409,3278],{},[1795,61411,2022],{},[2016,61413,61414,61416],{},[1795,61415,11],{},[1795,61417,2022],{},[1832,61419,1845],{"separator":246},[8181,61421,61422],{},[2035,61423,61424],{"scriptlevel":2028,"displaystyle":1837},[231,61425,61426,61428,61430,61432,61434,61436],{},[1795,61427,35129],{},[1832,61429,2477],{"stretchy":1837},[1795,61431,2760],{"mathvariant":2001},[1832,61433,2486],{"stretchy":1837},[1832,61435,23023],{},[1795,61437,61333],{},[8178,61439,61440,61451],{},[8181,61441,61442],{},[2035,61443,61444],{"scriptlevel":2028,"displaystyle":1837},[231,61445,61446,61449],{},[234,61447,61448],{},"reject",[1832,61450,1845],{"separator":246},[8181,61452,61453],{},[2035,61454,61455],{"scriptlevel":2028,"displaystyle":1837},[231,61456,61457,61459,61461,61463,61465,61467],{},[1795,61458,35129],{},[1832,61460,2477],{"stretchy":1837},[1795,61462,2760],{"mathvariant":2001},[1832,61464,2486],{"stretchy":1837},[1832,61466,3321],{},[1795,61468,61333],{},[238,61470,61471],{"encoding":240},"\\hat{y}(\\mathbf{x}) = \\begin{cases} \\arg\\max_k p_k, & u(\\mathbf{x}) \\le \\tau \\\\ \\text{reject}, & u(\\mathbf{x}) > \\tau \\end{cases}",[128,61473,61475,61543],{"className":61474,"ariaHidden":246},[245],[128,61476,61478,61481,61525,61528,61531,61534,61537,61540],{"className":61477},[250],[128,61479],{"className":61480,"style":1892},[254],[128,61482,61484],{"className":61483},[259,54949],[128,61485,61487,61516],{"className":61486},[274,321],[128,61488,61490,61513],{"className":61489},[278],[128,61491,61493,61501],{"className":61492,"style":12173},[282],[128,61494,61495,61498],{"style":54961},[128,61496],{"className":61497,"style":335},[290],[128,61499,1830],{"className":61500,"style":1874},[259,1873],[128,61502,61503,61506],{"style":54961},[128,61504],{"className":61505,"style":335},[290],[128,61507,61510],{"className":61508,"style":61509},[54983],"left:-0.1944em;",[128,61511,60020],{"className":61512},[259],[128,61514,347],{"className":61515},[346],[128,61517,61519],{"className":61518},[278],[128,61520,61523],{"className":61521,"style":61522},[282],"height:0.1944em;",[128,61524],{},[128,61526,2477],{"className":61527},[1896],[128,61529,2760],{"className":61530},[259,2151],[128,61532,2486],{"className":61533},[1928],[128,61535],{"className":61536,"style":1878},[269],[128,61538,1994],{"className":61539},[1882],[128,61541],{"className":61542,"style":1878},[269],[128,61544,61546,61550],{"className":61545},[250],[128,61547],{"className":61548,"style":61549},[254],"height:3em;vertical-align:-1.25em;",[128,61551,61553,61559,61805],{"className":61552},[1911],[128,61554,61556],{"className":61555,"style":2142},[1896,2141],[128,61557,1838],{"className":61558},[2146,10370],[128,61560,61562],{"className":61561},[259],[128,61563,61565,61714,61718],{"className":61564},[8172],[128,61566,61569],{"className":61567},[61568],"col-align-l",[128,61570,61572,61705],{"className":61571},[274,321],[128,61573,61575,61702],{"className":61574},[278],[128,61576,61579,61684],{"className":61577,"style":61578},[282],"height:1.69em;",[128,61580,61582,61586],{"style":61581},"top:-3.69em;",[128,61583],{"className":61584,"style":61585},[290],"height:3.008em;",[128,61587,61589,61595,61598,61638,61641,61681],{"className":61588},[259],[128,61590,61592,61593],{"className":61591},[2268],"ar",[128,61594,24505],{"style":17336},[128,61596],{"className":61597,"style":1907},[269],[128,61599,61601,61604],{"className":61600},[2268],[128,61602,61407],{"className":61603},[2268],[128,61605,61607],{"className":61606},[2087],[128,61608,61610,61630],{"className":61609},[274,321],[128,61611,61613,61627],{"className":61612},[278],[128,61614,61616],{"className":61615,"style":2218},[282],[128,61617,61618,61621],{"style":31837},[128,61619],{"className":61620,"style":291},[290],[128,61622,61624],{"className":61623},[299,300,301,298],[128,61625,2022],{"className":61626,"style":2231},[259,1873,298],[128,61628,347],{"className":61629},[346],[128,61631,61633],{"className":61632},[278],[128,61634,61636],{"className":61635,"style":2241},[282],[128,61637],{},[128,61639],{"className":61640,"style":1907},[269],[128,61642,61644,61647],{"className":61643},[259],[128,61645,11],{"className":61646},[259,1873],[128,61648,61650],{"className":61649},[2087],[128,61651,61653,61673],{"className":61652},[274,321],[128,61654,61656,61670],{"className":61655},[278],[128,61657,61659],{"className":61658,"style":2218},[282],[128,61660,61661,61664],{"style":2221},[128,61662],{"className":61663,"style":291},[290],[128,61665,61667],{"className":61666},[299,300,301,298],[128,61668,2022],{"className":61669,"style":2231},[259,1873,298],[128,61671,347],{"className":61672},[346],[128,61674,61676],{"className":61675},[278],[128,61677,61679],{"className":61678,"style":2241},[282],[128,61680],{},[128,61682,1845],{"className":61683},[1903],[128,61685,61687,61690],{"style":61686},"top:-2.25em;",[128,61688],{"className":61689,"style":61585},[290],[128,61691,61693,61699],{"className":61692},[259],[128,61694,61696],{"className":61695},[259,260],[128,61697,61448],{"className":61698},[259],[128,61700,1845],{"className":61701},[1903],[128,61703,347],{"className":61704},[346],[128,61706,61708],{"className":61707},[278],[128,61709,61712],{"className":61710,"style":61711},[282],"height:1.19em;",[128,61713],{},[128,61715],{"className":61716,"style":61717},[8388],"width:1em;",[128,61719,61721],{"className":61720},[61568],[128,61722,61724,61797],{"className":61723},[274,321],[128,61725,61727,61794],{"className":61726},[278],[128,61728,61730,61762],{"className":61729,"style":61578},[282],[128,61731,61732,61735],{"style":61581},[128,61733],{"className":61734,"style":61585},[290],[128,61736,61738,61741,61744,61747,61750,61753,61756,61759],{"className":61737},[259],[128,61739,35129],{"className":61740},[259,1873],[128,61742,2477],{"className":61743},[1896],[128,61745,2760],{"className":61746},[259,2151],[128,61748,2486],{"className":61749},[1928],[128,61751],{"className":61752,"style":1878},[269],[128,61754,23023],{"className":61755},[1882],[128,61757],{"className":61758,"style":1878},[269],[128,61760,61333],{"className":61761,"style":61349},[259,1873],[128,61763,61764,61767],{"style":61686},[128,61765],{"className":61766,"style":61585},[290],[128,61768,61770,61773,61776,61779,61782,61785,61788,61791],{"className":61769},[259],[128,61771,35129],{"className":61772},[259,1873],[128,61774,2477],{"className":61775},[1896],[128,61777,2760],{"className":61778},[259,2151],[128,61780,2486],{"className":61781},[1928],[128,61783],{"className":61784,"style":1878},[269],[128,61786,3321],{"className":61787},[1882],[128,61789],{"className":61790,"style":1878},[269],[128,61792,61333],{"className":61793,"style":61349},[259,1873],[128,61795,347],{"className":61796},[346],[128,61798,61800],{"className":61799},[278],[128,61801,61803],{"className":61802,"style":61711},[282],[128,61804],{},[128,61806],{"className":61807},[1928,5570],[11,61809,61810,61811,62018],{},"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 ",[128,61812,61814,61859],{"className":61813,"translate":218},[217],[128,61815,61817],{"className":61816},[222],[224,61818,61819],{"xmlns":226},[228,61820,61821,61856],{},[231,61822,61823,61826,61828,61830,61832,61834,61836,61838,61840,61846],{},[1795,61824,61825],{"mathvariant":1981},"LSE",[1832,61827,3278],{},[1832,61829,2477],{"stretchy":1837},[1795,61831,38997],{"mathvariant":2001},[1832,61833,2486],{"stretchy":1837},[1832,61835,1994],{},[1795,61837,24373],{},[1832,61839,3278],{},[2016,61841,61842,61844],{},[1832,61843,2042],{},[1795,61845,2022],{},[1977,61847,61848,61850],{},[1795,61849,3713],{},[2016,61851,61852,61854],{},[1795,61853,38997],{},[1795,61855,2022],{},[238,61857,61858],{"encoding":240},"\\operatorname{LSE}(\\mathbf{z}) = \\log\\sum_k e^{z_k}",[128,61860,61862,61892],{"className":61861,"ariaHidden":246},[245],[128,61863,61865,61868,61874,61877,61880,61883,61886,61889],{"className":61864},[250],[128,61866],{"className":61867,"style":1892},[254],[128,61869,61871],{"className":61870},[2268],[128,61872,61825],{"className":61873},[259,3353],[128,61875,2477],{"className":61876},[1896],[128,61878,38997],{"className":61879},[259,2151],[128,61881,2486],{"className":61882},[1928],[128,61884],{"className":61885,"style":1878},[269],[128,61887,1994],{"className":61888},[1882],[128,61890],{"className":61891,"style":1878},[269],[128,61893,61895,61898,61903,61906,61946,61949],{"className":61894},[250],[128,61896],{"className":61897,"style":7777},[254],[128,61899,24502,61901],{"className":61900},[2268],[128,61902,24505],{"style":17336},[128,61904],{"className":61905,"style":1907},[269],[128,61907,61909,61912],{"className":61908},[2268],[128,61910,2042],{"className":61911,"style":2274},[2268,2272,2273],[128,61913,61915],{"className":61914},[2087],[128,61916,61918,61938],{"className":61917},[274,321],[128,61919,61921,61935],{"className":61920},[278],[128,61922,61924],{"className":61923,"style":31692},[282],[128,61925,61926,61929],{"style":2290},[128,61927],{"className":61928,"style":291},[290],[128,61930,61932],{"className":61931},[299,300,301,298],[128,61933,2022],{"className":61934,"style":2231},[259,1873,298],[128,61936,347],{"className":61937},[346],[128,61939,61941],{"className":61940},[278],[128,61942,61944],{"className":61943,"style":2330},[282],[128,61945],{},[128,61947],{"className":61948,"style":1907},[269],[128,61950,61952,61955],{"className":61951},[259],[128,61953,3713],{"className":61954},[259,1873],[128,61956,61958],{"className":61957},[2087],[128,61959,61961],{"className":61960},[274],[128,61962,61964],{"className":61963},[278],[128,61965,61967],{"className":61966,"style":39307},[282],[128,61968,61969,61972],{"style":2452},[128,61970],{"className":61971,"style":291},[290],[128,61973,61975],{"className":61974},[299,300,301,298],[128,61976,61978],{"className":61977},[259,298],[128,61979,61981,61984],{"className":61980},[259,298],[128,61982,38997],{"className":61983,"style":39325},[259,1873,298],[128,61985,61987],{"className":61986},[2087],[128,61988,61990,62010],{"className":61989},[274,321],[128,61991,61993,62007],{"className":61992},[278],[128,61994,61996],{"className":61995,"style":24117},[282],[128,61997,61998,62001],{"style":39340},[128,61999],{"className":62000,"style":5790},[290],[128,62002,62004],{"className":62003},[299,5794,5795,298],[128,62005,2022],{"className":62006,"style":2231},[259,1873,298],[128,62008,347],{"className":62009},[346],[128,62011,62013],{"className":62012},[278],[128,62014,62016],{"className":62015,"style":28958},[282],[128,62017],{},"。将它们在性质上加以对照：",[33962,62020,62021,62037],{},[33965,62022,62023],{},[23026,62024,62025,62028,62031,62034],{},[33970,62026,62027],{"align":33972},"分数",[33970,62029,62030],{"align":33972},"依赖的结构",[33970,62032,62033],{"align":33972},"是否需要 OOD 数据",[33970,62035,62036],{"align":33972},"不确定性语汇",[33984,62038,62039,62053,62066,62079],{},[23026,62040,62041,62044,62047,62050],{},[33989,62042,62043],{"align":33972},"MSP \u002F 熵",[33989,62045,62046],{"align":33972},"softmax 输出",[33989,62048,62049],{"align":33972},"否",[33989,62051,62052],{"align":33972},"无（受 3.3 节缺陷支配）",[23026,62054,62055,62058,62061,62063],{},[33989,62056,62057],{"align":33972},"Mahalanobis",[33989,62059,62060],{"align":33972},"各特征层的类条件高斯",[33989,62062,62049],{"align":33972},[33989,62064,62065],{"align":33972},"距离，几何语义",[23026,62067,62068,62071,62074,62076],{},[33989,62069,62070],{"align":33972},"能量分数",[33989,62072,62073],{"align":33972},"logits 的对数配分",[33989,62075,62049],{"align":33972},[33989,62077,62078],{"align":33972},"无显式不确定性",[23026,62080,62081,62114,62145,62149],{},[33989,62082,62083],{"align":33972},[35,62084,62085,62086],{},"EDL 的 ",[128,62087,62089,62102],{"className":62088,"translate":218},[217],[128,62090,62092],{"className":62091},[222],[224,62093,62094],{"xmlns":226},[228,62095,62096,62100],{},[231,62097,62098],{},[1795,62099,35129],{},[238,62101,35129],{"encoding":240},[128,62103,62105],{"className":62104,"ariaHidden":246},[245],[128,62106,62108,62111],{"className":62107},[250],[128,62109],{"className":62110,"style":7758},[254],[128,62112,35129],{"className":62113},[259,1873],[33989,62115,62116,62117],{"align":33972},"迪利克雷总强度 ",[128,62118,62120,62133],{"className":62119,"translate":218},[217],[128,62121,62123],{"className":62122},[222],[224,62124,62125],{"xmlns":226},[228,62126,62127,62131],{},[231,62128,62129],{},[1795,62130,41957],{},[238,62132,41957],{"encoding":240},[128,62134,62136],{"className":62135,"ariaHidden":246},[245],[128,62137,62139,62142],{"className":62138},[250],[128,62140],{"className":62141,"style":283},[254],[128,62143,41957],{"className":62144,"style":42029},[259,1873],[33989,62146,62147],{"align":33972},[35,62148,62049],{},[33989,62150,62151],{"align":33972},"证据缺失量，可解释",[11,62153,62154,62155,62158],{},"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",[35,62156,62157],{},"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）。",[11,62160,62161],{},"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。",[2610,62163,62165],{"id":62164},"_52-校准与选择性预测","5.2 校准与选择性预测",[11,62167,62168,62171,62172,62392],{},[35,62169,62170],{},"校准","关心的是 ",[128,62173,62175,62220],{"className":62174,"translate":218},[217],[128,62176,62178],{"className":62177},[222],[224,62179,62180],{"xmlns":226},[228,62181,62182,62217],{},[231,62183,62184,62186,62188,62194,62196,62198,62200,62206,62208,62211,62213,62215],{},[1795,62185,23001],{"mathvariant":2008},[1832,62187,2477],{"stretchy":1837},[54905,62189,62190,62192],{"accent":246},[1795,62191,1830],{},[1832,62193,60020],{},[1832,62195,1994],{},[1795,62197,1830],{},[1832,62199,5443],{},[54905,62201,62202,62204],{"accent":246},[1795,62203,11],{},[1832,62205,60020],{},[1832,62207,1994],{},[1795,62209,62210],{},"q",[1832,62212,2486],{"stretchy":1837},[1832,62214,1994],{},[1795,62216,62210],{},[238,62218,62219],{"encoding":240},"\\mathbb{P}(\\hat{y} = y \\mid \\hat{p} = q) = q",[128,62221,62223,62286,62304,62362,62383],{"className":62222,"ariaHidden":246},[245],[128,62224,62226,62229,62232,62235,62277,62280,62283],{"className":62225},[250],[128,62227],{"className":62228,"style":1892},[254],[128,62230,23001],{"className":62231},[259,2167],[128,62233,2477],{"className":62234},[1896],[128,62236,62238],{"className":62237},[259,54949],[128,62239,62241,62269],{"className":62240},[274,321],[128,62242,62244,62266],{"className":62243},[278],[128,62245,62247,62255],{"className":62246,"style":12173},[282],[128,62248,62249,62252],{"style":54961},[128,62250],{"className":62251,"style":335},[290],[128,62253,1830],{"className":62254,"style":1874},[259,1873],[128,62256,62257,62260],{"style":54961},[128,62258],{"className":62259,"style":335},[290],[128,62261,62263],{"className":62262,"style":61509},[54983],[128,62264,60020],{"className":62265},[259],[128,62267,347],{"className":62268},[346],[128,62270,62272],{"className":62271},[278],[128,62273,62275],{"className":62274,"style":61522},[282],[128,62276],{},[128,62278],{"className":62279,"style":1878},[269],[128,62281,1994],{"className":62282},[1882],[128,62284],{"className":62285,"style":1878},[269],[128,62287,62289,62292,62295,62298,62301],{"className":62288},[250],[128,62290],{"className":62291,"style":1892},[254],[128,62293,1830],{"className":62294,"style":1874},[259,1873],[128,62296],{"className":62297,"style":1878},[269],[128,62299,5443],{"className":62300},[1882],[128,62302],{"className":62303,"style":1878},[269],[128,62305,62307,62310,62353,62356,62359],{"className":62306},[250],[128,62308],{"className":62309,"style":16030},[254],[128,62311,62313],{"className":62312},[259,54949],[128,62314,62316,62345],{"className":62315},[274,321],[128,62317,62319,62342],{"className":62318},[278],[128,62320,62322,62330],{"className":62321,"style":12173},[282],[128,62323,62324,62327],{"style":54961},[128,62325],{"className":62326,"style":335},[290],[128,62328,11],{"className":62329},[259,1873],[128,62331,62332,62335],{"style":54961},[128,62333],{"className":62334,"style":335},[290],[128,62336,62339],{"className":62337,"style":62338},[54983],"left:-0.1667em;",[128,62340,60020],{"className":62341},[259],[128,62343,347],{"className":62344},[346],[128,62346,62348],{"className":62347},[278],[128,62349,62351],{"className":62350,"style":61522},[282],[128,62352],{},[128,62354],{"className":62355,"style":1878},[269],[128,62357,1994],{"className":62358},[1882],[128,62360],{"className":62361,"style":1878},[269],[128,62363,62365,62368,62371,62374,62377,62380],{"className":62364},[250],[128,62366],{"className":62367,"style":1892},[254],[128,62369,62210],{"className":62370,"style":1874},[259,1873],[128,62372,2486],{"className":62373},[1928],[128,62375],{"className":62376,"style":1878},[269],[128,62378,1994],{"className":62379},[1882],[128,62381],{"className":62382,"style":1878},[269],[128,62384,62386,62389],{"className":62385},[250],[128,62387],{"className":62388,"style":11158},[254],[128,62390,62210],{"className":62391,"style":1874},[259,1873]," 是否成立，常用期望校准误差",[128,62394,62396],{"className":62395,"translate":218},[1962],[128,62397,62399,62485],{"className":62398,"translate":218},[217],[128,62400,62402],{"className":62401},[222],[224,62403,62404],{"xmlns":226,"display":1971},[228,62405,62406,62482],{},[231,62407,62408,62411,62413,62427,62443,62445,62448,62451,62453,62455,62461,62463,62465,62468,62470,62472,62478,62480],{},[234,62409,62410],{},"ECE",[1832,62412,1994],{},[6961,62414,62415,62417,62425],{},[1832,62416,2042],{},[231,62418,62419,62421,62423],{},[1795,62420,30849],{},[1832,62422,1994],{},[1840,62424,1842],{},[1795,62426,30641],{},[5451,62428,62429,62441],{},[231,62430,62431,62433,62439],{},[1795,62432,5443],{"mathvariant":1981},[2016,62434,62435,62437],{},[1795,62436,5459],{"mathvariant":1797},[1795,62438,30849],{},[1795,62440,5443],{"mathvariant":1981},[1795,62442,16280],{},[234,62444,6528],{},[1832,62446,5443],{"fence":1837,"stretchy":246,"minsize":62447,"maxsize":62447},"1.8em",[1795,62449,62450],{"mathvariant":1981},"acc",[1832,62452,3278],{},[1832,62454,2477],{"stretchy":1837},[2016,62456,62457,62459],{},[1795,62458,5459],{"mathvariant":1797},[1795,62460,30849],{},[1832,62462,2486],{"stretchy":1837},[1832,62464,1989],{},[1795,62466,62467],{"mathvariant":1981},"conf",[1832,62469,3278],{},[1832,62471,2477],{"stretchy":1837},[2016,62473,62474,62476],{},[1795,62475,5459],{"mathvariant":1797},[1795,62477,30849],{},[1832,62479,2486],{"stretchy":1837},[1832,62481,5443],{"fence":1837,"stretchy":246,"minsize":62447,"maxsize":62447},[238,62483,62484],{"encoding":240},"\\text{ECE} = \\sum_{m=1}^{M} \\frac{|\\mathcal{B}_m|}{n}\\,\\Big|\\operatorname{acc}(\\mathcal{B}_m) - \\operatorname{conf}(\\mathcal{B}_m)\\Big|",[128,62486,62488,62509,62808],{"className":62487,"ariaHidden":246},[245],[128,62489,62491,62494,62500,62503,62506],{"className":62490},[250],[128,62492],{"className":62493,"style":283},[254],[128,62495,62497],{"className":62496},[259,260],[128,62498,62410],{"className":62499},[259],[128,62501],{"className":62502,"style":1878},[269],[128,62504,1994],{"className":62505},[1882],[128,62507],{"className":62508,"style":1878},[269],[128,62510,62512,62516,62585,62588,62696,62699,62744,62747,62753,62756,62796,62799,62802,62805],{"className":62511},[250],[128,62513],{"className":62514,"style":62515},[254],"height:3.0954em;vertical-align:-1.2671em;",[128,62517,62519],{"className":62518},[2268,7074],[128,62520,62522,62576],{"className":62521},[274,321],[128,62523,62525,62573],{"className":62524},[278],[128,62526,62528,62549,62559],{"className":62527,"style":7084},[282],[128,62529,62531,62534],{"style":62530},"top:-1.8829em;margin-left:0em;",[128,62532],{"className":62533,"style":7091},[290],[128,62535,62537],{"className":62536},[299,300,301,298],[128,62538,62540,62543,62546],{"className":62539},[259,298],[128,62541,30849],{"className":62542},[259,1873,298],[128,62544,1994],{"className":62545},[1882,298],[128,62547,1842],{"className":62548},[259,298],[128,62550,62551,62554],{"style":7109},[128,62552],{"className":62553,"style":7091},[290],[128,62555,62556],{},[128,62557,2042],{"className":62558},[2268,2272,7118],[128,62560,62561,62564],{"style":7121},[128,62562],{"className":62563,"style":7091},[290],[128,62565,62567],{"className":62566},[299,300,301,298],[128,62568,62570],{"className":62569},[259,298],[128,62571,30641],{"className":62572,"style":26806},[259,1873,298],[128,62574,347],{"className":62575},[346],[128,62577,62579],{"className":62578},[278],[128,62580,62583],{"className":62581,"style":62582},[282],"height:1.2671em;",[128,62584],{},[128,62586],{"className":62587,"style":1907},[269],[128,62589,62591,62594,62693],{"className":62590},[259],[128,62592],{"className":62593},[1896,5570],[128,62595,62597],{"className":62596},[5451],[128,62598,62600,62685],{"className":62599},[274,321],[128,62601,62603,62682],{"className":62602},[278],[128,62604,62607,62618,62626],{"className":62605,"style":62606},[282],"height:1.427em;",[128,62608,62609,62612],{"style":13123},[128,62610],{"className":62611,"style":335},[290],[128,62613,62615],{"className":62614},[259],[128,62616,16280],{"className":62617},[259,1873],[128,62619,62620,62623],{"style":5617},[128,62621],{"className":62622,"style":335},[290],[128,62624],{"className":62625,"style":5625},[5624],[128,62627,62628,62631],{"style":13189},[128,62629],{"className":62630,"style":335},[290],[128,62632,62634,62637,62679],{"className":62633},[259],[128,62635,5443],{"className":62636},[259],[128,62638,62640,62644],{"className":62639},[259],[128,62641,5459],{"className":62642,"style":62643},[259,1813],"margin-right:0.0304em;",[128,62645,62647],{"className":62646},[2087],[128,62648,62650,62671],{"className":62649},[274,321],[128,62651,62653,62668],{"className":62652},[278],[128,62654,62656],{"className":62655,"style":28738},[282],[128,62657,62659,62662],{"style":62658},"top:-2.55em;margin-left:-0.0304em;margin-right:0.05em;",[128,62660],{"className":62661,"style":291},[290],[128,62663,62665],{"className":62664},[299,300,301,298],[128,62666,30849],{"className":62667},[259,1873,298],[128,62669,347],{"className":62670},[346],[128,62672,62674],{"className":62673},[278],[128,62675,62677],{"className":62676,"style":2241},[282],[128,62678],{},[128,62680,5443],{"className":62681},[259],[128,62683,347],{"className":62684},[346],[128,62686,62688],{"className":62687},[278],[128,62689,62691],{"className":62690,"style":38310},[282],[128,62692],{},[128,62694],{"className":62695},[1928,5570],[128,62697],{"className":62698,"style":1907},[269],[128,62700,62702],{"className":62701},[259],[128,62703,62705],{"className":62704},[2146,55303],[128,62706,62708,62735],{"className":62707},[274,321],[128,62709,62711,62732],{"className":62710},[278],[128,62712,62715],{"className":62713,"style":62714},[282],"height:1.15em;",[128,62716,62718,62722],{"style":62717},"top:-3.15em;",[128,62719],{"className":62720,"style":62721},[290],"height:3.8em;",[128,62723,62725],{"style":62724},"width:0.333em;height:1.8em;",[29411,62726,62729],{"xmlns":29413,"width":62727,"height":62447,"viewBox":62728},"0.333em","0 0 333 1800",[29419,62730],{"d":62731},"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",[128,62733,347],{"className":62734},[346],[128,62736,62738],{"className":62737},[278],[128,62739,62742],{"className":62740,"style":62741},[282],"height:0.65em;",[128,62743],{},[128,62745],{"className":62746,"style":1907},[269],[128,62748,62750],{"className":62749},[2268],[128,62751,62450],{"className":62752},[259,3353],[128,62754,2477],{"className":62755},[1896],[128,62757,62759,62762],{"className":62758},[259],[128,62760,5459],{"className":62761,"style":62643},[259,1813],[128,62763,62765],{"className":62764},[2087],[128,62766,62768,62788],{"className":62767},[274,321],[128,62769,62771,62785],{"className":62770},[278],[128,62772,62774],{"className":62773,"style":28738},[282],[128,62775,62776,62779],{"style":62658},[128,62777],{"className":62778,"style":291},[290],[128,62780,62782],{"className":62781},[299,300,301,298],[128,62783,30849],{"className":62784},[259,1873,298],[128,62786,347],{"className":62787},[346],[128,62789,62791],{"className":62790},[278],[128,62792,62794],{"className":62793,"style":2241},[282],[128,62795],{},[128,62797,2486],{"className":62798},[1928],[128,62800],{"className":62801,"style":2508},[269],[128,62803,1989],{"className":62804},[2115],[128,62806],{"className":62807,"style":2508},[269],[128,62809,62811,62814,62821,62824,62864,62867],{"className":62810},[250],[128,62812],{"className":62813,"style":2134},[254],[128,62815,62817],{"className":62816},[2268],[128,62818,62467],{"className":62819,"style":62820},[259,3353],"margin-right:0.0778em;",[128,62822,2477],{"className":62823},[1896],[128,62825,62827,62830],{"className":62826},[259],[128,62828,5459],{"className":62829,"style":62643},[259,1813],[128,62831,62833],{"className":62832},[2087],[128,62834,62836,62856],{"className":62835},[274,321],[128,62837,62839,62853],{"className":62838},[278],[128,62840,62842],{"className":62841,"style":28738},[282],[128,62843,62844,62847],{"style":62658},[128,62845],{"className":62846,"style":291},[290],[128,62848,62850],{"className":62849},[299,300,301,298],[128,62851,30849],{"className":62852},[259,1873,298],[128,62854,347],{"className":62855},[346],[128,62857,62859],{"className":62858},[278],[128,62860,62862],{"className":62861,"style":2241},[282],[128,62863],{},[128,62865,2486],{"className":62866},[1928],[128,62868,62870],{"className":62869},[259],[128,62871,62873],{"className":62872},[2146,55303],[128,62874,62876,62896],{"className":62875},[274,321],[128,62877,62879,62893],{"className":62878},[278],[128,62880,62882],{"className":62881,"style":62714},[282],[128,62883,62884,62887],{"style":62717},[128,62885],{"className":62886,"style":62721},[290],[128,62888,62889],{"style":62724},[29411,62890,62891],{"xmlns":29413,"width":62727,"height":62447,"viewBox":62728},[29419,62892],{"d":62731},[128,62894,347],{"className":62895},[346],[128,62897,62899],{"className":62898},[278],[128,62900,62902],{"className":62901,"style":62741},[282],[128,62903],{},[11,62905,62906,62907,62977],{},"度量，其中 ",[128,62908,62910,62928],{"className":62909,"translate":218},[217],[128,62911,62913],{"className":62912},[222],[224,62914,62915],{"xmlns":226},[228,62916,62917,62925],{},[231,62918,62919],{},[2016,62920,62921,62923],{},[1795,62922,5459],{"mathvariant":1797},[1795,62924,30849],{},[238,62926,62927],{"encoding":240},"\\mathcal{B}_m",[128,62929,62931],{"className":62930,"ariaHidden":246},[245],[128,62932,62934,62937],{"className":62933},[250],[128,62935],{"className":62936,"style":36058},[254],[128,62938,62940,62943],{"className":62939},[259],[128,62941,5459],{"className":62942,"style":62643},[259,1813],[128,62944,62946],{"className":62945},[2087],[128,62947,62949,62969],{"className":62948},[274,321],[128,62950,62952,62966],{"className":62951},[278],[128,62953,62955],{"className":62954,"style":28738},[282],[128,62956,62957,62960],{"style":62658},[128,62958],{"className":62959,"style":291},[290],[128,62961,62963],{"className":62962},[299,300,301,298],[128,62964,30849],{"className":62965},[259,1873,298],[128,62967,347],{"className":62968},[346],[128,62970,62972],{"className":62971},[278],[128,62973,62975],{"className":62974,"style":2241},[282],[128,62976],{}," 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。",[11,62979,62980,3637,62983,63011,63012,63078,63079,63111,63112,63140,63141,63203],{},[35,62981,62982],{},"选择性预测（selective prediction）",[128,62984,62986,62999],{"className":62985,"translate":218},[217],[128,62987,62989],{"className":62988},[222],[224,62990,62991],{"xmlns":226},[228,62992,62993,62997],{},[231,62994,62995],{},[1795,62996,35129],{},[238,62998,35129],{"encoding":240},[128,63000,63002],{"className":63001,"ariaHidden":246},[245],[128,63003,63005,63008],{"className":63004},[250],[128,63006],{"className":63007,"style":7758},[254],[128,63009,35129],{"className":63010},[259,1873]," 的更自然的落点。经典 Chow 规则指出，在已知真实后验 ",[128,63013,63015,63039],{"className":63014,"translate":218},[217],[128,63016,63018],{"className":63017},[222],[224,63019,63020],{"xmlns":226},[228,63021,63022,63036],{},[231,63023,63024,63026,63028,63030,63032,63034],{},[1795,63025,11],{},[1832,63027,2477],{"stretchy":1837},[1795,63029,1830],{},[1832,63031,5443],{},[1795,63033,2760],{"mathvariant":2001},[1832,63035,2486],{"stretchy":1837},[238,63037,63038],{"encoding":240},"p(y \\mid \\mathbf{x})",[128,63040,63042,63066],{"className":63041,"ariaHidden":246},[245],[128,63043,63045,63048,63051,63054,63057,63060,63063],{"className":63044},[250],[128,63046],{"className":63047,"style":1892},[254],[128,63049,11],{"className":63050},[259,1873],[128,63052,2477],{"className":63053},[1896],[128,63055,1830],{"className":63056,"style":1874},[259,1873],[128,63058],{"className":63059,"style":1878},[269],[128,63061,5443],{"className":63062},[1882],[128,63064],{"className":63065,"style":1878},[269],[128,63067,63069,63072,63075],{"className":63068},[250],[128,63070],{"className":63071,"style":1892},[254],[128,63073,2760],{"className":63074},[259,2151],[128,63076,2486],{"className":63077},[1928]," 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",[35,63080,63081,63082,63110],{},"依赖于 ",[128,63083,63085,63098],{"className":63084,"translate":218},[217],[128,63086,63088],{"className":63087},[222],[224,63089,63090],{"xmlns":226},[228,63091,63092,63096],{},[231,63093,63094],{},[1795,63095,11],{},[238,63097,11],{"encoding":240},[128,63099,63101],{"className":63100,"ariaHidden":246},[245],[128,63102,63104,63107],{"className":63103},[250],[128,63105],{"className":63106,"style":11158},[254],[128,63108,11],{"className":63109},[259,1873]," 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 ",[128,63113,63115,63128],{"className":63114,"translate":218},[217],[128,63116,63118],{"className":63117},[222],[224,63119,63120],{"xmlns":226},[228,63121,63122,63126],{},[231,63123,63124],{},[1795,63125,35129],{},[238,63127,35129],{"encoding":240},[128,63129,63131],{"className":63130,"ariaHidden":246},[245],[128,63132,63134,63137],{"className":63133},[250],[128,63135],{"className":63136,"style":7758},[254],[128,63138,35129],{"className":63139},[259,1873]," 或 ",[128,63142,63144,63167],{"className":63143,"translate":218},[217],[128,63145,63147],{"className":63146},[222],[224,63148,63149],{"xmlns":226},[228,63150,63151,63165],{},[231,63152,63153,63155,63157,63159,63161,63163],{},[1795,63154,30626],{},[1832,63156,2477],{"stretchy":1837},[1795,63158,1830],{},[1832,63160,13024],{"separator":246},[1795,63162,26389],{"mathvariant":4834},[1832,63164,2486],{"stretchy":1837},[238,63166,48574],{"encoding":240},[128,63168,63170],{"className":63169,"ariaHidden":246},[245],[128,63171,63173,63176,63179,63182,63185,63188,63191,63200],{"className":63172},[250],[128,63174],{"className":63175,"style":1892},[254],[128,63177,30626],{"className":63178,"style":30665},[259,1873],[128,63180,2477],{"className":63181},[1896],[128,63183,1830],{"className":63184,"style":1874},[259,1873],[128,63186,13024],{"className":63187},[1903],[128,63189],{"className":63190,"style":1907},[269],[128,63192,63194],{"className":63193},[259],[128,63195,63197],{"className":63196},[259],[128,63198,26389],{"className":63199,"style":26423},[259,4895],[128,63201,2486],{"className":63202},[1928]," 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）。",[2610,63205,63207],{"id":63206},"_53-主动学习与半监督学习","5.3 主动学习与半监督学习",[11,63209,63210,63213,63214,63140,63258,63336,63337,63365,63366,63394,63395,63398,63399,63427],{},[35,63211,63212],{},"主动学习。"," 采集函数可以直接取 ",[128,63215,63217,63237],{"className":63216,"translate":218},[217],[128,63218,63220],{"className":63219},[222],[224,63221,63222],{"xmlns":226},[228,63223,63224,63234],{},[231,63225,63226,63228,63230,63232],{},[1795,63227,35129],{},[1832,63229,2477],{"stretchy":1837},[1795,63231,2760],{"mathvariant":2001},[1832,63233,2486],{"stretchy":1837},[238,63235,63236],{"encoding":240},"u(\\mathbf{x})",[128,63238,63240],{"className":63239,"ariaHidden":246},[245],[128,63241,63243,63246,63249,63252,63255],{"className":63242},[250],[128,63244],{"className":63245,"style":1892},[254],[128,63247,35129],{"className":63248},[259,1873],[128,63250,2477],{"className":63251},[1896],[128,63253,2760],{"className":63254},[259,2151],[128,63256,2486],{"className":63257},[1928],[128,63259,63261,63291],{"className":63260,"translate":218},[217],[128,63262,63264],{"className":63263},[222],[224,63265,63266],{"xmlns":226},[228,63267,63268,63288],{},[231,63269,63270,63272,63274,63276,63278,63280,63282,63284,63286],{},[1795,63271,30626],{},[1832,63273,2477],{"stretchy":1837},[1795,63275,1830],{},[1832,63277,13024],{"separator":246},[1795,63279,26389],{"mathvariant":4834},[1832,63281,2486],{"stretchy":1837},[1832,63283,2477],{"stretchy":1837},[1795,63285,2760],{"mathvariant":2001},[1832,63287,2486],{"stretchy":1837},[238,63289,63290],{"encoding":240},"I(y;\\boldsymbol{\\pi})(\\mathbf{x})",[128,63292,63294],{"className":63293,"ariaHidden":246},[245],[128,63295,63297,63300,63303,63306,63309,63312,63315,63324,63327,63330,63333],{"className":63296},[250],[128,63298],{"className":63299,"style":1892},[254],[128,63301,30626],{"className":63302,"style":30665},[259,1873],[128,63304,2477],{"className":63305},[1896],[128,63307,1830],{"className":63308,"style":1874},[259,1873],[128,63310,13024],{"className":63311},[1903],[128,63313],{"className":63314,"style":1907},[269],[128,63316,63318],{"className":63317},[259],[128,63319,63321],{"className":63320},[259],[128,63322,26389],{"className":63323,"style":26423},[259,4895],[128,63325,2486],{"className":63326},[1928],[128,63328,2477],{"className":63329},[1896],[128,63331,2760],{"className":63332},[259,2151],[128,63334,2486],{"className":63335},[1928],"：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 ",[128,63338,63340,63353],{"className":63339,"translate":218},[217],[128,63341,63343],{"className":63342},[222],[224,63344,63345],{"xmlns":226},[228,63346,63347,63351],{},[231,63348,63349],{},[1795,63350,30626],{},[238,63352,30626],{"encoding":240},[128,63354,63356],{"className":63355,"ariaHidden":246},[245],[128,63357,63359,63362],{"className":63358},[250],[128,63360],{"className":63361,"style":283},[254],[128,63363,30626],{"className":63364,"style":30665},[259,1873]," 而非 ",[128,63367,63369,63382],{"className":63368,"translate":218},[217],[128,63370,63372],{"className":63371},[222],[224,63373,63374],{"xmlns":226},[228,63375,63376,63380],{},[231,63377,63378],{},[1795,63379,35129],{},[238,63381,35129],{"encoding":240},[128,63383,63385],{"className":63384,"ariaHidden":246},[245],[128,63386,63388,63391],{"className":63387},[250],[128,63389],{"className":63390,"style":7758},[254],[128,63392,35129],{"className":63393},[259,1873]," 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",[35,63396,63397],{},"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 ",[128,63400,63402,63415],{"className":63401,"translate":218},[217],[128,63403,63405],{"className":63404},[222],[224,63406,63407],{"xmlns":226},[228,63408,63409,63413],{},[231,63410,63411],{},[1795,63412,35129],{},[238,63414,35129],{"encoding":240},[128,63416,63418],{"className":63417,"ariaHidden":246},[245],[128,63419,63421,63424],{"className":63420},[250],[128,63422],{"className":63423,"style":7758},[254],[128,63425,35129],{"className":63426},[259,1873]," 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。",[11,63429,63430,63433,63434,63462,63463,63514,63515,63543],{},[35,63431,63432],{},"半监督与伪标签。"," 伪标签流程中，",[128,63435,63437,63450],{"className":63436,"translate":218},[217],[128,63438,63440],{"className":63439},[222],[224,63441,63442],{"xmlns":226},[228,63443,63444,63448],{},[231,63445,63446],{},[1795,63447,35129],{},[238,63449,35129],{"encoding":240},[128,63451,63453],{"className":63452,"ariaHidden":246},[245],[128,63454,63456,63459],{"className":63455},[250],[128,63457],{"className":63458,"style":7758},[254],[128,63460,35129],{"className":63461},[259,1873]," 提供了比「最大概率」更细的过滤准则：取 ",[128,63464,63466,63484],{"className":63465,"translate":218},[217],[128,63467,63469],{"className":63468},[222],[224,63470,63471],{"xmlns":226},[228,63472,63473,63481],{},[231,63474,63475,63477,63479],{},[1795,63476,35129],{},[1832,63478,4221],{},[1795,63480,61333],{},[238,63482,63483],{"encoding":240},"u \u003C \\tau",[128,63485,63487,63505],{"className":63486,"ariaHidden":246},[245],[128,63488,63490,63493,63496,63499,63502],{"className":63489},[250],[128,63491],{"className":63492,"style":6382},[254],[128,63494,35129],{"className":63495},[259,1873],[128,63497],{"className":63498,"style":1878},[269],[128,63500,4221],{"className":63501},[1882],[128,63503],{"className":63504,"style":1878},[269],[128,63506,63508,63511],{"className":63507},[250],[128,63509],{"className":63510,"style":7758},[254],[128,63512,61333],{"className":63513,"style":61349},[259,1873]," 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 ",[128,63516,63518,63531],{"className":63517,"translate":218},[217],[128,63519,63521],{"className":63520},[222],[224,63522,63523],{"xmlns":226},[228,63524,63525,63529],{},[231,63526,63527],{},[1795,63528,61333],{},[238,63530,61336],{"encoding":240},[128,63532,63534],{"className":63533,"ariaHidden":246},[245],[128,63535,63537,63540],{"className":63536},[250],[128,63538],{"className":63539,"style":7758},[254],[128,63541,61333],{"className":63542,"style":61349},[259,1873]," 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。",[2610,63545,63547],{"id":63546},"_54-安全关键场景","5.4 安全关键场景",[11,63549,63550,63551,44582],{},"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",[35,63552,63553],{},"可嵌入决策规则的二阶量",[35195,63555,63556,63646,63704,63739],{},[33251,63557,63558,63561,63562,63616,63617,63645],{},[35,63559,63560],{},"分割与体素级不确定性","：对每个体素输出 ",[128,63563,63565,63586],{"className":63564,"translate":218},[217],[128,63566,63568],{"className":63567},[222],[224,63569,63570],{"xmlns":226},[228,63571,63572,63584],{},[231,63573,63574,63576,63578,63580,63582],{},[1795,63575,5914],{"mathvariant":1981},[1832,63577,3278],{},[1832,63579,2477],{"stretchy":1837},[1795,63581,4835],{"mathvariant":4834},[1832,63583,2486],{"stretchy":1837},[238,63585,40766],{"encoding":240},[128,63587,63589],{"className":63588,"ariaHidden":246},[245],[128,63590,63592,63595,63601,63604,63613],{"className":63591},[250],[128,63593],{"className":63594,"style":1892},[254],[128,63596,63598],{"className":63597},[2268],[128,63599,5914],{"className":63600},[259,3353],[128,63602,2477],{"className":63603},[1896],[128,63605,63607],{"className":63606},[259],[128,63608,63610],{"className":63609},[259],[128,63611,4835],{"className":63612},[259,4895],[128,63614,2486],{"className":63615},[1928],"，得到逐像素的 ",[128,63618,63620,63633],{"className":63619,"translate":218},[217],[128,63621,63623],{"className":63622},[222],[224,63624,63625],{"xmlns":226},[228,63626,63627,63631],{},[231,63628,63629],{},[1795,63630,35129],{},[238,63632,35129],{"encoding":240},[128,63634,63636],{"className":63635,"ariaHidden":246},[245],[128,63637,63639,63642],{"className":63638},[250],[128,63640],{"className":63641,"style":7758},[254],[128,63643,35129],{"className":63644},[259,1873],"，可据此生成「需人工复核区域」的掩码。",[33251,63647,63648,63651,63652,63703],{},[35,63649,63650],{},"转诊（referral）机制","：将 ",[128,63653,63655,63673],{"className":63654,"translate":218},[217],[128,63656,63658],{"className":63657},[222],[224,63659,63660],{"xmlns":226},[228,63661,63662,63670],{},[231,63663,63664,63666,63668],{},[1795,63665,35129],{},[1832,63667,3321],{},[1795,63669,61333],{},[238,63671,63672],{"encoding":240},"u > \\tau",[128,63674,63676,63694],{"className":63675,"ariaHidden":246},[245],[128,63677,63679,63682,63685,63688,63691],{"className":63678},[250],[128,63680],{"className":63681,"style":6382},[254],[128,63683,35129],{"className":63684},[259,1873],[128,63686],{"className":63687,"style":1878},[269],[128,63689,3321],{"className":63690},[1882],[128,63692],{"className":63693,"style":1878},[269],[128,63695,63697,63700],{"className":63696},[250],[128,63698],{"className":63699,"style":7758},[254],[128,63701,61333],{"className":63702,"style":61349},[259,1873]," 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。",[33251,63705,63706,63709,63710,63738],{},[35,63707,63708],{},"开放集动作识别","：视频中存在未见动作时，",[128,63711,63713,63726],{"className":63712,"translate":218},[217],[128,63714,63716],{"className":63715},[222],[224,63717,63718],{"xmlns":226},[228,63719,63720,63724],{},[231,63721,63722],{},[1795,63723,35129],{},[238,63725,35129],{"encoding":240},[128,63727,63729],{"className":63728,"ariaHidden":246},[245],[128,63730,63732,63735],{"className":63731},[250],[128,63733],{"className":63734,"style":7758},[254],[128,63736,35129],{"className":63737},[259,1873]," 提供拒绝信号。",[33251,63740,63741,63744],{},[35,63742,63743],{},"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。",[11,63746,63747,63748,63751,63752,63780],{},"这些应用的共同点是：",[35,63749,63750],{},"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，",[128,63753,63755,63768],{"className":63754,"translate":218},[217],[128,63756,63758],{"className":63757},[222],[224,63759,63760],{"xmlns":226},[228,63761,63762,63766],{},[231,63763,63764],{},[1795,63765,35129],{},[238,63767,35129],{"encoding":240},[128,63769,63771],{"className":63770,"ariaHidden":246},[245],[128,63772,63774,63777],{"className":63773},[250],[128,63775],{"className":63776,"style":7758},[254],[128,63778,35129],{"className":63779},[259,1873]," 至多是一个监控指标。",[2610,63782,63784],{"id":63783},"_55-回归情形的推广","5.5 回归情形的推广",[11,63786,63787,63788,44582],{},"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",[35,63789,63790],{},"正态—逆 Gamma（Normal-Inverse-Gamma, NIG）先验",[128,63792,63794],{"className":63793,"translate":218},[1962],[128,63795,63797,63871],{"className":63796,"translate":218},[217],[128,63798,63800],{"className":63799},[222],[224,63801,63802],{"xmlns":226,"display":1971},[228,63803,63804,63868],{},[231,63805,63806,63808,63810,63812,63814,63836,63838,63840,63846,63848,63858,63860,63862,63864,63866],{},[1795,63807,20063],{},[1832,63809,5911],{},[1795,63811,26691],{"mathvariant":1797},[234,63813,8524],{},[231,63815,63816,63818,63820,63822,63834],{},[1832,63817,2477],{"fence":246},[1795,63819,11131],{},[1832,63821,1845],{"separator":246},[5451,63823,63824,63831],{},[1977,63825,63826,63829],{},[1795,63827,63828],{},"σ",[1840,63830,2639],{},[1795,63832,63833],{},"υ",[1832,63835,2486],{"fence":246},[1832,63837,1845],{"separator":246},[269,63839],{"width":11568},[1977,63841,63842,63844],{},[1795,63843,63828],{},[1840,63845,2639],{},[1832,63847,5911],{},[1977,63849,63850,63852],{},[1795,63851,6020],{"mathvariant":1981},[231,63853,63854,63856],{},[1832,63855,1989],{},[1840,63857,1842],{},[1832,63859,2477],{"stretchy":1837},[1795,63861,4835],{},[1832,63863,1845],{"separator":246},[1795,63865,18848],{},[1832,63867,2486],{"stretchy":1837},[238,63869,63870],{"encoding":240},"\\mu \\sim \\mathcal{N}\\!\\left(\\gamma, \\frac{\\sigma^2}{\\upsilon}\\right),\n\\qquad\n\\sigma^2 \\sim \\Gamma^{-1}(\\alpha, \\beta)",[128,63872,63874,63892,64071],{"className":63873,"ariaHidden":246},[245],[128,63875,63877,63880,63883,63886,63889],{"className":63876},[250],[128,63878],{"className":63879,"style":11158},[254],[128,63881,20063],{"className":63882},[259,1873],[128,63884],{"className":63885,"style":1878},[269],[128,63887,5911],{"className":63888},[1882],[128,63890],{"className":63891,"style":1878},[269],[128,63893,63895,63899,63903,63906,63909,64021,64024,64027,64030,64033,64062,64065,64068],{"className":63894},[250],[128,63896],{"className":63897,"style":63898},[254],"height:2.4411em;vertical-align:-0.95em;",[128,63900,26691],{"className":63901,"style":63902},[259,1813],"margin-right:0.1474em;",[128,63904],{"className":63905,"style":317},[269],[128,63907],{"className":63908,"style":1907},[269],[128,63910,63912,63918,63921,63924,63927,64015],{"className":63911},[1911],[128,63913,63915],{"className":63914,"style":2142},[1896,2141],[128,63916,2477],{"className":63917},[2146,301],[128,63919,11131],{"className":63920,"style":11165},[259,1873],[128,63922,1845],{"className":63923},[1903],[128,63925],{"className":63926,"style":1907},[269],[128,63928,63930,63933,64012],{"className":63929},[259],[128,63931],{"className":63932},[1896,5570],[128,63934,63936],{"className":63935},[5451],[128,63937,63939,64004],{"className":63938},[274,321],[128,63940,63942,64001],{"className":63941},[278],[128,63943,63945,63956,63964],{"className":63944,"style":13120},[282],[128,63946,63947,63950],{"style":13123},[128,63948],{"className":63949,"style":335},[290],[128,63951,63953],{"className":63952},[259],[128,63954,63833],{"className":63955,"style":1874},[259,1873],[128,63957,63958,63961],{"style":5617},[128,63959],{"className":63960,"style":335},[290],[128,63962],{"className":63963,"style":5625},[5624],[128,63965,63966,63969],{"style":13189},[128,63967],{"className":63968,"style":335},[290],[128,63970,63972],{"className":63971},[259],[128,63973,63975,63978],{"className":63974},[259],[128,63976,63828],{"className":63977,"style":1874},[259,1873],[128,63979,63981],{"className":63980},[2087],[128,63982,63984],{"className":63983},[274],[128,63985,63987],{"className":63986},[278],[128,63988,63990],{"className":63989,"style":9629},[282],[128,63991,63992,63995],{"style":2452},[128,63993],{"className":63994,"style":291},[290],[128,63996,63998],{"className":63997},[299,300,301,298],[128,63999,2639],{"className":64000},[259,298],[128,64002,347],{"className":64003},[346],[128,64005,64007],{"className":64006},[278],[128,64008,64010],{"className":64009,"style":38310},[282],[128,64011],{},[128,64013],{"className":64014},[1928,5570],[128,64016,64018],{"className":64017,"style":2142},[1928,2141],[128,64019,2486],{"className":64020},[2146,301],[128,64022],{"className":64023,"style":1907},[269],[128,64025,1845],{"className":64026},[1903],[128,64028],{"className":64029,"style":11756},[269],[128,64031],{"className":64032,"style":1907},[269],[128,64034,64036,64039],{"className":64035},[259],[128,64037,63828],{"className":64038,"style":1874},[259,1873],[128,64040,64042],{"className":64041},[2087],[128,64043,64045],{"className":64044},[274],[128,64046,64048],{"className":64047},[278],[128,64049,64051],{"className":64050,"style":9087},[282],[128,64052,64053,64056],{"style":2099},[128,64054],{"className":64055,"style":291},[290],[128,64057,64059],{"className":64058},[299,300,301,298],[128,64060,2639],{"className":64061},[259,298],[128,64063],{"className":64064,"style":1878},[269],[128,64066,5911],{"className":64067},[1882],[128,64069],{"className":64070,"style":1878},[269],[128,64072,64074,64078,64113,64116,64119,64122,64125,64128],{"className":64073},[250],[128,64075],{"className":64076,"style":64077},[254],"height:1.1141em;vertical-align:-0.25em;",[128,64079,64081,64084],{"className":64080},[259],[128,64082,6020],{"className":64083},[259],[128,64085,64087],{"className":64086},[2087],[128,64088,64090],{"className":64089},[274],[128,64091,64093],{"className":64092},[278],[128,64094,64096],{"className":64095,"style":9087},[282],[128,64097,64098,64101],{"style":2099},[128,64099],{"className":64100,"style":291},[290],[128,64102,64104],{"className":64103},[299,300,301,298],[128,64105,64107,64110],{"className":64106},[259,298],[128,64108,1989],{"className":64109},[259,298],[128,64111,1842],{"className":64112},[259,298],[128,64114,2477],{"className":64115},[1896],[128,64117,4835],{"className":64118,"style":4920},[259,1873],[128,64120,1845],{"className":64121},[1903],[128,64123],{"className":64124,"style":1907},[269],[128,64126,18848],{"className":64127,"style":18987},[259,1873],[128,64129,2486],{"className":64130},[1928],[11,64132,64133,64134,64212,64213,64247,64248,64277,64278,64349,64350,64433,64434,64554,64555,64247,64588,64616],{},"网络对每个输入输出四元组 ",[128,64135,64137,64167],{"className":64136,"translate":218},[217],[128,64138,64140],{"className":64139},[222],[224,64141,64142],{"xmlns":226},[228,64143,64144,64164],{},[231,64145,64146,64148,64150,64152,64154,64156,64158,64160,64162],{},[1832,64147,2477],{"stretchy":1837},[1795,64149,11131],{},[1832,64151,1845],{"separator":246},[1795,64153,63833],{},[1832,64155,1845],{"separator":246},[1795,64157,4835],{},[1832,64159,1845],{"separator":246},[1795,64161,18848],{},[1832,64163,2486],{"stretchy":1837},[238,64165,64166],{"encoding":240},"(\\gamma, \\upsilon, \\alpha, \\beta)",[128,64168,64170],{"className":64169,"ariaHidden":246},[245],[128,64171,64173,64176,64179,64182,64185,64188,64191,64194,64197,64200,64203,64206,64209],{"className":64172},[250],[128,64174],{"className":64175,"style":1892},[254],[128,64177,2477],{"className":64178},[1896],[128,64180,11131],{"className":64181,"style":11165},[259,1873],[128,64183,1845],{"className":64184},[1903],[128,64186],{"className":64187,"style":1907},[269],[128,64189,63833],{"className":64190,"style":1874},[259,1873],[128,64192,1845],{"className":64193},[1903],[128,64195],{"className":64196,"style":1907},[269],[128,64198,4835],{"className":64199,"style":4920},[259,1873],[128,64201,1845],{"className":64202},[1903],[128,64204],{"className":64205,"style":1907},[269],[128,64207,18848],{"className":64208,"style":18987},[259,1873],[128,64210,2486],{"className":64211},[1928],"，边缘预测为自由度 ",[128,64214,64216,64232],{"className":64215,"translate":218},[217],[128,64217,64219],{"className":64218},[222],[224,64220,64221],{"xmlns":226},[228,64222,64223,64229],{},[231,64224,64225,64227],{},[1840,64226,2639],{},[1795,64228,4835],{},[238,64230,64231],{"encoding":240},"2\\alpha",[128,64233,64235],{"className":64234,"ariaHidden":246},[245],[128,64236,64238,64241,64244],{"className":64237},[250],[128,64239],{"className":64240,"style":2594},[254],[128,64242,2639],{"className":64243},[259],[128,64245,4835],{"className":64246,"style":4920},[259,1873]," 的 Student-",[128,64249,64251,64264],{"className":64250,"translate":218},[217],[128,64252,64254],{"className":64253},[222],[224,64255,64256],{"xmlns":226},[228,64257,64258,64262],{},[231,64259,64260],{},[1795,64261,7023],{},[238,64263,7023],{"encoding":240},[128,64265,64267],{"className":64266,"ariaHidden":246},[245],[128,64268,64270,64274],{"className":64269},[250],[128,64271],{"className":64272,"style":64273},[254],"height:0.6151em;",[128,64275,7023],{"className":64276},[259,1873]," 分布。其预测方差可精确分解为偶然部分 ",[128,64279,64281,64307],{"className":64280,"translate":218},[217],[128,64282,64284],{"className":64283},[222],[224,64285,64286],{"xmlns":226},[228,64287,64288,64304],{},[231,64289,64290,64292,64294,64296,64298,64300,64302],{},[1795,64291,18848],{},[1795,64293,4751],{"mathvariant":1981},[1832,64295,2477],{"stretchy":1837},[1795,64297,4835],{},[1832,64299,1989],{},[1840,64301,1842],{},[1832,64303,2486],{"stretchy":1837},[238,64305,64306],{"encoding":240},"\\beta\u002F(\\alpha - 1)",[128,64308,64310,64337],{"className":64309,"ariaHidden":246},[245],[128,64311,64313,64316,64319,64322,64325,64328,64331,64334],{"className":64312},[250],[128,64314],{"className":64315,"style":1892},[254],[128,64317,18848],{"className":64318,"style":18987},[259,1873],[128,64320,4751],{"className":64321},[259],[128,64323,2477],{"className":64324},[1896],[128,64326,4835],{"className":64327,"style":4920},[259,1873],[128,64329],{"className":64330,"style":2508},[269],[128,64332,1989],{"className":64333},[2115],[128,64335],{"className":64336,"style":2508},[269],[128,64338,64340,64343,64346],{"className":64339},[250],[128,64341],{"className":64342,"style":1892},[254],[128,64344,1842],{"className":64345},[259],[128,64347,2486],{"className":64348},[1928]," 与认知部分 ",[128,64351,64353,64385],{"className":64352,"translate":218},[217],[128,64354,64356],{"className":64355},[222],[224,64357,64358],{"xmlns":226},[228,64359,64360,64382],{},[231,64361,64362,64364,64366,64368,64370,64372,64374,64376,64378,64380],{},[1795,64363,18848],{},[1795,64365,4751],{"mathvariant":1981},[1832,64367,16538],{"stretchy":1837},[1795,64369,63833],{},[1832,64371,2477],{"stretchy":1837},[1795,64373,4835],{},[1832,64375,1989],{},[1840,64377,1842],{},[1832,64379,2486],{"stretchy":1837},[1832,64381,16547],{"stretchy":1837},[238,64383,64384],{"encoding":240},"\\beta\u002F[\\upsilon(\\alpha - 1)]",[128,64386,64388,64421],{"className":64387,"ariaHidden":246},[245],[128,64389,64391,64394,64397,64400,64403,64406,64409,64412,64415,64418],{"className":64390},[250],[128,64392],{"className":64393,"style":1892},[254],[128,64395,18848],{"className":64396,"style":18987},[259,1873],[128,64398,4751],{"className":64399},[259],[128,64401,16538],{"className":64402},[1896],[128,64404,63833],{"className":64405,"style":1874},[259,1873],[128,64407,2477],{"className":64408},[1896],[128,64410,4835],{"className":64411,"style":4920},[259,1873],[128,64413],{"className":64414,"style":2508},[269],[128,64416,1989],{"className":64417},[2115],[128,64419],{"className":64420,"style":2508},[269],[128,64422,64424,64427,64430],{"className":64423},[250],[128,64425],{"className":64426,"style":1892},[254],[128,64428,1842],{"className":64429},[259],[128,64431,44995],{"className":64432},[1928],"，二者之和 ",[128,64435,64437,64479],{"className":64436,"translate":218},[217],[128,64438,64440],{"className":64439},[222],[224,64441,64442],{"xmlns":226},[228,64443,64444,64476],{},[231,64445,64446,64448,64450,64452,64454,64456,64458,64460,64462,64464,64466,64468,64470,64472,64474],{},[1795,64447,18848],{},[1832,64449,2477],{"stretchy":1837},[1795,64451,63833],{},[1832,64453,9486],{},[1840,64455,1842],{},[1832,64457,2486],{"stretchy":1837},[1795,64459,4751],{"mathvariant":1981},[1832,64461,16538],{"stretchy":1837},[1795,64463,63833],{},[1832,64465,2477],{"stretchy":1837},[1795,64467,4835],{},[1832,64469,1989],{},[1840,64471,1842],{},[1832,64473,2486],{"stretchy":1837},[1832,64475,16547],{"stretchy":1837},[238,64477,64478],{"encoding":240},"\\beta(\\upsilon + 1)\u002F[\\upsilon(\\alpha - 1)]",[128,64480,64482,64506,64542],{"className":64481,"ariaHidden":246},[245],[128,64483,64485,64488,64491,64494,64497,64500,64503],{"className":64484},[250],[128,64486],{"className":64487,"style":1892},[254],[128,64489,18848],{"className":64490,"style":18987},[259,1873],[128,64492,2477],{"className":64493},[1896],[128,64495,63833],{"className":64496,"style":1874},[259,1873],[128,64498],{"className":64499,"style":2508},[269],[128,64501,9486],{"className":64502},[2115],[128,64504],{"className":64505,"style":2508},[269],[128,64507,64509,64512,64515,64518,64521,64524,64527,64530,64533,64536,64539],{"className":64508},[250],[128,64510],{"className":64511,"style":1892},[254],[128,64513,1842],{"className":64514},[259],[128,64516,2486],{"className":64517},[1928],[128,64519,4751],{"className":64520},[259],[128,64522,16538],{"className":64523},[1896],[128,64525,63833],{"className":64526,"style":1874},[259,1873],[128,64528,2477],{"className":64529},[1896],[128,64531,4835],{"className":64532,"style":4920},[259,1873],[128,64534],{"className":64535,"style":2508},[269],[128,64537,1989],{"className":64538},[2115],[128,64540],{"className":64541,"style":2508},[269],[128,64543,64545,64548,64551],{"className":64544},[250],[128,64546],{"className":64547,"style":1892},[254],[128,64549,1842],{"className":64550},[259],[128,64552,44995],{"className":64553},[1928]," 即自由度 ",[128,64556,64558,64573],{"className":64557,"translate":218},[217],[128,64559,64561],{"className":64560},[222],[224,64562,64563],{"xmlns":226},[228,64564,64565,64571],{},[231,64566,64567,64569],{},[1840,64568,2639],{},[1795,64570,4835],{},[238,64572,64231],{"encoding":240},[128,64574,64576],{"className":64575,"ariaHidden":246},[245],[128,64577,64579,64582,64585],{"className":64578},[250],[128,64580],{"className":64581,"style":2594},[254],[128,64583,2639],{"className":64584},[259],[128,64586,4835],{"className":64587,"style":4920},[259,1873],[128,64589,64591,64604],{"className":64590,"translate":218},[217],[128,64592,64594],{"className":64593},[222],[224,64595,64596],{"xmlns":226},[228,64597,64598,64602],{},[231,64599,64600],{},[1795,64601,7023],{},[238,64603,7023],{"encoding":240},[128,64605,64607],{"className":64606,"ariaHidden":246},[245],[128,64608,64610,64613],{"className":64609},[250],[128,64611],{"className":64612,"style":64273},[254],[128,64614,7023],{"className":64615},[259,1873]," 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。",[11,64618,64619],{},"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。",[2610,64621,64623],{"id":64622},"_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",[11,64625,64626,64627,64789,64790,64939,64940,65098,65099,65239],{},"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 ",[128,64628,64630,64668],{"className":64629,"translate":218},[217],[128,64631,64633],{"className":64632},[222],[224,64634,64635],{"xmlns":226},[228,64636,64637,64665],{},[231,64638,64639,64645,64647,64649,64651,64653],{},[2016,64640,64641,64643],{},[1795,64642,5436],{"mathvariant":2001},[1795,64644,38844],{"mathvariant":4834},[1832,64646,2477],{"stretchy":1837},[1795,64648,2760],{"mathvariant":2001},[1832,64650,2486],{"stretchy":1837},[1832,64652,1834],{},[1977,64654,64655,64657],{},[1795,64656,41957],{"mathvariant":2008},[231,64658,64659,64661,64663],{},[1795,64660,4519],{},[1832,64662,1989],{},[1840,64664,1842],{},[238,64666,64667],{"encoding":240},"\\mathbf{f}_{\\boldsymbol{\\theta}}(\\mathbf{x}) \\in \\mathbb{S}^{d-1}",[128,64669,64671,64745],{"className":64670,"ariaHidden":246},[245],[128,64672,64674,64677,64727,64730,64733,64736,64739,64742],{"className":64673},[250],[128,64675],{"className":64676,"style":1892},[254],[128,64678,64680,64683],{"className":64679},[259],[128,64681,5436],{"className":64682,"style":26806},[259,2151],[128,64684,64686],{"className":64685},[2087],[128,64687,64689,64719],{"className":64688},[274,321],[128,64690,64692,64716],{"className":64691},[278],[128,64693,64695],{"className":64694,"style":2218},[282],[128,64696,64698,64701],{"style":64697},"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;",[128,64699],{"className":64700,"style":291},[290],[128,64702,64704],{"className":64703},[299,300,301,298],[128,64705,64707],{"className":64706},[259,298],[128,64708,64710],{"className":64709},[259,298],[128,64711,64713],{"className":64712},[259,298],[128,64714,38844],{"className":64715,"style":38908},[259,4895,298],[128,64717,347],{"className":64718},[346],[128,64720,64722],{"className":64721},[278],[128,64723,64725],{"className":64724,"style":2241},[282],[128,64726],{},[128,64728,2477],{"className":64729},[1896],[128,64731,2760],{"className":64732},[259,2151],[128,64734,2486],{"className":64735},[1928],[128,64737],{"className":64738,"style":1878},[269],[128,64740,1834],{"className":64741},[1882],[128,64743],{"className":64744,"style":1878},[269],[128,64746,64748,64751],{"className":64747},[250],[128,64749],{"className":64750,"style":20687},[254],[128,64752,64754,64757],{"className":64753},[259],[128,64755,41957],{"className":64756},[259,2167],[128,64758,64760],{"className":64759},[2087],[128,64761,64763],{"className":64762},[274],[128,64764,64766],{"className":64765},[278],[128,64767,64769],{"className":64768,"style":20687},[282],[128,64770,64771,64774],{"style":2452},[128,64772],{"className":64773,"style":291},[290],[128,64775,64777],{"className":64776},[299,300,301,298],[128,64778,64780,64783,64786],{"className":64779},[259,298],[128,64781,4519],{"className":64782},[259,1873,298],[128,64784,1989],{"className":64785},[2115,298],[128,64787,1842],{"className":64788},[259,298],"，各类原型为 ",[128,64791,64793,64830],{"className":64792,"translate":218},[217],[128,64794,64796],{"className":64795},[222],[224,64797,64798],{"xmlns":226},[228,64799,64800,64827],{},[231,64801,64802,64804,64810,64812,64815],{},[1832,64803,1838],{"stretchy":1837},[2016,64805,64806,64808],{},[1795,64807,32160],{"mathvariant":2001},[1795,64809,2022],{},[1832,64811,1856],{"stretchy":1837},[1832,64813,64814],{},"⊂",[1977,64816,64817,64819],{},[1795,64818,41957],{"mathvariant":2008},[231,64820,64821,64823,64825],{},[1795,64822,4519],{},[1832,64824,1989],{},[1840,64826,1842],{},[238,64828,64829],{"encoding":240},"\\{\\mathbf{v}_k\\} \\subset \\mathbb{S}^{d-1}",[128,64831,64833,64895],{"className":64832,"ariaHidden":246},[245],[128,64834,64836,64839,64842,64883,64886,64889,64892],{"className":64835},[250],[128,64837],{"className":64838,"style":1892},[254],[128,64840,1838],{"className":64841},[1896],[128,64843,64845,64848],{"className":64844},[259],[128,64846,32160],{"className":64847,"style":31116},[259,2151],[128,64849,64851],{"className":64850},[2087],[128,64852,64854,64875],{"className":64853},[274,321],[128,64855,64857,64872],{"className":64856},[278],[128,64858,64860],{"className":64859,"style":2218},[282],[128,64861,64863,64866],{"style":64862},"top:-2.55em;margin-left:-0.016em;margin-right:0.05em;",[128,64864],{"className":64865,"style":291},[290],[128,64867,64869],{"className":64868},[299,300,301,298],[128,64870,2022],{"className":64871,"style":2231},[259,1873,298],[128,64873,347],{"className":64874},[346],[128,64876,64878],{"className":64877},[278],[128,64879,64881],{"className":64880,"style":2241},[282],[128,64882],{},[128,64884,1856],{"className":64885},[1928],[128,64887],{"className":64888,"style":1878},[269],[128,64890,64814],{"className":64891},[1882],[128,64893],{"className":64894,"style":1878},[269],[128,64896,64898,64901],{"className":64897},[250],[128,64899],{"className":64900,"style":20687},[254],[128,64902,64904,64907],{"className":64903},[259],[128,64905,41957],{"className":64906},[259,2167],[128,64908,64910],{"className":64909},[2087],[128,64911,64913],{"className":64912},[274],[128,64914,64916],{"className":64915},[278],[128,64917,64919],{"className":64918,"style":20687},[282],[128,64920,64921,64924],{"style":2452},[128,64922],{"className":64923,"style":291},[290],[128,64925,64927],{"className":64926},[299,300,301,298],[128,64928,64930,64933,64936],{"className":64929},[259,298],[128,64931,4519],{"className":64932},[259,1873,298],[128,64934,1989],{"className":64935},[2115,298],[128,64937,1842],{"className":64938},[259,298],"，相似度 ",[128,64941,64943,64979],{"className":64942,"translate":218},[217],[128,64944,64946],{"className":64945},[222],[224,64947,64948],{"xmlns":226},[228,64949,64950,64976],{},[231,64951,64952,64958,64960,64963,64965,64967,64973],{},[2016,64953,64954,64956],{},[1795,64955,7590],{},[1795,64957,2022],{},[1832,64959,1994],{},[1832,64961,64962],{"stretchy":1837},"⟨",[1795,64964,5436],{"mathvariant":2001},[1832,64966,1845],{"separator":246},[2016,64968,64969,64971],{},[1795,64970,32160],{"mathvariant":2001},[1795,64972,2022],{},[1832,64974,64975],{"stretchy":1837},"⟩",[238,64977,64978],{"encoding":240},"s_k = \\langle \\mathbf{f}, \\mathbf{v}_k \\rangle",[128,64980,64982,65037],{"className":64981,"ariaHidden":246},[245],[128,64983,64985,64988,65028,65031,65034],{"className":64984},[250],[128,64986],{"className":64987,"style":4242},[254],[128,64989,64991,64994],{"className":64990},[259],[128,64992,7590],{"className":64993},[259,1873],[128,64995,64997],{"className":64996},[2087],[128,64998,65000,65020],{"className":64999},[274,321],[128,65001,65003,65017],{"className":65002},[278],[128,65004,65006],{"className":65005,"style":2218},[282],[128,65007,65008,65011],{"style":2221},[128,65009],{"className":65010,"style":291},[290],[128,65012,65014],{"className":65013},[299,300,301,298],[128,65015,2022],{"className":65016,"style":2231},[259,1873,298],[128,65018,347],{"className":65019},[346],[128,65021,65023],{"className":65022},[278],[128,65024,65026],{"className":65025,"style":2241},[282],[128,65027],{},[128,65029],{"className":65030,"style":1878},[269],[128,65032,1994],{"className":65033},[1882],[128,65035],{"className":65036,"style":1878},[269],[128,65038,65040,65043,65046,65049,65052,65055,65095],{"className":65039},[250],[128,65041],{"className":65042,"style":1892},[254],[128,65044,64962],{"className":65045},[1896],[128,65047,5436],{"className":65048,"style":26806},[259,2151],[128,65050,1845],{"className":65051},[1903],[128,65053],{"className":65054,"style":1907},[269],[128,65056,65058,65061],{"className":65057},[259],[128,65059,32160],{"className":65060,"style":31116},[259,2151],[128,65062,65064],{"className":65063},[2087],[128,65065,65067,65087],{"className":65066},[274,321],[128,65068,65070,65084],{"className":65069},[278],[128,65071,65073],{"className":65072,"style":2218},[282],[128,65074,65075,65078],{"style":64862},[128,65076],{"className":65077,"style":291},[290],[128,65079,65081],{"className":65080},[299,300,301,298],[128,65082,2022],{"className":65083,"style":2231},[259,1873,298],[128,65085,347],{"className":65086},[346],[128,65088,65090],{"className":65089},[278],[128,65091,65093],{"className":65092,"style":2241},[282],[128,65094],{},[128,65096,64975],{"className":65097},[1928],"。传统原型方法以 ",[128,65100,65102,65131],{"className":65101,"translate":218},[217],[128,65103,65105],{"className":65104},[222],[224,65106,65107],{"xmlns":226},[228,65108,65109,65128],{},[231,65110,65111,65117,65119,65122],{},[2016,65112,65113,65115],{},[1795,65114,38997],{"mathvariant":2001},[1795,65116,2022],{},[1832,65118,1994],{},[1795,65120,65121],{},"κ",[2016,65123,65124,65126],{},[1795,65125,7590],{},[1795,65127,2022],{},[238,65129,65130],{"encoding":240},"\\mathbf{z}_k = \\kappa s_k",[128,65132,65134,65190],{"className":65133,"ariaHidden":246},[245],[128,65135,65137,65141,65181,65184,65187],{"className":65136},[250],[128,65138],{"className":65139,"style":65140},[254],"height:0.5944em;vertical-align:-0.15em;",[128,65142,65144,65147],{"className":65143},[259],[128,65145,38997],{"className":65146},[259,2151],[128,65148,65150],{"className":65149},[2087],[128,65151,65153,65173],{"className":65152},[274,321],[128,65154,65156,65170],{"className":65155},[278],[128,65157,65159],{"className":65158,"style":2218},[282],[128,65160,65161,65164],{"style":2221},[128,65162],{"className":65163,"style":291},[290],[128,65165,65167],{"className":65166},[299,300,301,298],[128,65168,2022],{"className":65169,"style":2231},[259,1873,298],[128,65171,347],{"className":65172},[346],[128,65174,65176],{"className":65175},[278],[128,65177,65179],{"className":65178,"style":2241},[282],[128,65180],{},[128,65182],{"className":65183,"style":1878},[269],[128,65185,1994],{"className":65186},[1882],[128,65188],{"className":65189,"style":1878},[269],[128,65191,65193,65196,65199],{"className":65192},[250],[128,65194],{"className":65195,"style":4242},[254],[128,65197,65121],{"className":65198},[259,1873],[128,65200,65202,65205],{"className":65201},[259],[128,65203,7590],{"className":65204},[259,1873],[128,65206,65208],{"className":65207},[2087],[128,65209,65211,65231],{"className":65210},[274,321],[128,65212,65214,65228],{"className":65213},[278],[128,65215,65217],{"className":65216,"style":2218},[282],[128,65218,65219,65222],{"style":2221},[128,65220],{"className":65221,"style":291},[290],[128,65223,65225],{"className":65224},[299,300,301,298],[128,65226,2022],{"className":65227,"style":2231},[259,1873,298],[128,65229,347],{"className":65230},[346],[128,65232,65234],{"className":65233},[278],[128,65235,65237],{"className":65236,"style":2241},[282],[128,65238],{}," 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。",[11,65241,65242],{},"一个直接的融合方案是把相似度送入证据函数：",[128,65244,65246],{"className":65245,"translate":218},[1962],[128,65247,65249,65359],{"className":65248,"translate":218},[217],[128,65250,65252],{"className":65251},[222],[224,65253,65254],{"xmlns":226,"display":1971},[228,65255,65256,65356],{},[231,65257,65258,65264,65266,65268,65270,65272,65274,65280,65282,65284,65286,65292,65294,65296,65298,65300,65302,65304,65306,65312,65314,65316,65318,65320,65322,65324,65326,65340,65342,65344,65346,65348,65354],{},[2016,65259,65260,65262],{},[1795,65261,3713],{},[1795,65263,2022],{},[1832,65265,1994],{},[1795,65267,24505],{},[1832,65269,2477],{"stretchy":1837},[1795,65271,65121],{},[234,65273,6528],{},[2016,65275,65276,65278],{},[1795,65277,7590],{},[1795,65279,2022],{},[1832,65281,2486],{"stretchy":1837},[1832,65283,1845],{"separator":246},[269,65285],{"width":11568},[2016,65287,65288,65290],{},[1795,65289,4835],{},[1795,65291,2022],{},[1832,65293,1994],{},[1840,65295,1842],{},[1832,65297,9486],{},[1795,65299,24505],{},[1832,65301,2477],{"stretchy":1837},[1795,65303,65121],{},[234,65305,6528],{},[2016,65307,65308,65310],{},[1795,65309,7590],{},[1795,65311,2022],{},[1832,65313,2486],{"stretchy":1837},[1832,65315,1845],{"separator":246},[269,65317],{"width":11568},[1795,65319,41957],{},[1832,65321,1994],{},[1795,65323,1853],{},[1832,65325,9486],{},[6961,65327,65328,65330,65338],{},[1832,65329,2042],{},[231,65331,65332,65334,65336],{},[1795,65333,2022],{},[1832,65335,1994],{},[1840,65337,1842],{},[1795,65339,1853],{},[1795,65341,24505],{},[1832,65343,2477],{"stretchy":1837},[1795,65345,65121],{},[234,65347,6528],{},[2016,65349,65350,65352],{},[1795,65351,7590],{},[1795,65353,2022],{},[1832,65355,2486],{"stretchy":1837},[238,65357,65358],{"encoding":240},"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)",[128,65360,65362,65417,65536,65554,65636,65654],{"className":65361,"ariaHidden":246},[245],[128,65363,65365,65368,65408,65411,65414],{"className":65364},[250],[128,65366],{"className":65367,"style":4242},[254],[128,65369,65371,65374],{"className":65370},[259],[128,65372,3713],{"className":65373},[259,1873],[128,65375,65377],{"className":65376},[2087],[128,65378,65380,65400],{"className":65379},[274,321],[128,65381,65383,65397],{"className":65382},[278],[128,65384,65386],{"className":65385,"style":2218},[282],[128,65387,65388,65391],{"style":2221},[128,65389],{"className":65390,"style":291},[290],[128,65392,65394],{"className":65393},[299,300,301,298],[128,65395,2022],{"className":65396,"style":2231},[259,1873,298],[128,65398,347],{"className":65399},[346],[128,65401,65403],{"className":65402},[278],[128,65404,65406],{"className":65405,"style":2241},[282],[128,65407],{},[128,65409],{"className":65410,"style":1878},[269],[128,65412,1994],{"className":65413},[1882],[128,65415],{"className":65416,"style":1878},[269],[128,65418,65420,65423,65426,65429,65432,65435,65475,65478,65481,65484,65487,65527,65530,65533],{"className":65419},[250],[128,65421],{"className":65422,"style":1892},[254],[128,65424,24505],{"className":65425,"style":1874},[259,1873],[128,65427,2477],{"className":65428},[1896],[128,65430,65121],{"className":65431},[259,1873],[128,65433],{"className":65434,"style":1907},[269],[128,65436,65438,65441],{"className":65437},[259],[128,65439,7590],{"className":65440},[259,1873],[128,65442,65444],{"className":65443},[2087],[128,65445,65447,65467],{"className":65446},[274,321],[128,65448,65450,65464],{"className":65449},[278],[128,65451,65453],{"className":65452,"style":2218},[282],[128,65454,65455,65458],{"style":2221},[128,65456],{"className":65457,"style":291},[290],[128,65459,65461],{"className":65460},[299,300,301,298],[128,65462,2022],{"className":65463,"style":2231},[259,1873,298],[128,65465,347],{"className":65466},[346],[128,65468,65470],{"className":65469},[278],[128,65471,65473],{"className":65472,"style":2241},[282],[128,65474],{},[128,65476,2486],{"className":65477},[1928],[128,65479,1845],{"className":65480},[1903],[128,65482],{"className":65483,"style":11756},[269],[128,65485],{"className":65486,"style":1907},[269],[128,65488,65490,65493],{"className":65489},[259],[128,65491,4835],{"className":65492,"style":4920},[259,1873],[128,65494,65496],{"className":65495},[2087],[128,65497,65499,65519],{"className":65498},[274,321],[128,65500,65502,65516],{"className":65501},[278],[128,65503,65505],{"className":65504,"style":2218},[282],[128,65506,65507,65510],{"style":4935},[128,65508],{"className":65509,"style":291},[290],[128,65511,65513],{"className":65512},[299,300,301,298],[128,65514,2022],{"className":65515,"style":2231},[259,1873,298],[128,65517,347],{"className":65518},[346],[128,65520,65522],{"className":65521},[278],[128,65523,65525],{"className":65524,"style":2241},[282],[128,65526],{},[128,65528],{"className":65529,"style":1878},[269],[128,65531,1994],{"className":65532},[1882],[128,65534],{"className":65535,"style":1878},[269],[128,65537,65539,65542,65545,65548,65551],{"className":65538},[250],[128,65540],{"className":65541,"style":4298},[254],[128,65543,1842],{"className":65544},[259],[128,65546],{"className":65547,"style":2508},[269],[128,65549,9486],{"className":65550},[2115],[128,65552],{"className":65553,"style":2508},[269],[128,65555,65557,65560,65563,65566,65569,65572,65612,65615,65618,65621,65624,65627,65630,65633],{"className":65556},[250],[128,65558],{"className":65559,"style":1892},[254],[128,65561,24505],{"className":65562,"style":1874},[259,1873],[128,65564,2477],{"className":65565},[1896],[128,65567,65121],{"className":65568},[259,1873],[128,65570],{"className":65571,"style":1907},[269],[128,65573,65575,65578],{"className":65574},[259],[128,65576,7590],{"className":65577},[259,1873],[128,65579,65581],{"className":65580},[2087],[128,65582,65584,65604],{"className":65583},[274,321],[128,65585,65587,65601],{"className":65586},[278],[128,65588,65590],{"className":65589,"style":2218},[282],[128,65591,65592,65595],{"style":2221},[128,65593],{"className":65594,"style":291},[290],[128,65596,65598],{"className":65597},[299,300,301,298],[128,65599,2022],{"className":65600,"style":2231},[259,1873,298],[128,65602,347],{"className":65603},[346],[128,65605,65607],{"className":65606},[278],[128,65608,65610],{"className":65609,"style":2241},[282],[128,65611],{},[128,65613,2486],{"className":65614},[1928],[128,65616,1845],{"className":65617},[1903],[128,65619],{"className":65620,"style":11756},[269],[128,65622],{"className":65623,"style":1907},[269],[128,65625,41957],{"className":65626,"style":42029},[259,1873],[128,65628],{"className":65629,"style":1878},[269],[128,65631,1994],{"className":65632},[1882],[128,65634],{"className":65635,"style":1878},[269],[128,65637,65639,65642,65645,65648,65651],{"className":65638},[250],[128,65640],{"className":65641,"style":2705},[254],[128,65643,1853],{"className":65644,"style":1924},[259,1873],[128,65646],{"className":65647,"style":2508},[269],[128,65649,9486],{"className":65650},[2115],[128,65652],{"className":65653,"style":2508},[269],[128,65655,65657,65661,65727,65730,65733,65736,65739,65742,65782],{"className":65656},[250],[128,65658],{"className":65659,"style":65660},[254],"height:3.1304em;vertical-align:-1.3021em;",[128,65662,65664],{"className":65663},[2268,7074],[128,65665,65667,65718],{"className":65666},[274,321],[128,65668,65670,65715],{"className":65669},[278],[128,65671,65673,65694,65704],{"className":65672,"style":7084},[282],[128,65674,65676,65679],{"style":65675},"top:-1.8479em;margin-left:0em;",[128,65677],{"className":65678,"style":7091},[290],[128,65680,65682],{"className":65681},[299,300,301,298],[128,65683,65685,65688,65691],{"className":65684},[259,298],[128,65686,2022],{"className":65687,"style":2231},[259,1873,298],[128,65689,1994],{"className":65690},[1882,298],[128,65692,1842],{"className":65693},[259,298],[128,65695,65696,65699],{"style":7109},[128,65697],{"className":65698,"style":7091},[290],[128,65700,65701],{},[128,65702,2042],{"className":65703},[2268,2272,7118],[128,65705,65706,65709],{"style":7121},[128,65707],{"className":65708,"style":7091},[290],[128,65710,65712],{"className":65711},[299,300,301,298],[128,65713,1853],{"className":65714,"style":1924},[259,1873,298],[128,65716,347],{"className":65717},[346],[128,65719,65721],{"className":65720},[278],[128,65722,65725],{"className":65723,"style":65724},[282],"height:1.3021em;",[128,65726],{},[128,65728],{"className":65729,"style":1907},[269],[128,65731,24505],{"className":65732,"style":1874},[259,1873],[128,65734,2477],{"className":65735},[1896],[128,65737,65121],{"className":65738},[259,1873],[128,65740],{"className":65741,"style":1907},[269],[128,65743,65745,65748],{"className":65744},[259],[128,65746,7590],{"className":65747},[259,1873],[128,65749,65751],{"className":65750},[2087],[128,65752,65754,65774],{"className":65753},[274,321],[128,65755,65757,65771],{"className":65756},[278],[128,65758,65760],{"className":65759,"style":2218},[282],[128,65761,65762,65765],{"style":2221},[128,65763],{"className":65764,"style":291},[290],[128,65766,65768],{"className":65767},[299,300,301,298],[128,65769,2022],{"className":65770,"style":2231},[259,1873,298],[128,65772,347],{"className":65773},[346],[128,65775,65777],{"className":65776},[278],[128,65778,65780],{"className":65779,"style":2241},[282],[128,65781],{},[128,65783,2486],{"className":65784},[1928],[11,65786,50735,65787,65815,65816,65845,65846,65916,65917,65945,65946,65974,65975,66044,66045,893,66095],{},[128,65788,65790,65803],{"className":65789,"translate":218},[217],[128,65791,65793],{"className":65792},[222],[224,65794,65795],{"xmlns":226},[228,65796,65797,65801],{},[231,65798,65799],{},[1795,65800,24505],{},[238,65802,24505],{"encoding":240},[128,65804,65806],{"className":65805,"ariaHidden":246},[245],[128,65807,65809,65812],{"className":65808},[250],[128,65810],{"className":65811,"style":11158},[254],[128,65813,24505],{"className":65814,"style":1874},[259,1873]," 取 3.4 节的非负激活，",[128,65817,65819,65833],{"className":65818,"translate":218},[217],[128,65820,65822],{"className":65821},[222],[224,65823,65824],{"xmlns":226},[228,65825,65826,65830],{},[231,65827,65828],{},[1795,65829,65121],{},[238,65831,65832],{"encoding":240},"\\kappa",[128,65834,65836],{"className":65835,"ariaHidden":246},[245],[128,65837,65839,65842],{"className":65838},[250],[128,65840],{"className":65841,"style":7758},[254],[128,65843,65121],{"className":65844},[259,1873]," 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，",[128,65847,65849,65867],{"className":65848,"translate":218},[217],[128,65850,65852],{"className":65851},[222],[224,65853,65854],{"xmlns":226},[228,65855,65856,65864],{},[231,65857,65858],{},[2016,65859,65860,65862],{},[1795,65861,7590],{},[1795,65863,2022],{},[238,65865,65866],{"encoding":240},"s_k",[128,65868,65870],{"className":65869,"ariaHidden":246},[245],[128,65871,65873,65876],{"className":65872},[250],[128,65874],{"className":65875,"style":4242},[254],[128,65877,65879,65882],{"className":65878},[259],[128,65880,7590],{"className":65881},[259,1873],[128,65883,65885],{"className":65884},[2087],[128,65886,65888,65908],{"className":65887},[274,321],[128,65889,65891,65905],{"className":65890},[278],[128,65892,65894],{"className":65893,"style":2218},[282],[128,65895,65896,65899],{"style":2221},[128,65897],{"className":65898,"style":291},[290],[128,65900,65902],{"className":65901},[299,300,301,298],[128,65903,2022],{"className":65904,"style":2231},[259,1873,298],[128,65906,347],{"className":65907},[346],[128,65909,65911],{"className":65910},[278],[128,65912,65914],{"className":65913,"style":2241},[282],[128,65915],{}," 接近 ",[128,65918,65920,65933],{"className":65919,"translate":218},[217],[128,65921,65923],{"className":65922},[222],[224,65924,65925],{"xmlns":226},[228,65926,65927,65931],{},[231,65928,65929],{},[1840,65930,1842],{},[238,65932,1842],{"encoding":240},[128,65934,65936],{"className":65935,"ariaHidden":246},[245],[128,65937,65939,65942],{"className":65938},[250],[128,65940],{"className":65941,"style":2594},[254],[128,65943,1842],{"className":65944},[259],"、证据充分、",[128,65947,65949,65962],{"className":65948,"translate":218},[217],[128,65950,65952],{"className":65951},[222],[224,65953,65954],{"xmlns":226},[228,65955,65956,65960],{},[231,65957,65958],{},[1795,65959,35129],{},[238,65961,35129],{"encoding":240},[128,65963,65965],{"className":65964,"ariaHidden":246},[245],[128,65966,65968,65971],{"className":65967},[250],[128,65969],{"className":65970,"style":7758},[254],[128,65972,35129],{"className":65973},[259,1873]," 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 ",[128,65976,65978,65995],{"className":65977,"translate":218},[217],[128,65979,65981],{"className":65980},[222],[224,65982,65983],{"xmlns":226},[228,65984,65985,65993],{},[231,65986,65987],{},[2016,65988,65989,65991],{},[1795,65990,3713],{},[1795,65992,2022],{},[238,65994,41002],{"encoding":240},[128,65996,65998],{"className":65997,"ariaHidden":246},[245],[128,65999,66001,66004],{"className":66000},[250],[128,66002],{"className":66003,"style":4242},[254],[128,66005,66007,66010],{"className":66006},[259],[128,66008,3713],{"className":66009},[259,1873],[128,66011,66013],{"className":66012},[2087],[128,66014,66016,66036],{"className":66015},[274,321],[128,66017,66019,66033],{"className":66018},[278],[128,66020,66022],{"className":66021,"style":2218},[282],[128,66023,66024,66027],{"style":2221},[128,66025],{"className":66026,"style":291},[290],[128,66028,66030],{"className":66029},[299,300,301,298],[128,66031,2022],{"className":66032,"style":2231},[259,1873,298],[128,66034,347],{"className":66035},[346],[128,66037,66039],{"className":66038},[278],[128,66040,66042],{"className":66041,"style":2241},[282],[128,66043],{}," 同时趋零、",[128,66046,66048,66065],{"className":66047,"translate":218},[217],[128,66049,66051],{"className":66050},[222],[224,66052,66053],{"xmlns":226},[228,66054,66055,66063],{},[231,66056,66057,66059,66061],{},[1795,66058,35129],{},[1832,66060,22419],{},[1840,66062,1842],{},[238,66064,43991],{"encoding":240},[128,66066,66068,66086],{"className":66067,"ariaHidden":246},[245],[128,66069,66071,66074,66077,66080,66083],{"className":66070},[250],[128,66072],{"className":66073,"style":7758},[254],[128,66075,35129],{"className":66076},[259,1873],[128,66078],{"className":66079,"style":1878},[269],[128,66081,22419],{"className":66082},[1882],[128,66084],{"className":66085,"style":1878},[269],[128,66087,66089,66092],{"className":66088},[250],[128,66090],{"className":66091,"style":2594},[254],[128,66093,1842],{"className":66094},[259],[35,66096,66097],{},"「离原型远」与「证据不足」在此被同一个机制表达。",[11,66099,66100,66101,66104,66105,66108,66109,66181,66182,66210,66211,66214,66215,66249],{},"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",[35,66102,66103],{},"类概率单纯形","上，原型方法定义在",[35,66106,66107],{},"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。",[128,66110,66112,66136],{"className":66111,"translate":218},[217],[128,66113,66115],{"className":66114},[222],[224,66116,66117],{"xmlns":226},[228,66118,66119,66133],{},[231,66120,66121,66123,66125,66127,66129,66131],{},[1795,66122,2760],{"mathvariant":2001},[1832,66124,16313],{},[1795,66126,4835],{"mathvariant":4834},[1832,66128,2477],{"stretchy":1837},[1795,66130,2760],{"mathvariant":2001},[1832,66132,2486],{"stretchy":1837},[238,66134,66135],{"encoding":240},"\\mathbf{x} \\mapsto \\boldsymbol{\\alpha}(\\mathbf{x})",[128,66137,66139,66157],{"className":66138,"ariaHidden":246},[245],[128,66140,66142,66145,66148,66151,66154],{"className":66141},[250],[128,66143],{"className":66144,"style":16332},[254],[128,66146,2760],{"className":66147},[259,2151],[128,66149],{"className":66150,"style":1878},[269],[128,66152,16313],{"className":66153},[1882],[128,66155],{"className":66156,"style":1878},[269],[128,66158,66160,66163,66172,66175,66178],{"className":66159},[250],[128,66161],{"className":66162,"style":1892},[254],[128,66164,66166],{"className":66165},[259],[128,66167,66169],{"className":66168},[259],[128,66170,4835],{"className":66171},[259,4895],[128,66173,2477],{"className":66174},[1896],[128,66176,2760],{"className":66177},[259,2151],[128,66179,2486],{"className":66180},[1928]," 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——",[128,66183,66185,66198],{"className":66184,"translate":218},[217],[128,66186,66188],{"className":66187},[222],[224,66189,66190],{"xmlns":226},[228,66191,66192,66196],{},[231,66193,66194],{},[1795,66195,35129],{},[238,66197,35129],{"encoding":240},[128,66199,66201],{"className":66200,"ariaHidden":246},[245],[128,66202,66204,66207],{"className":66203},[250],[128,66205],{"className":66206,"style":7758},[254],[128,66208,35129],{"className":66209},[259,1873]," 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",[35,66212,66213],{},"联合","模型，例如令 ",[128,66216,66218,66231],{"className":66217,"translate":218},[217],[128,66219,66221],{"className":66220},[222],[224,66222,66223],{"xmlns":226},[228,66224,66225,66229],{},[231,66226,66227],{},[1795,66228,4835],{"mathvariant":4834},[238,66230,5875],{"encoding":240},[128,66232,66234],{"className":66233,"ariaHidden":246},[245],[128,66235,66237,66240],{"className":66236},[250],[128,66238],{"className":66239,"style":4439},[254],[128,66241,66243],{"className":66242},[259],[128,66244,66246],{"className":66245},[259],[128,66247,4835],{"className":66248},[259,4895]," 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。",[11,66251,66252],{},"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：",[33248,66254,66255,66319],{},[33251,66256,66257,66260,66261,66289,66290,66318],{},[35,66258,66259],{},"长尾与稀有类。"," 稀有类的原型天然缺乏证据支撑，",[128,66262,66264,66277],{"className":66263,"translate":218},[217],[128,66265,66267],{"className":66266},[222],[224,66268,66269],{"xmlns":226},[228,66270,66271,66275],{},[231,66272,66273],{},[1795,66274,35129],{},[238,66276,35129],{"encoding":240},[128,66278,66280],{"className":66279,"ariaHidden":246},[245],[128,66281,66283,66286],{"className":66282},[250],[128,66284],{"className":66285,"style":7758},[254],[128,66287,35129],{"className":66288},[259,1873]," 更高。这既可以被用作保护机制（在损失中对高 ",[128,66291,66293,66306],{"className":66292,"translate":218},[217],[128,66294,66296],{"className":66295},[222],[224,66297,66298],{"xmlns":226},[228,66299,66300,66304],{},[231,66301,66302],{},[1795,66303,35129],{},[238,66305,35129],{"encoding":240},[128,66307,66309],{"className":66308,"ariaHidden":246},[245],[128,66310,66312,66315],{"className":66311},[250],[128,66313],{"className":66314,"style":7758},[254],[128,66316,35129],{"className":66317},[259,1873]," 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。",[33251,66320,66321,66324,66325,63140,66353,66415,66416],{},[35,66322,66323],{},"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。",[128,66326,66328,66341],{"className":66327,"translate":218},[217],[128,66329,66331],{"className":66330},[222],[224,66332,66333],{"xmlns":226},[228,66334,66335,66339],{},[231,66336,66337],{},[1795,66338,35129],{},[238,66340,35129],{"encoding":240},[128,66342,66344],{"className":66343,"ariaHidden":246},[245],[128,66345,66347,66350],{"className":66346},[250],[128,66348],{"className":66349,"style":7758},[254],[128,66351,35129],{"className":66352},[259,1873],[128,66354,66356,66379],{"className":66355,"translate":218},[217],[128,66357,66359],{"className":66358},[222],[224,66360,66361],{"xmlns":226},[228,66362,66363,66377],{},[231,66364,66365,66367,66369,66371,66373,66375],{},[1795,66366,30626],{},[1832,66368,2477],{"stretchy":1837},[1795,66370,1830],{},[1832,66372,13024],{"separator":246},[1795,66374,26389],{"mathvariant":4834},[1832,66376,2486],{"stretchy":1837},[238,66378,48574],{"encoding":240},[128,66380,66382],{"className":66381,"ariaHidden":246},[245],[128,66383,66385,66388,66391,66394,66397,66400,66403,66412],{"className":66384},[250],[128,66386],{"className":66387,"style":1892},[254],[128,66389,30626],{"className":66390,"style":30665},[259,1873],[128,66392,2477],{"className":66393},[1896],[128,66395,1830],{"className":66396,"style":1874},[259,1873],[128,66398,13024],{"className":66399},[1903],[128,66401],{"className":66402,"style":1907},[269],[128,66404,66406],{"className":66405},[259],[128,66407,66409],{"className":66408},[259],[128,66410,26389],{"className":66411,"style":26423},[259,4895],[128,66413,2486],{"className":66414},[1928]," 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：",[35,66417,66418],{},"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。",[51,66420,1609],{"id":1609},[11,66422,66423],{},"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：",[35195,66425,66426,66536,66542],{},[33251,66427,66428,66431,66432,33431,66466,66535],{},[35,66429,66430],{},"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 ",[128,66433,66435,66448],{"className":66434,"translate":218},[217],[128,66436,66438],{"className":66437},[222],[224,66439,66440],{"xmlns":226},[228,66441,66442,66446],{},[231,66443,66444],{},[1795,66445,20063],{"mathvariant":4834},[238,66447,21168],{"encoding":240},[128,66449,66451],{"className":66450,"ariaHidden":246},[245],[128,66452,66454,66457],{"className":66453},[250],[128,66455],{"className":66456,"style":2564},[254],[128,66458,66460],{"className":66459},[259],[128,66461,66463],{"className":66462},[259],[128,66464,20063],{"className":66465},[259,4895],[128,66467,66469,66486],{"className":66468,"translate":218},[217],[128,66470,66472],{"className":66471},[222],[224,66473,66474],{"xmlns":226},[228,66475,66476,66484],{},[231,66477,66478],{},[2016,66479,66480,66482],{},[1795,66481,4835],{},[1840,66483,2028],{},[238,66485,21207],{"encoding":240},[128,66487,66489],{"className":66488,"ariaHidden":246},[245],[128,66490,66492,66495],{"className":66491},[250],[128,66493],{"className":66494,"style":4242},[254],[128,66496,66498,66501],{"className":66497},[259],[128,66499,4835],{"className":66500,"style":4920},[259,1873],[128,66502,66504],{"className":66503},[2087],[128,66505,66507,66527],{"className":66506},[274,321],[128,66508,66510,66524],{"className":66509},[278],[128,66511,66513],{"className":66512,"style":2945},[282],[128,66514,66515,66518],{"style":4935},[128,66516],{"className":66517,"style":291},[290],[128,66519,66521],{"className":66520},[299,300,301,298],[128,66522,2028],{"className":66523},[259,298],[128,66525,347],{"className":66526},[346],[128,66528,66530],{"className":66529},[278],[128,66531,66533],{"className":66532,"style":2241},[282],[128,66534],{}," 两个正交分量构成（命题 2.2）。",[33251,66537,66538,66541],{},[35,66539,66540],{},"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）。",[33251,66543,66544,66547],{},[35,66545,66546],{},"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。",[11,66549,66550,66551,66554,66555,66615],{},"证据深度学习的核心洞见可以压缩为一句话：",[35,66552,66553],{},"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 ",[128,66556,66558,66579],{"className":66557,"translate":218},[217],[128,66559,66561],{"className":66560},[222],[224,66562,66563],{"xmlns":226},[228,66564,66565,66577],{},[231,66566,66567,66569,66571,66573,66575],{},[1795,66568,35129],{},[1832,66570,1994],{},[1795,66572,1853],{},[1795,66574,4751],{"mathvariant":1981},[1795,66576,41957],{},[238,66578,44676],{"encoding":240},[128,66580,66582,66600],{"className":66581,"ariaHidden":246},[245],[128,66583,66585,66588,66591,66594,66597],{"className":66584},[250],[128,66586],{"className":66587,"style":7758},[254],[128,66589,35129],{"className":66590},[259,1873],[128,66592],{"className":66593,"style":1878},[269],[128,66595,1994],{"className":66596},[1882],[128,66598],{"className":66599,"style":1878},[269],[128,66601,66603,66606,66609,66612],{"className":66602},[250],[128,66604],{"className":66605,"style":1892},[254],[128,66607,1853],{"className":66608,"style":1924},[259,1873],[128,66610,4751],{"className":66611},[259],[128,66613,41957],{"className":66614,"style":42029},[259,1873]," 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。",[11,66617,66618],{},"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」。",[11,66620,66621,66622,66624,66625,66653,66654],{},"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",[35,66623,44716],{},"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）。",[128,66626,66628,66641],{"className":66627,"translate":218},[217],[128,66629,66631],{"className":66630},[222],[224,66632,66633],{"xmlns":226},[228,66634,66635,66639],{},[231,66636,66637],{},[1795,66638,35129],{},[238,66640,35129],{"encoding":240},[128,66642,66644],{"className":66643,"ariaHidden":246},[245],[128,66645,66647,66650],{"className":66646},[250],[128,66648],{"className":66649,"style":7758},[254],[128,66651,35129],{"className":66652},[259,1873]," 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：",[35,66655,66656],{},"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。",[11,66658,66659,66660,66663],{},"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，",[35,66661,66662],{},"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":123,"searchDepth":137,"depth":137,"links":66665},[66666,66672,66680,66688,66695,66703],{"id":2607,"depth":137,"text":2608,"children":66667},[66668,66669,66670,66671],{"id":2612,"depth":143,"text":2613},{"id":4812,"depth":143,"text":4813},{"id":11108,"depth":143,"text":11109},{"id":14237,"depth":143,"text":14238},{"id":16389,"depth":137,"text":16390,"children":66673},[66674,66675,66676,66677,66678,66679],{"id":16393,"depth":143,"text":16394},{"id":21147,"depth":143,"text":21148},{"id":23401,"depth":143,"text":23402},{"id":26367,"depth":143,"text":26368},{"id":30525,"depth":143,"text":30526},{"id":33207,"depth":143,"text":33208},{"id":34990,"depth":137,"text":34991,"children":66681},[66682,66683,66684,66685,66686,66687],{"id":34994,"depth":143,"text":34995},{"id":36651,"depth":143,"text":36652},{"id":38821,"depth":143,"text":38822},{"id":40037,"depth":143,"text":40038},{"id":41935,"depth":143,"text":41936},{"id":44647,"depth":143,"text":44648},{"id":49061,"depth":137,"text":49062,"children":66689},[66690,66691,66692,66693,66694],{"id":49152,"depth":143,"text":49153},{"id":52604,"depth":143,"text":52605},{"id":54792,"depth":143,"text":54793},{"id":59027,"depth":143,"text":59028},{"id":59678,"depth":143,"text":59679},{"id":61217,"depth":137,"text":61218,"children":66696},[66697,66698,66699,66700,66701,66702],{"id":61221,"depth":143,"text":61222},{"id":62164,"depth":143,"text":62165},{"id":63206,"depth":143,"text":63207},{"id":63546,"depth":143,"text":63547},{"id":63783,"depth":143,"text":63784},{"id":64622,"depth":143,"text":64623},{"id":1609,"depth":137,"text":1609},"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":1776,"description":66704},"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。",[66711,66712],"statistics","machine-learning","2026-10-01T18:52:06+08:00","PklX79kbgmXizMsWGOJ3PcHWRm9JgKQrfILpGImulBA",{"id":66716,"title":24,"body":66717,"description":104126,"draft":1760,"enableCodeHighlight":1760,"enableCodeHightlight":1760,"enableComment":1761,"enableD2":1761,"enableKatex":1761,"extension":1762,"image":123,"important":1760,"location":1763,"meta":104127,"navigation":1761,"ogImage":1765,"path":23,"seo":104128,"stem":104129,"summary":104130,"tags":104131,"time":104132,"__hash__":104133},"blog\u002Fblog\u002F2026\u002F0005-yin-guo-jie-gou-mo-xing-jian-lun.md",{"type":8,"value":66718,"toc":104098},[66719,67160,67166,67922,67929,67932,67936,68845,69734,69798,70317,70324,70691,70752,70756,70886,70893,70971,71215,71394,71400,71410,71416,71495,71705,71860,71865,71943,72255,72796,72888,72892,72895,73542,73917,74408,74447,74451,74454,74746,74752,74815,74822,75292,75302,75305,75683,75690,75961,75964,75971,75975,77573,78075,78458,78462,78898,79445,80115,80122,80126,80181,82390,82542,82545,82593,82597,83058,83631,83635,84522,84909,85246,85976,88232,88411,88415,88928,89427,90652,91597,91751,92131,92137,92397,92400,92404,92480,92750,92756,93112,94190,94294,94471,94794,94800,95150,95681,96097,96101,96259,96679,98292,98561,98564,99020,99138,99149,99865,100885,100888,100924,100927,100930,100934,100941,101511,101645,102031,102331,102675,102679,102682,102759,102762,102848,102851,102855,102858,103158,103161,103219,103223,103226,103362,103369,103373,103376,103762,103768,103771,103774,104085,104088,104095],[11,66720,66721,66722,66764,66765,66822,66823,66889,66890,66967,66968,66971,66972,31074,67028,11072,67093,67159],{},"为什么概率论不足以回答因果问题？设 ",[128,66723,66725,66743],{"className":66724,"translate":218},[217],[128,66726,66728],{"className":66727},[222],[224,66729,66730],{"xmlns":226},[228,66731,66732,66740],{},[231,66733,66734,66736,66738],{},[1795,66735,364],{},[1832,66737,1845],{"separator":246},[1795,66739,35023],{},[238,66741,66742],{"encoding":240},"X, Y",[128,66744,66746],{"className":66745,"ariaHidden":246},[245],[128,66747,66749,66752,66755,66758,66761],{"className":66748},[250],[128,66750],{"className":66751,"style":40674},[254],[128,66753,364],{"className":66754,"style":30665},[259,1873],[128,66756,1845],{"className":66757},[1903],[128,66759],{"className":66760,"style":1907},[269],[128,66762,35023],{"className":66763,"style":2508},[259,1873]," 为两个随机变量，概率论所能给出的全部工具是联合分布 ",[128,66766,66768,66792],{"className":66767,"translate":218},[217],[128,66769,66771],{"className":66770},[222],[224,66772,66773],{"xmlns":226},[228,66774,66775,66789],{},[231,66776,66777,66779,66781,66783,66785,66787],{},[1795,66778,23001],{},[1832,66780,2477],{"stretchy":1837},[1795,66782,364],{},[1832,66784,1845],{"separator":246},[1795,66786,35023],{},[1832,66788,2486],{"stretchy":1837},[238,66790,66791],{"encoding":240},"P(X,Y)",[128,66793,66795],{"className":66794,"ariaHidden":246},[245],[128,66796,66798,66801,66804,66807,66810,66813,66816,66819],{"className":66797},[250],[128,66799],{"className":66800,"style":1892},[254],[128,66802,23001],{"className":66803,"style":36065},[259,1873],[128,66805,2477],{"className":66806},[1896],[128,66808,364],{"className":66809,"style":30665},[259,1873],[128,66811,1845],{"className":66812},[1903],[128,66814],{"className":66815,"style":1907},[269],[128,66817,35023],{"className":66818,"style":2508},[259,1873],[128,66820,2486],{"className":66821},[1928],"、条件分布 ",[128,66824,66826,66850],{"className":66825,"translate":218},[217],[128,66827,66829],{"className":66828},[222],[224,66830,66831],{"xmlns":226},[228,66832,66833,66847],{},[231,66834,66835,66837,66839,66841,66843,66845],{},[1795,66836,23001],{},[1832,66838,2477],{"stretchy":1837},[1795,66840,35023],{},[1832,66842,5443],{},[1795,66844,364],{},[1832,66846,2486],{"stretchy":1837},[238,66848,66849],{"encoding":240},"P(Y\\mid X)",[128,66851,66853,66877],{"className":66852,"ariaHidden":246},[245],[128,66854,66856,66859,66862,66865,66868,66871,66874],{"className":66855},[250],[128,66857],{"className":66858,"style":1892},[254],[128,66860,23001],{"className":66861,"style":36065},[259,1873],[128,66863,2477],{"className":66864},[1896],[128,66866,35023],{"className":66867,"style":2508},[259,1873],[128,66869],{"className":66870,"style":1878},[269],[128,66872,5443],{"className":66873},[1882],[128,66875],{"className":66876,"style":1878},[269],[128,66878,66880,66883,66886],{"className":66879},[250],[128,66881],{"className":66882,"style":1892},[254],[128,66884,364],{"className":66885,"style":30665},[259,1873],[128,66887,2486],{"className":66888},[1928],"，以及由此导出的独立性关系 ",[128,66891,66893,66919],{"className":66892,"translate":218},[217],[128,66894,66896],{"className":66895},[222],[224,66897,66898],{"xmlns":226},[228,66899,66900,66916],{},[231,66901,66902,66904,66906,66908,66910,66912,66914],{},[1795,66903,364],{},[1832,66905,12150],{},[234,66907,8524],{},[234,66909,8524],{},[234,66911,8524],{},[1832,66913,12150],{},[1795,66915,35023],{},[238,66917,66918],{"encoding":240},"X \\perp\\!\\!\\!\\perp Y",[128,66920,66922,66946,66958],{"className":66921,"ariaHidden":246},[245],[128,66923,66925,66928,66931,66934,66937,66940,66943],{"className":66924},[250],[128,66926],{"className":66927,"style":12173},[254],[128,66929,364],{"className":66930,"style":30665},[259,1873],[128,66932],{"className":66933,"style":1878},[269],[128,66935,12150],{"className":66936},[1882],[128,66938],{"className":66939,"style":317},[269],[128,66941],{"className":66942,"style":317},[269],[128,66944],{"className":66945,"style":317},[269],[128,66947,66949,66952,66955],{"className":66948},[250],[128,66950],{"className":66951,"style":12173},[254],[128,66953,12150],{"className":66954},[1882],[128,66956],{"className":66957,"style":1878},[269],[128,66959,66961,66964],{"className":66960},[250],[128,66962],{"className":66963,"style":283},[254],[128,66965,35023],{"className":66966,"style":2508},[259,1873],"。这套语言在数学上是自洽的，但存在一个根本性的表达力缺陷：",[35,66969,66970],{},"概率分布对「对称性」是不敏感的","。若已知 ",[128,66973,66975,66998],{"className":66974,"translate":218},[217],[128,66976,66978],{"className":66977},[222],[224,66979,66980],{"xmlns":226},[228,66981,66982,66996],{},[231,66983,66984,66986,66988,66990,66992,66994],{},[1795,66985,23001],{},[1832,66987,2477],{"stretchy":1837},[1795,66989,364],{},[1832,66991,1845],{"separator":246},[1795,66993,35023],{},[1832,66995,2486],{"stretchy":1837},[238,66997,66791],{"encoding":240},[128,66999,67001],{"className":67000,"ariaHidden":246},[245],[128,67002,67004,67007,67010,67013,67016,67019,67022,67025],{"className":67003},[250],[128,67005],{"className":67006,"style":1892},[254],[128,67008,23001],{"className":67009,"style":36065},[259,1873],[128,67011,2477],{"className":67012},[1896],[128,67014,364],{"className":67015,"style":30665},[259,1873],[128,67017,1845],{"className":67018},[1903],[128,67020],{"className":67021,"style":1907},[269],[128,67023,35023],{"className":67024,"style":2508},[259,1873],[128,67026,2486],{"className":67027},[1928],[128,67029,67031,67054],{"className":67030,"translate":218},[217],[128,67032,67034],{"className":67033},[222],[224,67035,67036],{"xmlns":226},[228,67037,67038,67052],{},[231,67039,67040,67042,67044,67046,67048,67050],{},[1795,67041,23001],{},[1832,67043,2477],{"stretchy":1837},[1795,67045,35023],{},[1832,67047,5443],{},[1795,67049,364],{},[1832,67051,2486],{"stretchy":1837},[238,67053,66849],{"encoding":240},[128,67055,67057,67081],{"className":67056,"ariaHidden":246},[245],[128,67058,67060,67063,67066,67069,67072,67075,67078],{"className":67059},[250],[128,67061],{"className":67062,"style":1892},[254],[128,67064,23001],{"className":67065,"style":36065},[259,1873],[128,67067,2477],{"className":67068},[1896],[128,67070,35023],{"className":67071,"style":2508},[259,1873],[128,67073],{"className":67074,"style":1878},[269],[128,67076,5443],{"className":67077},[1882],[128,67079],{"className":67080,"style":1878},[269],[128,67082,67084,67087,67090],{"className":67083},[250],[128,67085],{"className":67086,"style":1892},[254],[128,67088,364],{"className":67089,"style":30665},[259,1873],[128,67091,2486],{"className":67092},[1928],[128,67094,67096,67120],{"className":67095,"translate":218},[217],[128,67097,67099],{"className":67098},[222],[224,67100,67101],{"xmlns":226},[228,67102,67103,67117],{},[231,67104,67105,67107,67109,67111,67113,67115],{},[1795,67106,23001],{},[1832,67108,2477],{"stretchy":1837},[1795,67110,364],{},[1832,67112,5443],{},[1795,67114,35023],{},[1832,67116,2486],{"stretchy":1837},[238,67118,67119],{"encoding":240},"P(X\\mid Y)",[128,67121,67123,67147],{"className":67122,"ariaHidden":246},[245],[128,67124,67126,67129,67132,67135,67138,67141,67144],{"className":67125},[250],[128,67127],{"className":67128,"style":1892},[254],[128,67130,23001],{"className":67131,"style":36065},[259,1873],[128,67133,2477],{"className":67134},[1896],[128,67136,364],{"className":67137,"style":30665},[259,1873],[128,67139],{"className":67140,"style":1878},[269],[128,67142,5443],{"className":67143},[1882],[128,67145],{"className":67146,"style":1878},[269],[128,67148,67150,67153,67156],{"className":67149},[250],[128,67151],{"className":67152,"style":1892},[254],[128,67154,35023],{"className":67155,"style":2508},[259,1873],[128,67157,2486],{"className":67158},[1928]," 皆可通过贝叶斯定理相互推出，二者在信息量上完全等价，谁也不比谁更「根本」。然而在实际世界中，「气压下降导致下雨」与「下雨导致气压下降」显然不是对称的两种表述——只有前者是对的。这种方向性、非对称性的知识，是概率分布本身无法编码的，必须由额外的结构承载。",[11,67161,67162,67163,44582],{},"Judea Pearl 将因果知识的层级组织为三层，通常称为",[35,67164,67165],{},"因果推断阶梯（Ladder of Causation）",[35195,67167,67168,67321,67491],{},[33251,67169,67170,67173,67174,67240,67241,22492,67292,67320],{},[35,67171,67172],{},"第一层（关联，Association）","：回答形如 ",[128,67175,67177,67201],{"className":67176,"translate":218},[217],[128,67178,67180],{"className":67179},[222],[224,67181,67182],{"xmlns":226},[228,67183,67184,67198],{},[231,67185,67186,67188,67190,67192,67194,67196],{},[1795,67187,23001],{},[1832,67189,2477],{"stretchy":1837},[1795,67191,1830],{},[1832,67193,5443],{},[1795,67195,2760],{},[1832,67197,2486],{"stretchy":1837},[238,67199,67200],{"encoding":240},"P(y\\mid x)",[128,67202,67204,67228],{"className":67203,"ariaHidden":246},[245],[128,67205,67207,67210,67213,67216,67219,67222,67225],{"className":67206},[250],[128,67208],{"className":67209,"style":1892},[254],[128,67211,23001],{"className":67212,"style":36065},[259,1873],[128,67214,2477],{"className":67215},[1896],[128,67217,1830],{"className":67218,"style":1874},[259,1873],[128,67220],{"className":67221,"style":1878},[269],[128,67223,5443],{"className":67224},[1882],[128,67226],{"className":67227,"style":1878},[269],[128,67229,67231,67234,67237],{"className":67230},[250],[128,67232],{"className":67233,"style":1892},[254],[128,67235,2760],{"className":67236},[259,1873],[128,67238,2486],{"className":67239},[1928]," 的问题，即「观察到 ",[128,67242,67244,67262],{"className":67243,"translate":218},[217],[128,67245,67247],{"className":67246},[222],[224,67248,67249],{"xmlns":226},[228,67250,67251,67259],{},[231,67252,67253,67255,67257],{},[1795,67254,364],{},[1832,67256,1994],{},[1795,67258,2760],{},[238,67260,67261],{"encoding":240},"X=x",[128,67263,67265,67283],{"className":67264,"ariaHidden":246},[245],[128,67266,67268,67271,67274,67277,67280],{"className":67267},[250],[128,67269],{"className":67270,"style":283},[254],[128,67272,364],{"className":67273,"style":30665},[259,1873],[128,67275],{"className":67276,"style":1878},[269],[128,67278,1994],{"className":67279},[1882],[128,67281],{"className":67282,"style":1878},[269],[128,67284,67286,67289],{"className":67285},[250],[128,67287],{"className":67288,"style":7758},[254],[128,67290,2760],{"className":67291},[259,1873],[128,67293,67295,67308],{"className":67294,"translate":218},[217],[128,67296,67298],{"className":67297},[222],[224,67299,67300],{"xmlns":226},[228,67301,67302,67306],{},[231,67303,67304],{},[1795,67305,35023],{},[238,67307,35023],{"encoding":240},[128,67309,67311],{"className":67310,"ariaHidden":246},[245],[128,67312,67314,67317],{"className":67313},[250],[128,67315],{"className":67316,"style":283},[254],[128,67318,35023],{"className":67319,"style":2508},[259,1873]," 的分布是什么」。这一层是纯统计学的领地。",[33251,67322,67323,67173,67326,67411,67412,2674,67462,67490],{},[35,67324,67325],{},"第二层（干预，Intervention）",[128,67327,67329,67362],{"className":67328,"translate":218},[217],[128,67330,67332],{"className":67331},[222],[224,67333,67334],{"xmlns":226},[228,67335,67336,67359],{},[231,67337,67338,67340,67342,67344,67346,67348,67351,67353,67355,67357],{},[1795,67339,23001],{},[1832,67341,2477],{"stretchy":1837},[1795,67343,1830],{},[1832,67345,5443],{},[1795,67347,4519],{},[1795,67349,67350],{},"o",[1832,67352,2477],{"stretchy":1837},[1795,67354,2760],{},[1832,67356,2486],{"stretchy":1837},[1832,67358,2486],{"stretchy":1837},[238,67360,67361],{"encoding":240},"P(y\\mid do(x))",[128,67363,67365,67389],{"className":67364,"ariaHidden":246},[245],[128,67366,67368,67371,67374,67377,67380,67383,67386],{"className":67367},[250],[128,67369],{"className":67370,"style":1892},[254],[128,67372,23001],{"className":67373,"style":36065},[259,1873],[128,67375,2477],{"className":67376},[1896],[128,67378,1830],{"className":67379,"style":1874},[259,1873],[128,67381],{"className":67382,"style":1878},[269],[128,67384,5443],{"className":67385},[1882],[128,67387],{"className":67388,"style":1878},[269],[128,67390,67392,67395,67398,67401,67404,67407],{"className":67391},[250],[128,67393],{"className":67394,"style":1892},[254],[128,67396,4519],{"className":67397},[259,1873],[128,67399,67350],{"className":67400},[259,1873],[128,67402,2477],{"className":67403},[1896],[128,67405,2760],{"className":67406},[259,1873],[128,67408,67410],{"className":67409},[1928],"))"," 的问题，即「若外部强行使 ",[128,67413,67415,67432],{"className":67414,"translate":218},[217],[128,67416,67418],{"className":67417},[222],[224,67419,67420],{"xmlns":226},[228,67421,67422,67430],{},[231,67423,67424,67426,67428],{},[1795,67425,364],{},[1832,67427,1994],{},[1795,67429,2760],{},[238,67431,67261],{"encoding":240},[128,67433,67435,67453],{"className":67434,"ariaHidden":246},[245],[128,67436,67438,67441,67444,67447,67450],{"className":67437},[250],[128,67439],{"className":67440,"style":283},[254],[128,67442,364],{"className":67443,"style":30665},[259,1873],[128,67445],{"className":67446,"style":1878},[269],[128,67448,1994],{"className":67449},[1882],[128,67451],{"className":67452,"style":1878},[269],[128,67454,67456,67459],{"className":67455},[250],[128,67457],{"className":67458,"style":7758},[254],[128,67460,2760],{"className":67461},[259,1873],[128,67463,67465,67478],{"className":67464,"translate":218},[217],[128,67466,67468],{"className":67467},[222],[224,67469,67470],{"xmlns":226},[228,67471,67472,67476],{},[231,67473,67474],{},[1795,67475,35023],{},[238,67477,35023],{"encoding":240},[128,67479,67481],{"className":67480,"ariaHidden":246},[245],[128,67482,67484,67487],{"className":67483},[250],[128,67485],{"className":67486,"style":283},[254],[128,67488,35023],{"className":67489,"style":2508},[259,1873]," 的分布是什么」。",[33251,67492,67493,67173,67496,67682,67683,67835,67836,67864,67865,2674,67893,67921],{},[35,67494,67495],{},"第三层（反事实，Counterfactual）",[128,67497,67499,67539],{"className":67498,"translate":218},[217],[128,67500,67502],{"className":67501},[222],[224,67503,67504],{"xmlns":226},[228,67505,67506,67536],{},[231,67507,67508,67510,67512,67518,67520,67526,67528,67534],{},[1795,67509,23001],{},[1832,67511,2477],{"stretchy":1837},[2016,67513,67514,67516],{},[1795,67515,1830],{},[1795,67517,2760],{},[1832,67519,5443],{},[1977,67521,67522,67524],{},[1795,67523,2760],{},[1832,67525,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},[1832,67527,1845],{"separator":246},[1977,67529,67530,67532],{},[1795,67531,1830],{},[1832,67533,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},[1832,67535,2486],{"stretchy":1837},[238,67537,67538],{"encoding":240},"P(y_x \\mid x', y')",[128,67540,67542,67603],{"className":67541,"ariaHidden":246},[245],[128,67543,67545,67548,67551,67554,67594,67597,67600],{"className":67544},[250],[128,67546],{"className":67547,"style":1892},[254],[128,67549,23001],{"className":67550,"style":36065},[259,1873],[128,67552,2477],{"className":67553},[1896],[128,67555,67557,67560],{"className":67556},[259],[128,67558,1830],{"className":67559,"style":1874},[259,1873],[128,67561,67563],{"className":67562},[2087],[128,67564,67566,67586],{"className":67565},[274,321],[128,67567,67569,67583],{"className":67568},[278],[128,67570,67572],{"className":67571,"style":28738},[282],[128,67573,67574,67577],{"style":28741},[128,67575],{"className":67576,"style":291},[290],[128,67578,67580],{"className":67579},[299,300,301,298],[128,67581,2760],{"className":67582},[259,1873,298],[128,67584,347],{"className":67585},[346],[128,67587,67589],{"className":67588},[278],[128,67590,67592],{"className":67591,"style":2241},[282],[128,67593],{},[128,67595],{"className":67596,"style":1878},[269],[128,67598,5443],{"className":67599},[1882],[128,67601],{"className":67602,"style":1878},[269],[128,67604,67606,67609,67641,67644,67647,67679],{"className":67605},[250],[128,67607],{"className":67608,"style":24908},[254],[128,67610,67612,67615],{"className":67611},[259],[128,67613,2760],{"className":67614},[259,1873],[128,67616,67618],{"className":67617},[2087],[128,67619,67621],{"className":67620},[274],[128,67622,67624],{"className":67623},[278],[128,67625,67627],{"className":67626,"style":24927},[282],[128,67628,67629,67632],{"style":2452},[128,67630],{"className":67631,"style":291},[290],[128,67633,67635],{"className":67634},[299,300,301,298],[128,67636,67638],{"className":67637},[259,298],[128,67639,24873],{"className":67640},[259,298],[128,67642,1845],{"className":67643},[1903],[128,67645],{"className":67646,"style":1907},[269],[128,67648,67650,67653],{"className":67649},[259],[128,67651,1830],{"className":67652,"style":1874},[259,1873],[128,67654,67656],{"className":67655},[2087],[128,67657,67659],{"className":67658},[274],[128,67660,67662],{"className":67661},[278],[128,67663,67665],{"className":67664,"style":24927},[282],[128,67666,67667,67670],{"style":2452},[128,67668],{"className":67669,"style":291},[290],[128,67671,67673],{"className":67672},[299,300,301,298],[128,67674,67676],{"className":67675},[259,298],[128,67677,24873],{"className":67678},[259,298],[128,67680,2486],{"className":67681},[1928]," 的问题，即「已经观测到 ",[128,67684,67686,67720],{"className":67685,"translate":218},[217],[128,67687,67689],{"className":67688},[222],[224,67690,67691],{"xmlns":226},[228,67692,67693,67717],{},[231,67694,67695,67697,67699,67705,67707,67709,67711],{},[1795,67696,364],{},[1832,67698,1994],{},[1977,67700,67701,67703],{},[1795,67702,2760],{},[1832,67704,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},[1832,67706,1845],{"separator":246},[1795,67708,35023],{},[1832,67710,1994],{},[1977,67712,67713,67715],{},[1795,67714,1830],{},[1832,67716,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},[238,67718,67719],{"encoding":240},"X=x', Y=y'",[128,67721,67723,67741,67797],{"className":67722,"ariaHidden":246},[245],[128,67724,67726,67729,67732,67735,67738],{"className":67725},[250],[128,67727],{"className":67728,"style":283},[254],[128,67730,364],{"className":67731,"style":30665},[259,1873],[128,67733],{"className":67734,"style":1878},[269],[128,67736,1994],{"className":67737},[1882],[128,67739],{"className":67740,"style":1878},[269],[128,67742,67744,67747,67779,67782,67785,67788,67791,67794],{"className":67743},[250],[128,67745],{"className":67746,"style":50766},[254],[128,67748,67750,67753],{"className":67749},[259],[128,67751,2760],{"className":67752},[259,1873],[128,67754,67756],{"className":67755},[2087],[128,67757,67759],{"className":67758},[274],[128,67760,67762],{"className":67761},[278],[128,67763,67765],{"className":67764,"style":24927},[282],[128,67766,67767,67770],{"style":2452},[128,67768],{"className":67769,"style":291},[290],[128,67771,67773],{"className":67772},[299,300,301,298],[128,67774,67776],{"className":67775},[259,298],[128,67777,24873],{"className":67778},[259,298],[128,67780,1845],{"className":67781},[1903],[128,67783],{"className":67784,"style":1907},[269],[128,67786,35023],{"className":67787,"style":2508},[259,1873],[128,67789],{"className":67790,"style":1878},[269],[128,67792,1994],{"className":67793},[1882],[128,67795],{"className":67796,"style":1878},[269],[128,67798,67800,67803],{"className":67799},[250],[128,67801],{"className":67802,"style":50766},[254],[128,67804,67806,67809],{"className":67805},[259],[128,67807,1830],{"className":67808,"style":1874},[259,1873],[128,67810,67812],{"className":67811},[2087],[128,67813,67815],{"className":67814},[274],[128,67816,67818],{"className":67817},[278],[128,67819,67821],{"className":67820,"style":24927},[282],[128,67822,67823,67826],{"style":2452},[128,67824],{"className":67825,"style":291},[290],[128,67827,67829],{"className":67828},[299,300,301,298],[128,67830,67832],{"className":67831},[259,298],[128,67833,24873],{"className":67834},[259,298]," 的这个个体，若当初 ",[128,67837,67839,67852],{"className":67838,"translate":218},[217],[128,67840,67842],{"className":67841},[222],[224,67843,67844],{"xmlns":226},[228,67845,67846,67850],{},[231,67847,67848],{},[1795,67849,364],{},[238,67851,364],{"encoding":240},[128,67853,67855],{"className":67854,"ariaHidden":246},[245],[128,67856,67858,67861],{"className":67857},[250],[128,67859],{"className":67860,"style":283},[254],[128,67862,364],{"className":67863,"style":30665},[259,1873]," 被设为 ",[128,67866,67868,67881],{"className":67867,"translate":218},[217],[128,67869,67871],{"className":67870},[222],[224,67872,67873],{"xmlns":226},[228,67874,67875,67879],{},[231,67876,67877],{},[1795,67878,2760],{},[238,67880,2760],{"encoding":240},[128,67882,67884],{"className":67883,"ariaHidden":246},[245],[128,67885,67887,67890],{"className":67886},[250],[128,67888],{"className":67889,"style":7758},[254],[128,67891,2760],{"className":67892},[259,1873],[128,67894,67896,67909],{"className":67895,"translate":218},[217],[128,67897,67899],{"className":67898},[222],[224,67900,67901],{"xmlns":226},[228,67902,67903,67907],{},[231,67904,67905],{},[1795,67906,35023],{},[238,67908,35023],{"encoding":240},[128,67910,67912],{"className":67911,"ariaHidden":246},[245],[128,67913,67915,67918],{"className":67914},[250],[128,67916],{"className":67917,"style":283},[254],[128,67919,35023],{"className":67920,"style":2508},[259,1873]," 会取什么值」。",[11,67923,67924,67925,67928],{},"Pearl 证明了一个重要的否定性结论：",[35,67926,67927],{},"在一般情形下，仅凭第一层的信息（即观测分布本身），不足以唯一确定第二层或第三层的量","，除非引入额外的结构假设。这正是因果图、结构因果模型与结构方程存在的意义——它们是在观测分布之外，显式引入的「结构性知识」，使得第二、三层的问题在数学上可解。本文将依次、系统地展开这三个层层递进的形式化工具；随后把这一体系与潜在结果框架、传统结构方程模型等相邻传统作对照，并讨论其成立所依赖的假设与适用边界。",[51,67930,67931],{"id":67931},"因果图",[2610,67933,67935],{"id":67934},"_11-有向无环图的形式化定义","1.1 有向无环图的形式化定义",[2615,67937,67939],{"title":67938},"定义 1.1（有向图）",[11,67940,67941,67942,7713,68018,68191,68192,68267,68268,68424,68425,68559,68560,68630,68631,11101,68701,2674,68704,68630,68773,11101,68842,893],{},"一个有向图是一个二元组 ",[128,67943,67945,67973],{"className":67944,"translate":218},[217],[128,67946,67948],{"className":67947},[222],[224,67949,67950],{"xmlns":226},[228,67951,67952,67970],{},[231,67953,67954,67957,67959,67961,67964,67966,67968],{},[1795,67955,67956],{},"G",[1832,67958,1994],{},[1832,67960,2477],{"stretchy":1837},[1795,67962,67963],{},"V",[1832,67965,1845],{"separator":246},[1795,67967,342],{},[1832,67969,2486],{"stretchy":1837},[238,67971,67972],{"encoding":240},"G = (V, E)",[128,67974,67976,67994],{"className":67975,"ariaHidden":246},[245],[128,67977,67979,67982,67985,67988,67991],{"className":67978},[250],[128,67980],{"className":67981,"style":283},[254],[128,67983,67956],{"className":67984},[259,1873],[128,67986],{"className":67987,"style":1878},[269],[128,67989,1994],{"className":67990},[1882],[128,67992],{"className":67993,"style":1878},[269],[128,67995,67997,68000,68003,68006,68009,68012,68015],{"className":67996},[250],[128,67998],{"className":67999,"style":1892},[254],[128,68001,2477],{"className":68002},[1896],[128,68004,67963],{"className":68005,"style":2508},[259,1873],[128,68007,1845],{"className":68008},[1903],[128,68010],{"className":68011,"style":1907},[269],[128,68013,342],{"className":68014,"style":42029},[259,1873],[128,68016,2486],{"className":68017},[1928],[128,68019,68021,68059],{"className":68020,"translate":218},[217],[128,68022,68024],{"className":68023},[222],[224,68025,68026],{"xmlns":226},[228,68027,68028,68056],{},[231,68029,68030,68032,68034,68036,68042,68044,68046,68048,68054],{},[1795,68031,67963],{},[1832,68033,1994],{},[1832,68035,1838],{"stretchy":1837},[2016,68037,68038,68040],{},[1795,68039,67963],{},[1840,68041,1842],{},[1832,68043,1845],{"separator":246},[1832,68045,1848],{},[1832,68047,1845],{"separator":246},[2016,68049,68050,68052],{},[1795,68051,67963],{},[1795,68053,16280],{},[1832,68055,1856],{"stretchy":1837},[238,68057,68058],{"encoding":240},"V = \\{V_1, \\dots, V_n\\}",[128,68060,68062,68080],{"className":68061,"ariaHidden":246},[245],[128,68063,68065,68068,68071,68074,68077],{"className":68064},[250],[128,68066],{"className":68067,"style":283},[254],[128,68069,67963],{"className":68070,"style":2508},[259,1873],[128,68072],{"className":68073,"style":1878},[269],[128,68075,1994],{"className":68076},[1882],[128,68078],{"className":68079,"style":1878},[269],[128,68081,68083,68086,68089,68130,68133,68136,68139,68142,68145,68148,68188],{"className":68082},[250],[128,68084],{"className":68085,"style":1892},[254],[128,68087,1838],{"className":68088},[1896],[128,68090,68092,68095],{"className":68091},[259],[128,68093,67963],{"className":68094,"style":2508},[259,1873],[128,68096,68098],{"className":68097},[2087],[128,68099,68101,68122],{"className":68100},[274,321],[128,68102,68104,68119],{"className":68103},[278],[128,68105,68107],{"className":68106,"style":2945},[282],[128,68108,68110,68113],{"style":68109},"top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;",[128,68111],{"className":68112,"style":291},[290],[128,68114,68116],{"className":68115},[299,300,301,298],[128,68117,1842],{"className":68118},[259,298],[128,68120,347],{"className":68121},[346],[128,68123,68125],{"className":68124},[278],[128,68126,68128],{"className":68127,"style":2241},[282],[128,68129],{},[128,68131,1845],{"className":68132},[1903],[128,68134],{"className":68135,"style":1907},[269],[128,68137,1848],{"className":68138},[1911],[128,68140],{"className":68141,"style":1907},[269],[128,68143,1845],{"className":68144},[1903],[128,68146],{"className":68147,"style":1907},[269],[128,68149,68151,68154],{"className":68150},[259],[128,68152,67963],{"className":68153,"style":2508},[259,1873],[128,68155,68157],{"className":68156},[2087],[128,68158,68160,68180],{"className":68159},[274,321],[128,68161,68163,68177],{"className":68162},[278],[128,68164,68166],{"className":68165,"style":28738},[282],[128,68167,68168,68171],{"style":68109},[128,68169],{"className":68170,"style":291},[290],[128,68172,68174],{"className":68173},[299,300,301,298],[128,68175,16280],{"className":68176},[259,1873,298],[128,68178,347],{"className":68179},[346],[128,68181,68183],{"className":68182},[278],[128,68184,68186],{"className":68185,"style":2241},[282],[128,68187],{},[128,68189,1856],{"className":68190},[1928]," 是节点（顶点）的有限集合，",[128,68193,68195,68219],{"className":68194,"translate":218},[217],[128,68196,68198],{"className":68197},[222],[224,68199,68200],{"xmlns":226},[228,68201,68202,68216],{},[231,68203,68204,68206,68209,68211,68214],{},[1795,68205,342],{},[1832,68207,68208],{},"⊆",[1795,68210,67963],{},[1832,68212,68213],{},"×",[1795,68215,67963],{},[238,68217,68218],{"encoding":240},"E \\subseteq V \\times V",[128,68220,68222,68240,68258],{"className":68221,"ariaHidden":246},[245],[128,68223,68225,68228,68231,68234,68237],{"className":68224},[250],[128,68226],{"className":68227,"style":2652},[254],[128,68229,342],{"className":68230,"style":42029},[259,1873],[128,68232],{"className":68233,"style":1878},[269],[128,68235,68208],{"className":68236},[1882],[128,68238],{"className":68239,"style":1878},[269],[128,68241,68243,68246,68249,68252,68255],{"className":68242},[250],[128,68244],{"className":68245,"style":2705},[254],[128,68247,67963],{"className":68248,"style":2508},[259,1873],[128,68250],{"className":68251,"style":2508},[269],[128,68253,68213],{"className":68254},[2115],[128,68256],{"className":68257,"style":2508},[269],[128,68259,68261,68264],{"className":68260},[250],[128,68262],{"className":68263,"style":283},[254],[128,68265,67963],{"className":68266,"style":2508},[259,1873]," 是有向边的集合。若 ",[128,68269,68271,68305],{"className":68270,"translate":218},[217],[128,68272,68274],{"className":68273},[222],[224,68275,68276],{"xmlns":226},[228,68277,68278,68302],{},[231,68279,68280,68282,68288,68290,68296,68298,68300],{},[1832,68281,2477],{"stretchy":1837},[2016,68283,68284,68286],{},[1795,68285,67963],{},[1795,68287,2801],{},[1832,68289,1845],{"separator":246},[2016,68291,68292,68294],{},[1795,68293,67963],{},[1795,68295,16495],{},[1832,68297,2486],{"stretchy":1837},[1832,68299,1834],{},[1795,68301,342],{},[238,68303,68304],{"encoding":240},"(V_i, V_j) \\in E",[128,68306,68308,68415],{"className":68307,"ariaHidden":246},[245],[128,68309,68311,68314,68317,68357,68360,68363,68403,68406,68409,68412],{"className":68310},[250],[128,68312],{"className":68313,"style":19704},[254],[128,68315,2477],{"className":68316},[1896],[128,68318,68320,68323],{"className":68319},[259],[128,68321,67963],{"className":68322,"style":2508},[259,1873],[128,68324,68326],{"className":68325},[2087],[128,68327,68329,68349],{"className":68328},[274,321],[128,68330,68332,68346],{"className":68331},[278],[128,68333,68335],{"className":68334,"style":3095},[282],[128,68336,68337,68340],{"style":68109},[128,68338],{"className":68339,"style":291},[290],[128,68341,68343],{"className":68342},[299,300,301,298],[128,68344,2801],{"className":68345},[259,1873,298],[128,68347,347],{"className":68348},[346],[128,68350,68352],{"className":68351},[278],[128,68353,68355],{"className":68354,"style":2241},[282],[128,68356],{},[128,68358,1845],{"className":68359},[1903],[128,68361],{"className":68362,"style":1907},[269],[128,68364,68366,68369],{"className":68365},[259],[128,68367,67963],{"className":68368,"style":2508},[259,1873],[128,68370,68372],{"className":68371},[2087],[128,68373,68375,68395],{"className":68374},[274,321],[128,68376,68378,68392],{"className":68377},[278],[128,68379,68381],{"className":68380,"style":3095},[282],[128,68382,68383,68386],{"style":68109},[128,68384],{"className":68385,"style":291},[290],[128,68387,68389],{"className":68388},[299,300,301,298],[128,68390,16495],{"className":68391,"style":16521},[259,1873,298],[128,68393,347],{"className":68394},[346],[128,68396,68398],{"className":68397},[278],[128,68399,68401],{"className":68400,"style":17424},[282],[128,68402],{},[128,68404,2486],{"className":68405},[1928],[128,68407],{"className":68408,"style":1878},[269],[128,68410,1834],{"className":68411},[1882],[128,68413],{"className":68414,"style":1878},[269],[128,68416,68418,68421],{"className":68417},[250],[128,68419],{"className":68420,"style":283},[254],[128,68422,342],{"className":68423,"style":42029},[259,1873],"，记作 ",[128,68426,68428,68454],{"className":68427,"translate":218},[217],[128,68429,68431],{"className":68430},[222],[224,68432,68433],{"xmlns":226},[228,68434,68435,68451],{},[231,68436,68437,68443,68445],{},[2016,68438,68439,68441],{},[1795,68440,67963],{},[1795,68442,2801],{},[1832,68444,22419],{},[2016,68446,68447,68449],{},[1795,68448,67963],{},[1795,68450,16495],{},[238,68452,68453],{"encoding":240},"V_i \\to V_j",[128,68455,68457,68512],{"className":68456,"ariaHidden":246},[245],[128,68458,68460,68463,68503,68506,68509],{"className":68459},[250],[128,68461],{"className":68462,"style":36058},[254],[128,68464,68466,68469],{"className":68465},[259],[128,68467,67963],{"className":68468,"style":2508},[259,1873],[128,68470,68472],{"className":68471},[2087],[128,68473,68475,68495],{"className":68474},[274,321],[128,68476,68478,68492],{"className":68477},[278],[128,68479,68481],{"className":68480,"style":3095},[282],[128,68482,68483,68486],{"style":68109},[128,68484],{"className":68485,"style":291},[290],[128,68487,68489],{"className":68488},[299,300,301,298],[128,68490,2801],{"className":68491},[259,1873,298],[128,68493,347],{"className":68494},[346],[128,68496,68498],{"className":68497},[278],[128,68499,68501],{"className":68500,"style":2241},[282],[128,68502],{},[128,68504],{"className":68505,"style":1878},[269],[128,68507,22419],{"className":68508},[1882],[128,68510],{"className":68511,"style":1878},[269],[128,68513,68515,68519],{"className":68514},[250],[128,68516],{"className":68517,"style":68518},[254],"height:0.9694em;vertical-align:-0.2861em;",[128,68520,68522,68525],{"className":68521},[259],[128,68523,67963],{"className":68524,"style":2508},[259,1873],[128,68526,68528],{"className":68527},[2087],[128,68529,68531,68551],{"className":68530},[274,321],[128,68532,68534,68548],{"className":68533},[278],[128,68535,68537],{"className":68536,"style":3095},[282],[128,68538,68539,68542],{"style":68109},[128,68540],{"className":68541,"style":291},[290],[128,68543,68545],{"className":68544},[299,300,301,298],[128,68546,16495],{"className":68547,"style":16521},[259,1873,298],[128,68549,347],{"className":68550},[346],[128,68552,68554],{"className":68553},[278],[128,68555,68557],{"className":68556,"style":17424},[282],[128,68558],{},"，称 ",[128,68561,68563,68581],{"className":68562,"translate":218},[217],[128,68564,68566],{"className":68565},[222],[224,68567,68568],{"xmlns":226},[228,68569,68570,68578],{},[231,68571,68572],{},[2016,68573,68574,68576],{},[1795,68575,67963],{},[1795,68577,2801],{},[238,68579,68580],{"encoding":240},"V_i",[128,68582,68584],{"className":68583,"ariaHidden":246},[245],[128,68585,68587,68590],{"className":68586},[250],[128,68588],{"className":68589,"style":36058},[254],[128,68591,68593,68596],{"className":68592},[259],[128,68594,67963],{"className":68595,"style":2508},[259,1873],[128,68597,68599],{"className":68598},[2087],[128,68600,68602,68622],{"className":68601},[274,321],[128,68603,68605,68619],{"className":68604},[278],[128,68606,68608],{"className":68607,"style":3095},[282],[128,68609,68610,68613],{"style":68109},[128,68611],{"className":68612,"style":291},[290],[128,68614,68616],{"className":68615},[299,300,301,298],[128,68617,2801],{"className":68618},[259,1873,298],[128,68620,347],{"className":68621},[346],[128,68623,68625],{"className":68624},[278],[128,68626,68628],{"className":68627,"style":2241},[282],[128,68629],{}," 为 ",[128,68632,68634,68652],{"className":68633,"translate":218},[217],[128,68635,68637],{"className":68636},[222],[224,68638,68639],{"xmlns":226},[228,68640,68641,68649],{},[231,68642,68643],{},[2016,68644,68645,68647],{},[1795,68646,67963],{},[1795,68648,16495],{},[238,68650,68651],{"encoding":240},"V_j",[128,68653,68655],{"className":68654,"ariaHidden":246},[245],[128,68656,68658,68661],{"className":68657},[250],[128,68659],{"className":68660,"style":68518},[254],[128,68662,68664,68667],{"className":68663},[259],[128,68665,67963],{"className":68666,"style":2508},[259,1873],[128,68668,68670],{"className":68669},[2087],[128,68671,68673,68693],{"className":68672},[274,321],[128,68674,68676,68690],{"className":68675},[278],[128,68677,68679],{"className":68678,"style":3095},[282],[128,68680,68681,68684],{"style":68109},[128,68682],{"className":68683,"style":291},[290],[128,68685,68687],{"className":68686},[299,300,301,298],[128,68688,16495],{"className":68689,"style":16521},[259,1873,298],[128,68691,347],{"className":68692},[346],[128,68694,68696],{"className":68695},[278],[128,68697,68699],{"className":68698,"style":17424},[282],[128,68700],{},[35,68702,68703],{},"父节点（parent）",[128,68705,68707,68724],{"className":68706,"translate":218},[217],[128,68708,68710],{"className":68709},[222],[224,68711,68712],{"xmlns":226},[228,68713,68714,68722],{},[231,68715,68716],{},[2016,68717,68718,68720],{},[1795,68719,67963],{},[1795,68721,16495],{},[238,68723,68651],{"encoding":240},[128,68725,68727],{"className":68726,"ariaHidden":246},[245],[128,68728,68730,68733],{"className":68729},[250],[128,68731],{"className":68732,"style":68518},[254],[128,68734,68736,68739],{"className":68735},[259],[128,68737,67963],{"className":68738,"style":2508},[259,1873],[128,68740,68742],{"className":68741},[2087],[128,68743,68745,68765],{"className":68744},[274,321],[128,68746,68748,68762],{"className":68747},[278],[128,68749,68751],{"className":68750,"style":3095},[282],[128,68752,68753,68756],{"style":68109},[128,68754],{"className":68755,"style":291},[290],[128,68757,68759],{"className":68758},[299,300,301,298],[128,68760,16495],{"className":68761,"style":16521},[259,1873,298],[128,68763,347],{"className":68764},[346],[128,68766,68768],{"className":68767},[278],[128,68769,68771],{"className":68770,"style":17424},[282],[128,68772],{},[128,68774,68776,68793],{"className":68775,"translate":218},[217],[128,68777,68779],{"className":68778},[222],[224,68780,68781],{"xmlns":226},[228,68782,68783,68791],{},[231,68784,68785],{},[2016,68786,68787,68789],{},[1795,68788,67963],{},[1795,68790,2801],{},[238,68792,68580],{"encoding":240},[128,68794,68796],{"className":68795,"ariaHidden":246},[245],[128,68797,68799,68802],{"className":68798},[250],[128,68800],{"className":68801,"style":36058},[254],[128,68803,68805,68808],{"className":68804},[259],[128,68806,67963],{"className":68807,"style":2508},[259,1873],[128,68809,68811],{"className":68810},[2087],[128,68812,68814,68834],{"className":68813},[274,321],[128,68815,68817,68831],{"className":68816},[278],[128,68818,68820],{"className":68819,"style":3095},[282],[128,68821,68822,68825],{"style":68109},[128,68823],{"className":68824,"style":291},[290],[128,68826,68828],{"className":68827},[299,300,301,298],[128,68829,2801],{"className":68830},[259,1873,298],[128,68832,347],{"className":68833},[346],[128,68835,68837],{"className":68836},[278],[128,68838,68840],{"className":68839,"style":2241},[282],[128,68841],{},[35,68843,68844],{},"子节点（child）",[2615,68846,68848],{"title":68847},"定义 1.2（路径）",[11,68849,68850,68851,68879,68880,68949,68950,69019,69020,69023,69024,69355,69356,2674,69384,11072,69454,69540,69541,69544,69545,17916,69678,69730,69731,893],{},"图 ",[128,68852,68854,68867],{"className":68853,"translate":218},[217],[128,68855,68857],{"className":68856},[222],[224,68858,68859],{"xmlns":226},[228,68860,68861,68865],{},[231,68862,68863],{},[1795,68864,67956],{},[238,68866,67956],{"encoding":240},[128,68868,68870],{"className":68869,"ariaHidden":246},[245],[128,68871,68873,68876],{"className":68872},[250],[128,68874],{"className":68875,"style":283},[254],[128,68877,67956],{"className":68878},[259,1873]," 中从 ",[128,68881,68883,68900],{"className":68882,"translate":218},[217],[128,68884,68886],{"className":68885},[222],[224,68887,68888],{"xmlns":226},[228,68889,68890,68898],{},[231,68891,68892],{},[2016,68893,68894,68896],{},[1795,68895,67963],{},[1795,68897,2801],{},[238,68899,68580],{"encoding":240},[128,68901,68903],{"className":68902,"ariaHidden":246},[245],[128,68904,68906,68909],{"className":68905},[250],[128,68907],{"className":68908,"style":36058},[254],[128,68910,68912,68915],{"className":68911},[259],[128,68913,67963],{"className":68914,"style":2508},[259,1873],[128,68916,68918],{"className":68917},[2087],[128,68919,68921,68941],{"className":68920},[274,321],[128,68922,68924,68938],{"className":68923},[278],[128,68925,68927],{"className":68926,"style":3095},[282],[128,68928,68929,68932],{"style":68109},[128,68930],{"className":68931,"style":291},[290],[128,68933,68935],{"className":68934},[299,300,301,298],[128,68936,2801],{"className":68937},[259,1873,298],[128,68939,347],{"className":68940},[346],[128,68942,68944],{"className":68943},[278],[128,68945,68947],{"className":68946,"style":2241},[282],[128,68948],{}," 到 ",[128,68951,68953,68970],{"className":68952,"translate":218},[217],[128,68954,68956],{"className":68955},[222],[224,68957,68958],{"xmlns":226},[228,68959,68960,68968],{},[231,68961,68962],{},[2016,68963,68964,68966],{},[1795,68965,67963],{},[1795,68967,16495],{},[238,68969,68651],{"encoding":240},[128,68971,68973],{"className":68972,"ariaHidden":246},[245],[128,68974,68976,68979],{"className":68975},[250],[128,68977],{"className":68978,"style":68518},[254],[128,68980,68982,68985],{"className":68981},[259],[128,68983,67963],{"className":68984,"style":2508},[259,1873],[128,68986,68988],{"className":68987},[2087],[128,68989,68991,69011],{"className":68990},[274,321],[128,68992,68994,69008],{"className":68993},[278],[128,68995,68997],{"className":68996,"style":3095},[282],[128,68998,68999,69002],{"style":68109},[128,69000],{"className":69001,"style":291},[290],[128,69003,69005],{"className":69004},[299,300,301,298],[128,69006,16495],{"className":69007,"style":16521},[259,1873,298],[128,69009,347],{"className":69010},[346],[128,69012,69014],{"className":69013},[278],[128,69015,69017],{"className":69016,"style":17424},[282],[128,69018],{}," 的一条",[35,69021,69022],{},"路径","是一个节点序列 ",[128,69025,69027,69086],{"className":69026,"translate":218},[217],[128,69028,69030],{"className":69029},[222],[224,69031,69032],{"xmlns":226},[228,69033,69034,69083],{},[231,69035,69036,69038,69044,69046,69053,69055,69061,69063,69065,69067,69073,69075,69081],{},[1832,69037,64962],{"stretchy":1837},[2016,69039,69040,69042],{},[1795,69041,67963],{},[1795,69043,2801],{},[1832,69045,1994],{},[2016,69047,69048,69051],{},[1795,69049,69050],{},"U",[1840,69052,2028],{},[1832,69054,1845],{"separator":246},[2016,69056,69057,69059],{},[1795,69058,69050],{},[1840,69060,1842],{},[1832,69062,1845],{"separator":246},[1832,69064,1848],{},[1832,69066,1845],{"separator":246},[2016,69068,69069,69071],{},[1795,69070,69050],{},[1795,69072,2022],{},[1832,69074,1994],{},[2016,69076,69077,69079],{},[1795,69078,67963],{},[1795,69080,16495],{},[1832,69082,64975],{"stretchy":1837},[238,69084,69085],{"encoding":240},"\\langle V_i = U_0, U_1, \\dots, U_k = V_j\\rangle",[128,69087,69089,69147,69306],{"className":69088,"ariaHidden":246},[245],[128,69090,69092,69095,69098,69138,69141,69144],{"className":69091},[250],[128,69093],{"className":69094,"style":1892},[254],[128,69096,64962],{"className":69097},[1896],[128,69099,69101,69104],{"className":69100},[259],[128,69102,67963],{"className":69103,"style":2508},[259,1873],[128,69105,69107],{"className":69106},[2087],[128,69108,69110,69130],{"className":69109},[274,321],[128,69111,69113,69127],{"className":69112},[278],[128,69114,69116],{"className":69115,"style":3095},[282],[128,69117,69118,69121],{"style":68109},[128,69119],{"className":69120,"style":291},[290],[128,69122,69124],{"className":69123},[299,300,301,298],[128,69125,2801],{"className":69126},[259,1873,298],[128,69128,347],{"className":69129},[346],[128,69131,69133],{"className":69132},[278],[128,69134,69136],{"className":69135,"style":2241},[282],[128,69137],{},[128,69139],{"className":69140,"style":1878},[269],[128,69142,1994],{"className":69143},[1882],[128,69145],{"className":69146,"style":1878},[269],[128,69148,69150,69153,69193,69196,69199,69239,69242,69245,69248,69251,69254,69257,69297,69300,69303],{"className":69149},[250],[128,69151],{"className":69152,"style":40674},[254],[128,69154,69156,69159],{"className":69155},[259],[128,69157,69050],{"className":69158,"style":26806},[259,1873],[128,69160,69162],{"className":69161},[2087],[128,69163,69165,69185],{"className":69164},[274,321],[128,69166,69168,69182],{"className":69167},[278],[128,69169,69171],{"className":69170,"style":2945},[282],[128,69172,69173,69176],{"style":64697},[128,69174],{"className":69175,"style":291},[290],[128,69177,69179],{"className":69178},[299,300,301,298],[128,69180,2028],{"className":69181},[259,298],[128,69183,347],{"className":69184},[346],[128,69186,69188],{"className":69187},[278],[128,69189,69191],{"className":69190,"style":2241},[282],[128,69192],{},[128,69194,1845],{"className":69195},[1903],[128,69197],{"className":69198,"style":1907},[269],[128,69200,69202,69205],{"className":69201},[259],[128,69203,69050],{"className":69204,"style":26806},[259,1873],[128,69206,69208],{"className":69207},[2087],[128,69209,69211,69231],{"className":69210},[274,321],[128,69212,69214,69228],{"className":69213},[278],[128,69215,69217],{"className":69216,"style":2945},[282],[128,69218,69219,69222],{"style":64697},[128,69220],{"className":69221,"style":291},[290],[128,69223,69225],{"className":69224},[299,300,301,298],[128,69226,1842],{"className":69227},[259,298],[128,69229,347],{"className":69230},[346],[128,69232,69234],{"className":69233},[278],[128,69235,69237],{"className":69236,"style":2241},[282],[128,69238],{},[128,69240,1845],{"className":69241},[1903],[128,69243],{"className":69244,"style":1907},[269],[128,69246,1848],{"className":69247},[1911],[128,69249],{"className":69250,"style":1907},[269],[128,69252,1845],{"className":69253},[1903],[128,69255],{"className":69256,"style":1907},[269],[128,69258,69260,69263],{"className":69259},[259],[128,69261,69050],{"className":69262,"style":26806},[259,1873],[128,69264,69266],{"className":69265},[2087],[128,69267,69269,69289],{"className":69268},[274,321],[128,69270,69272,69286],{"className":69271},[278],[128,69273,69275],{"className":69274,"style":2218},[282],[128,69276,69277,69280],{"style":64697},[128,69278],{"className":69279,"style":291},[290],[128,69281,69283],{"className":69282},[299,300,301,298],[128,69284,2022],{"className":69285,"style":2231},[259,1873,298],[128,69287,347],{"className":69288},[346],[128,69290,69292],{"className":69291},[278],[128,69293,69295],{"className":69294,"style":2241},[282],[128,69296],{},[128,69298],{"className":69299,"style":1878},[269],[128,69301,1994],{"className":69302},[1882],[128,69304],{"className":69305,"style":1878},[269],[128,69307,69309,69312,69352],{"className":69308},[250],[128,69310],{"className":69311,"style":19704},[254],[128,69313,69315,69318],{"className":69314},[259],[128,69316,67963],{"className":69317,"style":2508},[259,1873],[128,69319,69321],{"className":69320},[2087],[128,69322,69324,69344],{"className":69323},[274,321],[128,69325,69327,69341],{"className":69326},[278],[128,69328,69330],{"className":69329,"style":3095},[282],[128,69331,69332,69335],{"style":68109},[128,69333],{"className":69334,"style":291},[290],[128,69336,69338],{"className":69337},[299,300,301,298],[128,69339,16495],{"className":69340,"style":16521},[259,1873,298],[128,69342,347],{"className":69343},[346],[128,69345,69347],{"className":69346},[278],[128,69348,69350],{"className":69349,"style":17424},[282],[128,69351],{},[128,69353,64975],{"className":69354},[1928],"，使得对每个 ",[128,69357,69359,69372],{"className":69358,"translate":218},[217],[128,69360,69362],{"className":69361},[222],[224,69363,69364],{"xmlns":226},[228,69365,69366,69370],{},[231,69367,69368],{},[1795,69369,7023],{},[238,69371,7023],{"encoding":240},[128,69373,69375],{"className":69374,"ariaHidden":246},[245],[128,69376,69378,69381],{"className":69377},[250],[128,69379],{"className":69380,"style":64273},[254],[128,69382,7023],{"className":69383},[259,1873],[128,69385,69387,69405],{"className":69386,"translate":218},[217],[128,69388,69390],{"className":69389},[222],[224,69391,69392],{"xmlns":226},[228,69393,69394,69402],{},[231,69395,69396],{},[2016,69397,69398,69400],{},[1795,69399,69050],{},[1795,69401,7023],{},[238,69403,69404],{"encoding":240},"U_t",[128,69406,69408],{"className":69407,"ariaHidden":246},[245],[128,69409,69411,69414],{"className":69410},[250],[128,69412],{"className":69413,"style":36058},[254],[128,69415,69417,69420],{"className":69416},[259],[128,69418,69050],{"className":69419,"style":26806},[259,1873],[128,69421,69423],{"className":69422},[2087],[128,69424,69426,69446],{"className":69425},[274,321],[128,69427,69429,69443],{"className":69428},[278],[128,69430,69432],{"className":69431,"style":58540},[282],[128,69433,69434,69437],{"style":64697},[128,69435],{"className":69436,"style":291},[290],[128,69438,69440],{"className":69439},[299,300,301,298],[128,69441,7023],{"className":69442},[259,1873,298],[128,69444,347],{"className":69445},[346],[128,69447,69449],{"className":69448},[278],[128,69450,69452],{"className":69451,"style":2241},[282],[128,69453],{},[128,69455,69457,69481],{"className":69456,"translate":218},[217],[128,69458,69460],{"className":69459},[222],[224,69461,69462],{"xmlns":226},[228,69463,69464,69478],{},[231,69465,69466],{},[2016,69467,69468,69470],{},[1795,69469,69050],{},[231,69471,69472,69474,69476],{},[1795,69473,7023],{},[1832,69475,9486],{},[1840,69477,1842],{},[238,69479,69480],{"encoding":240},"U_{t+1}",[128,69482,69484],{"className":69483,"ariaHidden":246},[245],[128,69485,69487,69491],{"className":69486},[250],[128,69488],{"className":69489,"style":69490},[254],"height:0.8917em;vertical-align:-0.2083em;",[128,69492,69494,69497],{"className":69493},[259],[128,69495,69050],{"className":69496,"style":26806},[259,1873],[128,69498,69500],{"className":69499},[2087],[128,69501,69503,69532],{"className":69502},[274,321],[128,69504,69506,69529],{"className":69505},[278],[128,69507,69509],{"className":69508,"style":2945},[282],[128,69510,69511,69514],{"style":64697},[128,69512],{"className":69513,"style":291},[290],[128,69515,69517],{"className":69516},[299,300,301,298],[128,69518,69520,69523,69526],{"className":69519},[259,298],[128,69521,7023],{"className":69522},[259,1873,298],[128,69524,9486],{"className":69525},[2115,298],[128,69527,1842],{"className":69528},[259,298],[128,69530,347],{"className":69531},[346],[128,69533,69535],{"className":69534},[278],[128,69536,69538],{"className":69537,"style":4183},[282],[128,69539],{}," 之间存在一条边（不论方向）。若路径上所有边的方向都与路径前进方向一致，称为",[35,69542,69543],{},"有向路径","；若 ",[128,69546,69548,69574],{"className":69547,"translate":218},[217],[128,69549,69551],{"className":69550},[222],[224,69552,69553],{"xmlns":226},[228,69554,69555,69571],{},[231,69556,69557,69563,69565],{},[2016,69558,69559,69561],{},[1795,69560,69050],{},[1840,69562,2028],{},[1832,69564,1994],{},[2016,69566,69567,69569],{},[1795,69568,69050],{},[1795,69570,2022],{},[238,69572,69573],{"encoding":240},"U_0 = U_k",[128,69575,69577,69632],{"className":69576,"ariaHidden":246},[245],[128,69578,69580,69583,69623,69626,69629],{"className":69579},[250],[128,69581],{"className":69582,"style":36058},[254],[128,69584,69586,69589],{"className":69585},[259],[128,69587,69050],{"className":69588,"style":26806},[259,1873],[128,69590,69592],{"className":69591},[2087],[128,69593,69595,69615],{"className":69594},[274,321],[128,69596,69598,69612],{"className":69597},[278],[128,69599,69601],{"className":69600,"style":2945},[282],[128,69602,69603,69606],{"style":64697},[128,69604],{"className":69605,"style":291},[290],[128,69607,69609],{"className":69608},[299,300,301,298],[128,69610,2028],{"className":69611},[259,298],[128,69613,347],{"className":69614},[346],[128,69616,69618],{"className":69617},[278],[128,69619,69621],{"className":69620,"style":2241},[282],[128,69622],{},[128,69624],{"className":69625,"style":1878},[269],[128,69627,1994],{"className":69628},[1882],[128,69630],{"className":69631,"style":1878},[269],[128,69633,69635,69638],{"className":69634},[250],[128,69636],{"className":69637,"style":36058},[254],[128,69639,69641,69644],{"className":69640},[259],[128,69642,69050],{"className":69643,"style":26806},[259,1873],[128,69645,69647],{"className":69646},[2087],[128,69648,69650,69670],{"className":69649},[274,321],[128,69651,69653,69667],{"className":69652},[278],[128,69654,69656],{"className":69655,"style":2218},[282],[128,69657,69658,69661],{"style":64697},[128,69659],{"className":69660,"style":291},[290],[128,69662,69664],{"className":69663},[299,300,301,298],[128,69665,2022],{"className":69666,"style":2231},[259,1873,298],[128,69668,347],{"className":69669},[346],[128,69671,69673],{"className":69672},[278],[128,69674,69676],{"className":69675,"style":2241},[282],[128,69677],{},[128,69679,69681,69699],{"className":69680,"translate":218},[217],[128,69682,69684],{"className":69683},[222],[224,69685,69686],{"xmlns":226},[228,69687,69688,69696],{},[231,69689,69690,69692,69694],{},[1795,69691,2022],{},[1832,69693,2025],{},[1840,69695,1842],{},[238,69697,69698],{"encoding":240},"k \\geq 1",[128,69700,69702,69721],{"className":69701,"ariaHidden":246},[245],[128,69703,69705,69709,69712,69715,69718],{"className":69704},[250],[128,69706],{"className":69707,"style":69708},[254],"height:0.8304em;vertical-align:-0.136em;",[128,69710,2022],{"className":69711,"style":2231},[259,1873],[128,69713],{"className":69714,"style":1878},[269],[128,69716,2025],{"className":69717},[1882],[128,69719],{"className":69720,"style":1878},[269],[128,69722,69724,69727],{"className":69723},[250],[128,69725],{"className":69726,"style":2594},[254],[128,69728,1842],{"className":69729},[259],"，则称为一个",[35,69732,69733],{},"环（cycle）",[2615,69735,69737],{"title":69736},"定义 1.3（有向无环图，DAG）",[11,69738,69739,69740,69768,69769,69797],{},"若图 ",[128,69741,69743,69756],{"className":69742,"translate":218},[217],[128,69744,69746],{"className":69745},[222],[224,69747,69748],{"xmlns":226},[228,69749,69750,69754],{},[231,69751,69752],{},[1795,69753,67956],{},[238,69755,67956],{"encoding":240},[128,69757,69759],{"className":69758,"ariaHidden":246},[245],[128,69760,69762,69765],{"className":69761},[250],[128,69763],{"className":69764,"style":283},[254],[128,69766,67956],{"className":69767},[259,1873]," 中不存在任何环，则称 ",[128,69770,69772,69785],{"className":69771,"translate":218},[217],[128,69773,69775],{"className":69774},[222],[224,69776,69777],{"xmlns":226},[228,69778,69779,69783],{},[231,69780,69781],{},[1795,69782,67956],{},[238,69784,67956],{"encoding":240},[128,69786,69788],{"className":69787,"ariaHidden":246},[245],[128,69789,69791,69794],{"className":69790},[250],[128,69792],{"className":69793,"style":283},[254],[128,69795,67956],{"className":69796},[259,1873]," 为有向无环图。",[2615,69799,69801],{"title":69800},"定义 1.4（因果图）",[11,69802,69803,69804,69878,69879,2674,70034,70103,70104,11101,70173,70176,70177,70246,70247,70316],{},"一个因果图是一个 DAG ",[128,69805,69807,69833],{"className":69806,"translate":218},[217],[128,69808,69810],{"className":69809},[222],[224,69811,69812],{"xmlns":226},[228,69813,69814,69830],{},[231,69815,69816,69818,69820,69822,69824,69826,69828],{},[1795,69817,67956],{},[1832,69819,1994],{},[1832,69821,2477],{"stretchy":1837},[1795,69823,67963],{},[1832,69825,1845],{"separator":246},[1795,69827,342],{},[1832,69829,2486],{"stretchy":1837},[238,69831,69832],{"encoding":240},"G=(V,E)",[128,69834,69836,69854],{"className":69835,"ariaHidden":246},[245],[128,69837,69839,69842,69845,69848,69851],{"className":69838},[250],[128,69840],{"className":69841,"style":283},[254],[128,69843,67956],{"className":69844},[259,1873],[128,69846],{"className":69847,"style":1878},[269],[128,69849,1994],{"className":69850},[1882],[128,69852],{"className":69853,"style":1878},[269],[128,69855,69857,69860,69863,69866,69869,69872,69875],{"className":69856},[250],[128,69858],{"className":69859,"style":1892},[254],[128,69861,2477],{"className":69862},[1896],[128,69864,67963],{"className":69865,"style":2508},[259,1873],[128,69867,1845],{"className":69868},[1903],[128,69870],{"className":69871,"style":1907},[269],[128,69873,342],{"className":69874,"style":42029},[259,1873],[128,69876,2486],{"className":69877},[1928],"，附加如下语义解释：对任意 ",[128,69880,69882,69915],{"className":69881,"translate":218},[217],[128,69883,69885],{"className":69884},[222],[224,69886,69887],{"xmlns":226},[228,69888,69889,69913],{},[231,69890,69891,69893,69899,69901,69907,69909,69911],{},[1832,69892,2477],{"stretchy":1837},[2016,69894,69895,69897],{},[1795,69896,67963],{},[1795,69898,2801],{},[1832,69900,1845],{"separator":246},[2016,69902,69903,69905],{},[1795,69904,67963],{},[1795,69906,16495],{},[1832,69908,2486],{"stretchy":1837},[1832,69910,1834],{},[1795,69912,342],{},[238,69914,68304],{"encoding":240},[128,69916,69918,70025],{"className":69917,"ariaHidden":246},[245],[128,69919,69921,69924,69927,69967,69970,69973,70013,70016,70019,70022],{"className":69920},[250],[128,69922],{"className":69923,"style":19704},[254],[128,69925,2477],{"className":69926},[1896],[128,69928,69930,69933],{"className":69929},[259],[128,69931,67963],{"className":69932,"style":2508},[259,1873],[128,69934,69936],{"className":69935},[2087],[128,69937,69939,69959],{"className":69938},[274,321],[128,69940,69942,69956],{"className":69941},[278],[128,69943,69945],{"className":69944,"style":3095},[282],[128,69946,69947,69950],{"style":68109},[128,69948],{"className":69949,"style":291},[290],[128,69951,69953],{"className":69952},[299,300,301,298],[128,69954,2801],{"className":69955},[259,1873,298],[128,69957,347],{"className":69958},[346],[128,69960,69962],{"className":69961},[278],[128,69963,69965],{"className":69964,"style":2241},[282],[128,69966],{},[128,69968,1845],{"className":69969},[1903],[128,69971],{"className":69972,"style":1907},[269],[128,69974,69976,69979],{"className":69975},[259],[128,69977,67963],{"className":69978,"style":2508},[259,1873],[128,69980,69982],{"className":69981},[2087],[128,69983,69985,70005],{"className":69984},[274,321],[128,69986,69988,70002],{"className":69987},[278],[128,69989,69991],{"className":69990,"style":3095},[282],[128,69992,69993,69996],{"style":68109},[128,69994],{"className":69995,"style":291},[290],[128,69997,69999],{"className":69998},[299,300,301,298],[128,70000,16495],{"className":70001,"style":16521},[259,1873,298],[128,70003,347],{"className":70004},[346],[128,70006,70008],{"className":70007},[278],[128,70009,70011],{"className":70010,"style":17424},[282],[128,70012],{},[128,70014,2486],{"className":70015},[1928],[128,70017],{"className":70018,"style":1878},[269],[128,70020,1834],{"className":70021},[1882],[128,70023],{"className":70024,"style":1878},[269],[128,70026,70028,70031],{"className":70027},[250],[128,70029],{"className":70030,"style":283},[254],[128,70032,342],{"className":70033,"style":42029},[259,1873],[128,70035,70037,70054],{"className":70036,"translate":218},[217],[128,70038,70040],{"className":70039},[222],[224,70041,70042],{"xmlns":226},[228,70043,70044,70052],{},[231,70045,70046],{},[2016,70047,70048,70050],{},[1795,70049,67963],{},[1795,70051,2801],{},[238,70053,68580],{"encoding":240},[128,70055,70057],{"className":70056,"ariaHidden":246},[245],[128,70058,70060,70063],{"className":70059},[250],[128,70061],{"className":70062,"style":36058},[254],[128,70064,70066,70069],{"className":70065},[259],[128,70067,67963],{"className":70068,"style":2508},[259,1873],[128,70070,70072],{"className":70071},[2087],[128,70073,70075,70095],{"className":70074},[274,321],[128,70076,70078,70092],{"className":70077},[278],[128,70079,70081],{"className":70080,"style":3095},[282],[128,70082,70083,70086],{"style":68109},[128,70084],{"className":70085,"style":291},[290],[128,70087,70089],{"className":70088},[299,300,301,298],[128,70090,2801],{"className":70091},[259,1873,298],[128,70093,347],{"className":70094},[346],[128,70096,70098],{"className":70097},[278],[128,70099,70101],{"className":70100,"style":2241},[282],[128,70102],{}," 被假设为 ",[128,70105,70107,70124],{"className":70106,"translate":218},[217],[128,70108,70110],{"className":70109},[222],[224,70111,70112],{"xmlns":226},[228,70113,70114,70122],{},[231,70115,70116],{},[2016,70117,70118,70120],{},[1795,70119,67963],{},[1795,70121,16495],{},[238,70123,68651],{"encoding":240},[128,70125,70127],{"className":70126,"ariaHidden":246},[245],[128,70128,70130,70133],{"className":70129},[250],[128,70131],{"className":70132,"style":68518},[254],[128,70134,70136,70139],{"className":70135},[259],[128,70137,67963],{"className":70138,"style":2508},[259,1873],[128,70140,70142],{"className":70141},[2087],[128,70143,70145,70165],{"className":70144},[274,321],[128,70146,70148,70162],{"className":70147},[278],[128,70149,70151],{"className":70150,"style":3095},[282],[128,70152,70153,70156],{"style":68109},[128,70154],{"className":70155,"style":291},[290],[128,70157,70159],{"className":70158},[299,300,301,298],[128,70160,16495],{"className":70161,"style":16521},[259,1873,298],[128,70163,347],{"className":70164},[346],[128,70166,70168],{"className":70167},[278],[128,70169,70171],{"className":70170,"style":17424},[282],[128,70172],{},[35,70174,70175],{},"直接原因（direct cause）","——即存在至少一种对其余变量的取值组合，使得改变 ",[128,70178,70180,70197],{"className":70179,"translate":218},[217],[128,70181,70183],{"className":70182},[222],[224,70184,70185],{"xmlns":226},[228,70186,70187,70195],{},[231,70188,70189],{},[2016,70190,70191,70193],{},[1795,70192,67963],{},[1795,70194,2801],{},[238,70196,68580],{"encoding":240},[128,70198,70200],{"className":70199,"ariaHidden":246},[245],[128,70201,70203,70206],{"className":70202},[250],[128,70204],{"className":70205,"style":36058},[254],[128,70207,70209,70212],{"className":70208},[259],[128,70210,67963],{"className":70211,"style":2508},[259,1873],[128,70213,70215],{"className":70214},[2087],[128,70216,70218,70238],{"className":70217},[274,321],[128,70219,70221,70235],{"className":70220},[278],[128,70222,70224],{"className":70223,"style":3095},[282],[128,70225,70226,70229],{"style":68109},[128,70227],{"className":70228,"style":291},[290],[128,70230,70232],{"className":70231},[299,300,301,298],[128,70233,2801],{"className":70234},[259,1873,298],[128,70236,347],{"className":70237},[346],[128,70239,70241],{"className":70240},[278],[128,70242,70244],{"className":70243,"style":2241},[282],[128,70245],{}," 会改变 ",[128,70248,70250,70267],{"className":70249,"translate":218},[217],[128,70251,70253],{"className":70252},[222],[224,70254,70255],{"xmlns":226},[228,70256,70257,70265],{},[231,70258,70259],{},[2016,70260,70261,70263],{},[1795,70262,67963],{},[1795,70264,16495],{},[238,70266,68651],{"encoding":240},[128,70268,70270],{"className":70269,"ariaHidden":246},[245],[128,70271,70273,70276],{"className":70272},[250],[128,70274],{"className":70275,"style":68518},[254],[128,70277,70279,70282],{"className":70278},[259],[128,70280,67963],{"className":70281,"style":2508},[259,1873],[128,70283,70285],{"className":70284},[2087],[128,70286,70288,70308],{"className":70287},[274,321],[128,70289,70291,70305],{"className":70290},[278],[128,70292,70294],{"className":70293,"style":3095},[282],[128,70295,70296,70299],{"style":68109},[128,70297],{"className":70298,"style":291},[290],[128,70300,70302],{"className":70301},[299,300,301,298],[128,70303,16495],{"className":70304,"style":16521},[259,1873,298],[128,70306,347],{"className":70307},[346],[128,70309,70311],{"className":70310},[278],[128,70312,70314],{"className":70313,"style":17424},[282],[128,70315],{}," 的取值或分布。",[11,70318,70319,70320,70323],{},"需要强调：因果图的每一条边都是一个",[35,70321,70322],{},"不可从数据中验证的结构性假设","（除非借助特定的因果发现算法与额外假设），它来自领域知识、实验设计或时间先后关系等外部信息。这一点是因果图区别于「从数据拟合出的图模型」的本质特征。",[2615,70325,70327,70684],{"title":70326},"例 1.1",[11,70328,70329,70330,70436,70437,70465,70466,70679,70680,70683],{},"设变量集合 ",[128,70331,70333,70369],{"className":70332,"translate":218},[217],[128,70334,70336],{"className":70335},[222],[224,70337,70338],{"xmlns":226},[228,70339,70340,70366],{},[231,70341,70342,70344,70346,70348,70350,70352,70354,70356,70358,70360,70362,70364],{},[1795,70343,67963],{},[1832,70345,1994],{},[1832,70347,1838],{"stretchy":1837},[1795,70349,41957],{},[1832,70351,1845],{"separator":246},[1795,70353,2009],{},[1832,70355,1845],{"separator":246},[1795,70357,41957],{},[1795,70359,11],{},[1832,70361,1845],{"separator":246},[1795,70363,36679],{},[1832,70365,1856],{"stretchy":1837},[238,70367,70368],{"encoding":240},"V = \\{S, R, Sp, W\\}",[128,70370,70372,70390],{"className":70371,"ariaHidden":246},[245],[128,70373,70375,70378,70381,70384,70387],{"className":70374},[250],[128,70376],{"className":70377,"style":283},[254],[128,70379,67963],{"className":70380,"style":2508},[259,1873],[128,70382],{"className":70383,"style":1878},[269],[128,70385,1994],{"className":70386},[1882],[128,70388],{"className":70389,"style":1878},[269],[128,70391,70393,70396,70399,70402,70405,70408,70412,70415,70418,70421,70424,70427,70430,70433],{"className":70392},[250],[128,70394],{"className":70395,"style":1892},[254],[128,70397,1838],{"className":70398},[1896],[128,70400,41957],{"className":70401,"style":42029},[259,1873],[128,70403,1845],{"className":70404},[1903],[128,70406],{"className":70407,"style":1907},[269],[128,70409,2009],{"className":70410,"style":70411},[259,1873],"margin-right:0.0077em;",[128,70413,1845],{"className":70414},[1903],[128,70416],{"className":70417,"style":1907},[269],[128,70419,41957],{"className":70420,"style":42029},[259,1873],[128,70422,11],{"className":70423},[259,1873],[128,70425,1845],{"className":70426},[1903],[128,70428],{"className":70429,"style":1907},[269],[128,70431,36679],{"className":70432,"style":36065},[259,1873],[128,70434,1856],{"className":70435},[1928],"，分别代表季节（Season）、下雨（Rain）、洒水器开启（Sprinkler）、草坪潮湿（WetGrass）。因果图 ",[128,70438,70440,70453],{"className":70439,"translate":218},[217],[128,70441,70443],{"className":70442},[222],[224,70444,70445],{"xmlns":226},[228,70446,70447,70451],{},[231,70448,70449],{},[1795,70450,67956],{},[238,70452,67956],{"encoding":240},[128,70454,70456],{"className":70455,"ariaHidden":246},[245],[128,70457,70459,70462],{"className":70458},[250],[128,70460],{"className":70461,"style":283},[254],[128,70463,67956],{"className":70464},[259,1873]," 定义为：\n",[128,70467,70469,70529],{"className":70468,"translate":218},[217],[128,70470,70472],{"className":70471},[222],[224,70473,70474],{"xmlns":226},[228,70475,70476,70526],{},[231,70477,70478,70480,70482,70484,70486,70488,70490,70492,70494,70496,70498,70500,70502,70504,70506,70508,70510,70512,70514,70516,70518,70520,70522,70524],{},[1795,70479,342],{},[1832,70481,1994],{},[1832,70483,1838],{"stretchy":1837},[1795,70485,41957],{},[1832,70487,22419],{},[1795,70489,2009],{},[1832,70491,1845],{"separator":246},[234,70493,2033],{},[1795,70495,41957],{},[1832,70497,22419],{},[1795,70499,41957],{},[1795,70501,11],{},[1832,70503,1845],{"separator":246},[234,70505,2033],{},[1795,70507,2009],{},[1832,70509,22419],{},[1795,70511,36679],{},[1832,70513,1845],{"separator":246},[234,70515,2033],{},[1795,70517,41957],{},[1795,70519,11],{},[1832,70521,22419],{},[1795,70523,36679],{},[1832,70525,1856],{"stretchy":1837},[238,70527,70528],{"encoding":240},"E = \\{S \\to R,\\ S \\to Sp,\\ R \\to W,\\ Sp \\to W\\}",[128,70530,70532,70550,70571,70601,70634,70667],{"className":70531,"ariaHidden":246},[245],[128,70533,70535,70538,70541,70544,70547],{"className":70534},[250],[128,70536],{"className":70537,"style":283},[254],[128,70539,342],{"className":70540,"style":42029},[259,1873],[128,70542],{"className":70543,"style":1878},[269],[128,70545,1994],{"className":70546},[1882],[128,70548],{"className":70549,"style":1878},[269],[128,70551,70553,70556,70559,70562,70565,70568],{"className":70552},[250],[128,70554],{"className":70555,"style":1892},[254],[128,70557,1838],{"className":70558},[1896],[128,70560,41957],{"className":70561,"style":42029},[259,1873],[128,70563],{"className":70564,"style":1878},[269],[128,70566,22419],{"className":70567},[1882],[128,70569],{"className":70570,"style":1878},[269],[128,70572,70574,70577,70580,70583,70586,70589,70592,70595,70598],{"className":70573},[250],[128,70575],{"className":70576,"style":40674},[254],[128,70578,2009],{"className":70579,"style":70411},[259,1873],[128,70581,1845],{"className":70582},[1903],[128,70584,2033],{"className":70585},[269],[128,70587],{"className":70588,"style":1907},[269],[128,70590,41957],{"className":70591,"style":42029},[259,1873],[128,70593],{"className":70594,"style":1878},[269],[128,70596,22419],{"className":70597},[1882],[128,70599],{"className":70600,"style":1878},[269],[128,70602,70604,70607,70610,70613,70616,70619,70622,70625,70628,70631],{"className":70603},[250],[128,70605],{"className":70606,"style":40674},[254],[128,70608,41957],{"className":70609,"style":42029},[259,1873],[128,70611,11],{"className":70612},[259,1873],[128,70614,1845],{"className":70615},[1903],[128,70617,2033],{"className":70618},[269],[128,70620],{"className":70621,"style":1907},[269],[128,70623,2009],{"className":70624,"style":70411},[259,1873],[128,70626],{"className":70627,"style":1878},[269],[128,70629,22419],{"className":70630},[1882],[128,70632],{"className":70633,"style":1878},[269],[128,70635,70637,70640,70643,70646,70649,70652,70655,70658,70661,70664],{"className":70636},[250],[128,70638],{"className":70639,"style":40674},[254],[128,70641,36679],{"className":70642,"style":36065},[259,1873],[128,70644,1845],{"className":70645},[1903],[128,70647,2033],{"className":70648},[269],[128,70650],{"className":70651,"style":1907},[269],[128,70653,41957],{"className":70654,"style":42029},[259,1873],[128,70656,11],{"className":70657},[259,1873],[128,70659],{"className":70660,"style":1878},[269],[128,70662,22419],{"className":70663},[1882],[128,70665],{"className":70666,"style":1878},[269],[128,70668,70670,70673,70676],{"className":70669},[250],[128,70671],{"className":70672,"style":1892},[254],[128,70674,36679],{"className":70675,"style":36065},[259,1873],[128,70677,1856],{"className":70678},[1928],"\n此图断言：季节直接影响降雨与洒水器的开启概率；降雨与洒水器开启都直接影响草坪是否潮湿；而季节对草坪潮湿的影响完全通过降雨与洒水器这两条中介路径传递，不存在季节直接作用于草坪的边。这后一点——",[35,70681,70682],{},"某条边不存在","——与图中已画出的边同样重要，是因果图的核心信息量所在。整张图的形状如下：",[1441,70685,70686],{},[168,70687],{"height":70688,"width":70689,"style":1447,"data-d2-theme":1448,"alt":123,"src":70690},142,322,"data:image\u002Fsvg+xml;base64,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",[11,70692,70693,70694,70722,70723,70751],{},"其中季节 ",[128,70695,70697,70710],{"className":70696,"translate":218},[217],[128,70698,70700],{"className":70699},[222],[224,70701,70702],{"xmlns":226},[228,70703,70704,70708],{},[231,70705,70706],{},[1795,70707,41957],{},[238,70709,41957],{"encoding":240},[128,70711,70713],{"className":70712,"ariaHidden":246},[245],[128,70714,70716,70719],{"className":70715},[250],[128,70717],{"className":70718,"style":283},[254],[128,70720,41957],{"className":70721,"style":42029},[259,1873]," 是整套机制的源头，草坪潮湿 ",[128,70724,70726,70739],{"className":70725,"translate":218},[217],[128,70727,70729],{"className":70728},[222],[224,70730,70731],{"xmlns":226},[228,70732,70733,70737],{},[231,70734,70735],{},[1795,70736,36679],{},[238,70738,36679],{"encoding":240},[128,70740,70742],{"className":70741,"ariaHidden":246},[245],[128,70743,70745,70748],{"className":70744},[250],[128,70746],{"className":70747,"style":283},[254],[128,70749,36679],{"className":70750,"style":36065},[259,1873]," 是两条中介路径的汇合点。",[2610,70753,70755],{"id":70754},"_12-三种基本连接结构及其统计含义","1.2 三种基本连接结构及其统计含义",[11,70757,70758,70759,2674,70815,70843,70844,70885],{},"任意路径都可以分解为若干长度为 2 的子路径（即三节点结构），因此理解全图的依赖关系，可以归约为理解三种基本三节点结构。设三个节点 ",[128,70760,70762,70785],{"className":70761,"translate":218},[217],[128,70763,70765],{"className":70764},[222],[224,70766,70767],{"xmlns":226},[228,70768,70769,70782],{},[231,70770,70771,70773,70775,70778,70780],{},[1795,70772,364],{},[1832,70774,1845],{"separator":246},[1795,70776,70777],{},"Z",[1832,70779,1845],{"separator":246},[1795,70781,35023],{},[238,70783,70784],{"encoding":240},"X, Z, Y",[128,70786,70788],{"className":70787,"ariaHidden":246},[245],[128,70789,70791,70794,70797,70800,70803,70806,70809,70812],{"className":70790},[250],[128,70792],{"className":70793,"style":40674},[254],[128,70795,364],{"className":70796,"style":30665},[259,1873],[128,70798,1845],{"className":70799},[1903],[128,70801],{"className":70802,"style":1907},[269],[128,70804,70777],{"className":70805,"style":1924},[259,1873],[128,70807,1845],{"className":70808},[1903],[128,70810],{"className":70811,"style":1907},[269],[128,70813,35023],{"className":70814,"style":2508},[259,1873],[128,70816,70818,70831],{"className":70817,"translate":218},[217],[128,70819,70821],{"className":70820},[222],[224,70822,70823],{"xmlns":226},[228,70824,70825,70829],{},[231,70826,70827],{},[1795,70828,70777],{},[238,70830,70777],{"encoding":240},[128,70832,70834],{"className":70833,"ariaHidden":246},[245],[128,70835,70837,70840],{"className":70836},[250],[128,70838],{"className":70839,"style":283},[254],[128,70841,70777],{"className":70842,"style":1924},[259,1873]," 位于 ",[128,70845,70847,70864],{"className":70846,"translate":218},[217],[128,70848,70850],{"className":70849},[222],[224,70851,70852],{"xmlns":226},[228,70853,70854,70862],{},[231,70855,70856,70858,70860],{},[1795,70857,364],{},[1832,70859,1845],{"separator":246},[1795,70861,35023],{},[238,70863,66742],{"encoding":240},[128,70865,70867],{"className":70866,"ariaHidden":246},[245],[128,70868,70870,70873,70876,70879,70882],{"className":70869},[250],[128,70871],{"className":70872,"style":40674},[254],[128,70874,364],{"className":70875,"style":30665},[259,1873],[128,70877,1845],{"className":70878},[1903],[128,70880],{"className":70881,"style":1907},[269],[128,70883,35023],{"className":70884,"style":2508},[259,1873]," 之间的路径上。三种结构图示如下：",[1441,70887,70888],{},[168,70889],{"height":70890,"width":70891,"style":1447,"data-d2-theme":1448,"alt":123,"src":70892},42,300,"data:image\u002Fsvg+xml;base64,PHN2ZyB3aWR0aD0iMzIyIiBoZWlnaHQ9IjQyIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIGRhdGEtZDItdmVyc2lvbj0idjAuOS4wIiB2aWV3Qm94PSIwIDAgMzIyIDQyIj48c3ZnIHdpZHRoPSIzMjIiIGhlaWdodD0iNDIiIGNsYXNzPSJkMi0xNzk3NDE2Mzg1IGQyLXN2ZyIgdmlld0JveD0iLTEgLTEgMzIyIDQyIj48cmVjdCB3aWR0aD0iMzIyIiBoZWlnaHQ9IjQyIiB4PSItMSIgeT0iLTEiIHN0cm9rZS13aWR0aD0iMCIgcng9IjAiIHN0eWxlPSJmaWxsOiNmZmYiLz48c3R5bGU+LmQyLTE3OTc0MTYzODUgLnRleHQtYm9sZHtmb250LWZhbWlseTomcXVvdDtkMi0xNzk3NDE2Mzg1LWZvbnQtYm9sZCZxdW90O31AZm9udC1mYWNle2ZvbnQtZmFtaWx5OmQyLTE3OTc0MTYzODUtZm9udC1ib2xkO3NyYzp1cmwoZGF0YTphcHBsaWNhdGlvbi9mb250LXdvZmY7YmFzZTY0LGQwOUdSZ0FCQUFBQUFBYklBQW9BQUFBQUM0QUFBZ3VGQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFCUFV5OHlBQUFBOUFBQUFHQUFBQUJnWHhIWHJtTnRZWEFBQUFGVUFBQUFQZ0FBQUQ0QW5BQlVaMng1WmdBQUFaUUFBQUZHQUFBQlRQV1R4eUJvWldGa0FBQUMzQUFBQURZQUFBQTJHMzhlMUdob1pXRUFBQU1VQUFBQUpBQUFBQ1FLZndYRWFHMTBlQUFBQXpnQUFBQVVBQUFBRkFza0FMMXNiMk5oQUFBRFRBQUFBQXdBQUFBTUFPZ0JTbTFoZUhBQUFBTllBQUFBSUFBQUFDQUFIUUQzYm1GdFpRQUFBM2dBQUFNdkFBQUlLZ2p3VmtGd2IzTjBBQUFHcUFBQUFDQUFBQUFnLzlFQU1nQURBaW9DdkFBRkFBQUNpZ0pZQUFBQVN3S0tBbGdBQUFGZUFESUJLUUFBQWdzSEF3TUVBd0lDQkdBQUF2Y0FBQUFEQUFBQUFBQUFBQUJCUkVKUEFDQUFJUC8vQXU3L0JnQUFBOWdCRVNBQUFaOEFBQUFBQWZBQ2xBQUFBQ0FBQXdBQUFBRUFBd0FCQUFBQURBQUVBRElBQUFBR0FBUUFBUUFDQURFQVd2Ly9BQUFBTVFCWS8vLy8wLytwQUFFQUFBQUFBQUFBQkFBQkFBSUFBd0FBQUFCNG5GVE12MnNhWVJ6SDhjLzN1YXVIbmo4NDdkMVJFZlY2ZW9lbDIzUGUwWXBEQjZVZHBLNWlxZUFzZE9od1VGMWRpdDFFU2lCT2x5R1pFNUpJTXZwUFpNcm9YeEFDMFNmaHh1enYxeHR2MEFmWW1DMGhJWWtjOHRBQnJsbGFuYnV1clFROENHeFRDbHpTbEQ3TGk1UEliY2lOaHZ5aCtyL3laelNpM2srMlBFeUd2Zkg0WWRScWlmWDFSdnlqM3h1QW9BTHNJMXZnSGNBTEVqY053K1MrSHdSY0t0aXU0N2gySXFFbzZzVlo5RWsxTTdLcXA3emowL1BvUzlyTXlxcWh0dWs3dGFlR1Y2bDR4bFRjaUt0NWtaZkx2RGdIUU0rUEFOUFpBam1BTjErOTlkdnQrbk8ybUpHenBVenJhTHVqYUZYdk9FNm52aEkvZHJGRkRhQTlXeUFaVzdLYWxrNldYcU9xZUtLTnVDZDdRSmV6Z2ZnMmk5c3VRSGRzaW5UY2NzMXUrbjdBTmE1My80YmUxL2VUTUtSZncxVHA3V0VmQW5nQkFBRC8vd01BRTY1Tk5BQUFBQUVBQUFBQ0M0V0ZSRWYzWHc4ODlRQUJBK2dBQUFBQTJGMmdoQUFBQUFEZFppODIvamYreEFodEEvRUFBUUFEQUFJQUFBQUFBQUFBQVFBQUE5ais3d0FBQ0pqK04vNDNDRzBBQVFBQUFBQUFBQUFBQUFBQUFBQUFBQVVDc2dCUUFqY0FDd0lOLy9nQ0hRQWtBaEFBUmdBQUFDd0FXZ0I0QUk0QXBnQUJBQUFBQlFDUUFBd0FZd0FIQUFFQUFBQUFBQUFBQUFBQUFBQUFCQUFEZUp5Y2xNOXVHMlVVeFg5T2JOTUt3UUpGVmJxSnZnV0xJclZqVXlWVjI2d21wRlpHUkhId3VDQWtoRFMySjdibDhjeklNM1lhbm9BMWI4RmJkTVZEOEJ5SU5iclgxNjVkRUFVcmluVm01djQ1MzdubmZzQUJmN0pQcFhvZitLMmVHcTV3Vkw4MnZNZTkrb1hoZlZyMVBjTlZIdFYrTjF4alVGc1lydk41cldQNEk5NVdmekY4aitQcWo0YnZjMWh0R2Y2WXA5VUR3NS9zTy80dy9Dbkh2RjNpQ2p6blo4TVZEc2tONzNIQUQ0YjNlWURWckZSNVFOTndqYzg0TWx6bkNPZ3lwaVJoVE1vUXh3MWpoc3laRVZNUUVqTmp6QTB4QXh3QlBnbWx2azJKRkRtRy8vZzJJcVJrUnFRVlI1UTRFa0lTSWdwR1Z2RW56Y3E0MW83U1o2Wkl1dm1Vaklqb2FjYUVpQlJIeHBDTWxKaUoxaWtweVhsSmd3WUZmZVdiVTFMZ1VUQW13U05qeHBBR2JWcGMwbVhFbUFKSFN5c0pzNUNNRzBwdWliUy9zd2hScGs5TVNtR3M1cVFNbEtkVGZyRm1CMXppYUpOcjdHYmx5NjBLajNGOHE5bkNUV0ljWCtMcHY5dGd0dDEzeFNaaW9YcUtoajBTNVhtckV4eXA0dExYNXh2RkpTOXhPK216emVUREdnMlVuY3g2VEkrNXpsL21KM25DSk1XNVEzeENkVkRvSHVJNDArZUFVQlg1am9BdUY3UjVUVmVmZlRwMDhMbWlTOEFyelczVHdmRVZiYTQ0MTR4QThmSmJTeDF6eGZjNHZpYlFHS2tkbXo2aXVUeTlJVGQzQzNkeGhweGpTcTViSURPVzg0dno0NTBtTER1VWJibWpVRmYwZFk4a1V2WkFWSkU5aXhpYUszSjF4VlMxWEhtak1QMEc1Z2o1V3VwczMzMlhiVmpZN3EyMitJNU1kOWd4TjA0eXVTV2pEMDNWZTg4enQvcm5FVEVnbzZjUmZUS21OQ2k1MDdOZEV6RW53WEd1UHI3UUxTbngxem5TNTA1ZEVqTlZCZ0dwMXBtUjYyOWt2Z21OZTMvTDk4N3VFdG04cWU3b1pIMnFYYnBJNVhSalJxOVZ2ZFczMEZTT055YlFzS2xtbGlNVGxzckxrNHIzSmRyYjRoK3Erd3U5M1RLZWNFWkd3dUJ2TjhCVFBKb2NjOElwSSswZ2xWTVdkanMwOVlabzhvSlRQZjJFV0tQa3ZueWpPa21GRXp5ZWNjSUpMM2oybm80ckpzNjR1RFdYemQ0KzU1elI1dlEvbldJWjMrYU1WK3QzLzk3MVYyWGExTE00bnF5Zm51ODh4VWYvdzYxZjhIanJ2dXpvTFNDYnM3QnE3N2JpaW9pcGNIR0htMXE0aDNoL0FRQUEvLzhEQVBTM1QxRUFBQU1BQUFBQUFBRC96Z0F5QUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBPSl9LmNvbm5lY3Rpb24sLnNoYXBle3N0cm9rZS1saW5lam9pbjpyb3VuZH0uc2hhcGV7c2hhcGUtcmVuZGVyaW5nOmdlb21ldHJpY1ByZWNpc2lvbn0uY29ubmVjdGlvbntzdHJva2UtbGluZWNhcDpyb3VuZH0uZDItMTc5NzQxNjM4NSAuZmlsbC1OMXtmaWxsOiMwYTBmMjV9LmQyLTE3OTc0MTYzODUgLnN0cm9rZS1CMXtzdHJva2U6IzBkMzJiMn08L3N0eWxlPjxnIGNsYXNzPSJXREU9IGNhdXNhbF9ub2RlIj48ZyBjbGFzcz0ic2hhcGUiPjxjaXJjbGUgY3g9IjIwIiBjeT0iMjAiIHI9IjIwIiBmaWxsPSIjYWRkOGU2IiBzdHJva2U9IiMwZDMyYjIiIGNsYXNzPSJzaGFwZSBzdHJva2UtQjEiIHN0eWxlPSJzdHJva2Utd2lkdGg6MiIvPjwvZz48dGV4dCB4PSIyMCIgeT0iMjUuNSIgZmlsbD0iIzBhMGYyNSIgY2xhc3M9InRleHQtYm9sZCBmaWxsLU4xIiBzdHlsZT0idGV4dC1hbmNob3I6bWlkZGxlO2ZvbnQtc2l6ZToxNnB4Ij5YMTwvdGV4dD48L2c+PGcgY2xhc3M9IldqRT0gY2F1c2FsX25vZGUiPjxnIGNsYXNzPSJzaGFwZSI+PGNpcmNsZSBjeD0iMTYwIiBjeT0iMjAiIHI9IjIwIiBmaWxsPSIjYWRkOGU2IiBzdHJva2U9IiMwZDMyYjIiIGNsYXNzPSJzaGFwZSBzdHJva2UtQjEiIHN0eWxlPSJzdHJva2Utd2lkdGg6MiIvPjwvZz48dGV4dCB4PSIxNjAiIHk9IjI1LjUiIGZpbGw9IiMwYTBmMjUiIGNsYXNzPSJ0ZXh0LWJvbGQgZmlsbC1OMSIgc3R5bGU9InRleHQtYW5jaG9yOm1pZGRsZTtmb250LXNpemU6MTZweCI+WjE8L3RleHQ+PC9nPjxnIGNsYXNzPSJXVEU9IGNhdXNhbF9ub2RlIj48ZyBjbGFzcz0ic2hhcGUiPjxjaXJjbGUgY3g9IjMwMCIgY3k9IjIwIiByPSIyMCIgZmlsbD0iI2FkZDhlNiIgc3Ryb2tlPSIjMGQzMmIyIiBjbGFzcz0ic2hhcGUgc3Ryb2tlLUIxIiBzdHlsZT0ic3Ryb2tlLXdpZHRoOjIiLz48L2c+PHRleHQgeD0iMzAwIiB5PSIyNS41IiBmaWxsPSIjMGEwZjI1IiBjbGFzcz0idGV4dC1ib2xkIGZpbGwtTjEiIHN0eWxlPSJ0ZXh0LWFuY2hvcjptaWRkbGU7Zm9udC1zaXplOjE2cHgiPlkxPC90ZXh0PjwvZz48ZyBjbGFzcz0iS0ZneElDMG1aM1E3SUZveEtWc3dYUT09Ij48bWFya2VyIGlkPSJtay1kMi0xNzk3NDE2Mzg1LTM0ODgzNzgxMzQiIG1hcmtlckhlaWdodD0iMTIiIG1hcmtlclVuaXRzPSJ1c2VyU3BhY2VPblVzZSIgbWFya2VyV2lkdGg9IjEwIiBvcmllbnQ9ImF1dG8iIHJlZlg9IjciIHJlZlk9IjYiIHZpZXdCb3g9IjAgMCAxMCAxMiI+PHBhdGggc3Ryb2tlLXdpZHRoPSIyIiBkPSJtMCAwIDEwIDYtMTAgNnoiIGNsYXNzPSJjb25uZWN0aW9uIiBzdHlsZT0iZmlsbDojMGQzMmIyIi8+PC9tYXJrZXI+PHBhdGggZmlsbD0ibm9uZSIgc3Ryb2tlPSIjMGQzMmIyIiBtYXJrZXItZW5kPSJ1cmwoI21rLWQyLTE3OTc0MTYzODUtMzQ4ODM3ODEzNCkiIGQ9Ik00MiAyMGg5NCIgY2xhc3M9ImNvbm5lY3Rpb24gc3Ryb2tlLUIxIiBtYXNrPSJ1cmwoI2QyLTE3OTc0MTYzODUpIiBzdHlsZT0ic3Ryb2tlLXdpZHRoOjIiLz48L2c+PGcgY2xhc3M9IktGb3hJQzBtWjNRN0lGa3hLVnN3WFE9PSI+PHBhdGggZmlsbD0ibm9uZSIgc3Ryb2tlPSIjMGQzMmIyIiBtYXJrZXItZW5kPSJ1cmwoI21rLWQyLTE3OTc0MTYzODUtMzQ4ODM3ODEzNCkiIGQ9Ik0xODIgMjBoOTQiIGNsYXNzPSJjb25uZWN0aW9uIHN0cm9rZS1CMSIgbWFzaz0idXJsKCNkMi0xNzk3NDE2Mzg1KSIgc3R5bGU9InN0cm9rZS13aWR0aDoyIi8+PC9nPjxtYXNrIGlkPSJkMi0xNzk3NDE2Mzg1IiB3aWR0aD0iMzIyIiBoZWlnaHQ9IjQyIiB4PSItMSIgeT0iLTEiIG1hc2tVbml0cz0idXNlclNwYWNlT25Vc2UiPjxwYXRoIGZpbGw9IiNmZmYiIGQ9Ik0tMS0xaDMyMnY0MkgtMXoiLz48L21hc2s+PC9zdmc+PC9zdmc+",[11,70894,70895,1148,70898],{},[35,70896,70897],{},"结构一：链（Chain）",[128,70899,70901,70923],{"className":70900,"translate":218},[217],[128,70902,70904],{"className":70903},[222],[224,70905,70906],{"xmlns":226},[228,70907,70908,70920],{},[231,70909,70910,70912,70914,70916,70918],{},[1795,70911,364],{},[1832,70913,22419],{},[1795,70915,70777],{},[1832,70917,22419],{},[1795,70919,35023],{},[238,70921,70922],{"encoding":240},"X \\to Z \\to Y",[128,70924,70926,70944,70962],{"className":70925,"ariaHidden":246},[245],[128,70927,70929,70932,70935,70938,70941],{"className":70928},[250],[128,70930],{"className":70931,"style":283},[254],[128,70933,364],{"className":70934,"style":30665},[259,1873],[128,70936],{"className":70937,"style":1878},[269],[128,70939,22419],{"className":70940},[1882],[128,70942],{"className":70943,"style":1878},[269],[128,70945,70947,70950,70953,70956,70959],{"className":70946},[250],[128,70948],{"className":70949,"style":283},[254],[128,70951,70777],{"className":70952,"style":1924},[259,1873],[128,70954],{"className":70955,"style":1878},[269],[128,70957,22419],{"className":70958},[1882],[128,70960],{"className":70961,"style":1878},[269],[128,70963,70965,70968],{"className":70964},[250],[128,70966],{"className":70967,"style":283},[254],[128,70969,35023],{"className":70970,"style":2508},[259,1873],[2615,70972,70974],{"title":70973},"命题 1.1",[11,70975,70976,70977,71085,71086,71185,71186,71214],{},"在链式结构下，若结构方程满足一般位置条件（无退化取消），则 ",[128,70978,70980,71007],{"className":70979,"translate":218},[217],[128,70981,70983],{"className":70982},[222],[224,70984,70985],{"xmlns":226},[228,70986,70987,71004],{},[231,70988,70989,70991,70994,70996,70998,71000,71002],{},[1795,70990,364],{},[1832,70992,70993],{},"⊥̸",[234,70995,8524],{},[234,70997,8524],{},[234,70999,8524],{},[1832,71001,12150],{},[1795,71003,35023],{},[238,71005,71006],{"encoding":240},"X \\not\\perp\\!\\!\\!\\perp Y",[128,71008,71010,71064,71076],{"className":71009,"ariaHidden":246},[245],[128,71011,71013,71016,71019,71022,71049,71052,71055,71058,71061],{"className":71012},[250],[128,71014],{"className":71015,"style":16030},[254],[128,71017,364],{"className":71018,"style":30665},[259,1873],[128,71020],{"className":71021,"style":1878},[269],[128,71023,71025],{"className":71024},[1882],[128,71026,71028],{"className":71027},[259,17719],[128,71029,71031],{"className":71030},[17723],[128,71032,71034,71037,71046],{"className":71033},[17727],[128,71035],{"className":71036,"style":16030},[254],[128,71038,71040],{"className":71039},[17734],[128,71041,71043],{"className":71042},[259],[128,71044,17741],{"className":71045},[1882],[128,71047],{"className":71048},[17745],[128,71050],{"className":71051},[269,17749],[128,71053,12150],{"className":71054},[1882],[128,71056],{"className":71057,"style":317},[269],[128,71059],{"className":71060,"style":317},[269],[128,71062],{"className":71063,"style":317},[269],[128,71065,71067,71070,71073],{"className":71066},[250],[128,71068],{"className":71069,"style":12173},[254],[128,71071,12150],{"className":71072},[1882],[128,71074],{"className":71075,"style":1878},[269],[128,71077,71079,71082],{"className":71078},[250],[128,71080],{"className":71081,"style":283},[254],[128,71083,35023],{"className":71084,"style":2508},[259,1873],"（边际不独立），但 ",[128,71087,71089,71119],{"className":71088,"translate":218},[217],[128,71090,71092],{"className":71091},[222],[224,71093,71094],{"xmlns":226},[228,71095,71096,71116],{},[231,71097,71098,71100,71102,71104,71106,71108,71110,71112,71114],{},[1795,71099,364],{},[1832,71101,12150],{},[234,71103,8524],{},[234,71105,8524],{},[234,71107,8524],{},[1832,71109,12150],{},[1795,71111,35023],{},[1832,71113,5443],{},[1795,71115,70777],{},[238,71117,71118],{"encoding":240},"X \\perp\\!\\!\\!\\perp Y \\mid Z",[128,71120,71122,71146,71158,71176],{"className":71121,"ariaHidden":246},[245],[128,71123,71125,71128,71131,71134,71137,71140,71143],{"className":71124},[250],[128,71126],{"className":71127,"style":12173},[254],[128,71129,364],{"className":71130,"style":30665},[259,1873],[128,71132],{"className":71133,"style":1878},[269],[128,71135,12150],{"className":71136},[1882],[128,71138],{"className":71139,"style":317},[269],[128,71141],{"className":71142,"style":317},[269],[128,71144],{"className":71145,"style":317},[269],[128,71147,71149,71152,71155],{"className":71148},[250],[128,71150],{"className":71151,"style":12173},[254],[128,71153,12150],{"className":71154},[1882],[128,71156],{"className":71157,"style":1878},[269],[128,71159,71161,71164,71167,71170,71173],{"className":71160},[250],[128,71162],{"className":71163,"style":1892},[254],[128,71165,35023],{"className":71166,"style":2508},[259,1873],[128,71168],{"className":71169,"style":1878},[269],[128,71171,5443],{"className":71172},[1882],[128,71174],{"className":71175,"style":1878},[269],[128,71177,71179,71182],{"className":71178},[250],[128,71180],{"className":71181,"style":283},[254],[128,71183,70777],{"className":71184,"style":1924},[259,1873],"（给定 ",[128,71187,71189,71202],{"className":71188,"translate":218},[217],[128,71190,71192],{"className":71191},[222],[224,71193,71194],{"xmlns":226},[228,71195,71196,71200],{},[231,71197,71198],{},[1795,71199,70777],{},[238,71201,70777],{"encoding":240},[128,71203,71205],{"className":71204,"ariaHidden":246},[245],[128,71206,71208,71211],{"className":71207},[250],[128,71209],{"className":71210,"style":283},[254],[128,71212,70777],{"className":71213,"style":1924},[259,1873]," 时条件独立）。",[11,71216,71217,44582,71220,71248,71249,71277,71278,71306,71307,71335,71336,71364,71365,71393],{},[49051,71218,71219],{},"直观证明",[128,71221,71223,71236],{"className":71222,"translate":218},[217],[128,71224,71226],{"className":71225},[222],[224,71227,71228],{"xmlns":226},[228,71229,71230,71234],{},[231,71231,71232],{},[1795,71233,364],{},[238,71235,364],{"encoding":240},[128,71237,71239],{"className":71238,"ariaHidden":246},[245],[128,71240,71242,71245],{"className":71241},[250],[128,71243],{"className":71244,"style":283},[254],[128,71246,364],{"className":71247,"style":30665},[259,1873]," 对 ",[128,71250,71252,71265],{"className":71251,"translate":218},[217],[128,71253,71255],{"className":71254},[222],[224,71256,71257],{"xmlns":226},[228,71258,71259,71263],{},[231,71260,71261],{},[1795,71262,35023],{},[238,71264,35023],{"encoding":240},[128,71266,71268],{"className":71267,"ariaHidden":246},[245],[128,71269,71271,71274],{"className":71270},[250],[128,71272],{"className":71273,"style":283},[254],[128,71275,35023],{"className":71276,"style":2508},[259,1873]," 的全部影响必须经过 ",[128,71279,71281,71294],{"className":71280,"translate":218},[217],[128,71282,71284],{"className":71283},[222],[224,71285,71286],{"xmlns":226},[228,71287,71288,71292],{},[231,71289,71290],{},[1795,71291,70777],{},[238,71293,70777],{"encoding":240},[128,71295,71297],{"className":71296,"ariaHidden":246},[245],[128,71298,71300,71303],{"className":71299},[250],[128,71301],{"className":71302,"style":283},[254],[128,71304,70777],{"className":71305,"style":1924},[259,1873]," 传递。一旦 ",[128,71308,71310,71323],{"className":71309,"translate":218},[217],[128,71311,71313],{"className":71312},[222],[224,71314,71315],{"xmlns":226},[228,71316,71317,71321],{},[231,71318,71319],{},[1795,71320,70777],{},[238,71322,70777],{"encoding":240},[128,71324,71326],{"className":71325,"ariaHidden":246},[245],[128,71327,71329,71332],{"className":71328},[250],[128,71330],{"className":71331,"style":283},[254],[128,71333,70777],{"className":71334,"style":1924},[259,1873]," 的取值被固定，",[128,71337,71339,71352],{"className":71338,"translate":218},[217],[128,71340,71342],{"className":71341},[222],[224,71343,71344],{"xmlns":226},[228,71345,71346,71350],{},[231,71347,71348],{},[1795,71349,364],{},[238,71351,364],{"encoding":240},[128,71353,71355],{"className":71354,"ariaHidden":246},[245],[128,71356,71358,71361],{"className":71357},[250],[128,71359],{"className":71360,"style":283},[254],[128,71362,364],{"className":71363,"style":30665},[259,1873]," 就丧失了改变 ",[128,71366,71368,71381],{"className":71367,"translate":218},[217],[128,71369,71371],{"className":71370},[222],[224,71372,71373],{"xmlns":226},[228,71374,71375,71379],{},[231,71376,71377],{},[1795,71378,35023],{},[238,71380,35023],{"encoding":240},[128,71382,71384],{"className":71383,"ariaHidden":246},[245],[128,71385,71387,71390],{"className":71386},[250],[128,71388],{"className":71389,"style":283},[254],[128,71391,35023],{"className":71392,"style":2508},[259,1873]," 分布的任何「渠道」，因此二者在此条件下不再携带彼此的信息。",[2615,71395,71397],{"title":71396},"例 1.2",[11,71398,71399],{},"吸烟（Smoking）→ 焦油沉积（Tar）→ 肺癌（Cancer）。边际地看，吸烟与肺癌高度相关；但若将研究对象限定为「焦油沉积水平完全相同的人群」，则在这一子群体内，是否吸烟与是否患癌不再相关——因为吸烟致癌的全部机制已经被「焦油沉积」这一中介变量所概括。",[11,71401,71402,71405,71406,71409],{},[35,71403,71404],{},"需要强调这里隐含的假设","：上述结论真正成立的前提，是「焦油沉积」与「肺癌」之间不存在未观测的共同原因。这一点值得仔细分辨——它并不是「在数据中按焦油分层」，而是在说「若外部把焦油水平固定住，吸烟对肺癌就不再有效应」。二者只有在特定假设下才一致：一旦焦油与肺癌之间存在未观测的共同原因，条件化焦油反而会在中介与结果之间引入新的对撞偏差（其机制正是下文结构三）。因此例 1.2 应被理解为一个",[35,71407,71408],{},"理想化的机制分解","，而非一条可以在真实流行病学数据上直接执行的结论——这也正是 3.4 节中介分析必须依赖更强假设的原因。",[1441,71411,71412],{},[168,71413],{"height":70688,"width":71414,"style":1447,"data-d2-theme":1448,"alt":123,"src":71415},182,"data:image\u002Fsvg+xml;base64,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",[11,71417,71418,1148,71421],{},[35,71419,71420],{},"结构二：叉（Fork），共同原因结构",[128,71422,71424,71447],{"className":71423,"translate":218},[217],[128,71425,71427],{"className":71426},[222],[224,71428,71429],{"xmlns":226},[228,71430,71431,71444],{},[231,71432,71433,71435,71438,71440,71442],{},[1795,71434,364],{},[1832,71436,71437],{},"←",[1795,71439,70777],{},[1832,71441,22419],{},[1795,71443,35023],{},[238,71445,71446],{"encoding":240},"X \\leftarrow Z \\to Y",[128,71448,71450,71468,71486],{"className":71449,"ariaHidden":246},[245],[128,71451,71453,71456,71459,71462,71465],{"className":71452},[250],[128,71454],{"className":71455,"style":283},[254],[128,71457,364],{"className":71458,"style":30665},[259,1873],[128,71460],{"className":71461,"style":1878},[269],[128,71463,71437],{"className":71464},[1882],[128,71466],{"className":71467,"style":1878},[269],[128,71469,71471,71474,71477,71480,71483],{"className":71470},[250],[128,71472],{"className":71473,"style":283},[254],[128,71475,70777],{"className":71476,"style":1924},[259,1873],[128,71478],{"className":71479,"style":1878},[269],[128,71481,22419],{"className":71482},[1882],[128,71484],{"className":71485,"style":1878},[269],[128,71487,71489,71492],{"className":71488},[250],[128,71490],{"className":71491,"style":283},[254],[128,71493,35023],{"className":71494,"style":2508},[259,1873],[2615,71496,71498],{"title":71497},"命题 1.2",[11,71499,71500,71501,71085,71607,893],{},"在叉式结构下，",[128,71502,71504,71529],{"className":71503,"translate":218},[217],[128,71505,71507],{"className":71506},[222],[224,71508,71509],{"xmlns":226},[228,71510,71511,71527],{},[231,71512,71513,71515,71517,71519,71521,71523,71525],{},[1795,71514,364],{},[1832,71516,70993],{},[234,71518,8524],{},[234,71520,8524],{},[234,71522,8524],{},[1832,71524,12150],{},[1795,71526,35023],{},[238,71528,71006],{"encoding":240},[128,71530,71532,71586,71598],{"className":71531,"ariaHidden":246},[245],[128,71533,71535,71538,71541,71544,71571,71574,71577,71580,71583],{"className":71534},[250],[128,71536],{"className":71537,"style":16030},[254],[128,71539,364],{"className":71540,"style":30665},[259,1873],[128,71542],{"className":71543,"style":1878},[269],[128,71545,71547],{"className":71546},[1882],[128,71548,71550],{"className":71549},[259,17719],[128,71551,71553],{"className":71552},[17723],[128,71554,71556,71559,71568],{"className":71555},[17727],[128,71557],{"className":71558,"style":16030},[254],[128,71560,71562],{"className":71561},[17734],[128,71563,71565],{"className":71564},[259],[128,71566,17741],{"className":71567},[1882],[128,71569],{"className":71570},[17745],[128,71572],{"className":71573},[269,17749],[128,71575,12150],{"className":71576},[1882],[128,71578],{"className":71579,"style":317},[269],[128,71581],{"className":71582,"style":317},[269],[128,71584],{"className":71585,"style":317},[269],[128,71587,71589,71592,71595],{"className":71588},[250],[128,71590],{"className":71591,"style":12173},[254],[128,71593,12150],{"className":71594},[1882],[128,71596],{"className":71597,"style":1878},[269],[128,71599,71601,71604],{"className":71600},[250],[128,71602],{"className":71603,"style":283},[254],[128,71605,35023],{"className":71606,"style":2508},[259,1873],[128,71608,71610,71639],{"className":71609,"translate":218},[217],[128,71611,71613],{"className":71612},[222],[224,71614,71615],{"xmlns":226},[228,71616,71617,71637],{},[231,71618,71619,71621,71623,71625,71627,71629,71631,71633,71635],{},[1795,71620,364],{},[1832,71622,12150],{},[234,71624,8524],{},[234,71626,8524],{},[234,71628,8524],{},[1832,71630,12150],{},[1795,71632,35023],{},[1832,71634,5443],{},[1795,71636,70777],{},[238,71638,71118],{"encoding":240},[128,71640,71642,71666,71678,71696],{"className":71641,"ariaHidden":246},[245],[128,71643,71645,71648,71651,71654,71657,71660,71663],{"className":71644},[250],[128,71646],{"className":71647,"style":12173},[254],[128,71649,364],{"className":71650,"style":30665},[259,1873],[128,71652],{"className":71653,"style":1878},[269],[128,71655,12150],{"className":71656},[1882],[128,71658],{"className":71659,"style":317},[269],[128,71661],{"className":71662,"style":317},[269],[128,71664],{"className":71665,"style":317},[269],[128,71667,71669,71672,71675],{"className":71668},[250],[128,71670],{"className":71671,"style":12173},[254],[128,71673,12150],{"className":71674},[1882],[128,71676],{"className":71677,"style":1878},[269],[128,71679,71681,71684,71687,71690,71693],{"className":71680},[250],[128,71682],{"className":71683,"style":1892},[254],[128,71685,35023],{"className":71686,"style":2508},[259,1873],[128,71688],{"className":71689,"style":1878},[269],[128,71691,5443],{"className":71692},[1882],[128,71694],{"className":71695,"style":1878},[269],[128,71697,71699,71702],{"className":71698},[250],[128,71700],{"className":71701,"style":283},[254],[128,71703,70777],{"className":71704,"style":1924},[259,1873],[2615,71706,71708],{"title":71707},"例 1.3",[11,71709,71710,71711,71748,71749,71786,71787,71824,71825,2674,71828,71856,71857,893],{},"气温（Temperature）→ 冰淇淋销量（IceCream），气温 → 溺水人数（Drowning）。",[128,71712,71714,71730],{"className":71713,"translate":218},[217],[128,71715,71717],{"className":71716},[222],[224,71718,71719],{"xmlns":226},[228,71720,71721,71727],{},[231,71722,71723,71725],{},[1795,71724,364],{},[1832,71726,1994],{},[238,71728,71729],{"encoding":240},"X=",[128,71731,71733],{"className":71732,"ariaHidden":246},[245],[128,71734,71736,71739,71742,71745],{"className":71735},[250],[128,71737],{"className":71738,"style":283},[254],[128,71740,364],{"className":71741,"style":30665},[259,1873],[128,71743],{"className":71744,"style":1878},[269],[128,71746,1994],{"className":71747},[1882]," 冰淇淋销量，",[128,71750,71752,71768],{"className":71751,"translate":218},[217],[128,71753,71755],{"className":71754},[222],[224,71756,71757],{"xmlns":226},[228,71758,71759,71765],{},[231,71760,71761,71763],{},[1795,71762,35023],{},[1832,71764,1994],{},[238,71766,71767],{"encoding":240},"Y=",[128,71769,71771],{"className":71770,"ariaHidden":246},[245],[128,71772,71774,71777,71780,71783],{"className":71773},[250],[128,71775],{"className":71776,"style":283},[254],[128,71778,35023],{"className":71779,"style":2508},[259,1873],[128,71781],{"className":71782,"style":1878},[269],[128,71784,1994],{"className":71785},[1882]," 溺水人数，二者在夏季同步上升，边际相关系数显著为正；但若将数据按气温分层（即条件化 ",[128,71788,71790,71806],{"className":71789,"translate":218},[217],[128,71791,71793],{"className":71792},[222],[224,71794,71795],{"xmlns":226},[228,71796,71797,71803],{},[231,71798,71799,71801],{},[1795,71800,70777],{},[1832,71802,1994],{},[238,71804,71805],{"encoding":240},"Z=",[128,71807,71809],{"className":71808,"ariaHidden":246},[245],[128,71810,71812,71815,71818,71821],{"className":71811},[250],[128,71813],{"className":71814,"style":283},[254],[128,71816,70777],{"className":71817,"style":1924},[259,1873],[128,71819],{"className":71820,"style":1878},[269],[128,71822,1994],{"className":71823},[1882],"气温），在每一层内部冰淇淋销量与溺水人数不再相关。这类由共同原因导致的边际关联，称为",[35,71826,71827],{},"虚假关联（spurious association）",[128,71829,71831,71844],{"className":71830,"translate":218},[217],[128,71832,71834],{"className":71833},[222],[224,71835,71836],{"xmlns":226},[228,71837,71838,71842],{},[231,71839,71840],{},[1795,71841,70777],{},[238,71843,70777],{"encoding":240},[128,71845,71847],{"className":71846,"ariaHidden":246},[245],[128,71848,71850,71853],{"className":71849},[250],[128,71851],{"className":71852,"style":283},[254],[128,71854,70777],{"className":71855,"style":1924},[259,1873]," 称为",[35,71858,71859],{},"混杂因子（confounder）",[1441,71861,71862],{},[168,71863],{"height":70688,"width":71414,"style":1447,"data-d2-theme":1448,"alt":123,"src":71864},"data:image\u002Fsvg+xml;base64,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",[11,71866,71867,1148,71870],{},[35,71868,71869],{},"结构三：对撞（Collider）",[128,71871,71873,71895],{"className":71872,"translate":218},[217],[128,71874,71876],{"className":71875},[222],[224,71877,71878],{"xmlns":226},[228,71879,71880,71892],{},[231,71881,71882,71884,71886,71888,71890],{},[1795,71883,364],{},[1832,71885,22419],{},[1795,71887,70777],{},[1832,71889,71437],{},[1795,71891,35023],{},[238,71893,71894],{"encoding":240},"X \\to Z \\leftarrow Y",[128,71896,71898,71916,71934],{"className":71897,"ariaHidden":246},[245],[128,71899,71901,71904,71907,71910,71913],{"className":71900},[250],[128,71902],{"className":71903,"style":283},[254],[128,71905,364],{"className":71906,"style":30665},[259,1873],[128,71908],{"className":71909,"style":1878},[269],[128,71911,22419],{"className":71912},[1882],[128,71914],{"className":71915,"style":1878},[269],[128,71917,71919,71922,71925,71928,71931],{"className":71918},[250],[128,71920],{"className":71921,"style":283},[254],[128,71923,70777],{"className":71924,"style":1924},[259,1873],[128,71926],{"className":71927,"style":1878},[269],[128,71929,71437],{"className":71930},[1882],[128,71932],{"className":71933,"style":1878},[269],[128,71935,71937,71940],{"className":71936},[250],[128,71938],{"className":71939,"style":283},[254],[128,71941,35023],{"className":71942,"style":2508},[259,1873],[2615,71944,71946],{"title":71945},"命题 1.3（对撞偏差，Collider Bias）",[11,71947,71948,71949,71990,71991,72067,72068,71185,72197,72225,72226,72254],{},"在对撞结构下，若 ",[128,71950,71952,71969],{"className":71951,"translate":218},[217],[128,71953,71955],{"className":71954},[222],[224,71956,71957],{"xmlns":226},[228,71958,71959,71967],{},[231,71960,71961,71963,71965],{},[1795,71962,364],{},[1832,71964,1845],{"separator":246},[1795,71966,35023],{},[238,71968,66742],{"encoding":240},[128,71970,71972],{"className":71971,"ariaHidden":246},[245],[128,71973,71975,71978,71981,71984,71987],{"className":71974},[250],[128,71976],{"className":71977,"style":40674},[254],[128,71979,364],{"className":71980,"style":30665},[259,1873],[128,71982,1845],{"className":71983},[1903],[128,71985],{"className":71986,"style":1907},[269],[128,71988,35023],{"className":71989,"style":2508},[259,1873]," 无其他连接路径，则 ",[128,71992,71994,72019],{"className":71993,"translate":218},[217],[128,71995,71997],{"className":71996},[222],[224,71998,71999],{"xmlns":226},[228,72000,72001,72017],{},[231,72002,72003,72005,72007,72009,72011,72013,72015],{},[1795,72004,364],{},[1832,72006,12150],{},[234,72008,8524],{},[234,72010,8524],{},[234,72012,8524],{},[1832,72014,12150],{},[1795,72016,35023],{},[238,72018,66918],{"encoding":240},[128,72020,72022,72046,72058],{"className":72021,"ariaHidden":246},[245],[128,72023,72025,72028,72031,72034,72037,72040,72043],{"className":72024},[250],[128,72026],{"className":72027,"style":12173},[254],[128,72029,364],{"className":72030,"style":30665},[259,1873],[128,72032],{"className":72033,"style":1878},[269],[128,72035,12150],{"className":72036},[1882],[128,72038],{"className":72039,"style":317},[269],[128,72041],{"className":72042,"style":317},[269],[128,72044],{"className":72045,"style":317},[269],[128,72047,72049,72052,72055],{"className":72048},[250],[128,72050],{"className":72051,"style":12173},[254],[128,72053,12150],{"className":72054},[1882],[128,72056],{"className":72057,"style":1878},[269],[128,72059,72061,72064],{"className":72060},[250],[128,72062],{"className":72063,"style":283},[254],[128,72065,35023],{"className":72066,"style":2508},[259,1873],"（边际独立）；但 ",[128,72069,72071,72101],{"className":72070,"translate":218},[217],[128,72072,72074],{"className":72073},[222],[224,72075,72076],{"xmlns":226},[228,72077,72078,72098],{},[231,72079,72080,72082,72084,72086,72088,72090,72092,72094,72096],{},[1795,72081,364],{},[1832,72083,70993],{},[234,72085,8524],{},[234,72087,8524],{},[234,72089,8524],{},[1832,72091,12150],{},[1795,72093,35023],{},[1832,72095,5443],{},[1795,72097,70777],{},[238,72099,72100],{"encoding":240},"X \\not\\perp\\!\\!\\!\\perp Y \\mid Z",[128,72102,72104,72158,72170,72188],{"className":72103,"ariaHidden":246},[245],[128,72105,72107,72110,72113,72116,72143,72146,72149,72152,72155],{"className":72106},[250],[128,72108],{"className":72109,"style":16030},[254],[128,72111,364],{"className":72112,"style":30665},[259,1873],[128,72114],{"className":72115,"style":1878},[269],[128,72117,72119],{"className":72118},[1882],[128,72120,72122],{"className":72121},[259,17719],[128,72123,72125],{"className":72124},[17723],[128,72126,72128,72131,72140],{"className":72127},[17727],[128,72129],{"className":72130,"style":16030},[254],[128,72132,72134],{"className":72133},[17734],[128,72135,72137],{"className":72136},[259],[128,72138,17741],{"className":72139},[1882],[128,72141],{"className":72142},[17745],[128,72144],{"className":72145},[269,17749],[128,72147,12150],{"className":72148},[1882],[128,72150],{"className":72151,"style":317},[269],[128,72153],{"className":72154,"style":317},[269],[128,72156],{"className":72157,"style":317},[269],[128,72159,72161,72164,72167],{"className":72160},[250],[128,72162],{"className":72163,"style":12173},[254],[128,72165,12150],{"className":72166},[1882],[128,72168],{"className":72169,"style":1878},[269],[128,72171,72173,72176,72179,72182,72185],{"className":72172},[250],[128,72174],{"className":72175,"style":1892},[254],[128,72177,35023],{"className":72178,"style":2508},[259,1873],[128,72180],{"className":72181,"style":1878},[269],[128,72183,5443],{"className":72184},[1882],[128,72186],{"className":72187,"style":1878},[269],[128,72189,72191,72194],{"className":72190},[250],[128,72192],{"className":72193,"style":283},[254],[128,72195,70777],{"className":72196,"style":1924},[259,1873],[128,72198,72200,72213],{"className":72199,"translate":218},[217],[128,72201,72203],{"className":72202},[222],[224,72204,72205],{"xmlns":226},[228,72206,72207,72211],{},[231,72208,72209],{},[1795,72210,70777],{},[238,72212,70777],{"encoding":240},[128,72214,72216],{"className":72215,"ariaHidden":246},[245],[128,72217,72219,72222],{"className":72218},[250],[128,72220],{"className":72221,"style":283},[254],[128,72223,70777],{"className":72224,"style":1924},[259,1873],"，即便只是给定 ",[128,72227,72229,72242],{"className":72228,"translate":218},[217],[128,72230,72232],{"className":72231},[222],[224,72233,72234],{"xmlns":226},[228,72235,72236,72240],{},[231,72237,72238],{},[1795,72239,70777],{},[238,72241,70777],{"encoding":240},[128,72243,72245],{"className":72244,"ariaHidden":246},[245],[128,72246,72248,72251],{"className":72247},[250],[128,72249],{"className":72250,"style":283},[254],[128,72252,70777],{"className":72253,"style":1924},[259,1873]," 的后代变量，也会产生条件不独立）。",[11,72256,72257,72259,72260,72352,72353,72404,72405,72457,72458,72550,72551,72579,72580,72608,72609,72650,72651,72679,72680,72708,72709,72737,72738,72766,72767,72795],{},[49051,72258,71219],{},"：不失一般性设 ",[128,72261,72263,72295],{"className":72262,"translate":218},[217],[128,72264,72266],{"className":72265},[222],[224,72267,72268],{"xmlns":226},[228,72269,72270,72292],{},[231,72271,72272,72274,72276,72278,72280,72282,72284,72286,72288,72290],{},[1795,72273,70777],{},[1832,72275,1994],{},[1795,72277,5436],{},[1832,72279,2477],{"stretchy":1837},[1795,72281,364],{},[1832,72283,1845],{"separator":246},[1795,72285,35023],{},[1832,72287,1845],{"separator":246},[1795,72289,69050],{},[1832,72291,2486],{"stretchy":1837},[238,72293,72294],{"encoding":240},"Z = f(X, Y, U)",[128,72296,72298,72316],{"className":72297,"ariaHidden":246},[245],[128,72299,72301,72304,72307,72310,72313],{"className":72300},[250],[128,72302],{"className":72303,"style":283},[254],[128,72305,70777],{"className":72306,"style":1924},[259,1873],[128,72308],{"className":72309,"style":1878},[269],[128,72311,1994],{"className":72312},[1882],[128,72314],{"className":72315,"style":1878},[269],[128,72317,72319,72322,72325,72328,72331,72334,72337,72340,72343,72346,72349],{"className":72318},[250],[128,72320],{"className":72321,"style":1892},[254],[128,72323,5436],{"className":72324,"style":5514},[259,1873],[128,72326,2477],{"className":72327},[1896],[128,72329,364],{"className":72330,"style":30665},[259,1873],[128,72332,1845],{"className":72333},[1903],[128,72335],{"className":72336,"style":1907},[269],[128,72338,35023],{"className":72339,"style":2508},[259,1873],[128,72341,1845],{"className":72342},[1903],[128,72344],{"className":72345,"style":1907},[269],[128,72347,69050],{"className":72348,"style":26806},[259,1873],[128,72350,2486],{"className":72351},[1928],"。给定 ",[128,72354,72356,72374],{"className":72355,"translate":218},[217],[128,72357,72359],{"className":72358},[222],[224,72360,72361],{"xmlns":226},[228,72362,72363,72371],{},[231,72364,72365,72367,72369],{},[1795,72366,70777],{},[1832,72368,1994],{},[1795,72370,38997],{},[238,72372,72373],{"encoding":240},"Z = z",[128,72375,72377,72395],{"className":72376,"ariaHidden":246},[245],[128,72378,72380,72383,72386,72389,72392],{"className":72379},[250],[128,72381],{"className":72382,"style":283},[254],[128,72384,70777],{"className":72385,"style":1924},[259,1873],[128,72387],{"className":72388,"style":1878},[269],[128,72390,1994],{"className":72391},[1882],[128,72393],{"className":72394,"style":1878},[269],[128,72396,72398,72401],{"className":72397},[250],[128,72399],{"className":72400,"style":7758},[254],[128,72402,38997],{"className":72403,"style":39325},[259,1873]," 这一约束，相当于把 ",[128,72406,72408,72430],{"className":72407,"translate":218},[217],[128,72409,72411],{"className":72410},[222],[224,72412,72413],{"xmlns":226},[228,72414,72415,72427],{},[231,72416,72417,72419,72421,72423,72425],{},[1832,72418,2477],{"stretchy":1837},[1795,72420,364],{},[1832,72422,1845],{"separator":246},[1795,72424,35023],{},[1832,72426,2486],{"stretchy":1837},[238,72428,72429],{"encoding":240},"(X,Y)",[128,72431,72433],{"className":72432,"ariaHidden":246},[245],[128,72434,72436,72439,72442,72445,72448,72451,72454],{"className":72435},[250],[128,72437],{"className":72438,"style":1892},[254],[128,72440,2477],{"className":72441},[1896],[128,72443,364],{"className":72444,"style":30665},[259,1873],[128,72446,1845],{"className":72447},[1903],[128,72449],{"className":72450,"style":1907},[269],[128,72452,35023],{"className":72453,"style":2508},[259,1873],[128,72455,2486],{"className":72456},[1928]," 的取值限制在满足 ",[128,72459,72461,72493],{"className":72460,"translate":218},[217],[128,72462,72464],{"className":72463},[222],[224,72465,72466],{"xmlns":226},[228,72467,72468,72490],{},[231,72469,72470,72472,72474,72476,72478,72480,72482,72484,72486,72488],{},[1795,72471,5436],{},[1832,72473,2477],{"stretchy":1837},[1795,72475,364],{},[1832,72477,1845],{"separator":246},[1795,72479,35023],{},[1832,72481,1845],{"separator":246},[1795,72483,69050],{},[1832,72485,2486],{"stretchy":1837},[1832,72487,1994],{},[1795,72489,38997],{},[238,72491,72492],{"encoding":240},"f(X,Y,U)=z",[128,72494,72496,72541],{"className":72495,"ariaHidden":246},[245],[128,72497,72499,72502,72505,72508,72511,72514,72517,72520,72523,72526,72529,72532,72535,72538],{"className":72498},[250],[128,72500],{"className":72501,"style":1892},[254],[128,72503,5436],{"className":72504,"style":5514},[259,1873],[128,72506,2477],{"className":72507},[1896],[128,72509,364],{"className":72510,"style":30665},[259,1873],[128,72512,1845],{"className":72513},[1903],[128,72515],{"className":72516,"style":1907},[269],[128,72518,35023],{"className":72519,"style":2508},[259,1873],[128,72521,1845],{"className":72522},[1903],[128,72524],{"className":72525,"style":1907},[269],[128,72527,69050],{"className":72528,"style":26806},[259,1873],[128,72530,2486],{"className":72531},[1928],[128,72533],{"className":72534,"style":1878},[269],[128,72536,1994],{"className":72537},[1882],[128,72539],{"className":72540,"style":1878},[269],[128,72542,72544,72547],{"className":72543},[250],[128,72545],{"className":72546,"style":7758},[254],[128,72548,38997],{"className":72549,"style":39325},[259,1873]," 的一个子流形上。在这个子流形上，",[128,72552,72554,72567],{"className":72553,"translate":218},[217],[128,72555,72557],{"className":72556},[222],[224,72558,72559],{"xmlns":226},[228,72560,72561,72565],{},[231,72562,72563],{},[1795,72564,364],{},[238,72566,364],{"encoding":240},[128,72568,72570],{"className":72569,"ariaHidden":246},[245],[128,72571,72573,72576],{"className":72572},[250],[128,72574],{"className":72575,"style":283},[254],[128,72577,364],{"className":72578,"style":30665},[259,1873]," 的取值会反向约束 ",[128,72581,72583,72596],{"className":72582,"translate":218},[217],[128,72584,72586],{"className":72585},[222],[224,72587,72588],{"xmlns":226},[228,72589,72590,72594],{},[231,72591,72592],{},[1795,72593,35023],{},[238,72595,35023],{"encoding":240},[128,72597,72599],{"className":72598,"ariaHidden":246},[245],[128,72600,72602,72605],{"className":72601},[250],[128,72603],{"className":72604,"style":283},[254],[128,72606,35023],{"className":72607,"style":2508},[259,1873]," 的可能取值范围——即便 ",[128,72610,72612,72629],{"className":72611,"translate":218},[217],[128,72613,72615],{"className":72614},[222],[224,72616,72617],{"xmlns":226},[228,72618,72619,72627],{},[231,72620,72621,72623,72625],{},[1795,72622,364],{},[1832,72624,1845],{"separator":246},[1795,72626,35023],{},[238,72628,66742],{"encoding":240},[128,72630,72632],{"className":72631,"ariaHidden":246},[245],[128,72633,72635,72638,72641,72644,72647],{"className":72634},[250],[128,72636],{"className":72637,"style":40674},[254],[128,72639,364],{"className":72640,"style":30665},[259,1873],[128,72642,1845],{"className":72643},[1903],[128,72645],{"className":72646,"style":1907},[269],[128,72648,35023],{"className":72649,"style":2508},[259,1873]," 在无约束时相互独立，在此子流形上二者一般不再独立。这一现象与「解释消除（explaining away）」直觉一致：已知 ",[128,72652,72654,72667],{"className":72653,"translate":218},[217],[128,72655,72657],{"className":72656},[222],[224,72658,72659],{"xmlns":226},[228,72660,72661,72665],{},[231,72662,72663],{},[1795,72664,70777],{},[238,72666,70777],{"encoding":240},[128,72668,72670],{"className":72669,"ariaHidden":246},[245],[128,72671,72673,72676],{"className":72672},[250],[128,72674],{"className":72675,"style":283},[254],[128,72677,70777],{"className":72678,"style":1924},[259,1873]," 发生，若又得知 ",[128,72681,72683,72696],{"className":72682,"translate":218},[217],[128,72684,72686],{"className":72685},[222],[224,72687,72688],{"xmlns":226},[228,72689,72690,72694],{},[231,72691,72692],{},[1795,72693,364],{},[238,72695,364],{"encoding":240},[128,72697,72699],{"className":72698,"ariaHidden":246},[245],[128,72700,72702,72705],{"className":72701},[250],[128,72703],{"className":72704,"style":283},[254],[128,72706,364],{"className":72707,"style":30665},[259,1873]," 是导致 ",[128,72710,72712,72725],{"className":72711,"translate":218},[217],[128,72713,72715],{"className":72714},[222],[224,72716,72717],{"xmlns":226},[228,72718,72719,72723],{},[231,72720,72721],{},[1795,72722,70777],{},[238,72724,70777],{"encoding":240},[128,72726,72728],{"className":72727,"ariaHidden":246},[245],[128,72729,72731,72734],{"className":72730},[250],[128,72732],{"className":72733,"style":283},[254],[128,72735,70777],{"className":72736,"style":1924},[259,1873]," 的原因，则 ",[128,72739,72741,72754],{"className":72740,"translate":218},[217],[128,72742,72744],{"className":72743},[222],[224,72745,72746],{"xmlns":226},[228,72747,72748,72752],{},[231,72749,72750],{},[1795,72751,35023],{},[238,72753,35023],{"encoding":240},[128,72755,72757],{"className":72756,"ariaHidden":246},[245],[128,72758,72760,72763],{"className":72759},[250],[128,72761],{"className":72762,"style":283},[254],[128,72764,35023],{"className":72765,"style":2508},[259,1873]," 作为 ",[128,72768,72770,72783],{"className":72769,"translate":218},[217],[128,72771,72773],{"className":72772},[222],[224,72774,72775],{"xmlns":226},[228,72776,72777,72781],{},[231,72778,72779],{},[1795,72780,70777],{},[238,72782,70777],{"encoding":240},[128,72784,72786],{"className":72785,"ariaHidden":246},[245],[128,72787,72789,72792],{"className":72788},[250],[128,72790],{"className":72791,"style":283},[254],[128,72793,70777],{"className":72794,"style":1924},[259,1873]," 的另一原因的「责任」会被相应降低。",[2615,72797,72799],{"title":72798},"例 1.4",[11,72800,72801,72802,72879,72880,72883,72884,72887],{},"才华（Talent）→ 明星身份（Celebrity）← 美貌（Beauty）。设才华与美貌在总体人群中独立同分布，互不相关。若将研究样本限定为「已成为明星的人」（即条件化 ",[128,72803,72805,72828],{"className":72804,"translate":218},[217],[128,72806,72808],{"className":72807},[222],[224,72809,72810],{"xmlns":226},[228,72811,72812,72825],{},[231,72813,72814,72816,72818,72821,72823],{},[1795,72815,70777],{},[1832,72817,1994],{},[234,72819,72820],{},"Celebrity",[1832,72822,1994],{},[1840,72824,1842],{},[238,72826,72827],{"encoding":240},"Z=\\text{Celebrity}=1",[128,72829,72831,72849,72870],{"className":72830,"ariaHidden":246},[245],[128,72832,72834,72837,72840,72843,72846],{"className":72833},[250],[128,72835],{"className":72836,"style":283},[254],[128,72838,70777],{"className":72839,"style":1924},[259,1873],[128,72841],{"className":72842,"style":1878},[269],[128,72844,1994],{"className":72845},[1882],[128,72847],{"className":72848,"style":1878},[269],[128,72850,72852,72855,72861,72864,72867],{"className":72851},[250],[128,72853],{"className":72854,"style":16030},[254],[128,72856,72858],{"className":72857},[259,260],[128,72859,72820],{"className":72860},[259],[128,72862],{"className":72863,"style":1878},[269],[128,72865,1994],{"className":72866},[1882],[128,72868],{"className":72869,"style":1878},[269],[128,72871,72873,72876],{"className":72872},[250],[128,72874],{"className":72875,"style":2594},[254],[128,72877,1842],{"className":72878},[259],"），则在这一子群体中，才华与美貌会呈现出",[35,72881,72882],{},"负相关","——因为一个才华一般的人若能成为明星，多半是靠美貌弥补，反之亦然。这一负相关是样本选择造成的统计假象，并非二者之间存在任何真实的因果联系。这类偏差在流行病学中亦称",[35,72885,72886],{},"伯克森悖论（Berkson's Paradox）","，也是众多观测性研究中「选择偏差」的图论根源。",[2610,72889,72891],{"id":72890},"_13-d-分离路径阻断的一般判据","1.3 d-分离：路径阻断的一般判据",[11,72893,72894],{},"三种基本结构可统一为一个可在任意复杂 DAG 上递归判定的一般规则。",[2615,72896,72898,73156,73373],{"title":72897},"定义 1.5（路径的阻断）",[11,72899,1781,72900,72951,72952,68630,72980,11072,73008,73036,73037,73065,73066,1148,73094,73097,73098,73126,73127,73155],{},[128,72901,72903,72921],{"className":72902,"translate":218},[217],[128,72904,72906],{"className":72905},[222],[224,72907,72908],{"xmlns":226},[228,72909,72910,72918],{},[231,72911,72912,72914,72916],{},[1795,72913,41957],{},[1832,72915,68208],{},[1795,72917,67963],{},[238,72919,72920],{"encoding":240},"S \\subseteq V",[128,72922,72924,72942],{"className":72923,"ariaHidden":246},[245],[128,72925,72927,72930,72933,72936,72939],{"className":72926},[250],[128,72928],{"className":72929,"style":2652},[254],[128,72931,41957],{"className":72932,"style":42029},[259,1873],[128,72934],{"className":72935,"style":1878},[269],[128,72937,68208],{"className":72938},[1882],[128,72940],{"className":72941,"style":1878},[269],[128,72943,72945,72948],{"className":72944},[250],[128,72946],{"className":72947,"style":283},[254],[128,72949,67963],{"className":72950,"style":2508},[259,1873]," 为一组已条件化的节点集合，",[128,72953,72955,72968],{"className":72954,"translate":218},[217],[128,72956,72958],{"className":72957},[222],[224,72959,72960],{"xmlns":226},[228,72961,72962,72966],{},[231,72963,72964],{},[1795,72965,11],{},[238,72967,11],{"encoding":240},[128,72969,72971],{"className":72970,"ariaHidden":246},[245],[128,72972,72974,72977],{"className":72973},[250],[128,72975],{"className":72976,"style":11158},[254],[128,72978,11],{"className":72979},[259,1873],[128,72981,72983,72996],{"className":72982,"translate":218},[217],[128,72984,72986],{"className":72985},[222],[224,72987,72988],{"xmlns":226},[228,72989,72990,72994],{},[231,72991,72992],{},[1795,72993,364],{},[238,72995,364],{"encoding":240},[128,72997,72999],{"className":72998,"ariaHidden":246},[245],[128,73000,73002,73005],{"className":73001},[250],[128,73003],{"className":73004,"style":283},[254],[128,73006,364],{"className":73007,"style":30665},[259,1873],[128,73009,73011,73024],{"className":73010,"translate":218},[217],[128,73012,73014],{"className":73013},[222],[224,73015,73016],{"xmlns":226},[228,73017,73018,73022],{},[231,73019,73020],{},[1795,73021,35023],{},[238,73023,35023],{"encoding":240},[128,73025,73027],{"className":73026,"ariaHidden":246},[245],[128,73028,73030,73033],{"className":73029},[250],[128,73031],{"className":73032,"style":283},[254],[128,73034,35023],{"className":73035,"style":2508},[259,1873]," 之间的一条路径。称 ",[128,73038,73040,73053],{"className":73039,"translate":218},[217],[128,73041,73043],{"className":73042},[222],[224,73044,73045],{"xmlns":226},[228,73046,73047,73051],{},[231,73048,73049],{},[1795,73050,11],{},[238,73052,11],{"encoding":240},[128,73054,73056],{"className":73055,"ariaHidden":246},[245],[128,73057,73059,73062],{"className":73058},[250],[128,73060],{"className":73061,"style":11158},[254],[128,73063,11],{"className":73064},[259,1873]," 被 ",[128,73067,73069,73082],{"className":73068,"translate":218},[217],[128,73070,73072],{"className":73071},[222],[224,73073,73074],{"xmlns":226},[228,73075,73076,73080],{},[231,73077,73078],{},[1795,73079,41957],{},[238,73081,41957],{"encoding":240},[128,73083,73085],{"className":73084,"ariaHidden":246},[245],[128,73086,73088,73091],{"className":73087},[250],[128,73089],{"className":73090,"style":283},[254],[128,73092,41957],{"className":73093,"style":42029},[259,1873],[35,73095,73096],{},"阻断","，当且仅当 ",[128,73099,73101,73114],{"className":73100,"translate":218},[217],[128,73102,73104],{"className":73103},[222],[224,73105,73106],{"xmlns":226},[228,73107,73108,73112],{},[231,73109,73110],{},[1795,73111,11],{},[238,73113,11],{"encoding":240},[128,73115,73117],{"className":73116,"ariaHidden":246},[245],[128,73118,73120,73123],{"className":73119},[250],[128,73121],{"className":73122,"style":11158},[254],[128,73124,11],{"className":73125},[259,1873]," 上至少存在一个节点 ",[128,73128,73130,73143],{"className":73129,"translate":218},[217],[128,73131,73133],{"className":73132},[222],[224,73134,73135],{"xmlns":226},[228,73136,73137,73141],{},[231,73138,73139],{},[1795,73140,70777],{},[238,73142,70777],{"encoding":240},[128,73144,73146],{"className":73145,"ariaHidden":246},[245],[128,73147,73149,73152],{"className":73148},[250],[128,73150],{"className":73151,"style":283},[254],[128,73153,70777],{"className":73154,"style":1924},[259,1873]," 满足下列条件之一：",[11,73157,73158,73159,12133,73211,23604,73239,73267,73268,73320,73321,73372],{},"(i) ",[128,73160,73162,73180],{"className":73161,"translate":218},[217],[128,73163,73165],{"className":73164},[222],[224,73166,73167],{"xmlns":226},[228,73168,73169,73177],{},[231,73170,73171,73173,73175],{},[1795,73172,70777],{},[1832,73174,1834],{},[1795,73176,41957],{},[238,73178,73179],{"encoding":240},"Z \\in S",[128,73181,73183,73202],{"className":73182,"ariaHidden":246},[245],[128,73184,73186,73190,73193,73196,73199],{"className":73185},[250],[128,73187],{"className":73188,"style":73189},[254],"height:0.7224em;vertical-align:-0.0391em;",[128,73191,70777],{"className":73192,"style":1924},[259,1873],[128,73194],{"className":73195,"style":1878},[269],[128,73197,1834],{"className":73198},[1882],[128,73200],{"className":73201,"style":1878},[269],[128,73203,73205,73208],{"className":73204},[250],[128,73206],{"className":73207,"style":283},[254],[128,73209,41957],{"className":73210,"style":42029},[259,1873],[128,73212,73214,73227],{"className":73213,"translate":218},[217],[128,73215,73217],{"className":73216},[222],[224,73218,73219],{"xmlns":226},[228,73220,73221,73225],{},[231,73222,73223],{},[1795,73224,70777],{},[238,73226,70777],{"encoding":240},[128,73228,73230],{"className":73229,"ariaHidden":246},[245],[128,73231,73233,73236],{"className":73232},[250],[128,73234],{"className":73235,"style":283},[254],[128,73237,70777],{"className":73238,"style":1924},[259,1873],[128,73240,73242,73255],{"className":73241,"translate":218},[217],[128,73243,73245],{"className":73244},[222],[224,73246,73247],{"xmlns":226},[228,73248,73249,73253],{},[231,73250,73251],{},[1795,73252,11],{},[238,73254,11],{"encoding":240},[128,73256,73258],{"className":73257,"ariaHidden":246},[245],[128,73259,73261,73264],{"className":73260},[250],[128,73262],{"className":73263,"style":11158},[254],[128,73265,11],{"className":73266},[259,1873]," 上构成链结构（",[128,73269,73271,73289],{"className":73270,"translate":218},[217],[128,73272,73274],{"className":73273},[222],[224,73275,73276],{"xmlns":226},[228,73277,73278,73286],{},[231,73279,73280,73282,73284],{},[1832,73281,22419],{},[1795,73283,70777],{},[1832,73285,22419],{},[238,73287,73288],{"encoding":240},"\\to Z \\to",[128,73290,73292,73305],{"className":73291,"ariaHidden":246},[245],[128,73293,73295,73299,73302],{"className":73294},[250],[128,73296],{"className":73297,"style":73298},[254],"height:0.3669em;",[128,73300,22419],{"className":73301},[1882],[128,73303],{"className":73304,"style":1878},[269],[128,73306,73308,73311,73314,73317],{"className":73307},[250],[128,73309],{"className":73310,"style":283},[254],[128,73312,70777],{"className":73313,"style":1924},[259,1873],[128,73315],{"className":73316,"style":1878},[269],[128,73318,22419],{"className":73319},[1882],"）或叉结构（",[128,73322,73324,73342],{"className":73323,"translate":218},[217],[128,73325,73327],{"className":73326},[222],[224,73328,73329],{"xmlns":226},[228,73330,73331,73339],{},[231,73332,73333,73335,73337],{},[1832,73334,71437],{},[1795,73336,70777],{},[1832,73338,22419],{},[238,73340,73341],{"encoding":240},"\\leftarrow Z \\to",[128,73343,73345,73357],{"className":73344,"ariaHidden":246},[245],[128,73346,73348,73351,73354],{"className":73347},[250],[128,73349],{"className":73350,"style":73298},[254],[128,73352,71437],{"className":73353},[1882],[128,73355],{"className":73356,"style":1878},[269],[128,73358,73360,73363,73366,73369],{"className":73359},[250],[128,73361],{"className":73362,"style":283},[254],[128,73364,70777],{"className":73365,"style":1924},[259,1873],[128,73367],{"className":73368,"style":1878},[269],[128,73370,22419],{"className":73371},[1882],"）；",[11,73374,73375,73376,23604,73404,73432,73433,73484,73485,73513,73514,893],{},"(ii) ",[128,73377,73379,73392],{"className":73378,"translate":218},[217],[128,73380,73382],{"className":73381},[222],[224,73383,73384],{"xmlns":226},[228,73385,73386,73390],{},[231,73387,73388],{},[1795,73389,70777],{},[238,73391,70777],{"encoding":240},[128,73393,73395],{"className":73394,"ariaHidden":246},[245],[128,73396,73398,73401],{"className":73397},[250],[128,73399],{"className":73400,"style":283},[254],[128,73402,70777],{"className":73403,"style":1924},[259,1873],[128,73405,73407,73420],{"className":73406,"translate":218},[217],[128,73408,73410],{"className":73409},[222],[224,73411,73412],{"xmlns":226},[228,73413,73414,73418],{},[231,73415,73416],{},[1795,73417,11],{},[238,73419,11],{"encoding":240},[128,73421,73423],{"className":73422,"ariaHidden":246},[245],[128,73424,73426,73429],{"className":73425},[250],[128,73427],{"className":73428,"style":11158},[254],[128,73430,11],{"className":73431},[259,1873]," 上构成对撞结构（",[128,73434,73436,73454],{"className":73435,"translate":218},[217],[128,73437,73439],{"className":73438},[222],[224,73440,73441],{"xmlns":226},[228,73442,73443,73451],{},[231,73444,73445,73447,73449],{},[1832,73446,22419],{},[1795,73448,70777],{},[1832,73450,71437],{},[238,73452,73453],{"encoding":240},"\\to Z \\leftarrow",[128,73455,73457,73469],{"className":73456,"ariaHidden":246},[245],[128,73458,73460,73463,73466],{"className":73459},[250],[128,73461],{"className":73462,"style":73298},[254],[128,73464,22419],{"className":73465},[1882],[128,73467],{"className":73468,"style":1878},[269],[128,73470,73472,73475,73478,73481],{"className":73471},[250],[128,73473],{"className":73474,"style":283},[254],[128,73476,70777],{"className":73477,"style":1924},[259,1873],[128,73479],{"className":73480,"style":1878},[269],[128,73482,71437],{"className":73483},[1882],"），且 ",[128,73486,73488,73501],{"className":73487,"translate":218},[217],[128,73489,73491],{"className":73490},[222],[224,73492,73493],{"xmlns":226},[228,73494,73495,73499],{},[231,73496,73497],{},[1795,73498,70777],{},[238,73500,70777],{"encoding":240},[128,73502,73504],{"className":73503,"ariaHidden":246},[245],[128,73505,73507,73510],{"className":73506},[250],[128,73508],{"className":73509,"style":283},[254],[128,73511,70777],{"className":73512,"style":1924},[259,1873]," 本身及其**全部后代（descendants）**都不属于 ",[128,73515,73517,73530],{"className":73516,"translate":218},[217],[128,73518,73520],{"className":73519},[222],[224,73521,73522],{"xmlns":226},[228,73523,73524,73528],{},[231,73525,73526],{},[1795,73527,41957],{},[238,73529,41957],{"encoding":240},[128,73531,73533],{"className":73532,"ariaHidden":246},[245],[128,73534,73536,73539],{"className":73535},[250],[128,73537],{"className":73538,"style":283},[254],[128,73540,41957],{"className":73541,"style":42029},[259,1873],[2615,73543,73545],{"title":73544},"定义 1.6（d-分离）",[11,73546,23408,73547,11072,73575,73603,73604,73607,73608,73636,73637,11072,73665,73693,73694,73722,73723,68424,73726,893],{},[128,73548,73550,73563],{"className":73549,"translate":218},[217],[128,73551,73553],{"className":73552},[222],[224,73554,73555],{"xmlns":226},[228,73556,73557,73561],{},[231,73558,73559],{},[1795,73560,364],{},[238,73562,364],{"encoding":240},[128,73564,73566],{"className":73565,"ariaHidden":246},[245],[128,73567,73569,73572],{"className":73568},[250],[128,73570],{"className":73571,"style":283},[254],[128,73573,364],{"className":73574,"style":30665},[259,1873],[128,73576,73578,73591],{"className":73577,"translate":218},[217],[128,73579,73581],{"className":73580},[222],[224,73582,73583],{"xmlns":226},[228,73584,73585,73589],{},[231,73586,73587],{},[1795,73588,35023],{},[238,73590,35023],{"encoding":240},[128,73592,73594],{"className":73593,"ariaHidden":246},[245],[128,73595,73597,73600],{"className":73596},[250],[128,73598],{"className":73599,"style":283},[254],[128,73601,35023],{"className":73602,"style":2508},[259,1873]," 之间的",[35,73605,73606],{},"每一条","路径都被 ",[128,73609,73611,73624],{"className":73610,"translate":218},[217],[128,73612,73614],{"className":73613},[222],[224,73615,73616],{"xmlns":226},[228,73617,73618,73622],{},[231,73619,73620],{},[1795,73621,41957],{},[238,73623,41957],{"encoding":240},[128,73625,73627],{"className":73626,"ariaHidden":246},[245],[128,73628,73630,73633],{"className":73629},[250],[128,73631],{"className":73632,"style":283},[254],[128,73634,41957],{"className":73635,"style":42029},[259,1873]," 阻断，则称 ",[128,73638,73640,73653],{"className":73639,"translate":218},[217],[128,73641,73643],{"className":73642},[222],[224,73644,73645],{"xmlns":226},[228,73646,73647,73651],{},[231,73648,73649],{},[1795,73650,364],{},[238,73652,364],{"encoding":240},[128,73654,73656],{"className":73655,"ariaHidden":246},[245],[128,73657,73659,73662],{"className":73658},[250],[128,73660],{"className":73661,"style":283},[254],[128,73663,364],{"className":73664,"style":30665},[259,1873],[128,73666,73668,73681],{"className":73667,"translate":218},[217],[128,73669,73671],{"className":73670},[222],[224,73672,73673],{"xmlns":226},[228,73674,73675,73679],{},[231,73676,73677],{},[1795,73678,35023],{},[238,73680,35023],{"encoding":240},[128,73682,73684],{"className":73683,"ariaHidden":246},[245],[128,73685,73687,73690],{"className":73686},[250],[128,73688],{"className":73689,"style":283},[254],[128,73691,35023],{"className":73692,"style":2508},[259,1873]," 在给定 ",[128,73695,73697,73710],{"className":73696,"translate":218},[217],[128,73698,73700],{"className":73699},[222],[224,73701,73702],{"xmlns":226},[228,73703,73704,73708],{},[231,73705,73706],{},[1795,73707,41957],{},[238,73709,41957],{"encoding":240},[128,73711,73713],{"className":73712,"ariaHidden":246},[245],[128,73714,73716,73719],{"className":73715},[250],[128,73717],{"className":73718,"style":283},[254],[128,73720,41957],{"className":73721,"style":42029},[259,1873]," 时 ",[35,73724,73725],{},"d-分离",[128,73727,73729,73771],{"className":73728,"translate":218},[217],[128,73730,73732],{"className":73731},[222],[224,73733,73734],{"xmlns":226},[228,73735,73736,73768],{},[231,73737,73738,73740,73742,73744,73746,73748,73750,73756,73758,73760,73762],{},[1832,73739,2477],{"stretchy":1837},[1795,73741,364],{},[1832,73743,12150],{},[234,73745,8524],{},[234,73747,8524],{},[234,73749,8524],{},[2016,73751,73752,73754],{},[1832,73753,12150],{},[1795,73755,4519],{},[1795,73757,35023],{},[1832,73759,5443],{},[1795,73761,41957],{},[2016,73763,73764,73766],{},[1832,73765,2486],{"stretchy":1837},[1795,73767,67956],{},[238,73769,73770],{"encoding":240},"(X \\perp\\!\\!\\!\\perp_d Y \\mid S)_G",[128,73772,73774,73801,73850,73868],{"className":73773,"ariaHidden":246},[245],[128,73775,73777,73780,73783,73786,73789,73792,73795,73798],{"className":73776},[250],[128,73778],{"className":73779,"style":1892},[254],[128,73781,2477],{"className":73782},[1896],[128,73784,364],{"className":73785,"style":30665},[259,1873],[128,73787],{"className":73788,"style":1878},[269],[128,73790,12150],{"className":73791},[1882],[128,73793],{"className":73794,"style":317},[269],[128,73796],{"className":73797,"style":317},[269],[128,73799],{"className":73800,"style":317},[269],[128,73802,73804,73807,73847],{"className":73803},[250],[128,73805],{"className":73806,"style":36116},[254],[128,73808,73810,73813],{"className":73809},[1882],[128,73811,12150],{"className":73812},[1882],[128,73814,73816],{"className":73815},[2087],[128,73817,73819,73839],{"className":73818},[274,321],[128,73820,73822,73836],{"className":73821},[278],[128,73823,73825],{"className":73824,"style":2218},[282],[128,73826,73827,73830],{"style":2221},[128,73828],{"className":73829,"style":291},[290],[128,73831,73833],{"className":73832},[299,300,301,298],[128,73834,4519],{"className":73835},[259,1873,298],[128,73837,347],{"className":73838},[346],[128,73840,73842],{"className":73841},[278],[128,73843,73845],{"className":73844,"style":2241},[282],[128,73846],{},[128,73848],{"className":73849,"style":1878},[269],[128,73851,73853,73856,73859,73862,73865],{"className":73852},[250],[128,73854],{"className":73855,"style":1892},[254],[128,73857,35023],{"className":73858,"style":2508},[259,1873],[128,73860],{"className":73861,"style":1878},[269],[128,73863,5443],{"className":73864},[1882],[128,73866],{"className":73867,"style":1878},[269],[128,73869,73871,73874,73877],{"className":73870},[250],[128,73872],{"className":73873,"style":1892},[254],[128,73875,41957],{"className":73876,"style":42029},[259,1873],[128,73878,73880,73883],{"className":73879},[1928],[128,73881,2486],{"className":73882},[1928],[128,73884,73886],{"className":73885},[2087],[128,73887,73889,73909],{"className":73888},[274,321],[128,73890,73892,73906],{"className":73891},[278],[128,73893,73895],{"className":73894,"style":3004},[282],[128,73896,73897,73900],{"style":2221},[128,73898],{"className":73899,"style":291},[290],[128,73901,73903],{"className":73902},[299,300,301,298],[128,73904,67956],{"className":73905},[259,1873,298],[128,73907,347],{"className":73908},[346],[128,73910,73912],{"className":73911},[278],[128,73913,73915],{"className":73914,"style":2241},[282],[128,73916],{},[2615,73918,73920],{"title":73919},"定理 1.1（图 - 分布对应定理，Verma & Pearl, 1988）",[11,73921,73922,73923,73951,73952,73980,73981,74309,74310,74313,74314,74342,74343,74371,74372,74375,74376,74404,74405,893],{},"设分布 ",[128,73924,73926,73939],{"className":73925,"translate":218},[217],[128,73927,73929],{"className":73928},[222],[224,73930,73931],{"xmlns":226},[228,73932,73933,73937],{},[231,73934,73935],{},[1795,73936,23001],{},[238,73938,23001],{"encoding":240},[128,73940,73942],{"className":73941,"ariaHidden":246},[245],[128,73943,73945,73948],{"className":73944},[250],[128,73946],{"className":73947,"style":283},[254],[128,73949,23001],{"className":73950,"style":36065},[259,1873]," 由与 DAG ",[128,73953,73955,73968],{"className":73954,"translate":218},[217],[128,73956,73958],{"className":73957},[222],[224,73959,73960],{"xmlns":226},[228,73961,73962,73966],{},[231,73963,73964],{},[1795,73965,67956],{},[238,73967,67956],{"encoding":240},[128,73969,73971],{"className":73970,"ariaHidden":246},[245],[128,73972,73974,73977],{"className":73973},[250],[128,73975],{"className":73976,"style":283},[254],[128,73978,67956],{"className":73979},[259,1873]," 相容的 SCM 生成（见第二部分马尔可夫性假设）。则：\n",[128,73982,73984,74059],{"className":73983,"translate":218},[217],[128,73985,73987],{"className":73986},[222],[224,73988,73989],{"xmlns":226},[228,73990,73991,74056],{},[231,73992,73993,73995,73997,73999,74001,74003,74005,74011,74013,74015,74017,74023,74025,74028,74030,74032,74034,74036,74038,74040,74042,74044,74046,74048,74051,74053],{},[1832,73994,2477],{"stretchy":1837},[1795,73996,364],{},[1832,73998,12150],{},[234,74000,8524],{},[234,74002,8524],{},[234,74004,8524],{},[2016,74006,74007,74009],{},[1832,74008,12150],{},[1795,74010,4519],{},[1795,74012,35023],{},[1832,74014,5443],{},[1795,74016,41957],{},[2016,74018,74019,74021],{},[1832,74020,2486],{"stretchy":1837},[1795,74022,67956],{},[234,74024,26225],{},[1832,74026,74027],{},"⟹",[234,74029,26225],{},[1795,74031,364],{},[1832,74033,12150],{},[234,74035,8524],{},[234,74037,8524],{},[234,74039,8524],{},[1832,74041,12150],{},[1795,74043,35023],{},[1832,74045,5443],{},[1795,74047,41957],{},[234,74049,74050],{}," 在 ",[1795,74052,23001],{},[234,74054,74055],{}," 中成立",[238,74057,74058],{"encoding":240},"(X \\perp\\!\\!\\!\\perp_d Y \\mid S)_G \\implies X \\perp\\!\\!\\!\\perp Y \\mid S \\text{ 在 } P \\text{ 中成立}",[128,74060,74062,74089,74138,74156,74220,74244,74256,74274],{"className":74061,"ariaHidden":246},[245],[128,74063,74065,74068,74071,74074,74077,74080,74083,74086],{"className":74064},[250],[128,74066],{"className":74067,"style":1892},[254],[128,74069,2477],{"className":74070},[1896],[128,74072,364],{"className":74073,"style":30665},[259,1873],[128,74075],{"className":74076,"style":1878},[269],[128,74078,12150],{"className":74079},[1882],[128,74081],{"className":74082,"style":317},[269],[128,74084],{"className":74085,"style":317},[269],[128,74087],{"className":74088,"style":317},[269],[128,74090,74092,74095,74135],{"className":74091},[250],[128,74093],{"className":74094,"style":36116},[254],[128,74096,74098,74101],{"className":74097},[1882],[128,74099,12150],{"className":74100},[1882],[128,74102,74104],{"className":74103},[2087],[128,74105,74107,74127],{"className":74106},[274,321],[128,74108,74110,74124],{"className":74109},[278],[128,74111,74113],{"className":74112,"style":2218},[282],[128,74114,74115,74118],{"style":2221},[128,74116],{"className":74117,"style":291},[290],[128,74119,74121],{"className":74120},[299,300,301,298],[128,74122,4519],{"className":74123},[259,1873,298],[128,74125,347],{"className":74126},[346],[128,74128,74130],{"className":74129},[278],[128,74131,74133],{"className":74132,"style":2241},[282],[128,74134],{},[128,74136],{"className":74137,"style":1878},[269],[128,74139,74141,74144,74147,74150,74153],{"className":74140},[250],[128,74142],{"className":74143,"style":1892},[254],[128,74145,35023],{"className":74146,"style":2508},[259,1873],[128,74148],{"className":74149,"style":1878},[269],[128,74151,5443],{"className":74152},[1882],[128,74154],{"className":74155,"style":1878},[269],[128,74157,74159,74162,74165,74205,74208,74211,74214,74217],{"className":74158},[250],[128,74160],{"className":74161,"style":1892},[254],[128,74163,41957],{"className":74164,"style":42029},[259,1873],[128,74166,74168,74171],{"className":74167},[1928],[128,74169,2486],{"className":74170},[1928],[128,74172,74174],{"className":74173},[2087],[128,74175,74177,74197],{"className":74176},[274,321],[128,74178,74180,74194],{"className":74179},[278],[128,74181,74183],{"className":74182,"style":3004},[282],[128,74184,74185,74188],{"style":2221},[128,74186],{"className":74187,"style":291},[290],[128,74189,74191],{"className":74190},[299,300,301,298],[128,74192,67956],{"className":74193},[259,1873,298],[128,74195,347],{"className":74196},[346],[128,74198,74200],{"className":74199},[278],[128,74201,74203],{"className":74202,"style":2241},[282],[128,74204],{},[128,74206],{"className":74207,"style":1878},[269],[128,74209],{"className":74210,"style":1878},[269],[128,74212,74027],{"className":74213},[1882],[128,74215],{"className":74216,"style":1878},[269],[128,74218],{"className":74219,"style":1878},[269],[128,74221,74223,74226,74229,74232,74235,74238,74241],{"className":74222},[250],[128,74224],{"className":74225,"style":12173},[254],[128,74227,364],{"className":74228,"style":30665},[259,1873],[128,74230],{"className":74231,"style":1878},[269],[128,74233,12150],{"className":74234},[1882],[128,74236],{"className":74237,"style":317},[269],[128,74239],{"className":74240,"style":317},[269],[128,74242],{"className":74243,"style":317},[269],[128,74245,74247,74250,74253],{"className":74246},[250],[128,74248],{"className":74249,"style":12173},[254],[128,74251,12150],{"className":74252},[1882],[128,74254],{"className":74255,"style":1878},[269],[128,74257,74259,74262,74265,74268,74271],{"className":74258},[250],[128,74260],{"className":74261,"style":1892},[254],[128,74263,35023],{"className":74264,"style":2508},[259,1873],[128,74266],{"className":74267,"style":1878},[269],[128,74269,5443],{"className":74270},[1882],[128,74272],{"className":74273,"style":1878},[269],[128,74275,74277,74280,74283,74296,74299],{"className":74276},[250],[128,74278],{"className":74279,"style":283},[254],[128,74281,41957],{"className":74282,"style":42029},[259,1873],[128,74284,74286,74289,74293],{"className":74285},[259,260],[128,74287,2033],{"className":74288},[259],[128,74290,74292],{"className":74291},[259,15272],"在",[128,74294,2033],{"className":74295},[259],[128,74297,23001],{"className":74298,"style":36065},[259,1873],[128,74300,74302,74305],{"className":74301},[259,260],[128,74303,2033],{"className":74304},[259],[128,74306,74308],{"className":74307},[259,15272],"中成立","\n即 d-分离是概率独立性的",[35,74311,74312],{},"充分条件","。若进一步假设 ",[128,74315,74317,74330],{"className":74316,"translate":218},[217],[128,74318,74320],{"className":74319},[222],[224,74321,74322],{"xmlns":226},[228,74323,74324,74328],{},[231,74325,74326],{},[1795,74327,23001],{},[238,74329,23001],{"encoding":240},[128,74331,74333],{"className":74332,"ariaHidden":246},[245],[128,74334,74336,74339],{"className":74335},[250],[128,74337],{"className":74338,"style":283},[254],[128,74340,23001],{"className":74341,"style":36065},[259,1873]," 相对于 ",[128,74344,74346,74359],{"className":74345,"translate":218},[217],[128,74347,74349],{"className":74348},[222],[224,74350,74351],{"xmlns":226},[228,74352,74353,74357],{},[231,74354,74355],{},[1795,74356,67956],{},[238,74358,67956],{"encoding":240},[128,74360,74362],{"className":74361,"ariaHidden":246},[245],[128,74363,74365,74368],{"className":74364},[250],[128,74366],{"className":74367,"style":283},[254],[128,74369,67956],{"className":74370},[259,1873]," 满足",[35,74373,74374],{},"忠实性（faithfulness）","——即 ",[128,74377,74379,74392],{"className":74378,"translate":218},[217],[128,74380,74382],{"className":74381},[222],[224,74383,74384],{"xmlns":226},[228,74385,74386,74390],{},[231,74387,74388],{},[1795,74389,23001],{},[238,74391,23001],{"encoding":240},[128,74393,74395],{"className":74394,"ariaHidden":246},[245],[128,74396,74398,74401],{"className":74397},[250],[128,74399],{"className":74400,"style":283},[254],[128,74402,23001],{"className":74403,"style":36065},[259,1873]," 中不存在的独立性都不是偶然的参数取消所致——则该蕴含关系可加强为",[35,74406,74407],{},"当且仅当",[11,74409,74410,74411,74439,74440,74443,74444,893],{},"这一定理的实践意义极为重大：它把「该不该在回归分析中控制某个变量」这一问题，从一个凭经验拍脑袋的决策，转化为一个在图上可机械判定的组合问题。控制混杂因子（叉结构中的 ",[128,74412,74414,74427],{"className":74413,"translate":218},[217],[128,74415,74417],{"className":74416},[222],[224,74418,74419],{"xmlns":226},[228,74420,74421,74425],{},[231,74422,74423],{},[1795,74424,70777],{},[238,74426,70777],{"encoding":240},[128,74428,74430],{"className":74429,"ariaHidden":246},[245],[128,74431,74433,74436],{"className":74432},[250],[128,74434],{"className":74435,"style":283},[254],[128,74437,70777],{"className":74438,"style":1924},[259,1873],"）能够正确地消除虚假关联；但控制对撞因子（或对撞因子的后代）却会人为",[35,74441,74442],{},"制造","虚假关联——这正是所谓「越多变量控制越严谨」这一朴素直觉在因果推断框架下失效的根本原因，实践中称为",[35,74445,74446],{},"对撞偏差引发的过度控制谬误（overcontrol bias）",[2610,74448,74450],{"id":74449},"_14-因果图的来源因果发现","1.4 因果图的来源：因果发现",[11,74452,74453],{},"定义 1.4 之后我们强调过：图中的每一条边都是不可从数据中验证的结构性假设。但一个自然的问题是——这些假设究竟从哪里来？实践中主要有四个来源：",[33248,74455,74456,74462,74577,74740],{},[33251,74457,74458,74461],{},[35,74459,74460],{},"领域知识与物理机制","：电路中的欧姆定律、燃烧过程中的氧化反应，机制本身规定了方向；",[33251,74463,74464,74467,74468,74496,74497,31074,74525,74576],{},[35,74465,74466],{},"时间先后","：若 ",[128,74469,74471,74484],{"className":74470,"translate":218},[217],[128,74472,74474],{"className":74473},[222],[224,74475,74476],{"xmlns":226},[228,74477,74478,74482],{},[231,74479,74480],{},[1795,74481,364],{},[238,74483,364],{"encoding":240},[128,74485,74487],{"className":74486,"ariaHidden":246},[245],[128,74488,74490,74493],{"className":74489},[250],[128,74491],{"className":74492,"style":283},[254],[128,74494,364],{"className":74495,"style":30665},[259,1873]," 在时间上先于 ",[128,74498,74500,74513],{"className":74499,"translate":218},[217],[128,74501,74503],{"className":74502},[222],[224,74504,74505],{"xmlns":226},[228,74506,74507,74511],{},[231,74508,74509],{},[1795,74510,35023],{},[238,74512,35023],{"encoding":240},[128,74514,74516],{"className":74515,"ariaHidden":246},[245],[128,74517,74519,74522],{"className":74518},[250],[128,74520],{"className":74521,"style":283},[254],[128,74523,35023],{"className":74524,"style":2508},[259,1873],[128,74526,74528,74546],{"className":74527,"translate":218},[217],[128,74529,74531],{"className":74530},[222],[224,74532,74533],{"xmlns":226},[228,74534,74535,74543],{},[231,74536,74537,74539,74541],{},[1795,74538,35023],{},[1832,74540,22419],{},[1795,74542,364],{},[238,74544,74545],{"encoding":240},"Y \\to X",[128,74547,74549,74567],{"className":74548,"ariaHidden":246},[245],[128,74550,74552,74555,74558,74561,74564],{"className":74551},[250],[128,74553],{"className":74554,"style":283},[254],[128,74556,35023],{"className":74557,"style":2508},[259,1873],[128,74559],{"className":74560,"style":1878},[269],[128,74562,22419],{"className":74563},[1882],[128,74565],{"className":74566,"style":1878},[269],[128,74568,74570,74573],{"className":74569},[250],[128,74571],{"className":74572,"style":283},[254],[128,74574,364],{"className":74575,"style":30665},[259,1873]," 被排除；但反向并不自动成立，因为共同原因仍可能同时影响二者；",[33251,74578,74579,44582,74582,74653,74654,74682,74683,71248,74711,74739],{},[35,74580,74581],{},"实验干预",[128,74583,74585,74611],{"className":74584,"translate":218},[217],[128,74586,74588],{"className":74587},[222],[224,74589,74590],{"xmlns":226},[228,74591,74592,74608],{},[231,74593,74594,74596,74598,74600,74602,74604,74606],{},[1795,74595,4519],{},[1795,74597,67350],{},[1832,74599,2477],{"stretchy":1837},[1795,74601,364],{},[1832,74603,1994],{},[1795,74605,2760],{},[1832,74607,2486],{"stretchy":1837},[238,74609,74610],{"encoding":240},"do(X=x)",[128,74612,74614,74641],{"className":74613,"ariaHidden":246},[245],[128,74615,74617,74620,74623,74626,74629,74632,74635,74638],{"className":74616},[250],[128,74618],{"className":74619,"style":1892},[254],[128,74621,4519],{"className":74622},[259,1873],[128,74624,67350],{"className":74625},[259,1873],[128,74627,2477],{"className":74628},[1896],[128,74630,364],{"className":74631,"style":30665},[259,1873],[128,74633],{"className":74634,"style":1878},[269],[128,74636,1994],{"className":74637},[1882],[128,74639],{"className":74640,"style":1878},[269],[128,74642,74644,74647,74650],{"className":74643},[250],[128,74645],{"className":74646,"style":1892},[254],[128,74648,2760],{"className":74649},[259,1873],[128,74651,2486],{"className":74652},[1928]," 会切断 ",[128,74655,74657,74670],{"className":74656,"translate":218},[217],[128,74658,74660],{"className":74659},[222],[224,74661,74662],{"xmlns":226},[228,74663,74664,74668],{},[231,74665,74666],{},[1795,74667,364],{},[238,74669,364],{"encoding":240},[128,74671,74673],{"className":74672,"ariaHidden":246},[245],[128,74674,74676,74679],{"className":74675},[250],[128,74677],{"className":74678,"style":283},[254],[128,74680,364],{"className":74681,"style":30665},[259,1873]," 的全部入边，直接暴露 ",[128,74684,74686,74699],{"className":74685,"translate":218},[217],[128,74687,74689],{"className":74688},[222],[224,74690,74691],{"xmlns":226},[228,74692,74693,74697],{},[231,74694,74695],{},[1795,74696,364],{},[238,74698,364],{"encoding":240},[128,74700,74702],{"className":74701,"ariaHidden":246},[245],[128,74703,74705,74708],{"className":74704},[250],[128,74706],{"className":74707,"style":283},[254],[128,74709,364],{"className":74710,"style":30665},[259,1873],[128,74712,74714,74727],{"className":74713,"translate":218},[217],[128,74715,74717],{"className":74716},[222],[224,74718,74719],{"xmlns":226},[228,74720,74721,74725],{},[231,74722,74723],{},[1795,74724,35023],{},[238,74726,35023],{"encoding":240},[128,74728,74730],{"className":74729,"ariaHidden":246},[245],[128,74731,74733,74736],{"className":74732},[250],[128,74734],{"className":74735,"style":283},[254],[128,74737,35023],{"className":74738,"style":2508},[259,1873]," 的作用方向，是最可靠的来源；",[33251,74741,74742,74745],{},[35,74743,74744],{},"因果发现算法","：在额外假设下，由观测数据自动推断图的结构。",[11,74747,74748,74749,893],{},"第 4 条值得展开，因为它常被误解为「从数据中读出因果」，而其真实含义恰恰相反——",[35,74750,74751],{},"它是关于「在何种假设下，数据中的哪些部分能够约束图」的一组定理",[11,74753,74754,74755,74758,74759,74814],{},"首先要承认一个否定性结论：",[35,74756,74757],{},"仅凭观测分布，我们至多只能确定图所属的一个马尔可夫等价类（Markov equivalence class），而非图本身","。以三个变量 ",[128,74760,74762,74784],{"className":74761,"translate":218},[217],[128,74763,74765],{"className":74764},[222],[224,74766,74767],{"xmlns":226},[228,74768,74769,74781],{},[231,74770,74771,74773,74775,74777,74779],{},[1795,74772,364],{},[1832,74774,1845],{"separator":246},[1795,74776,35023],{},[1832,74778,1845],{"separator":246},[1795,74780,70777],{},[238,74782,74783],{"encoding":240},"X, Y, Z",[128,74785,74787],{"className":74786,"ariaHidden":246},[245],[128,74788,74790,74793,74796,74799,74802,74805,74808,74811],{"className":74789},[250],[128,74791],{"className":74792,"style":40674},[254],[128,74794,364],{"className":74795,"style":30665},[259,1873],[128,74797,1845],{"className":74798},[1903],[128,74800],{"className":74801,"style":1907},[269],[128,74803,35023],{"className":74804,"style":2508},[259,1873],[128,74806,1845],{"className":74807},[1903],[128,74809],{"className":74810,"style":1907},[269],[128,74812,70777],{"className":74813,"style":1924},[259,1873]," 为例，下面三个 DAG",[1441,74816,74817],{},[168,74818],{"height":74819,"width":74820,"style":1447,"data-d2-theme":1448,"alt":123,"src":74821},614,250,"data:image\u002Fsvg+xml;base64,<svg width="432" height="614" xmlns="http://www.w3.org/2000/svg" data-d2-version="v0.9.0" viewBox="0 0 432 614"><svg width="432" height="614" class="d2-2391033666 d2-svg" viewBox="19 15 432 614"><rect width="432" height="614" x="19" y="15" 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",[128,74826,74828,74853],{"className":74827,"translate":218},[217],[128,74829,74831],{"className":74830},[222],[224,74832,74833],{"xmlns":226},[228,74834,74835,74851],{},[231,74836,74837,74839,74841,74843,74845,74847,74849],{},[1795,74838,364],{},[1832,74840,70993],{},[234,74842,8524],{},[234,74844,8524],{},[234,74846,8524],{},[1832,74848,12150],{},[1795,74850,35023],{},[238,74852,71006],{"encoding":240},[128,74854,74856,74910,74922],{"className":74855,"ariaHidden":246},[245],[128,74857,74859,74862,74865,74868,74895,74898,74901,74904,74907],{"className":74858},[250],[128,74860],{"className":74861,"style":16030},[254],[128,74863,364],{"className":74864,"style":30665},[259,1873],[128,74866],{"className":74867,"style":1878},[269],[128,74869,74871],{"className":74870},[1882],[128,74872,74874],{"className":74873},[259,17719],[128,74875,74877],{"className":74876},[17723],[128,74878,74880,74883,74892],{"className":74879},[17727],[128,74881],{"className":74882,"style":16030},[254],[128,74884,74886],{"className":74885},[17734],[128,74887,74889],{"className":74888},[259],[128,74890,17741],{"className":74891},[1882],[128,74893],{"className":74894},[17745],[128,74896],{"className":74897},[269,17749],[128,74899,12150],{"className":74900},[1882],[128,74902],{"className":74903,"style":317},[269],[128,74905],{"className":74906,"style":317},[269],[128,74908],{"className":74909,"style":317},[269],[128,74911,74913,74916,74919],{"className":74912},[250],[128,74914],{"className":74915,"style":12173},[254],[128,74917,12150],{"className":74918},[1882],[128,74920],{"className":74921,"style":1878},[269],[128,74923,74925,74928],{"className":74924},[250],[128,74926],{"className":74927,"style":283},[254],[128,74929,35023],{"className":74930,"style":2508},[259,1873],[128,74932,74934,74960],{"className":74933,"translate":218},[217],[128,74935,74937],{"className":74936},[222],[224,74938,74939],{"xmlns":226},[228,74940,74941,74957],{},[231,74942,74943,74945,74947,74949,74951,74953,74955],{},[1795,74944,35023],{},[1832,74946,70993],{},[234,74948,8524],{},[234,74950,8524],{},[234,74952,8524],{},[1832,74954,12150],{},[1795,74956,70777],{},[238,74958,74959],{"encoding":240},"Y \\not\\perp\\!\\!\\!\\perp Z",[128,74961,74963,75017,75029],{"className":74962,"ariaHidden":246},[245],[128,74964,74966,74969,74972,74975,75002,75005,75008,75011,75014],{"className":74965},[250],[128,74967],{"className":74968,"style":16030},[254],[128,74970,35023],{"className":74971,"style":2508},[259,1873],[128,74973],{"className":74974,"style":1878},[269],[128,74976,74978],{"className":74977},[1882],[128,74979,74981],{"className":74980},[259,17719],[128,74982,74984],{"className":74983},[17723],[128,74985,74987,74990,74999],{"className":74986},[17727],[128,74988],{"className":74989,"style":16030},[254],[128,74991,74993],{"className":74992},[17734],[128,74994,74996],{"className":74995},[259],[128,74997,17741],{"className":74998},[1882],[128,75000],{"className":75001},[17745],[128,75003],{"className":75004},[269,17749],[128,75006,12150],{"className":75007},[1882],[128,75009],{"className":75010,"style":317},[269],[128,75012],{"className":75013,"style":317},[269],[128,75015],{"className":75016,"style":317},[269],[128,75018,75020,75023,75026],{"className":75019},[250],[128,75021],{"className":75022,"style":12173},[254],[128,75024,12150],{"className":75025},[1882],[128,75027],{"className":75028,"style":1878},[269],[128,75030,75032,75035],{"className":75031},[250],[128,75033],{"className":75034,"style":283},[254],[128,75036,70777],{"className":75037,"style":1924},[259,1873],[128,75039,75041,75071],{"className":75040,"translate":218},[217],[128,75042,75044],{"className":75043},[222],[224,75045,75046],{"xmlns":226},[228,75047,75048,75068],{},[231,75049,75050,75052,75054,75056,75058,75060,75062,75064,75066],{},[1795,75051,364],{},[1832,75053,12150],{},[234,75055,8524],{},[234,75057,8524],{},[234,75059,8524],{},[1832,75061,12150],{},[1795,75063,70777],{},[1832,75065,5443],{},[1795,75067,35023],{},[238,75069,75070],{"encoding":240},"X \\perp\\!\\!\\!\\perp Z \\mid Y",[128,75072,75074,75098,75110,75128],{"className":75073,"ariaHidden":246},[245],[128,75075,75077,75080,75083,75086,75089,75092,75095],{"className":75076},[250],[128,75078],{"className":75079,"style":12173},[254],[128,75081,364],{"className":75082,"style":30665},[259,1873],[128,75084],{"className":75085,"style":1878},[269],[128,75087,12150],{"className":75088},[1882],[128,75090],{"className":75091,"style":317},[269],[128,75093],{"className":75094,"style":317},[269],[128,75096],{"className":75097,"style":317},[269],[128,75099,75101,75104,75107],{"className":75100},[250],[128,75102],{"className":75103,"style":12173},[254],[128,75105,12150],{"className":75106},[1882],[128,75108],{"className":75109,"style":1878},[269],[128,75111,75113,75116,75119,75122,75125],{"className":75112},[250],[128,75114],{"className":75115,"style":1892},[254],[128,75117,70777],{"className":75118,"style":1924},[259,1873],[128,75120],{"className":75121,"style":1878},[269],[128,75123,5443],{"className":75124},[1882],[128,75126],{"className":75127,"style":1878},[269],[128,75129,75131,75134],{"className":75130},[250],[128,75132],{"className":75133,"style":283},[254],[128,75135,35023],{"className":75136,"style":2508},[259,1873],"，因此在任何与之相容的分布下，三者产生的数据在统计上无法区分。而第四个图，即对撞结构 ",[128,75139,75141,75163],{"className":75140,"translate":218},[217],[128,75142,75144],{"className":75143},[222],[224,75145,75146],{"xmlns":226},[228,75147,75148,75160],{},[231,75149,75150,75152,75154,75156,75158],{},[1795,75151,364],{},[1832,75153,22419],{},[1795,75155,35023],{},[1832,75157,71437],{},[1795,75159,70777],{},[238,75161,75162],{"encoding":240},"X \\to Y \\leftarrow Z",[128,75164,75166,75184,75202],{"className":75165,"ariaHidden":246},[245],[128,75167,75169,75172,75175,75178,75181],{"className":75168},[250],[128,75170],{"className":75171,"style":283},[254],[128,75173,364],{"className":75174,"style":30665},[259,1873],[128,75176],{"className":75177,"style":1878},[269],[128,75179,22419],{"className":75180},[1882],[128,75182],{"className":75183,"style":1878},[269],[128,75185,75187,75190,75193,75196,75199],{"className":75186},[250],[128,75188],{"className":75189,"style":283},[254],[128,75191,35023],{"className":75192,"style":2508},[259,1873],[128,75194],{"className":75195,"style":1878},[269],[128,75197,71437],{"className":75198},[1882],[128,75200],{"className":75201,"style":1878},[269],[128,75203,75205,75208],{"className":75204},[250],[128,75206],{"className":75207,"style":283},[254],[128,75209,70777],{"className":75210,"style":1924},[259,1873],"，蕴含的是边际独立 ",[128,75213,75215,75240],{"className":75214,"translate":218},[217],[128,75216,75218],{"className":75217},[222],[224,75219,75220],{"xmlns":226},[228,75221,75222,75238],{},[231,75223,75224,75226,75228,75230,75232,75234,75236],{},[1795,75225,364],{},[1832,75227,12150],{},[234,75229,8524],{},[234,75231,8524],{},[234,75233,8524],{},[1832,75235,12150],{},[1795,75237,35023],{},[238,75239,66918],{"encoding":240},[128,75241,75243,75267,75279],{"className":75242,"ariaHidden":246},[245],[128,75244,75246,75249,75252,75255,75258,75261,75264],{"className":75245},[250],[128,75247],{"className":75248,"style":12173},[254],[128,75250,364],{"className":75251,"style":30665},[259,1873],[128,75253],{"className":75254,"style":1878},[269],[128,75256,12150],{"className":75257},[1882],[128,75259],{"className":75260,"style":317},[269],[128,75262],{"className":75263,"style":317},[269],[128,75265],{"className":75266,"style":317},[269],[128,75268,75270,75273,75276],{"className":75269},[250],[128,75271],{"className":75272,"style":12173},[254],[128,75274,12150],{"className":75275},[1882],[128,75277],{"className":75278,"style":1878},[269],[128,75280,75282,75285],{"className":75281},[250],[128,75283],{"className":75284,"style":283},[254],[128,75286,35023],{"className":75287,"style":2508},[259,1873],"，与前三个不同，因此",[35,75290,75291],{},"它可以被数据认出来",[11,75293,75294,75295,75298,75299,893],{},"这一观察可以推广为一个一般结论：",[35,75296,75297],{},"观测分布唯一确定的是图的骨架（skeleton，忽略方向的边集）以及所有的对撞结构（v-结构），其余边的方向原则上不可识别","。这解释了为什么因果发现算法的输出往往不是一个 DAG，而是一张带有部分无向边的",[35,75300,75301],{},"本质图（CPDAG，亦称 pattern）",[11,75303,75304],{},"要在此基础上进一步定向，必须引入超出分布本身的假设，主要有三条路线：",[35195,75306,75307,75366,75372],{},[33251,75308,75309,75312,75313,75365],{},[35,75310,75311],{},"约束式方法（constraint-based）","：以忠实性假设为前提，反复检验条件独立关系并据此定向，代表算法为 PC。若允许存在未观测的混杂变量，则须改用 FCI，其输出（PAG）以双向边 ",[128,75314,75316,75335],{"className":75315,"translate":218},[217],[128,75317,75319],{"className":75318},[222],[224,75320,75321],{"xmlns":226},[228,75322,75323,75332],{},[231,75324,75325,75327,75330],{},[1795,75326,364],{},[1832,75328,75329],{},"↔",[1795,75331,35023],{},[238,75333,75334],{"encoding":240},"X \\leftrightarrow Y",[128,75336,75338,75356],{"className":75337,"ariaHidden":246},[245],[128,75339,75341,75344,75347,75350,75353],{"className":75340},[250],[128,75342],{"className":75343,"style":283},[254],[128,75345,364],{"className":75346,"style":30665},[259,1873],[128,75348],{"className":75349,"style":1878},[269],[128,75351,75329],{"className":75352},[1882],[128,75354],{"className":75355,"style":1878},[269],[128,75357,75359,75362],{"className":75358},[250],[128,75360],{"className":75361,"style":283},[254],[128,75363,35023],{"className":75364,"style":2508},[259,1873]," 显式标示「二者之间存在未观测的共同原因」。",[33251,75367,75368,75371],{},[35,75369,75370],{},"评分式方法（score-based）","：为每个 DAG 或等价类定义评分（如 BIC、贝叶斯后验），在等价类空间上做搜索，代表算法为 GES。它与约束式方法一样，仍然只能恢复到马尔可夫等价类。",[33251,75373,75374,75377,75378,17916,75469,75546,75547,75598,75599,75649,75650,75653,75654,75682],{},[35,75375,75376],{},"函数式方法（functional \u002F additive noise）","：假设结构方程取加性噪声形式 ",[128,75379,75381,75411],{"className":75380,"translate":218},[217],[128,75382,75384],{"className":75383},[222],[224,75385,75386],{"xmlns":226},[228,75387,75388,75408],{},[231,75389,75390,75392,75394,75396,75398,75400,75402,75404,75406],{},[1795,75391,35023],{},[1832,75393,2014],{},[1832,75395,1994],{},[1795,75397,5436],{},[1832,75399,2477],{"stretchy":1837},[1795,75401,364],{},[1832,75403,2486],{"stretchy":1837},[1832,75405,9486],{},[1795,75407,69050],{},[238,75409,75410],{"encoding":240},"Y := f(X) + U",[128,75412,75414,75433,75460],{"className":75413,"ariaHidden":246},[245],[128,75415,75417,75420,75423,75426,75430],{"className":75416},[250],[128,75418],{"className":75419,"style":283},[254],[128,75421,35023],{"className":75422,"style":2508},[259,1873],[128,75424],{"className":75425,"style":1878},[269],[128,75427,75429],{"className":75428},[1882],":=",[128,75431],{"className":75432,"style":1878},[269],[128,75434,75436,75439,75442,75445,75448,75451,75454,75457],{"className":75435},[250],[128,75437],{"className":75438,"style":1892},[254],[128,75440,5436],{"className":75441,"style":5514},[259,1873],[128,75443,2477],{"className":75444},[1896],[128,75446,364],{"className":75447,"style":30665},[259,1873],[128,75449,2486],{"className":75450},[1928],[128,75452],{"className":75453,"style":2508},[269],[128,75455,9486],{"className":75456},[2115],[128,75458],{"className":75459,"style":2508},[269],[128,75461,75463,75466],{"className":75462},[250],[128,75464],{"className":75465,"style":283},[254],[128,75467,69050],{"className":75468,"style":26806},[259,1873],[128,75470,75472,75498],{"className":75471,"translate":218},[217],[128,75473,75475],{"className":75474},[222],[224,75476,75477],{"xmlns":226},[228,75478,75479,75495],{},[231,75480,75481,75483,75485,75487,75489,75491,75493],{},[1795,75482,364],{},[1832,75484,12150],{},[234,75486,8524],{},[234,75488,8524],{},[234,75490,8524],{},[1832,75492,12150],{},[1795,75494,69050],{},[238,75496,75497],{"encoding":240},"X \\perp\\!\\!\\!\\perp U",[128,75499,75501,75525,75537],{"className":75500,"ariaHidden":246},[245],[128,75502,75504,75507,75510,75513,75516,75519,75522],{"className":75503},[250],[128,75505],{"className":75506,"style":12173},[254],[128,75508,364],{"className":75509,"style":30665},[259,1873],[128,75511],{"className":75512,"style":1878},[269],[128,75514,12150],{"className":75515},[1882],[128,75517],{"className":75518,"style":317},[269],[128,75520],{"className":75521,"style":317},[269],[128,75523],{"className":75524,"style":317},[269],[128,75526,75528,75531,75534],{"className":75527},[250],[128,75529],{"className":75530,"style":12173},[254],[128,75532,12150],{"className":75533},[1882],[128,75535],{"className":75536,"style":1878},[269],[128,75538,75540,75543],{"className":75539},[250],[128,75541],{"className":75542,"style":283},[254],[128,75544,69050],{"className":75545,"style":26806},[259,1873],"。此时「",[128,75548,75550,75568],{"className":75549,"translate":218},[217],[128,75551,75553],{"className":75552},[222],[224,75554,75555],{"xmlns":226},[228,75556,75557,75565],{},[231,75558,75559,75561,75563],{},[1795,75560,364],{},[1832,75562,22419],{},[1795,75564,35023],{},[238,75566,75567],{"encoding":240},"X \\to Y",[128,75569,75571,75589],{"className":75570,"ariaHidden":246},[245],[128,75572,75574,75577,75580,75583,75586],{"className":75573},[250],[128,75575],{"className":75576,"style":283},[254],[128,75578,364],{"className":75579,"style":30665},[259,1873],[128,75581],{"className":75582,"style":1878},[269],[128,75584,22419],{"className":75585},[1882],[128,75587],{"className":75588,"style":1878},[269],[128,75590,75592,75595],{"className":75591},[250],[128,75593],{"className":75594,"style":283},[254],[128,75596,35023],{"className":75597,"style":2508},[259,1873],"」与「",[128,75600,75602,75619],{"className":75601,"translate":218},[217],[128,75603,75605],{"className":75604},[222],[224,75606,75607],{"xmlns":226},[228,75608,75609,75617],{},[231,75610,75611,75613,75615],{},[1795,75612,35023],{},[1832,75614,22419],{},[1795,75616,364],{},[238,75618,74545],{"encoding":240},[128,75620,75622,75640],{"className":75621,"ariaHidden":246},[245],[128,75623,75625,75628,75631,75634,75637],{"className":75624},[250],[128,75626],{"className":75627,"style":283},[254],[128,75629,35023],{"className":75630,"style":2508},[259,1873],[128,75632],{"className":75633,"style":1878},[269],[128,75635,22419],{"className":75636},[1882],[128,75638],{"className":75639,"style":1878},[269],[128,75641,75643,75646],{"className":75642},[250],[128,75644],{"className":75645,"style":283},[254],[128,75647,364],{"className":75648,"style":30665},[259,1873],"」两个模型一般",[35,75651,75652],{},"不能互相拟合","——反向模型的噪声项会与输入相关，除非 ",[128,75655,75657,75670],{"className":75656,"translate":218},[217],[128,75658,75660],{"className":75659},[222],[224,75661,75662],{"xmlns":226},[228,75663,75664,75668],{},[231,75665,75666],{},[1795,75667,5436],{},[238,75669,5436],{"encoding":240},[128,75671,75673],{"className":75672,"ariaHidden":246},[245],[128,75674,75676,75679],{"className":75675},[250],[128,75677],{"className":75678,"style":16030},[254],[128,75680,5436],{"className":75681,"style":5514},[259,1873]," 为线性且噪声为高斯。于是方向变得可识别，线性非高斯情形下即得到 LiNGAM 家族算法。代价是引入了比忠实性更强的函数类假设，且判定结果对该假设相当敏感。",[11,75684,75685,75686,75689],{},"综上，因果发现把「边从哪来」这一问题从纯粹的先验判断，部分地转化为「在给定假设下可被数据检验」的问题；但",[35,75687,75688],{},"这些假设本身（忠实性、无隐变量、函数类）仍然无法从数据中获得","。这与本文的核心立场一致：数据只能在结构给定的前提下发挥作用，结构本身必须来自数据之外。",[2615,75691,75693],{"title":75692},"例 1.5",[11,75694,75695,75696,11072,75724,75752,75753,11072,75781,75809,75810,75887,75888,75960],{},"若已知 ",[128,75697,75699,75712],{"className":75698,"translate":218},[217],[128,75700,75702],{"className":75701},[222],[224,75703,75704],{"xmlns":226},[228,75705,75706,75710],{},[231,75707,75708],{},[1795,75709,364],{},[238,75711,364],{"encoding":240},[128,75713,75715],{"className":75714,"ariaHidden":246},[245],[128,75716,75718,75721],{"className":75717},[250],[128,75719],{"className":75720,"style":283},[254],[128,75722,364],{"className":75723,"style":30665},[259,1873],[128,75725,75727,75740],{"className":75726,"translate":218},[217],[128,75728,75730],{"className":75729},[222],[224,75731,75732],{"xmlns":226},[228,75733,75734,75738],{},[231,75735,75736],{},[1795,75737,35023],{},[238,75739,35023],{"encoding":240},[128,75741,75743],{"className":75742,"ariaHidden":246},[245],[128,75744,75746,75749],{"className":75745},[250],[128,75747],{"className":75748,"style":283},[254],[128,75750,35023],{"className":75751,"style":2508},[259,1873]," 依赖、",[128,75754,75756,75769],{"className":75755,"translate":218},[217],[128,75757,75759],{"className":75758},[222],[224,75760,75761],{"xmlns":226},[228,75762,75763,75767],{},[231,75764,75765],{},[1795,75766,35023],{},[238,75768,35023],{"encoding":240},[128,75770,75772],{"className":75771,"ariaHidden":246},[245],[128,75773,75775,75778],{"className":75774},[250],[128,75776],{"className":75777,"style":283},[254],[128,75779,35023],{"className":75780,"style":2508},[259,1873],[128,75782,75784,75797],{"className":75783,"translate":218},[217],[128,75785,75787],{"className":75786},[222],[224,75788,75789],{"xmlns":226},[228,75790,75791,75795],{},[231,75792,75793],{},[1795,75794,70777],{},[238,75796,70777],{"encoding":240},[128,75798,75800],{"className":75799,"ariaHidden":246},[245],[128,75801,75803,75806],{"className":75802},[250],[128,75804],{"className":75805,"style":283},[254],[128,75807,70777],{"className":75808,"style":1924},[259,1873]," 依赖，而又观测到 ",[128,75811,75813,75839],{"className":75812,"translate":218},[217],[128,75814,75816],{"className":75815},[222],[224,75817,75818],{"xmlns":226},[228,75819,75820,75836],{},[231,75821,75822,75824,75826,75828,75830,75832,75834],{},[1795,75823,364],{},[1832,75825,12150],{},[234,75827,8524],{},[234,75829,8524],{},[234,75831,8524],{},[1832,75833,12150],{},[1795,75835,70777],{},[238,75837,75838],{"encoding":240},"X \\perp\\!\\!\\!\\perp Z",[128,75840,75842,75866,75878],{"className":75841,"ariaHidden":246},[245],[128,75843,75845,75848,75851,75854,75857,75860,75863],{"className":75844},[250],[128,75846],{"className":75847,"style":12173},[254],[128,75849,364],{"className":75850,"style":30665},[259,1873],[128,75852],{"className":75853,"style":1878},[269],[128,75855,12150],{"className":75856},[1882],[128,75858],{"className":75859,"style":317},[269],[128,75861],{"className":75862,"style":317},[269],[128,75864],{"className":75865,"style":317},[269],[128,75867,75869,75872,75875],{"className":75868},[250],[128,75870],{"className":75871,"style":12173},[254],[128,75873,12150],{"className":75874},[1882],[128,75876],{"className":75877,"style":1878},[269],[128,75879,75881,75884],{"className":75880},[250],[128,75882],{"className":75883,"style":283},[254],[128,75885,70777],{"className":75886,"style":1924},[259,1873],"，则与之相容的三节点结构只剩下对撞 ",[128,75889,75891,75912],{"className":75890,"translate":218},[217],[128,75892,75894],{"className":75893},[222],[224,75895,75896],{"xmlns":226},[228,75897,75898,75910],{},[231,75899,75900,75902,75904,75906,75908],{},[1795,75901,364],{},[1832,75903,22419],{},[1795,75905,35023],{},[1832,75907,71437],{},[1795,75909,70777],{},[238,75911,75162],{"encoding":240},[128,75913,75915,75933,75951],{"className":75914,"ariaHidden":246},[245],[128,75916,75918,75921,75924,75927,75930],{"className":75917},[250],[128,75919],{"className":75920,"style":283},[254],[128,75922,364],{"className":75923,"style":30665},[259,1873],[128,75925],{"className":75926,"style":1878},[269],[128,75928,22419],{"className":75929},[1882],[128,75931],{"className":75932,"style":1878},[269],[128,75934,75936,75939,75942,75945,75948],{"className":75935},[250],[128,75937],{"className":75938,"style":283},[254],[128,75940,35023],{"className":75941,"style":2508},[259,1873],[128,75943],{"className":75944,"style":1878},[269],[128,75946,71437],{"className":75947},[1882],[128,75949],{"className":75950,"style":1878},[269],[128,75952,75954,75957],{"className":75953},[250],[128,75955],{"className":75956,"style":283},[254],[128,75958,70777],{"className":75959,"style":1924},[259,1873],"。这是因果发现中最基本的一条定向规则，也是「共同原因」与「因果链」两族结构唯一能被数据区分开的地方。",[51,75962,75963],{"id":75963},"结构因果模型",[11,75965,75966,75967,75970],{},"因果图给出的是变量间依赖关系的",[35,75968,75969],{},"定性拓扑","，尚不包含足以计算具体数值的信息。要将因果图提升为可定量计算的生成模型，需要引入结构因果模型。",[2610,75972,75974],{"id":75973},"_21-scm-的形式化定义","2.1 SCM 的形式化定义",[2615,75976,75978,76096],{"title":75977},"定义 2.1（结构因果模型）",[11,75979,75980,75981,76095],{},"一个结构因果模型是一个四元组\n",[128,75982,75984,76025],{"className":75983,"translate":218},[217],[128,75985,75987],{"className":75986},[222],[224,75988,75989],{"xmlns":226},[228,75990,75991,76022],{},[231,75992,75993,75995,75997,75999,76001,76003,76005,76007,76010,76012,76014,76016,76018,76020],{},[1795,75994,30641],{},[1832,75996,1994],{},[1832,75998,64962],{"stretchy":1837},[1795,76000,69050],{},[1832,76002,1845],{"separator":246},[1795,76004,67963],{},[1832,76006,1845],{"separator":246},[1795,76008,76009],{},"F",[1832,76011,1845],{"separator":246},[1795,76013,23001],{},[1832,76015,2477],{"stretchy":1837},[1795,76017,69050],{},[1832,76019,2486],{"stretchy":1837},[1832,76021,64975],{"stretchy":1837},[238,76023,76024],{"encoding":240},"M = \\langle U, V, F, P(U) \\rangle",[128,76026,76028,76046],{"className":76027,"ariaHidden":246},[245],[128,76029,76031,76034,76037,76040,76043],{"className":76030},[250],[128,76032],{"className":76033,"style":283},[254],[128,76035,30641],{"className":76036,"style":26806},[259,1873],[128,76038],{"className":76039,"style":1878},[269],[128,76041,1994],{"className":76042},[1882],[128,76044],{"className":76045,"style":1878},[269],[128,76047,76049,76052,76055,76058,76061,76064,76067,76070,76073,76076,76079,76082,76085,76088,76091],{"className":76048},[250],[128,76050],{"className":76051,"style":1892},[254],[128,76053,64962],{"className":76054},[1896],[128,76056,69050],{"className":76057,"style":26806},[259,1873],[128,76059,1845],{"className":76060},[1903],[128,76062],{"className":76063,"style":1907},[269],[128,76065,67963],{"className":76066,"style":2508},[259,1873],[128,76068,1845],{"className":76069},[1903],[128,76071],{"className":76072,"style":1907},[269],[128,76074,76009],{"className":76075,"style":36065},[259,1873],[128,76077,1845],{"className":76078},[1903],[128,76080],{"className":76081,"style":1907},[269],[128,76083,23001],{"className":76084,"style":36065},[259,1873],[128,76086,2477],{"className":76087},[1896],[128,76089,69050],{"className":76090,"style":26806},[259,1873],[128,76092,76094],{"className":76093},[1928],")⟩","\n其中：",[35195,76097,76098,76276,76453,77497],{},[33251,76099,76100,3637,76272,76275],{},[128,76101,76103,76141],{"className":76102,"translate":218},[217],[128,76104,76106],{"className":76105},[222],[224,76107,76108],{"xmlns":226},[228,76109,76110,76138],{},[231,76111,76112,76114,76116,76118,76124,76126,76128,76130,76136],{},[1795,76113,69050],{},[1832,76115,1994],{},[1832,76117,1838],{"stretchy":1837},[2016,76119,76120,76122],{},[1795,76121,69050],{},[1840,76123,1842],{},[1832,76125,1845],{"separator":246},[1832,76127,1848],{},[1832,76129,1845],{"separator":246},[2016,76131,76132,76134],{},[1795,76133,69050],{},[1795,76135,30849],{},[1832,76137,1856],{"stretchy":1837},[238,76139,76140],{"encoding":240},"U = \\{U_1, \\dots, U_m\\}",[128,76142,76144,76162],{"className":76143,"ariaHidden":246},[245],[128,76145,76147,76150,76153,76156,76159],{"className":76146},[250],[128,76148],{"className":76149,"style":283},[254],[128,76151,69050],{"className":76152,"style":26806},[259,1873],[128,76154],{"className":76155,"style":1878},[269],[128,76157,1994],{"className":76158},[1882],[128,76160],{"className":76161,"style":1878},[269],[128,76163,76165,76168,76171,76211,76214,76217,76220,76223,76226,76229,76269],{"className":76164},[250],[128,76166],{"className":76167,"style":1892},[254],[128,76169,1838],{"className":76170},[1896],[128,76172,76174,76177],{"className":76173},[259],[128,76175,69050],{"className":76176,"style":26806},[259,1873],[128,76178,76180],{"className":76179},[2087],[128,76181,76183,76203],{"className":76182},[274,321],[128,76184,76186,76200],{"className":76185},[278],[128,76187,76189],{"className":76188,"style":2945},[282],[128,76190,76191,76194],{"style":64697},[128,76192],{"className":76193,"style":291},[290],[128,76195,76197],{"className":76196},[299,300,301,298],[128,76198,1842],{"className":76199},[259,298],[128,76201,347],{"className":76202},[346],[128,76204,76206],{"className":76205},[278],[128,76207,76209],{"className":76208,"style":2241},[282],[128,76210],{},[128,76212,1845],{"className":76213},[1903],[128,76215],{"className":76216,"style":1907},[269],[128,76218,1848],{"className":76219},[1911],[128,76221],{"className":76222,"style":1907},[269],[128,76224,1845],{"className":76225},[1903],[128,76227],{"className":76228,"style":1907},[269],[128,76230,76232,76235],{"className":76231},[259],[128,76233,69050],{"className":76234,"style":26806},[259,1873],[128,76236,76238],{"className":76237},[2087],[128,76239,76241,76261],{"className":76240},[274,321],[128,76242,76244,76258],{"className":76243},[278],[128,76245,76247],{"className":76246,"style":28738},[282],[128,76248,76249,76252],{"style":64697},[128,76250],{"className":76251,"style":291},[290],[128,76253,76255],{"className":76254},[299,300,301,298],[128,76256,30849],{"className":76257},[259,1873,298],[128,76259,347],{"className":76260},[346],[128,76262,76264],{"className":76263},[278],[128,76265,76267],{"className":76266,"style":2241},[282],[128,76268],{},[128,76270,1856],{"className":76271},[1928],[35,76273,76274],{},"外生变量（exogenous variables）"," 集合，代表模型边界之外、不由模型内部机制解释的随机扰动源；",[33251,76277,76278,3637,76449,76452],{},[128,76279,76281,76318],{"className":76280,"translate":218},[217],[128,76282,76284],{"className":76283},[222],[224,76285,76286],{"xmlns":226},[228,76287,76288,76316],{},[231,76289,76290,76292,76294,76296,76302,76304,76306,76308,76314],{},[1795,76291,67963],{},[1832,76293,1994],{},[1832,76295,1838],{"stretchy":1837},[2016,76297,76298,76300],{},[1795,76299,67963],{},[1840,76301,1842],{},[1832,76303,1845],{"separator":246},[1832,76305,1848],{},[1832,76307,1845],{"separator":246},[2016,76309,76310,76312],{},[1795,76311,67963],{},[1795,76313,16280],{},[1832,76315,1856],{"stretchy":1837},[238,76317,68058],{"encoding":240},[128,76319,76321,76339],{"className":76320,"ariaHidden":246},[245],[128,76322,76324,76327,76330,76333,76336],{"className":76323},[250],[128,76325],{"className":76326,"style":283},[254],[128,76328,67963],{"className":76329,"style":2508},[259,1873],[128,76331],{"className":76332,"style":1878},[269],[128,76334,1994],{"className":76335},[1882],[128,76337],{"className":76338,"style":1878},[269],[128,76340,76342,76345,76348,76388,76391,76394,76397,76400,76403,76406,76446],{"className":76341},[250],[128,76343],{"className":76344,"style":1892},[254],[128,76346,1838],{"className":76347},[1896],[128,76349,76351,76354],{"className":76350},[259],[128,76352,67963],{"className":76353,"style":2508},[259,1873],[128,76355,76357],{"className":76356},[2087],[128,76358,76360,76380],{"className":76359},[274,321],[128,76361,76363,76377],{"className":76362},[278],[128,76364,76366],{"className":76365,"style":2945},[282],[128,76367,76368,76371],{"style":68109},[128,76369],{"className":76370,"style":291},[290],[128,76372,76374],{"className":76373},[299,300,301,298],[128,76375,1842],{"className":76376},[259,298],[128,76378,347],{"className":76379},[346],[128,76381,76383],{"className":76382},[278],[128,76384,76386],{"className":76385,"style":2241},[282],[128,76387],{},[128,76389,1845],{"className":76390},[1903],[128,76392],{"className":76393,"style":1907},[269],[128,76395,1848],{"className":76396},[1911],[128,76398],{"className":76399,"style":1907},[269],[128,76401,1845],{"className":76402},[1903],[128,76404],{"className":76405,"style":1907},[269],[128,76407,76409,76412],{"className":76408},[259],[128,76410,67963],{"className":76411,"style":2508},[259,1873],[128,76413,76415],{"className":76414},[2087],[128,76416,76418,76438],{"className":76417},[274,321],[128,76419,76421,76435],{"className":76420},[278],[128,76422,76424],{"className":76423,"style":28738},[282],[128,76425,76426,76429],{"style":68109},[128,76427],{"className":76428,"style":291},[290],[128,76430,76432],{"className":76431},[299,300,301,298],[128,76433,16280],{"className":76434},[259,1873,298],[128,76436,347],{"className":76437},[346],[128,76439,76441],{"className":76440},[278],[128,76442,76444],{"className":76443,"style":2241},[282],[128,76445],{},[128,76447,1856],{"className":76448},[1928],[35,76450,76451],{},"内生变量（endogenous variables）"," 集合，是模型所关心、由模型内部机制决定的变量；",[33251,76454,76455,3637,76627,76630,76631,76701,76702,24849,77117,21562,77194,77263,77264,77333,77334,77426,77427,77496],{},[128,76456,76458,76496],{"className":76457,"translate":218},[217],[128,76459,76461],{"className":76460},[222],[224,76462,76463],{"xmlns":226},[228,76464,76465,76493],{},[231,76466,76467,76469,76471,76473,76479,76481,76483,76485,76491],{},[1795,76468,76009],{},[1832,76470,1994],{},[1832,76472,1838],{"stretchy":1837},[2016,76474,76475,76477],{},[1795,76476,5436],{},[1840,76478,1842],{},[1832,76480,1845],{"separator":246},[1832,76482,1848],{},[1832,76484,1845],{"separator":246},[2016,76486,76487,76489],{},[1795,76488,5436],{},[1795,76490,16280],{},[1832,76492,1856],{"stretchy":1837},[238,76494,76495],{"encoding":240},"F = \\{f_1, \\dots, f_n\\}",[128,76497,76499,76517],{"className":76498,"ariaHidden":246},[245],[128,76500,76502,76505,76508,76511,76514],{"className":76501},[250],[128,76503],{"className":76504,"style":283},[254],[128,76506,76009],{"className":76507,"style":36065},[259,1873],[128,76509],{"className":76510,"style":1878},[269],[128,76512,1994],{"className":76513},[1882],[128,76515],{"className":76516,"style":1878},[269],[128,76518,76520,76523,76526,76566,76569,76572,76575,76578,76581,76584,76624],{"className":76519},[250],[128,76521],{"className":76522,"style":1892},[254],[128,76524,1838],{"className":76525},[1896],[128,76527,76529,76532],{"className":76528},[259],[128,76530,5436],{"className":76531,"style":5514},[259,1873],[128,76533,76535],{"className":76534},[2087],[128,76536,76538,76558],{"className":76537},[274,321],[128,76539,76541,76555],{"className":76540},[278],[128,76542,76544],{"className":76543,"style":2945},[282],[128,76545,76546,76549],{"style":38889},[128,76547],{"className":76548,"style":291},[290],[128,76550,76552],{"className":76551},[299,300,301,298],[128,76553,1842],{"className":76554},[259,298],[128,76556,347],{"className":76557},[346],[128,76559,76561],{"className":76560},[278],[128,76562,76564],{"className":76563,"style":2241},[282],[128,76565],{},[128,76567,1845],{"className":76568},[1903],[128,76570],{"className":76571,"style":1907},[269],[128,76573,1848],{"className":76574},[1911],[128,76576],{"className":76577,"style":1907},[269],[128,76579,1845],{"className":76580},[1903],[128,76582],{"className":76583,"style":1907},[269],[128,76585,76587,76590],{"className":76586},[259],[128,76588,5436],{"className":76589,"style":5514},[259,1873],[128,76591,76593],{"className":76592},[2087],[128,76594,76596,76616],{"className":76595},[274,321],[128,76597,76599,76613],{"className":76598},[278],[128,76600,76602],{"className":76601,"style":28738},[282],[128,76603,76604,76607],{"style":38889},[128,76605],{"className":76606,"style":291},[290],[128,76608,76610],{"className":76609},[299,300,301,298],[128,76611,16280],{"className":76612},[259,1873,298],[128,76614,347],{"className":76615},[346],[128,76617,76619],{"className":76618},[278],[128,76620,76622],{"className":76621,"style":2241},[282],[128,76623],{},[128,76625,1856],{"className":76626},[1928],[35,76628,76629],{},"结构方程（structural equations）"," 集合，每个 ",[128,76632,76634,76652],{"className":76633,"translate":218},[217],[128,76635,76637],{"className":76636},[222],[224,76638,76639],{"xmlns":226},[228,76640,76641,76649],{},[231,76642,76643],{},[2016,76644,76645,76647],{},[1795,76646,5436],{},[1795,76648,2801],{},[238,76650,76651],{"encoding":240},"f_i",[128,76653,76655],{"className":76654,"ariaHidden":246},[245],[128,76656,76658,76661],{"className":76657},[250],[128,76659],{"className":76660,"style":16030},[254],[128,76662,76664,76667],{"className":76663},[259],[128,76665,5436],{"className":76666,"style":5514},[259,1873],[128,76668,76670],{"className":76669},[2087],[128,76671,76673,76693],{"className":76672},[274,321],[128,76674,76676,76690],{"className":76675},[278],[128,76677,76679],{"className":76678,"style":3095},[282],[128,76680,76681,76684],{"style":38889},[128,76682],{"className":76683,"style":291},[290],[128,76685,76687],{"className":76686},[299,300,301,298],[128,76688,2801],{"className":76689},[259,1873,298],[128,76691,347],{"className":76692},[346],[128,76694,76696],{"className":76695},[278],[128,76697,76699],{"className":76698,"style":2241},[282],[128,76700],{}," 是一个确定性函数\n",[128,76703,76705,76786],{"className":76704,"translate":218},[217],[128,76706,76708],{"className":76707},[222],[224,76709,76710],{"xmlns":226},[228,76711,76712,76783],{},[231,76713,76714,76720,76722,76724,76730,76732,76742,76744,76750,76752,76754,76756,76766,76768,76770,76773,76775,76781],{},[2016,76715,76716,76718],{},[1795,76717,67963],{},[1795,76719,2801],{},[1832,76721,2014],{},[1832,76723,1994],{},[2016,76725,76726,76728],{},[1795,76727,5436],{},[1795,76729,2801],{},[1832,76731,2477],{"stretchy":1837},[2016,76733,76734,76740],{},[231,76735,76736,76738],{},[1795,76737,23001],{"mathvariant":1981},[1795,76739,21],{"mathvariant":1981},[1795,76741,2801],{},[1832,76743,1845],{"separator":246},[2016,76745,76746,76748],{},[1795,76747,69050],{},[1795,76749,2801],{},[1832,76751,2486],{"stretchy":1837},[1832,76753,1845],{"separator":246},[269,76755],{"width":11568},[2016,76757,76758,76764],{},[231,76759,76760,76762],{},[1795,76761,23001],{"mathvariant":1981},[1795,76763,21],{"mathvariant":1981},[1795,76765,2801],{},[1832,76767,68208],{},[1795,76769,67963],{},[1832,76771,76772],{},"∖",[1832,76774,1838],{"stretchy":1837},[2016,76776,76777,76779],{},[1795,76778,67963],{},[1795,76780,2801],{},[1832,76782,1856],{"stretchy":1837},[238,76784,76785],{"encoding":240},"V_i := f_i(\\mathrm{Pa}_i, U_i), \\qquad \\mathrm{Pa}_i \\subseteq V \\setminus \\{V_i\\}",[128,76787,76789,76844,77047,77065],{"className":76788,"ariaHidden":246},[245],[128,76790,76792,76795,76835,76838,76841],{"className":76791},[250],[128,76793],{"className":76794,"style":36058},[254],[128,76796,76798,76801],{"className":76797},[259],[128,76799,67963],{"className":76800,"style":2508},[259,1873],[128,76802,76804],{"className":76803},[2087],[128,76805,76807,76827],{"className":76806},[274,321],[128,76808,76810,76824],{"className":76809},[278],[128,76811,76813],{"className":76812,"style":3095},[282],[128,76814,76815,76818],{"style":68109},[128,76816],{"className":76817,"style":291},[290],[128,76819,76821],{"className":76820},[299,300,301,298],[128,76822,2801],{"className":76823},[259,1873,298],[128,76825,347],{"className":76826},[346],[128,76828,76830],{"className":76829},[278],[128,76831,76833],{"className":76832,"style":2241},[282],[128,76834],{},[128,76836],{"className":76837,"style":1878},[269],[128,76839,75429],{"className":76840},[1882],[128,76842],{"className":76843,"style":1878},[269],[128,76845,76847,76850,76890,76893,76937,76940,76943,76983,76986,76989,76992,76995,77038,77041,77044],{"className":76846},[250],[128,76848],{"className":76849,"style":1892},[254],[128,76851,76853,76856],{"className":76852},[259],[128,76854,5436],{"className":76855,"style":5514},[259,1873],[128,76857,76859],{"className":76858},[2087],[128,76860,76862,76882],{"className":76861},[274,321],[128,76863,76865,76879],{"className":76864},[278],[128,76866,76868],{"className":76867,"style":3095},[282],[128,76869,76870,76873],{"style":38889},[128,76871],{"className":76872,"style":291},[290],[128,76874,76876],{"className":76875},[299,300,301,298],[128,76877,2801],{"className":76878},[259,1873,298],[128,76880,347],{"className":76881},[346],[128,76883,76885],{"className":76884},[278],[128,76886,76888],{"className":76887,"style":2241},[282],[128,76889],{},[128,76891,2477],{"className":76892},[1896],[128,76894,76896,76903],{"className":76895},[259],[128,76897,76899],{"className":76898},[259],[128,76900,76902],{"className":76901},[259,3353],"Pa",[128,76904,76906],{"className":76905},[2087],[128,76907,76909,76929],{"className":76908},[274,321],[128,76910,76912,76926],{"className":76911},[278],[128,76913,76915],{"className":76914,"style":3095},[282],[128,76916,76917,76920],{"style":31837},[128,76918],{"className":76919,"style":291},[290],[128,76921,76923],{"className":76922},[299,300,301,298],[128,76924,2801],{"className":76925},[259,1873,298],[128,76927,347],{"className":76928},[346],[128,76930,76932],{"className":76931},[278],[128,76933,76935],{"className":76934,"style":2241},[282],[128,76936],{},[128,76938,1845],{"className":76939},[1903],[128,76941],{"className":76942,"style":1907},[269],[128,76944,76946,76949],{"className":76945},[259],[128,76947,69050],{"className":76948,"style":26806},[259,1873],[128,76950,76952],{"className":76951},[2087],[128,76953,76955,76975],{"className":76954},[274,321],[128,76956,76958,76972],{"className":76957},[278],[128,76959,76961],{"className":76960,"style":3095},[282],[128,76962,76963,76966],{"style":64697},[128,76964],{"className":76965,"style":291},[290],[128,76967,76969],{"className":76968},[299,300,301,298],[128,76970,2801],{"className":76971},[259,1873,298],[128,76973,347],{"className":76974},[346],[128,76976,76978],{"className":76977},[278],[128,76979,76981],{"className":76980,"style":2241},[282],[128,76982],{},[128,76984,2486],{"className":76985},[1928],[128,76987,1845],{"className":76988},[1903],[128,76990],{"className":76991,"style":11756},[269],[128,76993],{"className":76994,"style":1907},[269],[128,76996,76998,77004],{"className":76997},[259],[128,76999,77001],{"className":77000},[259],[128,77002,76902],{"className":77003},[259,3353],[128,77005,77007],{"className":77006},[2087],[128,77008,77010,77030],{"className":77009},[274,321],[128,77011,77013,77027],{"className":77012},[278],[128,77014,77016],{"className":77015,"style":3095},[282],[128,77017,77018,77021],{"style":31837},[128,77019],{"className":77020,"style":291},[290],[128,77022,77024],{"className":77023},[299,300,301,298],[128,77025,2801],{"className":77026},[259,1873,298],[128,77028,347],{"className":77029},[346],[128,77031,77033],{"className":77032},[278],[128,77034,77036],{"className":77035,"style":2241},[282],[128,77037],{},[128,77039],{"className":77040,"style":1878},[269],[128,77042,68208],{"className":77043},[1882],[128,77045],{"className":77046,"style":1878},[269],[128,77048,77050,77053,77056,77059,77062],{"className":77049},[250],[128,77051],{"className":77052,"style":1892},[254],[128,77054,67963],{"className":77055,"style":2508},[259,1873],[128,77057],{"className":77058,"style":2508},[269],[128,77060,76772],{"className":77061},[2115],[128,77063],{"className":77064,"style":2508},[269],[128,77066,77068,77071,77074,77114],{"className":77067},[250],[128,77069],{"className":77070,"style":1892},[254],[128,77072,1838],{"className":77073},[1896],[128,77075,77077,77080],{"className":77076},[259],[128,77078,67963],{"className":77079,"style":2508},[259,1873],[128,77081,77083],{"className":77082},[2087],[128,77084,77086,77106],{"className":77085},[274,321],[128,77087,77089,77103],{"className":77088},[278],[128,77090,77092],{"className":77091,"style":3095},[282],[128,77093,77094,77097],{"style":68109},[128,77095],{"className":77096,"style":291},[290],[128,77098,77100],{"className":77099},[299,300,301,298],[128,77101,2801],{"className":77102},[259,1873,298],[128,77104,347],{"className":77105},[346],[128,77107,77109],{"className":77108},[278],[128,77110,77112],{"className":77111,"style":2241},[282],[128,77113],{},[128,77115,1856],{"className":77116},[1928],[128,77118,77120,77142],{"className":77119,"translate":218},[217],[128,77121,77123],{"className":77122},[222],[224,77124,77125],{"xmlns":226},[228,77126,77127,77139],{},[231,77128,77129],{},[2016,77130,77131,77137],{},[231,77132,77133,77135],{},[1795,77134,23001],{"mathvariant":1981},[1795,77136,21],{"mathvariant":1981},[1795,77138,2801],{},[238,77140,77141],{"encoding":240},"\\mathrm{Pa}_i",[128,77143,77145],{"className":77144,"ariaHidden":246},[245],[128,77146,77148,77151],{"className":77147},[250],[128,77149],{"className":77150,"style":36058},[254],[128,77152,77154,77160],{"className":77153},[259],[128,77155,77157],{"className":77156},[259],[128,77158,76902],{"className":77159},[259,3353],[128,77161,77163],{"className":77162},[2087],[128,77164,77166,77186],{"className":77165},[274,321],[128,77167,77169,77183],{"className":77168},[278],[128,77170,77172],{"className":77171,"style":3095},[282],[128,77173,77174,77177],{"style":31837},[128,77175],{"className":77176,"style":291},[290],[128,77178,77180],{"className":77179},[299,300,301,298],[128,77181,2801],{"className":77182},[259,1873,298],[128,77184,347],{"className":77185},[346],[128,77187,77189],{"className":77188},[278],[128,77190,77192],{"className":77191,"style":2241},[282],[128,77193],{},[128,77195,77197,77214],{"className":77196,"translate":218},[217],[128,77198,77200],{"className":77199},[222],[224,77201,77202],{"xmlns":226},[228,77203,77204,77212],{},[231,77205,77206],{},[2016,77207,77208,77210],{},[1795,77209,67963],{},[1795,77211,2801],{},[238,77213,68580],{"encoding":240},[128,77215,77217],{"className":77216,"ariaHidden":246},[245],[128,77218,77220,77223],{"className":77219},[250],[128,77221],{"className":77222,"style":36058},[254],[128,77224,77226,77229],{"className":77225},[259],[128,77227,67963],{"className":77228,"style":2508},[259,1873],[128,77230,77232],{"className":77231},[2087],[128,77233,77235,77255],{"className":77234},[274,321],[128,77236,77238,77252],{"className":77237},[278],[128,77239,77241],{"className":77240,"style":3095},[282],[128,77242,77243,77246],{"style":68109},[128,77244],{"className":77245,"style":291},[290],[128,77247,77249],{"className":77248},[299,300,301,298],[128,77250,2801],{"className":77251},[259,1873,298],[128,77253,347],{"className":77254},[346],[128,77256,77258],{"className":77257},[278],[128,77259,77261],{"className":77260,"style":2241},[282],[128,77262],{}," 的「父集合」）是被假设直接影响 ",[128,77265,77267,77284],{"className":77266,"translate":218},[217],[128,77268,77270],{"className":77269},[222],[224,77271,77272],{"xmlns":226},[228,77273,77274,77282],{},[231,77275,77276],{},[2016,77277,77278,77280],{},[1795,77279,67963],{},[1795,77281,2801],{},[238,77283,68580],{"encoding":240},[128,77285,77287],{"className":77286,"ariaHidden":246},[245],[128,77288,77290,77293],{"className":77289},[250],[128,77291],{"className":77292,"style":36058},[254],[128,77294,77296,77299],{"className":77295},[259],[128,77297,67963],{"className":77298,"style":2508},[259,1873],[128,77300,77302],{"className":77301},[2087],[128,77303,77305,77325],{"className":77304},[274,321],[128,77306,77308,77322],{"className":77307},[278],[128,77309,77311],{"className":77310,"style":3095},[282],[128,77312,77313,77316],{"style":68109},[128,77314],{"className":77315,"style":291},[290],[128,77317,77319],{"className":77318},[299,300,301,298],[128,77320,2801],{"className":77321},[259,1873,298],[128,77323,347],{"className":77324},[346],[128,77326,77328],{"className":77327},[278],[128,77329,77331],{"className":77330,"style":2241},[282],[128,77332],{}," 的其余内生变量子集，",[128,77335,77337,77359],{"className":77336,"translate":218},[217],[128,77338,77340],{"className":77339},[222],[224,77341,77342],{"xmlns":226},[228,77343,77344,77356],{},[231,77345,77346,77352,77354],{},[2016,77347,77348,77350],{},[1795,77349,69050],{},[1795,77351,2801],{},[1832,77353,68208],{},[1795,77355,69050],{},[238,77357,77358],{"encoding":240},"U_i \\subseteq U",[128,77360,77362,77417],{"className":77361,"ariaHidden":246},[245],[128,77363,77365,77368,77408,77411,77414],{"className":77364},[250],[128,77366],{"className":77367,"style":36058},[254],[128,77369,77371,77374],{"className":77370},[259],[128,77372,69050],{"className":77373,"style":26806},[259,1873],[128,77375,77377],{"className":77376},[2087],[128,77378,77380,77400],{"className":77379},[274,321],[128,77381,77383,77397],{"className":77382},[278],[128,77384,77386],{"className":77385,"style":3095},[282],[128,77387,77388,77391],{"style":64697},[128,77389],{"className":77390,"style":291},[290],[128,77392,77394],{"className":77393},[299,300,301,298],[128,77395,2801],{"className":77396},[259,1873,298],[128,77398,347],{"className":77399},[346],[128,77401,77403],{"className":77402},[278],[128,77404,77406],{"className":77405,"style":2241},[282],[128,77407],{},[128,77409],{"className":77410,"style":1878},[269],[128,77412,68208],{"className":77413},[1882],[128,77415],{"className":77416,"style":1878},[269],[128,77418,77420,77423],{"className":77419},[250],[128,77421],{"className":77422,"style":283},[254],[128,77424,69050],{"className":77425,"style":26806},[259,1873]," 是影响 ",[128,77428,77430,77447],{"className":77429,"translate":218},[217],[128,77431,77433],{"className":77432},[222],[224,77434,77435],{"xmlns":226},[228,77436,77437,77445],{},[231,77438,77439],{},[2016,77440,77441,77443],{},[1795,77442,67963],{},[1795,77444,2801],{},[238,77446,68580],{"encoding":240},[128,77448,77450],{"className":77449,"ariaHidden":246},[245],[128,77451,77453,77456],{"className":77452},[250],[128,77454],{"className":77455,"style":36058},[254],[128,77457,77459,77462],{"className":77458},[259],[128,77460,67963],{"className":77461,"style":2508},[259,1873],[128,77463,77465],{"className":77464},[2087],[128,77466,77468,77488],{"className":77467},[274,321],[128,77469,77471,77485],{"className":77470},[278],[128,77472,77474],{"className":77473,"style":3095},[282],[128,77475,77476,77479],{"style":68109},[128,77477],{"className":77478,"style":291},[290],[128,77480,77482],{"className":77481},[299,300,301,298],[128,77483,2801],{"className":77484},[259,1873,298],[128,77486,347],{"className":77487},[346],[128,77489,77491],{"className":77490},[278],[128,77492,77494],{"className":77493,"style":2241},[282],[128,77495],{}," 的外生噪声；",[33251,77498,77499,77543,77544,77572],{},[128,77500,77502,77522],{"className":77501,"translate":218},[217],[128,77503,77505],{"className":77504},[222],[224,77506,77507],{"xmlns":226},[228,77508,77509,77519],{},[231,77510,77511,77513,77515,77517],{},[1795,77512,23001],{},[1832,77514,2477],{"stretchy":1837},[1795,77516,69050],{},[1832,77518,2486],{"stretchy":1837},[238,77520,77521],{"encoding":240},"P(U)",[128,77523,77525],{"className":77524,"ariaHidden":246},[245],[128,77526,77528,77531,77534,77537,77540],{"className":77527},[250],[128,77529],{"className":77530,"style":1892},[254],[128,77532,23001],{"className":77533,"style":36065},[259,1873],[128,77535,2477],{"className":77536},[1896],[128,77538,69050],{"className":77539,"style":26806},[259,1873],[128,77541,2486],{"className":77542},[1928]," 是外生变量集合 ",[128,77545,77547,77560],{"className":77546,"translate":218},[217],[128,77548,77550],{"className":77549},[222],[224,77551,77552],{"xmlns":226},[228,77553,77554,77558],{},[231,77555,77556],{},[1795,77557,69050],{},[238,77559,69050],{"encoding":240},[128,77561,77563],{"className":77562,"ariaHidden":246},[245],[128,77564,77566,77569],{"className":77565},[250],[128,77567],{"className":77568,"style":283},[254],[128,77570,69050],{"className":77571,"style":26806},[259,1873]," 上的联合概率分布。",[2615,77574,77576],{"title":77575},"定义 2.2（诱导因果图）",[11,77577,77578,77579,77607,77608,77678,77679,77771,77772,77800,77801,77941,77942,893],{},"给定 SCM ",[128,77580,77582,77595],{"className":77581,"translate":218},[217],[128,77583,77585],{"className":77584},[222],[224,77586,77587],{"xmlns":226},[228,77588,77589,77593],{},[231,77590,77591],{},[1795,77592,30641],{},[238,77594,30641],{"encoding":240},[128,77596,77598],{"className":77597,"ariaHidden":246},[245],[128,77599,77601,77604],{"className":77600},[250],[128,77602],{"className":77603,"style":283},[254],[128,77605,30641],{"className":77606,"style":26806},[259,1873],"，其对应的因果图 ",[128,77609,77611,77629],{"className":77610,"translate":218},[217],[128,77612,77614],{"className":77613},[222],[224,77615,77616],{"xmlns":226},[228,77617,77618,77626],{},[231,77619,77620],{},[2016,77621,77622,77624],{},[1795,77623,67956],{},[1795,77625,30641],{},[238,77627,77628],{"encoding":240},"G_M",[128,77630,77632],{"className":77631,"ariaHidden":246},[245],[128,77633,77635,77638],{"className":77634},[250],[128,77636],{"className":77637,"style":36058},[254],[128,77639,77641,77644],{"className":77640},[259],[128,77642,67956],{"className":77643},[259,1873],[128,77645,77647],{"className":77646},[2087],[128,77648,77650,77670],{"className":77649},[274,321],[128,77651,77653,77667],{"className":77652},[278],[128,77654,77656],{"className":77655,"style":3004},[282],[128,77657,77658,77661],{"style":2221},[128,77659],{"className":77660,"style":291},[290],[128,77662,77664],{"className":77663},[299,300,301,298],[128,77665,30641],{"className":77666,"style":26806},[259,1873,298],[128,77668,347],{"className":77669},[346],[128,77671,77673],{"className":77672},[278],[128,77674,77676],{"className":77675,"style":2241},[282],[128,77677],{}," 定义为：",[128,77680,77682,77704],{"className":77681,"translate":218},[217],[128,77683,77685],{"className":77684},[222],[224,77686,77687],{"xmlns":226},[228,77688,77689,77701],{},[231,77690,77691,77697,77699],{},[2016,77692,77693,77695],{},[1795,77694,67963],{},[1795,77696,30641],{},[1832,77698,1994],{},[1795,77700,67963],{},[238,77702,77703],{"encoding":240},"V_M = V",[128,77705,77707,77762],{"className":77706,"ariaHidden":246},[245],[128,77708,77710,77713,77753,77756,77759],{"className":77709},[250],[128,77711],{"className":77712,"style":36058},[254],[128,77714,77716,77719],{"className":77715},[259],[128,77717,67963],{"className":77718,"style":2508},[259,1873],[128,77720,77722],{"className":77721},[2087],[128,77723,77725,77745],{"className":77724},[274,321],[128,77726,77728,77742],{"className":77727},[278],[128,77729,77731],{"className":77730,"style":3004},[282],[128,77732,77733,77736],{"style":68109},[128,77734],{"className":77735,"style":291},[290],[128,77737,77739],{"className":77738},[299,300,301,298],[128,77740,30641],{"className":77741,"style":26806},[259,1873,298],[128,77743,347],{"className":77744},[346],[128,77746,77748],{"className":77747},[278],[128,77749,77751],{"className":77750,"style":2241},[282],[128,77752],{},[128,77754],{"className":77755,"style":1878},[269],[128,77757,1994],{"className":77758},[1882],[128,77760],{"className":77761,"style":1878},[269],[128,77763,77765,77768],{"className":77764},[250],[128,77766],{"className":77767,"style":283},[254],[128,77769,67963],{"className":77770,"style":2508},[259,1873],"，且对每个 ",[128,77773,77775,77788],{"className":77774,"translate":218},[217],[128,77776,77778],{"className":77777},[222],[224,77779,77780],{"xmlns":226},[228,77781,77782,77786],{},[231,77783,77784],{},[1795,77785,2801],{},[238,77787,2801],{"encoding":240},[128,77789,77791],{"className":77790,"ariaHidden":246},[245],[128,77792,77794,77797],{"className":77793},[250],[128,77795],{"className":77796,"style":23527},[254],[128,77798,2801],{"className":77799},[259,1873],"、每个 ",[128,77802,77804,77834],{"className":77803,"translate":218},[217],[128,77805,77807],{"className":77806},[222],[224,77808,77809],{"xmlns":226},[228,77810,77811,77831],{},[231,77812,77813,77819,77821],{},[2016,77814,77815,77817],{},[1795,77816,67963],{},[1795,77818,16495],{},[1832,77820,1834],{},[2016,77822,77823,77829],{},[231,77824,77825,77827],{},[1795,77826,23001],{"mathvariant":1981},[1795,77828,21],{"mathvariant":1981},[1795,77830,2801],{},[238,77832,77833],{"encoding":240},"V_j \\in \\mathrm{Pa}_i",[128,77835,77837,77892],{"className":77836,"ariaHidden":246},[245],[128,77838,77840,77843,77883,77886,77889],{"className":77839},[250],[128,77841],{"className":77842,"style":68518},[254],[128,77844,77846,77849],{"className":77845},[259],[128,77847,67963],{"className":77848,"style":2508},[259,1873],[128,77850,77852],{"className":77851},[2087],[128,77853,77855,77875],{"className":77854},[274,321],[128,77856,77858,77872],{"className":77857},[278],[128,77859,77861],{"className":77860,"style":3095},[282],[128,77862,77863,77866],{"style":68109},[128,77864],{"className":77865,"style":291},[290],[128,77867,77869],{"className":77868},[299,300,301,298],[128,77870,16495],{"className":77871,"style":16521},[259,1873,298],[128,77873,347],{"className":77874},[346],[128,77876,77878],{"className":77877},[278],[128,77879,77881],{"className":77880,"style":17424},[282],[128,77882],{},[128,77884],{"className":77885,"style":1878},[269],[128,77887,1834],{"className":77888},[1882],[128,77890],{"className":77891,"style":1878},[269],[128,77893,77895,77898],{"className":77894},[250],[128,77896],{"className":77897,"style":36058},[254],[128,77899,77901,77907],{"className":77900},[259],[128,77902,77904],{"className":77903},[259],[128,77905,76902],{"className":77906},[259,3353],[128,77908,77910],{"className":77909},[2087],[128,77911,77913,77933],{"className":77912},[274,321],[128,77914,77916,77930],{"className":77915},[278],[128,77917,77919],{"className":77918,"style":3095},[282],[128,77920,77921,77924],{"style":31837},[128,77922],{"className":77923,"style":291},[290],[128,77925,77927],{"className":77926},[299,300,301,298],[128,77928,2801],{"className":77929},[259,1873,298],[128,77931,347],{"className":77932},[346],[128,77934,77936],{"className":77935},[278],[128,77937,77939],{"className":77938,"style":2241},[282],[128,77940],{},"，画一条边 ",[128,77943,77945,77971],{"className":77944,"translate":218},[217],[128,77946,77948],{"className":77947},[222],[224,77949,77950],{"xmlns":226},[228,77951,77952,77968],{},[231,77953,77954,77960,77962],{},[2016,77955,77956,77958],{},[1795,77957,67963],{},[1795,77959,16495],{},[1832,77961,22419],{},[2016,77963,77964,77966],{},[1795,77965,67963],{},[1795,77967,2801],{},[238,77969,77970],{"encoding":240},"V_j \\to V_i",[128,77972,77974,78029],{"className":77973,"ariaHidden":246},[245],[128,77975,77977,77980,78020,78023,78026],{"className":77976},[250],[128,77978],{"className":77979,"style":68518},[254],[128,77981,77983,77986],{"className":77982},[259],[128,77984,67963],{"className":77985,"style":2508},[259,1873],[128,77987,77989],{"className":77988},[2087],[128,77990,77992,78012],{"className":77991},[274,321],[128,77993,77995,78009],{"className":77994},[278],[128,77996,77998],{"className":77997,"style":3095},[282],[128,77999,78000,78003],{"style":68109},[128,78001],{"className":78002,"style":291},[290],[128,78004,78006],{"className":78005},[299,300,301,298],[128,78007,16495],{"className":78008,"style":16521},[259,1873,298],[128,78010,347],{"className":78011},[346],[128,78013,78015],{"className":78014},[278],[128,78016,78018],{"className":78017,"style":17424},[282],[128,78019],{},[128,78021],{"className":78022,"style":1878},[269],[128,78024,22419],{"className":78025},[1882],[128,78027],{"className":78028,"style":1878},[269],[128,78030,78032,78035],{"className":78031},[250],[128,78033],{"className":78034,"style":36058},[254],[128,78036,78038,78041],{"className":78037},[259],[128,78039,67963],{"className":78040,"style":2508},[259,1873],[128,78042,78044],{"className":78043},[2087],[128,78045,78047,78067],{"className":78046},[274,321],[128,78048,78050,78064],{"className":78049},[278],[128,78051,78053],{"className":78052,"style":3095},[282],[128,78054,78055,78058],{"style":68109},[128,78056],{"className":78057,"style":291},[290],[128,78059,78061],{"className":78060},[299,300,301,298],[128,78062,2801],{"className":78063},[259,1873,298],[128,78065,347],{"className":78066},[346],[128,78068,78070],{"className":78069},[278],[128,78071,78073],{"className":78072,"style":2241},[282],[128,78074],{},[2615,78076,78078],{"title":78077},"定义 2.3（马尔可夫型 SCM，Markovian SCM）",[11,78079,23408,78080,78149,78150,78290,78291,78294,78295,78323,78324,78327,78328,78457],{},[128,78081,78083,78100],{"className":78082,"translate":218},[217],[128,78084,78086],{"className":78085},[222],[224,78087,78088],{"xmlns":226},[228,78089,78090,78098],{},[231,78091,78092],{},[2016,78093,78094,78096],{},[1795,78095,67956],{},[1795,78097,30641],{},[238,78099,77628],{"encoding":240},[128,78101,78103],{"className":78102,"ariaHidden":246},[245],[128,78104,78106,78109],{"className":78105},[250],[128,78107],{"className":78108,"style":36058},[254],[128,78110,78112,78115],{"className":78111},[259],[128,78113,67956],{"className":78114},[259,1873],[128,78116,78118],{"className":78117},[2087],[128,78119,78121,78141],{"className":78120},[274,321],[128,78122,78124,78138],{"className":78123},[278],[128,78125,78127],{"className":78126,"style":3004},[282],[128,78128,78129,78132],{"style":2221},[128,78130],{"className":78131,"style":291},[290],[128,78133,78135],{"className":78134},[299,300,301,298],[128,78136,30641],{"className":78137,"style":26806},[259,1873,298],[128,78139,347],{"className":78140},[346],[128,78142,78144],{"className":78143},[278],[128,78145,78147],{"className":78146,"style":2241},[282],[128,78148],{}," 是无环的，且各外生变量 ",[128,78151,78153,78183],{"className":78152,"translate":218},[217],[128,78154,78156],{"className":78155},[222],[224,78157,78158],{"xmlns":226},[228,78159,78160,78180],{},[231,78161,78162,78168,78170,78172,78174],{},[2016,78163,78164,78166],{},[1795,78165,69050],{},[1840,78167,1842],{},[1832,78169,1845],{"separator":246},[1832,78171,1848],{},[1832,78173,1845],{"separator":246},[2016,78175,78176,78178],{},[1795,78177,69050],{},[1795,78179,30849],{},[238,78181,78182],{"encoding":240},"U_1, \\dots, U_m",[128,78184,78186],{"className":78185,"ariaHidden":246},[245],[128,78187,78189,78192,78232,78235,78238,78241,78244,78247,78250],{"className":78188},[250],[128,78190],{"className":78191,"style":40674},[254],[128,78193,78195,78198],{"className":78194},[259],[128,78196,69050],{"className":78197,"style":26806},[259,1873],[128,78199,78201],{"className":78200},[2087],[128,78202,78204,78224],{"className":78203},[274,321],[128,78205,78207,78221],{"className":78206},[278],[128,78208,78210],{"className":78209,"style":2945},[282],[128,78211,78212,78215],{"style":64697},[128,78213],{"className":78214,"style":291},[290],[128,78216,78218],{"className":78217},[299,300,301,298],[128,78219,1842],{"className":78220},[259,298],[128,78222,347],{"className":78223},[346],[128,78225,78227],{"className":78226},[278],[128,78228,78230],{"className":78229,"style":2241},[282],[128,78231],{},[128,78233,1845],{"className":78234},[1903],[128,78236],{"className":78237,"style":1907},[269],[128,78239,1848],{"className":78240},[1911],[128,78242],{"className":78243,"style":1907},[269],[128,78245,1845],{"className":78246},[1903],[128,78248],{"className":78249,"style":1907},[269],[128,78251,78253,78256],{"className":78252},[259],[128,78254,69050],{"className":78255,"style":26806},[259,1873],[128,78257,78259],{"className":78258},[2087],[128,78260,78262,78282],{"className":78261},[274,321],[128,78263,78265,78279],{"className":78264},[278],[128,78266,78268],{"className":78267,"style":28738},[282],[128,78269,78270,78273],{"style":64697},[128,78271],{"className":78272,"style":291},[290],[128,78274,78276],{"className":78275},[299,300,301,298],[128,78277,30849],{"className":78278},[259,1873,298],[128,78280,347],{"className":78281},[346],[128,78283,78285],{"className":78284},[278],[128,78286,78288],{"className":78287,"style":2241},[282],[128,78289],{}," 两两",[35,78292,78293],{},"相互独立","（即不存在同时影响两个及以上内生变量的「隐藏共同噪声」），则称 ",[128,78296,78298,78311],{"className":78297,"translate":218},[217],[128,78299,78301],{"className":78300},[222],[224,78302,78303],{"xmlns":226},[228,78304,78305,78309],{},[231,78306,78307],{},[1795,78308,30641],{},[238,78310,30641],{"encoding":240},[128,78312,78314],{"className":78313,"ariaHidden":246},[245],[128,78315,78317,78320],{"className":78316},[250],[128,78318],{"className":78319,"style":283},[254],[128,78321,30641],{"className":78322,"style":26806},[259,1873]," 为马尔可夫型 SCM。若外生变量之间允许相关（对应存在未显式建模的混杂因子），则称为",[35,78325,78326],{},"半马尔可夫型（semi-Markovian）","，此时因果图通常需要补充双向虚线弧 ",[128,78329,78331,78361],{"className":78330,"translate":218},[217],[128,78332,78334],{"className":78333},[222],[224,78335,78336],{"xmlns":226},[228,78337,78338,78358],{},[231,78339,78340,78346,78352],{},[2016,78341,78342,78344],{},[1795,78343,67963],{},[1795,78345,2801],{},[2035,78347,78349],{"mathcolor":78348},"#cc0000",[234,78350,78351],{},"\\dashleftrightarrow",[2016,78353,78354,78356],{},[1795,78355,67963],{},[1795,78357,16495],{},[238,78359,78360],{"encoding":240},"V_i \\dashleftrightarrow V_j",[128,78362,78364],{"className":78363,"ariaHidden":246},[245],[128,78365,78367,78370,78410,78417],{"className":78366},[250],[128,78368],{"className":78369,"style":19704},[254],[128,78371,78373,78376],{"className":78372},[259],[128,78374,67963],{"className":78375,"style":2508},[259,1873],[128,78377,78379],{"className":78378},[2087],[128,78380,78382,78402],{"className":78381},[274,321],[128,78383,78385,78399],{"className":78384},[278],[128,78386,78388],{"className":78387,"style":3095},[282],[128,78389,78390,78393],{"style":68109},[128,78391],{"className":78392,"style":291},[290],[128,78394,78396],{"className":78395},[299,300,301,298],[128,78397,2801],{"className":78398},[259,1873,298],[128,78400,347],{"className":78401},[346],[128,78403,78405],{"className":78404},[278],[128,78406,78408],{"className":78407,"style":2241},[282],[128,78409],{},[128,78411,78414],{"className":78412,"style":78413},[259,260],"color:#cc0000;",[128,78415,78351],{"className":78416,"style":78413},[259],[128,78418,78420,78423],{"className":78419},[259],[128,78421,67963],{"className":78422,"style":2508},[259,1873],[128,78424,78426],{"className":78425},[2087],[128,78427,78429,78449],{"className":78428},[274,321],[128,78430,78432,78446],{"className":78431},[278],[128,78433,78435],{"className":78434,"style":3095},[282],[128,78436,78437,78440],{"style":68109},[128,78438],{"className":78439,"style":291},[290],[128,78441,78443],{"className":78442},[299,300,301,298],[128,78444,16495],{"className":78445,"style":16521},[259,1873,298],[128,78447,347],{"className":78448},[346],[128,78450,78452],{"className":78451},[278],[128,78453,78455],{"className":78454,"style":17424},[282],[128,78456],{}," 以标示这种隐藏依赖。本文后续讨论若无特别说明，均限于马尔可夫型 SCM。",[2610,78459,78461],{"id":78460},"_22-诱导分布与马尔可夫性","2.2 诱导分布与马尔可夫性",[2615,78463,78465],{"title":78464},"定义 2.4（诱导概率分布）",[11,78466,78467,78468,78496,78497,78525,78526,78674,78675,78703,78704,78747,78748,78776,78777,78862,78863,11101,78891,893],{},"给定马尔可夫型 SCM ",[128,78469,78471,78484],{"className":78470,"translate":218},[217],[128,78472,78474],{"className":78473},[222],[224,78475,78476],{"xmlns":226},[228,78477,78478,78482],{},[231,78479,78480],{},[1795,78481,30641],{},[238,78483,30641],{"encoding":240},[128,78485,78487],{"className":78486,"ariaHidden":246},[245],[128,78488,78490,78493],{"className":78489},[250],[128,78491],{"className":78492,"style":283},[254],[128,78494,30641],{"className":78495,"style":26806},[259,1873],"，由于每个内生变量都是外生变量的确定性函数（递归代入 ",[128,78498,78500,78513],{"className":78499,"translate":218},[217],[128,78501,78503],{"className":78502},[222],[224,78504,78505],{"xmlns":226},[228,78506,78507,78511],{},[231,78508,78509],{},[1795,78510,76009],{},[238,78512,76009],{"encoding":240},[128,78514,78516],{"className":78515,"ariaHidden":246},[245],[128,78517,78519,78522],{"className":78518},[250],[128,78520],{"className":78521,"style":283},[254],[128,78523,76009],{"className":78524,"style":36065},[259,1873]," 中所有方程后可得 ",[128,78527,78529,78561],{"className":78528,"translate":218},[217],[128,78530,78532],{"className":78531},[222],[224,78533,78534],{"xmlns":226},[228,78535,78536,78558],{},[231,78537,78538,78544,78546,78552,78554,78556],{},[2016,78539,78540,78542],{},[1795,78541,67963],{},[1795,78543,2801],{},[1832,78545,1994],{},[2016,78547,78548,78550],{},[1795,78549,24505],{},[1795,78551,2801],{},[1832,78553,2477],{"stretchy":1837},[1795,78555,69050],{},[1832,78557,2486],{"stretchy":1837},[238,78559,78560],{"encoding":240},"V_i = g_i(U)",[128,78562,78564,78619],{"className":78563,"ariaHidden":246},[245],[128,78565,78567,78570,78610,78613,78616],{"className":78566},[250],[128,78568],{"className":78569,"style":36058},[254],[128,78571,78573,78576],{"className":78572},[259],[128,78574,67963],{"className":78575,"style":2508},[259,1873],[128,78577,78579],{"className":78578},[2087],[128,78580,78582,78602],{"className":78581},[274,321],[128,78583,78585,78599],{"className":78584},[278],[128,78586,78588],{"className":78587,"style":3095},[282],[128,78589,78590,78593],{"style":68109},[128,78591],{"className":78592,"style":291},[290],[128,78594,78596],{"className":78595},[299,300,301,298],[128,78597,2801],{"className":78598},[259,1873,298],[128,78600,347],{"className":78601},[346],[128,78603,78605],{"className":78604},[278],[128,78606,78608],{"className":78607,"style":2241},[282],[128,78609],{},[128,78611],{"className":78612,"style":1878},[269],[128,78614,1994],{"className":78615},[1882],[128,78617],{"className":78618,"style":1878},[269],[128,78620,78622,78625,78665,78668,78671],{"className":78621},[250],[128,78623],{"className":78624,"style":1892},[254],[128,78626,78628,78631],{"className":78627},[259],[128,78629,24505],{"className":78630,"style":1874},[259,1873],[128,78632,78634],{"className":78633},[2087],[128,78635,78637,78657],{"className":78636},[274,321],[128,78638,78640,78654],{"className":78639},[278],[128,78641,78643],{"className":78642,"style":3095},[282],[128,78644,78645,78648],{"style":28741},[128,78646],{"className":78647,"style":291},[290],[128,78649,78651],{"className":78650},[299,300,301,298],[128,78652,2801],{"className":78653},[259,1873,298],[128,78655,347],{"className":78656},[346],[128,78658,78660],{"className":78659},[278],[128,78661,78663],{"className":78662,"style":2241},[282],[128,78664],{},[128,78666,2477],{"className":78667},[1896],[128,78669,69050],{"className":78670,"style":26806},[259,1873],[128,78672,2486],{"className":78673},[1928],"），",[128,78676,78678,78691],{"className":78677,"translate":218},[217],[128,78679,78681],{"className":78680},[222],[224,78682,78683],{"xmlns":226},[228,78684,78685,78689],{},[231,78686,78687],{},[1795,78688,69050],{},[238,78690,69050],{"encoding":240},[128,78692,78694],{"className":78693,"ariaHidden":246},[245],[128,78695,78697,78700],{"className":78696},[250],[128,78698],{"className":78699,"style":283},[254],[128,78701,69050],{"className":78702,"style":26806},[259,1873]," 上的分布 ",[128,78705,78707,78726],{"className":78706,"translate":218},[217],[128,78708,78710],{"className":78709},[222],[224,78711,78712],{"xmlns":226},[228,78713,78714,78724],{},[231,78715,78716,78718,78720,78722],{},[1795,78717,23001],{},[1832,78719,2477],{"stretchy":1837},[1795,78721,69050],{},[1832,78723,2486],{"stretchy":1837},[238,78725,77521],{"encoding":240},[128,78727,78729],{"className":78728,"ariaHidden":246},[245],[128,78730,78732,78735,78738,78741,78744],{"className":78731},[250],[128,78733],{"className":78734,"style":1892},[254],[128,78736,23001],{"className":78737,"style":36065},[259,1873],[128,78739,2477],{"className":78740},[1896],[128,78742,69050],{"className":78743,"style":26806},[259,1873],[128,78745,2486],{"className":78746},[1928]," 唯一诱导出 ",[128,78749,78751,78764],{"className":78750,"translate":218},[217],[128,78752,78754],{"className":78753},[222],[224,78755,78756],{"xmlns":226},[228,78757,78758,78762],{},[231,78759,78760],{},[1795,78761,67963],{},[238,78763,67963],{"encoding":240},[128,78765,78767],{"className":78766,"ariaHidden":246},[245],[128,78768,78770,78773],{"className":78769},[250],[128,78771],{"className":78772,"style":283},[254],[128,78774,67963],{"className":78775,"style":2508},[259,1873]," 上的一个联合分布 ",[128,78778,78780,78804],{"className":78779,"translate":218},[217],[128,78781,78783],{"className":78782},[222],[224,78784,78785],{"xmlns":226},[228,78786,78787,78801],{},[231,78788,78789,78795,78797,78799],{},[2016,78790,78791,78793],{},[1795,78792,23001],{},[1795,78794,30641],{},[1832,78796,2477],{"stretchy":1837},[1795,78798,67963],{},[1832,78800,2486],{"stretchy":1837},[238,78802,78803],{"encoding":240},"P_M(V)",[128,78805,78807],{"className":78806,"ariaHidden":246},[245],[128,78808,78810,78813,78853,78856,78859],{"className":78809},[250],[128,78811],{"className":78812,"style":1892},[254],[128,78814,78816,78819],{"className":78815},[259],[128,78817,23001],{"className":78818,"style":36065},[259,1873],[128,78820,78822],{"className":78821},[2087],[128,78823,78825,78845],{"className":78824},[274,321],[128,78826,78828,78842],{"className":78827},[278],[128,78829,78831],{"className":78830,"style":3004},[282],[128,78832,78833,78836],{"style":36080},[128,78834],{"className":78835,"style":291},[290],[128,78837,78839],{"className":78838},[299,300,301,298],[128,78840,30641],{"className":78841,"style":26806},[259,1873,298],[128,78843,347],{"className":78844},[346],[128,78846,78848],{"className":78847},[278],[128,78849,78851],{"className":78850,"style":2241},[282],[128,78852],{},[128,78854,2477],{"className":78855},[1896],[128,78857,67963],{"className":78858,"style":2508},[259,1873],[128,78860,2486],{"className":78861},[1928],"，称为 ",[128,78864,78866,78879],{"className":78865,"translate":218},[217],[128,78867,78869],{"className":78868},[222],[224,78870,78871],{"xmlns":226},[228,78872,78873,78877],{},[231,78874,78875],{},[1795,78876,30641],{},[238,78878,30641],{"encoding":240},[128,78880,78882],{"className":78881,"ariaHidden":246},[245],[128,78883,78885,78888],{"className":78884},[250],[128,78886],{"className":78887,"style":283},[254],[128,78889,30641],{"className":78890,"style":26806},[259,1873],[35,78892,78893,78894,78897],{},"诱导分布（induced distribution）",[35,78895,78896],{},"或","观测分布",[2615,78899,78901],{"title":78900},"定理 2.1（马尔可夫分解，Markov Factorization）",[11,78902,23408,78903,78931,78932,79016,79017,79444],{},[128,78904,78906,78919],{"className":78905,"translate":218},[217],[128,78907,78909],{"className":78908},[222],[224,78910,78911],{"xmlns":226},[228,78912,78913,78917],{},[231,78914,78915],{},[1795,78916,30641],{},[238,78918,30641],{"encoding":240},[128,78920,78922],{"className":78921,"ariaHidden":246},[245],[128,78923,78925,78928],{"className":78924},[250],[128,78926],{"className":78927,"style":283},[254],[128,78929,30641],{"className":78930,"style":26806},[259,1873]," 为马尔可夫型 SCM，其诱导分布 ",[128,78933,78935,78958],{"className":78934,"translate":218},[217],[128,78936,78938],{"className":78937},[222],[224,78939,78940],{"xmlns":226},[228,78941,78942,78956],{},[231,78943,78944,78950,78952,78954],{},[2016,78945,78946,78948],{},[1795,78947,23001],{},[1795,78949,30641],{},[1832,78951,2477],{"stretchy":1837},[1795,78953,67963],{},[1832,78955,2486],{"stretchy":1837},[238,78957,78803],{"encoding":240},[128,78959,78961],{"className":78960,"ariaHidden":246},[245],[128,78962,78964,78967,79007,79010,79013],{"className":78963},[250],[128,78965],{"className":78966,"style":1892},[254],[128,78968,78970,78973],{"className":78969},[259],[128,78971,23001],{"className":78972,"style":36065},[259,1873],[128,78974,78976],{"className":78975},[2087],[128,78977,78979,78999],{"className":78978},[274,321],[128,78980,78982,78996],{"className":78981},[278],[128,78983,78985],{"className":78984,"style":3004},[282],[128,78986,78987,78990],{"style":36080},[128,78988],{"className":78989,"style":291},[290],[128,78991,78993],{"className":78992},[299,300,301,298],[128,78994,30641],{"className":78995,"style":26806},[259,1873,298],[128,78997,347],{"className":78998},[346],[128,79000,79002],{"className":79001},[278],[128,79003,79005],{"className":79004,"style":2241},[282],[128,79006],{},[128,79008,2477],{"className":79009},[1896],[128,79011,67963],{"className":79012,"style":2508},[259,1873],[128,79014,2486],{"className":79015},[1928]," 可分解为：\n",[128,79018,79020,79100],{"className":79019,"translate":218},[217],[128,79021,79023],{"className":79022},[222],[224,79024,79025],{"xmlns":226},[228,79026,79027,79097],{},[231,79028,79029,79035,79037,79043,79045,79047,79049,79055,79057,79059,79073,79075,79077,79083,79085,79095],{},[2016,79030,79031,79033],{},[1795,79032,23001],{},[1795,79034,30641],{},[1832,79036,2477],{"stretchy":1837},[2016,79038,79039,79041],{},[1795,79040,32160],{},[1840,79042,1842],{},[1832,79044,1845],{"separator":246},[1832,79046,1848],{},[1832,79048,1845],{"separator":246},[2016,79050,79051,79053],{},[1795,79052,32160],{},[1795,79054,16280],{},[1832,79056,2486],{"stretchy":1837},[1832,79058,1994],{},[2038,79060,79061,79063,79071],{},[1832,79062,5470],{},[231,79064,79065,79067,79069],{},[1795,79066,2801],{},[1832,79068,1994],{},[1840,79070,1842],{},[1795,79072,16280],{},[1795,79074,23001],{},[1832,79076,2477],{"stretchy":1837},[2016,79078,79079,79081],{},[1795,79080,32160],{},[1795,79082,2801],{},[1832,79084,5443],{},[2016,79086,79087,79093],{},[231,79088,79089,79091],{},[1795,79090,11],{"mathvariant":1981},[1795,79092,21],{"mathvariant":1981},[1795,79094,2801],{},[1832,79096,2486],{"stretchy":1837},[238,79098,79099],{"encoding":240},"P_M(v_1, \\dots, v_n) = \\prod_{i=1}^n P(v_i \\mid \\mathrm{pa}_i)",[128,79101,79103,79262,79388],{"className":79102,"ariaHidden":246},[245],[128,79104,79106,79109,79149,79152,79192,79195,79198,79201,79204,79207,79210,79250,79253,79256,79259],{"className":79105},[250],[128,79107],{"className":79108,"style":1892},[254],[128,79110,79112,79115],{"className":79111},[259],[128,79113,23001],{"className":79114,"style":36065},[259,1873],[128,79116,79118],{"className":79117},[2087],[128,79119,79121,79141],{"className":79120},[274,321],[128,79122,79124,79138],{"className":79123},[278],[128,79125,79127],{"className":79126,"style":3004},[282],[128,79128,79129,79132],{"style":36080},[128,79130],{"className":79131,"style":291},[290],[128,79133,79135],{"className":79134},[299,300,301,298],[128,79136,30641],{"className":79137,"style":26806},[259,1873,298],[128,79139,347],{"className":79140},[346],[128,79142,79144],{"className":79143},[278],[128,79145,79147],{"className":79146,"style":2241},[282],[128,79148],{},[128,79150,2477],{"className":79151},[1896],[128,79153,79155,79158],{"className":79154},[259],[128,79156,32160],{"className":79157,"style":1874},[259,1873],[128,79159,79161],{"className":79160},[2087],[128,79162,79164,79184],{"className":79163},[274,321],[128,79165,79167,79181],{"className":79166},[278],[128,79168,79170],{"className":79169,"style":2945},[282],[128,79171,79172,79175],{"style":28741},[128,79173],{"className":79174,"style":291},[290],[128,79176,79178],{"className":79177},[299,300,301,298],[128,79179,1842],{"className":79180},[259,298],[128,79182,347],{"className":79183},[346],[128,79185,79187],{"className":79186},[278],[128,79188,79190],{"className":79189,"style":2241},[282],[128,79191],{},[128,79193,1845],{"className":79194},[1903],[128,79196],{"className":79197,"style":1907},[269],[128,79199,1848],{"className":79200},[1911],[128,79202],{"className":79203,"style":1907},[269],[128,79205,1845],{"className":79206},[1903],[128,79208],{"className":79209,"style":1907},[269],[128,79211,79213,79216],{"className":79212},[259],[128,79214,32160],{"className":79215,"style":1874},[259,1873],[128,79217,79219],{"className":79218},[2087],[128,79220,79222,79242],{"className":79221},[274,321],[128,79223,79225,79239],{"className":79224},[278],[128,79226,79228],{"className":79227,"style":28738},[282],[128,79229,79230,79233],{"style":28741},[128,79231],{"className":79232,"style":291},[290],[128,79234,79236],{"className":79235},[299,300,301,298],[128,79237,16280],{"className":79238},[259,1873,298],[128,79240,347],{"className":79241},[346],[128,79243,79245],{"className":79244},[278],[128,79246,79248],{"className":79247,"style":2241},[282],[128,79249],{},[128,79251,2486],{"className":79252},[1928],[128,79254],{"className":79255,"style":1878},[269],[128,79257,1994],{"className":79258},[1882],[128,79260],{"className":79261,"style":1878},[269],[128,79263,79265,79269,79330,79333,79336,79339,79379,79382,79385],{"className":79264},[250],[128,79266],{"className":79267,"style":79268},[254],"height:1.104em;vertical-align:-0.2997em;",[128,79270,79272,79275],{"className":79271},[2268],[128,79273,5470],{"className":79274,"style":2274},[2268,2272,2273],[128,79276,79278],{"className":79277},[2087],[128,79279,79281,79322],{"className":79280},[274,321],[128,79282,79284,79319],{"className":79283},[278],[128,79285,79288,79308],{"className":79286,"style":79287},[282],"height:0.8043em;",[128,79289,79290,79293],{"style":2290},[128,79291],{"className":79292,"style":291},[290],[128,79294,79296],{"className":79295},[299,300,301,298],[128,79297,79299,79302,79305],{"className":79298},[259,298],[128,79300,2801],{"className":79301},[259,1873,298],[128,79303,1994],{"className":79304},[1882,298],[128,79306,1842],{"className":79307},[259,298],[128,79309,79310,79313],{"style":2311},[128,79311],{"className":79312,"style":291},[290],[128,79314,79316],{"className":79315},[299,300,301,298],[128,79317,16280],{"className":79318},[259,1873,298],[128,79320,347],{"className":79321},[346],[128,79323,79325],{"className":79324},[278],[128,79326,79328],{"className":79327,"style":2330},[282],[128,79329],{},[128,79331],{"className":79332,"style":1907},[269],[128,79334,23001],{"className":79335,"style":36065},[259,1873],[128,79337,2477],{"className":79338},[1896],[128,79340,79342,79345],{"className":79341},[259],[128,79343,32160],{"className":79344,"style":1874},[259,1873],[128,79346,79348],{"className":79347},[2087],[128,79349,79351,79371],{"className":79350},[274,321],[128,79352,79354,79368],{"className":79353},[278],[128,79355,79357],{"className":79356,"style":3095},[282],[128,79358,79359,79362],{"style":28741},[128,79360],{"className":79361,"style":291},[290],[128,79363,79365],{"className":79364},[299,300,301,298],[128,79366,2801],{"className":79367},[259,1873,298],[128,79369,347],{"className":79370},[346],[128,79372,79374],{"className":79373},[278],[128,79375,79377],{"className":79376,"style":2241},[282],[128,79378],{},[128,79380],{"className":79381,"style":1878},[269],[128,79383,5443],{"className":79384},[1882],[128,79386],{"className":79387,"style":1878},[269],[128,79389,79391,79394,79441],{"className":79390},[250],[128,79392],{"className":79393,"style":1892},[254],[128,79395,79397,79404],{"className":79396},[259],[128,79398,79400],{"className":79399},[259],[128,79401,79403],{"className":79402},[259,3353],"pa",[128,79405,79407],{"className":79406},[2087],[128,79408,79410,79432],{"className":79409},[274,321],[128,79411,79413,79429],{"className":79412},[278],[128,79414,79417],{"className":79415,"style":79416},[282],"height:0.2175em;",[128,79418,79420,79423],{"style":79419},"top:-2.4559em;margin-right:0.05em;",[128,79421],{"className":79422,"style":291},[290],[128,79424,79426],{"className":79425},[299,300,301,298],[128,79427,2801],{"className":79428},[259,1873,298],[128,79430,347],{"className":79431},[346],[128,79433,79435],{"className":79434},[278],[128,79436,79439],{"className":79437,"style":79438},[282],"height:0.2441em;",[128,79440],{},[128,79442,2486],{"className":79443},[1928],"\n即联合分布可写成每个变量在给定其父节点条件下的条件分布之乘积。",[11,79446,79447,20648,79450,79520,79521,79590,79591,11072,79667,79736,79737,80114],{},[49051,79448,79449],{},"证明梗概",[128,79451,79453,79471],{"className":79452,"translate":218},[217],[128,79454,79456],{"className":79455},[222],[224,79457,79458],{"xmlns":226},[228,79459,79460,79468],{},[231,79461,79462],{},[2016,79463,79464,79466],{},[1795,79465,69050],{},[1795,79467,2801],{},[238,79469,79470],{"encoding":240},"U_i",[128,79472,79474],{"className":79473,"ariaHidden":246},[245],[128,79475,79477,79480],{"className":79476},[250],[128,79478],{"className":79479,"style":36058},[254],[128,79481,79483,79486],{"className":79482},[259],[128,79484,69050],{"className":79485,"style":26806},[259,1873],[128,79487,79489],{"className":79488},[2087],[128,79490,79492,79512],{"className":79491},[274,321],[128,79493,79495,79509],{"className":79494},[278],[128,79496,79498],{"className":79497,"style":3095},[282],[128,79499,79500,79503],{"style":64697},[128,79501],{"className":79502,"style":291},[290],[128,79504,79506],{"className":79505},[299,300,301,298],[128,79507,2801],{"className":79508},[259,1873,298],[128,79510,347],{"className":79511},[346],[128,79513,79515],{"className":79514},[278],[128,79516,79518],{"className":79517,"style":2241},[282],[128,79519],{}," 相互独立，且 ",[128,79522,79524,79541],{"className":79523,"translate":218},[217],[128,79525,79527],{"className":79526},[222],[224,79528,79529],{"xmlns":226},[228,79530,79531,79539],{},[231,79532,79533],{},[2016,79534,79535,79537],{},[1795,79536,67963],{},[1795,79538,2801],{},[238,79540,68580],{"encoding":240},[128,79542,79544],{"className":79543,"ariaHidden":246},[245],[128,79545,79547,79550],{"className":79546},[250],[128,79548],{"className":79549,"style":36058},[254],[128,79551,79553,79556],{"className":79552},[259],[128,79554,67963],{"className":79555,"style":2508},[259,1873],[128,79557,79559],{"className":79558},[2087],[128,79560,79562,79582],{"className":79561},[274,321],[128,79563,79565,79579],{"className":79564},[278],[128,79566,79568],{"className":79567,"style":3095},[282],[128,79569,79570,79573],{"style":68109},[128,79571],{"className":79572,"style":291},[290],[128,79574,79576],{"className":79575},[299,300,301,298],[128,79577,2801],{"className":79578},[259,1873,298],[128,79580,347],{"className":79581},[346],[128,79583,79585],{"className":79584},[278],[128,79586,79588],{"className":79587,"style":2241},[282],[128,79589],{}," 仅是 ",[128,79592,79594,79615],{"className":79593,"translate":218},[217],[128,79595,79597],{"className":79596},[222],[224,79598,79599],{"xmlns":226},[228,79600,79601,79613],{},[231,79602,79603],{},[2016,79604,79605,79611],{},[231,79606,79607,79609],{},[1795,79608,23001],{"mathvariant":1981},[1795,79610,21],{"mathvariant":1981},[1795,79612,2801],{},[238,79614,77141],{"encoding":240},[128,79616,79618],{"className":79617,"ariaHidden":246},[245],[128,79619,79621,79624],{"className":79620},[250],[128,79622],{"className":79623,"style":36058},[254],[128,79625,79627,79633],{"className":79626},[259],[128,79628,79630],{"className":79629},[259],[128,79631,76902],{"className":79632},[259,3353],[128,79634,79636],{"className":79635},[2087],[128,79637,79639,79659],{"className":79638},[274,321],[128,79640,79642,79656],{"className":79641},[278],[128,79643,79645],{"className":79644,"style":3095},[282],[128,79646,79647,79650],{"style":31837},[128,79648],{"className":79649,"style":291},[290],[128,79651,79653],{"className":79652},[299,300,301,298],[128,79654,2801],{"className":79655},[259,1873,298],[128,79657,347],{"className":79658},[346],[128,79660,79662],{"className":79661},[278],[128,79663,79665],{"className":79664,"style":2241},[282],[128,79666],{},[128,79668,79670,79687],{"className":79669,"translate":218},[217],[128,79671,79673],{"className":79672},[222],[224,79674,79675],{"xmlns":226},[228,79676,79677,79685],{},[231,79678,79679],{},[2016,79680,79681,79683],{},[1795,79682,69050],{},[1795,79684,2801],{},[238,79686,79470],{"encoding":240},[128,79688,79690],{"className":79689,"ariaHidden":246},[245],[128,79691,79693,79696],{"className":79692},[250],[128,79694],{"className":79695,"style":36058},[254],[128,79697,79699,79702],{"className":79698},[259],[128,79700,69050],{"className":79701,"style":26806},[259,1873],[128,79703,79705],{"className":79704},[2087],[128,79706,79708,79728],{"className":79707},[274,321],[128,79709,79711,79725],{"className":79710},[278],[128,79712,79714],{"className":79713,"style":3095},[282],[128,79715,79716,79719],{"style":64697},[128,79717],{"className":79718,"style":291},[290],[128,79720,79722],{"className":79721},[299,300,301,298],[128,79723,2801],{"className":79724},[259,1873,298],[128,79726,347],{"className":79727},[346],[128,79729,79731],{"className":79730},[278],[128,79732,79734],{"className":79733,"style":2241},[282],[128,79735],{}," 的函数，按图的拓扑序（即父节点排在子节点之前的节点序列）逐一代入，可归纳证明 ",[128,79738,79740,79810],{"className":79739,"translate":218},[217],[128,79741,79743],{"className":79742},[222],[224,79744,79745],{"xmlns":226},[228,79746,79747,79807],{},[231,79748,79749,79755,79757,79759,79761,79763,79765,79767,79773,79775,79781,79784,79790,79793,79795,79797],{},[2016,79750,79751,79753],{},[1795,79752,67963],{},[1795,79754,2801],{},[1832,79756,12150],{},[234,79758,8524],{},[234,79760,8524],{},[234,79762,8524],{},[1832,79764,12150],{},[1832,79766,1838],{"stretchy":1837},[2016,79768,79769,79771],{},[1795,79770,67963],{},[1795,79772,16495],{},[1832,79774,2014],{},[2016,79776,79777,79779],{},[1795,79778,67963],{},[1795,79780,16495],{},[234,79782,79783],{}," 非 ",[2016,79785,79786,79788],{},[1795,79787,67963],{},[1795,79789,2801],{},[234,79791,79792],{}," 的后代",[1832,79794,1856],{"stretchy":1837},[1832,79796,5443],{},[2016,79798,79799,79805],{},[231,79800,79801,79803],{},[1795,79802,23001],{"mathvariant":1981},[1795,79804,21],{"mathvariant":1981},[1795,79806,2801],{},[238,79808,79809],{"encoding":240},"V_i \\perp\\!\\!\\!\\perp \\{V_j : V_j \\text{ 非 } V_i\\text{ 的后代}\\} \\mid 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0,301,298],[128,80101,2801],{"className":80102},[259,1873,298],[128,80104,347],{"className":80105},[346],[128,80107,80109],{"className":80108},[278],[128,80110,80112],{"className":80111,"style":2241},[282],[128,80113],{},"，这正是定理 1.1 中马尔可夫性假设的来源，也是贝叶斯网络理论中「局部马尔可夫性」与「因子分解」等价性定理的因果版本。",[11,80116,80117,80118,80121],{},"这一定理揭示了 SCM 与传统贝叶斯网络的联系与区别：",[35,80119,80120],{},"二者在纯观测层面（第一层关联）诱导出相同的概率分解公式","，唯一的区别在于 SCM 额外赋予了每条边「直接原因」的因果语义，从而支持贝叶斯网络本身不具备的干预与反事实计算——这一区别将在第三部分具体展开。",[2610,80123,80125],{"id":80124},"_23-洒水器模型的-scm-表示","2.3 洒水器模型的 SCM 表示",[11,80127,80128,80129,44582],{},"沿用例 1.1 的因果图，一个具体的马尔可夫型 SCM 实例可定义如下。设内生变量均为二元 ",[128,80130,80132,80154],{"className":80131,"translate":218},[217],[128,80133,80135],{"className":80134},[222],[224,80136,80137],{"xmlns":226},[228,80138,80139,80151],{},[231,80140,80141,80143,80145,80147,80149],{},[1832,80142,1838],{"stretchy":1837},[1840,80144,2028],{},[1832,80146,1845],{"separator":246},[1840,80148,1842],{},[1832,80150,1856],{"stretchy":1837},[238,80152,80153],{"encoding":240},"\\{0,1\\}",[128,80155,80157],{"className":80156,"ariaHidden":246},[245],[128,80158,80160,80163,80166,80169,80172,80175,80178],{"className":80159},[250],[128,80161],{"className":80162,"style":1892},[254],[128,80164,1838],{"className":80165},[1896],[128,80167,2028],{"className":80168},[259],[128,80170,1845],{"className":80171},[1903],[128,80173],{"className":80174,"style":1907},[269],[128,80176,1842],{"className":80177},[259],[128,80179,1856],{"className":80180},[1928],[128,80182,80184],{"className":80183,"translate":218},[1962],[128,80185,80187,80832],{"className":80186,"translate":218},[217],[128,80188,80190],{"className":80189},[222],[224,80191,80192],{"xmlns":226,"display":1971},[228,80193,80194,80829],{},[8172,80195,80199,80276,80458,80659],{"rowspacing":80196,"columnalign":80197,"columnspacing":80198},"0.25em","right 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&:= U_S, &U_S &\\sim \\mathrm{Bernoulli}(0.3) \\\\\nR &:= \\mathbb{1}[S = 1] \\cdot U_R^{(1)} + \\mathbb{1}[S=0]\\cdot U_R^{(0)}, &U_R^{(1)} &\\sim \\mathrm{Bernoulli}(0.8),\\ U_R^{(0)} \\sim \\mathrm{Bernoulli}(0.1)\\\\\nSp &:= \\mathbb{1}[S=1]\\cdot U_{Sp}^{(1)} + \\mathbb{1}[S=0]\\cdot U_{Sp}^{(0)}, &U_{Sp}^{(1)} &\\sim \\mathrm{Bernoulli}(0.1),\\ U_{Sp}^{(0)} \\sim \\mathrm{Bernoulli}(0.6)\\\\\nW &:= \\max(R, Sp) \\cdot U_W + \\big(1-\\max(R,Sp)\\big)\\cdot U_W', &U_W &\\sim \\mathrm{Bernoulli}(0.95),\\ U_W' \\sim 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",[128,82394,82396,82409],{"className":82395,"translate":218},[217],[128,82397,82399],{"className":82398},[222],[224,82400,82401],{"xmlns":226},[228,82402,82403,82407],{},[231,82404,82405],{},[1795,82406,69050],{},[238,82408,69050],{"encoding":240},[128,82410,82412],{"className":82411,"ariaHidden":246},[245],[128,82413,82415,82418],{"className":82414},[250],[128,82416],{"className":82417,"style":283},[254],[128,82419,69050],{"className":82420,"style":26806},[259,1873]," 变量相互独立。这一具体赋值把因果图 ",[128,82423,82425,82438],{"className":82424,"translate":218},[217],[128,82426,82428],{"className":82427},[222],[224,82429,82430],{"xmlns":226},[228,82431,82432,82436],{},[231,82433,82434],{},[1795,82435,67956],{},[238,82437,67956],{"encoding":240},[128,82439,82441],{"className":82440,"ariaHidden":246},[245],[128,82442,82444,82447],{"className":82443},[250],[128,82445],{"className":82446,"style":283},[254],[128,82448,67956],{"className":82449},[259,1873]," 「填满」为一个可计算的生成过程：给定外生变量的一次采样（一次「自然实现」），内生变量的取值随之",[35,82452,82453],{},"唯一确定","。这正是结构方程「确定性」这一特征的体现——随机性完全由外生变量 ",[128,82456,82458,82471],{"className":82457,"translate":218},[217],[128,82459,82461],{"className":82460},[222],[224,82462,82463],{"xmlns":226},[228,82464,82465,82469],{},[231,82466,82467],{},[1795,82468,69050],{},[238,82470,69050],{"encoding":240},[128,82472,82474],{"className":82473,"ariaHidden":246},[245],[128,82475,82477,82480],{"className":82476},[250],[128,82478],{"className":82479,"style":283},[254],[128,82481,69050],{"className":82482,"style":26806},[259,1873]," 承担，内生变量之间的关系在给定 ",[128,82485,82487,82500],{"className":82486,"translate":218},[217],[128,82488,82490],{"className":82489},[222],[224,82491,82492],{"xmlns":226},[228,82493,82494,82498],{},[231,82495,82496],{},[1795,82497,69050],{},[238,82499,69050],{"encoding":240},[128,82501,82503],{"className":82502,"ariaHidden":246},[245],[128,82504,82506,82509],{"className":82505},[250],[128,82507],{"className":82508,"style":283},[254],[128,82510,69050],{"className":82511,"style":26806},[259,1873]," 后不再含有任何随机成分。这一设计并非技术上的简化，而是使后文反事实推理（第三部分 3.3 节）得以定义的必要前提：唯有把所有随机性封装进 ",[128,82514,82516,82529],{"className":82515,"translate":218},[217],[128,82517,82519],{"className":82518},[222],[224,82520,82521],{"xmlns":226},[228,82522,82523,82527],{},[231,82524,82525],{},[1795,82526,69050],{},[238,82528,69050],{"encoding":240},[128,82530,82532],{"className":82531,"ariaHidden":246},[245],[128,82533,82535,82538],{"className":82534},[250],[128,82536],{"className":82537,"style":283},[254],[128,82539,69050],{"className":82540,"style":26806},[259,1873],"，「同一个体在不同假设情景下会如何」这一问题才有明确的数学对象可以对应。",[51,82543,82544],{"id":82544},"结构方程与因果计算",[11,82546,82547,82548,82592],{},"第二部分给出的 SCM 已经具备了计算观测分布 ",[128,82549,82551,82571],{"className":82550,"translate":218},[217],[128,82552,82554],{"className":82553},[222],[224,82555,82556],{"xmlns":226},[228,82557,82558,82568],{},[231,82559,82560,82562,82564,82566],{},[1795,82561,23001],{},[1832,82563,2477],{"stretchy":1837},[1795,82565,67963],{},[1832,82567,2486],{"stretchy":1837},[238,82569,82570],{"encoding":240},"P(V)",[128,82572,82574],{"className":82573,"ariaHidden":246},[245],[128,82575,82577,82580,82583,82586,82589],{"className":82576},[250],[128,82578],{"className":82579,"style":1892},[254],[128,82581,23001],{"className":82582,"style":36065},[259,1873],[128,82584,2477],{"className":82585},[1896],[128,82587,67963],{"className":82588,"style":2508},[259,1873],[128,82590,2486],{"className":82591},[1928]," 的全部要素。本部分讨论结构方程如何进一步支持第二、三层的因果计算。",[2610,82594,82596],{"id":82595},"_31-结构方程的非对称性","3.1 结构方程的非对称性",[2615,82598,82600],{"title":82599},"定义 3.1（结构方程 vs. 代数方程）",[11,82601,82602,82603,82671,82672,82738,82739,82742,82743,82746,82747,82775,82776,82804,82805,82911,82912,2674,82963,82991,82992,82995,82996,83024,83025,83053,83054,83057],{},"形如 ",[128,82604,82606,82632],{"className":82605,"translate":218},[217],[128,82607,82609],{"className":82608},[222],[224,82610,82611],{"xmlns":226},[228,82612,82613,82629],{},[231,82614,82615,82617,82619,82621,82623,82625,82627],{},[1795,82616,35023],{},[1832,82618,2014],{},[1832,82620,1994],{},[1795,82622,5436],{},[1832,82624,2477],{"stretchy":1837},[1795,82626,364],{},[1832,82628,2486],{"stretchy":1837},[238,82630,82631],{"encoding":240},"Y := f(X)",[128,82633,82635,82653],{"className":82634,"ariaHidden":246},[245],[128,82636,82638,82641,82644,82647,82650],{"className":82637},[250],[128,82639],{"className":82640,"style":283},[254],[128,82642,35023],{"className":82643,"style":2508},[259,1873],[128,82645],{"className":82646,"style":1878},[269],[128,82648,75429],{"className":82649},[1882],[128,82651],{"className":82652,"style":1878},[269],[128,82654,82656,82659,82662,82665,82668],{"className":82655},[250],[128,82657],{"className":82658,"style":1892},[254],[128,82660,5436],{"className":82661,"style":5514},[259,1873],[128,82663,2477],{"className":82664},[1896],[128,82666,364],{"className":82667,"style":30665},[259,1873],[128,82669,2486],{"className":82670},[1928]," 的结构方程与代数方程 ",[128,82673,82675,82699],{"className":82674,"translate":218},[217],[128,82676,82678],{"className":82677},[222],[224,82679,82680],{"xmlns":226},[228,82681,82682,82696],{},[231,82683,82684,82686,82688,82690,82692,82694],{},[1795,82685,35023],{},[1832,82687,1994],{},[1795,82689,5436],{},[1832,82691,2477],{"stretchy":1837},[1795,82693,364],{},[1832,82695,2486],{"stretchy":1837},[238,82697,82698],{"encoding":240},"Y = f(X)",[128,82700,82702,82720],{"className":82701,"ariaHidden":246},[245],[128,82703,82705,82708,82711,82714,82717],{"className":82704},[250],[128,82706],{"className":82707,"style":283},[254],[128,82709,35023],{"className":82710,"style":2508},[259,1873],[128,82712],{"className":82713,"style":1878},[269],[128,82715,1994],{"className":82716},[1882],[128,82718],{"className":82719,"style":1878},[269],[128,82721,82723,82726,82729,82732,82735],{"className":82722},[250],[128,82724],{"className":82725,"style":1892},[254],[128,82727,5436],{"className":82728,"style":5514},[259,1873],[128,82730,2477],{"className":82731},[1896],[128,82733,364],{"className":82734,"style":30665},[259,1873],[128,82736,2486],{"className":82737},[1928]," 在数值上等价，但语义不同：结构方程蕴含一种非对称的",[35,82740,82741],{},"生成关系","，规定右边变量的取值决定左边变量的取值，而这一决定关系",[35,82744,82745],{},"不可逆","——即便 ",[128,82748,82750,82763],{"className":82749,"translate":218},[217],[128,82751,82753],{"className":82752},[222],[224,82754,82755],{"xmlns":226},[228,82756,82757,82761],{},[231,82758,82759],{},[1795,82760,5436],{},[238,82762,5436],{"encoding":240},[128,82764,82766],{"className":82765,"ariaHidden":246},[245],[128,82767,82769,82772],{"className":82768},[250],[128,82770],{"className":82771,"style":16030},[254],[128,82773,5436],{"className":82774,"style":5514},[259,1873]," 可逆，从 ",[128,82777,82779,82792],{"className":82778,"translate":218},[217],[128,82780,82782],{"className":82781},[222],[224,82783,82784],{"xmlns":226},[228,82785,82786,82790],{},[231,82787,82788],{},[1795,82789,1830],{},[238,82791,1830],{"encoding":240},[128,82793,82795],{"className":82794,"ariaHidden":246},[245],[128,82796,82798,82801],{"className":82797},[250],[128,82799],{"className":82800,"style":11158},[254],[128,82802,1830],{"className":82803,"style":1874},[259,1873]," 反解出 ",[128,82806,82808,82840],{"className":82807,"translate":218},[217],[128,82809,82811],{"className":82810},[222],[224,82812,82813],{"xmlns":226},[228,82814,82815,82837],{},[231,82816,82817,82819,82821,82831,82833,82835],{},[1795,82818,2760],{},[1832,82820,1994],{},[1977,82822,82823,82825],{},[1795,82824,5436],{},[231,82826,82827,82829],{},[1832,82828,1989],{},[1840,82830,1842],{},[1832,82832,2477],{"stretchy":1837},[1795,82834,1830],{},[1832,82836,2486],{"stretchy":1837},[238,82838,82839],{"encoding":240},"x = f^{-1}(y)",[128,82841,82843,82861],{"className":82842,"ariaHidden":246},[245],[128,82844,82846,82849,82852,82855,82858],{"className":82845},[250],[128,82847],{"className":82848,"style":7758},[254],[128,82850,2760],{"className":82851},[259,1873],[128,82853],{"className":82854,"style":1878},[269],[128,82856,1994],{"className":82857},[1882],[128,82859],{"className":82860,"style":1878},[269],[128,82862,82864,82867,82902,82905,82908],{"className":82863},[250],[128,82865],{"className":82866,"style":23130},[254],[128,82868,82870,82873],{"className":82869},[259],[128,82871,5436],{"className":82872,"style":5514},[259,1873],[128,82874,82876],{"className":82875},[2087],[128,82877,82879],{"className":82878},[274],[128,82880,82882],{"className":82881},[278],[128,82883,82885],{"className":82884,"style":9629},[282],[128,82886,82887,82890],{"style":2452},[128,82888],{"className":82889,"style":291},[290],[128,82891,82893],{"className":82892},[299,300,301,298],[128,82894,82896,82899],{"className":82895},[259,298],[128,82897,1989],{"className":82898},[259,298],[128,82900,1842],{"className":82901},[259,298],[128,82903,2477],{"className":82904},[1896],[128,82906,1830],{"className":82907,"style":1874},[259,1873],[128,82909,2486],{"className":82910},[1928]," 得到的也只是「给定 ",[128,82913,82915,82933],{"className":82914,"translate":218},[217],[128,82916,82918],{"className":82917},[222],[224,82919,82920],{"xmlns":226},[228,82921,82922,82930],{},[231,82923,82924,82926,82928],{},[1795,82925,35023],{},[1832,82927,1994],{},[1795,82929,1830],{},[238,82931,82932],{"encoding":240},"Y=y",[128,82934,82936,82954],{"className":82935,"ariaHidden":246},[245],[128,82937,82939,82942,82945,82948,82951],{"className":82938},[250],[128,82940],{"className":82941,"style":283},[254],[128,82943,35023],{"className":82944,"style":2508},[259,1873],[128,82946],{"className":82947,"style":1878},[269],[128,82949,1994],{"className":82950},[1882],[128,82952],{"className":82953,"style":1878},[269],[128,82955,82957,82960],{"className":82956},[250],[128,82958],{"className":82959,"style":11158},[254],[128,82961,1830],{"className":82962,"style":1874},[259,1873],[128,82964,82966,82979],{"className":82965,"translate":218},[217],[128,82967,82969],{"className":82968},[222],[224,82970,82971],{"xmlns":226},[228,82972,82973,82977],{},[231,82974,82975],{},[1795,82976,364],{},[238,82978,364],{"encoding":240},[128,82980,82982],{"className":82981,"ariaHidden":246},[245],[128,82983,82985,82988],{"className":82984},[250],[128,82986],{"className":82987,"style":283},[254],[128,82989,364],{"className":82990,"style":30665},[259,1873]," 的取值应为多少」这一",[35,82993,82994],{},"代数","关系，而非「改变 ",[128,82997,82999,83012],{"className":82998,"translate":218},[217],[128,83000,83002],{"className":83001},[222],[224,83003,83004],{"xmlns":226},[228,83005,83006,83010],{},[231,83007,83008],{},[1795,83009,364],{},[238,83011,364],{"encoding":240},[128,83013,83015],{"className":83014,"ariaHidden":246},[245],[128,83016,83018,83021],{"className":83017},[250],[128,83019],{"className":83020,"style":283},[254],[128,83022,364],{"className":83023,"style":30665},[259,1873]," 会如何改变 ",[128,83026,83028,83041],{"className":83027,"translate":218},[217],[128,83029,83031],{"className":83030},[222],[224,83032,83033],{"xmlns":226},[228,83034,83035,83039],{},[231,83036,83037],{},[1795,83038,35023],{},[238,83040,35023],{"encoding":240},[128,83042,83044],{"className":83043,"ariaHidden":246},[245],[128,83045,83047,83050],{"className":83046},[250],[128,83048],{"className":83049,"style":283},[254],[128,83051,35023],{"className":83052,"style":2508},[259,1873],"」这一",[35,83055,83056],{},"因果","关系的镜像。",[2615,83059,83061],{"title":83060},"例 3.1（欧姆定律的因果解读）",[11,83062,83063,83064,83092,83093,83121,83122,83185,83186,63140,83244,83307,83308,83311,83312,83405,83406,1148,83409,83437,83438,83535,83536,83564,83565,83627,83628,893],{},"设某电路中电压源固定输出 ",[128,83065,83067,83080],{"className":83066,"translate":218},[217],[128,83068,83070],{"className":83069},[222],[224,83071,83072],{"xmlns":226},[228,83073,83074,83078],{},[231,83075,83076],{},[1795,83077,67963],{},[238,83079,67963],{"encoding":240},[128,83081,83083],{"className":83082,"ariaHidden":246},[245],[128,83084,83086,83089],{"className":83085},[250],[128,83087],{"className":83088,"style":283},[254],[128,83090,67963],{"className":83091,"style":2508},[259,1873],"，电阻为 ",[128,83094,83096,83109],{"className":83095,"translate":218},[217],[128,83097,83099],{"className":83098},[222],[224,83100,83101],{"xmlns":226},[228,83102,83103,83107],{},[231,83104,83105],{},[1795,83106,2009],{},[238,83108,2009],{"encoding":240},[128,83110,83112],{"className":83111,"ariaHidden":246},[245],[128,83113,83115,83118],{"className":83114},[250],[128,83116],{"className":83117,"style":283},[254],[128,83119,2009],{"className":83120,"style":70411},[259,1873],"，依据电路物理机制，电流由前两者共同决定：结构方程应写作\n",[128,83123,83125,83149],{"className":83124,"translate":218},[217],[128,83126,83128],{"className":83127},[222],[224,83129,83130],{"xmlns":226},[228,83131,83132,83146],{},[231,83133,83134,83136,83138,83140,83142,83144],{},[1795,83135,30626],{},[1832,83137,2014],{},[1832,83139,1994],{},[1795,83141,67963],{},[1795,83143,4751],{"mathvariant":1981},[1795,83145,2009],{},[238,83147,83148],{"encoding":240},"I := V\u002FR",[128,83150,83152,83170],{"className":83151,"ariaHidden":246},[245],[128,83153,83155,83158,83161,83164,83167],{"className":83154},[250],[128,83156],{"className":83157,"style":283},[254],[128,83159,30626],{"className":83160,"style":30665},[259,1873],[128,83162],{"className":83163,"style":1878},[269],[128,83165,75429],{"className":83166},[1882],[128,83168],{"className":83169,"style":1878},[269],[128,83171,83173,83176,83179,83182],{"className":83172},[250],[128,83174],{"className":83175,"style":1892},[254],[128,83177,67963],{"className":83178,"style":2508},[259,1873],[128,83180,4751],{"className":83181},[259],[128,83183,2009],{"className":83184,"style":70411},[259,1873],"\n而非 ",[128,83187,83189,83211],{"className":83188,"translate":218},[217],[128,83190,83192],{"className":83191},[222],[224,83193,83194],{"xmlns":226},[228,83195,83196,83208],{},[231,83197,83198,83200,83202,83204,83206],{},[1795,83199,67963],{},[1832,83201,2014],{},[1832,83203,1994],{},[1795,83205,30626],{},[1795,83207,2009],{},[238,83209,83210],{"encoding":240},"V := IR",[128,83212,83214,83232],{"className":83213,"ariaHidden":246},[245],[128,83215,83217,83220,83223,83226,83229],{"className":83216},[250],[128,83218],{"className":83219,"style":283},[254],[128,83221,67963],{"className":83222,"style":2508},[259,1873],[128,83224],{"className":83225,"style":1878},[269],[128,83227,75429],{"className":83228},[1882],[128,83230],{"className":83231,"style":1878},[269],[128,83233,83235,83238,83241],{"className":83234},[250],[128,83236],{"className":83237,"style":283},[254],[128,83239,30626],{"className":83240,"style":30665},[259,1873],[128,83242,2009],{"className":83243,"style":70411},[259,1873],[128,83245,83247,83271],{"className":83246,"translate":218},[217],[128,83248,83250],{"className":83249},[222],[224,83251,83252],{"xmlns":226},[228,83253,83254,83268],{},[231,83255,83256,83258,83260,83262,83264,83266],{},[1795,83257,2009],{},[1832,83259,2014],{},[1832,83261,1994],{},[1795,83263,67963],{},[1795,83265,4751],{"mathvariant":1981},[1795,83267,30626],{},[238,83269,83270],{"encoding":240},"R := V\u002FI",[128,83272,83274,83292],{"className":83273,"ariaHidden":246},[245],[128,83275,83277,83280,83283,83286,83289],{"className":83276},[250],[128,83278],{"className":83279,"style":283},[254],[128,83281,2009],{"className":83282,"style":70411},[259,1873],[128,83284],{"className":83285,"style":1878},[269],[128,83287,75429],{"className":83288},[1882],[128,83290],{"className":83291,"style":1878},[269],[128,83293,83295,83298,83301,83304],{"className":83294},[250],[128,83296],{"className":83297,"style":1892},[254],[128,83299,67963],{"className":83300,"style":2508},[259,1873],[128,83302,4751],{"className":83303},[259],[128,83305,30626],{"className":83306,"style":30665},[259,1873],"。三个代数式在数值上完全等价，但只有前者正确刻画了该电路的",[35,83309,83310],{},"生成机制","。这一区分的实践意义在于：若外部操作者通过某种装置强行将电流设定为 ",[128,83313,83315,83337],{"className":83314,"translate":218},[217],[128,83316,83318],{"className":83317},[222],[224,83319,83320],{"xmlns":226},[228,83321,83322,83334],{},[231,83323,83324,83326,83328],{},[1795,83325,30626],{},[1832,83327,1994],{},[2016,83329,83330,83332],{},[1795,83331,2801],{},[1840,83333,2028],{},[238,83335,83336],{"encoding":240},"I = i_0",[128,83338,83340,83358],{"className":83339,"ariaHidden":246},[245],[128,83341,83343,83346,83349,83352,83355],{"className":83342},[250],[128,83344],{"className":83345,"style":283},[254],[128,83347,30626],{"className":83348,"style":30665},[259,1873],[128,83350],{"className":83351,"style":1878},[269],[128,83353,1994],{"className":83354},[1882],[128,83356],{"className":83357,"style":1878},[269],[128,83359,83361,83365],{"className":83360},[250],[128,83362],{"className":83363,"style":83364},[254],"height:0.8095em;vertical-align:-0.15em;",[128,83366,83368,83371],{"className":83367},[259],[128,83369,2801],{"className":83370},[259,1873],[128,83372,83374],{"className":83373},[2087],[128,83375,83377,83397],{"className":83376},[274,321],[128,83378,83380,83394],{"className":83379},[278],[128,83381,83383],{"className":83382,"style":2945},[282],[128,83384,83385,83388],{"style":2221},[128,83386],{"className":83387,"style":291},[290],[128,83389,83391],{"className":83390},[299,300,301,298],[128,83392,2028],{"className":83393},[259,298],[128,83395,347],{"className":83396},[346],[128,83398,83400],{"className":83399},[278],[128,83401,83403],{"className":83402,"style":2241},[282],[128,83404],{},"（例如接入恒流源），依据正确的结构方程，会导致",[35,83407,83408],{},"电压",[128,83410,83412,83425],{"className":83411,"translate":218},[217],[128,83413,83415],{"className":83414},[222],[224,83416,83417],{"xmlns":226},[228,83418,83419,83423],{},[231,83420,83421],{},[1795,83422,67963],{},[238,83424,67963],{"encoding":240},[128,83426,83428],{"className":83427,"ariaHidden":246},[245],[128,83429,83431,83434],{"className":83430},[250],[128,83432],{"className":83433,"style":283},[254],[128,83435,67963],{"className":83436,"style":2508},[259,1873]," 相应改变以满足 ",[128,83439,83441,83465],{"className":83440,"translate":218},[217],[128,83442,83444],{"className":83443},[222],[224,83445,83446],{"xmlns":226},[228,83447,83448,83462],{},[231,83449,83450,83452,83454,83460],{},[1795,83451,67963],{},[1832,83453,1994],{},[2016,83455,83456,83458],{},[1795,83457,2801],{},[1840,83459,2028],{},[1795,83461,2009],{},[238,83463,83464],{"encoding":240},"V = i_0 R",[128,83466,83468,83486],{"className":83467,"ariaHidden":246},[245],[128,83469,83471,83474,83477,83480,83483],{"className":83470},[250],[128,83472],{"className":83473,"style":283},[254],[128,83475,67963],{"className":83476,"style":2508},[259,1873],[128,83478],{"className":83479,"style":1878},[269],[128,83481,1994],{"className":83482},[1882],[128,83484],{"className":83485,"style":1878},[269],[128,83487,83489,83492,83532],{"className":83488},[250],[128,83490],{"className":83491,"style":36058},[254],[128,83493,83495,83498],{"className":83494},[259],[128,83496,2801],{"className":83497},[259,1873],[128,83499,83501],{"className":83500},[2087],[128,83502,83504,83524],{"className":83503},[274,321],[128,83505,83507,83521],{"className":83506},[278],[128,83508,83510],{"className":83509,"style":2945},[282],[128,83511,83512,83515],{"style":2221},[128,83513],{"className":83514,"style":291},[290],[128,83516,83518],{"className":83517},[299,300,301,298],[128,83519,2028],{"className":83520},[259,298],[128,83522,347],{"className":83523},[346],[128,83525,83527],{"className":83526},[278],[128,83528,83530],{"className":83529,"style":2241},[282],[128,83531],{},[128,83533,2009],{"className":83534,"style":70411},[259,1873],"，而电阻 ",[128,83537,83539,83552],{"className":83538,"translate":218},[217],[128,83540,83542],{"className":83541},[222],[224,83543,83544],{"xmlns":226},[228,83545,83546,83550],{},[231,83547,83548],{},[1795,83549,2009],{},[238,83551,2009],{"encoding":240},[128,83553,83555],{"className":83554,"ariaHidden":246},[245],[128,83556,83558,83561],{"className":83557},[250],[128,83559],{"className":83560,"style":283},[254],[128,83562,2009],{"className":83563,"style":70411},[259,1873]," 不受影响；若错误地采用 ",[128,83566,83568,83591],{"className":83567,"translate":218},[217],[128,83569,83571],{"className":83570},[222],[224,83572,83573],{"xmlns":226},[228,83574,83575,83589],{},[231,83576,83577,83579,83581,83583,83585,83587],{},[1795,83578,2009],{},[1832,83580,2014],{},[1832,83582,1994],{},[1795,83584,67963],{},[1795,83586,4751],{"mathvariant":1981},[1795,83588,30626],{},[238,83590,83270],{"encoding":240},[128,83592,83594,83612],{"className":83593,"ariaHidden":246},[245],[128,83595,83597,83600,83603,83606,83609],{"className":83596},[250],[128,83598],{"className":83599,"style":283},[254],[128,83601,2009],{"className":83602,"style":70411},[259,1873],[128,83604],{"className":83605,"style":1878},[269],[128,83607,75429],{"className":83608},[1882],[128,83610],{"className":83611,"style":1878},[269],[128,83613,83615,83618,83621,83624],{"className":83614},[250],[128,83616],{"className":83617,"style":1892},[254],[128,83619,67963],{"className":83620,"style":2508},[259,1873],[128,83622,4751],{"className":83623},[259],[128,83625,30626],{"className":83626,"style":30665},[259,1873]," 作为该情境下的结构方程，则会得出「电阻会因电流改变而改变」这一荒谬结论。",[35,83629,83630],{},"选对结构方程的方向，等价于选对了系统中「谁是自变量、谁是因变量」这一物理事实，这一信息无法从代数关系本身获得，必须来自对系统机制的外部知识",[2610,83632,83634],{"id":83633},"_32-干预与-do-算子","3.2 干预与 do-算子",[2615,83636,83638],{"title":83637},"定义 3.2（干预，do-operator）",[11,83639,77578,83640,83752,83753,83804,83805,83875,83876,1148,83879,84073,84074,84304,84305,84333,84334,84521],{},[128,83641,83643,83683],{"className":83642,"translate":218},[217],[128,83644,83646],{"className":83645},[222],[224,83647,83648],{"xmlns":226},[228,83649,83650,83680],{},[231,83651,83652,83654,83656,83658,83660,83662,83664,83666,83668,83670,83672,83674,83676,83678],{},[1795,83653,30641],{},[1832,83655,1994],{},[1832,83657,64962],{"stretchy":1837},[1795,83659,69050],{},[1832,83661,1845],{"separator":246},[1795,83663,67963],{},[1832,83665,1845],{"separator":246},[1795,83667,76009],{},[1832,83669,1845],{"separator":246},[1795,83671,23001],{},[1832,83673,2477],{"stretchy":1837},[1795,83675,69050],{},[1832,83677,2486],{"stretchy":1837},[1832,83679,64975],{"stretchy":1837},[238,83681,83682],{"encoding":240},"M = \\langle U,V,F,P(U)\\rangle",[128,83684,83686,83704],{"className":83685,"ariaHidden":246},[245],[128,83687,83689,83692,83695,83698,83701],{"className":83688},[250],[128,83690],{"className":83691,"style":283},[254],[128,83693,30641],{"className":83694,"style":26806},[259,1873],[128,83696],{"className":83697,"style":1878},[269],[128,83699,1994],{"className":83700},[1882],[128,83702],{"className":83703,"style":1878},[269],[128,83705,83707,83710,83713,83716,83719,83722,83725,83728,83731,83734,83737,83740,83743,83746,83749],{"className":83706},[250],[128,83708],{"className":83709,"style":1892},[254],[128,83711,64962],{"className":83712},[1896],[128,83714,69050],{"className":83715,"style":26806},[259,1873],[128,83717,1845],{"className":83718},[1903],[128,83720],{"className":83721,"style":1907},[269],[128,83723,67963],{"className":83724,"style":2508},[259,1873],[128,83726,1845],{"className":83727},[1903],[128,83729],{"className":83730,"style":1907},[269],[128,83732,76009],{"className":83733,"style":36065},[259,1873],[128,83735,1845],{"className":83736},[1903],[128,83738],{"className":83739,"style":1907},[269],[128,83741,23001],{"className":83742,"style":36065},[259,1873],[128,83744,2477],{"className":83745},[1896],[128,83747,69050],{"className":83748,"style":26806},[259,1873],[128,83750,76094],{"className":83751},[1928],"，对变量 ",[128,83754,83756,83774],{"className":83755,"translate":218},[217],[128,83757,83759],{"className":83758},[222],[224,83760,83761],{"xmlns":226},[228,83762,83763,83771],{},[231,83764,83765,83767,83769],{},[1795,83766,364],{},[1832,83768,1834],{},[1795,83770,67963],{},[238,83772,83773],{"encoding":240},"X \\in V",[128,83775,83777,83795],{"className":83776,"ariaHidden":246},[245],[128,83778,83780,83783,83786,83789,83792],{"className":83779},[250],[128,83781],{"className":83782,"style":73189},[254],[128,83784,364],{"className":83785,"style":30665},[259,1873],[128,83787],{"className":83788,"style":1878},[269],[128,83790,1834],{"className":83791},[1882],[128,83793],{"className":83794,"style":1878},[269],[128,83796,83798,83801],{"className":83797},[250],[128,83799],{"className":83800,"style":283},[254],[128,83802,67963],{"className":83803,"style":2508},[259,1873]," 施加干预 ",[128,83806,83808,83833],{"className":83807,"translate":218},[217],[128,83809,83811],{"className":83810},[222],[224,83812,83813],{"xmlns":226},[228,83814,83815,83831],{},[231,83816,83817,83819,83821,83823,83825,83827,83829],{},[1795,83818,4519],{},[1795,83820,67350],{},[1832,83822,2477],{"stretchy":1837},[1795,83824,364],{},[1832,83826,1994],{},[1795,83828,2760],{},[1832,83830,2486],{"stretchy":1837},[238,83832,74610],{"encoding":240},[128,83834,83836,83863],{"className":83835,"ariaHidden":246},[245],[128,83837,83839,83842,83845,83848,83851,83854,83857,83860],{"className":83838},[250],[128,83840],{"className":83841,"style":1892},[254],[128,83843,4519],{"className":83844},[259,1873],[128,83846,67350],{"className":83847},[259,1873],[128,83849,2477],{"className":83850},[1896],[128,83852,364],{"className":83853,"style":30665},[259,1873],[128,83855],{"className":83856,"style":1878},[269],[128,83858,1994],{"className":83859},[1882],[128,83861],{"className":83862,"style":1878},[269],[128,83864,83866,83869,83872],{"className":83865},[250],[128,83867],{"className":83868,"style":1892},[254],[128,83870,2760],{"className":83871},[259,1873],[128,83873,2486],{"className":83874},[1928],"，得到一个新的",[35,83877,83878],{},"子模型（submodel）",[128,83880,83882,83930],{"className":83881,"translate":218},[217],[128,83883,83885],{"className":83884},[222],[224,83886,83887],{"xmlns":226},[228,83888,83889,83927],{},[231,83890,83891,83897,83899,83901,83903,83905,83907,83909,83915,83917,83919,83921,83923,83925],{},[2016,83892,83893,83895],{},[1795,83894,30641],{},[1795,83896,2760],{},[1832,83898,1994],{},[1832,83900,64962],{"stretchy":1837},[1795,83902,69050],{},[1832,83904,1845],{"separator":246},[1795,83906,67963],{},[1832,83908,1845],{"separator":246},[2016,83910,83911,83913],{},[1795,83912,76009],{},[1795,83914,2760],{},[1832,83916,1845],{"separator":246},[1795,83918,23001],{},[1832,83920,2477],{"stretchy":1837},[1795,83922,69050],{},[1832,83924,2486],{"stretchy":1837},[1832,83926,64975],{"stretchy":1837},[238,83928,83929],{"encoding":240},"M_x = \\langle U, V, F_x, P(U)\\rangle",[128,83931,83933,83988],{"className":83932,"ariaHidden":246},[245],[128,83934,83936,83939,83979,83982,83985],{"className":83935},[250],[128,83937],{"className":83938,"style":36058},[254],[128,83940,83942,83945],{"className":83941},[259],[128,83943,30641],{"className":83944,"style":26806},[259,1873],[128,83946,83948],{"className":83947},[2087],[128,83949,83951,83971],{"className":83950},[274,321],[128,83952,83954,83968],{"className":83953},[278],[128,83955,83957],{"className":83956,"style":28738},[282],[128,83958,83959,83962],{"style":64697},[128,83960],{"className":83961,"style":291},[290],[128,83963,83965],{"className":83964},[299,300,301,298],[128,83966,2760],{"className":83967},[259,1873,298],[128,83969,347],{"className":83970},[346],[128,83972,83974],{"className":83973},[278],[128,83975,83977],{"className":83976,"style":2241},[282],[128,83978],{},[128,83980],{"className":83981,"style":1878},[269],[128,83983,1994],{"className":83984},[1882],[128,83986],{"className":83987,"style":1878},[269],[128,83989,83991,83994,83997,84000,84003,84006,84009,84012,84015,84055,84058,84061,84064,84067,84070],{"className":83990},[250],[128,83992],{"className":83993,"style":1892},[254],[128,83995,64962],{"className":83996},[1896],[128,83998,69050],{"className":83999,"style":26806},[259,1873],[128,84001,1845],{"className":84002},[1903],[128,84004],{"className":84005,"style":1907},[269],[128,84007,67963],{"className":84008,"style":2508},[259,1873],[128,84010,1845],{"className":84011},[1903],[128,84013],{"className":84014,"style":1907},[269],[128,84016,84018,84021],{"className":84017},[259],[128,84019,76009],{"className":84020,"style":36065},[259,1873],[128,84022,84024],{"className":84023},[2087],[128,84025,84027,84047],{"className":84026},[274,321],[128,84028,84030,84044],{"className":84029},[278],[128,84031,84033],{"className":84032,"style":28738},[282],[128,84034,84035,84038],{"style":36080},[128,84036],{"className":84037,"style":291},[290],[128,84039,84041],{"className":84040},[299,300,301,298],[128,84042,2760],{"className":84043},[259,1873,298],[128,84045,347],{"className":84046},[346],[128,84048,84050],{"className":84049},[278],[128,84051,84053],{"className":84052,"style":2241},[282],[128,84054],{},[128,84056,1845],{"className":84057},[1903],[128,84059],{"className":84060,"style":1907},[269],[128,84062,23001],{"className":84063,"style":36065},[259,1873],[128,84065,2477],{"className":84066},[1896],[128,84068,69050],{"className":84069,"style":26806},[259,1873],[128,84071,76094],{"className":84072},[1928],"，其中\n",[128,84075,84077,84130],{"className":84076,"translate":218},[217],[128,84078,84080],{"className":84079},[222],[224,84081,84082],{"xmlns":226},[228,84083,84084,84127],{},[231,84085,84086,84092,84094,84096,84098,84100,84102,84108,84110,84112,84115,84117,84119,84121,84123,84125],{},[2016,84087,84088,84090],{},[1795,84089,76009],{},[1795,84091,2760],{},[1832,84093,1994],{},[1832,84095,2477],{"stretchy":1837},[1795,84097,76009],{},[1832,84099,76772],{},[1832,84101,1838],{"stretchy":1837},[2016,84103,84104,84106],{},[1795,84105,5436],{},[1795,84107,364],{},[1832,84109,1856],{"stretchy":1837},[1832,84111,2486],{"stretchy":1837},[1832,84113,84114],{},"∪",[1832,84116,1838],{"stretchy":1837},[1795,84118,364],{},[1832,84120,2014],{},[1832,84122,1994],{},[1795,84124,2760],{},[1832,84126,1856],{"stretchy":1837},[238,84128,84129],{"encoding":240},"F_x = (F \\setminus \\{f_X\\}) \\cup \\{X := x\\}",[128,84131,84133,84188,84209,84271,84292],{"className":84132,"ariaHidden":246},[245],[128,84134,84136,84139,84179,84182,84185],{"className":84135},[250],[128,84137],{"className":84138,"style":36058},[254],[128,84140,84142,84145],{"className":84141},[259],[128,84143,76009],{"className":84144,"style":36065},[259,1873],[128,84146,84148],{"className":84147},[2087],[128,84149,84151,84171],{"className":84150},[274,321],[128,84152,84154,84168],{"className":84153},[278],[128,84155,84157],{"className":84156,"style":28738},[282],[128,84158,84159,84162],{"style":36080},[128,84160],{"className":84161,"style":291},[290],[128,84163,84165],{"className":84164},[299,300,301,298],[128,84166,2760],{"className":84167},[259,1873,298],[128,84169,347],{"className":84170},[346],[128,84172,84174],{"className":84173},[278],[128,84175,84177],{"className":84176,"style":2241},[282],[128,84178],{},[128,84180],{"className":84181,"style":1878},[269],[128,84183,1994],{"className":84184},[1882],[128,84186],{"className":84187,"style":1878},[269],[128,84189,84191,84194,84197,84200,84203,84206],{"className":84190},[250],[128,84192],{"className":84193,"style":1892},[254],[128,84195,2477],{"className":84196},[1896],[128,84198,76009],{"className":84199,"style":36065},[259,1873],[128,84201],{"className":84202,"style":2508},[269],[128,84204,76772],{"className":84205},[2115],[128,84207],{"className":84208,"style":2508},[269],[128,84210,84212,84215,84218,84258,84262,84265,84268],{"className":84211},[250],[128,84213],{"className":84214,"style":1892},[254],[128,84216,1838],{"className":84217},[1896],[128,84219,84221,84224],{"className":84220},[259],[128,84222,5436],{"className":84223,"style":5514},[259,1873],[128,84225,84227],{"className":84226},[2087],[128,84228,84230,84250],{"className":84229},[274,321],[128,84231,84233,84247],{"className":84232},[278],[128,84234,84236],{"className":84235,"style":3004},[282],[128,84237,84238,84241],{"style":38889},[128,84239],{"className":84240,"style":291},[290],[128,84242,84244],{"className":84243},[299,300,301,298],[128,84245,364],{"className":84246,"style":30665},[259,1873,298],[128,84248,347],{"className":84249},[346],[128,84251,84253],{"className":84252},[278],[128,84254,84256],{"className":84255,"style":2241},[282],[128,84257],{},[128,84259,84261],{"className":84260},[1928],"})",[128,84263],{"className":84264,"style":2508},[269],[128,84266,84114],{"className":84267},[2115],[128,84269],{"className":84270,"style":2508},[269],[128,84272,84274,84277,84280,84283,84286,84289],{"className":84273},[250],[128,84275],{"className":84276,"style":1892},[254],[128,84278,1838],{"className":84279},[1896],[128,84281,364],{"className":84282,"style":30665},[259,1873],[128,84284],{"className":84285,"style":1878},[269],[128,84287,75429],{"className":84288},[1882],[128,84290],{"className":84291,"style":1878},[269],[128,84293,84295,84298,84301],{"className":84294},[250],[128,84296],{"className":84297,"style":1892},[254],[128,84299,2760],{"className":84300},[259,1873],[128,84302,1856],{"className":84303},[1928],"\n即把 ",[128,84306,84308,84321],{"className":84307,"translate":218},[217],[128,84309,84311],{"className":84310},[222],[224,84312,84313],{"xmlns":226},[228,84314,84315,84319],{},[231,84316,84317],{},[1795,84318,364],{},[238,84320,364],{"encoding":240},[128,84322,84324],{"className":84323,"ariaHidden":246},[245],[128,84325,84327,84330],{"className":84326},[250],[128,84328],{"className":84329,"style":283},[254],[128,84331,364],{"className":84332,"style":30665},[259,1873]," 原有的结构方程 ",[128,84335,84337,84377],{"className":84336,"translate":218},[217],[128,84338,84340],{"className":84339},[222],[224,84341,84342],{"xmlns":226},[228,84343,84344,84374],{},[231,84345,84346,84352,84354,84364,84366,84372],{},[2016,84347,84348,84350],{},[1795,84349,5436],{},[1795,84351,364],{},[1832,84353,2477],{"stretchy":1837},[2016,84355,84356,84362],{},[231,84357,84358,84360],{},[1795,84359,23001],{"mathvariant":1981},[1795,84361,21],{"mathvariant":1981},[1795,84363,364],{},[1832,84365,1845],{"separator":246},[2016,84367,84368,84370],{},[1795,84369,69050],{},[1795,84371,364],{},[1832,84373,2486],{"stretchy":1837},[238,84375,84376],{"encoding":240},"f_X(\\mathrm{Pa}_X, U_X)",[128,84378,84380],{"className":84379,"ariaHidden":246},[245],[128,84381,84383,84386,84426,84429,84472,84475,84478,84518],{"className":84382},[250],[128,84384],{"className":84385,"style":1892},[254],[128,84387,84389,84392],{"className":84388},[259],[128,84390,5436],{"className":84391,"style":5514},[259,1873],[128,84393,84395],{"className":84394},[2087],[128,84396,84398,84418],{"className":84397},[274,321],[128,84399,84401,84415],{"className":84400},[278],[128,84402,84404],{"className":84403,"style":3004},[282],[128,84405,84406,84409],{"style":38889},[128,84407],{"className":84408,"style":291},[290],[128,84410,84412],{"className":84411},[299,300,301,298],[128,84413,364],{"className":84414,"style":30665},[259,1873,298],[128,84416,347],{"className":84417},[346],[128,84419,84421],{"className":84420},[278],[128,84422,84424],{"className":84423,"style":2241},[282],[128,84425],{},[128,84427,2477],{"className":84428},[1896],[128,84430,84432,84438],{"className":84431},[259],[128,84433,84435],{"className":84434},[259],[128,84436,76902],{"className":84437},[259,3353],[128,84439,84441],{"className":84440},[2087],[128,84442,84444,84464],{"className":84443},[274,321],[128,84445,84447,84461],{"className":84446},[278],[128,84448,84450],{"className":84449,"style":3004},[282],[128,84451,84452,84455],{"style":31837},[128,84453],{"className":84454,"style":291},[290],[128,84456,84458],{"className":84457},[299,300,301,298],[128,84459,364],{"className":84460,"style":30665},[259,1873,298],[128,84462,347],{"className":84463},[346],[128,84465,84467],{"className":84466},[278],[128,84468,84470],{"className":84469,"style":2241},[282],[128,84471],{},[128,84473,1845],{"className":84474},[1903],[128,84476],{"className":84477,"style":1907},[269],[128,84479,84481,84484],{"className":84480},[259],[128,84482,69050],{"className":84483,"style":26806},[259,1873],[128,84485,84487],{"className":84486},[2087],[128,84488,84490,84510],{"className":84489},[274,321],[128,84491,84493,84507],{"className":84492},[278],[128,84494,84496],{"className":84495,"style":3004},[282],[128,84497,84498,84501],{"style":64697},[128,84499],{"className":84500,"style":291},[290],[128,84502,84504],{"className":84503},[299,300,301,298],[128,84505,364],{"className":84506,"style":30665},[259,1873,298],[128,84508,347],{"className":84509},[346],[128,84511,84513],{"className":84512},[278],[128,84514,84516],{"className":84515,"style":2241},[282],[128,84517],{},[128,84519,2486],{"className":84520},[1928]," 整体替换为常量赋值，其余所有方程保持不变。",[2615,84523,84525],{"title":84524},"定义 3.3（干预分布）",[11,84526,84527,84528,84556,84557,84627,84628,84698,84699],{},"变量 ",[128,84529,84531,84544],{"className":84530,"translate":218},[217],[128,84532,84534],{"className":84533},[222],[224,84535,84536],{"xmlns":226},[228,84537,84538,84542],{},[231,84539,84540],{},[1795,84541,35023],{},[238,84543,35023],{"encoding":240},[128,84545,84547],{"className":84546,"ariaHidden":246},[245],[128,84548,84550,84553],{"className":84549},[250],[128,84551],{"className":84552,"style":283},[254],[128,84554,35023],{"className":84555,"style":2508},[259,1873]," 在干预 ",[128,84558,84560,84585],{"className":84559,"translate":218},[217],[128,84561,84563],{"className":84562},[222],[224,84564,84565],{"xmlns":226},[228,84566,84567,84583],{},[231,84568,84569,84571,84573,84575,84577,84579,84581],{},[1795,84570,4519],{},[1795,84572,67350],{},[1832,84574,2477],{"stretchy":1837},[1795,84576,364],{},[1832,84578,1994],{},[1795,84580,2760],{},[1832,84582,2486],{"stretchy":1837},[238,84584,74610],{"encoding":240},[128,84586,84588,84615],{"className":84587,"ariaHidden":246},[245],[128,84589,84591,84594,84597,84600,84603,84606,84609,84612],{"className":84590},[250],[128,84592],{"className":84593,"style":1892},[254],[128,84595,4519],{"className":84596},[259,1873],[128,84598,67350],{"className":84599},[259,1873],[128,84601,2477],{"className":84602},[1896],[128,84604,364],{"className":84605,"style":30665},[259,1873],[128,84607],{"className":84608,"style":1878},[269],[128,84610,1994],{"className":84611},[1882],[128,84613],{"className":84614,"style":1878},[269],[128,84616,84618,84621,84624],{"className":84617},[250],[128,84619],{"className":84620,"style":1892},[254],[128,84622,2760],{"className":84623},[259,1873],[128,84625,2486],{"className":84626},[1928]," 下的分布，定义为子模型 ",[128,84629,84631,84649],{"className":84630,"translate":218},[217],[128,84632,84634],{"className":84633},[222],[224,84635,84636],{"xmlns":226},[228,84637,84638,84646],{},[231,84639,84640],{},[2016,84641,84642,84644],{},[1795,84643,30641],{},[1795,84645,2760],{},[238,84647,84648],{"encoding":240},"M_x",[128,84650,84652],{"className":84651,"ariaHidden":246},[245],[128,84653,84655,84658],{"className":84654},[250],[128,84656],{"className":84657,"style":36058},[254],[128,84659,84661,84664],{"className":84660},[259],[128,84662,30641],{"className":84663,"style":26806},[259,1873],[128,84665,84667],{"className":84666},[2087],[128,84668,84670,84690],{"className":84669},[274,321],[128,84671,84673,84687],{"className":84672},[278],[128,84674,84676],{"className":84675,"style":28738},[282],[128,84677,84678,84681],{"style":64697},[128,84679],{"className":84680,"style":291},[290],[128,84682,84684],{"className":84683},[299,300,301,298],[128,84685,2760],{"className":84686},[259,1873,298],[128,84688,347],{"className":84689},[346],[128,84691,84693],{"className":84692},[278],[128,84694,84696],{"className":84695,"style":2241},[282],[128,84697],{}," 的诱导分布：\n",[128,84700,84702,84754],{"className":84701,"translate":218},[217],[128,84703,84705],{"className":84704},[222],[224,84706,84707],{"xmlns":226},[228,84708,84709,84751],{},[231,84710,84711,84713,84715,84717,84719,84721,84723,84725,84727,84729,84731,84733,84735,84745,84747,84749],{},[1795,84712,23001],{},[1832,84714,2477],{"stretchy":1837},[1795,84716,1830],{},[1832,84718,5443],{},[1795,84720,4519],{},[1795,84722,67350],{},[1832,84724,2477],{"stretchy":1837},[1795,84726,2760],{},[1832,84728,2486],{"stretchy":1837},[1832,84730,2486],{"stretchy":1837},[1832,84732,2014],{},[1832,84734,1994],{},[2016,84736,84737,84739],{},[1795,84738,23001],{},[2016,84740,84741,84743],{},[1795,84742,30641],{},[1795,84744,2760],{},[1832,84746,2477],{"stretchy":1837},[1795,84748,1830],{},[1832,84750,2486],{"stretchy":1837},[238,84752,84753],{"encoding":240},"P(y \\mid do(x)) := P_{M_x}(y)",[128,84755,84757,84781,84811],{"className":84756,"ariaHidden":246},[245],[128,84758,84760,84763,84766,84769,84772,84775,84778],{"className":84759},[250],[128,84761],{"className":84762,"style":1892},[254],[128,84764,23001],{"className":84765,"style":36065},[259,1873],[128,84767,2477],{"className":84768},[1896],[128,84770,1830],{"className":84771,"style":1874},[259,1873],[128,84773],{"className":84774,"style":1878},[269],[128,84776,5443],{"className":84777},[1882],[128,84779],{"className":84780,"style":1878},[269],[128,84782,84784,84787,84790,84793,84796,84799,84802,84805,84808],{"className":84783},[250],[128,84785],{"className":84786,"style":1892},[254],[128,84788,4519],{"className":84789},[259,1873],[128,84791,67350],{"className":84792},[259,1873],[128,84794,2477],{"className":84795},[1896],[128,84797,2760],{"className":84798},[259,1873],[128,84800,67410],{"className":84801},[1928],[128,84803],{"className":84804,"style":1878},[269],[128,84806,75429],{"className":84807},[1882],[128,84809],{"className":84810,"style":1878},[269],[128,84812,84814,84818,84900,84903,84906],{"className":84813},[250],[128,84815],{"className":84816,"style":84817},[254],"height:1.0001em;vertical-align:-0.2501em;",[128,84819,84821,84824],{"className":84820},[259],[128,84822,23001],{"className":84823,"style":36065},[259,1873],[128,84825,84827],{"className":84826},[2087],[128,84828,84830,84891],{"className":84829},[274,321],[128,84831,84833,84888],{"className":84832},[278],[128,84834,84836],{"className":84835,"style":3004},[282],[128,84837,84838,84841],{"style":36080},[128,84839],{"className":84840,"style":291},[290],[128,84842,84844],{"className":84843},[299,300,301,298],[128,84845,84847],{"className":84846},[259,298],[128,84848,84850,84853],{"className":84849},[259,298],[128,84851,30641],{"className":84852,"style":26806},[259,1873,298],[128,84854,84856],{"className":84855},[2087],[128,84857,84859,84880],{"className":84858},[274,321],[128,84860,84862,84877],{"className":84861},[278],[128,84863,84865],{"className":84864,"style":30995},[282],[128,84866,84868,84871],{"style":84867},"top:-2.357em;margin-left:-0.109em;margin-right:0.0714em;",[128,84869],{"className":84870,"style":5790},[290],[128,84872,84874],{"className":84873},[299,5794,5795,298],[128,84875,2760],{"className":84876},[259,1873,298],[128,84878,347],{"className":84879},[346],[128,84881,84883],{"className":84882},[278],[128,84884,84886],{"className":84885,"style":5808},[282],[128,84887],{},[128,84889,347],{"className":84890},[346],[128,84892,84894],{"className":84893},[278],[128,84895,84898],{"className":84896,"style":84897},[282],"height:0.2501em;",[128,84899],{},[128,84901,2477],{"className":84902},[1896],[128,84904,1830],{"className":84905,"style":1874},[259,1873],[128,84907,2486],{"className":84908},[1928],[11,84910,84911,84914,84915,84985,84986,85014,85015,85043,85044,85072,85073,85187,85188,85216,85217,85245],{},[35,84912,84913],{},"在图上的对应操作","：干预 ",[128,84916,84918,84943],{"className":84917,"translate":218},[217],[128,84919,84921],{"className":84920},[222],[224,84922,84923],{"xmlns":226},[228,84924,84925,84941],{},[231,84926,84927,84929,84931,84933,84935,84937,84939],{},[1795,84928,4519],{},[1795,84930,67350],{},[1832,84932,2477],{"stretchy":1837},[1795,84934,364],{},[1832,84936,1994],{},[1795,84938,2760],{},[1832,84940,2486],{"stretchy":1837},[238,84942,74610],{"encoding":240},[128,84944,84946,84973],{"className":84945,"ariaHidden":246},[245],[128,84947,84949,84952,84955,84958,84961,84964,84967,84970],{"className":84948},[250],[128,84950],{"className":84951,"style":1892},[254],[128,84953,4519],{"className":84954},[259,1873],[128,84956,67350],{"className":84957},[259,1873],[128,84959,2477],{"className":84960},[1896],[128,84962,364],{"className":84963,"style":30665},[259,1873],[128,84965],{"className":84966,"style":1878},[269],[128,84968,1994],{"className":84969},[1882],[128,84971],{"className":84972,"style":1878},[269],[128,84974,84976,84979,84982],{"className":84975},[250],[128,84977],{"className":84978,"style":1892},[254],[128,84980,2760],{"className":84981},[259,1873],[128,84983,2486],{"className":84984},[1928]," 对应从因果图 ",[128,84987,84989,85002],{"className":84988,"translate":218},[217],[128,84990,84992],{"className":84991},[222],[224,84993,84994],{"xmlns":226},[228,84995,84996,85000],{},[231,84997,84998],{},[1795,84999,67956],{},[238,85001,67956],{"encoding":240},[128,85003,85005],{"className":85004,"ariaHidden":246},[245],[128,85006,85008,85011],{"className":85007},[250],[128,85009],{"className":85010,"style":283},[254],[128,85012,67956],{"className":85013},[259,1873]," 中删去 ",[128,85016,85018,85031],{"className":85017,"translate":218},[217],[128,85019,85021],{"className":85020},[222],[224,85022,85023],{"xmlns":226},[228,85024,85025,85029],{},[231,85026,85027],{},[1795,85028,364],{},[238,85030,364],{"encoding":240},[128,85032,85034],{"className":85033,"ariaHidden":246},[245],[128,85035,85037,85040],{"className":85036},[250],[128,85038],{"className":85039,"style":283},[254],[128,85041,364],{"className":85042,"style":30665},[259,1873]," 的所有入边（即切断 ",[128,85045,85047,85060],{"className":85046,"translate":218},[217],[128,85048,85050],{"className":85049},[222],[224,85051,85052],{"xmlns":226},[228,85053,85054,85058],{},[231,85055,85056],{},[1795,85057,364],{},[238,85059,364],{"encoding":240},[128,85061,85063],{"className":85062,"ariaHidden":246},[245],[128,85064,85066,85069],{"className":85065},[250],[128,85067],{"className":85068,"style":283},[254],[128,85070,364],{"className":85071,"style":30665},[259,1873]," 与其父节点的连接），得到修改后的图 ",[128,85074,85076,85099],{"className":85075,"translate":218},[217],[128,85077,85079],{"className":85078},[222],[224,85080,85081],{"xmlns":226},[228,85082,85083,85096],{},[231,85084,85085],{},[2016,85086,85087,85089],{},[1795,85088,67956],{},[54905,85090,85091,85093],{"accent":246},[1795,85092,364],{},[1832,85094,85095],{"stretchy":246},"‾",[238,85097,85098],{"encoding":240},"G_{\\overline{X}}",[128,85100,85102],{"className":85101,"ariaHidden":246},[245],[128,85103,85105,85109],{"className":85104},[250],[128,85106],{"className":85107,"style":85108},[254],"height:0.9884em;vertical-align:-0.305em;",[128,85110,85112,85115],{"className":85111},[259],[128,85113,67956],{"className":85114},[259,1873],[128,85116,85118],{"className":85117},[2087],[128,85119,85121,85178],{"className":85120},[274,321],[128,85122,85124,85175],{"className":85123},[278],[128,85125,85127],{"className":85126,"style":24117},[282],[128,85128,85130,85133],{"style":85129},"top:-2.695em;margin-left:0em;margin-right:0.05em;",[128,85131],{"className":85132,"style":335},[290],[128,85134,85136],{"className":85135},[299,300,301,298],[128,85137,85139],{"className":85138},[259,298],[128,85140,85143],{"className":85141},[259,85142,298],"overline",[128,85144,85146],{"className":85145},[274],[128,85147,85149],{"className":85148},[278],[128,85150,85153,85164],{"className":85151,"style":85152},[282],"height:0.9283em;",[128,85154,85155,85158],{"style":54961},[128,85156],{"className":85157,"style":335},[290],[128,85159,85161],{"className":85160},[259,298],[128,85162,364],{"className":85163,"style":30665},[259,1873,298],[128,85165,85167,85170],{"style":85166},"top:-3.8303em;",[128,85168],{"className":85169,"style":335},[290],[128,85171],{"className":85172,"style":85174},[85173,298],"overline-line","border-bottom-width:0.049em;",[128,85176,347],{"className":85177},[346],[128,85179,85181],{"className":85180},[278],[128,85182,85185],{"className":85183,"style":85184},[282],"height:0.305em;",[128,85186],{},"，同时保留 ",[128,85189,85191,85204],{"className":85190,"translate":218},[217],[128,85192,85194],{"className":85193},[222],[224,85195,85196],{"xmlns":226},[228,85197,85198,85202],{},[231,85199,85200],{},[1795,85201,364],{},[238,85203,364],{"encoding":240},[128,85205,85207],{"className":85206,"ariaHidden":246},[245],[128,85208,85210,85213],{"className":85209},[250],[128,85211],{"className":85212,"style":283},[254],[128,85214,364],{"className":85215,"style":30665},[259,1873]," 的所有出边不变。这一操作直观地表达了「外部干预使得 ",[128,85218,85220,85233],{"className":85219,"translate":218},[217],[128,85221,85223],{"className":85222},[222],[224,85224,85225],{"xmlns":226},[228,85226,85227,85231],{},[231,85228,85229],{},[1795,85230,364],{},[238,85232,364],{"encoding":240},[128,85234,85236],{"className":85235,"ariaHidden":246},[245],[128,85237,85239,85242],{"className":85238},[250],[128,85240],{"className":85241,"style":283},[254],[128,85243,364],{"className":85244,"style":30665},[259,1873]," 不再由其自然原因决定，而是由外部力量强制设定」这一语义。",[2615,85247,85249],{"title":85248},"定理 3.1（截断因子分解公式，Truncated Factorization）",[11,85250,85251,85252,85942,85943,85975],{},"对马尔可夫型 SCM，\n",[128,85253,85255,85397],{"className":85254,"translate":218},[217],[128,85256,85258],{"className":85257},[222],[224,85259,85260],{"xmlns":226},[228,85261,85262,85394],{},[231,85263,85264,85266,85268,85274,85276,85278,85280,85286,85288,85290,85292,85294,85296,85298,85300,85302],{},[1795,85265,23001],{},[1832,85267,2477],{"stretchy":1837},[2016,85269,85270,85272],{},[1795,85271,32160],{},[1840,85273,1842],{},[1832,85275,1845],{"separator":246},[1832,85277,1848],{},[1832,85279,1845],{"separator":246},[2016,85281,85282,85284],{},[1795,85283,32160],{},[1795,85285,16280],{},[1832,85287,5443],{},[1795,85289,4519],{},[1795,85291,67350],{},[1832,85293,2477],{"stretchy":1837},[1795,85295,2760],{},[1832,85297,2486],{"stretchy":1837},[1832,85299,2486],{"stretchy":1837},[1832,85301,1994],{},[231,85303,85304,85306],{},[1832,85305,1838],{"fence":246},[8172,85307,85308,85379],{"rowspacing":61386,"columnalign":61387,"columnspacing":8176},[8178,85309,85310,85356],{},[8181,85311,85312],{},[2035,85313,85314],{"scriptlevel":2028,"displaystyle":1837},[231,85315,85316,85332,85334,85336,85342,85344,85354],{},[2016,85317,85318,85320],{},[1832,85319,5470],{},[231,85321,85322,85328,85330],{},[2016,85323,85324,85326],{},[1795,85325,67963],{},[1795,85327,2801],{},[1832,85329,16716],{"mathvariant":1981},[1795,85331,364],{},[1795,85333,23001],{},[1832,85335,2477],{"stretchy":1837},[2016,85337,85338,85340],{},[1795,85339,32160],{},[1795,85341,2801],{},[1832,85343,5443],{},[2016,85345,85346,85352],{},[231,85347,85348,85350],{},[1795,85349,11],{"mathvariant":1981},[1795,85351,21],{"mathvariant":1981},[1795,85353,2801],{},[1832,85355,2486],{"stretchy":1837},[8181,85357,85358],{},[2035,85359,85360],{"scriptlevel":2028,"displaystyle":1837},[231,85361,85362,85365,85367,85370,85372,85374,85376],{},[234,85363,85364],{},"若 ",[1795,85366,32160],{},[234,85368,85369],{}," 的取值与 ",[1795,85371,364],{},[1832,85373,1994],{},[1795,85375,2760],{},[234,85377,85378],{}," 相容",[8178,85380,85381,85387],{},[8181,85382,85383],{},[2035,85384,85385],{"scriptlevel":2028,"displaystyle":1837},[1840,85386,2028],{},[8181,85388,85389],{},[2035,85390,85391],{"scriptlevel":2028,"displaystyle":1837},[234,85392,85393],{},"否则",[238,85395,85396],{"encoding":240},"P(v_1,\\dots,v_n \\mid do(x)) = \\begin{cases} \\prod_{V_i \\neq X} P(v_i \\mid \\mathrm{pa}_i) & \\text{若 } v \\text{ 的取值与 } X=x \\text{ 相容} \\\\ 0 & \\text{否则}\\end{cases}",[128,85398,85400,85519,85549],{"className":85399,"ariaHidden":246},[245],[128,85401,85403,85406,85409,85412,85452,85455,85458,85461,85464,85467,85470,85510,85513,85516],{"className":85402},[250],[128,85404],{"className":85405,"style":1892},[254],[128,85407,23001],{"className":85408,"style":36065},[259,1873],[128,85410,2477],{"className":85411},[1896],[128,85413,85415,85418],{"className":85414},[259],[128,85416,32160],{"className":85417,"style":1874},[259,1873],[128,85419,85421],{"className":85420},[2087],[128,85422,85424,85444],{"className":85423},[274,321],[128,85425,85427,85441],{"className":85426},[278],[128,85428,85430],{"className":85429,"style":2945},[282],[128,85431,85432,85435],{"style":28741},[128,85433],{"className":85434,"style":291},[290],[128,85436,85438],{"className":85437},[299,300,301,298],[128,85439,1842],{"className":85440},[259,298],[128,85442,347],{"className":85443},[346],[128,85445,85447],{"className":85446},[278],[128,85448,85450],{"className":85449,"style":2241},[282],[128,85451],{},[128,85453,1845],{"className":85454},[1903],[128,85456],{"className":85457,"style":1907},[269],[128,85459,1848],{"className":85460},[1911],[128,85462],{"className":85463,"style":1907},[269],[128,85465,1845],{"className":85466},[1903],[128,85468],{"className":85469,"style":1907},[269],[128,85471,85473,85476],{"className":85472},[259],[128,85474,32160],{"className":85475,"style":1874},[259,1873],[128,85477,85479],{"className":85478},[2087],[128,85480,85482,85502],{"className":85481},[274,321],[128,85483,85485,85499],{"className":85484},[278],[128,85486,85488],{"className":85487,"style":28738},[282],[128,85489,85490,85493],{"style":28741},[128,85491],{"className":85492,"style":291},[290],[128,85494,85496],{"className":85495},[299,300,301,298],[128,85497,16280],{"className":85498},[259,1873,298],[128,85500,347],{"className":85501},[346],[128,85503,85505],{"className":85504},[278],[128,85506,85508],{"className":85507,"style":2241},[282],[128,85509],{},[128,85511],{"className":85512,"style":1878},[269],[128,85514,5443],{"className":85515},[1882],[128,85517],{"className":85518,"style":1878},[269],[128,85520,85522,85525,85528,85531,85534,85537,85540,85543,85546],{"className":85521},[250],[128,85523],{"className":85524,"style":1892},[254],[128,85526,4519],{"className":85527},[259,1873],[128,85529,67350],{"className":85530},[259,1873],[128,85532,2477],{"className":85533},[1896],[128,85535,2760],{"className":85536},[259,1873],[128,85538,67410],{"className":85539},[1928],[128,85541],{"className":85542,"style":1878},[269],[128,85544,1994],{"className":85545},[1882],[128,85547],{"className":85548,"style":1878},[269],[128,85550,85552,85555],{"className":85551},[250],[128,85553],{"className":85554,"style":61549},[254],[128,85556,85558,85564,85939],{"className":85557},[1911],[128,85559,85561],{"className":85560,"style":2142},[1896,2141],[128,85562,1838],{"className":85563},[2146,10370],[128,85565,85567],{"className":85566},[259],[128,85568,85570,85840,85843],{"className":85569},[8172],[128,85571,85573],{"className":85572},[61568],[128,85574,85576,85831],{"className":85575},[274,321],[128,85577,85579,85828],{"className":85578},[278],[128,85580,85583,85816],{"className":85581,"style":85582},[282],"height:1.6919em;",[128,85584,85586,85589],{"style":85585},"top:-3.6919em;",[128,85587],{"className":85588,"style":61585},[290],[128,85590,85592,85712,85715,85718,85721,85761,85764,85767,85770,85813],{"className":85591},[259],[128,85593,85595,85598],{"className":85594},[2268],[128,85596,5470],{"className":85597,"style":2274},[2268,2272,2273],[128,85599,85601],{"className":85600},[2087],[128,85602,85604,85704],{"className":85603},[274,321],[128,85605,85607,85701],{"className":85606},[278],[128,85608,85610],{"className":85609,"style":31692},[282],[128,85611,85612,85615],{"style":2290},[128,85613],{"className":85614,"style":291},[290],[128,85616,85618],{"className":85617},[299,300,301,298],[128,85619,85621,85662,85698],{"className":85620},[259,298],[128,85622,85624,85627],{"className":85623},[259,298],[128,85625,67963],{"className":85626,"style":2508},[259,1873,298],[128,85628,85630],{"className":85629},[2087],[128,85631,85633,85654],{"className":85632},[274,321],[128,85634,85636,85651],{"className":85635},[278],[128,85637,85639],{"className":85638,"style":5783},[282],[128,85640,85642,85645],{"style":85641},"top:-2.357em;margin-left:-0.2222em;margin-right:0.0714em;",[128,85643],{"className":85644,"style":5790},[290],[128,85646,85648],{"className":85647},[299,5794,5795,298],[128,85649,2801],{"className":85650},[259,1873,298],[128,85652,347],{"className":85653},[346],[128,85655,85657],{"className":85656},[278],[128,85658,85660],{"className":85659,"style":5808},[282],[128,85661],{},[128,85663,85665,85692,85695],{"className":85664},[1882,298],[128,85666,85668],{"className":85667},[1882,298],[128,85669,85671],{"className":85670},[259,17719,298],[128,85672,85674],{"className":85673},[17723,298],[128,85675,85677,85680,85689],{"className":85676},[17727,298],[128,85678],{"className":85679,"style":16030},[254],[128,85681,85683],{"className":85682},[17734],[128,85684,85686],{"className":85685},[259,298],[128,85687,17741],{"className":85688},[1882,298],[128,85690],{"className":85691},[17745],[128,85693],{"className":85694},[269,17749,298],[128,85696,1994],{"className":85697},[1882,298],[128,85699,364],{"className":85700,"style":30665},[259,1873,298],[128,85702,347],{"className":85703},[346],[128,85705,85707],{"className":85706},[278],[128,85708,85710],{"className":85709,"style":31756},[282],[128,85711],{},[128,85713],{"className":85714,"style":1907},[269],[128,85716,23001],{"className":85717,"style":36065},[259,1873],[128,85719,2477],{"className":85720},[1896],[128,85722,85724,85727],{"className":85723},[259],[128,85725,32160],{"className":85726,"style":1874},[259,1873],[128,85728,85730],{"className":85729},[2087],[128,85731,85733,85753],{"className":85732},[274,321],[128,85734,85736,85750],{"className":85735},[278],[128,85737,85739],{"className":85738,"style":3095},[282],[128,85740,85741,85744],{"style":28741},[128,85742],{"className":85743,"style":291},[290],[128,85745,85747],{"className":85746},[299,300,301,298],[128,85748,2801],{"className":85749},[259,1873,298],[128,85751,347],{"className":85752},[346],[128,85754,85756],{"className":85755},[278],[128,85757,85759],{"className":85758,"style":2241},[282],[128,85760],{},[128,85762],{"className":85763,"style":1878},[269],[128,85765,5443],{"className":85766},[1882],[128,85768],{"className":85769,"style":1878},[269],[128,85771,85773,85779],{"className":85772},[259],[128,85774,85776],{"className":85775},[259],[128,85777,79403],{"className":85778},[259,3353],[128,85780,85782],{"className":85781},[2087],[128,85783,85785,85805],{"className":85784},[274,321],[128,85786,85788,85802],{"className":85787},[278],[128,85789,85791],{"className":85790,"style":79416},[282],[128,85792,85793,85796],{"style":79419},[128,85794],{"className":85795,"style":291},[290],[128,85797,85799],{"className":85798},[299,300,301,298],[128,85800,2801],{"className":85801},[259,1873,298],[128,85803,347],{"className":85804},[346],[128,85806,85808],{"className":85807},[278],[128,85809,85811],{"className":85810,"style":79438},[282],[128,85812],{},[128,85814,2486],{"className":85815},[1928],[128,85817,85819,85822],{"style":85818},"top:-2.2481em;",[128,85820],{"className":85821,"style":61585},[290],[128,85823,85825],{"className":85824},[259],[128,85826,2028],{"className":85827},[259],[128,85829,347],{"className":85830},[346],[128,85832,85834],{"className":85833},[278],[128,85835,85838],{"className":85836,"style":85837},[282],"height:1.1919em;",[128,85839],{},[128,85841],{"className":85842,"style":61717},[8388],[128,85844,85846],{"className":85845},[61568],[128,85847,85849,85931],{"className":85848},[274,321],[128,85850,85852,85928],{"className":85851},[278],[128,85853,85855,85914],{"className":85854,"style":85582},[282],[128,85856,85857,85860],{"style":85585},[128,85858],{"className":85859,"style":61585},[290],[128,85861,85863,85873,85876,85889,85892,85895,85898,85901,85904],{"className":85862},[259],[128,85864,85866,85870],{"className":85865},[259,260],[128,85867,85869],{"className":85868},[259,15272],"若",[128,85871,2033],{"className":85872},[259],[128,85874,32160],{"className":85875,"style":1874},[259,1873],[128,85877,85879,85882,85886],{"className":85878},[259,260],[128,85880,2033],{"className":85881},[259],[128,85883,85885],{"className":85884},[259,15272],"的取值与",[128,85887,2033],{"className":85888},[259],[128,85890,364],{"className":85891,"style":30665},[259,1873],[128,85893],{"className":85894,"style":1878},[269],[128,85896,1994],{"className":85897},[1882],[128,85899],{"className":85900,"style":1878},[269],[128,85902,2760],{"className":85903},[259,1873],[128,85905,85907,85910],{"className":85906},[259,260],[128,85908,2033],{"className":85909},[259],[128,85911,85913],{"className":85912},[259,15272],"相容",[128,85915,85916,85919],{"style":85818},[128,85917],{"className":85918,"style":61585},[290],[128,85920,85922],{"className":85921},[259],[128,85923,85925],{"className":85924},[259,260],[128,85926,85393],{"className":85927},[259,15272],[128,85929,347],{"className":85930},[346],[128,85932,85934],{"className":85933},[278],[128,85935,85937],{"className":85936,"style":85837},[282],[128,85938],{},[128,85940],{"className":85941},[1928,5570],"\n即干预分布等于观测分布的马尔可夫分解式中",[35,85944,85945,85946,85974],{},"删去 ",[128,85947,85949,85962],{"className":85948,"translate":218},[217],[128,85950,85952],{"className":85951},[222],[224,85953,85954],{"xmlns":226},[228,85955,85956,85960],{},[231,85957,85958],{},[1795,85959,364],{},[238,85961,364],{"encoding":240},[128,85963,85965],{"className":85964,"ariaHidden":246},[245],[128,85966,85968,85971],{"className":85967},[250],[128,85969],{"className":85970,"style":283},[254],[128,85972,364],{"className":85973,"style":30665},[259,1873]," 对应因子后","的乘积。这一公式是连接观测数据（第一层）与干预效果（第二层）的桥梁，也是后续「后门准则」「前门准则」等可识别性理论的直接推论。",[2615,85977,85979,86039,87134],{"title":85978},"例 3.2（观察与干预的数值区分）",[11,85980,85981,85982,86038],{},"沿用洒水器例子。设已知 ",[128,85983,85985,86005],{"className":85984,"translate":218},[217],[128,85986,85988],{"className":85987},[222],[224,85989,85990],{"xmlns":226},[228,85991,85992,86002],{},[231,85993,85994,85996,85998,86000],{},[1795,85995,41957],{},[1795,85997,11],{},[1832,85999,1994],{},[1840,86001,1842],{},[238,86003,86004],{"encoding":240},"Sp=1",[128,86006,86008,86029],{"className":86007,"ariaHidden":246},[245],[128,86009,86011,86014,86017,86020,86023,86026],{"className":86010},[250],[128,86012],{"className":86013,"style":40674},[254],[128,86015,41957],{"className":86016,"style":42029},[259,1873],[128,86018,11],{"className":86019},[259,1873],[128,86021],{"className":86022,"style":1878},[269],[128,86024,1994],{"className":86025},[1882],[128,86027],{"className":86028,"style":1878},[269],[128,86030,86032,86035],{"className":86031},[250],[128,86033],{"className":86034,"style":2594},[254],[128,86036,1842],{"className":86037},[259],"（洒水器开着）。",[35195,86040,86041,86434],{},[33251,86042,86043,1148,86046,20648,86161,86217,86218,86246,86247,86302,86303,86354,86355,86433],{},[35,86044,86045],{},"观察情形",[128,86047,86049,86083],{"className":86048,"translate":218},[217],[128,86050,86052],{"className":86051},[222],[224,86053,86054],{"xmlns":226},[228,86055,86056,86080],{},[231,86057,86058,86060,86062,86064,86066,86068,86070,86072,86074,86076,86078],{},[1795,86059,23001],{},[1832,86061,2477],{"stretchy":1837},[1795,86063,2009],{},[1832,86065,1994],{},[1840,86067,1842],{},[1832,86069,5443],{},[1795,86071,41957],{},[1795,86073,11],{},[1832,86075,1994],{},[1840,86077,1842],{},[1832,86079,2486],{"stretchy":1837},[238,86081,86082],{"encoding":240},"P(R=1 \\mid Sp=1)",[128,86084,86086,86110,86128,86149],{"className":86085,"ariaHidden":246},[245],[128,86087,86089,86092,86095,86098,86101,86104,86107],{"className":86088},[250],[128,86090],{"className":86091,"style":1892},[254],[128,86093,23001],{"className":86094,"style":36065},[259,1873],[128,86096,2477],{"className":86097},[1896],[128,86099,2009],{"className":86100,"style":70411},[259,1873],[128,86102],{"className":86103,"style":1878},[269],[128,86105,1994],{"className":86106},[1882],[128,86108],{"className":86109,"style":1878},[269],[128,86111,86113,86116,86119,86122,86125],{"className":86112},[250],[128,86114],{"className":86115,"style":1892},[254],[128,86117,1842],{"className":86118},[259],[128,86120],{"className":86121,"style":1878},[269],[128,86123,5443],{"className":86124},[1882],[128,86126],{"className":86127,"style":1878},[269],[128,86129,86131,86134,86137,86140,86143,86146],{"className":86130},[250],[128,86132],{"className":86133,"style":40674},[254],[128,86135,41957],{"className":86136,"style":42029},[259,1873],[128,86138,11],{"className":86139},[259,1873],[128,86141],{"className":86142,"style":1878},[269],[128,86144,1994],{"className":86145},[1882],[128,86147],{"className":86148,"style":1878},[269],[128,86150,86152,86155,86158],{"className":86151},[250],[128,86153],{"className":86154,"style":1892},[254],[128,86156,1842],{"className":86157},[259],[128,86159,2486],{"className":86160},[1928],[128,86162,86164,86184],{"className":86163,"translate":218},[217],[128,86165,86167],{"className":86166},[222],[224,86168,86169],{"xmlns":226},[228,86170,86171,86181],{},[231,86172,86173,86175,86177,86179],{},[1795,86174,41957],{},[1832,86176,22419],{},[1795,86178,41957],{},[1795,86180,11],{},[238,86182,86183],{"encoding":240},"S \\to Sp",[128,86185,86187,86205],{"className":86186,"ariaHidden":246},[245],[128,86188,86190,86193,86196,86199,86202],{"className":86189},[250],[128,86191],{"className":86192,"style":283},[254],[128,86194,41957],{"className":86195,"style":42029},[259,1873],[128,86197],{"className":86198,"style":1878},[269],[128,86200,22419],{"className":86201},[1882],[128,86203],{"className":86204,"style":1878},[269],[128,86206,86208,86211,86214],{"className":86207},[250],[128,86209],{"className":86210,"style":40674},[254],[128,86212,41957],{"className":86213,"style":42029},[259,1873],[128,86215,11],{"className":86216},[259,1873],"，观察到洒水器开启会更新我们对季节 ",[128,86219,86221,86234],{"className":86220,"translate":218},[217],[128,86222,86224],{"className":86223},[222],[224,86225,86226],{"xmlns":226},[228,86227,86228,86232],{},[231,86229,86230],{},[1795,86231,41957],{},[238,86233,41957],{"encoding":240},[128,86235,86237],{"className":86236,"ariaHidden":246},[245],[128,86238,86240,86243],{"className":86239},[250],[128,86241],{"className":86242,"style":283},[254],[128,86244,41957],{"className":86245,"style":42029},[259,1873]," 的信念（贝叶斯反推），例如若干燥季节更常开洒水器，则观察到 ",[128,86248,86250,86269],{"className":86249,"translate":218},[217],[128,86251,86253],{"className":86252},[222],[224,86254,86255],{"xmlns":226},[228,86256,86257,86267],{},[231,86258,86259,86261,86263,86265],{},[1795,86260,41957],{},[1795,86262,11],{},[1832,86264,1994],{},[1840,86266,1842],{},[238,86268,86004],{"encoding":240},[128,86270,86272,86293],{"className":86271,"ariaHidden":246},[245],[128,86273,86275,86278,86281,86284,86287,86290],{"className":86274},[250],[128,86276],{"className":86277,"style":40674},[254],[128,86279,41957],{"className":86280,"style":42029},[259,1873],[128,86282,11],{"className":86283},[259,1873],[128,86285],{"className":86286,"style":1878},[269],[128,86288,1994],{"className":86289},[1882],[128,86291],{"className":86292,"style":1878},[269],[128,86294,86296,86299],{"className":86295},[250],[128,86297],{"className":86298,"style":2594},[254],[128,86300,1842],{"className":86301},[259]," 会提高「当前是干燥季节」的后验概率，进而压低 ",[128,86304,86306,86324],{"className":86305,"translate":218},[217],[128,86307,86309],{"className":86308},[222],[224,86310,86311],{"xmlns":226},[228,86312,86313,86321],{},[231,86314,86315,86317,86319],{},[1795,86316,2009],{},[1832,86318,1994],{},[1840,86320,1842],{},[238,86322,86323],{"encoding":240},"R=1",[128,86325,86327,86345],{"className":86326,"ariaHidden":246},[245],[128,86328,86330,86333,86336,86339,86342],{"className":86329},[250],[128,86331],{"className":86332,"style":283},[254],[128,86334,2009],{"className":86335,"style":70411},[259,1873],[128,86337],{"className":86338,"style":1878},[269],[128,86340,1994],{"className":86341},[1882],[128,86343],{"className":86344,"style":1878},[269],[128,86346,86348,86351],{"className":86347},[250],[128,86349],{"className":86350,"style":2594},[254],[128,86352,1842],{"className":86353},[259]," 的概率。此计算通过叉结构 ",[128,86356,86358,86382],{"className":86357,"translate":218},[217],[128,86359,86361],{"className":86360},[222],[224,86362,86363],{"xmlns":226},[228,86364,86365,86379],{},[231,86366,86367,86369,86371,86373,86375,86377],{},[1795,86368,2009],{},[1832,86370,71437],{},[1795,86372,41957],{},[1832,86374,22419],{},[1795,86376,41957],{},[1795,86378,11],{},[238,86380,86381],{"encoding":240},"R \\leftarrow S \\to Sp",[128,86383,86385,86403,86421],{"className":86384,"ariaHidden":246},[245],[128,86386,86388,86391,86394,86397,86400],{"className":86387},[250],[128,86389],{"className":86390,"style":283},[254],[128,86392,2009],{"className":86393,"style":70411},[259,1873],[128,86395],{"className":86396,"style":1878},[269],[128,86398,71437],{"className":86399},[1882],[128,86401],{"className":86402,"style":1878},[269],[128,86404,86406,86409,86412,86415,86418],{"className":86405},[250],[128,86407],{"className":86408,"style":283},[254],[128,86410,41957],{"className":86411,"style":42029},[259,1873],[128,86413],{"className":86414,"style":1878},[269],[128,86416,22419],{"className":86417},[1882],[128,86419],{"className":86420,"style":1878},[269],[128,86422,86424,86427,86430],{"className":86423},[250],[128,86425],{"className":86426,"style":40674},[254],[128,86428,41957],{"className":86429,"style":42029},[259,1873],[128,86431,11],{"className":86432},[259,1873]," 这条未被阻断的路径进行。",[33251,86435,86436,1148,86439,86571,86572,86627,86628,86656,86657,86734,86735,86790,86791,87133],{},[35,86437,86438],{},"干预情形",[128,86440,86442,86484],{"className":86441,"translate":218},[217],[128,86443,86445],{"className":86444},[222],[224,86446,86447],{"xmlns":226},[228,86448,86449,86481],{},[231,86450,86451,86453,86455,86457,86459,86461,86463,86465,86467,86469,86471,86473,86475,86477,86479],{},[1795,86452,23001],{},[1832,86454,2477],{"stretchy":1837},[1795,86456,2009],{},[1832,86458,1994],{},[1840,86460,1842],{},[1832,86462,5443],{},[1795,86464,4519],{},[1795,86466,67350],{},[1832,86468,2477],{"stretchy":1837},[1795,86470,41957],{},[1795,86472,11],{},[1832,86474,1994],{},[1840,86476,1842],{},[1832,86478,2486],{"stretchy":1837},[1832,86480,2486],{"stretchy":1837},[238,86482,86483],{"encoding":240},"P(R=1 \\mid do(Sp=1))",[128,86485,86487,86511,86529,86559],{"className":86486,"ariaHidden":246},[245],[128,86488,86490,86493,86496,86499,86502,86505,86508],{"className":86489},[250],[128,86491],{"className":86492,"style":1892},[254],[128,86494,23001],{"className":86495,"style":36065},[259,1873],[128,86497,2477],{"className":86498},[1896],[128,86500,2009],{"className":86501,"style":70411},[259,1873],[128,86503],{"className":86504,"style":1878},[269],[128,86506,1994],{"className":86507},[1882],[128,86509],{"className":86510,"style":1878},[269],[128,86512,86514,86517,86520,86523,86526],{"className":86513},[250],[128,86515],{"className":86516,"style":1892},[254],[128,86518,1842],{"className":86519},[259],[128,86521],{"className":86522,"style":1878},[269],[128,86524,5443],{"className":86525},[1882],[128,86527],{"className":86528,"style":1878},[269],[128,86530,86532,86535,86538,86541,86544,86547,86550,86553,86556],{"className":86531},[250],[128,86533],{"className":86534,"style":1892},[254],[128,86536,4519],{"className":86537},[259,1873],[128,86539,67350],{"className":86540},[259,1873],[128,86542,2477],{"className":86543},[1896],[128,86545,41957],{"className":86546,"style":42029},[259,1873],[128,86548,11],{"className":86549},[259,1873],[128,86551],{"className":86552,"style":1878},[269],[128,86554,1994],{"className":86555},[1882],[128,86557],{"className":86558,"style":1878},[269],[128,86560,86562,86565,86568],{"className":86561},[250],[128,86563],{"className":86564,"style":1892},[254],[128,86566,1842],{"className":86567},[259],[128,86569,67410],{"className":86570},[1928],"：依据定义 3.2，干预会切断 ",[128,86573,86575,86594],{"className":86574,"translate":218},[217],[128,86576,86578],{"className":86577},[222],[224,86579,86580],{"xmlns":226},[228,86581,86582,86592],{},[231,86583,86584,86586,86588,86590],{},[1795,86585,41957],{},[1832,86587,22419],{},[1795,86589,41957],{},[1795,86591,11],{},[238,86593,86183],{"encoding":240},[128,86595,86597,86615],{"className":86596,"ariaHidden":246},[245],[128,86598,86600,86603,86606,86609,86612],{"className":86599},[250],[128,86601],{"className":86602,"style":283},[254],[128,86604,41957],{"className":86605,"style":42029},[259,1873],[128,86607],{"className":86608,"style":1878},[269],[128,86610,22419],{"className":86611},[1882],[128,86613],{"className":86614,"style":1878},[269],[128,86616,86618,86621,86624],{"className":86617},[250],[128,86619],{"className":86620,"style":40674},[254],[128,86622,41957],{"className":86623,"style":42029},[259,1873],[128,86625,11],{"className":86626},[259,1873]," 这条边，于是 ",[128,86629,86631,86644],{"className":86630,"translate":218},[217],[128,86632,86634],{"className":86633},[222],[224,86635,86636],{"xmlns":226},[228,86637,86638,86642],{},[231,86639,86640],{},[1795,86641,41957],{},[238,86643,41957],{"encoding":240},[128,86645,86647],{"className":86646,"ariaHidden":246},[245],[128,86648,86650,86653],{"className":86649},[250],[128,86651],{"className":86652,"style":283},[254],[128,86654,41957],{"className":86655,"style":42029},[259,1873]," 的分布完全不受「我们把洒水器打开」这一操作的影响；而 ",[128,86658,86660,86683],{"className":86659,"translate":218},[217],[128,86661,86663],{"className":86662},[222],[224,86664,86665],{"xmlns":226},[228,86666,86667,86681],{},[231,86668,86669,86671,86673,86675,86677,86679],{},[1795,86670,2009],{},[1832,86672,71437],{},[1795,86674,41957],{},[1832,86676,22419],{},[1795,86678,41957],{},[1795,86680,11],{},[238,86682,86381],{"encoding":240},[128,86684,86686,86704,86722],{"className":86685,"ariaHidden":246},[245],[128,86687,86689,86692,86695,86698,86701],{"className":86688},[250],[128,86690],{"className":86691,"style":283},[254],[128,86693,2009],{"className":86694,"style":70411},[259,1873],[128,86696],{"className":86697,"style":1878},[269],[128,86699,71437],{"className":86700},[1882],[128,86702],{"className":86703,"style":1878},[269],[128,86705,86707,86710,86713,86716,86719],{"className":86706},[250],[128,86708],{"className":86709,"style":283},[254],[128,86711,41957],{"className":86712,"style":42029},[259,1873],[128,86714],{"className":86715,"style":1878},[269],[128,86717,22419],{"className":86718},[1882],[128,86720],{"className":86721,"style":1878},[269],[128,86723,86725,86728,86731],{"className":86724},[250],[128,86726],{"className":86727,"style":40674},[254],[128,86729,41957],{"className":86730,"style":42029},[259,1873],[128,86732,11],{"className":86733},[259,1873]," 这条路径由于 ",[128,86736,86738,86757],{"className":86737,"translate":218},[217],[128,86739,86741],{"className":86740},[222],[224,86742,86743],{"xmlns":226},[228,86744,86745,86755],{},[231,86746,86747,86749,86751,86753],{},[1795,86748,41957],{},[1832,86750,22419],{},[1795,86752,41957],{},[1795,86754,11],{},[238,86756,86183],{"encoding":240},[128,86758,86760,86778],{"className":86759,"ariaHidden":246},[245],[128,86761,86763,86766,86769,86772,86775],{"className":86762},[250],[128,86764],{"className":86765,"style":283},[254],[128,86767,41957],{"className":86768,"style":42029},[259,1873],[128,86770],{"className":86771,"style":1878},[269],[128,86773,22419],{"className":86774},[1882],[128,86776],{"className":86777,"style":1878},[269],[128,86779,86781,86784,86787],{"className":86780},[250],[128,86782],{"className":86783,"style":40674},[254],[128,86785,41957],{"className":86786,"style":42029},[259,1873],[128,86788,11],{"className":86789},[259,1873]," 边已被切断，不再传递任何信息。因此\n",[128,86792,86794,86882],{"className":86793,"translate":218},[217],[128,86795,86797],{"className":86796},[222],[224,86798,86799],{"xmlns":226},[228,86800,86801,86879],{},[231,86802,86803,86805,86807,86809,86811,86813,86815,86817,86819,86821,86823,86825,86827,86829,86831,86833,86835,86837,86839,86841,86843,86845,86847,86849,86855,86857,86859,86861,86863,86865,86867,86869,86871,86873,86875,86877],{},[1795,86804,23001],{},[1832,86806,2477],{"stretchy":1837},[1795,86808,2009],{},[1832,86810,1994],{},[1840,86812,1842],{},[1832,86814,5443],{},[1795,86816,4519],{},[1795,86818,67350],{},[1832,86820,2477],{"stretchy":1837},[1795,86822,41957],{},[1795,86824,11],{},[1832,86826,1994],{},[1840,86828,1842],{},[1832,86830,2486],{"stretchy":1837},[1832,86832,2486],{"stretchy":1837},[1832,86834,1994],{},[1795,86836,23001],{},[1832,86838,2477],{"stretchy":1837},[1795,86840,2009],{},[1832,86842,1994],{},[1840,86844,1842],{},[1832,86846,2486],{"stretchy":1837},[1832,86848,1994],{},[2016,86850,86851,86853],{},[1832,86852,2042],{},[1795,86854,7590],{},[1795,86856,23001],{},[1832,86858,2477],{"stretchy":1837},[1795,86860,2009],{},[1832,86862,1994],{},[1840,86864,1842],{},[1832,86866,5443],{},[1795,86868,7590],{},[1832,86870,2486],{"stretchy":1837},[1795,86872,23001],{},[1832,86874,2477],{"stretchy":1837},[1795,86876,7590],{},[1832,86878,2486],{"stretchy":1837},[238,86880,86881],{"encoding":240},"P(R=1 \\mid do(Sp=1)) = P(R=1) = \\sum_s P(R=1\\mid s)P(s)",[128,86883,86885,86909,86927,86957,86978,87002,87023,87091,87109],{"className":86884,"ariaHidden":246},[245],[128,86886,86888,86891,86894,86897,86900,86903,86906],{"className":86887},[250],[128,86889],{"className":86890,"style":1892},[254],[128,86892,23001],{"className":86893,"style":36065},[259,1873],[128,86895,2477],{"className":86896},[1896],[128,86898,2009],{"className":86899,"style":70411},[259,1873],[128,86901],{"className":86902,"style":1878},[269],[128,86904,1994],{"className":86905},[1882],[128,86907],{"className":86908,"style":1878},[269],[128,86910,86912,86915,86918,86921,86924],{"className":86911},[250],[128,86913],{"className":86914,"style":1892},[254],[128,86916,1842],{"className":86917},[259],[128,86919],{"className":86920,"style":1878},[269],[128,86922,5443],{"className":86923},[1882],[128,86925],{"className":86926,"style":1878},[269],[128,86928,86930,86933,86936,86939,86942,86945,86948,86951,86954],{"className":86929},[250],[128,86931],{"className":86932,"style":1892},[254],[128,86934,4519],{"className":86935},[259,1873],[128,86937,67350],{"className":86938},[259,1873],[128,86940,2477],{"className":86941},[1896],[128,86943,41957],{"className":86944,"style":42029},[259,1873],[128,86946,11],{"className":86947},[259,1873],[128,86949],{"className":86950,"style":1878},[269],[128,86952,1994],{"className":86953},[1882],[128,86955],{"className":86956,"style":1878},[269],[128,86958,86960,86963,86966,86969,86972,86975],{"className":86959},[250],[128,86961],{"className":86962,"style":1892},[254],[128,86964,1842],{"className":86965},[259],[128,86967,67410],{"className":86968},[1928],[128,86970],{"className":86971,"style":1878},[269],[128,86973,1994],{"className":86974},[1882],[128,86976],{"className":86977,"style":1878},[269],[128,86979,86981,86984,86987,86990,86993,86996,86999],{"className":86980},[250],[128,86982],{"className":86983,"style":1892},[254],[128,86985,23001],{"className":86986,"style":36065},[259,1873],[128,86988,2477],{"className":86989},[1896],[128,86991,2009],{"className":86992,"style":70411},[259,1873],[128,86994],{"className":86995,"style":1878},[269],[128,86997,1994],{"className":86998},[1882],[128,87000],{"className":87001,"style":1878},[269],[128,87003,87005,87008,87011,87014,87017,87020],{"className":87004},[250],[128,87006],{"className":87007,"style":1892},[254],[128,87009,1842],{"className":87010},[259],[128,87012,2486],{"className":87013},[1928],[128,87015],{"className":87016,"style":1878},[269],[128,87018,1994],{"className":87019},[1882],[128,87021],{"className":87022,"style":1878},[269],[128,87024,87026,87029,87070,87073,87076,87079,87082,87085,87088],{"className":87025},[250],[128,87027],{"className":87028,"style":7777},[254],[128,87030,87032,87035],{"className":87031},[2268],[128,87033,2042],{"className":87034,"style":2274},[2268,2272,2273],[128,87036,87038],{"className":87037},[2087],[128,87039,87041,87062],{"className":87040},[274,321],[128,87042,87044,87059],{"className":87043},[278],[128,87045,87048],{"className":87046,"style":87047},[282],"height:0.0017em;",[128,87049,87050,87053],{"style":2290},[128,87051],{"className":87052,"style":291},[290],[128,87054,87056],{"className":87055},[299,300,301,298],[128,87057,7590],{"className":87058},[259,1873,298],[128,87060,347],{"className":87061},[346],[128,87063,87065],{"className":87064},[278],[128,87066,87068],{"className":87067,"style":2330},[282],[128,87069],{},[128,87071],{"className":87072,"style":1907},[269],[128,87074,23001],{"className":87075,"style":36065},[259,1873],[128,87077,2477],{"className":87078},[1896],[128,87080,2009],{"className":87081,"style":70411},[259,1873],[128,87083],{"className":87084,"style":1878},[269],[128,87086,1994],{"className":87087},[1882],[128,87089],{"className":87090,"style":1878},[269],[128,87092,87094,87097,87100,87103,87106],{"className":87093},[250],[128,87095],{"className":87096,"style":1892},[254],[128,87098,1842],{"className":87099},[259],[128,87101],{"className":87102,"style":1878},[269],[128,87104,5443],{"className":87105},[1882],[128,87107],{"className":87108,"style":1878},[269],[128,87110,87112,87115,87118,87121,87124,87127,87130],{"className":87111},[250],[128,87113],{"className":87114,"style":1892},[254],[128,87116,7590],{"className":87117},[259,1873],[128,87119,2486],{"className":87120},[1928],[128,87122,23001],{"className":87123,"style":36065},[259,1873],[128,87125,2477],{"className":87126},[1896],[128,87128,7590],{"className":87129},[259,1873],[128,87131,2486],{"className":87132},[1928],"\n与是否干预洒水器完全无关。",[11,87135,87136,87139,87140,87168,87169,87197,87198,87501,87502,87684,87685,87946,87947,88176,88177,21562,88180,88231],{},[35,87137,87138],{},"数值验证","：把 2.3 节给出的具体参数代入，可以直接把这一差别算出来。由于 ",[128,87141,87143,87156],{"className":87142,"translate":218},[217],[128,87144,87146],{"className":87145},[222],[224,87147,87148],{"xmlns":226},[228,87149,87150,87154],{},[231,87151,87152],{},[1795,87153,41957],{},[238,87155,41957],{"encoding":240},[128,87157,87159],{"className":87158,"ariaHidden":246},[245],[128,87160,87162,87165],{"className":87161},[250],[128,87163],{"className":87164,"style":283},[254],[128,87166,41957],{"className":87167,"style":42029},[259,1873]," 是唯一影响 ",[128,87170,87172,87185],{"className":87171,"translate":218},[217],[128,87173,87175],{"className":87174},[222],[224,87176,87177],{"xmlns":226},[228,87178,87179,87183],{},[231,87180,87181],{},[1795,87182,2009],{},[238,87184,2009],{"encoding":240},[128,87186,87188],{"className":87187,"ariaHidden":246},[245],[128,87189,87191,87194],{"className":87190},[250],[128,87192],{"className":87193,"style":283},[254],[128,87195,2009],{"className":87196,"style":70411},[259,1873]," 的变量，\n",[128,87199,87201,87279],{"className":87200,"translate":218},[217],[128,87202,87204],{"className":87203},[222],[224,87205,87206],{"xmlns":226},[228,87207,87208,87276],{},[231,87209,87210,87212,87214,87216,87218,87220,87222,87224,87226,87228,87230,87232,87234,87236,87238,87240,87242,87244,87246,87248,87250,87252,87254,87256,87258,87260,87262,87264,87267,87269,87271,87273],{},[1795,87211,23001],{},[1832,87213,2477],{"stretchy":1837},[1795,87215,2009],{},[1832,87217,1994],{},[1840,87219,1842],{},[1832,87221,5443],{},[1795,87223,4519],{},[1795,87225,67350],{},[1832,87227,2477],{"stretchy":1837},[1795,87229,41957],{},[1795,87231,11],{},[1832,87233,1994],{},[1840,87235,1842],{},[1832,87237,2486],{"stretchy":1837},[1832,87239,2486],{"stretchy":1837},[1832,87241,1994],{},[1795,87243,23001],{},[1832,87245,2477],{"stretchy":1837},[1795,87247,2009],{},[1832,87249,1994],{},[1840,87251,1842],{},[1832,87253,2486],{"stretchy":1837},[1832,87255,1994],{},[1840,87257,80273],{},[1832,87259,68213],{},[1840,87261,80408],{},[1832,87263,9486],{},[1840,87265,87266],{},"0.7",[1832,87268,68213],{},[1840,87270,80455],{},[1832,87272,1994],{},[1840,87274,87275],{},"0.31",[238,87277,87278],{"encoding":240},"P(R=1\\mid do(Sp=1)) = P(R=1) = 0.3 \\times 0.8 + 0.7 \\times 0.1 = 0.31",[128,87280,87282,87306,87324,87354,87375,87399,87420,87438,87456,87474,87492],{"className":87281,"ariaHidden":246},[245],[128,87283,87285,87288,87291,87294,87297,87300,87303],{"className":87284},[250],[128,87286],{"className":87287,"style":1892},[254],[128,87289,23001],{"className":87290,"style":36065},[259,1873],[128,87292,2477],{"className":87293},[1896],[128,87295,2009],{"className":87296,"style":70411},[259,1873],[128,87298],{"className":87299,"style":1878},[269],[128,87301,1994],{"className":87302},[1882],[128,87304],{"className":87305,"style":1878},[269],[128,87307,87309,87312,87315,87318,87321],{"className":87308},[250],[128,87310],{"className":87311,"style":1892},[254],[128,87313,1842],{"className":87314},[259],[128,87316],{"className":87317,"style":1878},[269],[128,87319,5443],{"className":87320},[1882],[128,87322],{"className":87323,"style":1878},[269],[128,87325,87327,87330,87333,87336,87339,87342,87345,87348,87351],{"className":87326},[250],[128,87328],{"className":87329,"style":1892},[254],[128,87331,4519],{"className":87332},[259,1873],[128,87334,67350],{"className":87335},[259,1873],[128,87337,2477],{"className":87338},[1896],[128,87340,41957],{"className":87341,"style":42029},[259,1873],[128,87343,11],{"className":87344},[259,1873],[128,87346],{"className":87347,"style":1878},[269],[128,87349,1994],{"className":87350},[1882],[128,87352],{"className":87353,"style":1878},[269],[128,87355,87357,87360,87363,87366,87369,87372],{"className":87356},[250],[128,87358],{"className":87359,"style":1892},[254],[128,87361,1842],{"className":87362},[259],[128,87364,67410],{"className":87365},[1928],[128,87367],{"className":87368,"style":1878},[269],[128,87370,1994],{"className":87371},[1882],[128,87373],{"className":87374,"style":1878},[269],[128,87376,87378,87381,87384,87387,87390,87393,87396],{"className":87377},[250],[128,87379],{"className":87380,"style":1892},[254],[128,87382,23001],{"className":87383,"style":36065},[259,1873],[128,87385,2477],{"className":87386},[1896],[128,87388,2009],{"className":87389,"style":70411},[259,1873],[128,87391],{"className":87392,"style":1878},[269],[128,87394,1994],{"className":87395},[1882],[128,87397],{"className":87398,"style":1878},[269],[128,87400,87402,87405,87408,87411,87414,87417],{"className":87401},[250],[128,87403],{"className":87404,"style":1892},[254],[128,87406,1842],{"className":87407},[259],[128,87409,2486],{"className":87410},[1928],[128,87412],{"className":87413,"style":1878},[269],[128,87415,1994],{"className":87416},[1882],[128,87418],{"className":87419,"style":1878},[269],[128,87421,87423,87426,87429,87432,87435],{"className":87422},[250],[128,87424],{"className":87425,"style":4298},[254],[128,87427,80273],{"className":87428},[259],[128,87430],{"className":87431,"style":2508},[269],[128,87433,68213],{"className":87434},[2115],[128,87436],{"className":87437,"style":2508},[269],[128,87439,87441,87444,87447,87450,87453],{"className":87440},[250],[128,87442],{"className":87443,"style":4298},[254],[128,87445,80408],{"className":87446},[259],[128,87448],{"className":87449,"style":2508},[269],[128,87451,9486],{"className":87452},[2115],[128,87454],{"className":87455,"style":2508},[269],[128,87457,87459,87462,87465,87468,87471],{"className":87458},[250],[128,87460],{"className":87461,"style":4298},[254],[128,87463,87266],{"className":87464},[259],[128,87466],{"className":87467,"style":2508},[269],[128,87469,68213],{"className":87470},[2115],[128,87472],{"className":87473,"style":2508},[269],[128,87475,87477,87480,87483,87486,87489],{"className":87476},[250],[128,87478],{"className":87479,"style":2594},[254],[128,87481,80455],{"className":87482},[259],[128,87484],{"className":87485,"style":1878},[269],[128,87487,1994],{"className":87488},[1882],[128,87490],{"className":87491,"style":1878},[269],[128,87493,87495,87498],{"className":87494},[250],[128,87496],{"className":87497,"style":2594},[254],[128,87499,87275],{"className":87500},[259],"\n而由 ",[128,87503,87505,87552],{"className":87504,"translate":218},[217],[128,87506,87508],{"className":87507},[222],[224,87509,87510],{"xmlns":226},[228,87511,87512,87549],{},[231,87513,87514,87516,87518,87520,87522,87524,87526,87528,87530,87532,87534,87536,87538,87540,87542,87544,87546],{},[1795,87515,23001],{},[1832,87517,2477],{"stretchy":1837},[1795,87519,41957],{},[1795,87521,11],{},[1832,87523,1994],{},[1840,87525,1842],{},[1832,87527,2486],{"stretchy":1837},[1832,87529,1994],{},[1840,87531,80273],{},[1832,87533,68213],{},[1840,87535,80455],{},[1832,87537,9486],{},[1840,87539,87266],{},[1832,87541,68213],{},[1840,87543,80656],{},[1832,87545,1994],{},[1840,87547,87548],{},"0.45",[238,87550,87551],{"encoding":240},"P(Sp=1) = 0.3\\times 0.1 + 0.7\\times 0.6 = 0.45",[128,87553,87555,87582,87603,87621,87639,87657,87675],{"className":87554,"ariaHidden":246},[245],[128,87556,87558,87561,87564,87567,87570,87573,87576,87579],{"className":87557},[250],[128,87559],{"className":87560,"style":1892},[254],[128,87562,23001],{"className":87563,"style":36065},[259,1873],[128,87565,2477],{"className":87566},[1896],[128,87568,41957],{"className":87569,"style":42029},[259,1873],[128,87571,11],{"className":87572},[259,1873],[128,87574],{"className":87575,"style":1878},[269],[128,87577,1994],{"className":87578},[1882],[128,87580],{"className":87581,"style":1878},[269],[128,87583,87585,87588,87591,87594,87597,87600],{"className":87584},[250],[128,87586],{"className":87587,"style":1892},[254],[128,87589,1842],{"className":87590},[259],[128,87592,2486],{"className":87593},[1928],[128,87595],{"className":87596,"style":1878},[269],[128,87598,1994],{"className":87599},[1882],[128,87601],{"className":87602,"style":1878},[269],[128,87604,87606,87609,87612,87615,87618],{"className":87605},[250],[128,87607],{"className":87608,"style":4298},[254],[128,87610,80273],{"className":87611},[259],[128,87613],{"className":87614,"style":2508},[269],[128,87616,68213],{"className":87617},[2115],[128,87619],{"className":87620,"style":2508},[269],[128,87622,87624,87627,87630,87633,87636],{"className":87623},[250],[128,87625],{"className":87626,"style":4298},[254],[128,87628,80455],{"className":87629},[259],[128,87631],{"className":87632,"style":2508},[269],[128,87634,9486],{"className":87635},[2115],[128,87637],{"className":87638,"style":2508},[269],[128,87640,87642,87645,87648,87651,87654],{"className":87641},[250],[128,87643],{"className":87644,"style":4298},[254],[128,87646,87266],{"className":87647},[259],[128,87649],{"className":87650,"style":2508},[269],[128,87652,68213],{"className":87653},[2115],[128,87655],{"className":87656,"style":2508},[269],[128,87658,87660,87663,87666,87669,87672],{"className":87659},[250],[128,87661],{"className":87662,"style":2594},[254],[128,87664,80656],{"className":87665},[259],[128,87667],{"className":87668,"style":1878},[269],[128,87670,1994],{"className":87671},[1882],[128,87673],{"className":87674,"style":1878},[269],[128,87676,87678,87681],{"className":87677},[250],[128,87679],{"className":87680,"style":2594},[254],[128,87682,87548],{"className":87683},[259]," 及 ",[128,87686,87688,87751],{"className":87687,"translate":218},[217],[128,87689,87691],{"className":87690},[222],[224,87692,87693],{"xmlns":226},[228,87694,87695,87748],{},[231,87696,87697,87699,87701,87703,87705,87707,87709,87711,87713,87715,87717,87719,87721,87723,87725,87727,87729,87731,87733,87735,87737,87739,87741,87743,87745],{},[1795,87698,23001],{},[1832,87700,2477],{"stretchy":1837},[1795,87702,2009],{},[1832,87704,1994],{},[1840,87706,1842],{},[1832,87708,1845],{"separator":246},[1795,87710,41957],{},[1795,87712,11],{},[1832,87714,1994],{},[1840,87716,1842],{},[1832,87718,2486],{"stretchy":1837},[1832,87720,1994],{},[1840,87722,80273],{},[1832,87724,68213],{},[1840,87726,80408],{},[1832,87728,68213],{},[1840,87730,80455],{},[1832,87732,9486],{},[1840,87734,87266],{},[1832,87736,68213],{},[1840,87738,80455],{},[1832,87740,68213],{},[1840,87742,80656],{},[1832,87744,1994],{},[1840,87746,87747],{},"0.066",[238,87749,87750],{"encoding":240},"P(R=1, Sp=1) = 0.3\\times 0.8\\times 0.1 + 0.7\\times 0.1\\times 0.6 = 0.066",[128,87752,87754,87778,87808,87829,87847,87865,87883,87901,87919,87937],{"className":87753,"ariaHidden":246},[245],[128,87755,87757,87760,87763,87766,87769,87772,87775],{"className":87756},[250],[128,87758],{"className":87759,"style":1892},[254],[128,87761,23001],{"className":87762,"style":36065},[259,1873],[128,87764,2477],{"className":87765},[1896],[128,87767,2009],{"className":87768,"style":70411},[259,1873],[128,87770],{"className":87771,"style":1878},[269],[128,87773,1994],{"className":87774},[1882],[128,87776],{"className":87777,"style":1878},[269],[128,87779,87781,87784,87787,87790,87793,87796,87799,87802,87805],{"className":87780},[250],[128,87782],{"className":87783,"style":40674},[254],[128,87785,1842],{"className":87786},[259],[128,87788,1845],{"className":87789},[1903],[128,87791],{"className":87792,"style":1907},[269],[128,87794,41957],{"className":87795,"style":42029},[259,1873],[128,87797,11],{"className":87798},[259,1873],[128,87800],{"className":87801,"style":1878},[269],[128,87803,1994],{"className":87804},[1882],[128,87806],{"className":87807,"style":1878},[269],[128,87809,87811,87814,87817,87820,87823,87826],{"className":87810},[250],[128,87812],{"className":87813,"style":1892},[254],[128,87815,1842],{"className":87816},[259],[128,87818,2486],{"className":87819},[1928],[128,87821],{"className":87822,"style":1878},[269],[128,87824,1994],{"className":87825},[1882],[128,87827],{"className":87828,"style":1878},[269],[128,87830,87832,87835,87838,87841,87844],{"className":87831},[250],[128,87833],{"className":87834,"style":4298},[254],[128,87836,80273],{"className":87837},[259],[128,87839],{"className":87840,"style":2508},[269],[128,87842,68213],{"className":87843},[2115],[128,87845],{"className":87846,"style":2508},[269],[128,87848,87850,87853,87856,87859,87862],{"className":87849},[250],[128,87851],{"className":87852,"style":4298},[254],[128,87854,80408],{"className":87855},[259],[128,87857],{"className":87858,"style":2508},[269],[128,87860,68213],{"className":87861},[2115],[128,87863],{"className":87864,"style":2508},[269],[128,87866,87868,87871,87874,87877,87880],{"className":87867},[250],[128,87869],{"className":87870,"style":4298},[254],[128,87872,80455],{"className":87873},[259],[128,87875],{"className":87876,"style":2508},[269],[128,87878,9486],{"className":87879},[2115],[128,87881],{"className":87882,"style":2508},[269],[128,87884,87886,87889,87892,87895,87898],{"className":87885},[250],[128,87887],{"className":87888,"style":4298},[254],[128,87890,87266],{"className":87891},[259],[128,87893],{"className":87894,"style":2508},[269],[128,87896,68213],{"className":87897},[2115],[128,87899],{"className":87900,"style":2508},[269],[128,87902,87904,87907,87910,87913,87916],{"className":87903},[250],[128,87905],{"className":87906,"style":4298},[254],[128,87908,80455],{"className":87909},[259],[128,87911],{"className":87912,"style":2508},[269],[128,87914,68213],{"className":87915},[2115],[128,87917],{"className":87918,"style":2508},[269],[128,87920,87922,87925,87928,87931,87934],{"className":87921},[250],[128,87923],{"className":87924,"style":2594},[254],[128,87926,80656],{"className":87927},[259],[128,87929],{"className":87930,"style":1878},[269],[128,87932,1994],{"className":87933},[1882],[128,87935],{"className":87936,"style":1878},[269],[128,87938,87940,87943],{"className":87939},[250],[128,87941],{"className":87942,"style":2594},[254],[128,87944,87747],{"className":87945},[259],"，得\n",[128,87948,87950,87997],{"className":87949,"translate":218},[217],[128,87951,87953],{"className":87952},[222],[224,87954,87955],{"xmlns":226},[228,87956,87957,87994],{},[231,87958,87959,87961,87963,87965,87967,87969,87971,87973,87975,87977,87979,87981,87983,87989,87991],{},[1795,87960,23001],{},[1832,87962,2477],{"stretchy":1837},[1795,87964,2009],{},[1832,87966,1994],{},[1840,87968,1842],{},[1832,87970,5443],{},[1795,87972,41957],{},[1795,87974,11],{},[1832,87976,1994],{},[1840,87978,1842],{},[1832,87980,2486],{"stretchy":1837},[1832,87982,1994],{},[5451,87984,87985,87987],{},[1840,87986,87747],{},[1840,87988,87548],{},[1832,87990,58828],{},[1840,87992,87993],{},"0.147",[238,87995,87996],{"encoding":240},"P(R=1 \\mid Sp=1) = \\frac{0.066}{0.45} \\approx 0.147",[128,87998,88000,88024,88042,88063,88084,88167],{"className":87999,"ariaHidden":246},[245],[128,88001,88003,88006,88009,88012,88015,88018,88021],{"className":88002},[250],[128,88004],{"className":88005,"style":1892},[254],[128,88007,23001],{"className":88008,"style":36065},[259,1873],[128,88010,2477],{"className":88011},[1896],[128,88013,2009],{"className":88014,"style":70411},[259,1873],[128,88016],{"className":88017,"style":1878},[269],[128,88019,1994],{"className":88020},[1882],[128,88022],{"className":88023,"style":1878},[269],[128,88025,88027,88030,88033,88036,88039],{"className":88026},[250],[128,88028],{"className":88029,"style":1892},[254],[128,88031,1842],{"className":88032},[259],[128,88034],{"className":88035,"style":1878},[269],[128,88037,5443],{"className":88038},[1882],[128,88040],{"className":88041,"style":1878},[269],[128,88043,88045,88048,88051,88054,88057,88060],{"className":88044},[250],[128,88046],{"className":88047,"style":40674},[254],[128,88049,41957],{"className":88050,"style":42029},[259,1873],[128,88052,11],{"className":88053},[259,1873],[128,88055],{"className":88056,"style":1878},[269],[128,88058,1994],{"className":88059},[1882],[128,88061],{"className":88062,"style":1878},[269],[128,88064,88066,88069,88072,88075,88078,88081],{"className":88065},[250],[128,88067],{"className":88068,"style":1892},[254],[128,88070,1842],{"className":88071},[259],[128,88073,2486],{"className":88074},[1928],[128,88076],{"className":88077,"style":1878},[269],[128,88079,1994],{"className":88080},[1882],[128,88082],{"className":88083,"style":1878},[269],[128,88085,88087,88090,88158,88161,88164],{"className":88086},[250],[128,88088],{"className":88089,"style":44263},[254],[128,88091,88093,88096,88155],{"className":88092},[259],[128,88094],{"className":88095},[1896,5570],[128,88097,88099],{"className":88098},[5451],[128,88100,88102,88147],{"className":88101},[274,321],[128,88103,88105,88144],{"className":88104},[278],[128,88106,88108,88122,88130],{"className":88107,"style":5583},[282],[128,88109,88110,88113],{"style":5586},[128,88111],{"className":88112,"style":335},[290],[128,88114,88116],{"className":88115},[299,300,301,298],[128,88117,88119],{"className":88118},[259,298],[128,88120,87548],{"className":88121},[259,298],[128,88123,88124,88127],{"style":5617},[128,88125],{"className":88126,"style":335},[290],[128,88128],{"className":88129,"style":5625},[5624],[128,88131,88132,88135],{"style":5628},[128,88133],{"className":88134,"style":335},[290],[128,88136,88138],{"className":88137},[299,300,301,298],[128,88139,88141],{"className":88140},[259,298],[128,88142,87747],{"className":88143},[259,298],[128,88145,347],{"className":88146},[346],[128,88148,88150],{"className":88149},[278],[128,88151,88153],{"className":88152,"style":11919},[282],[128,88154],{},[128,88156],{"className":88157},[1928,5570],[128,88159],{"className":88160,"style":1878},[269],[128,88162,58828],{"className":88163},[1882],[128,88165],{"className":88166,"style":1878},[269],[128,88168,88170,88173],{"className":88169},[250],[128,88171],{"className":88172,"style":2594},[254],[128,88174,87993],{"className":88175},[259],"\n二者相差一倍以上，且方向与正文的分析完全一致：",[35,88178,88179],{},"观察到洒水器开着，反而使我们对「正在下雨」的信念大幅下降",[128,88181,88183,88201],{"className":88182,"translate":218},[217],[128,88184,88186],{"className":88185},[222],[224,88187,88188],{"xmlns":226},[228,88189,88190,88198],{},[231,88191,88192,88194,88196],{},[1840,88193,87993],{},[1832,88195,4221],{},[1840,88197,87275],{},[238,88199,88200],{"encoding":240},"0.147 \u003C 0.31",[128,88202,88204,88222],{"className":88203,"ariaHidden":246},[245],[128,88205,88207,88210,88213,88216,88219],{"className":88206},[250],[128,88208],{"className":88209,"style":34743},[254],[128,88211,87993],{"className":88212},[259],[128,88214],{"className":88215,"style":1878},[269],[128,88217,4221],{"className":88218},[1882],[128,88220],{"className":88221,"style":1878},[269],[128,88223,88225,88228],{"className":88224},[250],[128,88226],{"className":88227,"style":2594},[254],[128,88229,87275],{"className":88230},[259],"）——因为洒水器在旱季更常开启，观测到它本身即构成「当前是旱季」的证据，进而压低降雨概率。这两个数字之间的差距，就是「相关」与「因果」在同一个模型内部的全部分量。",[11,88233,88234,88235,88410],{},"一般地，",[128,88236,88238,88284],{"className":88237,"translate":218},[217],[128,88239,88241],{"className":88240},[222],[224,88242,88243],{"xmlns":226},[228,88244,88245,88281],{},[231,88246,88247,88249,88251,88253,88255,88257,88259,88261,88263,88265,88267,88269,88271,88273,88275,88277,88279],{},[1795,88248,23001],{},[1832,88250,2477],{"stretchy":1837},[1795,88252,1830],{},[1832,88254,5443],{},[1795,88256,2760],{},[1832,88258,2486],{"stretchy":1837},[1832,88260,16716],{"mathvariant":1981},[1795,88262,23001],{},[1832,88264,2477],{"stretchy":1837},[1795,88266,1830],{},[1832,88268,5443],{},[1795,88270,4519],{},[1795,88272,67350],{},[1832,88274,2477],{"stretchy":1837},[1795,88276,2760],{},[1832,88278,2486],{"stretchy":1837},[1832,88280,2486],{"stretchy":1837},[238,88282,88283],{"encoding":240},"P(y\\mid x) \\neq P(y \\mid do(x))",[128,88285,88287,88311,88365,88389],{"className":88286,"ariaHidden":246},[245],[128,88288,88290,88293,88296,88299,88302,88305,88308],{"className":88289},[250],[128,88291],{"className":88292,"style":1892},[254],[128,88294,23001],{"className":88295,"style":36065},[259,1873],[128,88297,2477],{"className":88298},[1896],[128,88300,1830],{"className":88301,"style":1874},[259,1873],[128,88303],{"className":88304,"style":1878},[269],[128,88306,5443],{"className":88307},[1882],[128,88309],{"className":88310,"style":1878},[269],[128,88312,88314,88317,88320,88323,88326,88362],{"className":88313},[250],[128,88315],{"className":88316,"style":1892},[254],[128,88318,2760],{"className":88319},[259,1873],[128,88321,2486],{"className":88322},[1928],[128,88324],{"className":88325,"style":1878},[269],[128,88327,88329,88356,88359],{"className":88328},[1882],[128,88330,88332],{"className":88331},[1882],[128,88333,88335],{"className":88334},[259,17719],[128,88336,88338],{"className":88337},[17723],[128,88339,88341,88344,88353],{"className":88340},[17727],[128,88342],{"className":88343,"style":16030},[254],[128,88345,88347],{"className":88346},[17734],[128,88348,88350],{"className":88349},[259],[128,88351,17741],{"className":88352},[1882],[128,88354],{"className":88355},[17745],[128,88357],{"className":88358},[269,17749],[128,88360,1994],{"className":88361},[1882],[128,88363],{"className":88364,"style":1878},[269],[128,88366,88368,88371,88374,88377,88380,88383,88386],{"className":88367},[250],[128,88369],{"className":88370,"style":1892},[254],[128,88372,23001],{"className":88373,"style":36065},[259,1873],[128,88375,2477],{"className":88376},[1896],[128,88378,1830],{"className":88379,"style":1874},[259,1873],[128,88381],{"className":88382,"style":1878},[269],[128,88384,5443],{"className":88385},[1882],[128,88387],{"className":88388,"style":1878},[269],[128,88390,88392,88395,88398,88401,88404,88407],{"className":88391},[250],[128,88393],{"className":88394,"style":1892},[254],[128,88396,4519],{"className":88397},[259,1873],[128,88399,67350],{"className":88400},[259,1873],[128,88402,2477],{"className":88403},[1896],[128,88405,2760],{"className":88406},[259,1873],[128,88408,67410],{"className":88409},[1928],"，二者的差异正是「相关不蕴含因果」这一箴言在结构方程框架下的精确定量表述：前者包含了通过混杂路径（如叉结构）传递的虚假信息，后者则通过对结构方程的手术式修改将其剔除。",[2610,88412,88414],{"id":88413},"_33-反事实从群体到个体","3.3 反事实：从群体到个体",[11,88416,88417,88418,88501,88502,88505,88506,2674,88556,88584,88585,88588,88589,88740,88741,67864,88769,88898,88899,88927],{},"干预分布 ",[128,88419,88421,88453],{"className":88420,"translate":218},[217],[128,88422,88424],{"className":88423},[222],[224,88425,88426],{"xmlns":226},[228,88427,88428,88450],{},[231,88429,88430,88432,88434,88436,88438,88440,88442,88444,88446,88448],{},[1795,88431,23001],{},[1832,88433,2477],{"stretchy":1837},[1795,88435,1830],{},[1832,88437,5443],{},[1795,88439,4519],{},[1795,88441,67350],{},[1832,88443,2477],{"stretchy":1837},[1795,88445,2760],{},[1832,88447,2486],{"stretchy":1837},[1832,88449,2486],{"stretchy":1837},[238,88451,88452],{"encoding":240},"P(y \\mid do(x))",[128,88454,88456,88480],{"className":88455,"ariaHidden":246},[245],[128,88457,88459,88462,88465,88468,88471,88474,88477],{"className":88458},[250],[128,88460],{"className":88461,"style":1892},[254],[128,88463,23001],{"className":88464,"style":36065},[259,1873],[128,88466,2477],{"className":88467},[1896],[128,88469,1830],{"className":88470,"style":1874},[259,1873],[128,88472],{"className":88473,"style":1878},[269],[128,88475,5443],{"className":88476},[1882],[128,88478],{"className":88479,"style":1878},[269],[128,88481,88483,88486,88489,88492,88495,88498],{"className":88482},[250],[128,88484],{"className":88485,"style":1892},[254],[128,88487,4519],{"className":88488},[259,1873],[128,88490,67350],{"className":88491},[259,1873],[128,88493,2477],{"className":88494},[1896],[128,88496,2760],{"className":88497},[259,1873],[128,88499,67410],{"className":88500},[1928]," 回答的是",[35,88503,88504],{},"群体或总体层面","的问题：「若对某个（服从既定分布的）个体施加干预 ",[128,88507,88509,88526],{"className":88508,"translate":218},[217],[128,88510,88512],{"className":88511},[222],[224,88513,88514],{"xmlns":226},[228,88515,88516,88524],{},[231,88517,88518,88520,88522],{},[1795,88519,364],{},[1832,88521,1994],{},[1795,88523,2760],{},[238,88525,67261],{"encoding":240},[128,88527,88529,88547],{"className":88528,"ariaHidden":246},[245],[128,88530,88532,88535,88538,88541,88544],{"className":88531},[250],[128,88533],{"className":88534,"style":283},[254],[128,88536,364],{"className":88537,"style":30665},[259,1873],[128,88539],{"className":88540,"style":1878},[269],[128,88542,1994],{"className":88543},[1882],[128,88545],{"className":88546,"style":1878},[269],[128,88548,88550,88553],{"className":88549},[250],[128,88551],{"className":88552,"style":7758},[254],[128,88554,2760],{"className":88555},[259,1873],[128,88557,88559,88572],{"className":88558,"translate":218},[217],[128,88560,88562],{"className":88561},[222],[224,88563,88564],{"xmlns":226},[228,88565,88566,88570],{},[231,88567,88568],{},[1795,88569,35023],{},[238,88571,35023],{"encoding":240},[128,88573,88575],{"className":88574,"ariaHidden":246},[245],[128,88576,88578,88581],{"className":88577},[250],[128,88579],{"className":88580,"style":283},[254],[128,88582,35023],{"className":88583,"style":2508},[259,1873]," 的分布会是什么」。而反事实推理进一步追问",[35,88586,88587],{},"特定已观测个体","层面的问题：「对于这个已经观测到 ",[128,88590,88592,88625],{"className":88591,"translate":218},[217],[128,88593,88595],{"className":88594},[222],[224,88596,88597],{"xmlns":226},[228,88598,88599,88623],{},[231,88600,88601,88603,88605,88611,88613,88615,88617],{},[1795,88602,364],{},[1832,88604,1994],{},[1977,88606,88607,88609],{},[1795,88608,2760],{},[1832,88610,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},[1832,88612,1845],{"separator":246},[1795,88614,35023],{},[1832,88616,1994],{},[1977,88618,88619,88621],{},[1795,88620,1830],{},[1832,88622,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},[238,88624,67719],{"encoding":240},[128,88626,88628,88646,88702],{"className":88627,"ariaHidden":246},[245],[128,88629,88631,88634,88637,88640,88643],{"className":88630},[250],[128,88632],{"className":88633,"style":283},[254],[128,88635,364],{"className":88636,"style":30665},[259,1873],[128,88638],{"className":88639,"style":1878},[269],[128,88641,1994],{"className":88642},[1882],[128,88644],{"className":88645,"style":1878},[269],[128,88647,88649,88652,88684,88687,88690,88693,88696,88699],{"className":88648},[250],[128,88650],{"className":88651,"style":50766},[254],[128,88653,88655,88658],{"className":88654},[259],[128,88656,2760],{"className":88657},[259,1873],[128,88659,88661],{"className":88660},[2087],[128,88662,88664],{"className":88663},[274],[128,88665,88667],{"className":88666},[278],[128,88668,88670],{"className":88669,"style":24927},[282],[128,88671,88672,88675],{"style":2452},[128,88673],{"className":88674,"style":291},[290],[128,88676,88678],{"className":88677},[299,300,301,298],[128,88679,88681],{"className":88680},[259,298],[128,88682,24873],{"className":88683},[259,298],[128,88685,1845],{"className":88686},[1903],[128,88688],{"className":88689,"style":1907},[269],[128,88691,35023],{"className":88692,"style":2508},[259,1873],[128,88694],{"className":88695,"style":1878},[269],[128,88697,1994],{"className":88698},[1882],[128,88700],{"className":88701,"style":1878},[269],[128,88703,88705,88708],{"className":88704},[250],[128,88706],{"className":88707,"style":50766},[254],[128,88709,88711,88714],{"className":88710},[259],[128,88712,1830],{"className":88713,"style":1874},[259,1873],[128,88715,88717],{"className":88716},[2087],[128,88718,88720],{"className":88719},[274],[128,88721,88723],{"className":88722},[278],[128,88724,88726],{"className":88725,"style":24927},[282],[128,88727,88728,88731],{"style":2452},[128,88729],{"className":88730,"style":291},[290],[128,88732,88734],{"className":88733},[299,300,301,298],[128,88735,88737],{"className":88736},[259,298],[128,88738,24873],{"className":88739},[259,298]," 的具体个体，若当初 ",[128,88742,88744,88757],{"className":88743,"translate":218},[217],[128,88745,88747],{"className":88746},[222],[224,88748,88749],{"xmlns":226},[228,88750,88751,88755],{},[231,88752,88753],{},[1795,88754,364],{},[238,88756,364],{"encoding":240},[128,88758,88760],{"className":88759,"ariaHidden":246},[245],[128,88761,88763,88766],{"className":88762},[250],[128,88764],{"className":88765,"style":283},[254],[128,88767,364],{"className":88768,"style":30665},[259,1873],[128,88770,88772,88800],{"className":88771,"translate":218},[217],[128,88773,88775],{"className":88774},[222],[224,88776,88777],{"xmlns":226},[228,88778,88779,88797],{},[231,88780,88781,88783,88785,88787,88789,88795],{},[1795,88782,2760],{},[234,88784,2033],{},[1832,88786,2477],{"stretchy":1837},[1832,88788,16716],{"mathvariant":1981},[1977,88790,88791,88793],{},[1795,88792,2760],{},[1832,88794,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},[1832,88796,2486],{"stretchy":1837},[238,88798,88799],{"encoding":240},"x \\ (\\neq x')",[128,88801,88803,88857],{"className":88802,"ariaHidden":246},[245],[128,88804,88806,88809,88812,88815,88818,88854],{"className":88805},[250],[128,88807],{"className":88808,"style":1892},[254],[128,88810,2760],{"className":88811},[259,1873],[128,88813,2033],{"className":88814},[269],[128,88816,2477],{"className":88817},[1896],[128,88819,88821,88848,88851],{"className":88820},[1882],[128,88822,88824],{"className":88823},[1882],[128,88825,88827],{"className":88826},[259,17719],[128,88828,88830],{"className":88829},[17723],[128,88831,88833,88836,88845],{"className":88832},[17727],[128,88834],{"className":88835,"style":16030},[254],[128,88837,88839],{"className":88838},[17734],[128,88840,88842],{"className":88841},[259],[128,88843,17741],{"className":88844},[1882],[128,88846],{"className":88847},[17745],[128,88849],{"className":88850},[269,17749],[128,88852,1994],{"className":88853},[1882],[128,88855],{"className":88856,"style":1878},[269],[128,88858,88860,88863,88895],{"className":88859},[250],[128,88861],{"className":88862,"style":24908},[254],[128,88864,88866,88869],{"className":88865},[259],[128,88867,2760],{"className":88868},[259,1873],[128,88870,88872],{"className":88871},[2087],[128,88873,88875],{"className":88874},[274],[128,88876,88878],{"className":88877},[278],[128,88879,88881],{"className":88880,"style":24927},[282],[128,88882,88883,88886],{"style":2452},[128,88884],{"className":88885,"style":291},[290],[128,88887,88889],{"className":88888},[299,300,301,298],[128,88890,88892],{"className":88891},[259,298],[128,88893,24873],{"className":88894},[259,298],[128,88896,2486],{"className":88897},[1928],"，其 ",[128,88900,88902,88915],{"className":88901,"translate":218},[217],[128,88903,88905],{"className":88904},[222],[224,88906,88907],{"xmlns":226},[228,88908,88909,88913],{},[231,88910,88911],{},[1795,88912,35023],{},[238,88914,35023],{"encoding":240},[128,88916,88918],{"className":88917,"ariaHidden":246},[245],[128,88919,88921,88924],{"className":88920},[250],[128,88922],{"className":88923,"style":283},[254],[128,88925,35023],{"className":88926,"style":2508},[259,1873]," 会是什么」。这需要更精细的结构。",[2615,88929,88931],{"title":88930},"定义 3.4（潜在结果，Potential Outcome）",[11,88932,77578,88933,88961,88962,89013,89014,89042,89043,89093,89094,89097,89098,23604,89167,89217,89218],{},[128,88934,88936,88949],{"className":88935,"translate":218},[217],[128,88937,88939],{"className":88938},[222],[224,88940,88941],{"xmlns":226},[228,88942,88943,88947],{},[231,88944,88945],{},[1795,88946,30641],{},[238,88948,30641],{"encoding":240},[128,88950,88952],{"className":88951,"ariaHidden":246},[245],[128,88953,88955,88958],{"className":88954},[250],[128,88956],{"className":88957,"style":283},[254],[128,88959,30641],{"className":88960,"style":26806},[259,1873]," 与其外生变量的一次具体实现 ",[128,88963,88965,88983],{"className":88964,"translate":218},[217],[128,88966,88968],{"className":88967},[222],[224,88969,88970],{"xmlns":226},[228,88971,88972,88980],{},[231,88973,88974,88976,88978],{},[1795,88975,69050],{},[1832,88977,1994],{},[1795,88979,35129],{},[238,88981,88982],{"encoding":240},"U=u",[128,88984,88986,89004],{"className":88985,"ariaHidden":246},[245],[128,88987,88989,88992,88995,88998,89001],{"className":88988},[250],[128,88990],{"className":88991,"style":283},[254],[128,88993,69050],{"className":88994,"style":26806},[259,1873],[128,88996],{"className":88997,"style":1878},[269],[128,88999,1994],{"className":89000},[1882],[128,89002],{"className":89003,"style":1878},[269],[128,89005,89007,89010],{"className":89006},[250],[128,89008],{"className":89009,"style":7758},[254],[128,89011,35129],{"className":89012},[259,1873],"（对应一个特定「个体」或「世界状态」），变量 ",[128,89015,89017,89030],{"className":89016,"translate":218},[217],[128,89018,89020],{"className":89019},[222],[224,89021,89022],{"xmlns":226},[228,89023,89024,89028],{},[231,89025,89026],{},[1795,89027,35023],{},[238,89029,35023],{"encoding":240},[128,89031,89033],{"className":89032,"ariaHidden":246},[245],[128,89034,89036,89039],{"className":89035},[250],[128,89037],{"className":89038,"style":283},[254],[128,89040,35023],{"className":89041,"style":2508},[259,1873]," 在假设 ",[128,89044,89046,89063],{"className":89045,"translate":218},[217],[128,89047,89049],{"className":89048},[222],[224,89050,89051],{"xmlns":226},[228,89052,89053,89061],{},[231,89054,89055,89057,89059],{},[1795,89056,364],{},[1832,89058,1994],{},[1795,89060,2760],{},[238,89062,67261],{"encoding":240},[128,89064,89066,89084],{"className":89065,"ariaHidden":246},[245],[128,89067,89069,89072,89075,89078,89081],{"className":89068},[250],[128,89070],{"className":89071,"style":283},[254],[128,89073,364],{"className":89074,"style":30665},[259,1873],[128,89076],{"className":89077,"style":1878},[269],[128,89079,1994],{"className":89080},[1882],[128,89082],{"className":89083,"style":1878},[269],[128,89085,89087,89090],{"className":89086},[250],[128,89088],{"className":89089,"style":7758},[254],[128,89091,2760],{"className":89092},[259,1873]," 下的",[35,89095,89096],{},"潜在结果","定义为子模型 ",[128,89099,89101,89118],{"className":89100,"translate":218},[217],[128,89102,89104],{"className":89103},[222],[224,89105,89106],{"xmlns":226},[228,89107,89108,89116],{},[231,89109,89110],{},[2016,89111,89112,89114],{},[1795,89113,30641],{},[1795,89115,2760],{},[238,89117,84648],{"encoding":240},[128,89119,89121],{"className":89120,"ariaHidden":246},[245],[128,89122,89124,89127],{"className":89123},[250],[128,89125],{"className":89126,"style":36058},[254],[128,89128,89130,89133],{"className":89129},[259],[128,89131,30641],{"className":89132,"style":26806},[259,1873],[128,89134,89136],{"className":89135},[2087],[128,89137,89139,89159],{"className":89138},[274,321],[128,89140,89142,89156],{"className":89141},[278],[128,89143,89145],{"className":89144,"style":28738},[282],[128,89146,89147,89150],{"style":64697},[128,89148],{"className":89149,"style":291},[290],[128,89151,89153],{"className":89152},[299,300,301,298],[128,89154,2760],{"className":89155},[259,1873,298],[128,89157,347],{"className":89158},[346],[128,89160,89162],{"className":89161},[278],[128,89163,89165],{"className":89164,"style":2241},[282],[128,89166],{},[128,89168,89170,89187],{"className":89169,"translate":218},[217],[128,89171,89173],{"className":89172},[222],[224,89174,89175],{"xmlns":226},[228,89176,89177,89185],{},[231,89178,89179,89181,89183],{},[1795,89180,69050],{},[1832,89182,1994],{},[1795,89184,35129],{},[238,89186,88982],{"encoding":240},[128,89188,89190,89208],{"className":89189,"ariaHidden":246},[245],[128,89191,89193,89196,89199,89202,89205],{"className":89192},[250],[128,89194],{"className":89195,"style":283},[254],[128,89197,69050],{"className":89198,"style":26806},[259,1873],[128,89200],{"className":89201,"style":1878},[269],[128,89203,1994],{"className":89204},[1882],[128,89206],{"className":89207,"style":1878},[269],[128,89209,89211,89214],{"className":89210},[250],[128,89212],{"className":89213,"style":7758},[254],[128,89215,35129],{"className":89216},[259,1873]," 下的取值：\n",[128,89219,89221,89265],{"className":89220,"translate":218},[217],[128,89222,89224],{"className":89223},[222],[224,89225,89226],{"xmlns":226},[228,89227,89228,89262],{},[231,89229,89230,89236,89238,89240,89242,89244,89246,89256,89258,89260],{},[2016,89231,89232,89234],{},[1795,89233,35023],{},[1795,89235,2760],{},[1832,89237,2477],{"stretchy":1837},[1795,89239,35129],{},[1832,89241,2486],{"stretchy":1837},[1832,89243,2014],{},[1832,89245,1994],{},[2016,89247,89248,89250],{},[1795,89249,35023],{},[2016,89251,89252,89254],{},[1795,89253,30641],{},[1795,89255,2760],{},[1832,89257,2477],{"stretchy":1837},[1795,89259,35129],{},[1832,89261,2486],{"stretchy":1837},[238,89263,89264],{"encoding":240},"Y_x(u) := Y_{M_x}(u)",[128,89266,89268,89332],{"className":89267,"ariaHidden":246},[245],[128,89269,89271,89274,89314,89317,89320,89323,89326,89329],{"className":89270},[250],[128,89272],{"className":89273,"style":1892},[254],[128,89275,89277,89280],{"className":89276},[259],[128,89278,35023],{"className":89279,"style":2508},[259,1873],[128,89281,89283],{"className":89282},[2087],[128,89284,89286,89306],{"className":89285},[274,321],[128,89287,89289,89303],{"className":89288},[278],[128,89290,89292],{"className":89291,"style":28738},[282],[128,89293,89294,89297],{"style":68109},[128,89295],{"className":89296,"style":291},[290],[128,89298,89300],{"className":89299},[299,300,301,298],[128,89301,2760],{"className":89302},[259,1873,298],[128,89304,347],{"className":89305},[346],[128,89307,89309],{"className":89308},[278],[128,89310,89312],{"className":89311,"style":2241},[282],[128,89313],{},[128,89315,2477],{"className":89316},[1896],[128,89318,35129],{"className":89319},[259,1873],[128,89321,2486],{"className":89322},[1928],[128,89324],{"className":89325,"style":1878},[269],[128,89327,75429],{"className":89328},[1882],[128,89330],{"className":89331,"style":1878},[269],[128,89333,89335,89338,89418,89421,89424],{"className":89334},[250],[128,89336],{"className":89337,"style":84817},[254],[128,89339,89341,89344],{"className":89340},[259],[128,89342,35023],{"className":89343,"style":2508},[259,1873],[128,89345,89347],{"className":89346},[2087],[128,89348,89350,89410],{"className":89349},[274,321],[128,89351,89353,89407],{"className":89352},[278],[128,89354,89356],{"className":89355,"style":3004},[282],[128,89357,89358,89361],{"style":68109},[128,89359],{"className":89360,"style":291},[290],[128,89362,89364],{"className":89363},[299,300,301,298],[128,89365,89367],{"className":89366},[259,298],[128,89368,89370,89373],{"className":89369},[259,298],[128,89371,30641],{"className":89372,"style":26806},[259,1873,298],[128,89374,89376],{"className":89375},[2087],[128,89377,89379,89399],{"className":89378},[274,321],[128,89380,89382,89396],{"className":89381},[278],[128,89383,89385],{"className":89384,"style":30995},[282],[128,89386,89387,89390],{"style":84867},[128,89388],{"className":89389,"style":5790},[290],[128,89391,89393],{"className":89392},[299,5794,5795,298],[128,89394,2760],{"className":89395},[259,1873,298],[128,89397,347],{"className":89398},[346],[128,89400,89402],{"className":89401},[278],[128,89403,89405],{"className":89404,"style":5808},[282],[128,89406],{},[128,89408,347],{"className":89409},[346],[128,89411,89413],{"className":89412},[278],[128,89414,89416],{"className":89415,"style":84897},[282],[128,89417],{},[128,89419,2477],{"className":89420},[1896],[128,89422,35129],{"className":89423},[259,1873],[128,89425,2486],{"className":89426},[1928],[2615,89428,89430,89789],{"title":89429},"算法 3.1（反事实查询的三步算法）",[11,89431,89432,89433,89484,89485,89636,89637,89788],{},"给定观测证据 ",[128,89434,89436,89454],{"className":89435,"translate":218},[217],[128,89437,89439],{"className":89438},[222],[224,89440,89441],{"xmlns":226},[228,89442,89443,89451],{},[231,89444,89445,89447,89449],{},[1795,89446,342],{},[1832,89448,1994],{},[1795,89450,3713],{},[238,89452,89453],{"encoding":240},"E=e",[128,89455,89457,89475],{"className":89456,"ariaHidden":246},[245],[128,89458,89460,89463,89466,89469,89472],{"className":89459},[250],[128,89461],{"className":89462,"style":283},[254],[128,89464,342],{"className":89465,"style":42029},[259,1873],[128,89467],{"className":89468,"style":1878},[269],[128,89470,1994],{"className":89471},[1882],[128,89473],{"className":89474,"style":1878},[269],[128,89476,89478,89481],{"className":89477},[250],[128,89479],{"className":89480,"style":7758},[254],[128,89482,3713],{"className":89483},[259,1873],"（例如 ",[128,89486,89488,89521],{"className":89487,"translate":218},[217],[128,89489,89491],{"className":89490},[222],[224,89492,89493],{"xmlns":226},[228,89494,89495,89519],{},[231,89496,89497,89499,89501,89507,89509,89511,89513],{},[1795,89498,364],{},[1832,89500,1994],{},[1977,89502,89503,89505],{},[1795,89504,2760],{},[1832,89506,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},[1832,89508,1845],{"separator":246},[1795,89510,35023],{},[1832,89512,1994],{},[1977,89514,89515,89517],{},[1795,89516,1830],{},[1832,89518,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},[238,89520,67719],{"encoding":240},[128,89522,89524,89542,89598],{"className":89523,"ariaHidden":246},[245],[128,89525,89527,89530,89533,89536,89539],{"className":89526},[250],[128,89528],{"className":89529,"style":283},[254],[128,89531,364],{"className":89532,"style":30665},[259,1873],[128,89534],{"className":89535,"style":1878},[269],[128,89537,1994],{"className":89538},[1882],[128,89540],{"className":89541,"style":1878},[269],[128,89543,89545,89548,89580,89583,89586,89589,89592,89595],{"className":89544},[250],[128,89546],{"className":89547,"style":50766},[254],[128,89549,89551,89554],{"className":89550},[259],[128,89552,2760],{"className":89553},[259,1873],[128,89555,89557],{"className":89556},[2087],[128,89558,89560],{"className":89559},[274],[128,89561,89563],{"className":89562},[278],[128,89564,89566],{"className":89565,"style":24927},[282],[128,89567,89568,89571],{"style":2452},[128,89569],{"className":89570,"style":291},[290],[128,89572,89574],{"className":89573},[299,300,301,298],[128,89575,89577],{"className":89576},[259,298],[128,89578,24873],{"className":89579},[259,298],[128,89581,1845],{"className":89582},[1903],[128,89584],{"className":89585,"style":1907},[269],[128,89587,35023],{"className":89588,"style":2508},[259,1873],[128,89590],{"className":89591,"style":1878},[269],[128,89593,1994],{"className":89594},[1882],[128,89596],{"className":89597,"style":1878},[269],[128,89599,89601,89604],{"className":89600},[250],[128,89602],{"className":89603,"style":50766},[254],[128,89605,89607,89610],{"className":89606},[259],[128,89608,1830],{"className":89609,"style":1874},[259,1873],[128,89611,89613],{"className":89612},[2087],[128,89614,89616],{"className":89615},[274],[128,89617,89619],{"className":89618},[278],[128,89620,89622],{"className":89621,"style":24927},[282],[128,89623,89624,89627],{"style":2452},[128,89625],{"className":89626,"style":291},[290],[128,89628,89630],{"className":89629},[299,300,301,298],[128,89631,89633],{"className":89632},[259,298],[128,89634,24873],{"className":89635},[259,298],"），欲计算反事实量 ",[128,89638,89640,89676],{"className":89639,"translate":218},[217],[128,89641,89643],{"className":89642},[222],[224,89644,89645],{"xmlns":226},[228,89646,89647,89673],{},[231,89648,89649,89651,89653,89659,89661,89663,89665,89667,89669,89671],{},[1795,89650,23001],{},[1832,89652,2477],{"stretchy":1837},[2016,89654,89655,89657],{},[1795,89656,35023],{},[1795,89658,2760],{},[1832,89660,1994],{},[1795,89662,1830],{},[1832,89664,5443],{},[1795,89666,342],{},[1832,89668,1994],{},[1795,89670,3713],{},[1832,89672,2486],{"stretchy":1837},[238,89674,89675],{"encoding":240},"P(Y_x = y \\mid E=e)",[128,89677,89679,89740,89758,89776],{"className":89678,"ariaHidden":246},[245],[128,89680,89682,89685,89688,89691,89731,89734,89737],{"className":89681},[250],[128,89683],{"className":89684,"style":1892},[254],[128,89686,23001],{"className":89687,"style":36065},[259,1873],[128,89689,2477],{"className":89690},[1896],[128,89692,89694,89697],{"className":89693},[259],[128,89695,35023],{"className":89696,"style":2508},[259,1873],[128,89698,89700],{"className":89699},[2087],[128,89701,89703,89723],{"className":89702},[274,321],[128,89704,89706,89720],{"className":89705},[278],[128,89707,89709],{"className":89708,"style":28738},[282],[128,89710,89711,89714],{"style":68109},[128,89712],{"className":89713,"style":291},[290],[128,89715,89717],{"className":89716},[299,300,301,298],[128,89718,2760],{"className":89719},[259,1873,298],[128,89721,347],{"className":89722},[346],[128,89724,89726],{"className":89725},[278],[128,89727,89729],{"className":89728,"style":2241},[282],[128,89730],{},[128,89732],{"className":89733,"style":1878},[269],[128,89735,1994],{"className":89736},[1882],[128,89738],{"className":89739,"style":1878},[269],[128,89741,89743,89746,89749,89752,89755],{"className":89742},[250],[128,89744],{"className":89745,"style":1892},[254],[128,89747,1830],{"className":89748,"style":1874},[259,1873],[128,89750],{"className":89751,"style":1878},[269],[128,89753,5443],{"className":89754},[1882],[128,89756],{"className":89757,"style":1878},[269],[128,89759,89761,89764,89767,89770,89773],{"className":89760},[250],[128,89762],{"className":89763,"style":283},[254],[128,89765,342],{"className":89766,"style":42029},[259,1873],[128,89768],{"className":89769,"style":1878},[269],[128,89771,1994],{"className":89772},[1882],[128,89774],{"className":89775,"style":1878},[269],[128,89777,89779,89782,89785],{"className":89778},[250],[128,89780],{"className":89781,"style":1892},[254],[128,89783,3713],{"className":89784},[259,1873],[128,89786,2486],{"className":89787},[1928],"，分三步进行：",[33248,89790,89791,89937,90084],{},[33251,89792,89793,89796,89797,89825,89826,89869,89870,89936],{},[35,89794,89795],{},"溯因（Abduction）","：利用观测证据 ",[128,89798,89800,89813],{"className":89799,"translate":218},[217],[128,89801,89803],{"className":89802},[222],[224,89804,89805],{"xmlns":226},[228,89806,89807,89811],{},[231,89808,89809],{},[1795,89810,3713],{},[238,89812,3713],{"encoding":240},[128,89814,89816],{"className":89815,"ariaHidden":246},[245],[128,89817,89819,89822],{"className":89818},[250],[128,89820],{"className":89821,"style":7758},[254],[128,89823,3713],{"className":89824},[259,1873],"，将外生变量的先验分布 ",[128,89827,89829,89848],{"className":89828,"translate":218},[217],[128,89830,89832],{"className":89831},[222],[224,89833,89834],{"xmlns":226},[228,89835,89836,89846],{},[231,89837,89838,89840,89842,89844],{},[1795,89839,23001],{},[1832,89841,2477],{"stretchy":1837},[1795,89843,69050],{},[1832,89845,2486],{"stretchy":1837},[238,89847,77521],{"encoding":240},[128,89849,89851],{"className":89850,"ariaHidden":246},[245],[128,89852,89854,89857,89860,89863,89866],{"className":89853},[250],[128,89855],{"className":89856,"style":1892},[254],[128,89858,23001],{"className":89859,"style":36065},[259,1873],[128,89861,2477],{"className":89862},[1896],[128,89864,69050],{"className":89865,"style":26806},[259,1873],[128,89867,2486],{"className":89868},[1928]," 更新为后验分布 ",[128,89871,89873,89897],{"className":89872,"translate":218},[217],[128,89874,89876],{"className":89875},[222],[224,89877,89878],{"xmlns":226},[228,89879,89880,89894],{},[231,89881,89882,89884,89886,89888,89890,89892],{},[1795,89883,23001],{},[1832,89885,2477],{"stretchy":1837},[1795,89887,69050],{},[1832,89889,5443],{},[1795,89891,3713],{},[1832,89893,2486],{"stretchy":1837},[238,89895,89896],{"encoding":240},"P(U \\mid e)",[128,89898,89900,89924],{"className":89899,"ariaHidden":246},[245],[128,89901,89903,89906,89909,89912,89915,89918,89921],{"className":89902},[250],[128,89904],{"className":89905,"style":1892},[254],[128,89907,23001],{"className":89908,"style":36065},[259,1873],[128,89910,2477],{"className":89911},[1896],[128,89913,69050],{"className":89914,"style":26806},[259,1873],[128,89916],{"className":89917,"style":1878},[269],[128,89919,5443],{"className":89920},[1882],[128,89922],{"className":89923,"style":1878},[269],[128,89925,89927,89930,89933],{"className":89926},[250],[128,89928],{"className":89929,"style":1892},[254],[128,89931,3713],{"className":89932},[259,1873],[128,89934,2486],{"className":89935},[1928],"，即根据「结果倒推该个体所处的具体随机情境」；",[33251,89938,89939,89942,89943,90013,90014,90083],{},[35,89940,89941],{},"行动（Action）","：对结构方程集合施加 ",[128,89944,89946,89971],{"className":89945,"translate":218},[217],[128,89947,89949],{"className":89948},[222],[224,89950,89951],{"xmlns":226},[228,89952,89953,89969],{},[231,89954,89955,89957,89959,89961,89963,89965,89967],{},[1795,89956,4519],{},[1795,89958,67350],{},[1832,89960,2477],{"stretchy":1837},[1795,89962,364],{},[1832,89964,1994],{},[1795,89966,2760],{},[1832,89968,2486],{"stretchy":1837},[238,89970,74610],{"encoding":240},[128,89972,89974,90001],{"className":89973,"ariaHidden":246},[245],[128,89975,89977,89980,89983,89986,89989,89992,89995,89998],{"className":89976},[250],[128,89978],{"className":89979,"style":1892},[254],[128,89981,4519],{"className":89982},[259,1873],[128,89984,67350],{"className":89985},[259,1873],[128,89987,2477],{"className":89988},[1896],[128,89990,364],{"className":89991,"style":30665},[259,1873],[128,89993],{"className":89994,"style":1878},[269],[128,89996,1994],{"className":89997},[1882],[128,89999],{"className":90000,"style":1878},[269],[128,90002,90004,90007,90010],{"className":90003},[250],[128,90005],{"className":90006,"style":1892},[254],[128,90008,2760],{"className":90009},[259,1873],[128,90011,2486],{"className":90012},[1928],"，得到子模型 ",[128,90015,90017,90034],{"className":90016,"translate":218},[217],[128,90018,90020],{"className":90019},[222],[224,90021,90022],{"xmlns":226},[228,90023,90024,90032],{},[231,90025,90026],{},[2016,90027,90028,90030],{},[1795,90029,30641],{},[1795,90031,2760],{},[238,90033,84648],{"encoding":240},[128,90035,90037],{"className":90036,"ariaHidden":246},[245],[128,90038,90040,90043],{"className":90039},[250],[128,90041],{"className":90042,"style":36058},[254],[128,90044,90046,90049],{"className":90045},[259],[128,90047,30641],{"className":90048,"style":26806},[259,1873],[128,90050,90052],{"className":90051},[2087],[128,90053,90055,90075],{"className":90054},[274,321],[128,90056,90058,90072],{"className":90057},[278],[128,90059,90061],{"className":90060,"style":28738},[282],[128,90062,90063,90066],{"style":64697},[128,90064],{"className":90065,"style":291},[290],[128,90067,90069],{"className":90068},[299,300,301,298],[128,90070,2760],{"className":90071},[259,1873,298],[128,90073,347],{"className":90074},[346],[128,90076,90078],{"className":90077},[278],[128,90079,90081],{"className":90080,"style":2241},[282],[128,90082],{},"（同定义 3.2）；",[33251,90085,90086,90089,90090,90159,90160,90226,90227,90255,90256],{},[35,90087,90088],{},"预测（Prediction）","：在子模型 ",[128,90091,90093,90110],{"className":90092,"translate":218},[217],[128,90094,90096],{"className":90095},[222],[224,90097,90098],{"xmlns":226},[228,90099,90100,90108],{},[231,90101,90102],{},[2016,90103,90104,90106],{},[1795,90105,30641],{},[1795,90107,2760],{},[238,90109,84648],{"encoding":240},[128,90111,90113],{"className":90112,"ariaHidden":246},[245],[128,90114,90116,90119],{"className":90115},[250],[128,90117],{"className":90118,"style":36058},[254],[128,90120,90122,90125],{"className":90121},[259],[128,90123,30641],{"className":90124,"style":26806},[259,1873],[128,90126,90128],{"className":90127},[2087],[128,90129,90131,90151],{"className":90130},[274,321],[128,90132,90134,90148],{"className":90133},[278],[128,90135,90137],{"className":90136,"style":28738},[282],[128,90138,90139,90142],{"style":64697},[128,90140],{"className":90141,"style":291},[290],[128,90143,90145],{"className":90144},[299,300,301,298],[128,90146,2760],{"className":90147},[259,1873,298],[128,90149,347],{"className":90150},[346],[128,90152,90154],{"className":90153},[278],[128,90155,90157],{"className":90156,"style":2241},[282],[128,90158],{}," 中，用第一步得到的后验分布 ",[128,90161,90163,90187],{"className":90162,"translate":218},[217],[128,90164,90166],{"className":90165},[222],[224,90167,90168],{"xmlns":226},[228,90169,90170,90184],{},[231,90171,90172,90174,90176,90178,90180,90182],{},[1795,90173,23001],{},[1832,90175,2477],{"stretchy":1837},[1795,90177,69050],{},[1832,90179,5443],{},[1795,90181,3713],{},[1832,90183,2486],{"stretchy":1837},[238,90185,90186],{"encoding":240},"P(U\\mid e)",[128,90188,90190,90214],{"className":90189,"ariaHidden":246},[245],[128,90191,90193,90196,90199,90202,90205,90208,90211],{"className":90192},[250],[128,90194],{"className":90195,"style":1892},[254],[128,90197,23001],{"className":90198,"style":36065},[259,1873],[128,90200,2477],{"className":90201},[1896],[128,90203,69050],{"className":90204,"style":26806},[259,1873],[128,90206],{"className":90207,"style":1878},[269],[128,90209,5443],{"className":90210},[1882],[128,90212],{"className":90213,"style":1878},[269],[128,90215,90217,90220,90223],{"className":90216},[250],[128,90218],{"className":90219,"style":1892},[254],[128,90221,3713],{"className":90222},[259,1873],[128,90224,2486],{"className":90225},[1928]," 计算 ",[128,90228,90230,90243],{"className":90229,"translate":218},[217],[128,90231,90233],{"className":90232},[222],[224,90234,90235],{"xmlns":226},[228,90236,90237,90241],{},[231,90238,90239],{},[1795,90240,35023],{},[238,90242,35023],{"encoding":240},[128,90244,90246],{"className":90245,"ariaHidden":246},[245],[128,90247,90249,90252],{"className":90248},[250],[128,90250],{"className":90251,"style":283},[254],[128,90253,35023],{"className":90254,"style":2508},[259,1873]," 的分布，即为所求反事实分布：\n",[128,90257,90259,90339],{"className":90258,"translate":218},[217],[128,90260,90262],{"className":90261},[222],[224,90263,90264],{"xmlns":226},[228,90265,90266,90336],{},[231,90267,90268,90270,90272,90278,90280,90282,90284,90286,90288,90290,90296,90298,90300,90310,90312,90314,90316,90318,90320,90322,90324,90326,90328,90330,90332,90334],{},[1795,90269,23001],{},[1832,90271,2477],{"stretchy":1837},[2016,90273,90274,90276],{},[1795,90275,35023],{},[1795,90277,2760],{},[1832,90279,1994],{},[1795,90281,1830],{},[1832,90283,5443],{},[1795,90285,3713],{},[1832,90287,2486],{"stretchy":1837},[1832,90289,1994],{},[2016,90291,90292,90294],{},[1832,90293,2042],{},[1795,90295,35129],{},[1795,90297,23001],{},[1832,90299,2477],{"stretchy":1837},[2016,90301,90302,90304],{},[1795,90303,35023],{},[2016,90305,90306,90308],{},[1795,90307,30641],{},[1795,90309,2760],{},[1832,90311,2477],{"stretchy":1837},[1795,90313,35129],{},[1832,90315,2486],{"stretchy":1837},[1832,90317,1994],{},[1795,90319,1830],{},[1832,90321,2486],{"stretchy":1837},[1832,90323,12935],{},[1795,90325,23001],{},[1832,90327,2477],{"stretchy":1837},[1795,90329,35129],{},[1832,90331,5443],{},[1795,90333,3713],{},[1832,90335,2486],{"stretchy":1837},[238,90337,90338],{"encoding":240},"P(Y_x = y \\mid e) = \\sum_u P(Y_{M_x}(u) = y) \\cdot P(u \\mid e)",[128,90340,90342,90403,90421,90442,90595,90616,90640],{"className":90341,"ariaHidden":246},[245],[128,90343,90345,90348,90351,90354,90394,90397,90400],{"className":90344},[250],[128,90346],{"className":90347,"style":1892},[254],[128,90349,23001],{"className":90350,"style":36065},[259,1873],[128,90352,2477],{"className":90353},[1896],[128,90355,90357,90360],{"className":90356},[259],[128,90358,35023],{"className":90359,"style":2508},[259,1873],[128,90361,90363],{"className":90362},[2087],[128,90364,90366,90386],{"className":90365},[274,321],[128,90367,90369,90383],{"className":90368},[278],[128,90370,90372],{"className":90371,"style":28738},[282],[128,90373,90374,90377],{"style":68109},[128,90375],{"className":90376,"style":291},[290],[128,90378,90380],{"className":90379},[299,300,301,298],[128,90381,2760],{"className":90382},[259,1873,298],[128,90384,347],{"className":90385},[346],[128,90387,90389],{"className":90388},[278],[128,90390,90392],{"className":90391,"style":2241},[282],[128,90393],{},[128,90395],{"className":90396,"style":1878},[269],[128,90398,1994],{"className":90399},[1882],[128,90401],{"className":90402,"style":1878},[269],[128,90404,90406,90409,90412,90415,90418],{"className":90405},[250],[128,90407],{"className":90408,"style":1892},[254],[128,90410,1830],{"className":90411,"style":1874},[259,1873],[128,90413],{"className":90414,"style":1878},[269],[128,90416,5443],{"className":90417},[1882],[128,90419],{"className":90420,"style":1878},[269],[128,90422,90424,90427,90430,90433,90436,90439],{"className":90423},[250],[128,90425],{"className":90426,"style":1892},[254],[128,90428,3713],{"className":90429},[259,1873],[128,90431,2486],{"className":90432},[1928],[128,90434],{"className":90435,"style":1878},[269],[128,90437,1994],{"className":90438},[1882],[128,90440],{"className":90441,"style":1878},[269],[128,90443,90445,90448,90488,90491,90494,90497,90577,90580,90583,90586,90589,90592],{"className":90444},[250],[128,90446],{"className":90447,"style":7777},[254],[128,90449,90451,90454],{"className":90450},[2268],[128,90452,2042],{"className":90453,"style":2274},[2268,2272,2273],[128,90455,90457],{"className":90456},[2087],[128,90458,90460,90480],{"className":90459},[274,321],[128,90461,90463,90477],{"className":90462},[278],[128,90464,90466],{"className":90465,"style":87047},[282],[128,90467,90468,90471],{"style":2290},[128,90469],{"className":90470,"style":291},[290],[128,90472,90474],{"className":90473},[299,300,301,298],[128,90475,35129],{"className":90476},[259,1873,298],[128,90478,347],{"className":90479},[346],[128,90481,90483],{"className":90482},[278],[128,90484,90486],{"className":90485,"style":2330},[282],[128,90487],{},[128,90489],{"className":90490,"style":1907},[269],[128,90492,23001],{"className":90493,"style":36065},[259,1873],[128,90495,2477],{"className":90496},[1896],[128,90498,90500,90503],{"className":90499},[259],[128,90501,35023],{"className":90502,"style":2508},[259,1873],[128,90504,90506],{"className":90505},[2087],[128,90507,90509,90569],{"className":90508},[274,321],[128,90510,90512,90566],{"className":90511},[278],[128,90513,90515],{"className":90514,"style":3004},[282],[128,90516,90517,90520],{"style":68109},[128,90518],{"className":90519,"style":291},[290],[128,90521,90523],{"className":90522},[299,300,301,298],[128,90524,90526],{"className":90525},[259,298],[128,90527,90529,90532],{"className":90528},[259,298],[128,90530,30641],{"className":90531,"style":26806},[259,1873,298],[128,90533,90535],{"className":90534},[2087],[128,90536,90538,90558],{"className":90537},[274,321],[128,90539,90541,90555],{"className":90540},[278],[128,90542,90544],{"className":90543,"style":30995},[282],[128,90545,90546,90549],{"style":84867},[128,90547],{"className":90548,"style":5790},[290],[128,90550,90552],{"className":90551},[299,5794,5795,298],[128,90553,2760],{"className":90554},[259,1873,298],[128,90556,347],{"className":90557},[346],[128,90559,90561],{"className":90560},[278],[128,90562,90564],{"className":90563,"style":5808},[282],[128,90565],{},[128,90567,347],{"className":90568},[346],[128,90570,90572],{"className":90571},[278],[128,90573,90575],{"className":90574,"style":84897},[282],[128,90576],{},[128,90578,2477],{"className":90579},[1896],[128,90581,35129],{"className":90582},[259,1873],[128,90584,2486],{"className":90585},[1928],[128,90587],{"className":90588,"style":1878},[269],[128,90590,1994],{"className":90591},[1882],[128,90593],{"className":90594,"style":1878},[269],[128,90596,90598,90601,90604,90607,90610,90613],{"className":90597},[250],[128,90599],{"className":90600,"style":1892},[254],[128,90602,1830],{"className":90603,"style":1874},[259,1873],[128,90605,2486],{"className":90606},[1928],[128,90608],{"className":90609,"style":2508},[269],[128,90611,12935],{"className":90612},[2115],[128,90614],{"className":90615,"style":2508},[269],[128,90617,90619,90622,90625,90628,90631,90634,90637],{"className":90618},[250],[128,90620],{"className":90621,"style":1892},[254],[128,90623,23001],{"className":90624,"style":36065},[259,1873],[128,90626,2477],{"className":90627},[1896],[128,90629,35129],{"className":90630},[259,1873],[128,90632],{"className":90633,"style":1878},[269],[128,90635,5443],{"className":90636},[1882],[128,90638],{"className":90639,"style":1878},[269],[128,90641,90643,90646,90649],{"className":90642},[250],[128,90644],{"className":90645,"style":1892},[254],[128,90647,3713],{"className":90648},[259,1873],[128,90650,2486],{"className":90651},[1928],[2615,90653,90655],{"title":90654},"例 3.3（反事实的具体计算）",[11,90656,90657,90658,90709,90710,90761,90762,90813,90814,91000,91001,91004,91005,91132,91133,91136,91137,91165,91166,91219,91220,91248,91249,91277,91278,91464,91465,91468,91469,91596],{},"设某病人服用了某药（",[128,90659,90661,90679],{"className":90660,"translate":218},[217],[128,90662,90664],{"className":90663},[222],[224,90665,90666],{"xmlns":226},[228,90667,90668,90676],{},[231,90669,90670,90672,90674],{},[1795,90671,364],{},[1832,90673,1994],{},[1840,90675,1842],{},[238,90677,90678],{"encoding":240},"X=1",[128,90680,90682,90700],{"className":90681,"ariaHidden":246},[245],[128,90683,90685,90688,90691,90694,90697],{"className":90684},[250],[128,90686],{"className":90687,"style":283},[254],[128,90689,364],{"className":90690,"style":30665},[259,1873],[128,90692],{"className":90693,"style":1878},[269],[128,90695,1994],{"className":90696},[1882],[128,90698],{"className":90699,"style":1878},[269],[128,90701,90703,90706],{"className":90702},[250],[128,90704],{"className":90705,"style":2594},[254],[128,90707,1842],{"className":90708},[259],"）后康复（",[128,90711,90713,90731],{"className":90712,"translate":218},[217],[128,90714,90716],{"className":90715},[222],[224,90717,90718],{"xmlns":226},[228,90719,90720,90728],{},[231,90721,90722,90724,90726],{},[1795,90723,35023],{},[1832,90725,1994],{},[1840,90727,1842],{},[238,90729,90730],{"encoding":240},"Y=1",[128,90732,90734,90752],{"className":90733,"ariaHidden":246},[245],[128,90735,90737,90740,90743,90746,90749],{"className":90736},[250],[128,90738],{"className":90739,"style":283},[254],[128,90741,35023],{"className":90742,"style":2508},[259,1873],[128,90744],{"className":90745,"style":1878},[269],[128,90747,1994],{"className":90748},[1882],[128,90750],{"className":90751,"style":1878},[269],[128,90753,90755,90758],{"className":90754},[250],[128,90756],{"className":90757,"style":2594},[254],[128,90759,1842],{"className":90760},[259],"）。欲问：「若该病人当初未服药（",[128,90763,90765,90783],{"className":90764,"translate":218},[217],[128,90766,90768],{"className":90767},[222],[224,90769,90770],{"xmlns":226},[228,90771,90772,90780],{},[231,90773,90774,90776,90778],{},[1795,90775,364],{},[1832,90777,1994],{},[1840,90779,2028],{},[238,90781,90782],{"encoding":240},"X=0",[128,90784,90786,90804],{"className":90785,"ariaHidden":246},[245],[128,90787,90789,90792,90795,90798,90801],{"className":90788},[250],[128,90790],{"className":90791,"style":283},[254],[128,90793,364],{"className":90794,"style":30665},[259,1873],[128,90796],{"className":90797,"style":1878},[269],[128,90799,1994],{"className":90800},[1882],[128,90802],{"className":90803,"style":1878},[269],[128,90805,90807,90810],{"className":90806},[250],[128,90808],{"className":90809,"style":2594},[254],[128,90811,2028],{"className":90812},[259],"），是否仍会康复？」——即求 ",[128,90815,90817,90861],{"className":90816,"translate":218},[217],[128,90818,90820],{"className":90819},[222],[224,90821,90822],{"xmlns":226},[228,90823,90824,90858],{},[231,90825,90826,90828,90830,90836,90838,90840,90842,90844,90846,90848,90850,90852,90854,90856],{},[1795,90827,23001],{},[1832,90829,2477],{"stretchy":1837},[2016,90831,90832,90834],{},[1795,90833,35023],{},[1840,90835,2028],{},[1832,90837,1994],{},[1840,90839,1842],{},[1832,90841,5443],{},[1795,90843,364],{},[1832,90845,1994],{},[1840,90847,1842],{},[1832,90849,1845],{"separator":246},[1795,90851,35023],{},[1832,90853,1994],{},[1840,90855,1842],{},[1832,90857,2486],{"stretchy":1837},[238,90859,90860],{"encoding":240},"P(Y_0 = 1 \\mid X=1, Y=1)",[128,90862,90864,90925,90943,90961,90988],{"className":90863,"ariaHidden":246},[245],[128,90865,90867,90870,90873,90876,90916,90919,90922],{"className":90866},[250],[128,90868],{"className":90869,"style":1892},[254],[128,90871,23001],{"className":90872,"style":36065},[259,1873],[128,90874,2477],{"className":90875},[1896],[128,90877,90879,90882],{"className":90878},[259],[128,90880,35023],{"className":90881,"style":2508},[259,1873],[128,90883,90885],{"className":90884},[2087],[128,90886,90888,90908],{"className":90887},[274,321],[128,90889,90891,90905],{"className":90890},[278],[128,90892,90894],{"className":90893,"style":2945},[282],[128,90895,90896,90899],{"style":68109},[128,90897],{"className":90898,"style":291},[290],[128,90900,90902],{"className":90901},[299,300,301,298],[128,90903,2028],{"className":90904},[259,298],[128,90906,347],{"className":90907},[346],[128,90909,90911],{"className":90910},[278],[128,90912,90914],{"className":90913,"style":2241},[282],[128,90915],{},[128,90917],{"className":90918,"style":1878},[269],[128,90920,1994],{"className":90921},[1882],[128,90923],{"className":90924,"style":1878},[269],[128,90926,90928,90931,90934,90937,90940],{"className":90927},[250],[128,90929],{"className":90930,"style":1892},[254],[128,90932,1842],{"className":90933},[259],[128,90935],{"className":90936,"style":1878},[269],[128,90938,5443],{"className":90939},[1882],[128,90941],{"className":90942,"style":1878},[269],[128,90944,90946,90949,90952,90955,90958],{"className":90945},[250],[128,90947],{"className":90948,"style":283},[254],[128,90950,364],{"className":90951,"style":30665},[259,1873],[128,90953],{"className":90954,"style":1878},[269],[128,90956,1994],{"className":90957},[1882],[128,90959],{"className":90960,"style":1878},[269],[128,90962,90964,90967,90970,90973,90976,90979,90982,90985],{"className":90963},[250],[128,90965],{"className":90966,"style":40674},[254],[128,90968,1842],{"className":90969},[259],[128,90971,1845],{"className":90972},[1903],[128,90974],{"className":90975,"style":1907},[269],[128,90977,35023],{"className":90978,"style":2508},[259,1873],[128,90980],{"className":90981,"style":1878},[269],[128,90983,1994],{"className":90984},[1882],[128,90986],{"className":90987,"style":1878},[269],[128,90989,90991,90994,90997],{"className":90990},[250],[128,90992],{"className":90993,"style":1892},[254],[128,90995,1842],{"className":90996},[259],[128,90998,2486],{"className":90999},[1928],"。这一问题",[35,91002,91003],{},"不能","简单地用干预分布 ",[128,91006,91008,91048],{"className":91007,"translate":218},[217],[128,91009,91011],{"className":91010},[222],[224,91012,91013],{"xmlns":226},[228,91014,91015,91045],{},[231,91016,91017,91019,91021,91023,91025,91027,91029,91031,91033,91035,91037,91039,91041,91043],{},[1795,91018,23001],{},[1832,91020,2477],{"stretchy":1837},[1795,91022,35023],{},[1832,91024,1994],{},[1840,91026,1842],{},[1832,91028,5443],{},[1795,91030,4519],{},[1795,91032,67350],{},[1832,91034,2477],{"stretchy":1837},[1795,91036,364],{},[1832,91038,1994],{},[1840,91040,2028],{},[1832,91042,2486],{"stretchy":1837},[1832,91044,2486],{"stretchy":1837},[238,91046,91047],{"encoding":240},"P(Y=1 \\mid do(X=0))",[128,91049,91051,91075,91093,91120],{"className":91050,"ariaHidden":246},[245],[128,91052,91054,91057,91060,91063,91066,91069,91072],{"className":91053},[250],[128,91055],{"className":91056,"style":1892},[254],[128,91058,23001],{"className":91059,"style":36065},[259,1873],[128,91061,2477],{"className":91062},[1896],[128,91064,35023],{"className":91065,"style":2508},[259,1873],[128,91067],{"className":91068,"style":1878},[269],[128,91070,1994],{"className":91071},[1882],[128,91073],{"className":91074,"style":1878},[269],[128,91076,91078,91081,91084,91087,91090],{"className":91077},[250],[128,91079],{"className":91080,"style":1892},[254],[128,91082,1842],{"className":91083},[259],[128,91085],{"className":91086,"style":1878},[269],[128,91088,5443],{"className":91089},[1882],[128,91091],{"className":91092,"style":1878},[269],[128,91094,91096,91099,91102,91105,91108,91111,91114,91117],{"className":91095},[250],[128,91097],{"className":91098,"style":1892},[254],[128,91100,4519],{"className":91101},[259,1873],[128,91103,67350],{"className":91104},[259,1873],[128,91106,2477],{"className":91107},[1896],[128,91109,364],{"className":91110,"style":30665},[259,1873],[128,91112],{"className":91113,"style":1878},[269],[128,91115,1994],{"className":91116},[1882],[128,91118],{"className":91119,"style":1878},[269],[128,91121,91123,91126,91129],{"className":91122},[250],[128,91124],{"className":91125,"style":1892},[254],[128,91127,2028],{"className":91128},[259],[128,91130,67410],{"className":91131},[1928],"（总体中未服药者的康复率）来回答，因为后者描述的是「随机抽取一个未服药个体」的康复概率，而反事实问题问的是",[35,91134,91135],{},"这同一个","已知服药后康复的病人。按照三步算法：首先根据「该病人服药后康复」这一证据，对可能导致其康复的外生因素（如自身免疫力 ",[128,91138,91140,91153],{"className":91139,"translate":218},[217],[128,91141,91143],{"className":91142},[222],[224,91144,91145],{"xmlns":226},[228,91146,91147,91151],{},[231,91148,91149],{},[1795,91150,69050],{},[238,91152,69050],{"encoding":240},[128,91154,91156],{"className":91155,"ariaHidden":246},[245],[128,91157,91159,91162],{"className":91158},[250],[128,91160],{"className":91161,"style":283},[254],[128,91163,69050],{"className":91164,"style":26806},[259,1873],"）的分布进行后验更新——服药后康复的人群中，「体质本身较好、即使不服药也可能康复」的后验概率会高于总体先验；随后在 ",[128,91167,91169,91189],{"className":91168,"translate":218},[217],[128,91170,91172],{"className":91171},[222],[224,91173,91174],{"xmlns":226},[228,91175,91176,91186],{},[231,91177,91178,91180,91182,91184],{},[1795,91179,364],{},[1832,91181,2014],{},[1832,91183,1994],{},[1840,91185,2028],{},[238,91187,91188],{"encoding":240},"X:=0",[128,91190,91192,91210],{"className":91191,"ariaHidden":246},[245],[128,91193,91195,91198,91201,91204,91207],{"className":91194},[250],[128,91196],{"className":91197,"style":283},[254],[128,91199,364],{"className":91200,"style":30665},[259,1873],[128,91202],{"className":91203,"style":1878},[269],[128,91205,75429],{"className":91206},[1882],[128,91208],{"className":91209,"style":1878},[269],[128,91211,91213,91216],{"className":91212},[250],[128,91214],{"className":91215,"style":2594},[254],[128,91217,2028],{"className":91218},[259]," 的子模型中，用这一更新后的 ",[128,91221,91223,91236],{"className":91222,"translate":218},[217],[128,91224,91226],{"className":91225},[222],[224,91227,91228],{"xmlns":226},[228,91229,91230,91234],{},[231,91231,91232],{},[1795,91233,69050],{},[238,91235,69050],{"encoding":240},[128,91237,91239],{"className":91238,"ariaHidden":246},[245],[128,91240,91242,91245],{"className":91241},[250],[128,91243],{"className":91244,"style":283},[254],[128,91246,69050],{"className":91247,"style":26806},[259,1873]," 分布重新计算 ",[128,91250,91252,91265],{"className":91251,"translate":218},[217],[128,91253,91255],{"className":91254},[222],[224,91256,91257],{"xmlns":226},[228,91258,91259,91263],{},[231,91260,91261],{},[1795,91262,35023],{},[238,91264,35023],{"encoding":240},[128,91266,91268],{"className":91267,"ariaHidden":246},[245],[128,91269,91271,91274],{"className":91270},[250],[128,91272],{"className":91273,"style":283},[254],[128,91275,35023],{"className":91276,"style":2508},[259,1873],"。这解释了为什么反事实概率 ",[128,91279,91281,91325],{"className":91280,"translate":218},[217],[128,91282,91284],{"className":91283},[222],[224,91285,91286],{"xmlns":226},[228,91287,91288,91322],{},[231,91289,91290,91292,91294,91300,91302,91304,91306,91308,91310,91312,91314,91316,91318,91320],{},[1795,91291,23001],{},[1832,91293,2477],{"stretchy":1837},[2016,91295,91296,91298],{},[1795,91297,35023],{},[1840,91299,2028],{},[1832,91301,1994],{},[1840,91303,1842],{},[1832,91305,5443],{},[1795,91307,364],{},[1832,91309,1994],{},[1840,91311,1842],{},[1832,91313,1845],{"separator":246},[1795,91315,35023],{},[1832,91317,1994],{},[1840,91319,1842],{},[1832,91321,2486],{"stretchy":1837},[238,91323,91324],{"encoding":240},"P(Y_0=1\\mid X=1,Y=1)",[128,91326,91328,91389,91407,91425,91452],{"className":91327,"ariaHidden":246},[245],[128,91329,91331,91334,91337,91340,91380,91383,91386],{"className":91330},[250],[128,91332],{"className":91333,"style":1892},[254],[128,91335,23001],{"className":91336,"style":36065},[259,1873],[128,91338,2477],{"className":91339},[1896],[128,91341,91343,91346],{"className":91342},[259],[128,91344,35023],{"className":91345,"style":2508},[259,1873],[128,91347,91349],{"className":91348},[2087],[128,91350,91352,91372],{"className":91351},[274,321],[128,91353,91355,91369],{"className":91354},[278],[128,91356,91358],{"className":91357,"style":2945},[282],[128,91359,91360,91363],{"style":68109},[128,91361],{"className":91362,"style":291},[290],[128,91364,91366],{"className":91365},[299,300,301,298],[128,91367,2028],{"className":91368},[259,298],[128,91370,347],{"className":91371},[346],[128,91373,91375],{"className":91374},[278],[128,91376,91378],{"className":91377,"style":2241},[282],[128,91379],{},[128,91381],{"className":91382,"style":1878},[269],[128,91384,1994],{"className":91385},[1882],[128,91387],{"className":91388,"style":1878},[269],[128,91390,91392,91395,91398,91401,91404],{"className":91391},[250],[128,91393],{"className":91394,"style":1892},[254],[128,91396,1842],{"className":91397},[259],[128,91399],{"className":91400,"style":1878},[269],[128,91402,5443],{"className":91403},[1882],[128,91405],{"className":91406,"style":1878},[269],[128,91408,91410,91413,91416,91419,91422],{"className":91409},[250],[128,91411],{"className":91412,"style":283},[254],[128,91414,364],{"className":91415,"style":30665},[259,1873],[128,91417],{"className":91418,"style":1878},[269],[128,91420,1994],{"className":91421},[1882],[128,91423],{"className":91424,"style":1878},[269],[128,91426,91428,91431,91434,91437,91440,91443,91446,91449],{"className":91427},[250],[128,91429],{"className":91430,"style":40674},[254],[128,91432,1842],{"className":91433},[259],[128,91435,1845],{"className":91436},[1903],[128,91438],{"className":91439,"style":1907},[269],[128,91441,35023],{"className":91442,"style":2508},[259,1873],[128,91444],{"className":91445,"style":1878},[269],[128,91447,1994],{"className":91448},[1882],[128,91450],{"className":91451,"style":1878},[269],[128,91453,91455,91458,91461],{"className":91454},[250],[128,91456],{"className":91457,"style":1892},[254],[128,91459,1842],{"className":91460},[259],[128,91462,2486],{"className":91463},[1928]," 一般会",[35,91466,91467],{},"高于","总体干预概率 ",[128,91470,91472,91512],{"className":91471,"translate":218},[217],[128,91473,91475],{"className":91474},[222],[224,91476,91477],{"xmlns":226},[228,91478,91479,91509],{},[231,91480,91481,91483,91485,91487,91489,91491,91493,91495,91497,91499,91501,91503,91505,91507],{},[1795,91482,23001],{},[1832,91484,2477],{"stretchy":1837},[1795,91486,35023],{},[1832,91488,1994],{},[1840,91490,1842],{},[1832,91492,5443],{},[1795,91494,4519],{},[1795,91496,67350],{},[1832,91498,2477],{"stretchy":1837},[1795,91500,364],{},[1832,91502,1994],{},[1840,91504,2028],{},[1832,91506,2486],{"stretchy":1837},[1832,91508,2486],{"stretchy":1837},[238,91510,91511],{"encoding":240},"P(Y=1\\mid do(X=0))",[128,91513,91515,91539,91557,91584],{"className":91514,"ariaHidden":246},[245],[128,91516,91518,91521,91524,91527,91530,91533,91536],{"className":91517},[250],[128,91519],{"className":91520,"style":1892},[254],[128,91522,23001],{"className":91523,"style":36065},[259,1873],[128,91525,2477],{"className":91526},[1896],[128,91528,35023],{"className":91529,"style":2508},[259,1873],[128,91531],{"className":91532,"style":1878},[269],[128,91534,1994],{"className":91535},[1882],[128,91537],{"className":91538,"style":1878},[269],[128,91540,91542,91545,91548,91551,91554],{"className":91541},[250],[128,91543],{"className":91544,"style":1892},[254],[128,91546,1842],{"className":91547},[259],[128,91549],{"className":91550,"style":1878},[269],[128,91552,5443],{"className":91553},[1882],[128,91555],{"className":91556,"style":1878},[269],[128,91558,91560,91563,91566,91569,91572,91575,91578,91581],{"className":91559},[250],[128,91561],{"className":91562,"style":1892},[254],[128,91564,4519],{"className":91565},[259,1873],[128,91567,67350],{"className":91568},[259,1873],[128,91570,2477],{"className":91571},[1896],[128,91573,364],{"className":91574,"style":30665},[259,1873],[128,91576],{"className":91577,"style":1878},[269],[128,91579,1994],{"className":91580},[1882],[128,91582],{"className":91583,"style":1878},[269],[128,91585,91587,91590,91593],{"className":91586},[250],[128,91588],{"className":91589,"style":1892},[254],[128,91591,2028],{"className":91592},[259],[128,91594,67410],{"className":91595},[1928],"——因为前者的条件化过程已经通过溯因步骤「筛选」出了体质更好的子群体。这一细微但本质的差别，是反事实推理（第三层）无法被干预计算（第二层）替代的直接例证，也是「个体化处理效应（Individual Treatment Effect）」这一概念在医学与政策评估中难以精确估计、却又极具价值的理论根源。",[11,91598,91599,91602,91603,41728,91606,91634,91635,91678,91679,11072,91707,91750],{},[35,91600,91601],{},"一个必须说清楚的边界：反事实的可识别性。"," 上述三步算法成立的前提是 SCM ",[35,91604,91605],{},"完全已知",[128,91607,91609,91622],{"className":91608,"translate":218},[217],[128,91610,91612],{"className":91611},[222],[224,91613,91614],{"xmlns":226},[228,91615,91616,91620],{},[231,91617,91618],{},[1795,91619,76009],{},[238,91621,76009],{"encoding":240},[128,91623,91625],{"className":91624,"ariaHidden":246},[245],[128,91626,91628,91631],{"className":91627},[250],[128,91629],{"className":91630,"style":283},[254],[128,91632,76009],{"className":91633,"style":36065},[259,1873]," 中的函数形式与 ",[128,91636,91638,91657],{"className":91637,"translate":218},[217],[128,91639,91641],{"className":91640},[222],[224,91642,91643],{"xmlns":226},[228,91644,91645,91655],{},[231,91646,91647,91649,91651,91653],{},[1795,91648,23001],{},[1832,91650,2477],{"stretchy":1837},[1795,91652,69050],{},[1832,91654,2486],{"stretchy":1837},[238,91656,77521],{"encoding":240},[128,91658,91660],{"className":91659,"ariaHidden":246},[245],[128,91661,91663,91666,91669,91672,91675],{"className":91662},[250],[128,91664],{"className":91665,"style":1892},[254],[128,91667,23001],{"className":91668,"style":36065},[259,1873],[128,91670,2477],{"className":91671},[1896],[128,91673,69050],{"className":91674,"style":26806},[259,1873],[128,91676,2486],{"className":91677},[1928]," 的分布都已指定。而在现实中我们通常只有观测数据，",[128,91680,91682,91695],{"className":91681,"translate":218},[217],[128,91683,91685],{"className":91684},[222],[224,91686,91687],{"xmlns":226},[228,91688,91689,91693],{},[231,91690,91691],{},[1795,91692,76009],{},[238,91694,76009],{"encoding":240},[128,91696,91698],{"className":91697,"ariaHidden":246},[245],[128,91699,91701,91704],{"className":91700},[250],[128,91702],{"className":91703,"style":283},[254],[128,91705,76009],{"className":91706,"style":36065},[259,1873],[128,91708,91710,91729],{"className":91709,"translate":218},[217],[128,91711,91713],{"className":91712},[222],[224,91714,91715],{"xmlns":226},[228,91716,91717,91727],{},[231,91718,91719,91721,91723,91725],{},[1795,91720,23001],{},[1832,91722,2477],{"stretchy":1837},[1795,91724,69050],{},[1832,91726,2486],{"stretchy":1837},[238,91728,77521],{"encoding":240},[128,91730,91732],{"className":91731,"ariaHidden":246},[245],[128,91733,91735,91738,91741,91744,91747],{"className":91734},[250],[128,91736],{"className":91737,"style":1892},[254],[128,91739,23001],{"className":91740,"style":36065},[259,1873],[128,91742,2477],{"className":91743},[1896],[128,91745,69050],{"className":91746,"style":26806},[259,1873],[128,91748,2486],{"className":91749},[1928]," 都是未知的。这一差别不是技术细节，而是第三层与第二层之间的一条硬边界：",[35195,91752,91753,91843],{},[33251,91754,91755,91756,91838,91839,91842],{},"第二层的量 ",[128,91757,91759,91790],{"className":91758,"translate":218},[217],[128,91760,91762],{"className":91761},[222],[224,91763,91764],{"xmlns":226},[228,91765,91766,91788],{},[231,91767,91768,91770,91772,91774,91776,91778,91780,91782,91784,91786],{},[1795,91769,23001],{},[1832,91771,2477],{"stretchy":1837},[1795,91773,1830],{},[1832,91775,5443],{},[1795,91777,4519],{},[1795,91779,67350],{},[1832,91781,2477],{"stretchy":1837},[1795,91783,2760],{},[1832,91785,2486],{"stretchy":1837},[1832,91787,2486],{"stretchy":1837},[238,91789,67361],{"encoding":240},[128,91791,91793,91817],{"className":91792,"ariaHidden":246},[245],[128,91794,91796,91799,91802,91805,91808,91811,91814],{"className":91795},[250],[128,91797],{"className":91798,"style":1892},[254],[128,91800,23001],{"className":91801,"style":36065},[259,1873],[128,91803,2477],{"className":91804},[1896],[128,91806,1830],{"className":91807,"style":1874},[259,1873],[128,91809],{"className":91810,"style":1878},[269],[128,91812,5443],{"className":91813},[1882],[128,91815],{"className":91816,"style":1878},[269],[128,91818,91820,91823,91826,91829,91832,91835],{"className":91819},[250],[128,91821],{"className":91822,"style":1892},[254],[128,91824,4519],{"className":91825},[259,1873],[128,91827,67350],{"className":91828},[259,1873],[128,91830,2477],{"className":91831},[1896],[128,91833,2760],{"className":91834},[259,1873],[128,91836,67410],{"className":91837},[1928]," 在满足后门准则或前门准则（见 3.5 节）时，",[35,91840,91841],{},"可以","仅用观测分布表达出来，因而能够由数据估计；",[33251,91844,91845,91846,91975,91976,15983,92007,92035,92036,92064,92065,893],{},"第三层的量 ",[128,91847,91849,91881],{"className":91848,"translate":218},[217],[128,91850,91852],{"className":91851},[222],[224,91853,91854],{"xmlns":226},[228,91855,91856,91878],{},[231,91857,91858,91860,91862,91868,91870,91872,91874,91876],{},[1795,91859,23001],{},[1832,91861,2477],{"stretchy":1837},[2016,91863,91864,91866],{},[1795,91865,35023],{},[1795,91867,2760],{},[1832,91869,1994],{},[1795,91871,1830],{},[1832,91873,5443],{},[1795,91875,3713],{},[1832,91877,2486],{"stretchy":1837},[238,91879,91880],{"encoding":240},"P(Y_x = y \\mid e)",[128,91882,91884,91945,91963],{"className":91883,"ariaHidden":246},[245],[128,91885,91887,91890,91893,91896,91936,91939,91942],{"className":91886},[250],[128,91888],{"className":91889,"style":1892},[254],[128,91891,23001],{"className":91892,"style":36065},[259,1873],[128,91894,2477],{"className":91895},[1896],[128,91897,91899,91902],{"className":91898},[259],[128,91900,35023],{"className":91901,"style":2508},[259,1873],[128,91903,91905],{"className":91904},[2087],[128,91906,91908,91928],{"className":91907},[274,321],[128,91909,91911,91925],{"className":91910},[278],[128,91912,91914],{"className":91913,"style":28738},[282],[128,91915,91916,91919],{"style":68109},[128,91917],{"className":91918,"style":291},[290],[128,91920,91922],{"className":91921},[299,300,301,298],[128,91923,2760],{"className":91924},[259,1873,298],[128,91926,347],{"className":91927},[346],[128,91929,91931],{"className":91930},[278],[128,91932,91934],{"className":91933,"style":2241},[282],[128,91935],{},[128,91937],{"className":91938,"style":1878},[269],[128,91940,1994],{"className":91941},[1882],[128,91943],{"className":91944,"style":1878},[269],[128,91946,91948,91951,91954,91957,91960],{"className":91947},[250],[128,91949],{"className":91950,"style":1892},[254],[128,91952,1830],{"className":91953,"style":1874},[259,1873],[128,91955],{"className":91956,"style":1878},[269],[128,91958,5443],{"className":91959},[1882],[128,91961],{"className":91962,"style":1878},[269],[128,91964,91966,91969,91972],{"className":91965},[250],[128,91967],{"className":91968,"style":1892},[254],[128,91970,3713],{"className":91971},[259,1873],[128,91973,2486],{"className":91974},[1928]," 则要求「同一个体在另一个可能世界中的取值」，也就是要求",[35,91977,91978,91979],{},"同一个 ",[128,91980,91982,91995],{"className":91981,"translate":218},[217],[128,91983,91985],{"className":91984},[222],[224,91986,91987],{"xmlns":226},[228,91988,91989,91993],{},[231,91990,91991],{},[1795,91992,35129],{},[238,91994,35129],{"encoding":240},[128,91996,91998],{"className":91997,"ariaHidden":246},[245],[128,91999,92001,92004],{"className":92000},[250],[128,92002],{"className":92003,"style":7758},[254],[128,92005,35129],{"className":92006},[259,1873],[128,92008,92010,92023],{"className":92009,"translate":218},[217],[128,92011,92013],{"className":92012},[222],[224,92014,92015],{"xmlns":226},[228,92016,92017,92021],{},[231,92018,92019],{},[1795,92020,35129],{},[238,92022,35129],{"encoding":240},[128,92024,92026],{"className":92025,"ariaHidden":246},[245],[128,92027,92029,92032],{"className":92028},[250],[128,92030],{"className":92031,"style":7758},[254],[128,92033,35129],{"className":92034},[259,1873]," 本身不可观测。观测数据只能给出内生变量 ",[128,92037,92039,92052],{"className":92038,"translate":218},[217],[128,92040,92042],{"className":92041},[222],[224,92043,92044],{"xmlns":226},[228,92045,92046,92050],{},[231,92047,92048],{},[1795,92049,67963],{},[238,92051,67963],{"encoding":240},[128,92053,92055],{"className":92054,"ariaHidden":246},[245],[128,92056,92058,92061],{"className":92057},[250],[128,92059],{"className":92060,"style":283},[254],[128,92062,67963],{"className":92063,"style":2508},[259,1873]," 的联合分布，一般无法唯一反解出 ",[128,92066,92068,92092],{"className":92067,"translate":218},[217],[128,92069,92071],{"className":92070},[222],[224,92072,92073],{"xmlns":226},[228,92074,92075,92089],{},[231,92076,92077,92079,92081,92083,92085,92087],{},[1795,92078,23001],{},[1832,92080,2477],{"stretchy":1837},[1795,92082,35129],{},[1832,92084,5443],{},[1795,92086,3713],{},[1832,92088,2486],{"stretchy":1837},[238,92090,92091],{"encoding":240},"P(u\\mid e)",[128,92093,92095,92119],{"className":92094,"ariaHidden":246},[245],[128,92096,92098,92101,92104,92107,92110,92113,92116],{"className":92097},[250],[128,92099],{"className":92100,"style":1892},[254],[128,92102,23001],{"className":92103,"style":36065},[259,1873],[128,92105,2477],{"className":92106},[1896],[128,92108,35129],{"className":92109},[259,1873],[128,92111],{"className":92112,"style":1878},[269],[128,92114,5443],{"className":92115},[1882],[128,92117],{"className":92118,"style":1878},[269],[128,92120,92122,92125,92128],{"className":92121},[250],[128,92123],{"className":92124,"style":1892},[254],[128,92126,3713],{"className":92127},[259,1873],[128,92129,2486],{"className":92130},[1928],[11,92132,92133,92134],{},"由此可以得到一个一般性判断：",[35,92135,92136],{},"反事实量在一般情形下不可从观测数据识别，只有在 SCM 被完整指定、或引入足够强的额外假设时才可计算。",[11,92138,92139,92140,92218,92219,92307,92308,2674,92336,92364,92365,92367,92368,92396],{},"一个极端而富有启发的例子是线性 SCM：此时 ",[128,92141,92143,92167],{"className":92142,"translate":218},[217],[128,92144,92146],{"className":92145},[222],[224,92147,92148],{"xmlns":226},[228,92149,92150,92164],{},[231,92151,92152,92154,92156,92158,92160,92162],{},[1795,92153,67963],{},[1832,92155,1994],{},[1795,92157,5459],{},[1795,92159,67963],{},[1832,92161,9486],{},[1795,92163,69050],{},[238,92165,92166],{"encoding":240},"V = BV + U",[128,92168,92170,92188,92209],{"className":92169,"ariaHidden":246},[245],[128,92171,92173,92176,92179,92182,92185],{"className":92172},[250],[128,92174],{"className":92175,"style":283},[254],[128,92177,67963],{"className":92178,"style":2508},[259,1873],[128,92180],{"className":92181,"style":1878},[269],[128,92183,1994],{"className":92184},[1882],[128,92186],{"className":92187,"style":1878},[269],[128,92189,92191,92194,92197,92200,92203,92206],{"className":92190},[250],[128,92192],{"className":92193,"style":2705},[254],[128,92195,5459],{"className":92196,"style":5599},[259,1873],[128,92198,67963],{"className":92199,"style":2508},[259,1873],[128,92201],{"className":92202,"style":2508},[269],[128,92204,9486],{"className":92205},[2115],[128,92207],{"className":92208,"style":2508},[269],[128,92210,92212,92215],{"className":92211},[250],[128,92213],{"className":92214,"style":283},[254],[128,92216,69050],{"className":92217,"style":26806},[259,1873]," 蕴含 ",[128,92220,92222,92250],{"className":92221,"translate":218},[217],[128,92223,92225],{"className":92224},[222],[224,92226,92227],{"xmlns":226},[228,92228,92229,92247],{},[231,92230,92231,92233,92235,92237,92239,92241,92243,92245],{},[1795,92232,69050],{},[1832,92234,1994],{},[1832,92236,2477],{"stretchy":1837},[1795,92238,30626],{},[1832,92240,1989],{},[1795,92242,5459],{},[1832,92244,2486],{"stretchy":1837},[1795,92246,67963],{},[238,92248,92249],{"encoding":240},"U = (I-B)V",[128,92251,92253,92271,92292],{"className":92252,"ariaHidden":246},[245],[128,92254,92256,92259,92262,92265,92268],{"className":92255},[250],[128,92257],{"className":92258,"style":283},[254],[128,92260,69050],{"className":92261,"style":26806},[259,1873],[128,92263],{"className":92264,"style":1878},[269],[128,92266,1994],{"className":92267},[1882],[128,92269],{"className":92270,"style":1878},[269],[128,92272,92274,92277,92280,92283,92286,92289],{"className":92273},[250],[128,92275],{"className":92276,"style":1892},[254],[128,92278,2477],{"className":92279},[1896],[128,92281,30626],{"className":92282,"style":30665},[259,1873],[128,92284],{"className":92285,"style":2508},[269],[128,92287,1989],{"className":92288},[2115],[128,92290],{"className":92291,"style":2508},[269],[128,92293,92295,92298,92301,92304],{"className":92294},[250],[128,92296],{"className":92297,"style":1892},[254],[128,92299,5459],{"className":92300,"style":5599},[259,1873],[128,92302,2486],{"className":92303},[1928],[128,92305,67963],{"className":92306,"style":2508},[259,1873],"，于是给定任一观测到的 ",[128,92309,92311,92324],{"className":92310,"translate":218},[217],[128,92312,92314],{"className":92313},[222],[224,92315,92316],{"xmlns":226},[228,92317,92318,92322],{},[231,92319,92320],{},[1795,92321,32160],{},[238,92323,32160],{"encoding":240},[128,92325,92327],{"className":92326,"ariaHidden":246},[245],[128,92328,92330,92333],{"className":92329},[250],[128,92331],{"className":92332,"style":7758},[254],[128,92334,32160],{"className":92335,"style":1874},[259,1873],[128,92337,92339,92352],{"className":92338,"translate":218},[217],[128,92340,92342],{"className":92341},[222],[224,92343,92344],{"xmlns":226},[228,92345,92346,92350],{},[231,92347,92348],{},[1795,92349,35129],{},[238,92351,35129],{"encoding":240},[128,92353,92355],{"className":92354,"ariaHidden":246},[245],[128,92356,92358,92361],{"className":92357},[250],[128,92359],{"className":92360,"style":7758},[254],[128,92362,35129],{"className":92363},[259,1873]," 被",[35,92366,82453],{},"，反事实分布退化为一个点质量，个体处理效应似乎唾手可得。但这一「可得」完全是线性与可加假设的产物，而非数据所提供的信息——一旦允许非线性或非高斯，「同一个 ",[128,92369,92371,92384],{"className":92370,"translate":218},[217],[128,92372,92374],{"className":92373},[222],[224,92375,92376],{"xmlns":226},[228,92377,92378,92382],{},[231,92379,92380],{},[1795,92381,35129],{},[238,92383,35129],{"encoding":240},[128,92385,92387],{"className":92386,"ariaHidden":246},[245],[128,92388,92390,92393],{"className":92389},[250],[128,92391],{"className":92392,"style":7758},[254],[128,92394,35129],{"className":92395},[259,1873],"」便重新变得不可复原。这也正是经典 SEM 传统（见 4.2 节）能够讨论「个体效应」、而现代因果推断对此极为谨慎的原因所在。",[11,92398,92399],{},"因此第三层虽然在形式上已被定义清楚，其实践可达性却最弱。本文余下部分把重点放在第二层的可识别性上，这并非理论上的偏好，而是数据所能支撑的边界所在。",[2610,92401,92403],{"id":92402},"_34-中介分析从总效应到直接效应与间接效应","3.4 中介分析：从总效应到直接效应与间接效应",[11,92405,92406,92407,92479],{},"第一部分曾用链结构 ",[128,92408,92410,92431],{"className":92409,"translate":218},[217],[128,92411,92413],{"className":92412},[222],[224,92414,92415],{"xmlns":226},[228,92416,92417,92429],{},[231,92418,92419,92421,92423,92425,92427],{},[1795,92420,364],{},[1832,92422,22419],{},[1795,92424,70777],{},[1832,92426,22419],{},[1795,92428,35023],{},[238,92430,70922],{"encoding":240},[128,92432,92434,92452,92470],{"className":92433,"ariaHidden":246},[245],[128,92435,92437,92440,92443,92446,92449],{"className":92436},[250],[128,92438],{"className":92439,"style":283},[254],[128,92441,364],{"className":92442,"style":30665},[259,1873],[128,92444],{"className":92445,"style":1878},[269],[128,92447,22419],{"className":92448},[1882],[128,92450],{"className":92451,"style":1878},[269],[128,92453,92455,92458,92461,92464,92467],{"className":92454},[250],[128,92456],{"className":92457,"style":283},[254],[128,92459,70777],{"className":92460,"style":1924},[259,1873],[128,92462],{"className":92463,"style":1878},[269],[128,92465,22419],{"className":92466},[1882],[128,92468],{"className":92469,"style":1878},[269],[128,92471,92473,92476],{"className":92472},[250],[128,92474],{"className":92475,"style":283},[254],[128,92477,35023],{"className":92478,"style":2508},[259,1873]," 说明「控制中介会切断全部影响」。当时给出的只是定性结论，现在有了 do-算子与反事实的语言，可以把「影响如何被分解」这件事精确化。",[11,92481,1781,92482,92510,92511,92539,92540,92568,92569,71248,92597,92625,92626,92699,92700,893],{},[128,92483,92485,92498],{"className":92484,"translate":218},[217],[128,92486,92488],{"className":92487},[222],[224,92489,92490],{"xmlns":226},[228,92491,92492,92496],{},[231,92493,92494],{},[1795,92495,364],{},[238,92497,364],{"encoding":240},[128,92499,92501],{"className":92500,"ariaHidden":246},[245],[128,92502,92504,92507],{"className":92503},[250],[128,92505],{"className":92506,"style":283},[254],[128,92508,364],{"className":92509,"style":30665},[259,1873]," 为处理变量，",[128,92512,92514,92527],{"className":92513,"translate":218},[217],[128,92515,92517],{"className":92516},[222],[224,92518,92519],{"xmlns":226},[228,92520,92521,92525],{},[231,92522,92523],{},[1795,92524,35023],{},[238,92526,35023],{"encoding":240},[128,92528,92530],{"className":92529,"ariaHidden":246},[245],[128,92531,92533,92536],{"className":92532},[250],[128,92534],{"className":92535,"style":283},[254],[128,92537,35023],{"className":92538,"style":2508},[259,1873]," 为结果，",[128,92541,92543,92556],{"className":92542,"translate":218},[217],[128,92544,92546],{"className":92545},[222],[224,92547,92548],{"xmlns":226},[228,92549,92550,92554],{},[231,92551,92552],{},[1795,92553,30641],{},[238,92555,30641],{"encoding":240},[128,92557,92559],{"className":92558,"ariaHidden":246},[245],[128,92560,92562,92565],{"className":92561},[250],[128,92563],{"className":92564,"style":283},[254],[128,92566,30641],{"className":92567,"style":26806},[259,1873]," 为介于二者之间的中介变量。",[128,92570,92572,92585],{"className":92571,"translate":218},[217],[128,92573,92575],{"className":92574},[222],[224,92576,92577],{"xmlns":226},[228,92578,92579,92583],{},[231,92580,92581],{},[1795,92582,364],{},[238,92584,364],{"encoding":240},[128,92586,92588],{"className":92587,"ariaHidden":246},[245],[128,92589,92591,92594],{"className":92590},[250],[128,92592],{"className":92593,"style":283},[254],[128,92595,364],{"className":92596,"style":30665},[259,1873],[128,92598,92600,92613],{"className":92599,"translate":218},[217],[128,92601,92603],{"className":92602},[222],[224,92604,92605],{"xmlns":226},[228,92606,92607,92611],{},[231,92608,92609],{},[1795,92610,35023],{},[238,92612,35023],{"encoding":240},[128,92614,92616],{"className":92615,"ariaHidden":246},[245],[128,92617,92619,92622],{"className":92618},[250],[128,92620],{"className":92621,"style":283},[254],[128,92623,35023],{"className":92624,"style":2508},[259,1873]," 的作用只可能经过两条通道：中介通道 ",[128,92627,92629,92651],{"className":92628,"translate":218},[217],[128,92630,92632],{"className":92631},[222],[224,92633,92634],{"xmlns":226},[228,92635,92636,92648],{},[231,92637,92638,92640,92642,92644,92646],{},[1795,92639,364],{},[1832,92641,22419],{},[1795,92643,30641],{},[1832,92645,22419],{},[1795,92647,35023],{},[238,92649,92650],{"encoding":240},"X \\to M \\to Y",[128,92652,92654,92672,92690],{"className":92653,"ariaHidden":246},[245],[128,92655,92657,92660,92663,92666,92669],{"className":92656},[250],[128,92658],{"className":92659,"style":283},[254],[128,92661,364],{"className":92662,"style":30665},[259,1873],[128,92664],{"className":92665,"style":1878},[269],[128,92667,22419],{"className":92668},[1882],[128,92670],{"className":92671,"style":1878},[269],[128,92673,92675,92678,92681,92684,92687],{"className":92674},[250],[128,92676],{"className":92677,"style":283},[254],[128,92679,30641],{"className":92680,"style":26806},[259,1873],[128,92682],{"className":92683,"style":1878},[269],[128,92685,22419],{"className":92686},[1882],[128,92688],{"className":92689,"style":1878},[269],[128,92691,92693,92696],{"className":92692},[250],[128,92694],{"className":92695,"style":283},[254],[128,92697,35023],{"className":92698,"style":2508},[259,1873]," 与直接通道 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Total Effect）",[128,92763,92765,92816],{"className":92764,"translate":218},[217],[128,92766,92768],{"className":92767},[222],[224,92769,92770],{"xmlns":226},[228,92771,92772,92813],{},[231,92773,92774,92780,92782,92784,92786,92792,92794,92796,92798,92800,92811],{},[231,92775,92776,92778],{},[1795,92777,313],{"mathvariant":1981},[1795,92779,342],{"mathvariant":1981},[1832,92781,1994],{},[1795,92783,342],{"mathvariant":2008},[1832,92785,16538],{"stretchy":1837},[2016,92787,92788,92790],{},[1795,92789,35023],{},[1795,92791,2760],{},[1832,92793,16547],{"stretchy":1837},[1832,92795,1989],{},[1795,92797,342],{"mathvariant":2008},[1832,92799,16538],{"stretchy":1837},[2016,92801,92802,92804],{},[1795,92803,35023],{},[1977,92805,92806,92808],{},[1795,92807,2760],{},[1832,92809,92810],{},"∗",[1832,92812,16547],{"stretchy":1837},[238,92814,92815],{"encoding":240},"\\mathrm{TE} = \\mathbb{E}[Y_{x}] - 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从参考水平 ",[128,93024,93026,93044],{"className":93025,"translate":218},[217],[128,93027,93029],{"className":93028},[222],[224,93030,93031],{"xmlns":226},[228,93032,93033,93041],{},[231,93034,93035],{},[1977,93036,93037,93039],{},[1795,93038,2760],{},[1832,93040,92810],{},[238,93042,93043],{"encoding":240},"x^*",[128,93045,93047],{"className":93046,"ariaHidden":246},[245],[128,93048,93050,93053],{"className":93049},[250],[128,93051],{"className":93052,"style":23776},[254],[128,93054,93056,93059],{"className":93055},[259],[128,93057,2760],{"className":93058},[259,1873],[128,93060,93062],{"className":93061},[2087],[128,93063,93065],{"className":93064},[274],[128,93066,93068],{"className":93067},[278],[128,93069,93071],{"className":93070,"style":23776},[282],[128,93072,93073,93076],{"style":2452},[128,93074],{"className":93075,"style":291},[290],[128,93077,93079],{"className":93078},[299,300,301,298],[128,93080,92810],{"className":93081},[2115,298]," 改为 ",[128,93084,93086,93099],{"className":93085,"translate":218},[217],[128,93087,93089],{"className":93088},[222],[224,93090,93091],{"xmlns":226},[228,93092,93093,93097],{},[231,93094,93095],{},[1795,93096,2760],{},[238,93098,2760],{"encoding":240},[128,93100,93102],{"className":93101,"ariaHidden":246},[245],[128,93103,93105,93108],{"className":93104},[250],[128,93106],{"className":93107,"style":7758},[254],[128,93109,2760],{"className":93110},[259,1873]," 时结果期望的净变化。为区分上述两条通道各自的贡献，Pearl 引入两个第三层的量：",[2615,93113,93115],{"title":93114},"定义 3.5（自然直接效应与自然间接效应）",[11,93116,93117,24849,93827,93984,93985,94013,94014,94042,94043,94071,94072,94189],{},[128,93118,93120,93268],{"className":93119,"translate":218},[217],[128,93121,93123],{"className":93122},[222],[224,93124,93125],{"xmlns":226},[228,93126,93127,93265],{},[231,93128,93129,93137,93139,93141,93143,93149,93151,93153,93155,93157,93177,93179,93181,93183,93185,93195,93197,93199,93201,93209,93211,93213,93215,93221,93223,93225,93227,93229,93235,93237,93239,93241,93243,93263],{},[231,93130,93131,93133,93135],{},[1795,93132,26691],{"mathvariant":1981},[1795,93134,59717],{"mathvariant":1981},[1795,93136,342],{"mathvariant":1981},[1832,93138,2477],{"stretchy":1837},[1795,93140,2760],{},[1832,93142,1845],{"separator":246},[1977,93144,93145,93147],{},[1795,93146,2760],{},[1832,93148,92810],{},[1832,93150,2486],{"stretchy":1837},[1832,93152,1994],{},[1795,93154,342],{"mathvariant":2008},[1832,93156,16538],{"stretchy":1837},[2016,93158,93159,93161],{},[1795,93160,35023],{},[231,93162,93163,93165,93167],{},[1795,93164,2760],{},[1832,93166,1845],{"separator":246},[2016,93168,93169,93171],{},[1795,93170,30641],{},[1977,93172,93173,93175],{},[1795,93174,2760],{},[1832,93176,92810],{},[1832,93178,16547],{"stretchy":1837},[1832,93180,1989],{},[1795,93182,342],{"mathvariant":2008},[1832,93184,16538],{"stretchy":1837},[2016,93186,93187,93189],{},[1795,93188,35023],{},[1977,93190,93191,93193],{},[1795,93192,2760],{},[1832,93194,92810],{},[1832,93196,16547],{"stretchy":1837},[1832,93198,1845],{"separator":246},[269,93200],{"width":11568},[231,93202,93203,93205,93207],{},[1795,93204,26691],{"mathvariant":1981},[1795,93206,30626],{"mathvariant":1981},[1795,93208,342],{"mathvariant":1981},[1832,93210,2477],{"stretchy":1837},[1795,93212,2760],{},[1832,93214,1845],{"separator":246},[1977,93216,93217,93219],{},[1795,93218,2760],{},[1832,93220,92810],{},[1832,93222,2486],{"stretchy":1837},[1832,93224,1994],{},[1795,93226,342],{"mathvariant":2008},[1832,93228,16538],{"stretchy":1837},[2016,93230,93231,93233],{},[1795,93232,35023],{},[1795,93234,2760],{},[1832,93236,16547],{"stretchy":1837},[1832,93238,1989],{},[1795,93240,342],{"mathvariant":2008},[1832,93242,16538],{"stretchy":1837},[2016,93244,93245,93247],{},[1795,93246,35023],{},[231,93248,93249,93251,93253],{},[1795,93250,2760],{},[1832,93252,1845],{"separator":246},[2016,93254,93255,93257],{},[1795,93256,30641],{},[1977,93258,93259,93261],{},[1795,93260,2760],{},[1832,93262,92810],{},[1832,93264,16547],{"stretchy":1837},[238,93266,93267],{"encoding":240},"\\mathrm{NDE}(x, x^*) = \\mathbb{E}[Y_{x, M_{x^*}}] - \\mathbb{E}[Y_{x^*}], \\qquad \\mathrm{NIE}(x, x^*) = \\mathbb{E}[Y_{x}] - \\mathbb{E}[Y_{x, M_{x^*}}]",[128,93269,93271,93337,93480,93633,93700],{"className":93270,"ariaHidden":246},[245],[128,93272,93274,93277,93284,93287,93290,93293,93296,93325,93328,93331,93334],{"className":93273},[250],[128,93275],{"className":93276,"style":1892},[254],[128,93278,93280],{"className":93279},[259],[128,93281,93283],{"className":93282},[259,3353],"NDE",[128,93285,2477],{"className":93286},[1896],[128,93288,2760],{"className":93289},[259,1873],[128,93291,1845],{"className":93292},[1903],[128,93294],{"className":93295,"style":1907},[269],[128,93297,93299,93302],{"className":93298},[259],[128,93300,2760],{"className":93301},[259,1873],[128,93303,93305],{"className":93304},[2087],[128,93306,93308],{"className":93307},[274],[128,93309,93311],{"className":93310},[278],[128,93312,93314],{"className":93313,"style":23776},[282],[128,93315,93316,93319],{"style":2452},[128,93317],{"className":93318,"style":291},[290],[128,93320,93322],{"className":93321},[299,300,301,298],[128,93323,92810],{"className":93324},[2115,298],[128,93326,2486],{"className":93327},[1928],[128,93329],{"className":93330,"style":1878},[269],[128,93332,1994],{"className":93333},[1882],[128,93335],{"className":93336,"style":1878},[269],[128,93338,93340,93344,93347,93350,93468,93471,93474,93477],{"className":93339},[250],[128,93341],{"className":93342,"style":93343},[254],"height:1.0383em;vertical-align:-0.2883em;",[128,93345,342],{"className":93346},[259,2167],[128,93348,16538],{"className":93349},[1896],[128,93351,93353,93356],{"className":93352},[259],[128,93354,35023],{"className":93355,"style":2508},[259,1873],[128,93357,93359],{"className":93358},[2087],[128,93360,93362,93459],{"className":93361},[274,321],[128,93363,93365,93456],{"className":93364},[278],[128,93366,93368],{"className":93367,"style":3004},[282],[128,93369,93370,93373],{"style":68109},[128,93371],{"className":93372,"style":291},[290],[128,93374,93376],{"className":93375},[299,300,301,298],[128,93377,93379,93382,93385],{"className":93378},[259,298],[128,93380,2760],{"className":93381},[259,1873,298],[128,93383,1845],{"className":93384},[1903,298],[128,93386,93388,93391],{"className":93387},[259,298],[128,93389,30641],{"className":93390,"style":26806},[259,1873,298],[128,93392,93394],{"className":93393},[2087],[128,93395,93397,93447],{"className":93396},[274,321],[128,93398,93400,93444],{"className":93399},[278],[128,93401,93403],{"className":93402,"style":24117},[282],[128,93404,93406,93410],{"style":93405},"top:-2.3448em;margin-left:-0.109em;margin-right:0.0714em;",[128,93407],{"className":93408,"style":93409},[290],"height:2.5423em;",[128,93411,93413],{"className":93412},[299,5794,5795,298],[128,93414,93416],{"className":93415},[259,298],[128,93417,93419,93422],{"className":93418},[259,298],[128,93420,2760],{"className":93421},[259,1873,298],[128,93423,93425],{"className":93424},[2087],[128,93426,93428],{"className":93427},[274],[128,93429,93431],{"className":93430},[278],[128,93432,93435],{"className":93433,"style":93434},[282],"height:0.7593em;",[128,93436,93438,93441],{"style":93437},"top:-2.794em;margin-right:0.1em;",[128,93439],{"className":93440,"style":5790},[290],[128,93442,92810],{"className":93443},[2115,298],[128,93445,347],{"className":93446},[346],[128,93448,93450],{"className":93449},[278],[128,93451,93454],{"className":93452,"style":93453},[282],"height:0.1975em;",[128,93455],{},[128,93457,347],{"className":93458},[346],[128,93460,93462],{"className":93461},[278],[128,93463,93466],{"className":93464,"style":93465},[282],"height:0.2883em;",[128,93467],{},[128,93469,16547],{"className":93470},[1928],[128,93472],{"className":93473,"style":2508},[269],[128,93475,1989],{"className":93476},[2115],[128,93478],{"className":93479,"style":2508},[269],[128,93481,93483,93486,93489,93492,93561,93564,93567,93570,93573,93580,93583,93586,93589,93592,93621,93624,93627,93630],{"className":93482},[250],[128,93484],{"className":93485,"style":1892},[254],[128,93487,342],{"className":93488},[259,2167],[128,93490,16538],{"className":93491},[1896],[128,93493,93495,93498],{"className":93494},[259],[128,93496,35023],{"className":93497,"style":2508},[259,1873],[128,93499,93501],{"className":93500},[2087],[128,93502,93504,93553],{"className":93503},[274,321],[128,93505,93507,93550],{"className":93506},[278],[128,93508,93510],{"className":93509,"style":92938},[282],[128,93511,93512,93515],{"style":68109},[128,93513],{"className":93514,"style":291},[290],[128,93516,93518],{"className":93517},[299,300,301,298],[128,93519,93521],{"className":93520},[259,298],[128,93522,93524,93527],{"className":93523},[259,298],[128,93525,2760],{"className":93526},[259,1873,298],[128,93528,93530],{"className":93529},[2087],[128,93531,93533],{"className":93532},[274],[128,93534,93536],{"className":93535},[278],[128,93537,93539],{"className":93538,"style":92968},[282],[128,93540,93541,93544],{"style":6609},[128,93542],{"className":93543,"style":5790},[290],[128,93545,93547],{"className":93546},[299,5794,5795,298],[128,93548,92810],{"className":93549},[2115,298],[128,93551,347],{"className":93552},[346],[128,93554,93556],{"className":93555},[278],[128,93557,93559],{"className":93558,"style":2241},[282],[128,93560],{},[128,93562,16547],{"className":93563},[1928],[128,93565,1845],{"className":93566},[1903],[128,93568],{"className":93569,"style":11756},[269],[128,93571],{"className":93572,"style":1907},[269],[128,93574,93576],{"className":93575},[259],[128,93577,93579],{"className":93578},[259,3353],"NIE",[128,93581,2477],{"className":93582},[1896],[128,93584,2760],{"className":93585},[259,1873],[128,93587,1845],{"className":93588},[1903],[128,93590],{"className":93591,"style":1907},[269],[128,93593,93595,93598],{"className":93594},[259],[128,93596,2760],{"className":93597},[259,1873],[128,93599,93601],{"className":93600},[2087],[128,93602,93604],{"className":93603},[274],[128,93605,93607],{"className":93606},[278],[128,93608,93610],{"className":93609,"style":23776},[282],[128,93611,93612,93615],{"style":2452},[128,93613],{"className":93614,"style":291},[290],[128,93616,93618],{"className":93617},[299,300,301,298],[128,93619,92810],{"className":93620},[2115,298],[128,93622,2486],{"className":93623},[1928],[128,93625],{"className":93626,"style":1878},[269],[128,93628,1994],{"className":93629},[1882],[128,93631],{"className":93632,"style":1878},[269],[128,93634,93636,93639,93642,93645,93688,93691,93694,93697],{"className":93635},[250],[128,93637],{"className":93638,"style":1892},[254],[128,93640,342],{"className":93641},[259,2167],[128,93643,16538],{"className":93644},[1896],[128,93646,93648,93651],{"className":93647},[259],[128,93649,35023],{"className":93650,"style":2508},[259,1873],[128,93652,93654],{"className":93653},[2087],[128,93655,93657,93680],{"className":93656},[274,321],[128,93658,93660,93677],{"className":93659},[278],[128,93661,93663],{"className":93662,"style":28738},[282],[128,93664,93665,93668],{"style":68109},[128,93666],{"className":93667,"style":291},[290],[128,93669,93671],{"className":93670},[299,300,301,298],[128,93672,93674],{"className":93673},[259,298],[128,93675,2760],{"className":93676},[259,1873,298],[128,93678,347],{"className":93679},[346],[128,93681,93683],{"className":93682},[278],[128,93684,93686],{"className":93685,"style":2241},[282],[128,93687],{},[128,93689,16547],{"className":93690},[1928],[128,93692],{"className":93693,"style":2508},[269],[128,93695,1989],{"className":93696},[2115],[128,93698],{"className":93699,"style":2508},[269],[128,93701,93703,93706,93709,93712,93824],{"className":93702},[250],[128,93704],{"className":93705,"style":93343},[254],[128,93707,342],{"className":93708},[259,2167],[128,93710,16538],{"className":93711},[1896],[128,93713,93715,93718],{"className":93714},[259],[128,93716,35023],{"className":93717,"style":2508},[259,1873],[128,93719,93721],{"className":93720},[2087],[128,93722,93724,93816],{"className":93723},[274,321],[128,93725,93727,93813],{"className":93726},[278],[128,93728,93730],{"className":93729,"style":3004},[282],[128,93731,93732,93735],{"style":68109},[128,93733],{"className":93734,"style":291},[290],[128,93736,93738],{"className":93737},[299,300,301,298],[128,93739,93741,93744,93747],{"className":93740},[259,298],[128,93742,2760],{"className":93743},[259,1873,298],[128,93745,1845],{"className":93746},[1903,298],[128,93748,93750,93753],{"className":93749},[259,298],[128,93751,30641],{"className":93752,"style":26806},[259,1873,298],[128,93754,93756],{"className":93755},[2087],[128,93757,93759,93805],{"className":93758},[274,321],[128,93760,93762,93802],{"className":93761},[278],[128,93763,93765],{"className":93764,"style":24117},[282],[128,93766,93767,93770],{"style":93405},[128,93768],{"className":93769,"style":93409},[290],[128,93771,93773],{"className":93772},[299,5794,5795,298],[128,93774,93776],{"className":93775},[259,298],[128,93777,93779,93782],{"className":93778},[259,298],[128,93780,2760],{"className":93781},[259,1873,298],[128,93783,93785],{"className":93784},[2087],[128,93786,93788],{"className":93787},[274],[128,93789,93791],{"className":93790},[278],[128,93792,93794],{"className":93793,"style":93434},[282],[128,93795,93796,93799],{"style":93437},[128,93797],{"className":93798,"style":5790},[290],[128,93800,92810],{"className":93801},[2115,298],[128,93803,347],{"className":93804},[346],[128,93806,93808],{"className":93807},[278],[128,93809,93811],{"className":93810,"style":93453},[282],[128,93812],{},[128,93814,347],{"className":93815},[346],[128,93817,93819],{"className":93818},[278],[128,93820,93822],{"className":93821,"style":93465},[282],[128,93823],{},[128,93825,16547],{"className":93826},[1928],[128,93828,93830,93862],{"className":93829,"translate":218},[217],[128,93831,93833],{"className":93832},[222],[224,93834,93835],{"xmlns":226},[228,93836,93837,93859],{},[231,93838,93839],{},[2016,93840,93841,93843],{},[1795,93842,35023],{},[231,93844,93845,93847,93849],{},[1795,93846,2760],{},[1832,93848,1845],{"separator":246},[2016,93850,93851,93853],{},[1795,93852,30641],{},[1977,93854,93855,93857],{},[1795,93856,2760],{},[1832,93858,92810],{},[238,93860,93861],{"encoding":240},"Y_{x, M_{x^*}}",[128,93863,93865],{"className":93864,"ariaHidden":246},[245],[128,93866,93868,93872],{"className":93867},[250],[128,93869],{"className":93870,"style":93871},[254],"height:0.9716em;vertical-align:-0.2883em;",[128,93873,93875,93878],{"className":93874},[259],[128,93876,35023],{"className":93877,"style":2508},[259,1873],[128,93879,93881],{"className":93880},[2087],[128,93882,93884,93976],{"className":93883},[274,321],[128,93885,93887,93973],{"className":93886},[278],[128,93888,93890],{"className":93889,"style":3004},[282],[128,93891,93892,93895],{"style":68109},[128,93893],{"className":93894,"style":291},[290],[128,93896,93898],{"className":93897},[299,300,301,298],[128,93899,93901,93904,93907],{"className":93900},[259,298],[128,93902,2760],{"className":93903},[259,1873,298],[128,93905,1845],{"className":93906},[1903,298],[128,93908,93910,93913],{"className":93909},[259,298],[128,93911,30641],{"className":93912,"style":26806},[259,1873,298],[128,93914,93916],{"className":93915},[2087],[128,93917,93919,93965],{"className":93918},[274,321],[128,93920,93922,93962],{"className":93921},[278],[128,93923,93925],{"className":93924,"style":24117},[282],[128,93926,93927,93930],{"style":93405},[128,93928],{"className":93929,"style":93409},[290],[128,93931,93933],{"className":93932},[299,5794,5795,298],[128,93934,93936],{"className":93935},[259,298],[128,93937,93939,93942],{"className":93938},[259,298],[128,93940,2760],{"className":93941},[259,1873,298],[128,93943,93945],{"className":93944},[2087],[128,93946,93948],{"className":93947},[274],[128,93949,93951],{"className":93950},[278],[128,93952,93954],{"className":93953,"style":93434},[282],[128,93955,93956,93959],{"style":93437},[128,93957],{"className":93958,"style":5790},[290],[128,93960,92810],{"className":93961},[2115,298],[128,93963,347],{"className":93964},[346],[128,93966,93968],{"className":93967},[278],[128,93969,93971],{"className":93970,"style":93453},[282],[128,93972],{},[128,93974,347],{"className":93975},[346],[128,93977,93979],{"className":93978},[278],[128,93980,93982],{"className":93981,"style":93465},[282],[128,93983],{}," 表示「把 ",[128,93986,93988,94001],{"className":93987,"translate":218},[217],[128,93989,93991],{"className":93990},[222],[224,93992,93993],{"xmlns":226},[228,93994,93995,93999],{},[231,93996,93997],{},[1795,93998,364],{},[238,94000,364],{"encoding":240},[128,94002,94004],{"className":94003,"ariaHidden":246},[245],[128,94005,94007,94010],{"className":94006},[250],[128,94008],{"className":94009,"style":283},[254],[128,94011,364],{"className":94012,"style":30665},[259,1873]," 设为 ",[128,94015,94017,94030],{"className":94016,"translate":218},[217],[128,94018,94020],{"className":94019},[222],[224,94021,94022],{"xmlns":226},[228,94023,94024,94028],{},[231,94025,94026],{},[1795,94027,2760],{},[238,94029,2760],{"encoding":240},[128,94031,94033],{"className":94032,"ariaHidden":246},[245],[128,94034,94036,94039],{"className":94035},[250],[128,94037],{"className":94038,"style":7758},[254],[128,94040,2760],{"className":94041},[259,1873],"，同时把 ",[128,94044,94046,94059],{"className":94045,"translate":218},[217],[128,94047,94049],{"className":94048},[222],[224,94050,94051],{"xmlns":226},[228,94052,94053,94057],{},[231,94054,94055],{},[1795,94056,30641],{},[238,94058,30641],{"encoding":240},[128,94060,94062],{"className":94061,"ariaHidden":246},[245],[128,94063,94065,94068],{"className":94064},[250],[128,94066],{"className":94067,"style":283},[254],[128,94069,30641],{"className":94070,"style":26806},[259,1873]," 设为",[35,94073,23408,94074,19116,94102,73722,94160,94188],{},[128,94075,94077,94090],{"className":94076,"translate":218},[217],[128,94078,94080],{"className":94079},[222],[224,94081,94082],{"xmlns":226},[228,94083,94084,94088],{},[231,94085,94086],{},[1795,94087,364],{},[238,94089,364],{"encoding":240},[128,94091,94093],{"className":94092,"ariaHidden":246},[245],[128,94094,94096,94099],{"className":94095},[250],[128,94097],{"className":94098,"style":283},[254],[128,94100,364],{"className":94101,"style":30665},[259,1873],[128,94103,94105,94122],{"className":94104,"translate":218},[217],[128,94106,94108],{"className":94107},[222],[224,94109,94110],{"xmlns":226},[228,94111,94112,94120],{},[231,94113,94114],{},[1977,94115,94116,94118],{},[1795,94117,2760],{},[1832,94119,92810],{},[238,94121,93043],{"encoding":240},[128,94123,94125],{"className":94124,"ariaHidden":246},[245],[128,94126,94128,94131],{"className":94127},[250],[128,94129],{"className":94130,"style":23776},[254],[128,94132,94134,94137],{"className":94133},[259],[128,94135,2760],{"className":94136},[259,1873],[128,94138,94140],{"className":94139},[2087],[128,94141,94143],{"className":94142},[274],[128,94144,94146],{"className":94145},[278],[128,94147,94149],{"className":94148,"style":23776},[282],[128,94150,94151,94154],{"style":2452},[128,94152],{"className":94153,"style":291},[290],[128,94155,94157],{"className":94156},[299,300,301,298],[128,94158,92810],{"className":94159},[2115,298],[128,94161,94163,94176],{"className":94162,"translate":218},[217],[128,94164,94166],{"className":94165},[222],[224,94167,94168],{"xmlns":226},[228,94169,94170,94174],{},[231,94171,94172],{},[1795,94173,30641],{},[238,94175,30641],{"encoding":240},[128,94177,94179],{"className":94178,"ariaHidden":246},[245],[128,94180,94182,94185],{"className":94181},[250],[128,94183],{"className":94184,"style":283},[254],[128,94186,30641],{"className":94187,"style":26806},[259,1873]," 本会取的值","」这一反事实量。",[11,94191,94192,94193,29131,94196],{},"由定义立即可得",[35,94194,94195],{},"总效应的精确分解",[128,94197,94199,94237],{"className":94198,"translate":218},[217],[128,94200,94202],{"className":94201},[222],[224,94203,94204],{"xmlns":226},[228,94205,94206,94234],{},[231,94207,94208,94214,94216,94224,94226],{},[231,94209,94210,94212],{},[1795,94211,313],{"mathvariant":1981},[1795,94213,342],{"mathvariant":1981},[1832,94215,1994],{},[231,94217,94218,94220,94222],{},[1795,94219,26691],{"mathvariant":1981},[1795,94221,59717],{"mathvariant":1981},[1795,94223,342],{"mathvariant":1981},[1832,94225,9486],{},[231,94227,94228,94230,94232],{},[1795,94229,26691],{"mathvariant":1981},[1795,94231,30626],{"mathvariant":1981},[1795,94233,342],{"mathvariant":1981},[238,94235,94236],{"encoding":240},"\\mathrm{TE} = \\mathrm{NDE} + \\mathrm{NIE}",[128,94238,94240,94261,94282],{"className":94239,"ariaHidden":246},[245],[128,94241,94243,94246,94252,94255,94258],{"className":94242},[250],[128,94244],{"className":94245,"style":283},[254],[128,94247,94249],{"className":94248},[259],[128,94250,92831],{"className":94251},[259,3353],[128,94253],{"className":94254,"style":1878},[269],[128,94256,1994],{"className":94257},[1882],[128,94259],{"className":94260,"style":1878},[269],[128,94262,94264,94267,94273,94276,94279],{"className":94263},[250],[128,94265],{"className":94266,"style":2705},[254],[128,94268,94270],{"className":94269},[259],[128,94271,93283],{"className":94272},[259,3353],[128,94274],{"className":94275,"style":2508},[269],[128,94277,9486],{"className":94278},[2115],[128,94280],{"className":94281,"style":2508},[269],[128,94283,94285,94288],{"className":94284},[250],[128,94286],{"className":94287,"style":283},[254],[128,94289,94291],{"className":94290},[259],[128,94292,93579],{"className":94293},[259,3353],[11,94295,94296,94297,94400,94401,94470],{},"其含义可以这样读：NDE 让中介停留在「另一个世界」的取值上，因此度量的正是直接通道；NIE 则度量中介由 ",[128,94298,94300,94322],{"className":94299,"translate":218},[217],[128,94301,94303],{"className":94302},[222],[224,94304,94305],{"xmlns":226},[228,94306,94307,94319],{},[231,94308,94309],{},[2016,94310,94311,94313],{},[1795,94312,30641],{},[1977,94314,94315,94317],{},[1795,94316,2760],{},[1832,94318,92810],{},[238,94320,94321],{"encoding":240},"M_{x^*}",[128,94323,94325],{"className":94324,"ariaHidden":246},[245],[128,94326,94328,94331],{"className":94327},[250],[128,94329],{"className":94330,"style":36058},[254],[128,94332,94334,94337],{"className":94333},[259],[128,94335,30641],{"className":94336,"style":26806},[259,1873],[128,94338,94340],{"className":94339},[2087],[128,94341,94343,94392],{"className":94342},[274,321],[128,94344,94346,94389],{"className":94345},[278],[128,94347,94349],{"className":94348,"style":92938},[282],[128,94350,94351,94354],{"style":64697},[128,94352],{"className":94353,"style":291},[290],[128,94355,94357],{"className":94356},[299,300,301,298],[128,94358,94360],{"className":94359},[259,298],[128,94361,94363,94366],{"className":94362},[259,298],[128,94364,2760],{"className":94365},[259,1873,298],[128,94367,94369],{"className":94368},[2087],[128,94370,94372],{"className":94371},[274],[128,94373,94375],{"className":94374},[278],[128,94376,94378],{"className":94377,"style":92968},[282],[128,94379,94380,94383],{"style":6609},[128,94381],{"className":94382,"style":5790},[290],[128,94384,94386],{"className":94385},[299,5794,5795,298],[128,94387,92810],{"className":94388},[2115,298],[128,94390,347],{"className":94391},[346],[128,94393,94395],{"className":94394},[278],[128,94396,94398],{"className":94397,"style":2241},[282],[128,94399],{}," 变为 ",[128,94402,94404,94421],{"className":94403,"translate":218},[217],[128,94405,94407],{"className":94406},[222],[224,94408,94409],{"xmlns":226},[228,94410,94411,94419],{},[231,94412,94413],{},[2016,94414,94415,94417],{},[1795,94416,30641],{},[1795,94418,2760],{},[238,94420,84648],{"encoding":240},[128,94422,94424],{"className":94423,"ariaHidden":246},[245],[128,94425,94427,94430],{"className":94426},[250],[128,94428],{"className":94429,"style":36058},[254],[128,94431,94433,94436],{"className":94432},[259],[128,94434,30641],{"className":94435,"style":26806},[259,1873],[128,94437,94439],{"className":94438},[2087],[128,94440,94442,94462],{"className":94441},[274,321],[128,94443,94445,94459],{"className":94444},[278],[128,94446,94448],{"className":94447,"style":28738},[282],[128,94449,94450,94453],{"style":64697},[128,94451],{"className":94452,"style":291},[290],[128,94454,94456],{"className":94455},[299,300,301,298],[128,94457,2760],{"className":94458},[259,1873,298],[128,94460,347],{"className":94461},[346],[128,94463,94465],{"className":94464},[278],[128,94466,94468],{"className":94467,"style":2241},[282],[128,94469],{}," 所贡献的间接部分。",[11,94472,94473,94474,94632,94633,94661,94662,11072,94712,94793],{},"需要特别注意，",[35,94475,94476,94631],{},[128,94477,94479,94510],{"className":94478,"translate":218},[217],[128,94480,94482],{"className":94481},[222],[224,94483,94484],{"xmlns":226},[228,94485,94486,94508],{},[231,94487,94488],{},[2016,94489,94490,94492],{},[1795,94491,35023],{},[231,94493,94494,94496,94498],{},[1795,94495,2760],{},[1832,94497,1845],{"separator":246},[2016,94499,94500,94502],{},[1795,94501,30641],{},[1977,94503,94504,94506],{},[1795,94505,2760],{},[1832,94507,92810],{},[238,94509,93861],{"encoding":240},[128,94511,94513],{"className":94512,"ariaHidden":246},[245],[128,94514,94516,94519],{"className":94515},[250],[128,94517],{"className":94518,"style":93871},[254],[128,94520,94522,94525],{"className":94521},[259],[128,94523,35023],{"className":94524,"style":2508},[259,1873],[128,94526,94528],{"className":94527},[2087],[128,94529,94531,94623],{"className":94530},[274,321],[128,94532,94534,94620],{"className":94533},[278],[128,94535,94537],{"className":94536,"style":3004},[282],[128,94538,94539,94542],{"style":68109},[128,94540],{"className":94541,"style":291},[290],[128,94543,94545],{"className":94544},[299,300,301,298],[128,94546,94548,94551,94554],{"className":94547},[259,298],[128,94549,2760],{"className":94550},[259,1873,298],[128,94552,1845],{"className":94553},[1903,298],[128,94555,94557,94560],{"className":94556},[259,298],[128,94558,30641],{"className":94559,"style":26806},[259,1873,298],[128,94561,94563],{"className":94562},[2087],[128,94564,94566,94612],{"className":94565},[274,321],[128,94567,94569,94609],{"className":94568},[278],[128,94570,94572],{"className":94571,"style":24117},[282],[128,94573,94574,94577],{"style":93405},[128,94575],{"className":94576,"style":93409},[290],[128,94578,94580],{"className":94579},[299,5794,5795,298],[128,94581,94583],{"className":94582},[259,298],[128,94584,94586,94589],{"className":94585},[259,298],[128,94587,2760],{"className":94588},[259,1873,298],[128,94590,94592],{"className":94591},[2087],[128,94593,94595],{"className":94594},[274],[128,94596,94598],{"className":94597},[278],[128,94599,94601],{"className":94600,"style":93434},[282],[128,94602,94603,94606],{"style":93437},[128,94604],{"className":94605,"style":5790},[290],[128,94607,92810],{"className":94608},[2115,298],[128,94610,347],{"className":94611},[346],[128,94613,94615],{"className":94614},[278],[128,94616,94618],{"className":94617,"style":93453},[282],[128,94619],{},[128,94621,347],{"className":94622},[346],[128,94624,94626],{"className":94625},[278],[128,94627,94629],{"className":94628,"style":93465},[282],[128,94630],{}," 是一个跨世界（cross-world）量","：它在同一个个体 ",[128,94634,94636,94649],{"className":94635,"translate":218},[217],[128,94637,94639],{"className":94638},[222],[224,94640,94641],{"xmlns":226},[228,94642,94643,94647],{},[231,94644,94645],{},[1795,94646,35129],{},[238,94648,35129],{"encoding":240},[128,94650,94652],{"className":94651,"ariaHidden":246},[245],[128,94653,94655,94658],{"className":94654},[250],[128,94656],{"className":94657,"style":7758},[254],[128,94659,35129],{"className":94660},[259,1873]," 上同时引用了 ",[128,94663,94665,94682],{"className":94664,"translate":218},[217],[128,94666,94668],{"className":94667},[222],[224,94669,94670],{"xmlns":226},[228,94671,94672,94680],{},[231,94673,94674,94676,94678],{},[1795,94675,364],{},[1832,94677,1994],{},[1795,94679,2760],{},[238,94681,67261],{"encoding":240},[128,94683,94685,94703],{"className":94684,"ariaHidden":246},[245],[128,94686,94688,94691,94694,94697,94700],{"className":94687},[250],[128,94689],{"className":94690,"style":283},[254],[128,94692,364],{"className":94693,"style":30665},[259,1873],[128,94695],{"className":94696,"style":1878},[269],[128,94698,1994],{"className":94699},[1882],[128,94701],{"className":94702,"style":1878},[269],[128,94704,94706,94709],{"className":94705},[250],[128,94707],{"className":94708,"style":7758},[254],[128,94710,2760],{"className":94711},[259,1873],[128,94713,94715,94737],{"className":94714,"translate":218},[217],[128,94716,94718],{"className":94717},[222],[224,94719,94720],{"xmlns":226},[228,94721,94722,94734],{},[231,94723,94724,94726,94728],{},[1795,94725,364],{},[1832,94727,1994],{},[1977,94729,94730,94732],{},[1795,94731,2760],{},[1832,94733,92810],{},[238,94735,94736],{"encoding":240},"X=x^*",[128,94738,94740,94758],{"className":94739,"ariaHidden":246},[245],[128,94741,94743,94746,94749,94752,94755],{"className":94742},[250],[128,94744],{"className":94745,"style":283},[254],[128,94747,364],{"className":94748,"style":30665},[259,1873],[128,94750],{"className":94751,"style":1878},[269],[128,94753,1994],{"className":94754},[1882],[128,94756],{"className":94757,"style":1878},[269],[128,94759,94761,94764],{"className":94760},[250],[128,94762],{"className":94763,"style":23776},[254],[128,94765,94767,94770],{"className":94766},[259],[128,94768,2760],{"className":94769},[259,1873],[128,94771,94773],{"className":94772},[2087],[128,94774,94776],{"className":94775},[274],[128,94777,94779],{"className":94778},[278],[128,94780,94782],{"className":94781,"style":23776},[282],[128,94783,94784,94787],{"style":2452},[128,94785],{"className":94786,"style":291},[290],[128,94788,94790],{"className":94789},[299,300,301,298],[128,94791,92810],{"className":94792},[2115,298]," 这两个互不相容的世界。因此中介分析在本质上属于第三层而非第二层——这也解释了为什么中介效应长期以来被认为是不可识别的。",[11,94795,94796,94799],{},[35,94797,94798],{},"可识别性条件（序贯可忽略性）","：要使 NDE 与 NIE 可由观测数据估计，需要同时满足",[33248,94801,94802,94889,94976,95062],{},[33251,94803,94804,11072,94832,94860,94861,73372],{},[128,94805,94807,94820],{"className":94806,"translate":218},[217],[128,94808,94810],{"className":94809},[222],[224,94811,94812],{"xmlns":226},[228,94813,94814,94818],{},[231,94815,94816],{},[1795,94817,364],{},[238,94819,364],{"encoding":240},[128,94821,94823],{"className":94822,"ariaHidden":246},[245],[128,94824,94826,94829],{"className":94825},[250],[128,94827],{"className":94828,"style":283},[254],[128,94830,364],{"className":94831,"style":30665},[259,1873],[128,94833,94835,94848],{"className":94834,"translate":218},[217],[128,94836,94838],{"className":94837},[222],[224,94839,94840],{"xmlns":226},[228,94841,94842,94846],{},[231,94843,94844],{},[1795,94845,35023],{},[238,94847,35023],{"encoding":240},[128,94849,94851],{"className":94850,"ariaHidden":246},[245],[128,94852,94854,94857],{"className":94853},[250],[128,94855],{"className":94856,"style":283},[254],[128,94858,35023],{"className":94859,"style":2508},[259,1873]," 之间无未观测混杂（给定协变量 ",[128,94862,94864,94877],{"className":94863,"translate":218},[217],[128,94865,94867],{"className":94866},[222],[224,94868,94869],{"xmlns":226},[228,94870,94871,94875],{},[231,94872,94873],{},[1795,94874,36679],{},[238,94876,36679],{"encoding":240},[128,94878,94880],{"className":94879,"ariaHidden":246},[245],[128,94881,94883,94886],{"className":94882},[250],[128,94884],{"className":94885,"style":283},[254],[128,94887,36679],{"className":94888,"style":36065},[259,1873],[33251,94890,94891,11072,94919,94947,94948,73372],{},[128,94892,94894,94907],{"className":94893,"translate":218},[217],[128,94895,94897],{"className":94896},[222],[224,94898,94899],{"xmlns":226},[228,94900,94901,94905],{},[231,94902,94903],{},[1795,94904,30641],{},[238,94906,30641],{"encoding":240},[128,94908,94910],{"className":94909,"ariaHidden":246},[245],[128,94911,94913,94916],{"className":94912},[250],[128,94914],{"className":94915,"style":283},[254],[128,94917,30641],{"className":94918,"style":26806},[259,1873],[128,94920,94922,94935],{"className":94921,"translate":218},[217],[128,94923,94925],{"className":94924},[222],[224,94926,94927],{"xmlns":226},[228,94928,94929,94933],{},[231,94930,94931],{},[1795,94932,35023],{},[238,94934,35023],{"encoding":240},[128,94936,94938],{"className":94937,"ariaHidden":246},[245],[128,94939,94941,94944],{"className":94940},[250],[128,94942],{"className":94943,"style":283},[254],[128,94945,35023],{"className":94946,"style":2508},[259,1873]," 之间无未观测混杂（给定 ",[128,94949,94951,94964],{"className":94950,"translate":218},[217],[128,94952,94954],{"className":94953},[222],[224,94955,94956],{"xmlns":226},[228,94957,94958,94962],{},[231,94959,94960],{},[1795,94961,36679],{},[238,94963,36679],{"encoding":240},[128,94965,94967],{"className":94966,"ariaHidden":246},[245],[128,94968,94970,94973],{"className":94969},[250],[128,94971],{"className":94972,"style":283},[254],[128,94974,36679],{"className":94975,"style":36065},[259,1873],[33251,94977,94978,11072,95006,94947,95034,73372],{},[128,94979,94981,94994],{"className":94980,"translate":218},[217],[128,94982,94984],{"className":94983},[222],[224,94985,94986],{"xmlns":226},[228,94987,94988,94992],{},[231,94989,94990],{},[1795,94991,364],{},[238,94993,364],{"encoding":240},[128,94995,94997],{"className":94996,"ariaHidden":246},[245],[128,94998,95000,95003],{"className":94999},[250],[128,95001],{"className":95002,"style":283},[254],[128,95004,364],{"className":95005,"style":30665},[259,1873],[128,95007,95009,95022],{"className":95008,"translate":218},[217],[128,95010,95012],{"className":95011},[222],[224,95013,95014],{"xmlns":226},[228,95015,95016,95020],{},[231,95017,95018],{},[1795,95019,30641],{},[238,95021,30641],{"encoding":240},[128,95023,95025],{"className":95024,"ariaHidden":246},[245],[128,95026,95028,95031],{"className":95027},[250],[128,95029],{"className":95030,"style":283},[254],[128,95032,30641],{"className":95033,"style":26806},[259,1873],[128,95035,95037,95050],{"className":95036,"translate":218},[217],[128,95038,95040],{"className":95039},[222],[224,95041,95042],{"xmlns":226},[228,95043,95044,95048],{},[231,95045,95046],{},[1795,95047,36679],{},[238,95049,36679],{"encoding":240},[128,95051,95053],{"className":95052,"ariaHidden":246},[245],[128,95054,95056,95059],{"className":95055},[250],[128,95057],{"className":95058,"style":283},[254],[128,95060,36679],{"className":95061,"style":36065},[259,1873],[33251,95063,95064,11072,95092,95120,95121,95149],{},[128,95065,95067,95080],{"className":95066,"translate":218},[217],[128,95068,95070],{"className":95069},[222],[224,95071,95072],{"xmlns":226},[228,95073,95074,95078],{},[231,95075,95076],{},[1795,95077,30641],{},[238,95079,30641],{"encoding":240},[128,95081,95083],{"className":95082,"ariaHidden":246},[245],[128,95084,95086,95089],{"className":95085},[250],[128,95087],{"className":95088,"style":283},[254],[128,95090,30641],{"className":95091,"style":26806},[259,1873],[128,95093,95095,95108],{"className":95094,"translate":218},[217],[128,95096,95098],{"className":95097},[222],[224,95099,95100],{"xmlns":226},[228,95101,95102,95106],{},[231,95103,95104],{},[1795,95105,35023],{},[238,95107,35023],{"encoding":240},[128,95109,95111],{"className":95110,"ariaHidden":246},[245],[128,95112,95114,95117],{"className":95113},[250],[128,95115],{"className":95116,"style":283},[254],[128,95118,35023],{"className":95119,"style":2508},[259,1873]," 之间不存在受 ",[128,95122,95124,95137],{"className":95123,"translate":218},[217],[128,95125,95127],{"className":95126},[222],[224,95128,95129],{"xmlns":226},[228,95130,95131,95135],{},[231,95132,95133],{},[1795,95134,364],{},[238,95136,364],{"encoding":240},[128,95138,95140],{"className":95139,"ariaHidden":246},[245],[128,95141,95143,95146],{"className":95142},[250],[128,95144],{"className":95145,"style":283},[254],[128,95147,364],{"className":95148,"style":30665},[259,1873]," 影响的混杂因子。",[11,95151,95152,95153,95156,95157,95582,95583,23397],{},"其中第 4 条最容易被忽略，也最强：它要求中介与结果之间不能存在被处理变量触及的共同原因。四条合称",[35,95154,95155],{},"序贯可忽略性（sequential ignorability）","。在此条件下，自然直接效应可由观测分布表达为\n",[128,95158,95160,95273],{"className":95159,"translate":218},[217],[128,95161,95163],{"className":95162},[222],[224,95164,95165],{"xmlns":226},[228,95166,95167,95270],{},[231,95168,95169,95177,95179,95192,95194,95196,95198,95200,95202,95204,95206,95208,95210,95212,95214,95216,95218,95220,95222,95224,95230,95232,95234,95236,95238,95240,95242,95244,95246,95248,95250,95256,95258,95260,95262,95264,95266,95268],{},[231,95170,95171,95173,95175],{},[1795,95172,26691],{"mathvariant":1981},[1795,95174,59717],{"mathvariant":1981},[1795,95176,342],{"mathvariant":1981},[1832,95178,1994],{},[2016,95180,95181,95183],{},[1832,95182,2042],{},[231,95184,95185,95187,95189],{},[1795,95186,30849],{},[1832,95188,1845],{"separator":246},[1795,95190,95191],{},"w",[1832,95193,16538],{"fence":1837,"stretchy":246,"minsize":62447,"maxsize":62447},[1795,95195,342],{"mathvariant":2008},[1832,95197,16538],{"stretchy":1837},[1795,95199,35023],{},[1832,95201,5443],{},[1795,95203,2760],{},[1832,95205,1845],{"separator":246},[1795,95207,30849],{},[1832,95209,1845],{"separator":246},[1795,95211,95191],{},[1832,95213,16547],{"stretchy":1837},[1832,95215,1989],{},[1795,95217,342],{"mathvariant":2008},[1832,95219,16538],{"stretchy":1837},[1795,95221,35023],{},[1832,95223,5443],{},[1977,95225,95226,95228],{},[1795,95227,2760],{},[1832,95229,92810],{},[1832,95231,1845],{"separator":246},[1795,95233,30849],{},[1832,95235,1845],{"separator":246},[1795,95237,95191],{},[1832,95239,16547],{"stretchy":1837},[1832,95241,16547],{"fence":1837,"stretchy":246,"minsize":62447,"maxsize":62447},[1795,95243,23001],{},[1832,95245,2477],{"stretchy":1837},[1795,95247,30849],{},[1832,95249,5443],{},[1977,95251,95252,95254],{},[1795,95253,2760],{},[1832,95255,92810],{},[1832,95257,1845],{"separator":246},[1795,95259,95191],{},[1832,95261,2486],{"stretchy":1837},[1795,95263,23001],{},[1832,95265,2477],{"stretchy":1837},[1795,95267,95191],{},[1832,95269,2486],{"stretchy":1837},[238,95271,95272],{"encoding":240},"\\mathrm{NDE} = \\sum_{m, w}\\Big[\\mathbb{E}[Y \\mid x, m, w] - \\mathbb{E}[Y \\mid x^*, m, w]\\Big] P(m \\mid x^*, w) P(w)",[128,95274,95276,95297,95380,95419,95443,95523],{"className":95275,"ariaHidden":246},[245],[128,95277,95279,95282,95288,95291,95294],{"className":95278},[250],[128,95280],{"className":95281,"style":283},[254],[128,95283,95285],{"className":95284},[259],[128,95286,93283],{"className":95287},[259,3353],[128,95289],{"className":95290,"style":1878},[269],[128,95292,1994],{"className":95293},[1882],[128,95295],{"className":95296,"style":1878},[269],[128,95298,95300,95303,95353,95356,95362,95365,95368,95371,95374,95377],{"className":95299},[250],[128,95301],{"className":95302,"style":2134},[254],[128,95304,95306,95309],{"className":95305},[2268],[128,95307,2042],{"className":95308,"style":2274},[2268,2272,2273],[128,95310,95312],{"className":95311},[2087],[128,95313,95315,95345],{"className":95314},[274,321],[128,95316,95318,95342],{"className":95317},[278],[128,95319,95321],{"className":95320,"style":87047},[282],[128,95322,95323,95326],{"style":2290},[128,95324],{"className":95325,"style":291},[290],[128,95327,95329],{"className":95328},[299,300,301,298],[128,95330,95332,95335,95338],{"className":95331},[259,298],[128,95333,30849],{"className":95334},[259,1873,298],[128,95336,1845],{"className":95337},[1903,298],[128,95339,95191],{"className":95340,"style":95341},[259,1873,298],"margin-right:0.0269em;",[128,95343,347],{"className":95344},[346],[128,95346,95348],{"className":95347},[278],[128,95349,95351],{"className":95350,"style":31756},[282],[128,95352],{},[128,95354],{"className":95355,"style":1907},[269],[128,95357,95359],{"className":95358},[259],[128,95360,16538],{"className":95361},[2146,2147],[128,95363,342],{"className":95364},[259,2167],[128,95366,16538],{"className":95367},[1896],[128,95369,35023],{"className":95370,"style":2508},[259,1873],[128,95372],{"className":95373,"style":1878},[269],[128,95375,5443],{"className":95376},[1882],[128,95378],{"className":95379,"style":1878},[269],[128,95381,95383,95386,95389,95392,95395,95398,95401,95404,95407,95410,95413,95416],{"className":95382},[250],[128,95384],{"className":95385,"style":1892},[254],[128,95387,2760],{"className":95388},[259,1873],[128,95390,1845],{"className":95391},[1903],[128,95393],{"className":95394,"style":1907},[269],[128,95396,30849],{"className":95397},[259,1873],[128,95399,1845],{"className":95400},[1903],[128,95402],{"className":95403,"style":1907},[269],[128,95405,95191],{"className":95406,"style":95341},[259,1873],[128,95408,16547],{"className":95409},[1928],[128,95411],{"className":95412,"style":2508},[269],[128,95414,1989],{"className":95415},[2115],[128,95417],{"className":95418,"style":2508},[269],[128,95420,95422,95425,95428,95431,95434,95437,95440],{"className":95421},[250],[128,95423],{"className":95424,"style":1892},[254],[128,95426,342],{"className":95427},[259,2167],[128,95429,16538],{"className":95430},[1896],[128,95432,35023],{"className":95433,"style":2508},[259,1873],[128,95435],{"className":95436,"style":1878},[269],[128,95438,5443],{"className":95439},[1882],[128,95441],{"className":95442,"style":1878},[269],[128,95444,95446,95449,95478,95481,95484,95487,95490,95493,95496,95499,95505,95508,95511,95514,95517,95520],{"className":95445},[250],[128,95447],{"className":95448,"style":2134},[254],[128,95450,95452,95455],{"className":95451},[259],[128,95453,2760],{"className":95454},[259,1873],[128,95456,95458],{"className":95457},[2087],[128,95459,95461],{"className":95460},[274],[128,95462,95464],{"className":95463},[278],[128,95465,95467],{"className":95466,"style":23776},[282],[128,95468,95469,95472],{"style":2452},[128,95470],{"className":95471,"style":291},[290],[128,95473,95475],{"className":95474},[299,300,301,298],[128,95476,92810],{"className":95477},[2115,298],[128,95479,1845],{"className":95480},[1903],[128,95482],{"className":95483,"style":1907},[269],[128,95485,30849],{"className":95486},[259,1873],[128,95488,1845],{"className":95489},[1903],[128,95491],{"className":95492,"style":1907},[269],[128,95494,95191],{"className":95495,"style":95341},[259,1873],[128,95497,16547],{"className":95498},[1928],[128,95500,95502],{"className":95501},[259],[128,95503,16547],{"className":95504},[2146,2147],[128,95506,23001],{"className":95507,"style":36065},[259,1873],[128,95509,2477],{"className":95510},[1896],[128,95512,30849],{"className":95513},[259,1873],[128,95515],{"className":95516,"style":1878},[269],[128,95518,5443],{"className":95519},[1882],[128,95521],{"className":95522,"style":1878},[269],[128,95524,95526,95529,95558,95561,95564,95567,95570,95573,95576,95579],{"className":95525},[250],[128,95527],{"className":95528,"style":1892},[254],[128,95530,95532,95535],{"className":95531},[259],[128,95533,2760],{"className":95534},[259,1873],[128,95536,95538],{"className":95537},[2087],[128,95539,95541],{"className":95540},[274],[128,95542,95544],{"className":95543},[278],[128,95545,95547],{"className":95546,"style":23776},[282],[128,95548,95549,95552],{"style":2452},[128,95550],{"className":95551,"style":291},[290],[128,95553,95555],{"className":95554},[299,300,301,298],[128,95556,92810],{"className":95557},[2115,298],[128,95559,1845],{"className":95560},[1903],[128,95562],{"className":95563,"style":1907},[269],[128,95565,95191],{"className":95566,"style":95341},[259,1873],[128,95568,2486],{"className":95569},[1928],[128,95571,23001],{"className":95572,"style":36065},[259,1873],[128,95574,2477],{"className":95575},[1896],[128,95577,95191],{"className":95578,"style":95341},[259,1873],[128,95580,2486],{"className":95581},[1928],"\n自然间接效应则相应地由 ",[128,95584,95586,95624],{"className":95585,"translate":218},[217],[128,95587,95589],{"className":95588},[222],[224,95590,95591],{"xmlns":226},[228,95592,95593,95621],{},[231,95594,95595,95603,95605,95611,95613],{},[231,95596,95597,95599,95601],{},[1795,95598,26691],{"mathvariant":1981},[1795,95600,30626],{"mathvariant":1981},[1795,95602,342],{"mathvariant":1981},[1832,95604,1994],{},[231,95606,95607,95609],{},[1795,95608,313],{"mathvariant":1981},[1795,95610,342],{"mathvariant":1981},[1832,95612,1989],{},[231,95614,95615,95617,95619],{},[1795,95616,26691],{"mathvariant":1981},[1795,95618,59717],{"mathvariant":1981},[1795,95620,342],{"mathvariant":1981},[238,95622,95623],{"encoding":240},"\\mathrm{NIE} = \\mathrm{TE} - \\mathrm{NDE}",[128,95625,95627,95648,95669],{"className":95626,"ariaHidden":246},[245],[128,95628,95630,95633,95639,95642,95645],{"className":95629},[250],[128,95631],{"className":95632,"style":283},[254],[128,95634,95636],{"className":95635},[259],[128,95637,93579],{"className":95638},[259,3353],[128,95640],{"className":95641,"style":1878},[269],[128,95643,1994],{"className":95644},[1882],[128,95646],{"className":95647,"style":1878},[269],[128,95649,95651,95654,95660,95663,95666],{"className":95650},[250],[128,95652],{"className":95653,"style":2705},[254],[128,95655,95657],{"className":95656},[259],[128,95658,92831],{"className":95659},[259,3353],[128,95661],{"className":95662,"style":2508},[269],[128,95664,1989],{"className":95665},[2115],[128,95667],{"className":95668,"style":2508},[269],[128,95670,95672,95675],{"className":95671},[250],[128,95673],{"className":95674,"style":283},[254],[128,95676,95678],{"className":95677},[259],[128,95679,93283],{"className":95680},[259,3353],[11,95682,95683,95686,95687,95760,95761,95789,95790,95818,95819,95822,95823,95826,95827,95855,95856,95884,95885,95913,95914,95986,95987,96015,96016,96067,96068,96096],{},[35,95684,95685],{},"回到例 1.2 的告诫","：实践中极易发生的一种错误，是把中介当作普通协变量放进回归模型 ",[128,95688,95690,95712],{"className":95689,"translate":218},[217],[128,95691,95693],{"className":95692},[222],[224,95694,95695],{"xmlns":226},[228,95696,95697,95709],{},[231,95698,95699,95701,95703,95705,95707],{},[1795,95700,35023],{},[1832,95702,5911],{},[1795,95704,364],{},[1832,95706,9486],{},[1795,95708,30641],{},[238,95710,95711],{"encoding":240},"Y \\sim X + M",[128,95713,95715,95733,95751],{"className":95714,"ariaHidden":246},[245],[128,95716,95718,95721,95724,95727,95730],{"className":95717},[250],[128,95719],{"className":95720,"style":283},[254],[128,95722,35023],{"className":95723,"style":2508},[259,1873],[128,95725],{"className":95726,"style":1878},[269],[128,95728,5911],{"className":95729},[1882],[128,95731],{"className":95732,"style":1878},[269],[128,95734,95736,95739,95742,95745,95748],{"className":95735},[250],[128,95737],{"className":95738,"style":2705},[254],[128,95740,364],{"className":95741,"style":30665},[259,1873],[128,95743],{"className":95744,"style":2508},[269],[128,95746,9486],{"className":95747},[2115],[128,95749],{"className":95750,"style":2508},[269],[128,95752,95754,95757],{"className":95753},[250],[128,95755],{"className":95756,"style":283},[254],[128,95758,30641],{"className":95759,"style":26806},[259,1873],"，再把 ",[128,95762,95764,95777],{"className":95763,"translate":218},[217],[128,95765,95767],{"className":95766},[222],[224,95768,95769],{"xmlns":226},[228,95770,95771,95775],{},[231,95772,95773],{},[1795,95774,364],{},[238,95776,364],{"encoding":240},[128,95778,95780],{"className":95779,"ariaHidden":246},[245],[128,95781,95783,95786],{"className":95782},[250],[128,95784],{"className":95785,"style":283},[254],[128,95787,364],{"className":95788,"style":30665},[259,1873]," 的系数解释为「",[128,95791,95793,95806],{"className":95792,"translate":218},[217],[128,95794,95796],{"className":95795},[222],[224,95797,95798],{"xmlns":226},[228,95799,95800,95804],{},[231,95801,95802],{},[1795,95803,364],{},[238,95805,364],{"encoding":240},[128,95807,95809],{"className":95808,"ariaHidden":246},[245],[128,95810,95812,95815],{"className":95811},[250],[128,95813],{"className":95814,"style":283},[254],[128,95816,364],{"className":95817,"style":30665},[259,1873]," 的效应」。由上述分解立即可见，这样做得到的其实只是",[35,95820,95821],{},"直接效应"," NDE，它系统性地",[35,95824,95825],{},"遗漏","了经由 ",[128,95828,95830,95843],{"className":95829,"translate":218},[217],[128,95831,95833],{"className":95832},[222],[224,95834,95835],{"xmlns":226},[228,95836,95837,95841],{},[231,95838,95839],{},[1795,95840,30641],{},[238,95842,30641],{"encoding":240},[128,95844,95846],{"className":95845,"ariaHidden":246},[245],[128,95847,95849,95852],{"className":95848},[250],[128,95850],{"className":95851,"style":283},[254],[128,95853,30641],{"className":95854,"style":26806},[259,1873]," 传递的间接部分，因而会低估 ",[128,95857,95859,95872],{"className":95858,"translate":218},[217],[128,95860,95862],{"className":95861},[222],[224,95863,95864],{"xmlns":226},[228,95865,95866,95870],{},[231,95867,95868],{},[1795,95869,364],{},[238,95871,364],{"encoding":240},[128,95873,95875],{"className":95874,"ariaHidden":246},[245],[128,95876,95878,95881],{"className":95877},[250],[128,95879],{"className":95880,"style":283},[254],[128,95882,364],{"className":95883,"style":30665},[259,1873]," 的总效应。而当「控制 ",[128,95886,95888,95901],{"className":95887,"translate":218},[217],[128,95889,95891],{"className":95890},[222],[224,95892,95893],{"xmlns":226},[228,95894,95895,95899],{},[231,95896,95897],{},[1795,95898,30641],{},[238,95900,30641],{"encoding":240},[128,95902,95904],{"className":95903,"ariaHidden":246},[245],[128,95905,95907,95910],{"className":95906},[250],[128,95908],{"className":95909,"style":283},[254],[128,95911,30641],{"className":95912,"style":26806},[259,1873],"」的动机恰恰是「我想排除混杂」时，这一操作等于是把待估计的那条因果通道本身切断了——这是链结构在实践中最重要的一个陷阱。即便只想得到 NDE，也仍然需要上述四条假设；只有在线性且无交互的特殊情形下，",[128,95915,95917,95938],{"className":95916,"translate":218},[217],[128,95918,95920],{"className":95919},[222],[224,95921,95922],{"xmlns":226},[228,95923,95924,95936],{},[231,95925,95926,95928,95930,95932,95934],{},[1795,95927,35023],{},[1832,95929,5911],{},[1795,95931,364],{},[1832,95933,9486],{},[1795,95935,30641],{},[238,95937,95711],{"encoding":240},[128,95939,95941,95959,95977],{"className":95940,"ariaHidden":246},[245],[128,95942,95944,95947,95950,95953,95956],{"className":95943},[250],[128,95945],{"className":95946,"style":283},[254],[128,95948,35023],{"className":95949,"style":2508},[259,1873],[128,95951],{"className":95952,"style":1878},[269],[128,95954,5911],{"className":95955},[1882],[128,95957],{"className":95958,"style":1878},[269],[128,95960,95962,95965,95968,95971,95974],{"className":95961},[250],[128,95963],{"className":95964,"style":2705},[254],[128,95966,364],{"className":95967,"style":30665},[259,1873],[128,95969],{"className":95970,"style":2508},[269],[128,95972,9486],{"className":95973},[2115],[128,95975],{"className":95976,"style":2508},[269],[128,95978,95980,95983],{"className":95979},[250],[128,95981],{"className":95982,"style":283},[254],[128,95984,30641],{"className":95985,"style":26806},[259,1873]," 中 ",[128,95988,95990,96003],{"className":95989,"translate":218},[217],[128,95991,95993],{"className":95992},[222],[224,95994,95995],{"xmlns":226},[228,95996,95997,96001],{},[231,95998,95999],{},[1795,96000,364],{},[238,96002,364],{"encoding":240},[128,96004,96006],{"className":96005,"ariaHidden":246},[245],[128,96007,96009,96012],{"className":96008},[250],[128,96010],{"className":96011,"style":283},[254],[128,96013,364],{"className":96014,"style":30665},[259,1873]," 的系数才恰好等于 NDE，一旦存在 ",[128,96017,96019,96037],{"className":96018,"translate":218},[217],[128,96020,96022],{"className":96021},[222],[224,96023,96024],{"xmlns":226},[228,96025,96026,96034],{},[231,96027,96028,96030,96032],{},[1795,96029,364],{},[1832,96031,68213],{},[1795,96033,30641],{},[238,96035,96036],{"encoding":240},"X \\times M",[128,96038,96040,96058],{"className":96039,"ariaHidden":246},[245],[128,96041,96043,96046,96049,96052,96055],{"className":96042},[250],[128,96044],{"className":96045,"style":2705},[254],[128,96047,364],{"className":96048,"style":30665},[259,1873],[128,96050],{"className":96051,"style":2508},[269],[128,96053,68213],{"className":96054},[2115],[128,96056],{"className":96057,"style":2508},[269],[128,96059,96061,96064],{"className":96060},[250],[128,96062],{"className":96063,"style":283},[254],[128,96065,30641],{"className":96066,"style":26806},[259,1873]," 交互或 ",[128,96069,96071,96084],{"className":96070,"translate":218},[217],[128,96072,96074],{"className":96073},[222],[224,96075,96076],{"xmlns":226},[228,96077,96078,96082],{},[231,96079,96080],{},[1795,96081,30641],{},[238,96083,30641],{"encoding":240},[128,96085,96087],{"className":96086,"ariaHidden":246},[245],[128,96088,96090,96093],{"className":96089},[250],[128,96091],{"className":96092,"style":283},[254],[128,96094,30641],{"className":96095,"style":26806},[259,1873]," 进入非线性的函数形式，该系数便失去直接效应的解释。",[2610,96098,96100],{"id":96099},"_35-可识别性do-演算后门准则与前门准则","3.5 可识别性：do-演算、后门准则与前门准则",[11,96102,96103,96104,96186,96187,893],{},"在实践中，我们通常只有观测数据（第一层），希望知道某个干预量 ",[128,96105,96107,96138],{"className":96106,"translate":218},[217],[128,96108,96110],{"className":96109},[222],[224,96111,96112],{"xmlns":226},[228,96113,96114,96136],{},[231,96115,96116,96118,96120,96122,96124,96126,96128,96130,96132,96134],{},[1795,96117,23001],{},[1832,96119,2477],{"stretchy":1837},[1795,96121,1830],{},[1832,96123,5443],{},[1795,96125,4519],{},[1795,96127,67350],{},[1832,96129,2477],{"stretchy":1837},[1795,96131,2760],{},[1832,96133,2486],{"stretchy":1837},[1832,96135,2486],{"stretchy":1837},[238,96137,67361],{"encoding":240},[128,96139,96141,96165],{"className":96140,"ariaHidden":246},[245],[128,96142,96144,96147,96150,96153,96156,96159,96162],{"className":96143},[250],[128,96145],{"className":96146,"style":1892},[254],[128,96148,23001],{"className":96149,"style":36065},[259,1873],[128,96151,2477],{"className":96152},[1896],[128,96154,1830],{"className":96155,"style":1874},[259,1873],[128,96157],{"className":96158,"style":1878},[269],[128,96160,5443],{"className":96161},[1882],[128,96163],{"className":96164,"style":1878},[269],[128,96166,96168,96171,96174,96177,96180,96183],{"className":96167},[250],[128,96169],{"className":96170,"style":1892},[254],[128,96172,4519],{"className":96173},[259,1873],[128,96175,67350],{"className":96176},[259,1873],[128,96178,2477],{"className":96179},[1896],[128,96181,2760],{"className":96182},[259,1873],[128,96184,67410],{"className":96185},[1928],"（第二层）能否用观测分布中的量表达出来，这一问题称为**可识别性（identifiability）**问题。Pearl 给出了一套完全在图的层面运作的工具：它只需要因果图本身，",[35,96188,96189,96190],{},"不需要知道任何结构方程的具体函数形式 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为从 ",[128,96367,96369,96382],{"className":96368,"translate":218},[217],[128,96370,96372],{"className":96371},[222],[224,96373,96374],{"xmlns":226},[228,96375,96376,96380],{},[231,96377,96378],{},[1795,96379,67956],{},[238,96381,67956],{"encoding":240},[128,96383,96385],{"className":96384,"ariaHidden":246},[245],[128,96386,96388,96391],{"className":96387},[250],[128,96389],{"className":96390,"style":283},[254],[128,96392,67956],{"className":96393},[259,1873]," 中删去所有指向 ",[128,96396,96398,96411],{"className":96397,"translate":218},[217],[128,96399,96401],{"className":96400},[222],[224,96402,96403],{"xmlns":226},[228,96404,96405,96409],{},[231,96406,96407],{},[1795,96408,364],{},[238,96410,364],{"encoding":240},[128,96412,96414],{"className":96413,"ariaHidden":246},[245],[128,96415,96417,96420],{"className":96416},[250],[128,96418],{"className":96419,"style":283},[254],[128,96421,364],{"className":96422,"style":30665},[259,1873]," 的边所得的图，",[128,96425,96427,96449],{"className":96426,"translate":218},[217],[128,96428,96430],{"className":96429},[222],[224,96431,96432],{"xmlns":226},[228,96433,96434,96446],{},[231,96435,96436],{},[2016,96437,96438,96440],{},[1795,96439,67956],{},[8606,96441,96442,96444],{"accentunder":246},[1795,96443,364],{},[1832,96445,85095],{"stretchy":246},[238,96447,96448],{"encoding":240},"G_{\\underline{X}}",[128,96450,96452],{"className":96451,"ariaHidden":246},[245],[128,96453,96455,96459],{"className":96454},[250],[128,96456],{"className":96457,"style":96458},[254],"height:1.0048em;vertical-align:-0.3215em;",[128,96460,96462,96465],{"className":96461},[259],[128,96463,67956],{"className":96464},[259,1873],[128,96466,96468],{"className":96467},[2087],[128,96469,96471,96538],{"className":96470},[274,321],[128,96472,96474,96535],{"className":96473},[278],[128,96475,96477],{"className":96476,"style":3004},[282],[128,96478,96480,96483],{"style":96479},"top:-2.85em;margin-left:0em;margin-right:0.05em;",[128,96481],{"className":96482,"style":335},[290],[128,96484,96486],{"className":96485},[299,300,301,298],[128,96487,96489],{"className":96488},[259,298],[128,96490,96493],{"className":96491},[259,96492,298],"underline",[128,96494,96496,96526],{"className":96495},[274,321],[128,96497,96499,96523],{"className":96498},[278],[128,96500,96502,96512],{"className":96501,"style":283},[282],[128,96503,96505,96508],{"style":96504},"top:-2.804em;",[128,96506],{"className":96507,"style":335},[290],[128,96509],{"className":96510,"style":85174},[96511,298],"underline-line",[128,96513,96514,96517],{"style":54961},[128,96515],{"className":96516,"style":335},[290],[128,96518,96520],{"className":96519},[259,298],[128,96521,364],{"className":96522,"style":30665},[259,1873,298],[128,96524,347],{"className":96525},[346],[128,96527,96529],{"className":96528},[278],[128,96530,96533],{"className":96531,"style":96532},[282],"height:0.245em;",[128,96534],{},[128,96536,347],{"className":96537},[346],[128,96539,96541],{"className":96540},[278],[128,96542,96545],{"className":96543,"style":96544},[282],"height:0.3215em;",[128,96546],{}," 为删去所有从 ",[128,96549,96551,96564],{"className":96550,"translate":218},[217],[128,96552,96554],{"className":96553},[222],[224,96555,96556],{"xmlns":226},[228,96557,96558,96562],{},[231,96559,96560],{},[1795,96561,364],{},[238,96563,364],{"encoding":240},[128,96565,96567],{"className":96566,"ariaHidden":246},[245],[128,96568,96570,96573],{"className":96569},[250],[128,96571],{"className":96572,"style":283},[254],[128,96574,364],{"className":96575,"style":30665},[259,1873]," 出发的边所得的图，并记 ",[128,96578,96580,96600],{"className":96579,"translate":218},[217],[128,96581,96583],{"className":96582},[222],[224,96584,96585],{"xmlns":226},[228,96586,96587,96597],{},[231,96588,96589,96591,96593,96595],{},[1795,96590,70777],{},[1832,96592,2477],{"stretchy":1837},[1795,96594,36679],{},[1832,96596,2486],{"stretchy":1837},[238,96598,96599],{"encoding":240},"Z(W)",[128,96601,96603],{"className":96602,"ariaHidden":246},[245],[128,96604,96606,96609,96612,96615,96618],{"className":96605},[250],[128,96607],{"className":96608,"style":1892},[254],[128,96610,70777],{"className":96611,"style":1924},[259,1873],[128,96613,2477],{"className":96614},[1896],[128,96616,36679],{"className":96617,"style":36065},[259,1873],[128,96619,2486],{"className":96620},[1928],[128,96622,96624,96637],{"className":96623,"translate":218},[217],[128,96625,96627],{"className":96626},[222],[224,96628,96629],{"xmlns":226},[228,96630,96631,96635],{},[231,96632,96633],{},[1795,96634,70777],{},[238,96636,70777],{"encoding":240},[128,96638,96640],{"className":96639,"ariaHidden":246},[245],[128,96641,96643,96646],{"className":96642},[250],[128,96644],{"className":96645,"style":283},[254],[128,96647,70777],{"className":96648,"style":1924},[259,1873]," 中不属于 ",[128,96651,96653,96666],{"className":96652,"translate":218},[217],[128,96654,96656],{"className":96655},[222],[224,96657,96658],{"xmlns":226},[228,96659,96660,96664],{},[231,96661,96662],{},[1795,96663,36679],{},[238,96665,36679],{"encoding":240},[128,96667,96669],{"className":96668,"ariaHidden":246},[245],[128,96670,96672,96675],{"className":96671},[250],[128,96673],{"className":96674,"style":283},[254],[128,96676,36679],{"className":96677,"style":36065},[259,1873]," 的后代的节点子集，则：",[2615,96680,96682,96753],{"title":96681},"定理 3.2（do-演算三规则）",[11,96683,96684,96685,44582],{},"对任意互不相交的变量集合 ",[128,96686,96688,96714],{"className":96687,"translate":218},[217],[128,96689,96691],{"className":96690},[222],[224,96692,96693],{"xmlns":226},[228,96694,96695,96711],{},[231,96696,96697,96699,96701,96703,96705,96707,96709],{},[1795,96698,364],{},[1832,96700,1845],{"separator":246},[1795,96702,35023],{},[1832,96704,1845],{"separator":246},[1795,96706,70777],{},[1832,96708,1845],{"separator":246},[1795,96710,36679],{},[238,96712,96713],{"encoding":240},"X, Y, Z, W",[128,96715,96717],{"className":96716,"ariaHidden":246},[245],[128,96718,96720,96723,96726,96729,96732,96735,96738,96741,96744,96747,96750],{"className":96719},[250],[128,96721],{"className":96722,"style":40674},[254],[128,96724,364],{"className":96725,"style":30665},[259,1873],[128,96727,1845],{"className":96728},[1903],[128,96730],{"className":96731,"style":1907},[269],[128,96733,35023],{"className":96734,"style":2508},[259,1873],[128,96736,1845],{"className":96737},[1903],[128,96739],{"className":96740,"style":1907},[269],[128,96742,70777],{"className":96743,"style":1924},[259,1873],[128,96745,1845],{"className":96746},[1903],[128,96748],{"className":96749,"style":1907},[269],[128,96751,36679],{"className":96752,"style":36065},[259,1873],[35195,96754,96755,97210,97747],{},[33251,96756,96757,74467,96760,49468,97006],{},[35,96758,96759],{},"规则 1（插入 \u002F 删除观测）",[128,96761,96763,96813],{"className":96762,"translate":218},[217],[128,96764,96766],{"className":96765},[222],[224,96767,96768],{"xmlns":226},[228,96769,96770,96810],{},[231,96771,96772,96774,96776,96778,96780,96782,96784,96786,96788,96790,96792,96794,96796],{},[1832,96773,2477],{"stretchy":1837},[1795,96775,35023],{},[1832,96777,12150],{},[234,96779,8524],{},[234,96781,8524],{},[234,96783,8524],{},[1832,96785,12150],{},[1795,96787,70777],{},[1832,96789,5443],{},[1795,96791,364],{},[1832,96793,1845],{"separator":246},[1795,96795,36679],{},[2016,96797,96798,96800],{},[1832,96799,2486],{"stretchy":1837},[2016,96801,96802,96804],{},[1795,96803,67956],{},[54905,96805,96806,96808],{"accent":246},[1795,96807,364],{},[1832,96809,85095],{"stretchy":246},[238,96811,96812],{"encoding":240},"(Y \\perp\\!\\!\\!\\perp Z \\mid X, 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删除干预）",[128,97753,97755,97821],{"className":97754,"translate":218},[217],[128,97756,97758],{"className":97757},[222],[224,97759,97760],{"xmlns":226},[228,97761,97762,97818],{},[231,97763,97764,97766,97768,97770,97772,97774,97776,97778,97780,97782,97784,97786,97788],{},[1832,97765,2477],{"stretchy":1837},[1795,97767,35023],{},[1832,97769,12150],{},[234,97771,8524],{},[234,97773,8524],{},[234,97775,8524],{},[1832,97777,12150],{},[1795,97779,70777],{},[1832,97781,5443],{},[1795,97783,364],{},[1832,97785,1845],{"separator":246},[1795,97787,36679],{},[2016,97789,97790,97792],{},[1832,97791,2486],{"stretchy":1837},[2016,97793,97794,97796],{},[1795,97795,67956],{},[231,97797,97798,97804],{},[54905,97799,97800,97802],{"accent":246},[1795,97801,364],{},[1832,97803,85095],{"stretchy":246},[54905,97805,97806,97816],{"accent":246},[231,97807,97808,97810,97812,97814],{},[1795,97809,70777],{},[1832,97811,2477],{"stretchy":1837},[1795,97813,36679],{},[1832,97815,2486],{"stretchy":1837},[1832,97817,85095],{"stretchy":246},[238,97819,97820],{"encoding":240},"(Y \\perp\\!\\!\\!\\perp Z \\mid X, W)_{G_{\\overline{X}\\overline{Z(W)}}}",[128,97822,97824,97851,97863,97881],{"className":97823,"ariaHidden":246},[245],[128,97825,97827,97830,97833,97836,97839,97842,97845,97848],{"className":97826},[250],[128,97828],{"className":97829,"style":1892},[254],[128,97831,2477],{"className":97832},[1896],[128,97834,35023],{"className":97835,"style":2508},[259,1873],[128,97837],{"className":97838,"style":1878},[269],[128,97840,12150],{"className":97841},[1882],[128,97843],{"className":97844,"style":317},[269],[128,97846],{"className":97847,"style":317},[269],[128,97849],{"className":97850,"style":317},[269],[128,97852,97854,97857,97860],{"className":97853},[250],[128,97855],{"className":97856,"style":12173},[254],[128,97858,12150],{"className":97859},[1882],[128,97861],{"className":97862,"style":1878},[269],[128,97864,97866,97869,97872,97875,97878],{"className":97865},[250],[128,97867],{"className":97868,"style":1892},[254],[128,97870,70777],{"className":97871,"style":1924},[259,1873],[128,97873],{"className":97874,"style":1878},[269],[128,97876,5443],{"className":97877},[1882],[128,97879],{"className":97880,"style":1878},[269],[128,97882,97884,97888,97891,97894,97897,97900],{"className":97883},[250],[128,97885],{"className":97886,"style":97887},[254],"height:1.2811em;vertical-align:-0.5311em;",[128,97889,364],{"className":97890,"style":30665},[259,1873],[128,97892,1845],{"className":97893},[1903],[128,97895],{"className":97896,"style":1907},[269],[128,97898,36679],{"className":97899,"style":36065},[259,1873],[128,97901,97903,97906],{"className":97902},[1928],[128,97904,2486],{"className":97905},[1928],[128,97907,97909],{"className":97908},[2087],[128,97910,97912,98059],{"className":97911},[274,321],[128,97913,97915,98056],{"className":97914},[278],[128,97916,97918],{"className":97917,"style":3004},[282],[128,97919,97920,97923],{"style":96479},[128,97921],{"className":97922,"style":335},[290],[128,97924,97926],{"className":97925},[299,300,301,298],[128,97927,97929],{"className":97928},[259,298],[128,97930,97932,97935],{"className":97931},[259,298],[128,97933,67956],{"className":97934},[259,1873,298],[128,97936,97938],{"className":97937},[2087],[128,97939,97941,98047],{"className":97940},[274,321],[128,97942,97944,98044],{"className":97943},[278],[128,97945,97947],{"className":97946,"style":24117},[282],[128,97948,97950,97953],{"style":97949},"top:-2.6341em;margin-left:0em;margin-right:0.0714em;",[128,97951],{"className":97952,"style":335},[290],[128,97954,97956],{"className":97955},[299,5794,5795,298],[128,97957,97959,97990],{"className":97958},[259,298],[128,97960,97962],{"className":97961},[259,85142,298],[128,97963,97965],{"className":97964},[274],[128,97966,97968],{"className":97967},[278],[128,97969,97971,97982],{"className":97970,"style":85152},[282],[128,97972,97973,97976],{"style":54961},[128,97974],{"className":97975,"style":335},[290],[128,97977,97979],{"className":97978},[259,298],[128,97980,364],{"className":97981,"style":30665},[259,1873,298],[128,97983,97984,97987],{"style":85166},[128,97985],{"className":97986,"style":335},[290],[128,97988],{"className":97989,"style":85174},[85173,298],[128,97991,97993],{"className":97992},[259,85142,298],[128,97994,97996,98035],{"className":97995},[274,321],[128,97997,97999,98032],{"className":97998},[278],[128,98000,98003,98023],{"className":98001,"style":98002},[282],"height:0.995em;",[128,98004,98005,98008],{"style":54961},[128,98006],{"className":98007,"style":335},[290],[128,98009,98011,98014,98017,98020],{"className":98010},[259,298],[128,98012,70777],{"className":98013,"style":1924},[259,1873,298],[128,98015,2477],{"className":98016},[1896,298],[128,98018,36679],{"className":98019,"style":36065},[259,1873,298],[128,98021,2486],{"className":98022},[1928,298],[128,98024,98026,98029],{"style":98025},"top:-3.897em;",[128,98027],{"className":98028,"style":335},[290],[128,98030],{"className":98031,"style":85174},[85173,298],[128,98033,347],{"className":98034},[346],[128,98036,98038],{"className":98037},[278],[128,98039,98042],{"className":98040,"style":98041},[282],"height:0.25em;",[128,98043],{},[128,98045,347],{"className":98046},[346],[128,98048,98050],{"className":98049},[278],[128,98051,98054],{"className":98052,"style":98053},[282],"height:0.5445em;",[128,98055],{},[128,98057,347],{"className":98058},[346],[128,98060,98062],{"className":98061},[278],[128,98063,98066],{"className":98064,"style":98065},[282],"height:0.5311em;",[128,98067],{},[128,98069,98071,98145],{"className":98070,"translate":218},[217],[128,98072,98074],{"className":98073},[222],[224,98075,98076],{"xmlns":226},[228,98077,98078,98142],{},[231,98079,98080,98082,98084,98086,98088,98090,98092,98094,98096,98098,98100,98102,98104,98106,98108,98110,98112,98114,98116,98118,98120,98122,98124,98126,98128,98130,98132,98134,98136,98138,98140],{},[1795,98081,23001],{},[1832,98083,2477],{"stretchy":1837},[1795,98085,1830],{},[1832,98087,5443],{},[1795,98089,4519],{},[1795,98091,67350],{},[1832,98093,247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\\mid do(x), do(z), w) = P(y \\mid do(x), w)",[128,98146,98148,98172,98235,98259],{"className":98147,"ariaHidden":246},[245],[128,98149,98151,98154,98157,98160,98163,98166,98169],{"className":98150},[250],[128,98152],{"className":98153,"style":1892},[254],[128,98155,23001],{"className":98156,"style":36065},[259,1873],[128,98158,2477],{"className":98159},[1896],[128,98161,1830],{"className":98162,"style":1874},[259,1873],[128,98164],{"className":98165,"style":1878},[269],[128,98167,5443],{"className":98168},[1882],[128,98170],{"className":98171,"style":1878},[269],[128,98173,98175,98178,98181,98184,98187,98190,98193,98196,98199,98202,98205,98208,98211,98214,98217,98220,98223,98226,98229,98232],{"className":98174},[250],[128,98176],{"className":98177,"style":1892},[254],[128,98179,4519],{"className":98180},[259,1873],[128,98182,67350],{"className":98183},[259,1873],[128,98185,2477],{"className":98186},[1896],[128,98188,2760],{"className":98189},[259,1873],[128,98191,2486],{"className":98192},[1928],[128,98194,1845],{"className":98195},[1903],[128,98197],{"className":98198,"style":1907},[269],[128,98200,4519],{"className":98201},[259,1873],[128,98203,67350],{"className":98204},[259,1873],[128,98206,2477],{"className":98207},[1896],[128,98209,38997],{"className":98210,"style":39325},[259,1873],[128,98212,2486],{"className":98213},[1928],[128,98215,1845],{"className":98216},[1903],[128,98218],{"className":98219,"style":1907},[269],[128,98221,95191],{"className":98222,"style":95341},[259,1873],[128,98224,2486],{"className":98225},[1928],[128,98227],{"className":98228,"style":1878},[269],[128,98230,1994],{"className":98231},[1882],[128,98233],{"className":98234,"style":1878},[269],[128,98236,98238,98241,98244,98247,98250,98253,98256],{"className":98237},[250],[128,98239],{"className":98240,"style":1892},[254],[128,98242,23001],{"className":98243,"style":36065},[259,1873],[128,98245,2477],{"className":98246},[1896],[128,98248,1830],{"className":98249,"style":1874},[259,1873],[128,98251],{"className":98252,"style":1878},[269],[128,98254,5443],{"className":98255},[1882],[128,98257],{"className":98258,"style":1878},[269],[128,98260,98262,98265,98268,98271,98274,98277,98280,98283,98286,98289],{"className":98261},[250],[128,98263],{"className":98264,"style":1892},[254],[128,98266,4519],{"className":98267},[259,1873],[128,98269,67350],{"className":98270},[259,1873],[128,98272,2477],{"className":98273},[1896],[128,98275,2760],{"className":98276},[259,1873],[128,98278,2486],{"className":98279},[1928],[128,98281,1845],{"className":98282},[1903],[128,98284],{"className":98285,"style":1907},[269],[128,98287,95191],{"className":98288,"style":95341},[259,1873],[128,98290,2486],{"className":98291},[1928],[11,98293,98294,98295,98329,98330,98363,98364,98397,98398,98480,98481,98518,98519,98522,98523,98556,98557,98560],{},"三条规则的形态高度一致：每一条都在某个 d-分离判据成立时，把一个含 ",[128,98296,98298,98314],{"className":98297,"translate":218},[217],[128,98299,98301],{"className":98300},[222],[224,98302,98303],{"xmlns":226},[228,98304,98305,98311],{},[231,98306,98307,98309],{},[1795,98308,4519],{},[1795,98310,67350],{},[238,98312,98313],{"encoding":240},"do",[128,98315,98317],{"className":98316,"ariaHidden":246},[245],[128,98318,98320,98323,98326],{"className":98319},[250],[128,98321],{"className":98322,"style":12173},[254],[128,98324,4519],{"className":98325},[259,1873],[128,98327,67350],{"className":98328},[259,1873]," 算子的表达式改写为 ",[128,98331,98333,98348],{"className":98332,"translate":218},[217],[128,98334,98336],{"className":98335},[222],[224,98337,98338],{"xmlns":226},[228,98339,98340,98346],{},[231,98341,98342,98344],{},[1795,98343,4519],{},[1795,98345,67350],{},[238,98347,98313],{"encoding":240},[128,98349,98351],{"className":98350,"ariaHidden":246},[245],[128,98352,98354,98357,98360],{"className":98353},[250],[128,98355],{"className":98356,"style":12173},[254],[128,98358,4519],{"className":98359},[259,1873],[128,98361,67350],{"className":98362},[259,1873]," 算子更少（或不含 ",[128,98365,98367,98382],{"className":98366,"translate":218},[217],[128,98368,98370],{"className":98369},[222],[224,98371,98372],{"xmlns":226},[228,98373,98374,98380],{},[231,98375,98376,98378],{},[1795,98377,4519],{},[1795,98379,67350],{},[238,98381,98313],{"encoding":240},[128,98383,98385],{"className":98384,"ariaHidden":246},[245],[128,98386,98388,98391,98394],{"className":98387},[250],[128,98389],{"className":98390,"style":12173},[254],[128,98392,4519],{"className":98393},[259,1873],[128,98395,67350],{"className":98396},[259,1873],"）的表达式。因此判断 ",[128,98399,98401,98432],{"className":98400,"translate":218},[217],[128,98402,98404],{"className":98403},[222],[224,98405,98406],{"xmlns":226},[228,98407,98408,98430],{},[231,98409,98410,98412,98414,98416,98418,98420,98422,98424,98426,98428],{},[1795,98411,23001],{},[1832,98413,2477],{"stretchy":1837},[1795,98415,1830],{},[1832,98417,5443],{},[1795,98419,4519],{},[1795,98421,67350],{},[1832,98423,2477],{"stretchy":1837},[1795,98425,2760],{},[1832,98427,2486],{"stretchy":1837},[1832,98429,2486],{"stretchy":1837},[238,98431,67361],{"encoding":240},[128,98433,98435,98459],{"className":98434,"ariaHidden":246},[245],[128,98436,98438,98441,98444,98447,98450,98453,98456],{"className":98437},[250],[128,98439],{"className":98440,"style":1892},[254],[128,98442,23001],{"className":98443,"style":36065},[259,1873],[128,98445,2477],{"className":98446},[1896],[128,98448,1830],{"className":98449,"style":1874},[259,1873],[128,98451],{"className":98452,"style":1878},[269],[128,98454,5443],{"className":98455},[1882],[128,98457],{"className":98458,"style":1878},[269],[128,98460,98462,98465,98468,98471,98474,98477],{"className":98461},[250],[128,98463],{"className":98464,"style":1892},[254],[128,98466,4519],{"className":98467},[259,1873],[128,98469,67350],{"className":98470},[259,1873],[128,98472,2477],{"className":98473},[1896],[128,98475,2760],{"className":98476},[259,1873],[128,98478,67410],{"className":98479},[1928]," 是否可识别的过程，就是反复应用三条规则、尝试",[35,98482,98483,98484,98517],{},"消去全部 ",[128,98485,98487,98502],{"className":98486,"translate":218},[217],[128,98488,98490],{"className":98489},[222],[224,98491,98492],{"xmlns":226},[228,98493,98494,98500],{},[231,98495,98496,98498],{},[1795,98497,4519],{},[1795,98499,67350],{},[238,98501,98313],{"encoding":240},[128,98503,98505],{"className":98504,"ariaHidden":246},[245],[128,98506,98508,98511,98514],{"className":98507},[250],[128,98509],{"className":98510,"style":12173},[254],[128,98512,4519],{"className":98513},[259,1873],[128,98515,67350],{"className":98516},[259,1873]," 算子","的过程。Shpitser 与 Pearl（2006）进一步证明了这套规则对可识别性是",[35,98520,98521],{},"完备的","：若不存在任何有限次的规则应用序列能把目标量化为不含 ",[128,98524,98526,98541],{"className":98525,"translate":218},[217],[128,98527,98529],{"className":98528},[222],[224,98530,98531],{"xmlns":226},[228,98532,98533,98539],{},[231,98534,98535,98537],{},[1795,98536,4519],{},[1795,98538,67350],{},[238,98540,98313],{"encoding":240},[128,98542,98544],{"className":98543,"ariaHidden":246},[245],[128,98545,98547,98550,98553],{"className":98546},[250],[128,98548],{"className":98549,"style":12173},[254],[128,98551,4519],{"className":98552},[259,1873],[128,98554,67350],{"className":98555},[259,1873]," 的形式，则该量确实不可由观测分布识别。这一点很重要——它为「不可识别」这一否定性结论提供了",[35,98558,98559],{},"证明手段","，而不只是「暂时没想到办法」。",[11,98562,98563],{},"若不想每次都从三条规则出发作推导，可以使用若干直接给出识别公式的充分性准则。其中最重要的一条是后门准则：",[2615,98565,98567],{"title":98566},"定理 3.3（后门准则，Back-door Criterion）",[11,98568,98569,98570,98598,98599,98627,98628,98656,98657,98685,98686,98727,98728,98756,98757,98986,98987,99015,99016,99019],{},"若变量集合 ",[128,98571,98573,98586],{"className":98572,"translate":218},[217],[128,98574,98576],{"className":98575},[222],[224,98577,98578],{"xmlns":226},[228,98579,98580,98584],{},[231,98581,98582],{},[1795,98583,41957],{},[238,98585,41957],{"encoding":240},[128,98587,98589],{"className":98588,"ariaHidden":246},[245],[128,98590,98592,98595],{"className":98591},[250],[128,98593],{"className":98594,"style":283},[254],[128,98596,41957],{"className":98597,"style":42029},[259,1873]," 满足：(i) ",[128,98600,98602,98615],{"className":98601,"translate":218},[217],[128,98603,98605],{"className":98604},[222],[224,98606,98607],{"xmlns":226},[228,98608,98609,98613],{},[231,98610,98611],{},[1795,98612,41957],{},[238,98614,41957],{"encoding":240},[128,98616,98618],{"className":98617,"ariaHidden":246},[245],[128,98619,98621,98624],{"className":98620},[250],[128,98622],{"className":98623,"style":283},[254],[128,98625,41957],{"className":98626,"style":42029},[259,1873]," 中不包含 ",[128,98629,98631,98644],{"className":98630,"translate":218},[217],[128,98632,98634],{"className":98633},[222],[224,98635,98636],{"xmlns":226},[228,98637,98638,98642],{},[231,98639,98640],{},[1795,98641,364],{},[238,98643,364],{"encoding":240},[128,98645,98647],{"className":98646,"ariaHidden":246},[245],[128,98648,98650,98653],{"className":98649},[250],[128,98651],{"className":98652,"style":283},[254],[128,98654,364],{"className":98655,"style":30665},[259,1873]," 的任何后代；(ii) ",[128,98658,98660,98673],{"className":98659,"translate":218},[217],[128,98661,98663],{"className":98662},[222],[224,98664,98665],{"xmlns":226},[228,98666,98667,98671],{},[231,98668,98669],{},[1795,98670,41957],{},[238,98672,41957],{"encoding":240},[128,98674,98676],{"className":98675,"ariaHidden":246},[245],[128,98677,98679,98682],{"className":98678},[250],[128,98680],{"className":98681,"style":283},[254],[128,98683,41957],{"className":98684,"style":42029},[259,1873]," 阻断了 ",[128,98687,98689,98706],{"className":98688,"translate":218},[217],[128,98690,98692],{"className":98691},[222],[224,98693,98694],{"xmlns":226},[228,98695,98696,98704],{},[231,98697,98698,98700,98702],{},[1795,98699,364],{},[1832,98701,1845],{"separator":246},[1795,98703,35023],{},[238,98705,66742],{"encoding":240},[128,98707,98709],{"className":98708,"ariaHidden":246},[245],[128,98710,98712,98715,98718,98721,98724],{"className":98711},[250],[128,98713],{"className":98714,"style":40674},[254],[128,98716,364],{"className":98717,"style":30665},[259,1873],[128,98719,1845],{"className":98720},[1903],[128,98722],{"className":98723,"style":1907},[269],[128,98725,35023],{"className":98726,"style":2508},[259,1873]," 之间所有以指向 ",[128,98729,98731,98744],{"className":98730,"translate":218},[217],[128,98732,98734],{"className":98733},[222],[224,98735,98736],{"xmlns":226},[228,98737,98738,98742],{},[231,98739,98740],{},[1795,98741,364],{},[238,98743,364],{"encoding":240},[128,98745,98747],{"className":98746,"ariaHidden":246},[245],[128,98748,98750,98753],{"className":98749},[250],[128,98751],{"className":98752,"style":283},[254],[128,98754,364],{"className":98755,"style":30665},[259,1873]," 的边起始的路径（「后门路径」），则\n",[128,98758,98760,98826],{"className":98759,"translate":218},[217],[128,98761,98763],{"className":98762},[222],[224,98764,98765],{"xmlns":226},[228,98766,98767,98823],{},[231,98768,98769,98771,98773,98775,98777,98779,98781,98783,98785,98787,98789,98791,98797,98799,98801,98803,98805,98807,98809,98811,98813,98815,98817,98819,98821],{},[1795,98770,23001],{},[1832,98772,2477],{"stretchy":1837},[1795,98774,1830],{},[1832,98776,5443],{},[1795,98778,4519],{},[1795,98780,67350],{},[1832,98782,2477],{"stretchy":1837},[1795,98784,2760],{},[1832,98786,2486],{"stretchy":1837},[1832,98788,2486],{"stretchy":1837},[1832,98790,1994],{},[2016,98792,98793,98795],{},[1832,98794,2042],{},[1795,98796,7590],{},[1795,98798,23001],{},[1832,98800,2477],{"stretchy":1837},[1795,98802,1830],{},[1832,98804,5443],{},[1795,98806,2760],{},[1832,98808,1845],{"separator":246},[1795,98810,7590],{},[1832,98812,2486],{"stretchy":1837},[234,98814,6528],{},[1795,98816,23001],{},[1832,98818,2477],{"stretchy":1837},[1795,98820,7590],{},[1832,98822,2486],{"stretchy":1837},[238,98824,98825],{"encoding":240},"P(y \\mid do(x)) = \\sum_s P(y \\mid x, s) \\, P(s)",[128,98827,98829,98853,98883,98950],{"className":98828,"ariaHidden":246},[245],[128,98830,98832,98835,98838,98841,98844,98847,98850],{"className":98831},[250],[128,98833],{"className":98834,"style":1892},[254],[128,98836,23001],{"className":98837,"style":36065},[259,1873],[128,98839,2477],{"className":98840},[1896],[128,98842,1830],{"className":98843,"style":1874},[259,1873],[128,98845],{"className":98846,"style":1878},[269],[128,98848,5443],{"className":98849},[1882],[128,98851],{"className":98852,"style":1878},[269],[128,98854,98856,98859,98862,98865,98868,98871,98874,98877,98880],{"className":98855},[250],[128,98857],{"className":98858,"style":1892},[254],[128,98860,4519],{"className":98861},[259,1873],[128,98863,67350],{"className":98864},[259,1873],[128,98866,2477],{"className":98867},[1896],[128,98869,2760],{"className":98870},[259,1873],[128,98872,67410],{"className":98873},[1928],[128,98875],{"className":98876,"style":1878},[269],[128,98878,1994],{"className":98879},[1882],[128,98881],{"className":98882,"style":1878},[269],[128,98884,98886,98889,98929,98932,98935,98938,98941,98944,98947],{"className":98885},[250],[128,98887],{"className":98888,"style":7777},[254],[128,98890,98892,98895],{"className":98891},[2268],[128,98893,2042],{"className":98894,"style":2274},[2268,2272,2273],[128,98896,98898],{"className":98897},[2087],[128,98899,98901,98921],{"className":98900},[274,321],[128,98902,98904,98918],{"className":98903},[278],[128,98905,98907],{"className":98906,"style":87047},[282],[128,98908,98909,98912],{"style":2290},[128,98910],{"className":98911,"style":291},[290],[128,98913,98915],{"className":98914},[299,300,301,298],[128,98916,7590],{"className":98917},[259,1873,298],[128,98919,347],{"className":98920},[346],[128,98922,98924],{"className":98923},[278],[128,98925,98927],{"className":98926,"style":2330},[282],[128,98928],{},[128,98930],{"className":98931,"style":1907},[269],[128,98933,23001],{"className":98934,"style":36065},[259,1873],[128,98936,2477],{"className":98937},[1896],[128,98939,1830],{"className":98940,"style":1874},[259,1873],[128,98942],{"className":98943,"style":1878},[269],[128,98945,5443],{"className":98946},[1882],[128,98948],{"className":98949,"style":1878},[269],[128,98951,98953,98956,98959,98962,98965,98968,98971,98974,98977,98980,98983],{"className":98952},[250],[128,98954],{"className":98955,"style":1892},[254],[128,98957,2760],{"className":98958},[259,1873],[128,98960,1845],{"className":98961},[1903],[128,98963],{"className":98964,"style":1907},[269],[128,98966,7590],{"className":98967},[259,1873],[128,98969,2486],{"className":98970},[1928],[128,98972],{"className":98973,"style":1907},[269],[128,98975,23001],{"className":98976,"style":36065},[259,1873],[128,98978,2477],{"className":98979},[1896],[128,98981,7590],{"className":98982},[259,1873],[128,98984,2486],{"className":98985},[1928],"\n即干预效果可以通过对满足后门准则的变量集合 ",[128,98988,98990,99003],{"className":98989,"translate":218},[217],[128,98991,98993],{"className":98992},[222],[224,98994,98995],{"xmlns":226},[228,98996,98997,99001],{},[231,98998,98999],{},[1795,99000,41957],{},[238,99002,41957],{"encoding":240},[128,99004,99006],{"className":99005,"ariaHidden":246},[245],[128,99007,99009,99012],{"className":99008},[250],[128,99010],{"className":99011,"style":283},[254],[128,99013,41957],{"className":99014,"style":42029},[259,1873]," 做",[35,99017,99018],{},"分层加权平均（standardization）","，完全由观测数据估计得出，而无需真正实施干预、进行随机对照实验。",[11,99021,99022,99023,99051,99052,99080,99081,11072,99109,99137],{},"条件 (i) 的必要性，正是第一部分对撞结构那一结论的直接后果：一旦把 ",[128,99024,99026,99039],{"className":99025,"translate":218},[217],[128,99027,99029],{"className":99028},[222],[224,99030,99031],{"xmlns":226},[228,99032,99033,99037],{},[231,99034,99035],{},[1795,99036,364],{},[238,99038,364],{"encoding":240},[128,99040,99042],{"className":99041,"ariaHidden":246},[245],[128,99043,99045,99048],{"className":99044},[250],[128,99046],{"className":99047,"style":283},[254],[128,99049,364],{"className":99050,"style":30665},[259,1873]," 的后代放进 ",[128,99053,99055,99068],{"className":99054,"translate":218},[217],[128,99056,99058],{"className":99057},[222],[224,99059,99060],{"xmlns":226},[228,99061,99062,99066],{},[231,99063,99064],{},[1795,99065,41957],{},[238,99067,41957],{"encoding":240},[128,99069,99071],{"className":99070,"ariaHidden":246},[245],[128,99072,99074,99077],{"className":99073},[250],[128,99075],{"className":99076,"style":283},[254],[128,99078,41957],{"className":99079,"style":42029},[259,1873],"，就可能在 ",[128,99082,99084,99097],{"className":99083,"translate":218},[217],[128,99085,99087],{"className":99086},[222],[224,99088,99089],{"xmlns":226},[228,99090,99091,99095],{},[231,99092,99093],{},[1795,99094,364],{},[238,99096,364],{"encoding":240},[128,99098,99100],{"className":99099,"ariaHidden":246},[245],[128,99101,99103,99106],{"className":99102},[250],[128,99104],{"className":99105,"style":283},[254],[128,99107,364],{"className":99108,"style":30665},[259,1873],[128,99110,99112,99125],{"className":99111,"translate":218},[217],[128,99113,99115],{"className":99114},[222],[224,99116,99117],{"xmlns":226},[228,99118,99119,99123],{},[231,99120,99121],{},[1795,99122,35023],{},[238,99124,35023],{"encoding":240},[128,99126,99128],{"className":99127,"ariaHidden":246},[245],[128,99129,99131,99134],{"className":99130},[250],[128,99132],{"className":99133,"style":283},[254],[128,99135,35023],{"className":99136,"style":2508},[259,1873]," 之间人为打开一条对撞路径，制造出并不存在的关联。",[11,99139,99140,99141,99144,99145,99148],{},"不过后门准则有一个明显的局限：它要求所有混杂变量",[35,99142,99143],{},"都被观测到、且可以被条件化","。而在现实中，这一要求经常落空。以下这条准则则可以在",[35,99146,99147],{},"存在未观测混杂","的情形下绕过这一困难：",[2615,99150,99152],{"title":99151},"定理 3.4（前门准则，Front-door Criterion）",[11,99153,70329,99154,98598,99182,99210,99211,99239,99240,11101,99268,99270,99271,71248,99299,99327,99328,99356,99357,68949,99385,99413,99414,99442,99443],{},[128,99155,99157,99170],{"className":99156,"translate":218},[217],[128,99158,99160],{"className":99159},[222],[224,99161,99162],{"xmlns":226},[228,99163,99164,99168],{},[231,99165,99166],{},[1795,99167,30641],{},[238,99169,30641],{"encoding":240},[128,99171,99173],{"className":99172,"ariaHidden":246},[245],[128,99174,99176,99179],{"className":99175},[250],[128,99177],{"className":99178,"style":283},[254],[128,99180,30641],{"className":99181,"style":26806},[259,1873],[128,99183,99185,99198],{"className":99184,"translate":218},[217],[128,99186,99188],{"className":99187},[222],[224,99189,99190],{"xmlns":226},[228,99191,99192,99196],{},[231,99193,99194],{},[1795,99195,30641],{},[238,99197,30641],{"encoding":240},[128,99199,99201],{"className":99200,"ariaHidden":246},[245],[128,99202,99204,99207],{"className":99203},[250],[128,99205],{"className":99206,"style":283},[254],[128,99208,30641],{"className":99209,"style":26806},[259,1873]," 阻断了所有从 ",[128,99212,99214,99227],{"className":99213,"translate":218},[217],[128,99215,99217],{"className":99216},[222],[224,99218,99219],{"xmlns":226},[228,99220,99221,99225],{},[231,99222,99223],{},[1795,99224,364],{},[238,99226,364],{"encoding":240},[128,99228,99230],{"className":99229,"ariaHidden":246},[245],[128,99231,99233,99236],{"className":99232},[250],[128,99234],{"className":99235,"style":283},[254],[128,99237,364],{"className":99238,"style":30665},[259,1873]," 指向 ",[128,99241,99243,99256],{"className":99242,"translate":218},[217],[128,99244,99246],{"className":99245},[222],[224,99247,99248],{"xmlns":226},[228,99249,99250,99254],{},[231,99251,99252],{},[1795,99253,35023],{},[238,99255,35023],{"encoding":240},[128,99257,99259],{"className":99258,"ariaHidden":246},[245],[128,99260,99262,99265],{"className":99261},[250],[128,99263],{"className":99264,"style":283},[254],[128,99266,35023],{"className":99267,"style":2508},[259,1873],[35,99269,69543],{},"（即 ",[128,99272,99274,99287],{"className":99273,"translate":218},[217],[128,99275,99277],{"className":99276},[222],[224,99278,99279],{"xmlns":226},[228,99280,99281,99285],{},[231,99282,99283],{},[1795,99284,364],{},[238,99286,364],{"encoding":240},[128,99288,99290],{"className":99289,"ariaHidden":246},[245],[128,99291,99293,99296],{"className":99292},[250],[128,99294],{"className":99295,"style":283},[254],[128,99297,364],{"className":99298,"style":30665},[259,1873],[128,99300,99302,99315],{"className":99301,"translate":218},[217],[128,99303,99305],{"className":99304},[222],[224,99306,99307],{"xmlns":226},[228,99308,99309,99313],{},[231,99310,99311],{},[1795,99312,35023],{},[238,99314,35023],{"encoding":240},[128,99316,99318],{"className":99317,"ariaHidden":246},[245],[128,99319,99321,99324],{"className":99320},[250],[128,99322],{"className":99323,"style":283},[254],[128,99325,35023],{"className":99326,"style":2508},[259,1873]," 的全部因果影响都经过 ",[128,99329,99331,99344],{"className":99330,"translate":218},[217],[128,99332,99334],{"className":99333},[222],[224,99335,99336],{"xmlns":226},[228,99337,99338,99342],{},[231,99339,99340],{},[1795,99341,30641],{},[238,99343,30641],{"encoding":240},[128,99345,99347],{"className":99346,"ariaHidden":246},[245],[128,99348,99350,99353],{"className":99349},[250],[128,99351],{"className":99352,"style":283},[254],[128,99354,30641],{"className":99355,"style":26806},[259,1873]," 传送）；(ii) 不存在从 ",[128,99358,99360,99373],{"className":99359,"translate":218},[217],[128,99361,99363],{"className":99362},[222],[224,99364,99365],{"xmlns":226},[228,99366,99367,99371],{},[231,99368,99369],{},[1795,99370,30641],{},[238,99372,30641],{"encoding":240},[128,99374,99376],{"className":99375,"ariaHidden":246},[245],[128,99377,99379,99382],{"className":99378},[250],[128,99380],{"className":99381,"style":283},[254],[128,99383,30641],{"className":99384,"style":26806},[259,1873],[128,99386,99388,99401],{"className":99387,"translate":218},[217],[128,99389,99391],{"className":99390},[222],[224,99392,99393],{"xmlns":226},[228,99394,99395,99399],{},[231,99396,99397],{},[1795,99398,35023],{},[238,99400,35023],{"encoding":240},[128,99402,99404],{"className":99403,"ariaHidden":246},[245],[128,99405,99407,99410],{"className":99406},[250],[128,99408],{"className":99409,"style":283},[254],[128,99411,35023],{"className":99412,"style":2508},[259,1873]," 的、未被 ",[128,99415,99417,99430],{"className":99416,"translate":218},[217],[128,99418,99420],{"className":99419},[222],[224,99421,99422],{"xmlns":226},[228,99423,99424,99428],{},[231,99425,99426],{},[1795,99427,364],{},[238,99429,364],{"encoding":240},[128,99431,99433],{"className":99432,"ariaHidden":246},[245],[128,99434,99436,99439],{"className":99435},[250],[128,99437],{"className":99438,"style":283},[254],[128,99440,364],{"className":99441,"style":30665},[259,1873]," 阻断的后门路径。则\n",[128,99444,99446,99540],{"className":99445,"translate":218},[217],[128,99447,99449],{"className":99448},[222],[224,99450,99451],{"xmlns":226},[228,99452,99453,99537],{},[231,99454,99455,99457,99459,99461,99463,99465,99467,99469,99471,99473,99475,99477,99483,99485,99487,99489,99491,99493,99495,99505,99507,99509,99511,99513,99515,99517,99523,99525,99527,99529,99535],{},[1795,99456,23001],{},[1832,99458,2477],{"stretchy":1837},[1795,99460,1830],{},[1832,99462,5443],{},[1795,99464,4519],{},[1795,99466,67350],{},[1832,99468,2477],{"stretchy":1837},[1795,99470,2760],{},[1832,99472,2486],{"stretchy":1837},[1832,99474,2486],{"stretchy":1837},[1832,99476,1994],{},[2016,99478,99479,99481],{},[1832,99480,2042],{},[1795,99482,30849],{},[1795,99484,23001],{},[1832,99486,2477],{"stretchy":1837},[1795,99488,30849],{},[1832,99490,5443],{},[1795,99492,2760],{},[1832,99494,2486],{"stretchy":1837},[2016,99496,99497,99499],{},[1832,99498,2042],{},[1977,99500,99501,99503],{},[1795,99502,2760],{},[1832,99504,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},[1795,99506,23001],{},[1832,99508,2477],{"stretchy":1837},[1795,99510,1830],{},[1832,99512,5443],{},[1795,99514,30849],{},[1832,99516,1845],{"separator":246},[1977,99518,99519,99521],{},[1795,99520,2760],{},[1832,99522,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},[1832,99524,2486],{"stretchy":1837},[1795,99526,23001],{},[1832,99528,2477],{"stretchy":1837},[1977,99530,99531,99533],{},[1795,99532,2760],{},[1832,99534,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},[1832,99536,2486],{"stretchy":1837},[238,99538,99539],{"encoding":240},"P(y \\mid do(x)) = \\sum_m P(m \\mid x) \\sum_{x'} P(y \\mid m, x') P(x')",[128,99541,99543,99567,99597,99664,99774],{"className":99542,"ariaHidden":246},[245],[128,99544,99546,99549,99552,99555,99558,99561,99564],{"className":99545},[250],[128,99547],{"className":99548,"style":1892},[254],[128,99550,23001],{"className":99551,"style":36065},[259,1873],[128,99553,2477],{"className":99554},[1896],[128,99556,1830],{"className":99557,"style":1874},[259,1873],[128,99559],{"className":99560,"style":1878},[269],[128,99562,5443],{"className":99563},[1882],[128,99565],{"className":99566,"style":1878},[269],[128,99568,99570,99573,99576,99579,99582,99585,99588,99591,99594],{"className":99569},[250],[128,99571],{"className":99572,"style":1892},[254],[128,99574,4519],{"className":99575},[259,1873],[128,99577,67350],{"className":99578},[259,1873],[128,99580,2477],{"className":99581},[1896],[128,99583,2760],{"className":99584},[259,1873],[128,99586,67410],{"className":99587},[1928],[128,99589],{"className":99590,"style":1878},[269],[128,99592,1994],{"className":99593},[1882],[128,99595],{"className":99596,"style":1878},[269],[128,99598,99600,99603,99643,99646,99649,99652,99655,99658,99661],{"className":99599},[250],[128,99601],{"className":99602,"style":7777},[254],[128,99604,99606,99609],{"className":99605},[2268],[128,99607,2042],{"className":99608,"style":2274},[2268,2272,2273],[128,99610,99612],{"className":99611},[2087],[128,99613,99615,99635],{"className":99614},[274,321],[128,99616,99618,99632],{"className":99617},[278],[128,99619,99621],{"className":99620,"style":87047},[282],[128,99622,99623,99626],{"style":2290},[128,99624],{"className":99625,"style":291},[290],[128,99627,99629],{"className":99628},[299,300,301,298],[128,99630,30849],{"className":99631},[259,1873,298],[128,99633,347],{"className":99634},[346],[128,99636,99638],{"className":99637},[278],[128,99639,99641],{"className":99640,"style":2330},[282],[128,99642],{},[128,99644],{"className":99645,"style":1907},[269],[128,99647,23001],{"className":99648,"style":36065},[259,1873],[128,99650,2477],{"className":99651},[1896],[128,99653,30849],{"className":99654},[259,1873],[128,99656],{"className":99657,"style":1878},[269],[128,99659,5443],{"className":99660},[1882],[128,99662],{"className":99663,"style":1878},[269],[128,99665,99667,99670,99673,99676,99679,99753,99756,99759,99762,99765,99768,99771],{"className":99666},[250],[128,99668],{"className":99669,"style":7777},[254],[128,99671,2760],{"className":99672},[259,1873],[128,99674,2486],{"className":99675},[1928],[128,99677],{"className":99678,"style":1907},[269],[128,99680,99682,99685],{"className":99681},[2268],[128,99683,2042],{"className":99684,"style":2274},[2268,2272,2273],[128,99686,99688],{"className":99687},[2087],[128,99689,99691,99745],{"className":99690},[274,321],[128,99692,99694,99742],{"className":99693},[278],[128,99695,99698],{"className":99696,"style":99697},[282],"height:0.1783em;",[128,99699,99700,99703],{"style":2290},[128,99701],{"className":99702,"style":291},[290],[128,99704,99706],{"className":99705},[299,300,301,298],[128,99707,99709],{"className":99708},[259,298],[128,99710,99712,99715],{"className":99711},[259,298],[128,99713,2760],{"className":99714},[259,1873,298],[128,99716,99718],{"className":99717},[2087],[128,99719,99721],{"className":99720},[274],[128,99722,99724],{"className":99723},[278],[128,99725,99728],{"className":99726,"style":99727},[282],"height:0.6828em;",[128,99729,99730,99733],{"style":6609},[128,99731],{"className":99732,"style":5790},[290],[128,99734,99736],{"className":99735},[299,5794,5795,298],[128,99737,99739],{"className":99738},[259,298],[128,99740,24873],{"className":99741},[259,298],[128,99743,347],{"className":99744},[346],[128,99746,99748],{"className":99747},[278],[128,99749,99751],{"className":99750,"style":2330},[282],[128,99752],{},[128,99754],{"className":99755,"style":1907},[269],[128,99757,23001],{"className":99758,"style":36065},[259,1873],[128,99760,2477],{"className":99761},[1896],[128,99763,1830],{"className":99764,"style":1874},[259,1873],[128,99766],{"className":99767,"style":1878},[269],[128,99769,5443],{"className":99770},[1882],[128,99772],{"className":99773,"style":1878},[269],[128,99775,99777,99780,99783,99786,99789,99821,99824,99827,99830,99862],{"className":99776},[250],[128,99778],{"className":99779,"style":24908},[254],[128,99781,30849],{"className":99782},[259,1873],[128,99784,1845],{"className":99785},[1903],[128,99787],{"className":99788,"style":1907},[269],[128,99790,99792,99795],{"className":99791},[259],[128,99793,2760],{"className":99794},[259,1873],[128,99796,99798],{"className":99797},[2087],[128,99799,99801],{"className":99800},[274],[128,99802,99804],{"className":99803},[278],[128,99805,99807],{"className":99806,"style":24927},[282],[128,99808,99809,99812],{"style":2452},[128,99810],{"className":99811,"style":291},[290],[128,99813,99815],{"className":99814},[299,300,301,298],[128,99816,99818],{"className":99817},[259,298],[128,99819,24873],{"className":99820},[259,298],[128,99822,2486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3.4",[11,99869,99870,99871,99899,99900,99951,99952,100003,100004,7713,100076,100104],{},"回到例 1.2 的吸烟模型，但这次显式承认存在未观测的混杂：设 ",[128,99872,99874,99887],{"className":99873,"translate":218},[217],[128,99875,99877],{"className":99876},[222],[224,99878,99879],{"xmlns":226},[228,99880,99881,99885],{},[231,99882,99883],{},[1795,99884,69050],{},[238,99886,69050],{"encoding":240},[128,99888,99890],{"className":99889,"ariaHidden":246},[245],[128,99891,99893,99896],{"className":99892},[250],[128,99894],{"className":99895,"style":283},[254],[128,99897,69050],{"className":99898,"style":26806},[259,1873]," 为不可观测的遗传因素，",[128,99901,99903,99921],{"className":99902,"translate":218},[217],[128,99904,99906],{"className":99905},[222],[224,99907,99908],{"xmlns":226},[228,99909,99910,99918],{},[231,99911,99912,99914,99916],{},[1795,99913,69050],{},[1832,99915,22419],{},[1795,99917,364],{},[238,99919,99920],{"encoding":240},"U \\to X",[128,99922,99924,99942],{"className":99923,"ariaHidden":246},[245],[128,99925,99927,99930,99933,99936,99939],{"className":99926},[250],[128,99928],{"className":99929,"style":283},[254],[128,99931,69050],{"className":99932,"style":26806},[259,1873],[128,99934],{"className":99935,"style":1878},[269],[128,99937,22419],{"className":99938},[1882],[128,99940],{"className":99941,"style":1878},[269],[128,99943,99945,99948],{"className":99944},[250],[128,99946],{"className":99947,"style":283},[254],[128,99949,364],{"className":99950,"style":30665},[259,1873],"（吸烟）且 ",[128,99953,99955,99973],{"className":99954,"translate":218},[217],[128,99956,99958],{"className":99957},[222],[224,99959,99960],{"xmlns":226},[228,99961,99962,99970],{},[231,99963,99964,99966,99968],{},[1795,99965,69050],{},[1832,99967,22419],{},[1795,99969,35023],{},[238,99971,99972],{"encoding":240},"U \\to Y",[128,99974,99976,99994],{"className":99975,"ariaHidden":246},[245],[128,99977,99979,99982,99985,99988,99991],{"className":99978},[250],[128,99980],{"className":99981,"style":283},[254],[128,99983,69050],{"className":99984,"style":26806},[259,1873],[128,99986],{"className":99987,"style":1878},[269],[128,99989,22419],{"className":99990},[1882],[128,99992],{"className":99993,"style":1878},[269],[128,99995,99997,100000],{"className":99996},[250],[128,99998],{"className":99999,"style":283},[254],[128,100001,35023],{"className":100002,"style":2508},[259,1873],"（肺癌）；已知的结构为 ",[128,100005,100007,100028],{"className":100006,"translate":218},[217],[128,100008,100010],{"className":100009},[222],[224,100011,100012],{"xmlns":226},[228,100013,100014,100026],{},[231,100015,100016,100018,100020,100022,100024],{},[1795,100017,364],{},[1832,100019,22419],{},[1795,100021,30641],{},[1832,100023,22419],{},[1795,100025,35023],{},[238,100027,92650],{"encoding":240},[128,100029,100031,100049,100067],{"className":100030,"ariaHidden":246},[245],[128,100032,100034,100037,100040,100043,100046],{"className":100033},[250],[128,100035],{"className":100036,"style":283},[254],[128,100038,364],{"className":100039,"style":30665},[259,1873],[128,100041],{"className":100042,"style":1878},[269],[128,100044,22419],{"className":100045},[1882],[128,100047],{"className":100048,"style":1878},[269],[128,100050,100052,100055,100058,100061,100064],{"className":100051},[250],[128,100053],{"className":100054,"style":283},[254],[128,100056,30641],{"className":100057,"style":26806},[259,1873],[128,100059],{"className":100060,"style":1878},[269],[128,100062,22419],{"className":100063},[1882],[128,100065],{"className":100066,"style":1878},[269],[128,100068,100070,100073],{"className":100069},[250],[128,100071],{"className":100072,"style":283},[254],[128,100074,35023],{"className":100075,"style":2508},[259,1873],[128,100077,100079,100092],{"className":100078,"translate":218},[217],[128,100080,100082],{"className":100081},[222],[224,100083,100084],{"xmlns":226},[228,100085,100086,100090],{},[231,100087,100088],{},[1795,100089,30641],{},[238,100091,30641],{"encoding":240},[128,100093,100095],{"className":100094,"ariaHidden":246},[245],[128,100096,100098,100101],{"className":100097},[250],[128,100099],{"className":100100,"style":283},[254],[128,100102,30641],{"className":100103,"style":26806},[259,1873]," 为焦油沉积。",[1441,100106,100107],{},[168,100108],{"height":92754,"width":100109,"style":1447,"data-d2-theme":1448,"alt":123,"src":100110},462,"data:image\u002Fsvg+xml;base64,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",[11,100112,100113,100114,11072,100142,100170,100171,100244,100245,100273,100274,100302,100303,12133,100375,68949,100403,100431,100432,100460,100461,100880,100881,100884],{},"此时 ",[128,100115,100117,100130],{"className":100116,"translate":218},[217],[128,100118,100120],{"className":100119},[222],[224,100121,100122],{"xmlns":226},[228,100123,100124,100128],{},[231,100125,100126],{},[1795,100127,364],{},[238,100129,364],{"encoding":240},[128,100131,100133],{"className":100132,"ariaHidden":246},[245],[128,100134,100136,100139],{"className":100135},[250],[128,100137],{"className":100138,"style":283},[254],[128,100140,364],{"className":100141,"style":30665},[259,1873],[128,100143,100145,100158],{"className":100144,"translate":218},[217],[128,100146,100148],{"className":100147},[222],[224,100149,100150],{"xmlns":226},[228,100151,100152,100156],{},[231,100153,100154],{},[1795,100155,35023],{},[238,100157,35023],{"encoding":240},[128,100159,100161],{"className":100160,"ariaHidden":246},[245],[128,100162,100164,100167],{"className":100163},[250],[128,100165],{"className":100166,"style":283},[254],[128,100168,35023],{"className":100169,"style":2508},[259,1873]," 之间的后门路径 ",[128,100172,100174,100196],{"className":100173,"translate":218},[217],[128,100175,100177],{"className":100176},[222],[224,100178,100179],{"xmlns":226},[228,100180,100181,100193],{},[231,100182,100183,100185,100187,100189,100191],{},[1795,100184,364],{},[1832,100186,71437],{},[1795,100188,69050],{},[1832,100190,22419],{},[1795,100192,35023],{},[238,100194,100195],{"encoding":240},"X \\leftarrow U \\to Y",[128,100197,100199,100217,100235],{"className":100198,"ariaHidden":246},[245],[128,100200,100202,100205,100208,100211,100214],{"className":100201},[250],[128,100203],{"className":100204,"style":283},[254],[128,100206,364],{"className":100207,"style":30665},[259,1873],[128,100209],{"className":100210,"style":1878},[269],[128,100212,71437],{"className":100213},[1882],[128,100215],{"className":100216,"style":1878},[269],[128,100218,100220,100223,100226,100229,100232],{"className":100219},[250],[128,100221],{"className":100222,"style":283},[254],[128,100224,69050],{"className":100225,"style":26806},[259,1873],[128,100227],{"className":100228,"style":1878},[269],[128,100230,22419],{"className":100231},[1882],[128,100233],{"className":100234,"style":1878},[269],[128,100236,100238,100241],{"className":100237},[250],[128,100239],{"className":100240,"style":283},[254],[128,100242,35023],{"className":100243,"style":2508},[259,1873]," 无法被阻断（",[128,100246,100248,100261],{"className":100247,"translate":218},[217],[128,100249,100251],{"className":100250},[222],[224,100252,100253],{"xmlns":226},[228,100254,100255,100259],{},[231,100256,100257],{},[1795,100258,69050],{},[238,100260,69050],{"encoding":240},[128,100262,100264],{"className":100263,"ariaHidden":246},[245],[128,100265,100267,100270],{"className":100266},[250],[128,100268],{"className":100269,"style":283},[254],[128,100271,69050],{"className":100272,"style":26806},[259,1873]," 不可观测），后门准则失效。但 ",[128,100275,100277,100290],{"className":100276,"translate":218},[217],[128,100278,100280],{"className":100279},[222],[224,100281,100282],{"xmlns":226},[228,100283,100284,100288],{},[231,100285,100286],{},[1795,100287,30641],{},[238,100289,30641],{"encoding":240},[128,100291,100293],{"className":100292,"ariaHidden":246},[245],[128,100294,100296,100299],{"className":100295},[250],[128,100297],{"className":100298,"style":283},[254],[128,100300,30641],{"className":100301,"style":26806},[259,1873]," 阻断了唯一的因果路径 ",[128,100304,100306,100327],{"className":100305,"translate":218},[217],[128,100307,100309],{"className":100308},[222],[224,100310,100311],{"xmlns":226},[228,100312,100313,100325],{},[231,100314,100315,100317,100319,100321,100323],{},[1795,100316,364],{},[1832,100318,22419],{},[1795,100320,30641],{},[1832,100322,22419],{},[1795,100324,35023],{},[238,100326,92650],{"encoding":240},[128,100328,100330,100348,100366],{"className":100329,"ariaHidden":246},[245],[128,100331,100333,100336,100339,100342,100345],{"className":100332},[250],[128,100334],{"className":100335,"style":283},[254],[128,100337,364],{"className":100338,"style":30665},[259,1873],[128,100340],{"className":100341,"style":1878},[269],[128,100343,22419],{"className":100344},[1882],[128,100346],{"className":100347,"style":1878},[269],[128,100349,100351,100354,100357,100360,100363],{"className":100350},[250],[128,100352],{"className":100353,"style":283},[254],[128,100355,30641],{"className":100356,"style":26806},[259,1873],[128,100358],{"className":100359,"style":1878},[269],[128,100361,22419],{"className":100362},[1882],[128,100364],{"className":100365,"style":1878},[269],[128,100367,100369,100372],{"className":100368},[250],[128,100370],{"className":100371,"style":283},[254],[128,100373,35023],{"className":100374,"style":2508},[259,1873],[128,100376,100378,100391],{"className":100377,"translate":218},[217],[128,100379,100381],{"className":100380},[222],[224,100382,100383],{"xmlns":226},[228,100384,100385,100389],{},[231,100386,100387],{},[1795,100388,30641],{},[238,100390,30641],{"encoding":240},[128,100392,100394],{"className":100393,"ariaHidden":246},[245],[128,100395,100397,100400],{"className":100396},[250],[128,100398],{"className":100399,"style":283},[254],[128,100401,30641],{"className":100402,"style":26806},[259,1873],[128,100404,100406,100419],{"className":100405,"translate":218},[217],[128,100407,100409],{"className":100408},[222],[224,100410,100411],{"xmlns":226},[228,100412,100413,100417],{},[231,100414,100415],{},[1795,100416,35023],{},[238,100418,35023],{"encoding":240},[128,100420,100422],{"className":100421,"ariaHidden":246},[245],[128,100423,100425,100428],{"className":100424},[250],[128,100426],{"className":100427,"style":283},[254],[128,100429,35023],{"className":100430,"style":2508},[259,1873]," 不存在除经由 ",[128,100433,100435,100448],{"className":100434,"translate":218},[217],[128,100436,100438],{"className":100437},[222],[224,100439,100440],{"xmlns":226},[228,100441,100442,100446],{},[231,100443,100444],{},[1795,100445,364],{},[238,100447,364],{"encoding":240},[128,100449,100451],{"className":100450,"ariaHidden":246},[245],[128,100452,100454,100457],{"className":100453},[250],[128,100455],{"className":100456,"style":283},[254],[128,100458,364],{"className":100459,"style":30665},[259,1873]," 之外的后门路径，因此前门准则给出\n",[128,100462,100464,100557],{"className":100463,"translate":218},[217],[128,100465,100467],{"className":100466},[222],[224,100468,100469],{"xmlns":226},[228,100470,100471,100555],{},[231,100472,100473,100475,100477,100479,100481,100483,100485,100487,100489,100491,100493,100495,100501,100503,100505,100507,100509,100511,100513,100523,100525,100527,100529,100531,100533,100535,100541,100543,100545,100547,100553],{},[1795,100474,23001],{},[1832,100476,2477],{"stretchy":1837},[1795,100478,1830],{},[1832,100480,5443],{},[1795,100482,4519],{},[1795,100484,67350],{},[1832,100486,2477],{"stretchy":1837},[1795,100488,2760],{},[1832,100490,2486],{"stretchy":1837},[1832,100492,2486],{"stretchy":1837},[1832,100494,1994],{},[2016,100496,100497,100499],{},[1832,100498,2042],{},[1795,100500,30849],{},[1795,100502,23001],{},[1832,100504,2477],{"stretchy":1837},[1795,100506,30849],{},[1832,100508,5443],{},[1795,100510,2760],{},[1832,100512,2486],{"stretchy":1837},[2016,100514,100515,100517],{},[1832,100516,2042],{},[1977,100518,100519,100521],{},[1795,100520,2760],{},[1832,100522,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},[1795,100524,23001],{},[1832,100526,2477],{"stretchy":1837},[1795,100528,1830],{},[1832,100530,5443],{},[1795,100532,30849],{},[1832,100534,1845],{"separator":246},[1977,100536,100537,100539],{},[1795,100538,2760],{},[1832,100540,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},[1832,100542,2486],{"stretchy":1837},[1795,100544,23001],{},[1832,100546,2477],{"stretchy":1837},[1977,100548,100549,100551],{},[1795,100550,2760],{},[1832,100552,24873],{"mathvariant":1981,"lspace":24872,"rspace":24872},[1832,100554,2486],{"stretchy":1837},[238,100556,99539],{"encoding":240},[128,100558,100560,100584,100614,100681,100789],{"className":100559,"ariaHidden":246},[245],[128,100561,100563,100566,100569,100572,100575,100578,100581],{"className":100562},[250],[128,100564],{"className":100565,"style":1892},[254],[128,100567,23001],{"className":100568,"style":36065},[259,1873],[128,100570,2477],{"className":100571},[1896],[128,100573,1830],{"className":100574,"style":1874},[259,1873],[128,100576],{"className":100577,"style":1878},[269],[128,100579,5443],{"className":100580},[1882],[128,100582],{"className":100583,"style":1878},[269],[128,100585,100587,100590,100593,100596,100599,100602,100605,100608,100611],{"className":100586},[250],[128,100588],{"className":100589,"style":1892},[254],[128,100591,4519],{"className":100592},[259,1873],[128,100594,67350],{"className":100595},[259,1873],[128,100597,2477],{"className":100598},[1896],[128,100600,2760],{"className":100601},[259,1873],[128,100603,67410],{"className":100604},[1928],[128,100606],{"className":100607,"style":1878},[269],[128,100609,1994],{"className":100610},[1882],[128,100612],{"className":100613,"style":1878},[269],[128,100615,100617,100620,100660,100663,100666,100669,100672,100675,100678],{"className":100616},[250],[128,100618],{"className":100619,"style":7777},[254],[128,100621,100623,100626],{"className":100622},[2268],[128,100624,2042],{"className":100625,"style":2274},[2268,2272,2273],[128,100627,100629],{"className":100628},[2087],[128,100630,100632,100652],{"className":100631},[274,321],[128,100633,100635,100649],{"className":100634},[278],[128,100636,100638],{"className":100637,"style":87047},[282],[128,100639,100640,100643],{"style":2290},[128,100641],{"className":100642,"style":291},[290],[128,100644,100646],{"className":100645},[299,300,301,298],[128,100647,30849],{"className":100648},[259,1873,298],[128,100650,347],{"className":100651},[346],[128,100653,100655],{"className":100654},[278],[128,100656,100658],{"className":100657,"style":2330},[282],[128,100659],{},[128,100661],{"className":100662,"style":1907},[269],[128,100664,23001],{"className":100665,"style":36065},[259,1873],[128,100667,2477],{"className":100668},[1896],[128,100670,30849],{"className":100671},[259,1873],[128,100673],{"className":100674,"style":1878},[269],[128,100676,5443],{"className":100677},[1882],[128,100679],{"className":100680,"style":1878},[269],[128,100682,100684,100687,100690,100693,100696,100768,100771,100774,100777,100780,100783,100786],{"className":100683},[250],[128,100685],{"className":100686,"style":7777},[254],[128,100688,2760],{"className":100689},[259,1873],[128,100691,2486],{"className":100692},[1928],[128,100694],{"className":100695,"style":1907},[269],[128,100697,100699,100702],{"className":100698},[2268],[128,100700,2042],{"className":100701,"style":2274},[2268,2272,2273],[128,100703,100705],{"className":100704},[2087],[128,100706,100708,100760],{"className":100707},[274,321],[128,100709,100711,100757],{"className":100710},[278],[128,100712,100714],{"className":100713,"style":99697},[282],[128,100715,100716,100719],{"style":2290},[128,100717],{"className":100718,"style":291},[290],[128,100720,100722],{"className":100721},[299,300,301,298],[128,100723,100725],{"className":100724},[259,298],[128,100726,100728,100731],{"className":100727},[259,298],[128,100729,2760],{"className":100730},[259,1873,298],[128,100732,100734],{"className":100733},[2087],[128,100735,100737],{"className":100736},[274],[128,100738,100740],{"className":100739},[278],[128,100741,100743],{"className":100742,"style":99727},[282],[128,100744,100745,100748],{"style":6609},[128,100746],{"className":100747,"style":5790},[290],[128,100749,100751],{"className":100750},[299,5794,5795,298],[128,100752,100754],{"className":100753},[259,298],[128,100755,24873],{"className":100756},[259,298],[128,100758,347],{"className":100759},[346],[128,100761,100763],{"className":100762},[278],[128,100764,100766],{"className":100765,"style":2330},[282],[128,100767],{},[128,100769],{"className":100770,"style":1907},[269],[128,100772,23001],{"className":100773,"style":36065},[259,1873],[128,100775,2477],{"className":100776},[1896],[128,100778,1830],{"className":100779,"style":1874},[259,1873],[128,100781],{"className":100782,"style":1878},[269],[128,100784,5443],{"className":100785},[1882],[128,100787],{"className":100788,"style":1878},[269],[128,100790,100792,100795,100798,100801,100804,100836,100839,100842,100845,100877],{"className":100791},[250],[128,100793],{"className":100794,"style":24908},[254],[128,100796,30849],{"className":100797},[259,1873],[128,100799,1845],{"className":100800},[1903],[128,100802],{"className":100803,"style":1907},[269],[128,100805,100807,100810],{"className":100806},[259],[128,100808,2760],{"className":100809},[259,1873],[128,100811,100813],{"className":100812},[2087],[128,100814,100816],{"className":100815},[274],[128,100817,100819],{"className":100818},[278],[128,100820,100822],{"className":100821,"style":24927},[282],[128,100823,100824,100827],{"style":2452},[128,100825],{"className":100826,"style":291},[290],[128,100828,100830],{"className":100829},[299,300,301,298],[128,100831,100833],{"className":100832},[259,298],[128,100834,24873],{"className":100835},[259,298],[128,100837,2486],{"className":100838},[1928],[128,100840,23001],{"className":100841,"style":36065},[259,1873],[128,100843,2477],{"className":100844},[1896],[128,100846,100848,100851],{"className":100847},[259],[128,100849,2760],{"className":100850},[259,1873],[128,100852,100854],{"className":100853},[2087],[128,100855,100857],{"className":100856},[274],[128,100858,100860],{"className":100859},[278],[128,100861,100863],{"className":100862,"style":24927},[282],[128,100864,100865,100868],{"style":2452},[128,100866],{"className":100867,"style":291},[290],[128,100869,100871],{"className":100870},[299,300,301,298],[128,100872,100874],{"className":100873},[259,298],[128,100875,24873],{"className":100876},[259,298],[128,100878,2486],{"className":100879},[1928],"\n即：",[35,100882,100883],{},"即便存在不可观测的混杂，只要有一个满足前门条件的中介变量，吸烟对肺癌的因果效应仍然可以从纯观测数据中识别出来。"," 这是因果图相对于纯统计框架的一个相当反直觉的力量所在——它把「哪些数据是可用的」与「哪些机制是可靠的」分开处理，从而在因果推断看似无从下手之处找回了一条通路。",[11,100886,100887],{},"前门准则同时也是 2.1 节中「半马尔可夫型 SCM」这一概念唯一的实际用武之地：当外生变量之间存在相关的隐藏噪声时，正是这类准则在继续保证可识别性。但必须强调，前门准则的适用面很窄——它要求恰好存在一个阻断全部因果路径的中介变量，并且该中介与结果之间不存在未观测的混杂。对一般结构的半马尔可夫型 SCM，可识别性并不自动成立。",[11,100889,100890,100891,100919,100920,100923],{},"这一准则将第一部分中「该控制哪些变量」的图论直觉，与第三部分的干预定义精确对接：叉结构中的混杂因子正是典型的满足后门准则的调整集合，而对撞结构中的变量则应被排除在 ",[128,100892,100894,100907],{"className":100893,"translate":218},[217],[128,100895,100897],{"className":100896},[222],[224,100898,100899],{"xmlns":226},[228,100900,100901,100905],{},[231,100902,100903],{},[1795,100904,41957],{},[238,100906,41957],{"encoding":240},[128,100908,100910],{"className":100909,"ariaHidden":246},[245],[128,100911,100913,100916],{"className":100912},[250],[128,100914],{"className":100915,"style":283},[254],[128,100917,41957],{"className":100918,"style":42029},[259,1873]," 之外。这一对应关系并非巧合：",[35,100921,100922],{},"满足后门准则的调整集合，正是一个能够阻断全部非因果路径的 d-分离集合","，第一部分与第三部分在此处精确接榫。至此，本文从因果图出发、经由结构因果模型、最终落脚于结构方程与 do-演算的逻辑链条已经闭合。剩下要问的是：这一体系与统计学、计量经济学中既有的因果推断工具相比处于什么位置，以及它的成立依赖哪些假设。",[51,100925,100926],{"id":100926},"相邻框架与适用边界",[11,100928,100929],{},"本文至此勾勒的是一套自洽的形式化体系。但因果推断在统计学、计量经济学与机器学习中并非只有这一种语言。本部分把它与两个最重要的相邻传统作对照，说明各自的着眼点与互补之处，最后梳理该体系成立所依赖的假设与边界。",[2610,100931,100933],{"id":100932},"_41-潜在结果框架一种等价的语言","4.1 潜在结果框架：一种等价的语言",[11,100935,100936,100937,100940],{},"与结构因果模型并行发展的，是由 Rubin 等人推动的",[35,100938,100939],{},"潜在结果框架（Potential Outcome Framework，亦称 Rubin 因果模型）","。它不诉诸图，而是从个体层面的潜在结果出发：",[2615,100942,100944],{"title":100943},"定义 4.1（潜在结果与因果效应）",[11,100945,1781,100946,101020,101021,101049,101050,101135,101136,101221,101222,101385,101386,893],{},[128,100947,100949,100975],{"className":100948,"translate":218},[217],[128,100950,100952],{"className":100951},[222],[224,100953,100954],{"xmlns":226},[228,100955,100956,100972],{},[231,100957,100958,100960,100962,100964,100966,100968,100970],{},[1795,100959,364],{},[1832,100961,1834],{},[1832,100963,1838],{"stretchy":1837},[1840,100965,2028],{},[1832,100967,1845],{"separator":246},[1840,100969,1842],{},[1832,100971,1856],{"stretchy":1837},[238,100973,100974],{"encoding":240},"X \\in \\{0,1\\}",[128,100976,100978,100996],{"className":100977,"ariaHidden":246},[245],[128,100979,100981,100984,100987,100990,100993],{"className":100980},[250],[128,100982],{"className":100983,"style":73189},[254],[128,100985,364],{"className":100986,"style":30665},[259,1873],[128,100988],{"className":100989,"style":1878},[269],[128,100991,1834],{"className":100992},[1882],[128,100994],{"className":100995,"style":1878},[269],[128,100997,100999,101002,101005,101008,101011,101014,101017],{"className":100998},[250],[128,101000],{"className":101001,"style":1892},[254],[128,101003,1838],{"className":101004},[1896],[128,101006,2028],{"className":101007},[259],[128,101009,1845],{"className":101010},[1903],[128,101012],{"className":101013,"style":1907},[269],[128,101015,1842],{"className":101016},[259],[128,101018,1856],{"className":101019},[1928]," 为处理指示变量。对每个个体 ",[128,101022,101024,101037],{"className":101023,"translate":218},[217],[128,101025,101027],{"className":101026},[222],[224,101028,101029],{"xmlns":226},[228,101030,101031,101035],{},[231,101032,101033],{},[1795,101034,2801],{},[238,101036,2801],{"encoding":240},[128,101038,101040],{"className":101039,"ariaHidden":246},[245],[128,101041,101043,101046],{"className":101042},[250],[128,101044],{"className":101045,"style":23527},[254],[128,101047,2801],{"className":101048},[259,1873],"，定义两个潜在结果 ",[128,101051,101053,101077],{"className":101052,"translate":218},[217],[128,101054,101056],{"className":101055},[222],[224,101057,101058],{"xmlns":226},[228,101059,101060,101074],{},[231,101061,101062,101068,101070,101072],{},[2016,101063,101064,101066],{},[1795,101065,35023],{},[1795,101067,2801],{},[1832,101069,2477],{"stretchy":1837},[1840,101071,1842],{},[1832,101073,2486],{"stretchy":1837},[238,101075,101076],{"encoding":240},"Y_i(1)",[128,101078,101080],{"className":101079,"ariaHidden":246},[245],[128,101081,101083,101086,101126,101129,101132],{"className":101082},[250],[128,101084],{"className":101085,"style":1892},[254],[128,101087,101089,101092],{"className":101088},[259],[128,101090,35023],{"className":101091,"style":2508},[259,1873],[128,101093,101095],{"className":101094},[2087],[128,101096,101098,101118],{"className":101097},[274,321],[128,101099,101101,101115],{"className":101100},[278],[128,101102,101104],{"className":101103,"style":3095},[282],[128,101105,101106,101109],{"style":68109},[128,101107],{"className":101108,"style":291},[290],[128,101110,101112],{"className":101111},[299,300,301,298],[128,101113,2801],{"className":101114},[259,1873,298],[128,101116,347],{"className":101117},[346],[128,101119,101121],{"className":101120},[278],[128,101122,101124],{"className":101123,"style":2241},[282],[128,101125],{},[128,101127,2477],{"className":101128},[1896],[128,101130,1842],{"className":101131},[259],[128,101133,2486],{"className":101134},[1928],"（接受处理时的结果）与 ",[128,101137,101139,101163],{"className":101138,"translate":218},[217],[128,101140,101142],{"className":101141},[222],[224,101143,101144],{"xmlns":226},[228,101145,101146,101160],{},[231,101147,101148,101154,101156,101158],{},[2016,101149,101150,101152],{},[1795,101151,35023],{},[1795,101153,2801],{},[1832,101155,2477],{"stretchy":1837},[1840,101157,2028],{},[1832,101159,2486],{"stretchy":1837},[238,101161,101162],{"encoding":240},"Y_i(0)",[128,101164,101166],{"className":101165,"ariaHidden":246},[245],[128,101167,101169,101172,101212,101215,101218],{"className":101168},[250],[128,101170],{"className":101171,"style":1892},[254],[128,101173,101175,101178],{"className":101174},[259],[128,101176,35023],{"className":101177,"style":2508},[259,1873],[128,101179,101181],{"className":101180},[2087],[128,101182,101184,101204],{"className":101183},[274,321],[128,101185,101187,101201],{"className":101186},[278],[128,101188,101190],{"className":101189,"style":3095},[282],[128,101191,101192,101195],{"style":68109},[128,101193],{"className":101194,"style":291},[290],[128,101196,101198],{"className":101197},[299,300,301,298],[128,101199,2801],{"className":101200},[259,1873,298],[128,101202,347],{"className":101203},[346],[128,101205,101207],{"className":101206},[278],[128,101208,101210],{"className":101209,"style":2241},[282],[128,101211],{},[128,101213,2477],{"className":101214},[1896],[128,101216,2028],{"className":101217},[259],[128,101219,2486],{"className":101220},[1928],"（未接受处理时的结果）。个体因果效应定义为 ",[128,101223,101225,101263],{"className":101224,"translate":218},[217],[128,101226,101228],{"className":101227},[222],[224,101229,101230],{"xmlns":226},[228,101231,101232,101260],{},[231,101233,101234,101240,101242,101244,101246,101248,101254,101256,101258],{},[2016,101235,101236,101238],{},[1795,101237,35023],{},[1795,101239,2801],{},[1832,101241,2477],{"stretchy":1837},[1840,101243,1842],{},[1832,101245,2486],{"stretchy":1837},[1832,101247,1989],{},[2016,101249,101250,101252],{},[1795,101251,35023],{},[1795,101253,2801],{},[1832,101255,2477],{"stretchy":1837},[1840,101257,2028],{},[1832,101259,2486],{"stretchy":1837},[238,101261,101262],{"encoding":240},"Y_i(1) - Y_i(0)",[128,101264,101266,101330],{"className":101265,"ariaHidden":246},[245],[128,101267,101269,101272,101312,101315,101318,101321,101324,101327],{"className":101268},[250],[128,101270],{"className":101271,"style":1892},[254],[128,101273,101275,101278],{"className":101274},[259],[128,101276,35023],{"className":101277,"style":2508},[259,1873],[128,101279,101281],{"className":101280},[2087],[128,101282,101284,101304],{"className":101283},[274,321],[128,101285,101287,101301],{"className":101286},[278],[128,101288,101290],{"className":101289,"style":3095},[282],[128,101291,101292,101295],{"style":68109},[128,101293],{"className":101294,"style":291},[290],[128,101296,101298],{"className":101297},[299,300,301,298],[128,101299,2801],{"className":101300},[259,1873,298],[128,101302,347],{"className":101303},[346],[128,101305,101307],{"className":101306},[278],[128,101308,101310],{"className":101309,"style":2241},[282],[128,101311],{},[128,101313,2477],{"className":101314},[1896],[128,101316,1842],{"className":101317},[259],[128,101319,2486],{"className":101320},[1928],[128,101322],{"className":101323,"style":2508},[269],[128,101325,1989],{"className":101326},[2115],[128,101328],{"className":101329,"style":2508},[269],[128,101331,101333,101336,101376,101379,101382],{"className":101332},[250],[128,101334],{"className":101335,"style":1892},[254],[128,101337,101339,101342],{"className":101338},[259],[128,101340,35023],{"className":101341,"style":2508},[259,1873],[128,101343,101345],{"className":101344},[2087],[128,101346,101348,101368],{"className":101347},[274,321],[128,101349,101351,101365],{"className":101350},[278],[128,101352,101354],{"className":101353,"style":3095},[282],[128,101355,101356,101359],{"style":68109},[128,101357],{"className":101358,"style":291},[290],[128,101360,101362],{"className":101361},[299,300,301,298],[128,101363,2801],{"className":101364},[259,1873,298],[128,101366,347],{"className":101367},[346],[128,101369,101371],{"className":101370},[278],[128,101372,101374],{"className":101373,"style":2241},[282],[128,101375],{},[128,101377,2477],{"className":101378},[1896],[128,101380,2028],{"className":101381},[259],[128,101383,2486],{"className":101384},[1928],"，平均处理效应定义为 ",[128,101387,101389,101435],{"className":101388,"translate":218},[217],[128,101390,101392],{"className":101391},[222],[224,101393,101394],{"xmlns":226},[228,101395,101396,101432],{},[231,101397,101398,101406,101408,101410,101412,101414,101416,101418,101420,101422,101424,101426,101428,101430],{},[231,101399,101400,101402,101404],{},[1795,101401,302],{"mathvariant":1981},[1795,101403,313],{"mathvariant":1981},[1795,101405,342],{"mathvariant":1981},[1832,101407,1994],{},[1795,101409,342],{"mathvariant":2008},[1832,101411,16538],{"stretchy":1837},[1795,101413,35023],{},[1832,101415,2477],{"stretchy":1837},[1840,101417,1842],{},[1832,101419,2486],{"stretchy":1837},[1832,101421,1989],{},[1795,101423,35023],{},[1832,101425,2477],{"stretchy":1837},[1840,101427,2028],{},[1832,101429,2486],{"stretchy":1837},[1832,101431,16547],{"stretchy":1837},[238,101433,101434],{"encoding":240},"\\mathrm{ATE} = \\mathbb{E}[Y(1) - Y(0)]",[128,101436,101438,101460,101493],{"className":101437,"ariaHidden":246},[245],[128,101439,101441,101444,101451,101454,101457],{"className":101440},[250],[128,101442],{"className":101443,"style":283},[254],[128,101445,101447],{"className":101446},[259],[128,101448,101450],{"className":101449},[259,3353],"ATE",[128,101452],{"className":101453,"style":1878},[269],[128,101455,1994],{"className":101456},[1882],[128,101458],{"className":101459,"style":1878},[269],[128,101461,101463,101466,101469,101472,101475,101478,101481,101484,101487,101490],{"className":101462},[250],[128,101464],{"className":101465,"style":1892},[254],[128,101467,342],{"className":101468},[259,2167],[128,101470,16538],{"className":101471},[1896],[128,101473,35023],{"className":101474,"style":2508},[259,1873],[128,101476,2477],{"className":101477},[1896],[128,101479,1842],{"className":101480},[259],[128,101482,2486],{"className":101483},[1928],[128,101485],{"className":101486,"style":2508},[269],[128,101488,1989],{"className":101489},[2115],[128,101491],{"className":101492,"style":2508},[269],[128,101494,101496,101499,101502,101505,101508],{"className":101495},[250],[128,101497],{"className":101498,"style":1892},[254],[128,101500,35023],{"className":101501,"style":2508},[259,1873],[128,101503,2477],{"className":101504},[1896],[128,101506,2028],{"className":101507},[259],[128,101509,44995],{"className":101510},[1928],[11,101512,101513,101514,101517,101518,101644],{},"这一框架的核心困难称作",[35,101515,101516],{},"因果推断的根本问题（Fundamental Problem of Causal Inference）","：对任何个体，我们只能观测到 ",[128,101519,101521,101549],{"className":101520,"translate":218},[217],[128,101522,101524],{"className":101523},[222],[224,101525,101526],{"xmlns":226},[228,101527,101528,101546],{},[231,101529,101530,101536,101538,101544],{},[2016,101531,101532,101534],{},[1795,101533,35023],{},[1795,101535,2801],{},[1832,101537,2477],{"stretchy":1837},[2016,101539,101540,101542],{},[1795,101541,364],{},[1795,101543,2801],{},[1832,101545,2486],{"stretchy":1837},[238,101547,101548],{"encoding":240},"Y_i(X_i)",[128,101550,101552],{"className":101551,"ariaHidden":246},[245],[128,101553,101555,101558,101598,101601,101641],{"className":101554},[250],[128,101556],{"className":101557,"style":1892},[254],[128,101559,101561,101564],{"className":101560},[259],[128,101562,35023],{"className":101563,"style":2508},[259,1873],[128,101565,101567],{"className":101566},[2087],[128,101568,101570,101590],{"className":101569},[274,321],[128,101571,101573,101587],{"className":101572},[278],[128,101574,101576],{"className":101575,"style":3095},[282],[128,101577,101578,101581],{"style":68109},[128,101579],{"className":101580,"style":291},[290],[128,101582,101584],{"className":101583},[299,300,301,298],[128,101585,2801],{"className":101586},[259,1873,298],[128,101588,347],{"className":101589},[346],[128,101591,101593],{"className":101592},[278],[128,101594,101596],{"className":101595,"style":2241},[282],[128,101597],{},[128,101599,2477],{"className":101600},[1896],[128,101602,101604,101607],{"className":101603},[259],[128,101605,364],{"className":101606,"style":30665},[259,1873],[128,101608,101610],{"className":101609},[2087],[128,101611,101613,101633],{"className":101612},[274,321],[128,101614,101616,101630],{"className":101615},[278],[128,101617,101619],{"className":101618,"style":3095},[282],[128,101620,101621,101624],{"style":30680},[128,101622],{"className":101623,"style":291},[290],[128,101625,101627],{"className":101626},[299,300,301,298],[128,101628,2801],{"className":101629},[259,1873,298],[128,101631,347],{"className":101632},[346],[128,101634,101636],{"className":101635},[278],[128,101637,101639],{"className":101638,"style":2241},[282],[128,101640],{},[128,101642,2486],{"className":101643},[1928],"，另一个潜在结果永远缺失。因此个体因果效应原则上不可观测，只能转而估计总体层面的量。",[11,101646,101647,101648,101733,101734,101904,101905,101933,101934,102026,102027,102030],{},"这与本文 3.3 节的三步算法形成直接对照：潜在结果框架中的 ",[128,101649,101651,101675],{"className":101650,"translate":218},[217],[128,101652,101654],{"className":101653},[222],[224,101655,101656],{"xmlns":226},[228,101657,101658,101672],{},[231,101659,101660,101666,101668,101670],{},[2016,101661,101662,101664],{},[1795,101663,35023],{},[1795,101665,2801],{},[1832,101667,2477],{"stretchy":1837},[1795,101669,2760],{},[1832,101671,2486],{"stretchy":1837},[238,101673,101674],{"encoding":240},"Y_i(x)",[128,101676,101678],{"className":101677,"ariaHidden":246},[245],[128,101679,101681,101684,101724,101727,101730],{"className":101680},[250],[128,101682],{"className":101683,"style":1892},[254],[128,101685,101687,101690],{"className":101686},[259],[128,101688,35023],{"className":101689,"style":2508},[259,1873],[128,101691,101693],{"className":101692},[2087],[128,101694,101696,101716],{"className":101695},[274,321],[128,101697,101699,101713],{"className":101698},[278],[128,101700,101702],{"className":101701,"style":3095},[282],[128,101703,101704,101707],{"style":68109},[128,101705],{"className":101706,"style":291},[290],[128,101708,101710],{"className":101709},[299,300,301,298],[128,101711,2801],{"className":101712},[259,1873,298],[128,101714,347],{"className":101715},[346],[128,101717,101719],{"className":101718},[278],[128,101720,101722],{"className":101721,"style":2241},[282],[128,101723],{},[128,101725,2477],{"className":101726},[1896],[128,101728,2760],{"className":101729},[259,1873],[128,101731,2486],{"className":101732},[1928]," 正是 SCM 中的 ",[128,101735,101737,101769],{"className":101736,"translate":218},[217],[128,101738,101740],{"className":101739},[222],[224,101741,101742],{"xmlns":226},[228,101743,101744,101766],{},[231,101745,101746,101756,101758,101764],{},[2016,101747,101748,101750],{},[1795,101749,35023],{},[2016,101751,101752,101754],{},[1795,101753,30641],{},[1795,101755,2760],{},[1832,101757,2477],{"stretchy":1837},[2016,101759,101760,101762],{},[1795,101761,35129],{},[1795,101763,2801],{},[1832,101765,2486],{"stretchy":1837},[238,101767,101768],{"encoding":240},"Y_{M_x}(u_i)",[128,101770,101772],{"className":101771,"ariaHidden":246},[245],[128,101773,101775,101778,101858,101861,101901],{"className":101774},[250],[128,101776],{"className":101777,"style":84817},[254],[128,101779,101781,101784],{"className":101780},[259],[128,101782,35023],{"className":101783,"style":2508},[259,1873],[128,101785,101787],{"className":101786},[2087],[128,101788,101790,101850],{"className":101789},[274,321],[128,101791,101793,101847],{"className":101792},[278],[128,101794,101796],{"className":101795,"style":3004},[282],[128,101797,101798,101801],{"style":68109},[128,101799],{"className":101800,"style":291},[290],[128,101802,101804],{"className":101803},[299,300,301,298],[128,101805,101807],{"className":101806},[259,298],[128,101808,101810,101813],{"className":101809},[259,298],[128,101811,30641],{"className":101812,"style":26806},[259,1873,298],[128,101814,101816],{"className":101815},[2087],[128,101817,101819,101839],{"className":101818},[274,321],[128,101820,101822,101836],{"className":101821},[278],[128,101823,101825],{"className":101824,"style":30995},[282],[128,101826,101827,101830],{"style":84867},[128,101828],{"className":101829,"style":5790},[290],[128,101831,101833],{"className":101832},[299,5794,5795,298],[128,101834,2760],{"className":101835},[259,1873,298],[128,101837,347],{"className":101838},[346],[128,101840,101842],{"className":101841},[278],[128,101843,101845],{"className":101844,"style":5808},[282],[128,101846],{},[128,101848,347],{"className":101849},[346],[128,101851,101853],{"className":101852},[278],[128,101854,101856],{"className":101855,"style":84897},[282],[128,101857],{},[128,101859,2477],{"className":101860},[1896],[128,101862,101864,101867],{"className":101863},[259],[128,101865,35129],{"className":101866},[259,1873],[128,101868,101870],{"className":101869},[2087],[128,101871,101873,101893],{"className":101872},[274,321],[128,101874,101876,101890],{"className":101875},[278],[128,101877,101879],{"className":101878,"style":3095},[282],[128,101880,101881,101884],{"style":2221},[128,101882],{"className":101883,"style":291},[290],[128,101885,101887],{"className":101886},[299,300,301,298],[128,101888,2801],{"className":101889},[259,1873,298],[128,101891,347],{"className":101892},[346],[128,101894,101896],{"className":101895},[278],[128,101897,101899],{"className":101898,"style":2241},[282],[128,101900],{},[128,101902,2486],{"className":101903},[1928],"，个体 ",[128,101906,101908,101921],{"className":101907,"translate":218},[217],[128,101909,101911],{"className":101910},[222],[224,101912,101913],{"xmlns":226},[228,101914,101915,101919],{},[231,101916,101917],{},[1795,101918,2801],{},[238,101920,2801],{"encoding":240},[128,101922,101924],{"className":101923,"ariaHidden":246},[245],[128,101925,101927,101930],{"className":101926},[250],[128,101928],{"className":101929,"style":23527},[254],[128,101931,2801],{"className":101932},[259,1873]," 即外生变量的一次实现 ",[128,101935,101937,101959],{"className":101936,"translate":218},[217],[128,101938,101940],{"className":101939},[222],[224,101941,101942],{"xmlns":226},[228,101943,101944,101956],{},[231,101945,101946,101948,101950],{},[1795,101947,69050],{},[1832,101949,1994],{},[2016,101951,101952,101954],{},[1795,101953,35129],{},[1795,101955,2801],{},[238,101957,101958],{"encoding":240},"U = u_i",[128,101960,101962,101980],{"className":101961,"ariaHidden":246},[245],[128,101963,101965,101968,101971,101974,101977],{"className":101964},[250],[128,101966],{"className":101967,"style":283},[254],[128,101969,69050],{"className":101970,"style":26806},[259,1873],[128,101972],{"className":101973,"style":1878},[269],[128,101975,1994],{"className":101976},[1882],[128,101978],{"className":101979,"style":1878},[269],[128,101981,101983,101986],{"className":101982},[250],[128,101984],{"className":101985,"style":4242},[254],[128,101987,101989,101992],{"className":101988},[259],[128,101990,35129],{"className":101991},[259,1873],[128,101993,101995],{"className":101994},[2087],[128,101996,101998,102018],{"className":101997},[274,321],[128,101999,102001,102015],{"className":102000},[278],[128,102002,102004],{"className":102003,"style":3095},[282],[128,102005,102006,102009],{"style":2221},[128,102007],{"className":102008,"style":291},[290],[128,102010,102012],{"className":102011},[299,300,301,298],[128,102013,2801],{"className":102014},[259,1873,298],[128,102016,347],{"className":102017},[346],[128,102019,102021],{"className":102020},[278],[128,102022,102024],{"className":102023,"style":2241},[282],[128,102025],{},"。事实上，在只涉及可操纵变量、且不引用跨世界量的范围内，两套形式化被证明是",[35,102028,102029],{},"等价的","；SCM 的表达力略宽一些，例如它可以容纳不可操纵的变量（如年龄、性别），而这在严格的潜在结果表述中会造成困难。二者共享同一组识别性条件，只是表述方式不同：",[35195,102032,102033,102040],{},[33251,102034,102035,102036,102039],{},"SCM 用 ",[35,102037,102038],{},"d-分离与后门准则","回答「应当控制哪些变量」，把这一判断变成图上的机械判定；",[33251,102041,102042,102043,1148,102046,102204,102205,102330],{},"潜在结果框架用",[35,102044,102045],{},"可忽略性假设（ignorability）",[128,102047,102049,102099],{"className":102048,"translate":218},[217],[128,102050,102052],{"className":102051},[222],[224,102053,102054],{"xmlns":226},[228,102055,102056,102096],{},[231,102057,102058,102060,102062,102064,102066,102068,102070,102072,102074,102076,102078,102080,102082,102084,102086,102088,102090,102092,102094],{},[1832,102059,2477],{"fence":1837,"stretchy":246,"minsize":46539,"maxsize":46539},[1795,102061,35023],{},[1832,102063,2477],{"stretchy":1837},[1840,102065,1842],{},[1832,102067,2486],{"stretchy":1837},[1832,102069,1845],{"separator":246},[1795,102071,35023],{},[1832,102073,2477],{"stretchy":1837},[1840,102075,2028],{},[1832,102077,2486],{"stretchy":1837},[1832,102079,2486],{"fence":1837,"stretchy":246,"minsize":46539,"maxsize":46539},[1832,102081,12150],{},[234,102083,8524],{},[234,102085,8524],{},[234,102087,8524],{},[1832,102089,12150],{},[1795,102091,364],{},[1832,102093,5443],{},[1795,102095,36679],{},[238,102097,102098],{"encoding":240},"\\big(Y(1), Y(0)\\big) \\perp\\!\\!\\!\\perp X \\mid W",[128,102100,102102,102165,102177,102195],{"className":102101,"ariaHidden":246},[245],[128,102103,102105,102108,102114,102117,102120,102123,102126,102129,102132,102135,102138,102141,102144,102150,102153,102156,102159,102162],{"className":102104},[250],[128,102106],{"className":102107,"style":46966},[254],[128,102109,102111],{"className":102110},[259],[128,102112,2477],{"className":102113},[2146,5795],[128,102115,35023],{"className":102116,"style":2508},[259,1873],[128,102118,2477],{"className":102119},[1896],[128,102121,1842],{"className":102122},[259],[128,102124,2486],{"className":102125},[1928],[128,102127,1845],{"className":102128},[1903],[128,102130],{"className":102131,"style":1907},[269],[128,102133,35023],{"className":102134,"style":2508},[259,1873],[128,102136,2477],{"className":102137},[1896],[128,102139,2028],{"className":102140},[259],[128,102142,2486],{"className":102143},[1928],[128,102145,102147],{"className":102146},[259],[128,102148,2486],{"className":102149},[2146,5795],[128,102151],{"className":102152,"style":1878},[269],[128,102154,12150],{"className":102155},[1882],[128,102157],{"className":102158,"style":317},[269],[128,102160],{"className":102161,"style":317},[269],[128,102163],{"className":102164,"style":317},[269],[128,102166,102168,102171,102174],{"className":102167},[250],[128,102169],{"className":102170,"style":12173},[254],[128,102172,12150],{"className":102173},[1882],[128,102175],{"className":102176,"style":1878},[269],[128,102178,102180,102183,102186,102189,102192],{"className":102179},[250],[128,102181],{"className":102182,"style":1892},[254],[128,102184,364],{"className":102185,"style":30665},[259,1873],[128,102187],{"className":102188,"style":1878},[269],[128,102190,5443],{"className":102191},[1882],[128,102193],{"className":102194,"style":1878},[269],[128,102196,102198,102201],{"className":102197},[250],[128,102199],{"className":102200,"style":283},[254],[128,102202,36679],{"className":102203,"style":36065},[259,1873]," 表达同一件事，并由此导出倾向得分 ",[128,102206,102208,102246],{"className":102207,"translate":218},[217],[128,102209,102211],{"className":102210},[222],[224,102212,102213],{"xmlns":226},[228,102214,102215,102243],{},[231,102216,102217,102219,102221,102223,102225,102227,102229,102231,102233,102235,102237,102239,102241],{},[1795,102218,3713],{},[1832,102220,2477],{"stretchy":1837},[1795,102222,36679],{},[1832,102224,2486],{"stretchy":1837},[1832,102226,1994],{},[1795,102228,23001],{},[1832,102230,2477],{"stretchy":1837},[1795,102232,364],{},[1832,102234,1994],{},[1840,102236,1842],{},[1832,102238,5443],{},[1795,102240,36679],{},[1832,102242,2486],{"stretchy":1837},[238,102244,102245],{"encoding":240},"e(W) = P(X = 1 \\mid W)",[128,102247,102249,102276,102300,102318],{"className":102248,"ariaHidden":246},[245],[128,102250,102252,102255,102258,102261,102264,102267,102270,102273],{"className":102251},[250],[128,102253],{"className":102254,"style":1892},[254],[128,102256,3713],{"className":102257},[259,1873],[128,102259,2477],{"className":102260},[1896],[128,102262,36679],{"className":102263,"style":36065},[259,1873],[128,102265,2486],{"className":102266},[1928],[128,102268],{"className":102269,"style":1878},[269],[128,102271,1994],{"className":102272},[1882],[128,102274],{"className":102275,"style":1878},[269],[128,102277,102279,102282,102285,102288,102291,102294,102297],{"className":102278},[250],[128,102280],{"className":102281,"style":1892},[254],[128,102283,23001],{"className":102284,"style":36065},[259,1873],[128,102286,2477],{"className":102287},[1896],[128,102289,364],{"className":102290,"style":30665},[259,1873],[128,102292],{"className":102293,"style":1878},[269],[128,102295,1994],{"className":102296},[1882],[128,102298],{"className":102299,"style":1878},[269],[128,102301,102303,102306,102309,102312,102315],{"className":102302},[250],[128,102304],{"className":102305,"style":1892},[254],[128,102307,1842],{"className":102308},[259],[128,102310],{"className":102311,"style":1878},[269],[128,102313,5443],{"className":102314},[1882],[128,102316],{"className":102317,"style":1878},[269],[128,102319,102321,102324,102327],{"className":102320},[250],[128,102322],{"className":102323,"style":1892},[254],[128,102325,36679],{"className":102326,"style":36065},[259,1873],[128,102328,2486],{"className":102329},[1928],"，以及逆概率加权（IPW）、双重稳健估计等成熟的估计工具。",[11,102332,102333,102334,102476,102477,102505,102506,102534,102535,102538,102539,21562,102542,102674],{},"值得注意的是，",[128,102335,102337,102383],{"className":102336,"translate":218},[217],[128,102338,102340],{"className":102339},[222],[224,102341,102342],{"xmlns":226},[228,102343,102344,102380],{},[231,102345,102346,102348,102350,102352,102354,102356,102358,102360,102362,102364,102366,102368,102370,102372,102374,102376,102378],{},[1795,102347,35023],{},[1832,102349,2477],{"stretchy":1837},[1840,102351,1842],{},[1832,102353,2486],{"stretchy":1837},[1832,102355,1845],{"separator":246},[1795,102357,35023],{},[1832,102359,2477],{"stretchy":1837},[1840,102361,2028],{},[1832,102363,2486],{"stretchy":1837},[1832,102365,12150],{},[234,102367,8524],{},[234,102369,8524],{},[234,102371,8524],{},[1832,102373,12150],{},[1795,102375,364],{},[1832,102377,5443],{},[1795,102379,36679],{},[238,102381,102382],{"encoding":240},"Y(1), Y(0) \\perp\\!\\!\\!\\perp X \\mid W",[128,102384,102386,102437,102449,102467],{"className":102385,"ariaHidden":246},[245],[128,102387,102389,102392,102395,102398,102401,102404,102407,102410,102413,102416,102419,102422,102425,102428,102431,102434],{"className":102388},[250],[128,102390],{"className":102391,"style":1892},[254],[128,102393,35023],{"className":102394,"style":2508},[259,1873],[128,102396,2477],{"className":102397},[1896],[128,102399,1842],{"className":102400},[259],[128,102402,2486],{"className":102403},[1928],[128,102405,1845],{"className":102406},[1903],[128,102408],{"className":102409,"style":1907},[269],[128,102411,35023],{"className":102412,"style":2508},[259,1873],[128,102414,2477],{"className":102415},[1896],[128,102417,2028],{"className":102418},[259],[128,102420,2486],{"className":102421},[1928],[128,102423],{"className":102424,"style":1878},[269],[128,102426,12150],{"className":102427},[1882],[128,102429],{"className":102430,"style":317},[269],[128,102432],{"className":102433,"style":317},[269],[128,102435],{"className":102436,"style":317},[269],[128,102438,102440,102443,102446],{"className":102439},[250],[128,102441],{"className":102442,"style":12173},[254],[128,102444,12150],{"className":102445},[1882],[128,102447],{"className":102448,"style":1878},[269],[128,102450,102452,102455,102458,102461,102464],{"className":102451},[250],[128,102453],{"className":102454,"style":1892},[254],[128,102456,364],{"className":102457,"style":30665},[259,1873],[128,102459],{"className":102460,"style":1878},[269],[128,102462,5443],{"className":102463},[1882],[128,102465],{"className":102466,"style":1878},[269],[128,102468,102470,102473],{"className":102469},[250],[128,102471],{"className":102472,"style":283},[254],[128,102474,36679],{"className":102475,"style":36065},[259,1873]," 与「",[128,102478,102480,102493],{"className":102479,"translate":218},[217],[128,102481,102483],{"className":102482},[222],[224,102484,102485],{"xmlns":226},[228,102486,102487,102491],{},[231,102488,102489],{},[1795,102490,36679],{},[238,102492,36679],{"encoding":240},[128,102494,102496],{"className":102495,"ariaHidden":246},[245],[128,102497,102499,102502],{"className":102498},[250],[128,102500],{"className":102501,"style":283},[254],[128,102503,36679],{"className":102504,"style":36065},[259,1873]," 满足后门准则」所刻画的正是同一组条件：随机化（或条件随机化）在图上做的事情，恰恰就是删除指向 ",[128,102507,102509,102522],{"className":102508,"translate":218},[217],[128,102510,102512],{"className":102511},[222],[224,102513,102514],{"xmlns":226},[228,102515,102516,102520],{},[231,102517,102518],{},[1795,102519,364],{},[238,102521,364],{"encoding":240},[128,102523,102525],{"className":102524,"ariaHidden":246},[245],[128,102526,102528,102531],{"className":102527},[250],[128,102529],{"className":102530,"style":283},[254],[128,102532,364],{"className":102533,"style":30665},[259,1873]," 的全部入边。此外，潜在结果框架还引入了 SCM 表述中不显式出现的两条假设——",[35,102536,102537],{},"SUTVA","（个体的结果不受他人处理状态的影响，且处理版本唯一）与",[35,102540,102541],{},"重叠性",[128,102543,102545,102581],{"className":102544,"translate":218},[217],[128,102546,102548],{"className":102547},[222],[224,102549,102550],{"xmlns":226},[228,102551,102552,102578],{},[231,102553,102554,102556,102558,102560,102562,102564,102566,102568,102570,102572,102574,102576],{},[1840,102555,2028],{},[1832,102557,4221],{},[1795,102559,23001],{},[1832,102561,2477],{"stretchy":1837},[1795,102563,364],{},[1832,102565,1994],{},[1840,102567,1842],{},[1832,102569,5443],{},[1795,102571,36679],{},[1832,102573,2486],{"stretchy":1837},[1832,102575,4221],{},[1840,102577,1842],{},[238,102579,102580],{"encoding":240},"0 \u003C P(X=1\\mid W) \u003C 1",[128,102582,102584,102602,102626,102644,102665],{"className":102583,"ariaHidden":246},[245],[128,102585,102587,102590,102593,102596,102599],{"className":102586},[250],[128,102588],{"className":102589,"style":34743},[254],[128,102591,2028],{"className":102592},[259],[128,102594],{"className":102595,"style":1878},[269],[128,102597,4221],{"className":102598},[1882],[128,102600],{"className":102601,"style":1878},[269],[128,102603,102605,102608,102611,102614,102617,102620,102623],{"className":102604},[250],[128,102606],{"className":102607,"style":1892},[254],[128,102609,23001],{"className":102610,"style":36065},[259,1873],[128,102612,2477],{"className":102613},[1896],[128,102615,364],{"className":102616,"style":30665},[259,1873],[128,102618],{"className":102619,"style":1878},[269],[128,102621,1994],{"className":102622},[1882],[128,102624],{"className":102625,"style":1878},[269],[128,102627,102629,102632,102635,102638,102641],{"className":102628},[250],[128,102630],{"className":102631,"style":1892},[254],[128,102633,1842],{"className":102634},[259],[128,102636],{"className":102637,"style":1878},[269],[128,102639,5443],{"className":102640},[1882],[128,102642],{"className":102643,"style":1878},[269],[128,102645,102647,102650,102653,102656,102659,102662],{"className":102646},[250],[128,102648],{"className":102649,"style":1892},[254],[128,102651,36679],{"className":102652,"style":36065},[259,1873],[128,102654,2486],{"className":102655},[1928],[128,102657],{"className":102658,"style":1878},[269],[128,102660,4221],{"className":102661},[1882],[128,102663],{"className":102664,"style":1878},[269],[128,102666,102668,102671],{"className":102667},[250],[128,102669],{"className":102670,"style":2594},[254],[128,102672,1842],{"className":102673},[259],"）。前者在存在干扰或溢出效应（如疫苗接种、社交网络中的实验）时会被违反，而这类情形在图上需要特殊的结构才能建模。这是两个框架互补而非竞争的一个典型例子。",[2610,102676,102678],{"id":102677},"_42-传统结构方程模型同一名称下的另一条传统","4.2 传统结构方程模型：同一名称下的另一条传统",[11,102680,102681],{},"「结构方程模型」这一术语在统计学、心理测量学与社会科学中已有数十年的历史，其含义与本文所述并不相同。为避免混淆，此处有必要作一辨析。",[11,102683,102684,102685,102688,102689,102692,102693,102696,102697,102758],{},"经典意义上的 SEM 由两部分组成：",[35,102686,102687],{},"测量模型","（潜变量与观测指标之间的因子结构，即验证性因子分析）与",[35,102690,102691],{},"结构模型","（潜变量之间的路径系数）。它以观测变量的",[35,102694,102695],{},"协方差矩阵","为拟合对象，通过极大似然等方法估计参数，并以 ",[128,102698,102700,102719],{"className":102699,"translate":218},[217],[128,102701,102703],{"className":102702},[222],[224,102704,102705],{"xmlns":226},[228,102706,102707,102716],{},[231,102708,102709],{},[1977,102710,102711,102714],{},[1795,102712,102713],{},"χ",[1840,102715,2639],{},[238,102717,102718],{"encoding":240},"\\chi^2",[128,102720,102722],{"className":102721,"ariaHidden":246},[245],[128,102723,102725,102729],{"className":102724},[250],[128,102726],{"className":102727,"style":102728},[254],"height:1.0085em;vertical-align:-0.1944em;",[128,102730,102732,102735],{"className":102731},[259],[128,102733,102713],{"className":102734},[259,1873],[128,102736,102738],{"className":102737},[2087],[128,102739,102741],{"className":102740},[274],[128,102742,102744],{"className":102743},[278],[128,102745,102747],{"className":102746,"style":9629},[282],[128,102748,102749,102752],{"style":2452},[128,102750],{"className":102751,"style":291},[290],[128,102753,102755],{"className":102754},[299,300,301,298],[128,102756,2639],{"className":102757},[259,298],"、CFI、RMSEA 等指标评价模型与数据的整体拟合优度，典型应用是心理量表与社会科学的潜变量建模。",[11,102760,102761],{},"与本文的因果结构模型相比，二者的差别可以归纳为三点：",[33248,102763,102764,102774,102784],{},[33251,102765,102766,102769,102770,102773],{},[35,102767,102768],{},"边的语义不同","。经典 SEM 的路径图本质上是对协方差结构分解的图解，方向由理论约定，模型检验关心的是「这个协方差模式能否被这个路径图解释」；而本文的 SCM 把每条边当作「直接原因」这一",[35,102771,102772],{},"不可从数据验证的结构性假设","（见 1.1 节），并强调它必须来自数据之外。",[33251,102775,102776,102779,102780,102783],{},[35,102777,102778],{},"是否具备 do-算子","。经典 SEM 没有干预的语义，其路径系数",[35,102781,102782],{},"不能被直接解释为干预效应","，只有在额外假设（通常等同于后门准则）下，这些参数才恰好与因果效应一致。这也正是同一份协方差矩阵可以同时被多个方向不同的路径图拟合的原因。",[33251,102785,102786,102789,102790,102818,102819,102847],{},[35,102787,102788],{},"反事实的可识别性来自假设而非数据","。经典 SEM 通常假设线性、可加且噪声服从高斯分布，而正如 3.3 节所指出的，在这一特殊设定下 ",[128,102791,102793,102806],{"className":102792,"translate":218},[217],[128,102794,102796],{"className":102795},[222],[224,102797,102798],{"xmlns":226},[228,102799,102800,102804],{},[231,102801,102802],{},[1795,102803,69050],{},[238,102805,69050],{"encoding":240},[128,102807,102809],{"className":102808,"ariaHidden":246},[245],[128,102810,102812,102815],{"className":102811},[250],[128,102813],{"className":102814,"style":283},[254],[128,102816,69050],{"className":102817,"style":26806},[259,1873]," 可由 ",[128,102820,102822,102835],{"className":102821,"translate":218},[217],[128,102823,102825],{"className":102824},[222],[224,102826,102827],{"xmlns":226},[228,102828,102829,102833],{},[231,102830,102831],{},[1795,102832,67963],{},[238,102834,67963],{"encoding":240},[128,102836,102838],{"className":102837,"ariaHidden":246},[245],[128,102839,102841,102844],{"className":102840},[250],[128,102842],{"className":102843,"style":283},[254],[128,102845,67963],{"className":102846,"style":2508},[259,1873]," 唯一反解，反事实量因此「自动可识别」。这既是它能够讨论个体效应的原因，也是它最脆弱的地方：结论的强度完全由函数形式的假设承担。",[11,102849,102850],{},"一句话概括：经典 SEM 关心的是「协方差结构能否被一个路径图解释」，而结构因果模型关心的是「若外部改变某个变量，其余变量将如何变化」。",[2610,102852,102854],{"id":102853},"_43-随机对照试验的因果语义","4.3 随机对照试验的因果语义",[11,102856,102857],{},"本文的形式化工具同时给出了随机对照试验（RCT）为何享有「黄金标准」地位的一个精确解释。",[11,102859,102860,102861,102889,102890,102918,102919,102922,102923,102977,102978,103120,103121,103124,103125,103128,103129,103157],{},"在因果图中，随机分配意味着 ",[128,102862,102864,102877],{"className":102863,"translate":218},[217],[128,102865,102867],{"className":102866},[222],[224,102868,102869],{"xmlns":226},[228,102870,102871,102875],{},[231,102872,102873],{},[1795,102874,364],{},[238,102876,364],{"encoding":240},[128,102878,102880],{"className":102879,"ariaHidden":246},[245],[128,102881,102883,102886],{"className":102882},[250],[128,102884],{"className":102885,"style":283},[254],[128,102887,364],{"className":102888,"style":30665},[259,1873]," 的取值由模型之外的机制（随机数生成器）决定，因此 ",[128,102891,102893,102906],{"className":102892,"translate":218},[217],[128,102894,102896],{"className":102895},[222],[224,102897,102898],{"xmlns":226},[228,102899,102900,102904],{},[231,102901,102902],{},[1795,102903,364],{},[238,102905,364],{"encoding":240},[128,102907,102909],{"className":102908,"ariaHidden":246},[245],[128,102910,102912,102915],{"className":102911},[250],[128,102913],{"className":102914,"style":283},[254],[128,102916,364],{"className":102917,"style":30665},[259,1873]," 在图中",[35,102920,102921],{},"没有任何父节点","，也就不存在任何后门路径。由后门准则（取 ",[128,102924,102926,102945],{"className":102925,"translate":218},[217],[128,102927,102929],{"className":102928},[222],[224,102930,102931],{"xmlns":226},[228,102932,102933,102942],{},[231,102934,102935,102937,102939],{},[1795,102936,41957],{},[1832,102938,1994],{},[1795,102940,102941],{"mathvariant":1981},"∅",[238,102943,102944],{"encoding":240},"S = \\varnothing",[128,102946,102948,102966],{"className":102947,"ariaHidden":246},[245],[128,102949,102951,102954,102957,102960,102963],{"className":102950},[250],[128,102952],{"className":102953,"style":283},[254],[128,102955,41957],{"className":102956,"style":42029},[259,1873],[128,102958],{"className":102959,"style":1878},[269],[128,102961,1994],{"className":102962},[1882],[128,102964],{"className":102965,"style":1878},[269],[128,102967,102969,102973],{"className":102968},[250],[128,102970],{"className":102971,"style":102972},[254],"height:0.6633em;vertical-align:-0.0817em;",[128,102974,102941],{"className":102975},[259,102976],"amsrm","）立即得到\n",[128,102979,102981,103027],{"className":102980,"translate":218},[217],[128,102982,102984],{"className":102983},[222],[224,102985,102986],{"xmlns":226},[228,102987,102988,103024],{},[231,102989,102990,102992,102994,102996,102998,103000,103002,103004,103006,103008,103010,103012,103014,103016,103018,103020,103022],{},[1795,102991,23001],{},[1832,102993,2477],{"stretchy":1837},[1795,102995,1830],{},[1832,102997,5443],{},[1795,102999,4519],{},[1795,103001,67350],{},[1832,103003,2477],{"stretchy":1837},[1795,103005,2760],{},[1832,103007,2486],{"stretchy":1837},[1832,103009,2486],{"stretchy":1837},[1832,103011,1994],{},[1795,103013,23001],{},[1832,103015,2477],{"stretchy":1837},[1795,103017,1830],{},[1832,103019,5443],{},[1795,103021,2760],{},[1832,103023,2486],{"stretchy":1837},[238,103025,103026],{"encoding":240},"P(y \\mid do(x)) = P(y \\mid x)",[128,103028,103030,103054,103084,103108],{"className":103029,"ariaHidden":246},[245],[128,103031,103033,103036,103039,103042,103045,103048,103051],{"className":103032},[250],[128,103034],{"className":103035,"style":1892},[254],[128,103037,23001],{"className":103038,"style":36065},[259,1873],[128,103040,2477],{"className":103041},[1896],[128,103043,1830],{"className":103044,"style":1874},[259,1873],[128,103046],{"className":103047,"style":1878},[269],[128,103049,5443],{"className":103050},[1882],[128,103052],{"className":103053,"style":1878},[269],[128,103055,103057,103060,103063,103066,103069,103072,103075,103078,103081],{"className":103056},[250],[128,103058],{"className":103059,"style":1892},[254],[128,103061,4519],{"className":103062},[259,1873],[128,103064,67350],{"className":103065},[259,1873],[128,103067,2477],{"className":103068},[1896],[128,103070,2760],{"className":103071},[259,1873],[128,103073,67410],{"className":103074},[1928],[128,103076],{"className":103077,"style":1878},[269],[128,103079,1994],{"className":103080},[1882],[128,103082],{"className":103083,"style":1878},[269],[128,103085,103087,103090,103093,103096,103099,103102,103105],{"className":103086},[250],[128,103088],{"className":103089,"style":1892},[254],[128,103091,23001],{"className":103092,"style":36065},[259,1873],[128,103094,2477],{"className":103095},[1896],[128,103097,1830],{"className":103098,"style":1874},[259,1873],[128,103100],{"className":103101,"style":1878},[269],[128,103103,5443],{"className":103104},[1882],[128,103106],{"className":103107,"style":1878},[269],[128,103109,103111,103114,103117],{"className":103110},[250],[128,103112],{"className":103113,"style":1892},[254],[128,103115,2760],{"className":103116},[259,1873],[128,103118,2486],{"className":103119},[1928],"\n即",[35,103122,103123],{},"干预分布与条件分布重合，观测数据可以直接回答第二层的问题","。用一句话说：",[35,103126,103127],{},"随机化就是人造的 do-算子","——它在物理上执行了定义 3.2 中「删去 ",[128,103130,103132,103145],{"className":103131,"translate":218},[217],[128,103133,103135],{"className":103134},[222],[224,103136,103137],{"xmlns":226},[228,103138,103139,103143],{},[231,103140,103141],{},[1795,103142,364],{},[238,103144,364],{"encoding":240},[128,103146,103148],{"className":103147,"ariaHidden":246},[245],[128,103149,103151,103154],{"className":103150},[250],[128,103152],{"className":103153,"style":283},[254],[128,103155,364],{"className":103156,"style":30665},[259,1873]," 全部入边」这一手术。",[11,103159,103160],{},"这一视角同时划出了 RCT 的边界：",[33248,103162,103163,103169,103176,103212],{},[33251,103164,103165,103166,103168],{},"它回答的是第二层问题，",[35,103167,91003],{},"回答个体反事实（见 3.3 节的可识别性边界）；",[33251,103170,103171,103172,103175],{},"它识别的是",[35,103173,103174],{},"实际实施的处理版本","，若存在不依从（non-compliance），随机化在图上即被违反，需要借助工具变量等额外结构才能恢复效应估计；",[33251,103177,103178,103179,103182,103183,103211],{},"随机化只保证",[35,103180,103181],{},"组间可比","，若存在干扰或溢出效应（SUTVA 违反），",[128,103184,103186,103199],{"className":103185,"translate":218},[217],[128,103187,103189],{"className":103188},[222],[224,103190,103191],{"xmlns":226},[228,103192,103193,103197],{},[231,103194,103195],{},[1795,103196,364],{},[238,103198,364],{"encoding":240},[128,103200,103202],{"className":103201,"ariaHidden":246},[245],[128,103203,103205,103208],{"className":103204},[250],[128,103206],{"className":103207,"style":283},[254],[128,103209,364],{"className":103210,"style":30665},[259,1873]," 与结果之间仍可能经由个体之间的相互影响产生关联；",[33251,103213,103214,103215,103218],{},"它保证的是",[35,103216,103217],{},"内部有效性","，外部有效性并不会自动成立——这引出下一小节。",[2610,103220,103222],{"id":103221},"_44-可迁移性与外部有效性","4.4 可迁移性与外部有效性",[11,103224,103225],{},"一个在实践中反复出现的问题是：在某一人群（或地区、时间）中估计出的因果效应，能否搬到另一个人群中去？纯统计框架对这一问题通常只能给出「谨慎泛化」这样的告诫，而因果图可以提供更精确的回答。",[11,103227,103228,103229,893],{},"Pearl 与 Bareinboim 提出的",[35,103230,103231,103232,103325,103326,103361],{},"可迁移性（transportability）",[35,103233,103234,103235,103264,103265,103324],{},"理论把这类问题形式化如下：设源总体为 ",[128,103236,103238,103252],{"className":103237,"translate":218},[217],[128,103239,103241],{"className":103240},[222],[224,103242,103243],{"xmlns":226},[228,103244,103245,103249],{},[231,103246,103247],{},[1795,103248,26389],{},[238,103250,103251],{"encoding":240},"\\pi",[128,103253,103255],{"className":103254,"ariaHidden":246},[245],[128,103256,103258,103261],{"className":103257},[250],[128,103259],{"className":103260,"style":7758},[254],[128,103262,26389],{"className":103263,"style":1874},[259,1873],"、目标总体为 ",[128,103266,103268,103286],{"className":103267,"translate":218},[217],[128,103269,103271],{"className":103270},[222],[224,103272,103273],{"xmlns":226},[228,103274,103275,103283],{},[231,103276,103277],{},[1977,103278,103279,103281],{},[1795,103280,26389],{},[1832,103282,92810],{},[238,103284,103285],{"encoding":240},"\\pi^*",[128,103287,103289],{"className":103288,"ariaHidden":246},[245],[128,103290,103292,103295],{"className":103291},[250],[128,103293],{"className":103294,"style":23776},[254],[128,103296,103298,103301],{"className":103297},[259],[128,103299,26389],{"className":103300,"style":1874},[259,1873],[128,103302,103304],{"className":103303},[2087],[128,103305,103307],{"className":103306},[274],[128,103308,103310],{"className":103309},[278],[128,103311,103313],{"className":103312,"style":23776},[282],[128,103314,103315,103318],{"style":2452},[128,103316],{"className":103317,"style":291},[290],[128,103319,103321],{"className":103320},[299,300,301,298],[128,103322,92810],{"className":103323},[2115,298],"，在","选择图（selection diagram）",[35,103327,103328,103329,103360],{},"中用方框记号 ",[128,103330,103332,103347],{"className":103331,"translate":218},[217],[128,103333,103335],{"className":103334},[222],[224,103336,103337],{"xmlns":226},[228,103338,103339,103344],{},[231,103340,103341],{},[1795,103342,103343],{"mathvariant":1981},"□",[238,103345,103346],{"encoding":240},"\\square",[128,103348,103350],{"className":103349,"ariaHidden":246},[245],[128,103351,103353,103357],{"className":103352},[250],[128,103354],{"className":103355,"style":103356},[254],"height:0.675em;",[128,103358,103343],{"className":103359},[259,102976]," 标出两个总体之间机制存在差异的节点。有了这一标注，就可以像 do-演算那样通过图上的判定，确定哪些机制可以在两个总体之间共享（因而可以搬运）、哪些必须在目标总体中重新估计，并给出相应的","传输公式（transport formula）",[11,103363,103364,103365,103368],{},"这一工具的意义在于：",[35,103366,103367],{},"外部有效性被从一句笼统的方法论警告，转化为一个在图上可判定的问题。"," 例如，某药物在临床试验人群中的效应能否外推到儿童，取决于两个人群之间的差异所触及的机制是否落在从用药到疗效的因果路径上——若差异只影响与结果无关的变量，效应可以直接搬运；若差异恰好作用于效应的关键中介或调节变量，则必须重新估计。这可以视为 SCM 相对于纯统计框架的一个独有优势。",[2610,103370,103372],{"id":103371},"_45-假设边界与开放问题","4.5 假设边界与开放问题",[11,103374,103375],{},"本文的体系并非无条件成立。把全部预设集中列出，既是诚实，也是使用时的核对清单：",[33248,103377,103378,103474,103592,103675,103746,103752],{},[33251,103379,103380,103383,103384,103387,103388,103391,103392,103473],{},[35,103381,103382],{},"无环性","。DAG 假设排除了反馈回路与均衡，但现实中的经济系统（供给与需求互相决定）、生态系统与控制系统本质上是",[35,103385,103386],{},"有环","的。一种自然的放松方向是",[35,103389,103390],{},"有环结构方程模型","：允许 ",[128,103393,103395,103425],{"className":103394,"translate":218},[217],[128,103396,103398],{"className":103397},[222],[224,103399,103400],{"xmlns":226},[228,103401,103402,103422],{},[231,103403,103404,103406,103408,103410,103412,103414,103416,103418,103420],{},[1795,103405,67963],{},[1832,103407,2014],{},[1832,103409,1994],{},[1795,103411,5436],{},[1832,103413,2477],{"stretchy":1837},[1795,103415,67963],{},[1832,103417,1845],{"separator":246},[1795,103419,69050],{},[1832,103421,2486],{"stretchy":1837},[238,103423,103424],{"encoding":240},"V := f(V, U)",[128,103426,103428,103446],{"className":103427,"ariaHidden":246},[245],[128,103429,103431,103434,103437,103440,103443],{"className":103430},[250],[128,103432],{"className":103433,"style":283},[254],[128,103435,67963],{"className":103436,"style":2508},[259,1873],[128,103438],{"className":103439,"style":1878},[269],[128,103441,75429],{"className":103442},[1882],[128,103444],{"className":103445,"style":1878},[269],[128,103447,103449,103452,103455,103458,103461,103464,103467,103470],{"className":103448},[250],[128,103450],{"className":103451,"style":1892},[254],[128,103453,5436],{"className":103454,"style":5514},[259,1873],[128,103456,2477],{"className":103457},[1896],[128,103459,67963],{"className":103460,"style":2508},[259,1873],[128,103462,1845],{"className":103463},[1903],[128,103465],{"className":103466,"style":1907},[269],[128,103468,69050],{"className":103469,"style":26806},[259,1873],[128,103471,2486],{"className":103472},[1928],"，并以该系统的不动点作为均衡解来定义干预与反事实，此时「因果」的语义变为「均衡状态的移动」。时间序列情形下的动态贝叶斯网络（沿时间维展开后重新成为 DAG）是另一条常见路线。",[33251,103475,103476,103479,103480,103508,103509,103537,103538,103541,103542,103591],{},[35,103477,103478],{},"Granger 因果不等于干预因果","。计量经济学中的 Granger 因果检验，其定义是「利用 ",[128,103481,103483,103496],{"className":103482,"translate":218},[217],[128,103484,103486],{"className":103485},[222],[224,103487,103488],{"xmlns":226},[228,103489,103490,103494],{},[231,103491,103492],{},[1795,103493,364],{},[238,103495,364],{"encoding":240},[128,103497,103499],{"className":103498,"ariaHidden":246},[245],[128,103500,103502,103505],{"className":103501},[250],[128,103503],{"className":103504,"style":283},[254],[128,103506,364],{"className":103507,"style":30665},[259,1873]," 的历史能否改善对 ",[128,103510,103512,103525],{"className":103511,"translate":218},[217],[128,103513,103515],{"className":103514},[222],[224,103516,103517],{"xmlns":226},[228,103518,103519,103523],{},[231,103520,103521],{},[1795,103522,35023],{},[238,103524,35023],{"encoding":240},[128,103526,103528],{"className":103527,"ariaHidden":246},[245],[128,103529,103531,103534],{"className":103530},[250],[128,103532],{"className":103533,"style":283},[254],[128,103535,35023],{"className":103536,"style":2508},[259,1873]," 的预测」，这是一个纯粹的",[35,103539,103540],{},"可预测性","概念，与「在 ",[128,103543,103545,103567],{"className":103544,"translate":218},[217],[128,103546,103548],{"className":103547},[222],[224,103549,103550],{"xmlns":226},[228,103551,103552,103564],{},[231,103553,103554,103556,103558,103560,103562],{},[1795,103555,4519],{},[1795,103557,67350],{},[1832,103559,2477],{"stretchy":1837},[1795,103561,364],{},[1832,103563,2486],{"stretchy":1837},[238,103565,103566],{"encoding":240},"do(X)",[128,103568,103570],{"className":103569,"ariaHidden":246},[245],[128,103571,103573,103576,103579,103582,103585,103588],{"className":103572},[250],[128,103574],{"className":103575,"style":1892},[254],[128,103577,4519],{"className":103578},[259,1873],[128,103580,67350],{"className":103581},[259,1873],[128,103583,2477],{"className":103584},[1896],[128,103586,364],{"className":103587,"style":30665},[259,1873],[128,103589,2486],{"className":103590},[1928]," 下保持不变」的机制性因果概念分属两个不同的层级。在存在共同驱动因素（尤其是同时驱动二者但滞后不同的因素）时，Granger 因果会给出与干预无关的结论。把二者等同，是应用中最常见的概念混淆之一。",[33251,103593,103594,103597,103598,103674],{},[35,103595,103596],{},"忠实性不可检验","。1.3 节的「当且仅当」版本依赖忠实性假设，即分布中不存在的独立性都不是参数偶然相消的产物。然而参数相消（例如路径系数恰好满足 ",[128,103599,103601,103625],{"className":103600,"translate":218},[217],[128,103602,103604],{"className":103603},[222],[224,103605,103606],{"xmlns":226},[228,103607,103608,103622],{},[231,103609,103610,103612,103614,103616,103618,103620],{},[1795,103611,21],{},[1795,103613,35124],{},[1832,103615,9486],{},[1795,103617,39501],{},[1832,103619,1994],{},[1840,103621,2028],{},[238,103623,103624],{"encoding":240},"ab + c = 0",[128,103626,103628,103647,103665],{"className":103627,"ariaHidden":246},[245],[128,103629,103631,103634,103638,103641,103644],{"className":103630},[250],[128,103632],{"className":103633,"style":48070},[254],[128,103635,103637],{"className":103636},[259,1873],"ab",[128,103639],{"className":103640,"style":2508},[269],[128,103642,9486],{"className":103643},[2115],[128,103645],{"className":103646,"style":2508},[269],[128,103648,103650,103653,103656,103659,103662],{"className":103649},[250],[128,103651],{"className":103652,"style":7758},[254],[128,103654,39501],{"className":103655},[259,1873],[128,103657],{"className":103658,"style":1878},[269],[128,103660,1994],{"className":103661},[1882],[128,103663],{"className":103664,"style":1878},[269],[128,103666,103668,103671],{"className":103667},[250],[128,103669],{"className":103670,"style":2594},[254],[128,103672,2028],{"className":103673},[259],"）在数学上完全合法，且在某些自然的参数化下（如线性高斯模型的某些先验）几乎必然发生。忠实性无法从数据中检验，只能被接受或拒绝。",[33251,103676,103677,103680,103681,103684,103685,11072,103713,103741,103742,103745],{},[35,103678,103679],{},"马尔可夫型假设与不可识别性","。本文默认不存在未观测的混杂（2.1 节）。3.5 节的前门准则可以在",[35,103682,103683],{},"特定的中介结构","下绕过这一限制，但它远非一般性的解决方案。对一般的半马尔可夫型 SCM，存在根本不可识别的结构（例如 ",[128,103686,103688,103701],{"className":103687,"translate":218},[217],[128,103689,103691],{"className":103690},[222],[224,103692,103693],{"xmlns":226},[228,103694,103695,103699],{},[231,103696,103697],{},[1795,103698,364],{},[238,103700,364],{"encoding":240},[128,103702,103704],{"className":103703,"ariaHidden":246},[245],[128,103705,103707,103710],{"className":103706},[250],[128,103708],{"className":103709,"style":283},[254],[128,103711,364],{"className":103712,"style":30665},[259,1873],[128,103714,103716,103729],{"className":103715,"translate":218},[217],[128,103717,103719],{"className":103718},[222],[224,103720,103721],{"xmlns":226},[228,103722,103723,103727],{},[231,103724,103725],{},[1795,103726,35023],{},[238,103728,35023],{"encoding":240},[128,103730,103732],{"className":103731,"ariaHidden":246},[245],[128,103733,103735,103738],{"className":103734},[250],[128,103736],{"className":103737,"style":283},[254],[128,103739,35023],{"className":103740,"style":2508},[259,1873]," 之间存在未观测混杂、且不存在满足前门条件的中介），此时唯一的出路是用",[35,103743,103744],{},"部分识别","方法给出效应的上下界，而非一个点估计。",[33251,103747,103748,103751],{},[35,103749,103750],{},"选择与缺失","。d-分离的判据默认全部相关变量均已被观测，而样本选择本身就是在某些节点上做条件化——例 1.4 的伯克森悖论正是选择偏差的图论根源。同理，缺失数据的机制（MCAR \u002F MAR \u002F MNAR）在因果图中对应何种结构、会对可识别性造成何种影响，是一条自然而且实用的延伸方向。",[33251,103753,103754,103757,103758,103761],{},[35,103755,103756],{},"因果发现的可扩展性","。1.4 节所述的算法在假设成立、样本充分时具有理论保证，但在有限样本下，条件独立检验的误差会逐层累积，输出的图往往并不稳定；同时这些算法对忠实性、无隐变量、函数类等假设相当敏感，其输出应当被当作",[35,103759,103760],{},"待检验的假设候选","，而不是结论。",[11,103763,103764,103765],{},"以上限制并未削弱这套理论的价值，反而界定了它的使用条件：",[35,103766,103767],{},"因果推断的可靠程度，等于你愿意且能够承担的假设的强度。",[51,103769,103770],{"id":103770},"其他结语",[11,103772,103773],{},"回顾全文，因果图、结构因果模型、结构方程三者并非彼此独立的工具，而是同一理论体系在不同抽象层级上的展开：",[35195,103775,103776,103788,103854],{},[33251,103777,103778,74292,103780,103783,103784,103787],{},[35,103779,67931],{},[35,103781,103782],{},"定性层面","编码「谁影响谁」。它给出 d-分离这一可在图上机械判定的独立性判据，从而把「该控制哪些变量」从一个凭经验判断的问题，转化为一个组合问题；而它最主要的信息量，恰恰集中在那些",[35,103785,103786],{},"没有被画出来的边","上。",[33251,103789,103790,74292,103792,103795,103796,103824,103825,103853],{},[35,103791,75963],{},[35,103793,103794],{},"生成层面","把图提升为一个可以生成数据的机制。它通过外生变量 ",[128,103797,103799,103812],{"className":103798,"translate":218},[217],[128,103800,103802],{"className":103801},[222],[224,103803,103804],{"xmlns":226},[228,103805,103806,103810],{},[231,103807,103808],{},[1795,103809,69050],{},[238,103811,69050],{"encoding":240},[128,103813,103815],{"className":103814,"ariaHidden":246},[245],[128,103816,103818,103821],{"className":103817},[250],[128,103819],{"className":103820,"style":283},[254],[128,103822,69050],{"className":103823,"style":26806},[259,1873]," 与结构方程 ",[128,103826,103828,103841],{"className":103827,"translate":218},[217],[128,103829,103831],{"className":103830},[222],[224,103832,103833],{"xmlns":226},[228,103834,103835,103839],{},[231,103836,103837],{},[1795,103838,76009],{},[238,103840,76009],{"encoding":240},[128,103842,103844],{"className":103843,"ariaHidden":246},[245],[128,103845,103847,103850],{"className":103846},[250],[128,103848],{"className":103849,"style":283},[254],[128,103851,76009],{"className":103852,"style":36065},[259,1873]," 明确了「观测分布」与「干预分布」的区别，使第二层的问题第一次拥有了明确的数学对象。",[33251,103855,103856,74292,103859,103862,103863,103893,103894,103998,103999,104084],{},[35,103857,103858],{},"结构方程",[35,103860,103861],{},"操作层面","给出这套机制的可改写形式。非对称的 ",[128,103864,103866,103881],{"className":103865,"translate":218},[217],[128,103867,103869],{"className":103868},[222],[224,103870,103871],{"xmlns":226},[228,103872,103873,103879],{},[231,103874,103875,103877],{},[1832,103876,2014],{},[1832,103878,1994],{},[238,103880,75429],{"encoding":240},[128,103882,103884],{"className":103883,"ariaHidden":246},[245],[128,103885,103887,103890],{"className":103886},[250],[128,103888],{"className":103889,"style":7758},[254],[128,103891,75429],{"className":103892},[1882]," 使得 do-算子可以理解为一次对机制的手术式局部替换（",[128,103895,103897,103918],{"className":103896,"translate":218},[217],[128,103898,103900],{"className":103899},[222],[224,103901,103902],{"xmlns":226},[228,103903,103904,103916],{},[231,103905,103906],{},[2016,103907,103908,103910],{},[1795,103909,67956],{},[54905,103911,103912,103914],{"accent":246},[1795,103913,364],{},[1832,103915,85095],{"stretchy":246},[238,103917,85098],{"encoding":240},[128,103919,103921],{"className":103920,"ariaHidden":246},[245],[128,103922,103924,103927],{"className":103923},[250],[128,103925],{"className":103926,"style":85108},[254],[128,103928,103930,103933],{"className":103929},[259],[128,103931,67956],{"className":103932},[259,1873],[128,103934,103936],{"className":103935},[2087],[128,103937,103939,103990],{"className":103938},[274,321],[128,103940,103942,103987],{"className":103941},[278],[128,103943,103945],{"className":103944,"style":24117},[282],[128,103946,103947,103950],{"style":85129},[128,103948],{"className":103949,"style":335},[290],[128,103951,103953],{"className":103952},[299,300,301,298],[128,103954,103956],{"className":103955},[259,298],[128,103957,103959],{"className":103958},[259,85142,298],[128,103960,103962],{"className":103961},[274],[128,103963,103965],{"className":103964},[278],[128,103966,103968,103979],{"className":103967,"style":85152},[282],[128,103969,103970,103973],{"style":54961},[128,103971],{"className":103972,"style":335},[290],[128,103974,103976],{"className":103975},[259,298],[128,103977,364],{"className":103978,"style":30665},[259,1873,298],[128,103980,103981,103984],{"style":85166},[128,103982],{"className":103983,"style":335},[290],[128,103985],{"className":103986,"style":85174},[85173,298],[128,103988,347],{"className":103989},[346],[128,103991,103993],{"className":103992},[278],[128,103994,103996],{"className":103995,"style":85184},[282],[128,103997],{},"），并经潜在结果 ",[128,104000,104002,104026],{"className":104001,"translate":218},[217],[128,104003,104005],{"className":104004},[222],[224,104006,104007],{"xmlns":226},[228,104008,104009,104023],{},[231,104010,104011,104017,104019,104021],{},[2016,104012,104013,104015],{},[1795,104014,35023],{},[1795,104016,2760],{},[1832,104018,2477],{"stretchy":1837},[1795,104020,35129],{},[1832,104022,2486],{"stretchy":1837},[238,104024,104025],{"encoding":240},"Y_x(u)",[128,104027,104029],{"className":104028,"ariaHidden":246},[245],[128,104030,104032,104035,104075,104078,104081],{"className":104031},[250],[128,104033],{"className":104034,"style":1892},[254],[128,104036,104038,104041],{"className":104037},[259],[128,104039,35023],{"className":104040,"style":2508},[259,1873],[128,104042,104044],{"className":104043},[2087],[128,104045,104047,104067],{"className":104046},[274,321],[128,104048,104050,104064],{"className":104049},[278],[128,104051,104053],{"className":104052,"style":28738},[282],[128,104054,104055,104058],{"style":68109},[128,104056],{"className":104057,"style":291},[290],[128,104059,104061],{"className":104060},[299,300,301,298],[128,104062,2760],{"className":104063},[259,1873,298],[128,104065,347],{"className":104066},[346],[128,104068,104070],{"className":104069},[278],[128,104071,104073],{"className":104072,"style":2241},[282],[128,104074],{},[128,104076,2477],{"className":104077},[1896],[128,104079,35129],{"className":104080},[259,1873],[128,104082,2486],{"className":104083},[1928]," 通向第三层的反事实。",[11,104086,104087],{},"第四部分则表明，这一体系与潜在结果框架、传统结构方程模型之间并无高下之分，而是对同一批问题的不同表述：本文的框架以图换取「该控制什么」的可判定性，潜在结果框架以概率表述换取成熟的估计工具，而传统 SEM 关心的始终是协方差结构能否被一个路径图解释；至于随机化实验，其全部因果语义就是一次在物理上实施的 do-算子。",[11,104089,104090,104091,104094],{},"这一体系最深刻的洞见在于：",[35,104092,104093],{},"因果知识本质上是关于「世界如何生成数据」的知识，而非「数据本身呈现出何种模式」的知识","。正因如此，仅凭再大规模、再高维度的观测数据，也无法在没有结构性假设（即因果图）的前提下唯一确定因果效应——这既是因果推断这一领域存在的根本原因，也是它与纯粹的统计学习、机器学习范式在认识论上的分界线所在。",[11,104096,104097],{},"同时也应记住 4.5 节列出的代价：这套理论的可识别性结论，无一例外地建立在无环、忠实、无未观测混杂等假设之上，而其中若干假设本身并不能由数据检验。因此使用因果图时最值得追问的，往往不是「这张图算出了什么」，而是「这张图凭什么长成这样」，以及「若换一张同样合理的图，结论是否仍然成立」。",{"title":123,"searchDepth":137,"depth":137,"links":104099},[104100,104106,104111,104118,104125],{"id":67931,"depth":137,"text":67931,"children":104101},[104102,104103,104104,104105],{"id":67934,"depth":143,"text":67935},{"id":70754,"depth":143,"text":70755},{"id":72890,"depth":143,"text":72891},{"id":74449,"depth":143,"text":74450},{"id":75963,"depth":137,"text":75963,"children":104107},[104108,104109,104110],{"id":75973,"depth":143,"text":75974},{"id":78460,"depth":143,"text":78461},{"id":80124,"depth":143,"text":80125},{"id":82544,"depth":137,"text":82544,"children":104112},[104113,104114,104115,104116,104117],{"id":82595,"depth":143,"text":82596},{"id":83633,"depth":143,"text":83634},{"id":88413,"depth":143,"text":88414},{"id":92402,"depth":143,"text":92403},{"id":96099,"depth":143,"text":96100},{"id":100926,"depth":137,"text":100926,"children":104119},[104120,104121,104122,104123,104124],{"id":100932,"depth":143,"text":100933},{"id":102677,"depth":143,"text":102678},{"id":102853,"depth":143,"text":102854},{"id":103221,"depth":143,"text":103222},{"id":103371,"depth":143,"text":103372},{"id":103770,"depth":137,"text":103770},"为什么概率论不足以回答因果问题？设 X,YX, YX,Y 为两个随机变量，概率论所能给出的全部工具是联合分布 P(X,Y)P(X,Y)P(X,Y)、条件分布 P(Y∣X)P(Y\\mid X)P(Y∣X)，以及由此导出的独立性关系 X⊥ ⁣ ⁣ ⁣⊥YX \\perp\\!\\!\\!\\perp YX⊥⊥Y。这套语言在数学上是自洽的，但存在一个根本性的表达力缺陷：概率分布对「对称性」是不敏感的。若已知 P(X,Y)P(X,Y)P(X,Y)，则 P(Y∣X)P(Y\\mid X)P(Y∣X) 与 P(X∣Y)P(X\\mid Y)P(X∣Y) 皆可通过贝叶斯定理相互推出，二者在信息量上完全等价，谁也不比谁更「根本」。然而在实际世界中，「气压下降导致下雨」与「下雨导致气压下降」显然不是对称的两种表述——只有前者是对的。这种方向性、非对称性的知识，是概率分布本身无法编码的，必须由额外的结构承载。",{},{"title":24,"description":104126},"blog\u002F2026\u002F0005-yin-guo-jie-gou-mo-xing-jian-lun","为什么概率论不足以回答因果问题？本文以 Judea Pearl 的因果推断阶梯为线索，依次展开因果图、结构因果模型与结构方程这三层层层递进的形式化工具，进而讨论因果发现、中介分析、do-演算与前门准则，并对照潜在结果框架与传统结构方程模型，梳理这一体系成立所依赖的假设与适用边界。",[66712],"2026-09-20T23:05:13+08:00","ake4o4yRZlycgfEsxxOFs9VqjSNrQEe7RxE7RRuLx7U",1794483698519]